Download Effect of Current Injection Cable on Lightning Surge

THE SCIENCE AND ENGINEERING REVIEW OF DOSHISHA UNIVERSITY, VOL. 55, No. 4 JANUARY 2015
Effect of Current Injection Cable on Lightning Surge Measurement
for Scaled Circuit
Diah PERMATA*, Yoki IKEDA*, Naoto NAGAOKA*
(Received November 4, 2014)
Transient characteristic of a current injection cable, which is used for a surge measurement, is investigated in this paper.
Measurements are carried out in order to confirm the accuracy of a numerical simulation by means of a circuit analysis program,
Electromagnetic Transients Program (EMTP). The measured results are physically explained by theoretical calculations using
travelling wave theory. The characteristic impedance of the current injection cable is finally calculated. The results show that the
recursive convolution line model, which is known as Semlyen’s frequency-dependent line model, can be used to represent the current
injection cable. If the core is terminated by a low impedance and the sheath is open-circuited at the receiving-end, an earth-return
mode is generated by a reflection at the receiving end from a coaxial mode component.
.H\ZRUGVcurrent injection cable, travelling wave, coefficient of reflection, characteristic impedance
measuring system composed of a voltage reference wire,
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a current lead wire and a voltage probe for a vertical
conductor has been reported2). However, the transient
Measurement of a lightning surge voltage on
characteristic of the current injection cable itself in the
large-sized equipment such as a transmission tower or a
scaled-down measurement has not yet been clarified.
building is difficult. The lightning overvoltage has to be
Finite-difference time-domain (FDTD) method
investigated by a scaled-down measurement in a
has been widely used to simulate the surge overvoltage
laboratory. A pulse generator (PG) is widely used to
on a tower. However, it is difficult to calculate the
simulate the lightning current, and a coaxial cable is
transient characteristic including a current injection cable
commonly used to feed the current to the object. The
because its cross-sectional size is far smaller than that of
transient characteristic of the cable should be clearly
the structure. If the cable is modeled by a thin wire
understood for the investigation of the transient
conductor (core) surrounded by a metallic sheath with a
characteristic of the object because the cable could affect
main insulator, the cell size of the FDTD analysis should
the measured result.
be set to small enough to express the thin materials. It
The validity of the scaled-down measurement on
increases the memory capacity required for the
a metallic plate, which expresses earth surface, has been
simulation, and also the circular cross-section of the
reported for a horizontal conductor1). The paper
cable cannot be accurately expressed. Furthermore, the
concludes that the length of the current lead wire should
data generation for the FDTD analysis becomes
be longer than 10 m to avoid the effect of the internal
complicate and the simulation is time consuming. A
circuit of the PG on a measured result. The effect of the
* Department of Electrical and Electronic Engineering, Graduate School of Science and Engineering, Doshisha University, Kyoto
Telephone: +81-774-65-6337, E-mail: [email protected]
( 61 )
Diah PERMATA, Yoki IKEDA, Naoto NAGAOKA
362
circuit analysis program such as Electromagnetic
(case So) and the sheath both at the sending-end and the
Transients Program (EMTP) is an alternative method to
receiving-end are grounded (case Ss).
calculate the transient characteristic.
The effect of a voltage reference wire is taken into
consideration in the measurement of the voltage at the
receiving-end (Case II).
7UDQVLHQW&KDUDFWHULVWLFV
2.1 Measurement
An experimental setup for a measurement of the
V I
transient characteristic of a current injection cable is
PG
illustrated in Fig. 1. A coaxial cable, 3D2V, is used as the
current injection cable. The transient characteristic is
2.6 m
I
2.9 cm
V
Al-plate
investigated in three cable arrangements; Case I: a
horizontal cable with a length of 2.6 m, and Cases II: a
(a) Case I
vertical inverted-L type cable of 6 m length, and Cases
III: a vertical inverted-U type cable of 8 m length. The
B (2.6 m)
configuration of Case II is used to feed a current to a
C (0.7 m)
measuring object (scaled model of a tower or building).
In all cases, the sheath of the current injection
A (2.7 m)
cable is connected to the ground at the sending-end, i.e.,
I
the cold terminal of the PG is grounded. The core of the
PG
current injection cable is open- or short-circuited at the
10 m
V
2.7 m
V
Al-plate
receiving-end (Case Co or Cs) in Cases I and III. The core
(b) Case II
cannot be grounded in Case II. The applied voltages
from the PG for the open- and short-circuited conditions
are 500 V and 100 V, respectively.
B (2.6 m)
The transient voltage and currents are measured
by a digital oscilloscope (Textronix DPO 4104, 1 GHz)
C (2.7 m)
A (2.7 m)
with a voltage probe (Textronix P6139A, 500 MHz, 8pF
I
10 MΩ) and a current probe (Textronix CT-2). A
step-like voltage is supplied from a pulse generator
PG
(Noise Ken, PG, type INS-4040).
V
2.7 m
I
V
Al-plate
2.2 Simulation
(c) Case III
In this paper, the EMTP is used to calculate the
Fig. 1. Three configurations of a current injection cable.
transient voltage and current. The current injection cable
2.3 Measured and simulated results
is modeled by a recursive convolution line model, which
The measured and simulated results at the
is known as Semlyen’s frequency dependent line
sending-end and the receiving-end for the three
model 3, 4).
circuits-configurations are shown in Figs. 2 and 3. The
For an investigation of the effect of the sheath
measured results for Case So are represented by the bold
grounding at the receiving-end of a cable, the sheath is
lines and the simulated results are shown by the dashed
grounded (Case Ss) or open-circuited (Case So), i.e., only
lines for case So and the dashed-dotted lines for case Ss.
the sheath at the sending-end of the cable is grounded
( 62 )
Effect of Current Injection Cable
800
120
700
100
80
500
Voltage [V]
Voltage [V]
600
400
300
200
60
40
20
100
0
0
-100 0
50
100
Time [ns]
150
200
0
-20
(a) Sending-end core voltage
5
6
4
4
3
Current [A]
Current [A]
8
2
0
0
50
100
150
200
2
1
0
-1
-4
20 40 60 80 100 120 140 160 180 200
Time [ns]
(b) Sending-end core current
(b) Sending-end core current
1000
4
800
3
Current [A]
5
Voltage [V]
0
Time [ns]
1200
600
400
200
2
1
0
0
-200
20 40 60 80 100 120 140 160 180 200
Time [ns]
(a) Sending-end core voltage
-2
363
0
50
100
150
200
-1
0
50
100
150
Time [ns]
Time [ns]
(c) Receiving-end core voltage
(c) Receiving-end core current
Cable 2.6 m
Cable 6 m
Cable 8 m
Cable 2.6 m
200
Cable 8 m
Fig. 2. Measured and simulated results core at the
Fig. 3. Measured and simulated results core at the
receiving-end is open circuited (case Co).
receiving-end is short circuited (case Cs).
The simulated results show that there is no
There is no similarity between the core voltages
difference in the sending-end voltage and current (Fig. 2
of the current injection cable at the receiving-end shown
(a) and (b)) whether the sheath is grounded (Case Ss,
in Fig. 2 (c). The receiving-end voltages oscillate due to
dashed-dotted) or not grounded (Case So, dashed) if the
the capacitance of the probe, which is used to measure
core at the receiving-end is open-circuited (Case Co).
the core voltage. The effect of the capacitance of the
( 63 )
Diah PERMATA, Yoki IKEDA, Naoto NAGAOKA
364
probe can be negated by grounding the sheath at the
receiving-end (Case Co-Ss).
U Zt Y0 Eb2 Zt Yo U E f 2
Eb2 Z t Y0 U 1 Z t Y0 U E f 2
(3)
Fig. 2 (c) in Case III shows a travelling wave
To take into account the induction between the
observed before one round trip (t<2W=2l/v=16m/200m/Ps,
core and the sheath of the coaxial cable, the impedances
at around t=80 ns) which is not found in the other cases.
of the circuit should be expressed by 2-by-2 square
It is due to a reflected wave from the connecting point of
matrices. The impedances connected to the cable at the
sections C and B illustrated in Fig. 1.
receiving-end and sending-end are assumed to be Zt and
The effect of the sheath grounding at the
Zp, respectively. The reflection coefficients at the
receiving-end is clearly observed if the core at the
sending-end and receiving-end T1 and T2 become
receiving-end is short-circuited (case Cs, Fig. 3). The
matrices.
sending-end voltage and current (Fig. 3 (a) and 3 (b))
Zt: impedance of cable at the receiving-end.
change to the opposite direction at one round trip (t=2W)
depending on the sheath grounding. The amplitude of the
Zt
ª Rct
«
¬ 0
0 º
»
Rst ¼
receiving-end current of Case Ss is much higher than that
where Rct and Rst are core and sheath grounding
of Case So at the beginning (Fig. 3 (c)).
impedance, respectively.
Zo: characteristic impedance of any coaxial cable in a
7KHRUHWLFDO&DOFXODWLRQ
high frequency region.
3.1 Travelling wave calculation
The travelling waves of the voltage and current up
to one round time (2W) are analytically calculated in this
section. The transient voltage and current characteristics
are obtained from a circuit shown in Fig. 4.
I1
V1
E f 1 Eb1
I1
Y0 E f 1 Eb1 I 2
V2
E f 2 Eb2
Y0 E f 2 Eb2
E f 1e
impedance, respectively.
high frequency region.
Eb1e
Y0
Jl
Y0 E f 1e Jl Eb1eJl
The reflection coefficient at the receiving-end is
(1)
obtained from Eq. (1).
where T is reflection coefficient.
The relationship between the voltage and the
>T2 @ >Zt @>Y0 @ >U @ 1 >Zt @>Y0 @ >U @ the sending-end (T1) is:
(2)
From Eq. (2) and the travelling wave theory, the
Eb2 Z t Y0 Eb2
>T @ >Z @>Y @ >U @ >Z @>Y @ >U @ 1
1
p
0
p
0
(6)
The sending-end impedance is expressed by
reflection coefficient can be obtained.
Z t Y0 E f 2 Eb2
(5)
In the same manner, the reflection coefficient at
current at the receiving-end should follow the Ohm law:
Eb2 E f 2
(4)
where U: 2x2 identity matrix
backward waves at the receiving end is defined as:
Zt I 2
1 º
»
Zc »
Zc Z s »
»
ZcZ s ¼
>Eb2 @ >Zt @>Y0 @ >U @ 1 >Zt @>Y0 @ >U @ >E f 2 @
The relationship between the forward and the
V2
ª 1
«
« Zc
« 1
«
¬ Zc
Hence Eq. (3) becomes:
Fig. 4. Bergeron model to calculate the travelling wave.
TE f
Zs º
»
Zs ¼
Yo: characteristic admittance of any coaxial cable in a
V2
Jl
ªZ c Z s
«
¬ Zs
where Zc and ZS are coaxial and earth-return mode surge
I2
V1
Eb
Z0
Eq. (7) because the PG consists of a coaxial cable.
Z t Y0 E f 2 E f 2
( 64 )
Effect of Current Injection Cable
Zp
ªZ c Z c
« c c s
«¬ Z s
Z sc º
»
Z s c »¼
365
Zp
(7)
Zc = 50Ω
Ef0
T1
where Zcc(=26.75 Ω) is expressed by the characteristic
Zt
Ef2
T2
Eb2
impedance of the RG55-U cable installed in the PG
(53.5 Ω) and a termination resistor (53.5 Ω) which is
Eb1
2W
connected in parallel; Zcs is the impedance of the sheath.
Ef1
The sending-end reflection coefficient (T1) has the
following value if the sheath is short-circuited at the
sending-end:
T1
[Ef1]= [T1]˜[Eb1]
ª0.303 0.697º
«
», Z p
1 ¼
¬ 0
ª26.75 0º
«
»:
0¼
¬ 0
Fig. 5. Calculation of transient voltage and current using
(8)
lattice diagram.
The reflection coefficient at the receiving-end (T2)
The following is an example of the theoretical
is expressed by the following equations according to the
calculation. Case Cs-So will be calculated with the
receiving-end conditions:
configuration of Case I, i.e., cable length of 2.6 m. If
Case Co-So: The core and the sheath are open-circuited.
T2
ª1 0º
«
», Z t
¬0 1¼
ªf 0 º
«
»:
¬ 0 f¼
Zc = 50 : and Zs = 207 :, the characteristic admittance
of coaxial cable Y0 and the reflection coefficient T2
(9)
become:
Case Co-Ss: The core is open-circuited while the sheath is
Yo
short-circuited.
T2
ª1 2º ªf 0º
«
», Z t «
»:
¬0 1¼ ¬ 0 0¼
ª1 0 º
«
», Z t
¬ 0 1¼
ª0 0º
«
»:
¬0 0¼
Ef0
ª66.7º
«
»
¬ 0 ¼
ªVc1 º
« »
¬Vs1 ¼
I1
ª I c1 º
« » Y0 E f 1 Eb1
¬ I s1 ¼
E f 0 Eb1
ª 1 0º
«
»
¬ 1.61 1¼
ª66.7º ª0º
«
»« »
¬ 0 ¼ ¬0¼
ª66.7º
«
»V
¬ 0 ¼
ª 1.33 º
«
»A
¬ 1.33¼
At t = W (=2.6m/200m/Ps=13 ns):
open-circuited.
T2
E f1
V1
(11)
Case Cs-So: The core is short-circuited while the sheath is
ª 1
« 2Z s
«
¬« Z c Z s
ª 0.02 0.02º
«
», T 2
¬ 0.02 0.025¼
At t = 0:
(10)
Case Cs-Ss: The core and the sheath are short-circuited.
T2
[Eb2] = [T2] [Ef2]
0º
»
1», Z t
¼»
ª0 0 º
«
»:
¬0 f¼
Ef 2
(12)
E f 1 t W ª 66.7 º
«
»
¬ 107.4¼
Eb2 T 2 ˜ E f 2
The travel of the travelling wave is illustrated in a
lattice diagram shown in Fig. 5 with the reflection
coefficients T1 and T2, and the diagram determines the
transient voltage and current waveform. The voltage and
V2
ªVc 2 º
« »
¬Vs 2 ¼
I2
ª I c1 º
« » Y0 E f 2 Eb 2
¬ I s1 ¼
E f 2 Eb 2
ª 0 º
«
»V
¬ 107.4¼
ª0.52º
«
»A
¬ 0 ¼
current at the sending-end are calculated assuming that
At t = 2W (=2(2.6m/200m/Ps)=26 ns):
the sheath at the sending-end is connected to the ground.
Eb1
Eb2 t W ª 95.1 º
E f 1 T1 ˜ Eb1 «
»
¬107.4¼
( 65 )
Diah PERMATA, Yoki IKEDA, Naoto NAGAOKA
366
V1
ªVc1 º
« »
¬Vs1 ¼
I1
ª I c1 º
« » Y0 E f 0 E f 1 Eb1
¬ I s1 ¼
>
similar to the voltage waveform. The receiving-end of
ª95.1º
«
»V
¬ 0 ¼
E f 0 E f 1 Eb1
@
the core of the current injection cable can be regarded as
open-circuited.
ª0.27º
«
»A
¬ 0.8 ¼
If the core is short-circuited and the sheath is
open-circuited at the receiving-end (Case Cs-So), an earth
The results abovementioned are based on
return current is also generated. A voltage on the
theoretical calculation. They were compared to the
receiving-end sheath also appears in the earth-return
measured and simulated results by EMTP (Fig. 3 (a) and
current. The earth-return current is generated due to the
3 (b)) in the similar case as shown in Fig. 6. It shows that
element T2-21 of the reflection coefficient. The transient
voltage and current in the core, which are obtained from
characteristic of the current injection cable terminated by
theoretical calculation, agree with the simulated and
a resistor of small resistance can be roughly explained by
measured results.
the result of case Cs (the core is short-circuited).
3.2 Surge impedance
100
Measured
Simulated
90
80
70
Voltage [V]
Surge impedance or characteristic impedance is
Theoretical
one of properties of a distributed parameter circuit such
60
as cable. It is defined as a ratio between a voltage and a
50
current of a travelling wave propagating along a line. The
40
30
estimated surge impedance of the current injection cable
20
10
can be obtained from a measured and a simulated result
0
0
10 W
20
2W
30
40
using the Eq. (13)2):
50
Time [ns]
Z0
(a) Sending-end core voltage
2
and tp is the time to peak voltage, which is less than the
Theoretical
1.4
Current [A]
voltage, I(tp) is the current at the time of the peak voltage
Simulated
1.6
(13)
where Z0 is the estimated surge impedance, Vp is the peak
Measured
1.8
Vp I t p
round-trip time (2W) of a travelling wave.
1.2
1
Table 1 shows the calculated results of the surge
0.8
impedance Z0 based on the measured and simulated
0.6
0.4
results. The difference between the measured- and
0.2
0
0
10
20
Time [ns]
30
40
simulated-surge impedance is less than 6 %.
50
Table 1. Surge impedance of the current injection cable.
(b) Sending-end core current
Fig. 6. Theoretical, measured and simulated results at
sending-end in case Cs-So with configuration Case I.
If the receiving-end core is open circuited (Cases
I
Co-So, Co-Ss) or both the core and sheath are
short-circuited (Case Cs-Ss), the coaxial current of the
II
cable is generated. The current flows into the core and
returns from the sheath. From a practical point of view,
III
the cable is terminated by a higher impedance than the
characteristic impedance of the cable to inject a current
( 66 )
Z0 [Ω]
Measurement
Simulation
Difference
(%)
Co-So
54.5
51.5
5.7
Cs-So
54.2
51.5
5.1
Co-So
54.9
51.9
5.6
Co-So
55
52.4
4.8
Cs-So
53.4
52.4
1.9
Case
Effect of Current Injection Cable
3.3 Sheath Surge impedance
The
The theoretical sheath surge impedance is defined
by Eq. (14).
Zs
60ln 2h rS
367
analytical
calculation
shows
if
the
receiving-end core is open-circuited or both the core and
sheath are short-circuited, the reflection can be explained
(14)
only by the coaxial mode. If the core is short-circuited
Where h and rs are height and outer radius of the metallic
and the sheath is open-circuited at the receiving-end, an
sheath (1.85 mm), respectively.
earth return current is also generated. A voltage on the
The sheath surge impedance is determined by the
sheath appears in the earth return mode. The current
height of the current injection cable. When the cable is
generation can be explained by the reflection coefficient
placed on the floor (h|5mm), the measured and
at the receiving end. The measured results of the surge
theoretical sheath surge impedance are 130 Ω and 100 Ω,
respectively.
As aforementioned, in case the sending end
sheath is open-circuited (Cs-So), the earth return current
is generated due to the element T2-21 of the reflection
impedance agree with the simulated ones.
The accuracy of the Semlyen line model of EMTP
was confirmed by comparing with the measured results.
The line model is suitable for a numerical simulation
including a current injection cable.
coefficient. The theoretical calculation in the previous
5HIHUHQFHV
section clearly shows the receiving-end sheath voltage
Vs2 is generated due to this element. The element T2-21 is
a function of sheath surge impedance and coaxial surge
1)
Okabe, “On the Equivalence of a Conducting Plate in a
impedance. Therefore, in case the sending-end sheath is
Laboratory Experiment to a Real Earth”, IEEE Trans.
Electromagn. Compat., 52[3],691-698 (2010).
open-circuited, the sheath surge impedance should not be
2)
ignored.
A. Ametani, M. Nishitsuji, N. Nagaoka, Y. Baba and S.
P. Yuttagowith, A. Ametani, N. Nagaoka, and Y. Baba,
“ Influence of a Measuring System to a Transient Voltage
on a Vertical Conductor”, IEEJ Trans. Electrical and
Electronic Engineering, 5, 221-228 (2010).
&RQFOXVLRQ
3)
Workshop on Advanced Technologies for Power System
Transient characteristics of the current injection
cable
were
measured, simulated and
analytically
N. Nagaoka, “Cable Transient,” Proc. of International
Simulations, 116-134 (2011).
4)
D. V. Dommelen and H. W. Dommel, ATP Rule Book,
(LEC., Belgium, 1987), p. 614-630.
calculated in this paper.
( 67 )