30th International Conference on Lightning Protection - ICLP 2010
(Cagliari, Italy - September 13th -17th, 2010)
Lightning Surge Analysis by EMTP
and Numerical Electromagnetic Analysis Method
Akihiro AMETANI aametani@mail.doshisha.ac.jp
Doshisha University, Kyo-Tanabe, Kyoto 610-0321, Japan
Abstract− This paper summarizes basic assumption, related problems and the application limit of the well-known EMTP for a
lightning surge analysis. As an alternative to the EMTP, numerical electromagnetic analysis (NEA) methods are briefly
explained and application examples are demonstrated. Also, a difference between the EMTP and FDTD simulations is discussed.
Because the NEA methods solves Maxwell’s equation directly with no assumption of a wave propagation mode, the NEA methods
are becoming a very powerful approach for the lightning surge analysis.
Keywords: lightning surge, EMTP, numerical electromagnetic analysis,
I. Introduction
It is not necessary to explain the significance of a lightning surge analysis in a power system. For the last 30 years,
the electromagnetic transients program (EMTP) originally developed by the Bonnevill Power Administration, US
Department o Energy [1, 2], has been the most powerful tool to carry out a predictive calculation of lightning overvoltages
for insulation design and coordination of a substation and transmission lines. However, it is well-known that the EMTP is
based on a circuit theory assuming TEM mode wave propagation, and the parameters of a circuit are to be given for an
EMTP simulation [3].
Recently, digital control circuits have become quite common in power stations / substations and in intelligent
buildings, and a number of electromagnetic disturbances due to lightning and switching operation have been reported [4].
Also, traveling wave propagation of a partial discharge on a gas-insulated bus [5] and a detailed analysis of archon flashover
on a transmission tower [6] become significant for a more reliable operation and insulation coordination. These
phenomena involves non-TEM mode propagation in a very high frequency range, and can not be analyzed by a conventional
circuit- theory based approach such as the EMTP. Because of the above explained situation, numerical electromagnetic
analysis methods are becoming an alternative but a very effective approach to analyze a lightning surge [7, 8].
This paper summarizes basic assumptions and related problems of the EMTP and thus explains the application limit
of the EMTP for a lightning surge analysis. Then, a brief summary of a numerical electromagnetic analysis (NEA)
methods is presented together with application examples. Finally, a difference between the EMTP and the FDTD
simulations is investigated.
II. Recommended Modeling Method by EMTP [3]
The EMTP is based on a circuit theory which is derived from TEM mode wave propagation. Therefore, it should be
noted that the EMTP is not applicable to a phenomenon associated with non-TEM mode propagation. Also, all the
Zl=400Ω
lightning current
tower
No. 5
matching impedance
eA eC eB eB eC eA AC source
Fig. 1
xt
tower
No. 2
tower
No. 1
8-phase
line
model
8-phase
line
model
Rf
xt
I(t)
Rf
archorn
xs
gantry
8-phase
line
model
Rf
substation
Rfg
Simplified illustration of the recommended model system for a lightning surge simulation
L1-1
parameters of a circuit are to be prepared. Fig. 1 illustrates a basic configuration of a model system recommended in Japan
for a lightning surge simulation by EMTP.
A.
Number of towers
Five towers from a substation gantry are to be considered, because traveling waves reflected from the towers affect a
lightning surge voltage in a substation in Fig.1. The first reflection, when lightning strikes the first tower at t =0, from the
last tower arrives at the substation entrance after two travel times T between the first and the last towers.
For example, xt =300m with light velocity c0 =300m/µs gives the time T ≈ 10 µs. Thus, a simulation result is
accurate up to 10µs, which is enough in general to observe the maximum overvoltage and the time to the peak.
B.
AC sources and matching termination
The left side of the last tower is represented by a multiphase matching impedance (resistance matrix), which is given
as a characteristic impedance matrix including a mutual impedance of the transmission line at a dominant transient
frequency ft defined by [9] :
ft = 1 / 4τ : open-circuited line
= 1 / 2τ : short-circuited line
≈ 1 / 3τ : matching termination line
(1)
where τ = x 0 / c , x 0 =5xt+xs : total line length
An ac voltage source is connected to the other side of the matching impedance as illustrated in Fig. 1 to take into
account the effect of the ac steady state voltage on a lightning surge.
C.
Lightning current and impedance
A lightning current is represented by a ramp waveform with the wavefront duration Tf =1µs and the wavetail
Tt =70µs. Occasionally a concave current of which the waveform is defined in the following equation is adopted in Japan
to represent a real lightning current more accurately [10], [11].
I (t ) = I 0{1 − cos(ωt )}
for t ≤ Tf
(2)
=linearly decreasing function for t ≥ Tf
where I 0 : peak current, ω = π / 2Tf , i.e. f = 1 / 4Tf
The recommended value of the lightning current amplitude is given in Table 1 for various transmission voltage in
Japan.
The impedance of a lightning path is represented as a parallel resistance to a current source as illustrated in Fig. 1.
The resistance value is taken to be 400Ω which was derived by Bewley [12].
D. Tower and gantry
A transmission tower is represented by four distributed-parameter lines [13] as illustrated in Fig. 2, where
Zt1 : tower top to the upper phase arm=upper to middle=middle to lower,
Zt 4 : lower to tower bottom
Table 1 gives a typical value of the surge impedance.
The propagation velocity c of a traveling wave along a tower is taken to be :
c 0 = 300 m/µs : light velocity in free space
(3)
To represent traveling wave attenuation and distortion, an RL parallel circuit is added to each part as illustrated in Fig.
2. The values of the R and L are defined in the following equation.
Ri = ∆Ri ⋅ xi , Li = 2τRi
∆R1 = ∆R 2 = ∆R 3 = 2 Zt1 ⋅ ln(1 / α 1) /( h − x 4)
(4)
∆R 4 = 2Zt 4 ⋅ ln(1 / α 4) / h
where τ = h / c 0 : traveling time along the tower
α 1 = α 4 = 0.89 : attenuation along the tower
h : tower height
A substation gantry is represented by a single distributed line with no loss.
E. Tower footing impedance
A tower footing impedance is suggested in Japan to be modeled as a simple linear resistance Rf , although a
current-dependent nonlinear resistance is recommended by the IEEE and the CIGRE [14]-[17] and the inductive and
capacitive characteristics of the footing impedance are well-known. A recommended value of the resistance for each
voltage class is given in Table 1.
F. Archorn flashover
An archorn flashover is represented either by a piecewise linear inductance model with time controlled switches as
illustrated in Fig. 3(a) or by a nonlinear inductance in Fig. 3(b) based on a leader progression model [18], [19]. The
parameters Li (i= 1 to 3) and ti-ti-1 assuming the initial time to = 0 in Fig. 3(a) are determined from a measured result of the
L1-2
h=h 1
SW1
GW
L1
Zt1 , c0
R 1, L1
h2
L3/2
SW3
Zt1 , c0
L3/2
(a) A piecewise linear model
Fig. 3
R 2, L2
middle
Zt1 , c0
x3
h4
R 3, L3
lower
Zt4 , c 0
x4
R 4, L4
Rｆ
Fig. 2
Ln
L0
SW2
upper
x2
h3
SW1
SW2
L2
x1
A model circuit of a tower
Table 1
(b)
A nonlinear inductance model
An archorn flashover model
Recommended values of lightning parameters
system
voltage
lightning
current
tower height / geometry
[m]
surge imp.
[Ω]
footing
res. [Ω]
[kV]
[kA]
h
x1
x2
x3
Zt1
Zt4
Rf
1100
200
107
12.5
18.5
18.5
130
90
10
10
500
150
79.5
7.5
14.5
14.5
220
150
275
100
52.0
9.0
7.6
7.6
220
150
10
154(110)
60
45.8
6.2
4.3
4.3
220
150
10
77(66)
30, 40
28.0
3.5
4.0
3.5
220
150
10-20
V-I characteristic of an archorn flashover. Then the first EMTP simulation with no archorn flashover is carried out in Fig. 1,
and the first flashover phase and the initial time to are determined from the simulation results of the voltage waveforms across all the
archorns. By adopting the above parameters, the second EMTP simulation only with the first phase flashover is carried out to determine
the second flashover phase. By repeating the above procedure until no flashover occurs, a lightning surge simulation by the piecewise
linear model is completed. Thus, a number of pre-calculations are necessary in the case of multiphase flashovers, while the nonlinear
inductance model needs no pre-calculation and is easily applied to multiphase flashovers. The detail of the leader progression model is
explained in Reference [18], and that of the nonlinear
inductance model in Reference [19].
G. Transmission line
Most transmission lines in Japan are of twin-circuit vertical configuration with two ground wires, and thus are
composed of eight conductors. It is recommended to represent the line by a frequency-dependent model of the EMTP.
But, a distributed-line model with a fixed propagation velocity, attenuation and surge impedance, i.e. fixed-parameter
distributed-line model explained in Sec. 4.2.2.4 of Reference [2], is often used, and is, in general, good enough.
H. Corona wave deformation
Japanese guideline neglects corona wave deformation, although it is taken into account in the CIGRE and the IEEE
guidelines [14]-[17]. The reason for neglecting the corona wave deformation is that the resultant evervoltage is in the
safety side in general.
I.
Arrester
An inductance of a lead wire and the arrester itself is connected in series to the arrester model, because it affects a
transient voltage and current of the arrester. Also, a capacitance of the arrester is considered if necessary. To represent a
very fast impulse characteristic of the arrester, an IEEE model [20] or a model of a nonlinear resistance with a nonlinear
inductance [21] is occasionally adopted. The latter model takes into account the hysterisis of an arrester V-I characteristic
by adding the nonlinear inductance to the nonlinear resistance in series.
J. Substation
(1) Gas insulated bus and cable
A cable and a gas-insulated bus are represented either as three single-phase distributed lines with its coaxial mode
surge impedance and propagation velocity or as a three-phase distributed line system. For a gas-insulated substation
involves quite a number of gas-insulated buses/lines, the pipes are, in most cases, eliminated by assuming the voltage being
zero.
(2)
Circuit breaker, disconnector, transformer, bushing
A circuit breaker (CB) and a disconnector are represented by lumped capacitances between the poles and to the earth.
A transformer is also represented by a capacitance to the earth unless a transferred surge to the secondary circuit is needed to
be calculated. A bushing is represented by a capacitance. Occasionally it is represented by a distributed line.
(3)
Grounding mesh
A grounding mesh is in general not considered in a lightning surge simulation, and is regarded as a zero-potential
surface. When dealing with an incoming surge to a low-voltage control circuit, the transient voltage of the grounding mesh
should not be assumed zero, and its representation becomes an important but difficult subject [22].
L1-3
III. Applicable Limits and Problems of EMTP
A. Lightning current and impedance
(1) Lightning current waveform
Advanced technologies of measuring a lightning performance has revealed that a lightning current waveform is not as
simple as a double exponential wave and a ramp wave [23], [24]. Unless a measured waveform or a recommended
waveform is given, the EMTP can not handle a lightning current.
(2)
Lightning path impedance
The lightning-path impedance of 400Ω in Fig. 1 was derived by Bewley [12], but the value seems not correct, because
the lightning velocity is assumed equal to the light velocity in free space. On the contrary, Diesendorf suggested the value as
1000 to 2000 Ω[25].
The impedance value of a real lightning path has not been made clear, and requires further investigation.
B.
AC source voltage
An ac source voltage is often neglected in a lightning surge simulation. It, however, has been found that the ac
source voltage affects a flashover phase of an archorn especially in the case of a rather small lightning current. Fig. 4 is a
measured result of archorn flashover phases as a function of the ac source voltage on a 77kV transmission line in Japan for a
summer [26]. The measurements were carried out in two 77 kV substations by surge recorders installed in the substations.
From the recorded voltages and currents, Fig. 4 was obtained. The figure clearly shows that the archorn flashover phase is
quite dependent on the ac source voltage, i.e. a flashover occurs at a phase of which the ac voltage is in the opposite polarity
of a lightning current. Table 2 shows a simulation result of archorn peak voltages (archorn not operating) on (a) the
77kV line and (b) a 500kV line [27]. The simulation was carried out in a similar circuit to Fig. 1, but another five towers
were added instead of the gantry and the substation.
The parameters are the same as those in Table 1 for a 77 kV system except the lightning current of 40 kA based on the
field measurement[26]. The lower phase archorn voltage is relatively smaller than the other phase archorn voltages on the
500kV line compared with those on the 77kV line. Thus, an archorn flashover phase on an EHV line is rather independent
from the ac source voltage, and the lower phase flashover is less probable than the other phase flashover. On the contrary,
flashover probability is rather same on each phase and a flashover is dependent on the ac source voltage on a low voltage
line.
C. Tower model
(1) Problem of recommended tower model
Fig. 5 shows simulation results of archorn flashover phases by a simple distributed line “tower model” i.e. neglecting
the RL circuit in Fig. 2 with the parameters in Table1, and by the recommended model illustrated in Fig. 2. The simulation
circuit is the same as that described for Table 2 in the previous section. This figure should be compared with the field test
result shown in Fig. 4. It is clear that the recommended model can not duplicate the field test result, while the simple
80
lower
middle
upper
60
voltage [kV]
40
20
angle [deg.]
0
-20
0
30
60
90
120 150 180 210 240 270 300 330 360
-40
-60
-80
Fig. 4
Measured results of archorn flashover phases on a 77kV transmission line
* single-phase FO, × two-phase FO, ○ three-phase FO
Table 2
Maximum archorn voltages and the time of appearance
transmission voltage
upper
middle
lower
maximum voltage [kV] / time of appearance [µs]
77kV
873.0 / 1.012
820.2 / 1.024
720.0 / 1.035
500kV
4732 / 1.025
4334 / 1.073
3423 / 1.122
L1-4
Lower
Middle
Upper
Phase [deg.]
30 60 90 120 150 180 210 240 270 300 330 360
Voltage[kV]
Voltage[kV]
80
60
40
20
0
0
-20
-40
-60
-80
80
60
40
20
0
0
-20
-40
-60
-80
(a) A simple distributed line model
Lower
Middle
Upper
Phase [deg.]
30 60 90 120 150 180 210 240 270 300 330 360
(b) Recommended tower model
Fig. 5 Simulation results of archorn flashover phases corresponding to Fig.5
• : single-phase FO × : two-phase FO
distributed line model shows a good agreement with the field test result. The reason for the poor accuracy of the
recommended model is that the model was developed originally for a 500kV line on which the lower phase flashover was
less probable as explained in the previous section. Thus, the recommended tower model tends to result in lower flashover
probability of the lower phase archorn. An R-L parallel circuit between two distributed lines in Fig. 2 represents traveling
wave attenuation and distortion along a tower. The R and L values were determined originally based on a field
measurement ( α in eq. (4)), and thus those are correct only for the tower on which the measurement was carried out.
Sometimes, the R-L circuit generates unreal high frequency oscillation. This indicated a necessity of further investigation of
the R-L circuit.
(2)
Impedance and admittance formulas
A number of tower models have been proposed, but most of them are not general, i.e. a tower model shows a
good agreement with a specific case explained in the paper where the model is proposed. The following IEEE/CIGRE
formula of the tower surge impedance is well-known and is widely adopted in a lightning surge simulation [15], [17].
Z t = 60 ln[cot{0.5 tan − 1( R / h)}]
(5)
where R = (r1h1 + r2 h + r3 h2 ) / h : equivalent radius of the tower represented by a truncated cone, h = h1 + h 2
r 1 , r 2 , r 3 : tower top, midsection and base radii [m]
h1 : height from midsection to top [m]
h 2 : height from base to midsection [m]
When the tower is not a cone but a cylinder, then the above equation is rewritten by :
Z t = 60 ln(h / r )
(6)
where r : radius of a cylinder representing a tower
Table 3 compares various tower models (surge impedance) with measured results [28]. As is clear from the average
error to the measured results given at the bottom of the table, Ametani’s formula shows the highest accuracy [28]. Hara’s
empirical formula also shows a quite high accuracy [29]. The IEEE/CIGRE model shows a rather poor accuracy.
The recommended value of a tower surge impedance for each voltage class in Table 1 was determined by field
measurements in Japan. Although the surge impedance is a representative value, it can not be applied to every tower as is
clear in Table 3.
Wave deformation on tower structures (L- or T-shape iron conductor) can be included in a lightning surge analysis, if
required, based on the approach in Reference [30].
(3)
Frequency-dependent effect of a tower
The frequency-dependent effect of a tower is readily taken into account in a transient simulation by combining the
frequency-dependent tower impedance [28] with Semlyen’s or Marti’s line model [31], [32] in the EMTP [33].
(4)
Influence of surge impedance and frequency- dependent effect
It should be pointed out that the influence of the surge impedance and the frequency-dependent effect of a tower is
heavily dependent on the modeling of a tower footing impedance, which will be discussed in the following section. When
the footing impedance is represented by a resistive model as recommended in Japan or by a capacitance model, then the
influence of the tower surge impedance and the frequency-dependent effect of a traveling wave along the tower becomes
rather noticeable. On the contrary, those cause only a minor effect when the footing impedance is represented either by an
inductive model or by a nonlinear resistance. Fig. 6 shows an example [7], [33]. The measurement was carried out on a
500 kV tower by applying a current in Fig. 6(a-1) to the top of the tower. The tower top voltage predicted by a
distributed-line model with a constant tower surge impedance and no R-L circuit, Fig. 6(c-1), differs from that by the
frequency-dependent tower model, Fig. 6(b) which agrees with the measured result, in the case of the footing impedance
being a resistance. On the contrary, in the case of an inductive footing model, the tower top voltage obtained by the
distributed-line model shows a rather good agreement with the measured result. It should be also noted that some 10%
variation of the tower surge impedance does not affect the result in the inductive footing impedance case.
L1-5
Ref.
height
h [m]
[31]
radius
r [mm]
Table 3 Measured and calculated surge impedances of vertical conductors
measured
Wagner*2
Sargent*3
Ametani
Jordan*1
Ref. [28]
Ref. [29]
Ref. [30]
Ref. [27]
Zmes [Ω]
15.0
25.4
15.0
2.5
9.0
2.5
6.0
2.5
3.0
50.0
3.0
25.0
3.0
2.5
2.0
2.5
0.608
43.375
0.608
9.45
0.608
3.1125
average of absolute error [%]
[30]
320.0
459.0
432.0
424.0
181.0
235.0
373.0
345.0
112.0
180.0
250.0
323.0
462.0
431.3
407.0
187.2
228.0
365.5
341.2
104.7
191.2
256.9
2.5
322.9
462.0
431.3
407.0
185.7
227.2
365.4
341.1
98.4
189.8
256.5
2.7
445.2
584.4
553.7
529.4
308.0
349.6
487.8
463.5
220.8
312.2
378.9
44.8
385.2
524.4
493.7
469.4
248.0
289.6
427.8
403.5
160.8
252.2
318.9
22.6
Hara*4
Ref. [31]
325.2
464.4
433.7
409.4
188.0
229.6
367.8
343.5
100.8
192.2
258.9
2.8
*1 : Zj = 60 ln(h / r ) − 60 = 60 ln(h / er ) , *2 : Zw = 60 ln(2 2 h / r ) = Zj + 122.4 , *3 : Zs = Zw − 60 = Zj + 62.4 , *4 : Zh = Zw − 120 = Zj + 2.4
Voltage [V]
300
200
100
0
(1) Applied current
(2) Tower top voltage
300
300
200
200
200
0
Voltage [V]
300
100
100
1
2
Time [µs]
3
(1) Resistive footing impedance
(c)
3
4
0
-100
-100
0
2
Time [µs]
100
0
-100
1
(b) Frequency-dependent tower model with a
resistive footing impedance
Measured result
Voltage [V]
Voltage [V]
(a)
0
0
1
2
Time [µs]
3
(2) Inductive footing impedance
0
1
2
Time [µs]
3
(3) Capacitive footing impedance
Distributed-line tower model with various footing impedances
Fig. 6 Influence of a tower model on the tower top voltage
Thus, it is concluded that the frequency-dependent effect of wave propagation along a tower can be neglected and the
value of the surge impedance is not significant unless a tower footing impedance is represented by a resistive or a capacitive
model.
(5)
TEM mode propagation
All the above discussions are based on TEM mode propagation of an electromagnetic wave along a vertical tower.
It has been pointed out in many publications that the electromagnetic wave along the tower is not the TEM mode especially
at the time of lightning instance to the tower [8], [34]. The same is applied to the lightning path impedance.
D. Tower footing impedance
(1) Linear footing impedance
It has been known in general that the footing impedance tends to be capacitive in the case of a high resistivity earth,
and inductive in the low resistivity earth case. A problem of the representation is: The footing impedance can be resistive,
inductive and capacitive depending on the season and the weather when a measurement is made, i.e. the impedance is
temperature- and soil moisture-dependent. Therefore, it is not easy to select a model of the footing impedance and this is
the reason why a resistance model is adopted in Japan.
(2) Current-dependent nonlinearity
A number of papers have discussed the current-dependence of a tower footing impedance, and have proposed various
models of the nonlinear footing impedance. It has been a common understanding that the current-dependence decreases a
L1-6
lightning surge voltage at the tower and thus decreases a lightning overvoltage at a substation. Therefore a simulation
neglecting the current dependence gives a severer overvoltage, i.e. a safer side result from the insulation design viewpoint.
By this reason, again a pure resistance model is recommended in Japan.
(3) Non-uniform and frequency-dependent characteristics
All the grounding electrodes, either horizontal (counterpoise) or vertical, show a non-uniform characteristic [35],
which corresponds a so-called critical length of the electrode [36]. The characteristic can be taken into account in an
EMTP simulation by adopting a model circuit described in Reference [35] together with the frequency-dependent effect.
However, this approach requires a measured result of the grounding electrode to be simulated.
A general solution for a transient response of a grounding electrode is rather easily obtained by a numerical
electromagnetic analysis method such as a finite-difference time-domain (FDTD) method [8], [37] including non-TEM
mode propagation.
E.
Archorn flashover model
There exist a number of archorn flashover models. To investigate the accuracy, phase-wire voltages at the first tower
in Fig. 1 are calculated by various archorn models and are compared[38]. A switch (time-controlled) model and a
flashover switch model show not satisfactory agreement especially in the wavefront with the nonlinear inductance model of
which the accuracy has been confirmed to be high in comparison with an experimental result [19]. A v-t characteristic
model and a piecewise linear inductance model show a reasonable accuracy except that the maximum voltage of the former
is greater and that of the latter is lower than that calculated by the nonlinear inductance model. It might be noteworthy that
a current and energy consumed by an arrester in a substation are dependent on an archorn model. The switch and the
flashover switch models result in much higher energy consumed by an arrester.
An archon flashover might be affected by transient electromagnetic coupling between a lightning path, a tower and
phase conductors which are perpendicular to the tower and the lightning path. Such coupling can not be handled by the
EMTP and is easily solved by a numerical electromagnetic analysis [7], [8], [39].
F. Transmission line, feeder, gas-insulated bus
(1) Frequency-dependent transmission line impedance
Although a frequency-dependent line model, i.e. Semlyen’s or Marti’s model [31], [32], is recommended, the
maximum error of Marti‘s model is observed to be about 15 % at the wavefront of an impulse voltage on an 1100 kV
untransposed vertical twin-circuit line in comparison with a field test result [40] of which a surge waveform is shown in Fig.
7 in comparison with EMTP simulation result. The estimation of possible errors incurred by using these models in a
lightning overvoltage simulation is not straightforward, because it involves a nonlinearity due to an archorn flashover
dependent on a lightning current, an ac source voltage, a flashover phase and so on. This is an important subject to be
investigated in future.
Z t1 Vt1 l1 = 12.5m
L1
R1
Z t 2 Vt 2
0 .7 km
No.2
2. 0km
No.3
5 .8km
No.4
10. 4km
No .5
21 .7 km
No.6
40 .0 km 44.8 km
No.7
No.8
Z t3 Vt 3
L3
l 3 = 20.0m
Z t1− 3 [Ω]
Z t 4 [Ω]
Vt1− 4 [m / µs]
120
10.19
l 4 = 68.0m
R1[Ω]
L1[µH ]
R2− 3 [Ω]
L2− 3 [µH ]
R4 [Ω]
L4 [µH ]
42.80
R3
Z t 4 Vt 4
L4
R4
R f = 10.0
(a) Tested 1100kV transmission line
120
300
8.186
16.31
13.10
34.38
(b) 1100kV transmission tower
1
Voltage [pu]
1
Voltage [pu]
0 km
No.1
l 2 = 20. 0m
R2
L2
0.5
0.5
500Ωm
1000Ωm
2000Ωm
4000Ωm
実測波形
0
0
10
20[µsec] 30
Time
500Ωm
1000Ωm
2000Ωm
4000Ωm
実測波形
0
40
0
10
20
30
Time [µsec]
40
(c) Simulation results by Marti model
(d) Simulation results by Dommel model. (f=3.348kHz)
Fig.7 Surge characteristics on an 1100kV line
L1-7
Carson
fin
Carson
2
10kHz
fin
0
50Hz
Carson
-2
-4
fin
101
102
103
length x [m]
2.5
f=1MHz
50Hz
Carson
Li [mH/km]
log10Ri [Ω/km]
4
2
fin
Carson
fin
Carson
1.5
10kHz
f=1MHz
fin
104
1
101
103
length x [m]
(a) Resistance
(b) Inductance
Fig. 8 Finite line impedance in comparison with Carson’s impedance
fin = finite line, eq. (7)
(2) Finite length of a line and a gas-insulated bus
Carson’s and Pollaczek’s earth return impedance of an overhead line and an underground cable were derived based on
the assumption of an infinitely long line on the basis of TEM mode propagation [41]-[44]. A real line is not infinitely long
at all. The separation distance x of a UHV/EHV transmission line between adjacent towers and the length of a
gas-insulated bus are in the same order of their height h . If the condition, that x is far greater than h and h is far
greater than the radius r , is not satisfied, Carson’s and Pollaczek’s impedances are not applicable. Fig. 8 shows an
example of the impedance of a finite length line evaluated by the following equation [45].
Zfinite =
1 + 1 + (dij / x ) 2
jωµ 0
Sij
{x ln
+ x ln − x 2 + dij 2 + x 2 + Sij 2 + dij − Sij} [Ω]
2
2π
dij
1 + 1 + (Sij / x )
(7)
where dij = (hi − hj) 2 + y 2 , Sij = (hi + hj + 2he) 2 + y 2
y : horizontal separation between conductors i and j
hi, hj : height of conductors i and j
h e = ρ e / jωµ o : complex penetration depth [46]
It should be clear in Fig. 8 that Carson’s impedance assuming an infinitely long line is far greater than that of a real
finite line, when x / h is not greater enough than 1. The reason for this is readily understood from the following equation
[43].
ZCar = ∫ 0∞ ∫ 0∞ A( xi, xj)dxidxj = ∫ 0∞ B( xi )dxi
(8)
Zfin = ∫ 0X1 ∫ 0X 2 A( xi, xj)dxidxj = ∫ 0X1 B' ( xi )dxi
(9)
As is clear from the above equations, ZCar involves mutual coupling from the infinitely long conductor “j”, while
Zfin involves mutual coupling from the conductor “j” with the finite length X 2 . In fact, ZCar becomes infinite because
of the infinite length, and thus “per unit length” impedance is necessarily defined. It should be noted that the per unit
length impedance ∆ZCar of eq. (8) has included the mutual coupling from the infinitely long conductor “j”. On the
contrary, ∆Zfin , if we define the per unit length impedance in eq. (9), includes the mutual coupling only for the finite length
X 2 . Thus,
(10)
∆ZCarson > ∆Zfinite
On the contrary, the per unit length admittance of an infinitely long line is smaller than that of a finite length line.
From the above discussion, it should now be clear that Carson’s and Pollaczek’s earth return impedances may not be
applied to a lightning surge analysis, because the separation distance x between adjacent towers is the same order as the
line height. The same is true for a gas-insulated bus, because its length, height and radius are in the same order. This
requires further work which is interesting and significant.
It is noteworthy that the propagation constants of a finite line is nearly the same as that of an infinitely long line, but
the characteristic (surge) impedance is smaller, because of a smaller series impedance and a greater shunt admittance of the
finite line. Furthermore the ratio of the surge impedances of two finite lines is nearly the same as that of two infinitely
long lines. Finally, traveling wave reflection, refraction and deformation on the finite line is not much different from those
on the infinitely long line.
(3) Feeding line from a transmission line to a substation – Inclined conductor
A feeding line from the first tower to the substation via the gantry in Fig. 1 is inclined, i.e. the height is gradually
decreased. As a result, its surge impedance is also decreased gradually and thus no significant reflection of traveling waves
occurs along the feeding line until the substation entrance in physical reality. Because the surge impedance (about 70Ω) of
a gas-insulated bus or a bushing is much smaller than that of an overhead line (300 to 500Ω), noticeable reflection appears
at the substation entrance, if the inclined configuration of the overhead feeding line is not considered. It is better to
consider the inclined configuration of a feeding line if an accurate simulation is required. A maximum difference of 7% in
a substation entrance voltage is observed when the inclined configuration is considered [43], [45].
L1-8
1
Rg=∞ , Rp=∞
Rg=7Ω , Rp=∞
Rg=7Ω , Rp=500Ω
Rg=7Ω , Rp=70Ω
8
6
normalized K [pu]
normalized K [pu]
10
4
2
0.8
0.6
Rg=∞ , Rp=∞
Rg=7Ω , Rp=∞
Rg=7Ω , Rp=500Ω
Rg=7Ω , Rp=70Ω
0.4
0.2
0
0
0
200
400
600
800
applied voltage E0 [kV]
0
1000
200
400
600
800
applied voltage E0 [kV]
1000
(a) Without back-flashover
(b) With back-flashover
Fig. 9 Measured result of normalized voltage ratio K – Effect of corona wave deformation
800
600
Voltage [kV]
a-b
a-c
b-c
phase a
b
c
400
200
0
0
60
120
180
240
300
360
ac source phase angle [degree]
Fig. 10 Phase-to-phase lightning surge on a 77kV line
G.
Corona wave deformation
The reason for corona wave deformation being not considered in a lightning surge simulation in Japanese guideline is
that a simulation result neglecting the corona is expected to be higher than that considering corona and thus the result is on a
safer side from the insulation viewpoint. The possible errors incurred by ignoring corona are observed to be less than 10 %
when lightning strikes the first tower in Fig. 1[11]. Although sophisticated corona models have been proposed [48], [49], the
reliability and stability in a lightning overvoltage simulation is not confirmed.
It is noteworthy that the corona wave deformation can result in a higher overvoltage at a substation entrance under a specific
condition. Fig. 9 shows a field test result of a normalized voltage ratio K for the negative polarity case defined in the
following equation on a 6.6kV line [50], [51].
K = Vn / V 0 [pu]
(11)
where Vn = Vm / E 0 : normalized by applied voltage E 0
Vm : maximum phase-wire (PW) voltage at the receiving end (substation entrance)
V 0 : normalized voltage with no corona discharge
The experiment was carried out on a 6.6 kV line with one phase wire and one ground wire which were terminated by
resistances Rp and Rg at the remote end. An impulse voltage up to 800 kV was applied to the sending end of the ground
wire. The back flashover in Fig. 9 was represented by short-circuit of the ground and phase wires. For corona wave
deformation decreases a traveling wave voltage on a line, it is a common understanding that the line voltage is decreased by
the corona wave deformation and thus the ratio K is less than 1. In the case of no corona discharge, K is nearly equal
to 1 on a short distance line. It was observed that a measured result of K on a single-phase line was less than 1.
Fig. 9(a) shows that K in the case of no back-flashover becomes greater than 1 as the applied voltage is increased,
i.e. corona discharge occurs. On the contrary in Fig. 9(b), K is less than 1. The reason for the phenomena is readily
explained as a result of different attenuation on a phase wire and a ground wire due to corona discharge, and negative
reflection of a heavily attenuated traveling wave on the ground wire. The phenomena are less noticeable in the positive
polarity case. The detail has been explained in References [50] and [51]. The phenomena have been also realized
qualitatively by an EMTP simulation. The increase of a phase-wire voltage at a substation entrance is expected to be more
pronounced on an EHV/UHV transmission line on which a corona discharge hardly occurs on a phase wire because of a
multiple bundled conductor, while a heavy corona discharge is expected on a ground wire.
H.
Phase-to-phase lightning surge
Most of the previous studies on a lightning overvoltage concerned an overvoltage to the earth. A phase-to-phase
overvoltage, however, can damage insulation between phases such as core-to-core insulation in a gas-insulated bus in which
three-phase cores are enclosed in the pipe. Fig. 10 shows an EMTP simulation result of an inter-phase lightning
overvoltage at a substation entrance on a 77kV vertical twin-circuit line, when phases a and b’ flashovers. The simulation
was carried out on a system composed of a 10 km 245/77kV quadruple circuit line and a 10 km 77 kV line. The 77 kV line
was connected to a substation through a three-phase underground XLPE cable with the length of 500 m. Because of a lower
attenuation of aerial propagation modes, the phase-to-phase overvoltage becomes greater than the phase-to-earth
overvoltage especially in the case of a lightning strike to a tower far from a substation.
The phase-to-phase lightning overvoltage needs further investigation.
L1-9
Table 4 Various methods of nnumerical electromagnetic analysis
partition
space
discretization/do
main
fnite difference
time-domain
FDTD
TD-FI
boundary
boundary length
3D circuit
TLM
TD-FEM
FEM
frequency
━
FI
━
━
base equationn
Maxwell
diffrential
Maxwell
integral
Maxwell
characteristic
D’Alembert
solution
feature
easy
programing
multi media
circuit theory extension
hard
program.
finte
element
easy program.
MOM
(TWTDA)
MOM
field integral
wide
application
Small CPU
nonlinear in
time domain
IV. Numerical Electromagnetic Analysis Method for Lightning Surges
It is hard to handle a transient associated with non-TEM mode propagation by conventional circuit-theory based tools
such as the EMTP, because the tools are based on TEM mode propagation. To overcome the problem, a numerical
electromagnetic analysis method looks most promised among existing transient analysis approaches for it solves Maxwell’s
equation directly without any assumptions often made for the circuit-theory based tools.
This chapter describes the basic theory of two representative methods, i.e. method of moment (MoM) and
finite-difference time-domain (FDTD) method, of the numerical electromagnetic analysis. Also, to demonstrate the
usefulness and advantages, four typical examples are presented.
A. Numerical Electromagnetic Analysis Method
(1) Various method, at present
Table 4 categorized various methods of numerical electromagnetic analysis (NEA) [7, 8]. The method of moments
(MoM) in the frequency and time domains [52-57], and the finite-difference time-domain (FDTD) method [58, 59], both for
solving Maxwell’s equations numerically, have frequently been used in calculating surges on power systems. Applications
of the finite element method (FEM) and the transmission line method (TLM) to surge calculations have been rare at present.
The MoM and the FDTD method are, therefore, two representative approaches in surge calculations.
(2) Methods of Moments (MoMs) in the Time and Frequency Domains
a) MoM in the Time Domain
The MoM in the time domain [52, 53] is widely used in analyzing responses of thin-wire metallic structures to
external time-varying electromagnetic fields. The entire conducting structure representing the lightning channel is modeled
by a combination of cylindrical wire segments whose radii are much smaller than the wavelengths of interest. The so-called
electric-field integral equation for a perfectly conducting thin wire in air as in Fig. 11, assuming that current I and charge q
are confined to the wire axis (thin-wire approximation) and that the boundary condition on the tangential electric field on the
surface of the wire (this field must be equal to zero) is fulfilled, is given by
ŝ ⋅ E inc (r , t ) =
ŝ ⋅ R ∂I(s′, t′)
ŝ ⋅ R
µ 0 ⎡ ŝ ⋅ ŝ′ ∂I(s′, t′)
⎤
− c 2 3 q (s′, t′)⎥ds′
+c 2
∫C ⎢
4π ⎣ R
R
R
∂s′
∂t′
⎦
t′
where q( s ′,t ′ ) = − ∫−∞
(12)
∂I ( s ′,τ )
dτ
∂s ′
C is an integration path along the wire axis, Einc denotes the incident electric field that induces current I, R=r -r’, r and
t denote the observation location (a point on the wire surface) and time, respectively, r’ and t’ denote the source location (a
point on the wire axis) and time, respectively, s and s’ denote the distance along the wire surface at r and that along the wire
axis at r’, ŝ and ŝ' denote unit vectors tangent to path C in (12) at r and r’, µ0 is the permeability of vacuum, and c is the
speed of light. Through numerically solving (12), which is based on Maxwell’s equations, the time-dependent current
distribution along the wire structure (lightning channel), excited by a lumped source, is obtained.
The thin-wire time-domain (TWTD) code [52] (available from the Lawrence Livermore National Laboratory) is based
on the MoM in the time domain. One of the advantages of the use of the time-domain MoM is that it can incorporate
nonlinear effects such as the lightning attachment process [54], although it does not allow lossy ground and wires buried in
lossy ground to be incorporated.
b)
MoM in the Frequency Domain
The MoM in the frequency domain [55] is widely used in analyzing the electromagnetic scattering by antennas and
other metallic structures. In order to obtain the time-varying responses, Fourier and inverse Fourier transforms are employed.
The electric-field integral equation derived for a perfectly conducting thin wire in air as in Fig. 11 in the frequency domain
is given by
L1-10
I (s’ )
^
s’
^
s
r
r’
C(r)
Origin
Fig. 11 Thin-wire segment for MoM-based calculations. Current is confined to the wire axis,
and the tangential electric field on the surface of the wire is set to zero.
− ŝ ⋅ E inc ( r ) =
⎛ 2
∂2 ⎞
jη
⎟g ( r , r ′ )ds ′
∫C I ( s ′ )⎜⎜ k ŝ ⋅ ŝ ′ −
∂s∂s ′ ⎟⎠
4πk
⎝
⎛ − jk r − r ′
where g( r , r ′ ) = exp⎜
⎜ r − r′
⎝
⎞
⎟, k = ω µ0 ε 0 , η =
⎟
⎠
(13)
µ0
ε0
ω is the angular frequency, µ0 is the permeability of vacuum, and ε0 is the permittivity of vacuum. Other quantities in
eq.(13) are the same as those in eq.(12). Current distribution along the lightning channel can be obtained numerically
solving eq.(13).
This method allows lossy ground and wires in lossy ground (for example, grounding of a tall strike object) to be
incorporated into the model. The commercially available numerical electromagnetic codes [56], [57], are based on the MoM
in the frequency domain.
(3) Finite-Difference Time-Domain (FDTD) Method
The FDTD method [58] employs a simple way to discretize Maxwell’s equations in differential form. In the Cartesian
coordinate system, it requires discretization of the entire space of interest into small cubic or rectangular-parallelepiped cells.
Cells for specifying or computing electric field (electric field cells) and magnetic field cells are placed relative to each other
as shown in Fig. 12. Electric and magnetic fields of the cells are calculated using the discretized Maxwell’s equations given
below.
1⎞
1 ⎞ 1 − σ (i, j, k + 1 2) ∆ t [2 ε (i, j, k + 1 2) ]
n⎛
n −1 ⎛
E z ⎜ i, j, k + ⎟ =
× E z ⎜ i, j, k + ⎟
2⎠
2 ⎠ 1 + σ (i, j, k + 1 2) ∆ t [2 ε (i, j, k + 1 2) ]
⎝
⎝
1
⎤
⎡ n− 1
n−
H y 2 (i + 1 2 , j, k + 1 2)∆y − H y 2 (i − 1 2 , j, k + 1 2)∆y ⎥
∆t ε(i, j, k + 1 2)
1
⎢
×
+
1
1
⎥
1 + σ(i, j, k + 1 2)∆t [2ε(i, j, k + 1 2)] ∆x∆y ⎢
n−
n−
⎢⎣− H x 2 (i, j + 1 2 , k + 1 2)∆x + H x 2 (i, j − 1 2 , k + 1 2)∆x ⎥⎦
Hx
n+
1
2
1
1
1⎞
1
1⎞
1
∆t
⎛
n− ⎛
⎜ i, j − , k + ⎟ = H x 2 ⎜ i, j − , k + ⎟ +
2
2⎠
2
2 ⎠ µ(i, j − 1 2 , k + 1 2) ∆y∆z
⎝
⎝
(14)
(15)
⎡− E z n (i, j, k + 1 2)∆z + E z n (i, j − 1, k + 1 2)∆z ⎤
⎥
×⎢
n
n
⎢⎣+ E y (i, j − 1 2 , k + 1)∆y − E y (i, j − 1 2 , k )∆y⎥⎦
Equation (14) , which is based on Ampere’s law, is an equation updating z component of electric field, Ez(i, j, k+1/2),
at point x=i∆x, y=j∆y, and z=(k+1/2)∆z, and at time t=n∆t. Eq. (15), which is based on Faraday’s law, is an equation
updating x component of magnetic field, Hx(i, j-1/2, k+1/2), at point x=i∆x, y=(j-1/2)∆y, and z=(k+1/2)∆z, and at time
t=(n+1/2)∆t. Equations updating x and y components of electric field, and y and z components of magnetic field can be
written in a similar manner. Note that σ(i, j, k+1/2) and ε(i, j, k+1/2) are the conductivity and permittivity at point x=i∆x,
y=j∆y, and z=(k+1/2)∆z, respectively, µ(i, j-1/2, k+1/2) is the permeability at point x=i∆x, y=(j-1/2)∆y, and z=(k+1/2)∆z. By
updating electric and magnetic fields at every point using eq.(14) and (15), transient fields throughout the computational
domain are obtained. Since the material constants of each cell can be specified individually, a complex inhomogeneous
medium can be analyzed easily.
In order to analyze fields in unbounded space, an absorbing boundary condition has to be set on each plane which
limits the space to be analyzed, so as to avoid reflections there. The FDTD method allows one to incorporate wires buried in
lossy ground, such as strike-object grounding electrodes [59], and nonlinear effects.
L1-11
E-field cell
∆y
Ez (i, j, k+1/2)
∆x
Hy (i-1/2, j, k+1/2)
Hx (i, j+1/2, k+1/2)
Hx (i, j-1/2, k+1/2)
∆z
Hy (i+1/2, j, k+1/2)
H-field cell
Ey (i, j-1/2, k+1)
E-field cell
Ez (i, j-1, k+1/2)
Hx (i, j-1/2, k+1/2)
Ez (i, j, k+1/2)
Ey (i, j-1/2, k)
H-field cell
Fig. 12 Placement of electric-field and magnetic-field cells for solving discretized
Maxwell’s equations using the FDTD method.
measured result
simulation result
(a)
(b)
Fig. 13 Simulation of the transient response of a
grounding electrode by the FDTD method.
B. Application Examples
(1) A transient response on a grounding electrode
The impedance and admittance of a given electrical circuit are essential to analyze its steady and transient
characteristics by a circuit-theory based approach such as the Electromagnetic Transients Program (EMTP) [1, 2]. Sunde’s
formula of the admittance of a grounding electrode [60] is well-known and has been widely used in the world. However, the
formula is only for a steady state. Sunde also proposed impedance and admittance formulas for a transient, but those require
iterative calculations and the accuracy is found not satisfactory enough [61].
An electromagnetic interference due to mutual coupling between a grounding mesh and a control cable becomes a
significant subject in power stations and substations [4, 62-64]. To analyze this problem, a transient impedance and
admittance are indispensable. Unfortunately no formula is available, and numerical identification from a measured result
looks only a promised method presently as far as the circuit-theory based approach concerns, although many grounding
electrode models have been proposed [65]. On the contrary, an NEA approach requires no impedance and admittance,
because those are evaluated as a part of an NEA calculation.
Fig.13 (a) illustrates the geometrical configuration of a tested grounding electrode and the experimental circuit, where
only geometrical and physical parameters are required in the NEA calculation [37]. Fig.13 (b) is a comparison of an FDTD
simulation result with the measured one. A satisfactory accuracy of the FDTD method is confirmed from the results. This
example shows that the numerical electromagnetic analysis can solve a problem of which the impedance and admittance are
not known, for the method requires no circuit parameter. Also, the mode of wave propagation may not be TEM, while the
circuit-theory based approach is restricted only for the TEM propagation. Also, it should be noted that the phenomenon is
three-dimensional as is clear from Fig.13 (a).
(2) Partial-discharge pulse propagation in a gas-insulated bus
Fig.14 (a) presents the geometrical configuration of a gas-insulated bus in which a pulse is generated due to a partial
discharge. It should be clear in the figure that a part of the conductor is perpendicular to the remaining part. Such a
conductor can not be handled by the EMTP. Furthermore, the phenomenon in this system involves a radial wave propagation
other than axial one. Fig.14 (b) shows a simulation result by MoM, which reproduces the reflection from the corner of the
L1-12
(b)
(a)
Fig. 14 Simulation of partial-discharge pulse propagation in a gas-insulated switchgear by MoM.
voltage reference wire
measurement point
of tower-top
voltage rise
PG
current injection wire
77 m
1.37
A
21.7 V
600 ns
600 ns
(a) injected current
0
0
−1
1.37 A
1.5 A
−2
(b) tower-top voltage rise
(b) Field test result
voltage [V]
current [A]
(a) Test configuration for a tower
67.8 V
0
200
400
time [ns]
600
800
−20
−40
−60
−80
69.2 V
0
200
400
time [ns]
600
800
(c) FDTD simulation result
Fig. 15 Simulation of tower-top voltage rise of a 500-kV transmission tower
bus due to electromagnetic wave scattering. The scattering at the corner can not be simulated by a circuit-theory based
method. The approach is applied to develop life estimation of a power apparatus [5].
(3) Step response of a transmission tower for lightning overvoltage studies
Fig.15 (a) illustrates the configuration of a pulse test for obtaining the step response of a 500 kV transmission tower for
lightning overvoltage studies. Fig.15 (b) shows the measured result of the pulse test, where a voltage-rise waveform at the
tower top when a step current is injected into the tower top is measured. Fig. 15(c) shows the corresponding simulation
result by FDTD method. The calculated waveforms closely reproduce the measured ones. In this problem, the tower in
Fig.15 (a) is modeled three-dimensionally [7, 59]. It is hard to analyze a three-dimensional phenomenon by a conventional
circuit-theory approach. Also, the transient at the wavefront might involve non-TEM coupling within the tower structures
which will be demonstrated in the next example.
V.
Comparison of EMTP and NEA Simulations
The theory and simulation results of the EMTP and numerical electromagnetic analysis methods (NEA) have been
explained in the previous sections. A comparison of simulation results by the both methods will be presented in this
section.
A.
Transient Responses of a Grounding Electrode
Fig. 16 illustrates a model circuit of a grounding electrode for an EMTP simulation of which the parameters are given
in the following equations [22].
C1 = C s − C 0 , G 1 = G s , C 2 = nC1
C s = πε e x / A, G s = πx / ρ e A, A = An (2 x / e 2d ⋅ r2 )
(16)
C 0 = 2πε 0 / An (r2 / r1 )
where r1: radius of a bare conductor
L1-13
(a) A distributed line
(b) Yg for a horizontal conductor
Fig. 16 Grounding electrode model
voltage [V]
150
measured
FDTD
100
50
0
0
100
200
300
time [ns]
400
500
(a) EMTP simulation
(b) FDTD simulation
Fig. 17 Comparison of measured and simulation results
r1=1mm, d=0.2m, x=8m
d: buried depth of the conductor
r2: r1+∆: radius of an artificial outer insulator
εe: earth permittivity, ε0: free space permittivity
ρe: earth resistivity, e=2.718…, n≈5
Cs and Gs in the above equation is well-known Sunde’s formula [60] of a steady-state capacitance and conductance of
a horizontal grounding electrode.
Fig. 17 shows a comparison of EMTP and FDTD simulation results with a measured result [66]. The simulation
results in Fig. 17 show a reasonable agreement with the measured result.
It should be noted that the EMTP simulation result is quite dependent on the parameters adopted in the simulation
which is a function of geometrical and physical constants of a conductor as is clear in eq (16). On the contrary, an FDTD
simulation depends very much on the analytical space, absorbing boundary, cell size and time step. The above observation
has indicated that the EMTP has been numerically completed quite well, while the FDTD requires a further improvement of
its numerical stability.
B.
Transient responses of a tower
Fig. 18 illustrates an experimental circuit of a gas tower system, which is an 1/30th scale model of a real system, and a
measured result [67]. The circuit is the same as that of a wind generation tower if there is no pipeline connected to the gas
tower, and also the same as that of a transmission tower if the tower is represented by a cylindrical conductor [28] and
ground and phase wires are added.
(1) EMTP Simulation
The tower in Fig. 18 is represented as a distributed-parameter line with a surge impedance Z0 and a propagation
velocity c of which the values are evaluated by the impedance and the admittance formulas derived in Reference [28]. Fig.
19 shows a simulation result by the EMTP.
(2) FDTD simulation
Fig. 20 shows a simulation result by the FDTD.
It is observed that the simulation results in Fig.19 by the EMTP and in Fig. 20 by the FDTD agree reasonably well
with the measured result in Fig. 19. A difference observed between the measured and the EMTP simulation results is
estimated due to mutual coupling between the tower, the pipeline and measuring wires. Also, the frequency-dependent
effect of the conductor affects the difference. A difference between the measured and the FDTD simulation results seems
to be caused by a perfect conductor assumption of the FDTD method.
C.
Archone voltage during a back-flashover
The electromagnetic field around a transmission tower hit by lightning changes dynamically while electromagnetic
waves make several round-trips between a shield wire and the ground. During this interval, the waveforms of archorn
voltages vary complexly. For a tall structure such as an EHV twin-circuit tower, the contribution of the tower surge
characteristic to the archorn voltages becomes dominant because the travel time of a surge along the tower is comparable to
the rise time of a lightning current. Particularly in the case of a back-flashover at such a tall tower, a powerful
electromagnetic impulse is produced since the archorn voltage of several MV is chopped steeply. The electromagnetic
impulse expands spherically and couples with the other phase lines. Such electromagnetic coupling is different from the
TEM coupling and it may influence significantly the archorn voltages of other phases. This issue, however, has been paid
little attention in analyzing a multiphase back-flashover.
L1-14
Fig. 18 Experimental setup: RP=150Ω
160
80
Voltage[V]
Voltage[V]
60
EXP
EMTP
120
40
0
40
20
0
-40
-80
EXP
EMTP
-20
0
50
100
150
200
0
50
Time[ns]
(a) Tower top
150
200
(b) Pipe sending end
60
40
20
40
Voltage[V]
Voltage[V]
100
Time[ns]
20
0
0
50
100
150
-20
-40
EXP
EMTP
-20
0
EXP
EMTP
-60
200
0
50
Time[ns]
100
150
200
Time[ns]
(c) Pipe receiving end
(d) control line receiving end
Fig. 19 Measured EMTP simulation result
160
80
FDTD
FDTD
Voltage[V]
Voltage[V]
120
80
40
40
0
0
-40
-40
0
50
100
150
200
0
50
Time[ns]
(a) Tower top
150
200
(b) Pipe sending end
60
40
FDTD
FDTD
20
40
Voltage[V]
Voltage[V]
100
Time[ns]
20
0
0
-20
-40
-20
-60
0
50
100
Time[ns]
150
200
0
50
100
150
200
Time[ns]
(c) Pipe receiving end
(d) control line receiving end
Fig. 20 FDTD simulation results
L1-15
29.0m
r = 20mm
3
11.6m
4.0m
12.0m
4.0m
r = 0.373m
44.0m
2
1
-1
(a) The structure of a model tower subject to analysis.
Upper phase
Middle phase
Lower phase
Voltage [MV]
6
4
2
(1)
0
0
1
Time [µs]
(1)
0
0
1
3
2
1
(2)
0
2
Time [µs]
3
-1
0
1
2
Time [µs]
3
(b) Measured waveforms of the voltage of a 3 m gap
and the current flowing through it [2], and those
computed with the TWTDA code including
Motoyama’s flashover model. (1) Voltage. (2) Current.
Upper phase
Middle phase
Lower phase
6
4
2
(2)
0
2
Measured [6]
Calculated
4
Current [kA]
80.0m
Measured [6]
Calculated
Voltage [MV]
12.0m
4.0m
Voltage [MV]
11.2m
16.0m
5
4
8.0m
0
1
Time [µs]
2
(c) Waveforms of archorn voltages computed by (1) TWTDA and by (2) EMTP, in the
case of a middle-phase back-flashover. ( 150 kA, 1.0 µs ramp current injection )
Fig.21 Archorn voltages during a back-flashover
To analyze such a very-fast transient electromagnetic field around a three-dimensional conductor system,
electromagnetic modeling codes are appropriate. Among many available codes, the Thin-Wire Time-Domain Analysis
(TWTDA) code [52, 68] based on the method of moments [53] is chosen in the present work, for this code allows to
incorporate nonlinear effects into the analysis [6].
In this section, archorn voltages of a simulated 500 kV twin-circuit tower in Fig.21 (a) hit by lightning, in the case of
one-phase back-flashover, are analyzed by a modified TWTDA code that includes a recently proposed flashover model [69,
70]. A similar analysis is also carried out by EMTP [1], and the results are compared with those computed by the modified
TWTDA code.
Fig.21 (b) shows measured waveforms of the voltage of a 3 m gap representing an archorn and the current flowing
through it [70], and those computed by the TWTDA code. Fig.21 (c) are the archorn voltages computed by (1)TWTDA and
(2)EMTP. In the EMTP simulation, the multistory tower model [13] is used, and Motoyama’s flashover model is represented
by a general-purpose description language ‘MODELS’ [71] in EMTP. The archorn voltages computed by EMTP agree well
with those computed by TWTDA before the back-flashover on one phase. On the other hand, after the back-flashover, the
archorn voltages of the other two phases computed by EMTP decay more steeply than those computed by TWTDA, and
they deviate from the results computed by TWTDA during about 1 µs after that. The deviation is noticeable particularly in
the case of the middle- or the lower-phase back-flashover although the settling values of both results are in good agreement.
One of the reasons for these discrepancies may be attributed to somewhat high lumped resistors of the multistory
tower model, which are employed to reproduce the peak values of archorn voltages for step current injection into the tower
top. A very steep wave, injected into the top of this tower model, propagates downward without reflection at nodes, but an
upward propagating wave, which may be a reflected wave at the ground or the associated with the middle- or lower-phase
back-flashover, attenuates much at these nodes. The difference of induction or coupling between the actual dynamic
electromagnetic field around a tower struck by lightning and the TEM mode, which is a basis of an EMTP multiconductor
model, must be another reason.
VI. Conclusion
This paper has presented a lightning surge analysis by the EMTP and by numerical electromagnetic analysis methods.
Because the EMTP is based on a circuit theory assuming TEM mode propagation, it can not give an accurate solution
for a high frequency transient which involves non-TEM mode propagation. Also, the EMTP can not deal with a circuit of
which the parameters are not known.
On the contrary, a numerical electromagnetic analysis method can deal with a transient associated with both TEM and
non-TEM mode propagation. Furthermore, it requires not circuit parameter but geometrical and physical parameters of a
given system. However, it other results in numerical instability if the analytical space, the boundary conditions, the cell
size etc are not appropriate. Also, it requires a large amount of computer resources, and existing codes are not general
enough to deal with various type of transients especially in a large network.
L1-16
VII. References
[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]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
[51]
W. Scott-Meyer: EMTP Rule Book, B.P.A., 1980.4
H. W. Dommel: EMTP Theory Book, B.P.A., 1986.8
A. Ametani and T. Kawamura: A method of a lightning surge analysis recommended in Japan using EMTP, IEEE Trans. PWRD, vol.20, no.2,
pp.867-875, 2005.4
A. Ametani, H. Motoyama, K. Ohkawara, H. Yamakawa and N. Suga: Electromagnetic disturbances of control circuits in power station and
substation experienced in Japan, IET Proc. GTD, vol.3, no.9, pp.801-815, 2009
S. Sakaguch and M. Oyama: Application of Maxwell solvers to PD propagation Part III: PD propagation in GIS, IEEE EI Magazine, vol.19, no.1,
pp.6-12, 2003
T. Mozumi, Y. Baba, M.Ishii, N. Nagaoka and A. Ametani: Numerical electromagnetic field analysis of archon voltages during a back flashover on a
500kV twin-circuit line, IEEE Trans. PWRD, vo.18, no.1, pp.207-213, 2003.1
IEE Japan WG: Numerical Transient Electromagnetic Analysis Methods, IEE Japan, 2008.3
A. Ametani, T. Hoshino, M. Ishii, T. Noda, S. Okabe and K. Tanabe: Numerical electromagnetic analysis method and its application to surge
phenomena, CIGRE 2008 General Meeting, Paper C4-108, 2008.8
A. Ametani: Distributed-Parameter Circuit Theory, Corona Pub. Co., Tokyo, 1990
Japanese standard, ‘High-voltage testing method’, JEC-0102-1994, IEE Japan, 1994
IEE Japan WG Report, ‘A new method of a lightning surge analysis in a power system’, Technical Report No. 244, March 1987
L. V. Bewley, ‘Traveling Waves on Transmission Systems’, Dover (N.Y.), 1963
M. Ishii, T. Kawamura, T. Kouno, E. Ohsaki, K. Shiokawa, K. Murotani and T. Higuchi, “Multistory transmission tower model for lightning surge
analysis” IEEE Trans. Power Delivery, vol.6, no.3, July, pp.1327-1335, 1991
IEEE Working Group Report, ‘A simplified method for estimating lightning performance of transmission lines’, IEEE Trans., Vol. PAS-104, 919,
1985
IEEE Working Group Report, ‘Estimating lightning performance of transmission lines, II-Update to analytical models’, IEEE Trans., Vol. PWRD-8,
1254, 1993
IEEE Guide for Improving the Lightning Performance of Transmission Lines, IEEE Standard1243-1997, 1997
CIGRE SC33-WG01, ‘Guide to Procedures for Estimating Lightning Performance of Transmission Lines’, Technical Brochure, Oct. 1991
T. Shindo and T. Suzuki, ‘A new calculation method of breakdown voltage-time characteristics of long air gaps’, IEEE Trans., Vol. PAS-104, 1556,
1985
N. Nagaoka, ‘An archorn flashover model by means of a nonlinear inductance’, Trans. IEE Japan, Vol. B-111(5), 529, 1991
IEEE Working Group 3. 4. 11, ‘Modeling of metal oxide surge arresters’, IEEE Trans., Vol. PWRD-7(1), 302, 1992
I. Kim et al., ‘Study of ZnO arrester model for steep front wave’, IEEE Trans., Vol. PWRD-11(2), 834, 1996
A. Ametani at el : Modeling of a buried conductor for an electromgnetic transient simulation, IEE Japan Trans. EEE, vol.1, no.1, pp.45-55, June
2006
R. B. Anderson and A. J. Eriksson, ‘Lightning parameters for engineering application’, Electra, No. 69, 65, 1980
S. Yokoyama: “Development of lightning observation methods for current waveforms and discharge progressing manner”, Asia-Pacific EMC,
Beijing, China, Paper TH-PM-E1-1, April 2010.
W. Diesendorf, ‘ Insulation Co-ordination in High Voltage Electric Power Systems‘, Butterworths, 1974.
T. Ueda, M. Yoda and I. Miyachi, ‘Characteristics of lightning surges observed at 77kV substations’, Trans. IEE Japan, Vol. 116-B(11), 1422, 1996
A. Ametani, et al., ‘Investigation of flashover phases in a lightning surge by new archorn and tower models’, Proceedings of IEEE PES T&D
Conference 2002, Yokohama, pp. 1241-1246, 2002
A. Ametani, et al., ‘A frequency-dependent impedance of vertical conductors on a multiconductor tower model’, IEE Proc.-GTD, Vol. 141(4), pp.
339-345, 1994
T. Hara, O. Yamamoto, M. Hayashi and C. Uenoson: “Empirical formulas of surge impedance for a single and multiple vertical cylinder”, Trans.
IEEJ, vol.B-110, pp.129-136, 1990
A. Ametani, et al., ‘Wave propagation characteristics of iron conductors in an intelligent building’, Trans. IEE Japan, Vol. 120-B(1), 31, 2000
A. Semlyen and A. Dabuleanu, ‘Fast and accurate switching transient calculations on transmission lines with ground return using recursive
convolutions‘, IEEE Trans., Vol. PAS-95(5), 561, 1975
J. R. Marti, ‘ Accurate modeling of frequency-dependent transmission lines in electromagnetic transient simulations‘, IEEE Trans., Vol. PAS-101(1),
147, 1982.
N. Nagaoka, ‘Development of frequency-dependent tower model’, Trans. IEE Japan, vol. 111-B, 51, 1991
M.Ishii and Y. Baba: Numerical electromagnetic field analysis of tower surge response, IEEE Trans. PWRD, vol.12, no.1, pp.483-488, Jan. 1997
A. K. Mishra, A. Ametani, Y. Baba, N. Nagaoka and S. Okabe: “Nonuniform characteristics of a horizontal grounding electrode”, IEEE Trans.
PWRD, vol.22 (4), pp. 2327-2334, Oct. 2007
M. Loboda: “Essential requirements for earthing system determining the efficiency of lightning protection”, Asia-Pacific EMC, Beijing, China,
Paper WE-PM-E2-1, April 2010
K. Tanabe “Novel method for analyzing dynamic behovior of grounding systems based on the finite-difference time-domain method“, IEEE Power
Engineering Review, vol.21, no.9, pp.55-57, 2001
N. Nagaoka and A. Ametani, ‘A lightning surge analysis considering multiphase flashovers’, IEE Japan, Research Meeting, Paper HV-95-50, 1995.
10
CRIEPI: Visual Surge Test Lab. (VSTL), http://criepi.denken.or.jp/jp/electric/substance/09.pdf, 2007
A. Ametani, K. Adachi and T. Narita, ‘An investigation of surge propagation characteristics on an 1100 kV transmission line’, IEEJ Trans. PE, vol.
123(4), 513, 2003
J. R. Carson : Wave propagation in overhead wires with ground return, Bell Syst. Tech. J., vol.5, pp539-554, 1926
F. Pollaczek : Uber das Feld einer unendlich langen wechselstromdurchflossenen Einfachleitung, ENT, Heft 9, Band 3, pp.339-359, July 1926
A. Ametani, ‘Wave propagation on a nonuniform line and its impedance and admittance’, Sci. Eng. Review, Doshisha Univ., Vol. 43(3), 136, 2002
A. Ametani, T. Yoneda, Y. Baba and N. Nagaoka : An investigation of earth-return impedance between overhead and underground conductors and its
approximation, IEEE Trans. EMC, vol.51, no.3, pp.860-867, Aug. 2009
A. Ametani and A. Ishihara, ‘Investigation of impedance and line parameters of a finite-length multiconductor system’, Trans. IEE Japan, Vol.
113-B(8), 905, 1993.
A. Deri et al., ‘The complex ground return plane : a simplified model for homogeneous and multi-layer earth return’, IEEE Trans. Vol. PAS-100(8),
3686, 1981
A. Ametani and A. Ishihara, ‘Impedance of a non-parallel conductor system and its circuit analysis’, IEE Japan, Research Meeting, Paper PE-92-173,
1992. 10
Celia de Jusus and M. T. Correia de Barros, ‘ Modeling of corona dynamics for surge propagation studies’, IEEE Trans, Vol, PWRD-9(3), 1564,
1994
J. F. Guiller, M. Poloujadoff and M. Rioul, ‘ Damping model of traveling waves by corona effect along extra high voltage three phase line’, IEEE
Trans. Vol. PWRD-10(4), 1851, 1995
A. Ametani, et al., ‘A study of phase-wire voltage variations due to corona wave-deformation’, Proceeding of the IPST ’99, Budapest, Hungary, pp.
433-438, June, 1999
A. Ametani, et al., ‘A basic investigation of substation entrance voltage variation due to corona wave deformation’, Trans. IEE Japan, Vol. 120-B(3),
L1-17
403, 2000
[52] M. Van Baricum, and E. K. Miller, “TWTD --- A Computer Program for Time-Domain Analysis of Thin-Wire Structures“ UCRL-51-277, Lawrence
Livermore Laboratory, California, 1972
[53] E. K. Miller, A. J. Poggio, and G. J. Burke, “An integro-differential equation technique for the time-domain analysis of thin wire structures” J.
Computational Phys., vol. 12, pp. 24-48, 1973
[54] A. S. Podgorski, and J. A. Landt, “Three dimensional time domain modelling of lightning” IEEE Trans. Power Delivery, vol. PWRD-2, no. 3, Jul.,
pp.931-938, 1987
[55] R. F. Harrington, Field Computation by Moment Methods Macmillan Co., New York, 1968
[56] G. J. Burke, and A. J. Poggio, “Numerical Electromagnetic Code (NEC) --- Method of Moments“ Technical Document 116, Naval Ocean Systems
Center, San Diego, 1980
[57] G. J. Burke, “Numerical Electromagnetic Code (NEC-4) --- Method of Moments“ UCRL-MA-109338, Lawrence Livermore National Laboratory,
California, 1992
[58] K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,”(IEEE Trans. Antennas
Propagat., vol. AP-14, no. 3, Mar., pp. 302-307, 1966
[59] T. Noda, A. Tetematsu, and S. Yokoyama, “Improvements of an FDTD-based surge simulation code and its application to the lightning overvoltage
calculation of a transmission tower” IPST05-138-24c, Montreal, Canada, Jun. 2005
[60] E. D. Sunde “Earth Conduction Effects in Transmission Systems“ Dover Publications, New York, 1968
[61] A. K. Mishra, A. Ametani, N. Nagaoka, and S. Okabe “A study on frequency-dependent parameters and Sunde’s formula of a counterpoise“ IEEJ
Trans. PE, vol.127, no.1, pp.299-305, 2007
[62] CIGRE WG36.04 “Guide on EMC in power plants and substations“ CIGRE Pub.124, Paris, France, Dec. 1997
[63] S. Agematu et al, “High-frequency switching surge in substation and its effects on operation of digital relays in Japan” CIGRE 2006, General
Meeting, Paper C4-304, Sept.2006
[64] A.Ametani et al “Electromagnetic disturbances of control circuits in power stations and substations experienced in Japan “UPEC 2007, 12-31/12-32,
Brightion, UK, Sept.2007
[65] A. K. Mishra, N. Nagaoka and A. Ametani “Frequency-dependent distributed-parameter modeling of counterpoise by time-domain fitting“ IEE Proc.
GTD, vol.153, no.4, July, pp.485-492, 2006
[66] A. Aemtani, T. Chikara, Y. Baba, N. Nagaoka and S. Okabe : “A characteristic of a grounding electrode on the earth sargace “, IWHV 2008/Kyoto,
Paper HV-08-76, 2008-10
[67] A. Ametani, K. Oshio, N. Nagaoka and Y. Baba: “Lightning surge characteristics in a chemical plant”, EEUG 2010 / Helsinki, 2010.8
[68] R. Moini, B. Kordi and M. Abedi, “Evaluation of LEMP effects on complex wire structures located above a perfectly conducting ground using
electric field integral equation in time domain,” IEEE Trans. Electromagnetic Compatibility, vol.40, no.2, May, pp.154-162, 1998
[69] H. Motoyama, K. Shinjo, Y. Matsumoto and N. Itamoto, “Observation and analysis of multiphase back flashover on the Okushishiku test
transmission line caused by winter lightning” IEEE Trans. Power Delivery, vol.13, no.4, October, pp.1391-1398, 1998
[70] H. Motoyama, “Development of a new flashover model for lightning surge analysis” IEEE Trans. Power Delivery, vol.11, no.2, April, pp.972-979,
1996
[71] L. Dube and I. Bonfanti, “MODELS: A new simulation tool in the EMTP” European Trans. Electrical Power Engineering, vol.2, no.1,
January/February, pp.45-50, 1992
A. Ametani, (M’71-SM’84-F’92-LF’10) received the Ph.D. degree from the University of Manchester Institute of Science and Technology, Manchester, U.
K., in 1973. Currently, he is a Professor at Doshisha University, Kyoto, Japan.
L1-18