This document evaluates different parameters for calculating the transient impedance of grounding systems using the finite-difference time-domain (FDTD) method. It first adjusts the derivation of transient current to obtain more accurate impedance values. It then evaluates the FDTD calculation model to determine optimized parameters that accurately predict impedance without requiring huge computational resources. Specifically, it analyzes the effects of transient voltage integration path, reference electrode length and distance, injected current type and height. It finds that integrating the transient voltage parallel to the connecting line provides the most accurate impedance results without large computational needs.

1. IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 56, NO. 5, OCTOBER 2014 1155
FDTD Calculation Model for the Transient Analyses
of Grounding Systems
Run Xiong, Bin Chen, Member, IEEE, Cheng Gao, Member, IEEE, Yun Yi, and Wen Yang
Abstract—Transient performance of grounding systems is sim-
ulated using the finite-difference time-domain (FDTD) method for
solving Maxwell’s equations. The derivation of the transient cur-
rent is first adjusted to obtain accurate impedance. Then, the FDTD
calculation model is optimized to predict the grounding system
impedance accurately without resulting in huge computational re-
sources. From evaluation, the direction parallel to the connecting
line is supposed to integrate the transient voltage. The transient
voltage should be integrated 20 m in length and the reference elec-
trode to be 30 m from the grounding system, and these lengths
should be further enlarged for a large dimension grounding sys-
tem. The transient impedance of the five lightning current compo-
nents is very close to each other except the multiple burst, and the
current should be injected close to the ground.
Index Terms—Calculation model, finite-difference time-
domain (FDTD) method, grounding system, transient grounding
impedance.
I. INTRODUCTION
GROUNDING systems are often parts of the lightning pro-
tection systems, which provide a channel for current to
flow into ground. These systems should have sufficiently low
impedance and current-carrying capacity to prevent voltage rise
that may result in undue hazard to connected equipments and to
persons [1], [2]. Grounding electrode performance under normal
and fault conditions is well understood [3]. However, the dy-
namic behavior of grounding electrodes might be quite different
during lightning discharge.
Transient response of grounding systems has been inves-
tigated by experimental work [4], [5], simplified computa-
tional model [6]–[15], and numerical analyses based on the
method of moments, finite element method, and finite-difference
time-domain (FDTD) method for solving Maxwell’s equations
[16]–[22].
The FDTD method [23], which has been widely applied in
analyzing many types of electromagnetic problems, is very suit-
Manuscript received October 8, 2013; revised December 27, 2013 and Febru-
ary 17, 2014; accepted March 25, 2014. Date of publication April 18, 2014; date
of current version September 26, 2014. This work was supported in part by the
Chinese National Science Foundation under Grant 51277182, Grant 41305017,
and Grant 61271106, and in part by the School Foundation under Grant KYGY-
ZLYY1306.
R.Xiong iswith theNationalKey laboratory on ElectromagneticEnvironment
and Electro-optical Engineering, PLA University of Science and Technology,
Nanjing 210007, China and also with Command Institute of Engineering Corps,
Xuzhou 221004, China (e-mail: xiongrun1983@sina.com).
B. Chen, C. Gao, and Y. Yi are with the National Key
laboratory on Electromagnetic Environment and Electro-optical Engineering,
PLA University of Science and Technology, Nanjing 210007, China (e-mail:
emcchen@163.com; gaocheng1965@163.com; yunyi1976@163.com).
W. Yang is with the Engineering and Design Institute, Chengdu Military Area
of PLA, Yunnan 650222, China (e-mail: 76077381@qq.com).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TEMC.2014.2313918
able for the transient analyses of grounding systems. In [19]
pioneer work, the FDTD method is used to evaluate the hori-
zontal grounding electrode performance, as it can simulate the
transient and steady-state characteristics of grounding systems
(low-frequency performance).
The FDTD calculation model is widely used to investigate
the grounding system [19]–[22] and thin wire performances
[24]–[26]. The transient voltage is integrated 8–50 m vertical
andparallel tothecurrent leadwirein[19], whileintegrated50m
vertical to the current lead wire in [20] and [22]. The distance
between the reference electrode and the grounding system is set
to be 8–15 m in [19], 20–50 m in [20], and 30 m in [24]–[26].
The connecting line height is 1 m in [24]–[26] and 4 m in [19].
The transient current is derived from magnetic field integral
along the FDTD cell edge in [20] and [22], but the magnetic field
is varied along the edge in an FDTD cell. In [20], parallel im-
plementation is introduced to analyze a large grounding system,
but the FDTD calculation model has not been evaluated. While
in [19], transient responses of a horizontal grounding electrode
is analyzed to evaluate the voltage reference direction effect, but
the computational domain and the voltage reference wire length
effect are not considered.
In this paper, the derivation of the transient current is first ad-
justed to obtain accurate impedance. Then, the transient ground-
ing impedance calculation model is evaluated to find the opti-
mized parameters to predict the grounding impedance accu-
rately without resulting in huge computational resources. From
evaluation of three grounding system impedance under varied
voltage integrating path length, reference electrode length and
distance and current type, and injected height, the optimized
FDTD calculation model parameters are derived to predict tran-
sient impedance accurately without resulting in huge computa-
tional resources.
II. TRANSIENT IMPEDANCE CALCULATION MODEL
The computational model as shown in Fig. 1 is adopted
[19]–[22]. A remote electrode, which is used to provide a path
for current flowing into ground, is placed parallel to and away
from the grounding electrode. The grounding electrode and the
reference electrode are connected by vertical lifting lines and
connected by an overhead horizontal thin wire.
In Fig. 1, Lc is the connecting line length, hc is the connecting
line height from the ground, Li is the transient voltage integrat-
ing path length, lr is the reference electrode length, and hs is
the injected source height.
A homogenous ground is involved in this paper, and it is
assumed that the ground has a constant constitutive parameter.
0018-9375 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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2. 1156 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 56, NO. 5, OCTOBER 2014
Fig. 1. Transient impedance calculation model.
The conductivity is set at σg = 0.005 S/m, and the relative
permittivity of the ground is εr g = 10.
Lightning restrike is selected as the current source, which can
be represented by
I(t) = I0(e−αt
− e−βt
) (1)
where I0 = 109 405 V/m, α = 22 708 s−1
, β = 1 294 530 s−1
.
The transient impedance is defined as a ratio of the transient
voltage to the transient current [10], [27]
Z(t) =
V (t)
I(t)
. (2)
A. Transient Voltage
The transient voltage V (t) is the transient potential from the
lifting line to an infinite distance, which can be derived from
V (t) =
∞
Nl
E · dl (3)
where Nl is FDTD mesh index of the point of the lifting line
entering ground in Fig. 1.
In the FDTD analysis, the voltage between the two sides of a
cell can be defined as [20]–[23]
Vj = Ej · Δsj . (4)
By integrating the electric field along the air–ground interface
from the lifting line to the computational domain boundary (see
point K of Fig. 1), the transient voltage V (t) can be obtained
V (t) = −
NK
j=Nl
Vj = −
NK
j=Nl
Ej Δsj (5)
where Ej is the electric field component in the air–ground inter-
face, Δsj is the grid dimension, and NK is FDTD mesh indexes
of the point K of Fig. 1.
B. Transient Current
To derive the current I(t) injected to the grounding system,
Ampere’s circuit law is applied to the FDTD cells containing
the grounding system lifting line [20] as shown in Fig. 2, and the
Fig. 2. Ampere’s loop to derive the transient current.
Fig. 3. Three used grounding systems, where system S is a single vertical
electrode, system T is a line-set system composed of three vertical electrodes,
and system F is a cross-set system composed of five vertical electrodes.
calculation would refer to the space distribution of the current
in the ground. In [20] and [22], I(t) is derived from magnetic
field integral along the FDTD cell edge. However, as pointed
out in [24] and [28], the magnetic field is varied as 1/r near a
line, where r is the distance from the metal line. The distance
from the integral path to the lifting line is varied from Δx/2 at
(i0, j0 − 1
2 , k0 + 1
2 ) to Δ2
x + Δ2
z /2 at (i0 − 1
2 , j0 − 1
2 , k0 +
1
2 ) for the Hx component, which means the magnetic field Hx at
(i0, j0 − 1
2 , k0 + 1
2 ) is
√
2 times larger than that at (i0 − 1
2 , j0 −
1
2 , k0 + 1
2 ) for the case that Δ = Δx = Δz .
In this paper, the current I(t) is derived from integration of
the magnetic field in the Ampere’s circuit whose radius is Δ/2,
as shown in Fig. 3, and I(t) can be obtained from
I(t) = πΔHΔ/2. (6)
A round Ampere circuit is used here instead of square cir-
cuit [20], [22]. The magnetic field component along the round
integral path, whose radius is Δ/2, is constant. Thus, the I(t)
derived from (6) is an more accurate simulation of the grounding
system injected current.
The magnetic field component HΔ/2 in (6) is approximated
from the weighted average of the four magnetic field compo-
nents adjacent to the lifting line (7), as shown at the bottom of
the next page, where (i0, j0, k0) is the point of the lifting line
entering ground. Substituting (7) into (6) derives
I(t) =
Hz i0 − 1
2 , j0 − 1
2 , k0 −Hz i0 + 1
2 , j0 − 1
2 , k0 πΔz
4
+
Hx i0, j0 − 1
2 , k0 + 1
2 −Hx i0, j0 − 1
2 , k0 − 1
2 πΔx
4
.
(8)

3. XIONG et al.: FDTD CALCULATION MODEL FOR THE TRANSIENT ANALYSES OF GROUNDING SYSTEMS 1157
Fig. 4. Four typical transient voltage integrating paths.
The three selected grounding systems in this paper are shown
in Fig. 3, where the vertical electrode radius is 1 cm. The radius
of the lifting line, connecting line and reference electrode is
1 mm. Cubic FDTD cells with the grid dimension Δ = Δx =
Δy = Δz = 0.15 m is used and the time step is Δt = Δ/2 c,
where c is the speed of light in the free space. The computational
domain is terminated by a 15-layer CPML [29].
III. EVALUATION OF THE CALCULATION MODEL
In this section, transient voltage integrating path direction and
length, reference electrode length and distance, current type
and injected height are evaluated, respectively, to derive the
optimized transient impedance calculation model parameters.
A. Transient Voltage Integrating Direction
The transient voltage integrating direction effect on the tran-
sient impedance of the grounding system is analyzed in this part.
There are four typical paths for integrating the transient voltage,
as shown in Fig. 4. Here, path K1 is below the connecting line in
the −z direction; K2 is parallel to the connecting line and to the
computational edge in the z-direction; K3 and K4 are vertical
to the connecting line and to the computational edge in x and
−x direction, respectively.
First of all, the field distribution in the air–ground interface
is evaluated. Considering that the integrated field component is
Ex in path K1, K2 and Ez in K3, K4, the |Ex| and |Ez | field
distribution in the air–ground interface is observed, respectively,
as shown in Fig. 5, where Lc = 10 m and Li = 6 m.
It can be seen from Fig. 5 that the electric field component
decreases rapidly from the lifting line and the reference elec-
trode to the surrounding areas. Both the |Ex| and |Ez | fields are
symmetrically distributed in the x-direction in the air–ground
interface.
Fig. 5. Electric field distribution in the air–ground interface when system S is
used as the grounding system and L = 10 m: (a) the |Ex | distribution and (b)
the |Ez | distribution.
From Fig. 5(a), one can see that field strength singularities
occur in the z-direction near the lifting line and the reference
electrode and under the connecting line for the Ex field compo-
nent. Additionally, the Ex field is much larger in the x-direction
than that the z-direction at the same distance from the lifting
line and the reference electrode.
From Fig. 5(b), we can see that singularities occur in the x
direction near the lifting line and the reference electrode for the
Ez field component. Additionally, the Ez field is much smaller
in the x-direction than that the z-direction at the same distance
from the lifting line and the reference electrode in the air–ground
interface. What’s more, the Ez field in path K1 is larger than
that in path K2 at the same distance from the lifting line.
The electric field in K2 is absolutely determined by the current
dissipating through the grounding system, while the electric
field in K1 is mainly determined by the grounding system and
strongly enhanced by the reference electrode. Additionally, the
field in K3 and K4 is mainly determined by the grounding
system and affected by the reference electrode to some extend.
Thus, the voltage derived from K1 is much larger than that from
the other paths, while the voltage derived from K2 is a little
larger than that from K3 and K4.
HΔ/2 =
1
4Δ
⎧
⎪⎪⎨
⎪⎪⎩
Hz i0 −
1
2
, j0 −
1
2
, k0 − Hz i0 +
1
2
, j0 −
1
2
, k0 Δz
+ Hx i0, j0 −
1
2
, k0 +
1
2
− Hx i0, j0 −
1
2
, k0 −
1
2
Δx
⎫
⎪⎪⎬
⎪⎪⎭
(7)

4. 1158 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 56, NO. 5, OCTOBER 2014
Fig. 6. Transient impedance calculated from the three transient voltage inte-
grating paths.
Second, the transient impedance of grounding system S and
F calculated from different transient voltage integrating paths
is plotted in Fig. 6, where the path K4 impedance is not graphed
because of its symmetry to path K3.
It can be seen from Fig. 6 that the transient voltage integrating
path K1 gives much larger transient impedance than the other
paths, which enhances the conclusion drawn from Fig. 5. It can
also be seen from Fig. 6 that the impedance derived from path
K2 and K3 is very close to each other, and both of them can
be occupied. However, the involved computational domain is
quite different when the two paths are occupied to integrate the
transient voltage.
It worth to note that the calculated resistance for a single
electrode at late time as shown in Fig. 6(a) is 64.1 Ω, while the
calculated quasistatic resistance from [30] is 64.8 Ω. The two
results show good agreement with each other.
Third, the computational domain usage is compared when
path K2 and K3 are involved. It is demonstrated in Part B that
the transient voltage integrating length path should be 20 m
and Part C points out that the distance between the lifting line
and the reference electrode should be L = 30 m. The distance
between the computational edge and the grounding system is
6 m here. Thus, the computational domain is 26 m × 42 m in
the xoz plane when path K3 is occupied, compared with 12 m ×
56 m when path K2 is occupied. This means the computational
domain when path K2 is occupied is only 65% of that when
path K3 is occupied.
The initial impedance peak is a manifestation of the ground
plane surge response, and it is affected by the lifting wire height
and the ground parameter [31]–[34].
Therefore, it can be concluded that the transient voltage inte-
grating path K2, which is parallel to the connecting line in the
z-direction, is the optimized path to integrate the transient volt-
age. In the following analyses, path K2 is used to integrate the
transient voltage. The conclusion drawn here show good agree-
ment with the Zed-Meter calculations result [35], [36] using
frequency-domain methods (NEC 4).
B. Transient Voltage Integrating Path Length
To get the transient voltage accurately, it is needed to integrate
the electric field from the lifting line to a point where the electric
Fig. 7. Transient voltage integrating path length effect on the grounding sys-
tem impedance. (a) Transient impedance of various integrating path lengths,
where the impedance at infinite distance from the grounding system derived
from linear regression is also graphed. (b) Steady impedance of grounding
systems versus the integrating path length in different soil conductivity.
field vanishes. However, in the numerical calculation it is im-
possible to simulate so large a domain. Thus, it is necessary to
find the length convergence of the transient voltage integrating
path with respect to acceptable accurate.
To observe the transient voltage integrating path length effect
on the grounding system impedance, the transient impedance
of the grounding system at varying transient voltage integrating
path lengths is calculated as shown in Fig. 7(a). To provide
a benchmark, linear regression of impedance versus inverse
distance is used to derive the impedance at infinite distance [36].
By taking linear regression of the resistance when Li = 2, 4, 6,
and 8 m against the inverse of distance, the impedance at infinite
distance are obtained, which are also graphed in Fig. 7(a).
It can be seen that the transient voltage integrating path length
does not affect the transient performance of the grounding sys-
tem at the first 0.1 μs, because the current has only dissipated
to a limited area near the grounding system. However, the path
length effect the transient impedance appears as time goes on.
The steady impedance increases as the length of transient volt-
age integrating path increases but the slope decreases.
To determine the transient voltage integrating path length,
the path length is varied from 0.15 to 200 m and the transient
impedance is calculated. Fig. 7(b) plots the steady impedance
variation versus integrating path length when the three

5. XIONG et al.: FDTD CALCULATION MODEL FOR THE TRANSIENT ANALYSES OF GROUNDING SYSTEMS 1159
TABLE I
RELATIVE STEADY IMPEDANCE ERROR Rerror COMPARED WITH THAT WHEN
INTEGRATING TO AN INFINITE DISTANCE AWAY (%)
grounding systems are considered, where soil conductivity ef-
fect can also be evaluated. It can be seen that steady impedance
increases significantly as integrating path length increases
when it is shorter than 10 m, and the steady impedance does not
increase obviously when the integrating path length is longer
than 20 m. From comparison of the impedance of grounding
system F at different soil conductivity, it can also be seen that
the steady impedance is much lower for better conductivity soil
at the same grounding system and integrating path length.
To show the steady impedance convergence as integrating
length increases, the relative steady impedance error
Rerror =
Zf − Zl
Zf
(9)
is chosen, where Zf is impedance extrapolated to infinite dis-
tance from the grounding system derived from linear regression,
and Zl is the steady impedance when the integrating length is Li.
Table I gives the relative steady impedance error Rerror when
the integrating path length is increased from 10 to 50 m.
It can be seen from Fig. 7(b) that better ground conductivity
and large dimension grounding system result in lower steady
impedance. However, from comparing the relative error when
the grounding conductivity is 0.005 and 0.01 S/m in Table I,
it can be seen that the ground conductivity affects the length
convergence of the transient voltage integrating path slightly.
From comparison of the relative impedance error of ground-
ing system S, T, and F, it can be seen a longer integrating path
length is needed to obtain the impedance convergence for a large
dimension grounding system.
As can be seen from Fig. 7(a), the transient impedance of
the peak impedance is hardly affected by the transient voltage
integrating path length. While the transient impedance varia-
tion versus time after 0.2 μs is in accordance with the steady
impedance variation. So the integrating path length conclusions
drawn from the analysis of the steady impedance can be applied
to the transient voltage integrating path length.
Therefore, the transient voltage should be integrated at least
20 m for a small dimension grounding system and the voltage
integrating path should be further enlarged when a much larger
dimension grounding system is involved.
C. Reference Electrode
To derive the grounding system impedance accurately, the
reference electrode should be far enough from the grounding
system to ensure that the return reflection from the reference
electrode will not arrive before the FDTD simulation is termi-
Fig. 8. Electric field |Ez | distribution in the air–ground interface at different
reference electrode distances when system S is used as the grounding system:
(a) Lc = 10 m and (b) Lc = 15 m.
nated. However, that would result in huge computational re-
sources or even make it impossible to be simulated. Thus, it is
needed to find a reasonable reference electrode program for the
FDTD simulation.
To analyze the reference electrode effect on the transient
impedance, the Ez component distribution in the air–ground
interface is first monitored. Then, the transient grounding sys-
tem impedance at different reference electrode distances is also
compared with each other to derive the optimized reference
electrode position. Third, the length of the reference electrode
is chose.
First, electric field component |Ez | distribution in the air–
ground interface when Lc = 10 m as shown in Fig. 8(a) is
compared with that when Lc = 15 m, as shown in Fig. 8(b).
The reference electrode is located at the point (6 m, 6 m) and
the grounding electrode is located at the point (6 m, 16 m) for
Fig. 8(a) and (6 m, 21 m) for Fig. 8(b).
As graphed in Fig. 8, the electric field Ez decreases from the
lifting line and the reference electrode to the surrounding areas.
Additionally, the region area of the same field strength at the
inner side is larger than that at the outer side.
From Fig. 8(a), it can be seen that the electric field compo-
nent near the grounding electrode is seriously affected by the
reference electrode field when Lc = 10 m. However, when the
connecting line length is enlarged to Lc = 15 m, the effect of
the reference electrode on the field near the grounding electrode
is greatly eased. It can also be seen that the inner side high field

6. 1160 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 56, NO. 5, OCTOBER 2014
Fig. 9. Transient impedance of varied reference electrode distances from the
grounding system lifting line.
TABLE II
REFLECTION REACHES TIME AS THE REFERENCE ELECTRODE
DISTANCE VARIES
strength region area when Lc = 10 m is larger than that when
Lc = 15 m.
From comparing Fig. 8(a) and (b), it is easy to see that the
calculated impedance when Lc = 10 m is more seriously af-
fected by the mutual impedance of the reference electrode than
that when Lc = 15 m. Thus, the reference electrode should be
set to a certain distance away from the grounding electrode to
reduce the mutual resistance.
Second, to observe the reference electrode distance effect
on the system impedance, the transient impedance of the three
grounding systems as the reference electrode distance Lc varied
from 6 to 250 m is calculated and graphed in Fig. 9. The transient
impedance when Lc = 250 m was selected as a reference value
here, because the return reflection introduced by the reference
electrode has not reached for only a 1.5 μs simulation is involved
here.
It can be seen from Fig. 9 that the transient impedance of 0–
0.2 μs when Lc = 30 m is the same as that when Lc = 250 m, but
singularity occurs at 0.2 μs. Similar conclusions can be drawn
for Lc = 50 m and Lc = 80 m, but the time when the impedance
singularity occurs is delayed as the reference electrode distance
enlarges.
To evaluate the relationship between the transient impedance
singularity occur time and the reference electrode distance Lc ,
Table II gives the singularity occurs time as Lc varies from 30
to 120 m, where the electromagnetic wave propagating distance
at these times is also given.
From Table II, it can be seen that the singularity occur time is
very close to the time that the electromagnetic wave propagates
to the reference electrode and back. Thus, it can be concluded
that the reflections in Fig. 9 are mainly brought about by the mis-
match between connecting line surge impedance and reference
electrode resistance. An efficient way of reducing the mismatch
is selecting a matching resistor [37]. It can be demonstrated that
Fig. 10. Transient impedance at varied reference electrode lengths.
TABLE III
LIGHTNING INDIRECT EFFECT WAVEFORM PARAMETERS
the matching resistor can diminish the reflection by a factor of
three or more.
To avoid singularity brought about by reference electrode,
it should be set to be far enough from the grounding system to
make sure that the reflection will not reach before the simulation
is terminated. However, it is difficult to simulate so large a do-
main in the numerical calculation, and we suggest the reference
electrode to be 30 m from the lifting line.
Third, the length of the reference electrode is varied from 1
to 50 m when Lc = 30 m, and the transient impedance of the
grounding system is calculated and graphed in Fig. 10. It can
be seen that the reference electrode length has limited effect on
the grounding system impedance and the impedance when the
lr = 3 m is very close to that when lr = 50 m. Thus, a 3-m-long
reference electrode can be efficient.
Therefore, the reference electrode should be located at least
30 m for a small dimension grounding system and the dis-
tance should be further enlarged when a much larger dimension
grounding system is involved. The reference electrode should
be lr = 3 m in length.
D. Injected Source
In this part, both the injected source type and height effect
on the transient impedance are considered. First, the five cur-
rent components [38] of different lightning steps, as shown in
Table III, are occupied as the injected source, and the transient
impedance is calculated and graphed in Fig. 11(a).
Fig. 11(a) shows that the transient impedance is very close
to each other when the current components A, B, and D are
used as the injected source. However, the transient impedance

7. XIONG et al.: FDTD CALCULATION MODEL FOR THE TRANSIENT ANALYSES OF GROUNDING SYSTEMS 1161
Fig. 11. Injected current component effect on the transient impedance.
(a) Transient impedance of different current components. (b) Transient
impedance at different injected positions.
of the current component H is quite different from the transient
impedance of the other current components before the time
1.0 μs, because the frequency spectra of A, B, and D are very
close to each other, while H is quite different from the others.
Second, the current component D is selected as the source
and the injected position effect on the transient impedance is
analyzed. Here, the injected height is varied from hc = 0.225
to 2.025 m. The transient impedance is calculated as shown in
Fig. 11(b), where the 0–0.06 μs transient impedance of system
S is zoomed. The current component is introduced through the
Ampere’s law, which means the injected source is located at half
an FDTD cell position. The transient current is integrated half
an FDTD cell above the ground (j0-0.5)Δ, thus the source can
injected 1.5Δ (0.225 m) or higher above the ground.
As can be seen from Fig. 11(b) that the source injected po-
sition can hardly affect the transient impedance after 0.1 μs,
but the peak impedance increases as the injected current height
increases. The peak impedance is 83.1 Ω, when hc = 0.225 m,
and increase to 86.2, 89.9, 96.2, and 100.0 Ω as hc increases to
0.525, 0.975, 1.575, and 2.025 m, respectively. Additionally, the
high injected source position results in a late peak impedance
value time.
Therefore, the multiple burst transient impedance is quite
different from the other four lightning steps and the current
should be injected at a low position above the ground to get the
real peak impedance of the grounding system.
IV. CONCLUSION
In this study, the derivation of the transient current is first
adjusted to obtain accurate impedance. Then, the FDTD cal-
culation model is evaluated in order to predict the transient
grounding system impedance accurately without resulting in
huge computational resources. From evaluation, it can be con-
cluded that:
1) The transient voltage should be integrated along the path
parallel to the connecting line.
2) The transient voltage should be integrated at least 20 m
for a small dimension grounding system and longer for a
large dimension grounding system.
3) The reference electrode should be located at least 30 m
from the grounding system for a small dimension system
and the distance should be further enlarged when a large
dimension grounding system is involved. The reference
electrode should be 3 m in length.
4) Among the current components of different lightning
steps, the transient impedance of the current component
multiple burst is different from the other steps. The current
should be injected at the point close to the ground.
The adjusted and optimized FDTD calculation model would
be useful in impedance calculation of the grounding systems.
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[1] IEEE Standard Dictionary of Electrical and Electronics Terms, IEEE Std.
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tures and Life Hazard, IEC 62305-3, 2006.
[3] IEEE Guide for Safety in AC Substation Grounding, IEEE Std.80-2000,
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[4] S. Visacro and R. Alipio, “Frequency dependence of soil parameters:
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Run Xiong was born in Sichuan, China, in 1983.
He received the B.S. and M.S. degrees in electric
systems and automation in 2005 and 2010, respec-
tively, from the Engineering Institute of Corps of En-
gineers, PLA University of Science and Technology,
Nanjing, China, where he is currently working toward
the Ph.D. degree.
He is currently with the National Key Laboratory
on Electromagnetic Environment and Electro-optical
Engineering, PLA University of Science and Tech-
nology. His current research interests include com-
putational electromagnetics and EMC.
Bin Chen (S’02–M’03) was born in Jiangsu, China,
in 1957. He received the B.S. and M.S. degrees in
electrical engineering from Beijing Institute of Tech-
nology, Beijing, China, in 1982 and 1987, respec-
tively, and the Ph.D. degree in electrical engineering
from Nanjing University of Science and Technology,
Nanjing, China, in 1997.
He is currently a Professor at the National Key
Laboratory on Electromagnetic Environment and
Electro-optical Engineering, PLA University of Sci-
ence and Technology, Nanjing, China. His current
research interests include computational electromagnetics, EMC, and EMP.
Cheng Gao (M’98) was born in Jiangsu, China, in
1964. He received the B.S. degree from the Naval
Aeronautical Engineering Institute, Yantai, China,
the M.S. degree from the Nanjing University of Aero-
nautics and Astronautics, Nanjing, China, and the
Ph.D. degree from the Nanjing Engineering Institute,
Nanjing, in 1985, 1994, and 2003, all in electrical
engineering.
He is currently a Professor at the National Key
Laboratory on Electromagnetic Environment and
Electro-optical Engineering, PLA University of Sci-
ence and Technology, Nanjing. His current research interests include electro-
magnetic compatibility and electromagnetic pulse protection.
Yun Yi was born in Changsha, China, in 1978. She
received both the B.S. and M.S. degrees in electric
system and its automation in 2000 and 2003, respec-
tively, from Nanjing Engineering Institute, Nanjing,
China, where she is currently working toward the
Ph.D. degree in disaster prevention and reduction en-
gineering and protective engineering.
Her current research interest includes computa-
tional electromagnetics.
Wen Yang was born in Tongren, China, in 1982.
He received the B.S. degree in electric system and
its automation from Nanjing Engineering Institute,
Nanjing, China, in 2005.
He is currently a Pioneer Engineer with the Engi-
neering and Design Institute, Chengdu Military Area
of PLA, Yunnan, China. His current research inter-
ests include computational electromagnetics and the
electric system design.