Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 2
,
A
p
r
il
201
6, p
p
.
79
2
~
79
9
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
2.9
527
7
92
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Integration of Frequency Depende
nt Soil E
l
ect
ri
cal
Prop
erti
es
in Grounding Electrode Circuit Model
Mehrd
a
d
Mokhtari,
Z
u
lku
r
nain Ab
dul-Malek
, Chin Leon
g
W
o
oi
Institute of High
Voltag
e
and Hi
gh Current
(IVAT), Facul
t
y
of
El
ectr
i
cal
Engineer
ing, Univ
ersiti
T
e
knologi
Malay
s
ia,
Johor, Mala
y
s
ia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 9, 2015
Rev
i
sed
D
ec 11
, 20
15
Accepte
d Ja
n
3, 2016
The eff
ect of fr
equency
d
e
pend
ent soil proper
t
ies on the impedance
and
transien
t respo
n
se of the gr
ounding electro
de was investigated
. Th
e
frequency
dep
e
n
d
ent soil models as propos
ed by
Scott, Smith-Lo
ngmire, and
Visacro-Alipio
were critically
r
e
viewed
. A novel method was proposed to
integr
ate
the
fr
equenc
y
depend
ent soil
el
ec
tric
al prop
erti
es in
the
cir
c
ui
t
model of grounding electrod
e
.
To valid
at
e the
application of th
e method in
circu
it model, th
e voltage r
e
sponses of
the groun
ding electrod
e
o
b
tain
ed
b
y
the circuitand
electromagnetic
models were
compared
. The vo
ltag
e responses
obtain
e
d
b
y
th
e
cir
c
uit and electrom
agnetic models we
re in exc
e
ll
ent
agreem
ent
in te
rm
s
of voltage peaks
and wa
ve s
h
apes
. Th
e
differen
ces
between vo
ltag
e
peaks obtained
b
y
th
e
circuit and electr
omagnetic models
were found
less than 1%.
Keyword:
Circu
it m
o
d
e
l
El
ect
rom
a
gnet
i
c
m
odel
Fre
que
ncy
dep
e
nde
nt
G
r
o
und
ing
electr
od
e
Soil electrical properties
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Zul
k
ur
nai
n
A
b
dul
-M
al
ek,
In
stitu
te o
f
Hi
gh
Vo
ltag
e
and
High
C
u
rren
t (IVAT),
Un
i
v
ersiti Tekn
o
l
o
g
i
Malaysia,
Jo
hor
Bah
r
u
813
10
, Joho
r, Malaysia
Em
a
il: zu
lk
u
r
nain
@u
tm
.
m
y
1.
INTRODUCTION
Transient currents cause
d
by faults
an
d l
i
g
ht
ni
n
g
st
ri
kes
have si
g
n
i
f
i
cant
effect
s
o
n
p
o
we
r sy
st
em
per
f
o
r
m
a
nce [1, 2]
. T
h
w
hi
gh am
pl
i
t
ude cur
r
ent
s
are
d
i
sperse
d i
n
t
o
t
h
e eart
h
t
h
r
o
ug
h t
h
e g
r
ou
ndi
n
g
el
ect
rodes em
bedde
d i
n
si
de t
h
e soi
l
[3]
.
Th
e perf
orm
a
nce
of gr
o
u
n
d
i
ng
el
ect
rodes i
s
d
e
pen
d
e
n
t
on t
h
e soi
l
electrical properties, electrode
di
m
e
n
s
io
n
s
, an
d
cu
rren
t p
a
ram
e
ters [4-7
]. Th
e
so
il co
ndu
ctivity an
d
p
e
rm
itt
iv
ity are in
fl
u
e
n
c
ed
by sev
e
ral
p
a
rameters su
ch
as
soil c
o
m
p
action, tem
p
erature, m
o
isture, a
n
d
grai
n
size [8]. In a
d
dition, they a
r
e also
i
n
fl
uenc
ed
by
t
h
e
f
r
eq
uency
o
f
t
h
e
c
u
rrent. T
h
e
higher the
fre
que
n
cy, the
lo
wer th
e so
il co
ndu
ctiv
ity a
n
d
p
e
rm
itt
iv
ity
[9
, 10
]. As a resu
lt, th
e transien
t i
m
p
e
d
a
n
c
e o
f
th
e electro
d
e
i
s
also affected [11-14].
Despit
e all th
e above, the effect of fre
que
ncy on
so
il electrical p
r
op
erties is usu
a
lly
di
sre
g
ar
de
d i
n
hi
g
h
fre
qu
en
cy
gr
ou
n
d
i
n
g
sy
st
em
an
aly
s
es. F
o
r i
n
stan
ce, in C
D
EG
S so
ftwa
re (C
ur
re
n
t
D
i
str
i
bu
tio
n, Electr
o
m
a
g
n
e
tic Field
s
, Gr
ound
ing
and
So
il Str
u
ct
u
r
e
A
n
al
ysis p
r
ogr
am
p
r
ov
id
ed
b
y
th
e Saf
e
Engineeri
n
g Services a
n
d T
echnolo
gies Lt
d., Qué
b
ec, C
a
nada
), t
h
e measure
d
s
o
il c
o
nductivity and s
o
il
p
e
rm
itt
iv
ity are u
s
ed
in th
e
co
m
p
u
t
atio
n
,
even
thou
gh
t
h
e
co
ndu
ctiv
ity an
d p
e
rm
it
tiv
ity
are
u
s
u
a
lly
measu
r
ed
b
y
u
s
ing
eith
er DC o
r
low freq
u
e
n
c
y sources. In
add
itio
n, in
circu
it ap
pro
ach, th
e ap
p
licatio
n
of th
e
fre
que
ncy de
pende
nt soil prope
rties in i
m
pulse cond
ition is neglected. This is because applying
each
i
ndi
vi
dual
f
r
eq
uency
o
f
l
i
g
ht
n
i
ng
c
u
rre
nt
i
s
d
i
ffi
cul
t
.
In t
h
i
s
pa
per, t
h
e f
r
eq
ue
ncy
d
e
pen
d
e
n
t
soi
l
m
odel
s
as pro
pos
ed
by
Scot
t
[9]
,
Sm
i
t
h
-Lo
ngm
i
r
e [1
5]
,
an
d
Visacro-Alip
io
[1
6
]
are critically rev
i
ewed
.
In
add
iti
on,
t
h
e si
m
u
l
t
a
neous ef
fect
o
f
f
r
e
que
ncy
o
n
b
o
t
h
s
o
i
l
con
d
u
ct
i
v
i
t
y
and
perm
i
t
t
i
v
i
t
y
, and
hence
on
t
h
e gr
o
u
n
d
i
n
g el
ect
rode i
m
pedance i
s
di
sc
us
sed. A
no
vel
m
e
t
h
o
d
i
s
pro
p
o
se
d t
o
i
n
cor
p
orat
e t
h
e freq
u
e
n
cy
de
pen
d
e
n
t
soi
l
el
ect
ri
cal
pro
p
er
t
i
e
s i
n
ci
rcui
t
m
odel
of gr
o
u
ndi
ng
el
ect
rode
. The
di
ffe
rence
be
t
w
een t
h
e
vol
t
a
ge res
p
onse
s
obt
ai
ne
d by
t
h
e p
r
o
p
o
se
d m
e
t
hod i
n
t
h
e
ci
rcui
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
79
2 – 7
9
9
79
3
m
odel
and o
b
t
ai
ned by
t
h
e
el
ect
rom
a
gnet
i
c
wi
t
h
t
h
e
m
e
t
hod
of m
o
m
e
nt
(EM
-
M
o
M
)
un
de
r fi
r
s
t
and
subseque
nt ret
u
rn st
roke c
u
rrents
was
found less tha
n
1%.
The re
sul
t
s
h
o
w
s t
h
at
t
h
e i
n
fl
ue
nce o
f
f
r
e
que
ncy
o
n
t
h
e
gr
o
u
n
d
i
n
g i
m
peda
nce a
n
d i
t
s
t
r
ansi
ent
per
f
o
r
m
a
nce m
u
st
be t
a
ke
n i
n
t
o
acc
ou
nt
whe
n
ca
rry
i
n
g
out
a g
r
o
u
ndi
ng
sy
st
em
t
r
ansi
ent
anal
y
s
i
s
.
2.
FREQUENC
Y
DEPENDENT
SOIL
MODELS
Seve
ral
m
odel
s
ha
ve bee
n
p
r
o
p
o
sed t
o
d
e
t
e
rm
i
n
e t
h
e soi
l
el
ect
ri
cal
prope
rt
i
e
s as a
fu
nct
i
o
n o
f
fre
que
ncy
[9
,
15
,
16]
.
I
n
t
h
i
s
sect
i
o
n
,
t
h
e m
odel
s
p
r
o
p
o
se
d
by
Scot
t
[9]
,
Sm
i
t
h
-Lo
ngm
i
r
e [
1
5]
, a
n
d
Vi
sacro
-
Al
i
p
i
o
[1
6]
are
descri
be
d. I
n
t
h
i
s
st
u
d
y
,
t
h
e
f
r
eq
ue
ncy
de
pe
nde
nt
s
o
i
l
el
ect
ri
cal
param
e
t
e
rs o
b
t
a
i
n
ed
by
t
h
ese
m
odels had be
en c
o
m
p
ared
with the e
x
perimental val
u
es.
2.
1.
Scott Model
The f
r
eq
ue
ncy
depe
n
d
ent
co
nd
uct
i
v
i
t
y
,
σ
(
f
), an
d f
r
eq
ue
n
c
y
depe
nde
nt
rel
a
t
i
v
e perm
i
t
t
i
v
i
t
y
,
ε
(
f
),
were
det
e
rm
i
n
ed
usi
n
g t
h
e f
o
rm
ul
as pr
op
ose
d
by
Sc
ot
t
[
9
]
as
2
0
2
0
0
018
.
0
046
.
0
036
.
0
068
.
0
1.098
0.028
=
)
(
f
f
f
f
(1
)
2
0
2
0
0
067
.
0
114
.
0
069
.
0
097
.
1
946
.
0
491
.
5
)
(
f
f
f
f
r
(2
)
whe
r
e
σ
0
is th
e n
o
m
in
al lo
w
frequ
e
n
c
y so
il co
ndu
ctiv
ity
, and
f
i
s
t
h
e a
ppl
i
e
d f
r
e
que
ncy
i
n
t
h
e
ra
nge
o
f
10
0
H
z
to
1
M
Hz.
2.
2.
Smith-L
o
n
g
m
i
re Model
Th
e Sm
ith
an
d
Lo
ng
m
i
re ex
p
r
ession
s were u
s
ed
to
co
m
p
ute th
e so
il rela
tiv
e p
e
rm
it
tiv
it
y an
d
so
i
l
co
ndu
ctiv
ity valu
es. Th
e
frequ
en
cy
-d
ep
en
d
e
n
t
so
il relativ
e
p
e
rm
itt
iv
ity an
d
co
ndu
ctiv
ity are
18
1
2
1
)
(
i
i
i
r
F
f
a
f
(3
)
18
1
2
2
0
1
2
)
(
i
i
i
i
i
DC
F
f
F
f
F
a
f
(4
)
whe
r
e
σ
DC
is dc so
il con
d
u
c
ti
v
ity,
ε
∞
i
s
hi
g
h
fre
que
ncy
l
i
m
it
of t
h
e
di
el
ect
ri
c co
nst
a
nt
,
w
h
i
c
h
w
as set
t
o
5. T
h
e
value of
c
o
efficient
a
i
was ref
e
rre
d fr
om
Tabl
e
1.
The param
e
ters
F
i
i
s
obt
ai
ned
usi
n
g
1
10
.
i
DC
i
F
F
(5
)
W
h
er
e
8312
.
0
125
DC
DC
F
(6
)
Table 1.
C
o
effi
cient
a
i
i a
i
i
a
i
1 3.
40×10
6
8 1.
25×10
1
2 2.
74×10
5
9
4.
80×10
0
3 2.
58×10
4
10
2.
17×10
0
4 3.
38×10
3
11
9.
80×10
-1
5 5.
26×10
2
12
3.
92×10
-1
6 1.
33×10
2
13
1.
73×10
-1
7 2.
72×10
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Int
e
grat
i
o
n
of
Freq
uency
De
pen
d
e
n
t
S
o
i
l
El
ect
rica
l Prop
erties in
G
r
ou
nd
i
n
g Electrod
e
…
(
Z
ul
kur
nai
n A.M.)
79
4
2.
3.
Visa
cro
-
Alipio
Model
The V
i
sacro-Alipio
expres
sions
we
re
obtained according to lar
g
e num
b
er of field m
easurem
ents.
Th
e
frequ
en
cy
d
e
p
e
nd
en
t
relativ
e p
e
rm
it
tiv
it
y an
d cond
u
c
ti
v
ity o
f
so
il
were ob
tain
ed using
3
.
1
10
6
.
7
)
(
4
.
0
3
f
f
r
(7
)
65
.
0
73
.
0
0
6
0
100
.
1
10
2
.
1
1
f
f
(8
)
whe
r
e
σ
0
is
n
o
min
a
l lo
w frequ
e
n
c
y so
il cond
u
c
tiv
ity
, an
d
f
is ap
p
lied freq
u
e
n
c
y in th
e
rang
e
o
f
100
Hz to
4M
Hz.
2.
4.
Co
mpa
r
iso
n
of the So
il Mo
dels
Th
e
f
r
e
q
u
en
cy
d
e
p
e
nd
en
t so
i
l
p
r
o
p
e
r
ties obtain
e
d
b
y
Sco
tt, Sm
i
t
h
-
Longmir
e, and
V
i
sacr
o-
A
lip
i
o
form
ulas were then com
p
are
d
with the experim
e
ntal
value to evaluate
the accu
racy
of the soil models
.
Co
m
p
ariso
n
s
of th
e
frequ
en
cy d
e
p
e
nd
en
t so
il
p
r
op
ertie
s fo
r low fre
q
u
ency
soil
resi
stiv
ity v
a
lu
es of
9
3
.2
Ω
.m
,
and 34
3
Ω
.m
are sh
own
in
Fi
gu
res
1
an
d
2
.
As seen
in
bo
t
h
figu
res, all s
o
il
m
o
d
e
ls were ab
le to
p
r
ed
i
c
t th
e
fre
que
ncy
dep
e
nde
nt
s
o
i
l
res
i
st
i
v
i
t
y
val
u
es i
n
di
ffe
rent
f
r
eq
ue
nci
e
s co
m
p
ared t
o
t
h
e
ex
peri
m
e
nt
al
val
u
es
.
Howev
e
r, in term
o
f
p
r
ed
ictin
g th
e relativ
e p
e
rm
i
ttiv
it
y valu
es, t
h
e
Visacro-Alip
i
o
’s soil
m
o
d
e
l was fo
und
u
n
a
b
l
e to pro
p
erly p
r
ed
ict th
e frequ
en
cy
d
e
pen
d
e
n
t
relativ
e p
e
rm
i
ttiv
it
y v
a
lu
es.
(a)
ρ
(
f) (
b
)
ε
r
(f
)
Fi
gu
re
1.
Fre
q
uency
de
pen
d
e
n
t
s
o
i
l
el
ect
ri
cal
pr
o
p
ert
i
e
s f
o
r
ρ
0
=9
3.
2
Ω
.m
ob
tain
ed b
y
d
i
fferen
t
so
il m
o
dels
(a)
ρ
(
f) (
b
)
ε
r
(f
)
Fi
gu
re
2.
Fre
q
uency
de
pen
d
e
n
t
s
o
i
l
el
ect
ri
cal
pr
o
p
ert
i
e
s f
o
r
ρ
0
=343
Ω
.m
obt
ai
ned
by
di
f
f
e
rent
s
o
i
l
m
o
d
e
l
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
79
2 – 7
9
9
79
5
3.
HARMONIC GROUNDING
ELECTROD
E IMPEDANCE
CHARACTERISTIC
Thi
s
sect
i
o
n
d
i
scusses t
h
e ef
fect
o
f
f
r
e
que
n
c
y
on
ha
rm
oni
c gr
o
u
n
d
i
n
g el
ect
ro
de i
m
pedance
un
de
r
fi
rst
an
d s
u
bse
que
nt
ret
u
r
n
st
ro
ke c
u
r
r
ent
s
.
A h
o
r
i
z
o
n
t
a
l
cop
p
e
r
el
ect
ro
d
e
wi
t
h
10
-m
l
e
ngt
h an
d
5-m
m
radi
us
was ass
u
m
e
d l
o
cat
ed at
1-m
dept
h i
n
a u
n
i
f
orm
soi
l
.
Th
ree d
i
fferen
t types of so
il
with lo
w
resistiv
ity v
a
lu
e
(
ρ
=100
Ω
.m
),
and
hi
gh
resi
st
i
v
i
t
y
val
u
e
(
ρ
=
1
00
0
Ω
.m
) were
co
nside
r
ed
.
The fi
rst
ret
u
rn
st
ro
ke cu
rre
nt
had a
pea
k
val
u
e o
f
3
0
kA
, m
a
xi
m
u
m
st
eepness of
1
2
k
A
/
μ
s, and zero
t
o
pea
k
t
i
m
e
of
8 µs. T
h
e s
u
b
s
eq
uent
ret
u
r
n
st
ro
ke cu
rre
nt
had a
pea
k
val
u
e o
f
1
2
kA
, a
m
a
xim
u
m
st
eepne
ss
of 4
0
kA/
μ
s,
a
n
d
zer
o t
o
pea
k
t
i
m
e of 0
.
8
µ
s
. T
h
e t
w
o
wa
vef
o
rm
s were
r
e
prese
n
t
e
d
u
s
i
n
g
Hei
d
l
e
r’
s f
u
nct
i
o
n
[1
7]
, t
h
e
pa
ram
e
t
e
rs o
f
w
h
i
c
h
are
gi
ve
n i
n
[
1
8]
.
The im
pedanc
e characteristic
of th
e electrodes according to the diffe
re
nt soil
m
odels under first and
sub
s
eq
ue
nt
ret
u
r
n
st
ro
ke cu
rr
ent
s
are sh
ow
n
i
n
Fi
gure
s
3 a
nd
4. The
harm
oni
c i
m
pedanc
e was obt
ai
ned
as t
h
e
rat
i
o
o
f
gr
o
u
n
d
i
n
g el
ect
r
ode
vol
t
a
ge
, a
n
d
c
u
r
r
ent
as
Z
(
ω
)=
V
(
ω
)/
I
(
ω
).
A
s
seen i
n
bot
h
fi
g
u
res
,
t
h
e
ha
rm
oni
c
im
pedance c
h
a
r
acteristics obtained
by Sc
ott and
Sm
ith
-Longm
ire
m
odels were i
n
accordance. T
h
e
harm
onic
im
pedances
ob
t
a
i
n
ed by
Vi
sa
cro
-
Al
i
p
i
o
’s m
odel
ha
d l
a
r
g
e di
ffe
re
nce com
p
are
d
t
o
t
h
e ha
rm
oni
c im
pedanc
e
s
obt
ai
ne
d
by
Sc
ot
t
an
d Sm
i
t
h
-Lo
ngm
i
r
e m
odel
s
.
(a) Im
pedance
(b
) An
gle
Fi
gu
re
3.
Im
pedance
cha
r
act
e
r
i
s
t
i
c
s of
t
h
e
g
r
ou
n
d
i
n
g el
ect
r
ode
ρ
0
=100
Ω
.m
(a) Im
pedance
(b
) An
gle
Fi
gu
re
4.
Im
pedance
cha
r
act
e
r
i
s
t
i
c
s of
t
h
e
g
r
ou
n
d
i
n
g el
ect
r
ode
ρ
0
=1
00
0
Ω
.m
4.
TIME DOMAIN
VOLTAGE RESP
ONSE OF THE E
LECTRODE
Thi
s
sect
i
o
n di
scusses t
h
e det
e
rm
i
n
at
i
on of t
h
e v
o
l
t
a
ge
res
p
ons
e of the ele
c
tr
od
e with
resp
ect to
th
e
fre
que
ncy
de
p
e
nde
nt
soi
l
p
r
ope
rt
i
e
s t
h
r
o
u
gh c
o
m
put
at
i
on.
A n
o
v
el
m
e
t
h
o
d
was a
p
pl
i
e
d t
o
i
n
t
e
gr
at
e t
h
e
fre
que
ncy
de
p
e
nde
nt
soi
l
p
r
o
p
ert
i
e
s i
n
ci
rcu
i
t
appr
oach
. T
h
i
s
m
e
t
hod i
m
pr
o
v
ed t
h
e
vol
t
a
ge resp
o
n
se
of t
h
e
el
ect
rode
wi
t
h
respect
t
o
t
h
e f
r
eq
ue
ncy
de
pe
nde
nt
s
o
i
l
p
r
o
p
e
rt
i
e
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Int
e
grat
i
o
n
of
Freq
uency
De
pen
d
e
n
t
S
o
i
l
El
ect
rica
l Prop
erties in
G
r
ou
nd
i
n
g Electrod
e
…
(
Z
ul
kur
nai
n A.M.)
79
6
4.
1.
Electrom
a
gne
t
ic Model with
the
Meth
od
of
M
o
men
t
The electrom
a
gnetic m
odel
with the m
e
thod
of m
o
m
e
nt is known as the m
o
st accurate
m
odel to
anal
y
ze t
h
e g
r
o
u
ndi
ng el
ect
ro
de. T
h
e m
e
t
h
o
dol
ogy
use
d
i
n
t
h
e el
ect
rom
a
gnet
i
c
m
odel
i
n
di
ssc
u
ssed.
Ho
we
ver
,
m
o
r
e
det
a
i
l
s
can be fou
n
d
i
n
[1
9]
. In el
ect
rom
a
gnet
i
c
app
r
oac
h
wi
t
h
t
h
e
m
e
t
hod
of m
o
m
e
nt
(EM
-
MoM), the injected cu
rrent is specified as
an im
pulse signal.
Fa
st Fourier trans
f
orm
(FFT)
was us
ed t
o
decom
pose t
h
e t
i
m
e
dom
ain cu
rre
nt
i
(
t
)
i
n
t
o
i
t
s
cor
r
e
sp
on
di
n
g
f
r
e
que
ncy
s
p
ect
r
u
m
i
(
ω
). The
discrete
fre
que
ncy
s
p
ec
t
r
um
of t
h
e
i
n
put
c
u
rre
nt
wa
s i
n
a
ra
nge
f
r
o
m
t
h
e l
o
west
fre
que
ncy
t
o
t
h
e
hi
g
h
est
f
r
e
q
uency
(Nyqu
ist frequen
c
y). First, the electro
d
e
was d
i
scretized
i
n
to
N
equal conductor segm
ents. The current in
each se
gm
ent was t
h
en dete
rmined
by appl
ying M
o
M to
enforce
the
continuity
of
the
tange
ntial compone
n
t
of the electric field along
t
h
e
segm
ents. Once the curre
nt in each c
o
nduct
o
rse
g
m
e
nt was
known, the el
ectric
field (
E
) ca
use
d
by
t
h
e cu
rre
nt
s at
al
l
com
put
at
i
on
p
o
i
n
t
s
i
n
t
h
e s
o
i
l
co
ul
d be
o
b
t
a
i
n
e
d
.
C
onse
q
uent
l
y
,
ot
he
r
electro
m
a
g
n
e
tic field
v
a
lu
es
an
d
d
e
ri
v
e
d
qu
an
tities, su
ch as electro
d
e
v
o
ltag
e
, cou
l
d also
b
e
ob
tain
ed. To
obt
ai
n
t
h
e
v
o
l
t
a
ge i
n
t
i
m
e dom
ai
n, fast
i
nve
rse F
o
uri
e
r
t
r
a
n
sf
orm
(IF
FT
)
was a
p
pl
i
e
d.
4.
2.
Circuit Model
A
gr
o
u
n
d
i
n
g e
l
ect
rode
can
b
e
p
r
esent
e
d as
an e
qui
val
e
nt
l
u
m
p
ed ci
rc
ui
t
m
odel
[2
0,
2
1
]
.
T
h
e m
odel
cont
ai
n
s
R
,
L
, and
C
elem
en
ts. Sin
ce th
e so
i
l
io
n
i
zatio
n
facto
r
was no
t taken
in
to
accou
nt in
th
is stu
d
y
d
u
e
t
o
th
e app
licatio
n o
f
low am
p
lit
u
d
e
curren
t
, R
u
d
e
nb
erg
circu
it
m
o
d
e
l, as illu
strated in
Fi
gu
re
5
[20
]
,
was u
s
ed
to
m
odel
t
h
e gro
u
n
d
i
n
g el
ect
ro
de. T
h
e
R
-
L
-
C
ele
m
ents w
e
re set as the groundi
ng re
sistance
R
in
Ω
(or
alternatively, the c
o
nductanc
e
G
in S), the
e
l
ectrode i
n
duct
a
nce
L
i
n
µ
H
,
and the s
o
il ca
pacitance
C
in
F. No
te
t
h
at
un
der
fas
t
-fr
o
n
t
e
d cu
rre
nt
s, t
h
e p
r
op
o
s
ed m
e
t
hod i
n
[2
1]
was t
a
k
e
n i
n
t
o
acc
ou
nt
t
o
det
e
rm
i
n
e t
h
e
electrode i
n
ductance. For a
horizontal
grounding electrode in a
uni
form so
il, th
e circu
it ele
m
en
ts co
u
l
d
b
e
o
b
t
ain
e
d
u
s
i
n
g th
e
form
u
l
as
in
itially
p
r
op
osed
b
y
Su
nd
e [22
]
:
]
1
)
2
2
[ln(
1
ad
l
l
G
R
(9
)
]
1
)
2
[ln(
2
a
l
l
L
(1
0)
R
C
(1
1)
whe
r
e
ρ
is
so
il
resistiv
ity in
[
Ω
.m
]
,
l
is len
g
th
of th
e electro
d
e
in
[m
],
a
i
s
ra
di
us
of
t
h
e
el
ect
rode
i
n
[
m
]
,
d
is
bu
ri
al
de
pt
h i
n
[m
]
,
µ
is so
il perm
eab
ili
ty (4
π
×1
0-
7H
/m
)
,
an
d
ε
is
p
e
rm
itt
i
v
ity o
f
so
il in
[F/
m
]. Ob
v
i
o
u
sly, th
e
im
port
a
nt
m
a
teri
al
pr
ope
rt
i
e
s seen i
n
(9
)
t
o
(1
1
)
are
ρ
,
µ
, and
ε
for the
resista
n
ce, inductanc
e
, and
cap
acitan
ce, resp
ectiv
ely.
Howev
e
r, on
ly the resistiv
ity
an
d
perm
i
t
t
i
v
i
t
y
are f
r
e
que
ncy
depe
n
d
ent
,
a
n
d
he
nc
e
o
n
l
y th
ese two
p
a
ram
e
ters were con
s
id
ered in th
is
work.
Fi
gu
re
5.
R
e
p
r
esent
a
t
i
o
n
o
f
a
t
y
pi
cal
gr
ou
n
d
i
n
g
el
ect
ro
de
b
y
an e
qui
val
e
nt
l
u
m
p
ed ci
rc
ui
t
m
odel
It is k
nown
t
h
at th
e circu
it app
r
o
a
ch
is a si
mp
le
approac
h
c
o
m
p
ared to t
h
e
electrom
a
gnetic approac
h
t
o
anal
y
ze t
h
e t
r
ansi
ent
be
ha
vi
o
r
of t
h
e gr
ou
n
d
i
n
g el
ect
rode
. H
o
we
ve
r,
t
h
e di
ffi
c
u
l
t
y
of i
n
c
o
r
p
orat
i
n
g t
h
e
freq
u
e
n
c
y
d
e
pen
d
e
n
t
so
il
p
r
o
p
e
rties limits
th
e app
licatio
n
o
f
th
e app
r
oach
i
n
tran
sien
t an
alysis, si
n
ce t
h
e
l
i
ght
ni
n
g
cu
rre
nt
has
fre
q
u
en
cy
com
pone
nt
s
.
T
o
i
nvest
i
g
at
e t
h
e e
ffect
o
f
l
i
ght
ni
n
g
cu
rre
nt
’s
fr
o
n
t
t
i
m
e,
T
f
, on
th
e resistiv
ity an
d
p
e
rm
i
ttiv
it
y, th
e equ
i
v
a
len
t
frequ
en
cy,
f
eq
, of t
h
e l
i
ght
n
i
ng c
u
r
r
ent
[2
3
,
2
4
]
w
as
det
e
r
m
i
n
ed
usi
n
g
f
eq
T
f
4
1
(1
2)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
79
2 – 7
9
9
79
7
f
eq
was th
en
u
s
ed
in
freq
u
e
n
c
y d
e
p
e
n
d
e
n
t
soil p
r
op
erties soil
m
o
d
e
ls. Fin
a
lly, th
e circu
it ele
m
en
t v
a
lu
es o
f
th
e
el
ect
rode
m
odel
as sh
o
w
n
i
n
F
i
gu
re
5
wi
t
h
t
h
e
frequ
en
cy
d
e
p
e
nd
en
t so
il p
r
o
p
e
rties were
ob
tain
ed.
5.
VALI
D
ATIO
N O
F
THE
M
ETHOD
Fo
r valid
atio
n, th
e
v
o
ltage resp
on
ses ob
tain
ed
b
y
th
e ci
rcu
i
t
m
o
d
e
l an
d EM-Mo
M
were
co
m
p
ared
. In
t
h
i
s
com
p
ari
s
o
n
, t
h
e t
y
pi
cal
el
ect
rode a
n
d l
i
ght
ni
ng c
u
rre
nt
s de
fi
ne
d i
n
Sect
i
on
2 w
e
r
e
t
a
ken i
n
t
o
ac
cou
n
t
.
The e
q
ui
val
e
n
t
fre
que
nci
e
s
fo
r t
h
e
fi
r
s
t
a
n
d
su
bse
q
uent
ret
u
rn
st
r
oke
cu
rre
nt
s
wer
e
f
eq
=31.
2
5
kH
z
a
n
d
f
eq
=3
1
2
.5
k
H
z, resp
ectiv
ely.
Sco
tt so
il m
o
d
e
l was tak
e
n i
n
t
o
acco
u
n
t
t
o
det
e
rm
i
n
e t
h
e
fr
eq
ue
ncy
de
p
e
nde
nt
so
il p
r
o
p
e
rties. Th
e vo
ltag
e
respo
n
s
es
ob
tain
ed
b
y
th
e circu
it an
d
EM-Mo
M
were i
n
ex
cellen
t
ag
reemen
t in
t
e
rm
s of b
o
t
h
peak
val
u
es a
n
d
wa
ve
fo
rm
s as s
h
o
w
n i
n
Fi
gu
res
6 a
n
d
7.
The
di
ffe
re
nces
bet
w
ee
n
vol
t
a
g
e
peak
s o
b
t
a
i
n
e
d
by
t
h
e ci
rc
ui
t
m
odel
and EM
-M
oM
f
o
r t
h
e
fi
rst
an
d s
ubse
que
nt
ret
u
r
n
st
ro
ke c
u
r
r
ent
s
whe
n
ρ
0
=100
Ω
.m
were 0
.
5
%
and
0
.
5
%
, resp
ecti
v
ely. In
ad
d
itio
n, th
e d
i
fferen
ces b
e
t
w
een
v
o
ltag
e
p
e
ak
s o
b
t
ain
e
d
by
t
h
e ci
rcui
t
m
odel
and E
M
-M
oM
f
o
r t
h
e fi
rst
a
nd s
u
bse
que
nt
ret
u
r
n
st
r
oke c
u
r
r
e
n
t
s
w
h
en
ρ
0
=
1
00
0
Ω
.m
were
0.
9% an
d 1%
, res
p
ect
i
v
el
y
.
These
di
ffe
rences
pr
o
v
e
t
h
at
i
n
t
e
grat
i
ng t
h
e
fre
q
u
e
n
cy
de
pen
d
e
n
t
soi
l
p
r
op
erties in th
e ap
p
lication of eq
u
i
v
a
len
t
frequ
en
cy
in
circu
it m
o
d
e
l
is an
app
r
op
ri
ate
m
e
th
o
d
in circu
it
approach.
(a) Res
p
on
se t
o
first ret
u
r
n
st
ro
ke
(b
) Res
p
o
n
se
to s
u
b
s
eq
ue
nt r
e
tur
n
str
o
ke
Fi
gu
re 6.
V
o
l
t
a
ge resp
o
n
ses o
b
t
a
i
n
ed
by
t
h
e ci
rcui
t
an
d EM
-M
oM
fo
r
ρ
0
=1
00
Ω
.m
(a) Res
p
on
se t
o
first ret
u
r
n
st
ro
ke
(b
) Res
p
o
n
se
to s
u
b
s
eq
ue
nt r
e
tur
n
str
o
ke
Fi
gu
re 7.
V
o
l
t
a
ge resp
o
n
ses o
b
t
a
i
n
ed
by
t
h
e ci
rcui
t
an
d EM
-M
oM
fo
r
ρ
0
=1
000
Ω
.m
6.
CO
NCL
USI
O
N
The fre
que
ncy
depe
ndent s
o
il
m
odels have
been
revie
w
e
d
. T
h
e accurac
y
of the m
ode
ls has bee
n
i
nvest
i
g
at
e
d
b
y
com
p
ari
ng t
h
e re
sul
t
s
obt
ai
ned
by
t
h
e
m
odel
s
and e
xpe
ri
m
e
nt
al
val
u
es. T
h
e c
o
m
p
ari
s
on
am
ong t
h
e m
odels and e
xpe
rim
e
ntal values show t
h
at
Scott and Sm
ith-Longm
ire
m
odels are m
o
re accurat
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Int
e
grat
i
o
n
of
Freq
uency
De
pen
d
e
n
t
S
o
i
l
El
ect
rica
l Prop
erties in
G
r
ou
nd
i
n
g Electrod
e
…
(
Z
ul
kur
nai
n A.M.)
79
8
com
p
ared t
o
the Visacro-Alipio’s
m
odel
.
Th
e effect
o
f
t
h
e
fre
que
ncy
dep
e
nde
nt
s
o
i
l
el
ect
ri
cal
pr
ope
rt
i
e
s
o
n
gr
o
u
n
d
i
n
g el
ec
t
r
o
d
e i
m
pedan
ce has
bee
n
i
n
vest
i
g
at
ed
by
usi
n
g t
h
e
fre
q
u
ency
de
pe
nde
nt
s
o
i
l
m
odel
s
. It
i
s
fo
u
nd t
h
at
t
h
e i
m
pedance of t
h
e t
y
pi
cal
gro
u
ndi
ng el
ect
r
o
d
e
bu
ri
ed i
n
s
o
i
l
chan
ges as a f
unct
i
o
n o
f
f
r
eq
uency
.
The characteri
s
tic of the groundi
ng elect
rode is fo
und
d
e
pen
d
e
n
t
on
th
e so
il resistiv
ity. Th
e characteri
s
tics o
f
th
e g
r
ou
nd
ing
electro
d
e
in
low resistiv
ity an
d
h
i
gh
resistiv
ity so
ils are d
o
m
in
an
tly cap
acitiv
e an
d
indu
ctiv
e,
resp
ectiv
ely.
In
ad
d
ition
,
a
n
o
v
e
l m
e
th
o
d
is p
r
op
o
s
ed
t
o
im
p
r
o
v
e
th
e v
o
ltag
e
respon
se
o
f
t
h
e electrod
e
obt
ai
ne
d
by
t
h
e ci
rcui
t
m
ode
l
of t
h
e g
r
ou
n
d
i
n
g el
ect
ro
de.
The ap
pl
i
cat
i
on
of t
h
e m
e
tho
d
i
n
ci
rc
ui
t
m
odel
sho
w
s t
h
at
t
h
e vol
t
a
ge
res
p
ons
es o
b
t
a
i
n
e
d
by
t
h
e
pr
o
p
o
se
d m
e
t
hod and el
ect
r
o
m
a
gnet
i
c
m
odel
are i
n
excel
l
e
nt
agre
em
ent
i
n
t
e
r
m
s of pea
k
val
u
e and wa
ve
s
h
ape
.
The di
fferences
b
e
tween
th
e vo
ltag
e
p
eak
s
obt
ai
ne
d by
t
h
e pr
op
ose
d
m
e
t
h
o
d
an
d el
ect
rom
a
gnet
i
c
m
odel
are fo
u
nd l
e
ss t
h
an 1
%
. T
h
i
s
fi
n
d
i
n
g sh
o
w
s t
h
at
an overall improvem
ent of
gr
o
u
n
d
i
n
g el
ect
ro
de per
f
o
r
m
ance can be
achi
e
ved
by
appl
y
i
n
g
t
h
e p
r
o
p
o
se
d
m
e
thod i
n
to the circuit m
odels of the
grounding electro
des whe
n
ca
rrying out
t
r
ansi
e
n
t grounding
a
n
alyses.
ACKNOWLE
DGE
M
ENTS
Thi
s
w
o
r
k
wa
s sup
p
o
rt
e
d
i
n
part
by
t
h
e M
a
l
a
y
s
i
a
n M
i
ni
st
ry
of
Hi
g
h
e
r Ed
ucat
i
o
n and
Uni
v
ersi
t
i
Tekn
o
l
o
g
i
Mal
a
ysia, G
r
an
t
Nu
m
b
er
s 4F291an
d
10H
61
.
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il
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ode
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y
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o S. Frequency
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o S. Impulse Effici
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i M
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il El
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c
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l
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a
ram
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ils
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e
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u
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re
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S
SN
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2
088
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08
IJEC
E V
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l
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p
ri
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16
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79
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Stoll RL, Chen G, Pilling N. Com
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[24]
Bellas
c
hi PL, Armington RE, Snowden
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r
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h
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e
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l
e
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i
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3
.
BIOGRAP
HI
ES OF
AUTH
ORS
M. Mokhtari received
the B.Sc.
de
gree in
electrical
engineering
fr
om the Univ
ersity
of Applied
Science and
Technolog
y
,
Tehran
, Iran
,
in 2003
,
the M.E. degr
ee
in electr
i
cal
eng
i
neer
ing from
the Universiti Teknologi Malay
s
ia, Johor, Malaysia
, in 2013
, and
is currently
purs
u
ing the Ph.D.
degree in e
l
e
c
tr
ica
l
engine
ering
at the Ins
titut
e
of High Voltage and High Current (IVAT),
Universiti Tekn
ologi
M
a
l
a
y
s
ia
. His
research
int
e
re
st
includ
es th
e high vo
lt
age
e
ngineer
ing,
the
power s
y
stem
tr
ansient sim
u
lation, software
d
e
v
e
lopm
ent forhig
h-frequency
gro
unding s
y
stem
s,
and insulation
coordination
.
Z. Abdul-Malek
received
th
e B
.
E. degr
ee
in
electr
i
cal and
co
mputer
s
y
stems from Monash
University
, Melbourne, Australia, in 1989, th
e M.
Sc. degree in
electric
al and
electromagnetic
engineering with
industrial appli
cations from the University
of
Wa
les Cardiff,
Cardiff, U.K., i
n
1995 and th
e Ph.D. degree in
hig
h
voltag
e
engineer
ing from Card
iff University
, Cardiff, U.K
.,
in
1999.He was a
Lecturer with Universiti Tekno
logi
Malay
s
ia (U
TM) for 26
y
ear
s, where he is
currently
a Prof
essor of High Voltage
Engin
eerin
gw
ith the
F
acul
t
y
of
El
ectr
i
c
a
l
E
ngineer
ing. He
is curren
t
l
y
the
Director
of th
e I
n
stitute
of High
Voltage
and Hig
h
Current
(IVAT), UTM
.
He has
published two books, and has authored and co-a
uthor
ed more than 100 papers in varioust
echni
cal
journa
ls
and conf
ere
n
ce pro
ceed
ing
s
. H
i
s
res
ear
ch
inter
e
s
t
s
inc
l
u
d
ehigh-volt
a
ge
instrumentation, lightning prot
ection, detectio
n and warning
sy
ste
m
s,
pa
rtia
l disc
ha
rge
s
,
nanodielectrics
,
and cond
ition
m
onitoring
of pow
er equ
i
pm
ents.
Professor Abdul
-Malek is activ
el
y
invo
lved in
m
a
n
y
nation
a
l com
m
ittees. He is the Chairm
an,
Working Group on High-Voltag
e
and High-Curr
ent Te
st Techniques. He is
also a member of
IEC Certifi
c
a
tio
n Bod
y
M
a
nage
m
e
nt Comm
ittee
,
Techn
i
c
a
l Com
m
ittee on High Voltage P
o
wer
Transmission,
Working Group on High Vo
ltage
Switchgear
and Con
t
rolg
ears, Techn
i
cal
Working Group for Electr
i
calTesting,
and Depa
rtment of Standards IEC 17
025 Techn
i
cal
Asse
ssor
s
.
He
is
a
m
e
m
be
r of the
Powe
r a
nd Ene
r
gy
Soc
i
e
t
y
,
Die
l
e
c
t
ric
s
a
nd Ele
c
t
ric
a
l Insula
tion
S
o
ciet
y,
and
CI
G
R
E.
C. L
.
W
ooi r
e
c
e
i
v
ed th
e B.S
c
. d
e
gree
in e
l
e
c
tri
cal
and
ele
c
troni
c
e
ngineer
ing from
the Univ
ersiti
M
a
la
y
s
ia
S
a
bah
,
M
a
la
ysi
a
,
in 20
11, th
e M
.
E
.
deg
r
ee
in
ele
c
tri
c
a
l
engine
ering f
r
o
m
the Universi
ti
Teknologi Malay
s
ia, Johor, Malay
s
ia, in 2013
,
and
is
currently pursuing th
e P
h
.D. degree in
ele
c
tri
cal
engine
ering at th
e Institut
e
of
High Voltage and Hi
gh Curre
nt (IVAT), Universit
i
Teknologi Malay
s
ia. His research interest in
clud
es
the high voltage engineering
,
electromagnetic
field
and
ligh
t
ni
ng m
eas
urem
ent
.
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