Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 4
,
A
ugu
st
2016
, pp
. 14
41
~
1
455
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
4.1
063
7
1
441
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
Ass
e
ssm
ent of St
ep and T
o
uch Vol
t
ages
f
o
r Diff
eren
t Multilayer
Soil Models of Comp
lex Grounding Grid
Srete Nikolovski
,
Goran Knež
evi
ć
, Z
o
ran
Baus
Department o
f
P
o
wer Engin
eer
in
g, Facu
lty
of
Ele
c
tri
cal
Eng
i
neer
i
ng, Osijek
,
Cro
a
tia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Mar 26, 2016
Rev
i
sed
May 18
, 20
16
Accepte
d
J
u
n 3, 2016
In this p
a
per
the
influen
ce of
diff
eren
t soil models on step
and tou
c
h voltages
are pres
en
ted
.
S
o
il res
i
s
tiv
it
y is
t
h
e bas
i
c ch
ara
c
t
e
ris
t
i
c
of s
o
il which aff
ects
a
number of par
a
meters (temper
a
ture, hum
idity
,
s
a
lt content)
. Bas
i
c methods
of measuring soil resistivity
presented
in
this p
a
per
are:
W
e
nn
er m
e
thod
,
Schlumberger method, Gene
r
a
l
method, Driven
rod (3-probe) m
e
thod and
the
Dipole-Dipole
method. Soil res
i
stivity
measurements are used
to obtain
an
equiva
lent soil
m
odel (uniform m
ode
l, two-la
yer horizont
al m
odel, m
u
lti-
lay
e
r horizontal model, ve
rtical model and others
). The CDEGS software
packag
e is us
ed
for computing G
P
R (G
round Potential R
i
se), tou
c
h and
step
voltag
e
with sev
e
ral di
fferen
t
soi
l
m
odels. The r
e
sulting effe
ct of
soil m
odels
on the grounding resistance, GPR at the
surface, touch and step voltag
e
s are
shown. The 3D
spatial distribu
tion and
2D pres
enta
tion of
al
l c
h
arac
teris
t
i
c
values for
safety analy
s
is
ar
e pr
esented
and p
l
otted.
Keyword:
Co
m
p
u
t
er Simu
latio
n
Gro
und
Po
ten
tial Rise
Gr
ou
n
d
in
g Gri
d
Safety Lim
its
So
il Resistiv
ity Mo
dels
Step
Vo
ltag
e
To
uch
V
o
l
t
a
ge
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
:
Srete Nikolovs
ki,
Depa
rt
m
e
nt
of Po
wer En
gi
nee
r
i
n
g,
Faculty of Elec
trical Engin
eering, J
o
sip
Juraj Strossm
ay
er Un
i
v
ersity of
Osij
ek
,
K
.
Trp
i
mir
a
2B, 310
00
O
s
ij
ek
, C
r
o
a
tia.
Em
a
il: srete.n
i
k
o
l
o
v
sk
i@et
fos.hr
1.
INTRODUCTION
Th
e
p
r
im
ary task
o
f
th
is
p
a
p
e
r is to sh
ow
ho
w d
i
ffe
rent m
odels
of s
o
il affect the calc
u
l
a
tion
of the
gr
o
u
n
d
i
n
g.
G
r
ou
n
d
i
n
g sy
st
e
m
i
s
an i
m
port
a
nt
pa
rt
o
f
e
v
e
r
y
p
o
we
r sy
st
e
m
, whi
c
h i
s
re
qui
red t
o
e
n
s
u
r
e
pr
o
p
er
ope
ration of el
ectrical equipmen
t, en
sure th
e u
s
ers’ secu
rity o
f
th
ese
devi
ces, an
d t
o
t
a
ke away
sh
ort
ci
rcui
t
currents or
lightning
[1]. T
o
create a better
m
odel of the s
o
il, it is necess
a
ry to kno
w the characte
r
istics of
t
h
e soi
l
.
The
m
o
st
im
port
a
n
t
charact
eri
s
t
i
c
of t
h
e s
o
i
l
i
s
a speci
fi
c soi
l
resi
st
i
v
i
t
y
, whos
e am
ount
can be
obt
ai
ne
d by
o
n
e
of t
h
e t
ech
ni
que
s of m
easuri
n
g speci
fi
c re
si
st
ance [2]
,
[3]
.
The com
p
l
e
t
e
d m
odel
of t
h
e
soi
l
affects fu
rt
h
e
r
th
e typ
e
an
d
di
m
e
n
s
io
n
s
o
f
t
h
e groun
d
i
n
g
an
d
t
h
e d
e
p
t
h
to
wh
ich
it will b
e
b
u
ried
.
Use of
co
m
p
u
t
er so
ft
ware fo
r m
o
d
e
lin
g
and
calcu
latio
n of
g
r
ou
nd
ing
h
a
s greatly facilitate
d
an
d en
sured m
o
re
accurate m
odel
s
of s
o
il and ground cal
culation com
p
are
d
to
pre
v
iously us
ed em
pirical and graphical methods
o
f
so
il m
o
d
e
lin
g. CDEGS (
C
u
rrent
Di
st
ri
but
i
o
n,
El
ect
r
o
m
a
gnet
i
c
Fi
e
l
ds,
Gr
ou
n
d
i
n
g
an
d
S
o
i
l
St
r
u
ct
ure
Analysis
) i
s
so
ft
ware
packa
g
e
com
posed o
f
ei
ght
di
f
f
ere
n
t
m
odul
es t
h
at
offe
r a com
p
l
e
te gr
ou
n
d
i
n
g an
al
y
s
i
s
[4]
.
Whe
n
g
r
ou
n
d
i
ng a
n
o
b
j
ect
(p
ow
er pl
a
n
t
s
,
subst
a
t
i
o
ns, t
r
ansm
i
ssi
on l
i
n
es,
net
w
or
ks,
et
c.), t
h
e
assu
m
p
tio
n
is th
at th
e so
il is a g
ood
con
d
u
c
to
r and
th
at
the cu
rren
t will freely flo
w
t
h
rou
g
h
it.
However, th
is
m
a
y
not
be s
o
,
as t
h
e c
o
n
d
u
ct
ors
o
f
di
ffe
rent
m
a
t
e
ri
al
s
are characte
r
ized
by diffe
rent s
p
e
c
ific resistance
s and
th
e sam
e
h
a
ppen
s
w
ith
t
h
e
gr
oun
d. So
, like an
y con
d
u
c
t
o
r, the
s
o
il in
electrical ter
m
s is c
h
aracteri
zed
by
resistance whi
c
h provides the passage
of c
u
rrent. T
h
e res
i
stance of the
so
il can be de
fined as the res
i
stance
b
e
tween
th
e op
po
site sid
e
s of th
e cub
e
floor with
a le
n
g
t
h o
f
on
e m
e
ter
site. Th
e g
e
n
e
ral so
il resistiv
ity is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
14
41
–
1
455
1
442
very high
c
o
mpare
d
with
t
h
e specifi
c resistance of
classic metal
conduct
o
rs
. F
o
r
diffe
re
nt s
o
il ty
pes, s
p
ecific
resistiv
ity tak
e
s th
e
v
a
lu
e of sev
e
ral
oh
m
-
m
e
ters to
sev
e
ral t
h
ou
sand
o
h
m
-meters.
2.
MAI
N
CH
A
R
ACTE
R
ISTI
CS OF SOIL
Whe
n
g
r
ou
n
d
i
ng a
n
o
b
j
ect
(p
ow
er pl
a
n
t
s
,
subst
a
t
i
o
ns, t
r
ansm
i
ssi
on l
i
n
es,
net
w
or
ks,
et
c.), t
h
e
assu
m
p
tio
n
is th
at th
e so
il is a g
ood
con
d
u
c
to
r and
th
at
the cu
rren
t will freely flo
w
t
h
rou
g
h
it.
However, th
is
m
a
y
not
be s
o
,
as t
h
e c
o
n
d
u
ct
ors
o
f
di
ffe
rent
m
a
t
e
ri
al
s
are characte
r
ized
by diffe
rent s
p
e
c
ific resistance
s and
th
e sam
e
h
a
ppen
s
w
ith
t
h
e
gr
oun
d. So
, like an
y con
d
u
c
t
o
r, the
s
o
il in
electrical ter
m
s is c
h
aracteri
zed
by
resistance whi
c
h provides the passage
of c
u
rrent. T
h
e res
i
stance of the
so
il can be de
fined as the res
i
stance
b
e
tween
th
e op
po
site sid
e
s of th
e cub
e
floor with
a le
n
g
t
h o
f
on
e m
e
ter
site. Th
e g
e
n
e
ral so
il resistiv
ity is
very high
c
o
mpare
d
with
t
h
e specifi
c resistance of
classic metal
conduct
o
rs
. F
o
r
diffe
re
nt s
o
il ty
pes, s
p
ecific
resistiv
ity tak
e
s th
e
v
a
lu
e
o
f
sev
e
ral oh
m
-
meters
t
o
sev
e
ral
t
h
ousa
n
d
ohm
-m
et
ers. F
i
gu
re 1
s
h
o
w
s
h
o
w
speci
fi
c soi
l
r
e
si
st
i
v
i
t
y
changes de
pe
ndi
ng
on t
h
e
perc
e
n
t
a
ge c
h
an
ge i
n
t
h
e co
nt
e
n
t
of m
o
i
s
t
u
re, s
a
l
t
and
di
ffe
re
nt
t
e
m
p
erat
ure
s
[
2
]
.
1
2
34
5
67
8
9
10
%
%
0
51
0
15
20
25
30
35
40
45
‐
25
‐
20
‐
15
‐
10
‐
50
+
5
+1
0
+
1
5
+2
0
°C
sa
l
t
hu
m
i
d
i
t
y
te
m
p
e
r
at
u
r
e
50
10
0
500
1
000
5
000
ρ
[
Ω
m]
te
m
p
e
r
a
t
u
r
e
hu
m
i
dit
y
sa
l
t
Fi
gu
re
1.
De
pe
nde
nce
o
f
s
o
i
l
resi
st
i
v
i
t
y
ρ
o
n
th
e
p
e
rcen
tag
e
of m
o
istu
re, salt an
d
tem
p
eratu
r
e
[2
]
Al
so t
h
e f
r
e
q
u
e
ncy
can ha
ve t
h
e i
n
fl
ue
nce o
n
soi
l
pr
o
p
ert
i
e
s and t
h
e g
r
ou
ndi
ng i
m
pedan
ce whi
c
h i
s
p
r
esen
ted in
[5].
3.
TECHNI
Q
UE
S OF
ME
AS
URING S
P
ECI
F
IC
SOIL
RE
SISTIVITY
Measu
r
em
en
t o
f
sp
ecif
i
c so
il r
e
sistiv
ity is p
e
r
f
o
r
m
e
d
in
such
a
w
a
y th
at th
e cur
r
en
t is let g
o
t
h
ro
ugh
tw
o
o
u
t
er
pr
obes, cur
r
e
n
t
pr
ob
es,
w
h
ile on
t
h
e two
pr
ob
es
whic
h are in t
h
e sam
e
direction locate
d
bet
w
een
t
h
em
,
t
h
e vol
t
a
ge (
pot
e
n
t
i
a
l
)
p
r
o
b
es, t
h
e am
ount
o
f
v
o
l
t
a
ge i
s
m
easured [
6
]
.
B
a
sed o
n
t
h
e
rel
eased c
u
r
r
en
t
and
m
easured
vol
t
a
ge,
usi
n
g
O
h
m
'
s l
a
w,
t
h
e
resi
s
t
ance
val
u
e
i
s
cal
cul
a
t
e
d, a
n
d
,
d
e
pe
n
d
i
n
g
on
t
h
e
ge
om
et
ry
of
t
h
e
m
e
t
hod
use
d
t
o
m
easure, t
h
e
val
u
e
of t
h
e a
ppa
re
nt
speci
fi
c soi
l
resi
st
i
v
i
t
y
i
n
Ohm
– m
e
t
e
rs i
s
cal
cul
a
t
e
d. I
n
Fi
gu
re
2 –
Fi
gu
re
6 di
ffe
re
nt
m
e
t
hods
of
soi
l
resi
st
anc
e
m
easurem
ent
are sh
o
w
n
.
Wen
n
e
r
'
s
m
e
tho
d
of
m
easuri
n
g s
p
e
c
i
f
i
c
gr
o
u
n
d
re
si
st
ance i
s
p
r
es
ent
e
d i
n
Fi
g
u
r
e 2.
Schl
um
berger'
s
m
e
t
hod o
f
m
easuri
n
g
sp
eci
fi
c
g
r
ou
nd
r
e
sistance is pr
esen
ted
in
Figur
e
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Assessmen
t o
f
S
t
ep
an
d
To
u
c
h
Vo
ltag
e
s
for Differen
t
Mu
lti
la
yer
S
o
il Mo
dels o
f
.... (S
ret
e
Niko
lo
vski)
1
443
a
a
a
b
V
I
P
1
P
2
S
1
S
2
b
V
I
P
1
P
2
S
1
S
2
c
d
c
Fi
gu
re
2.
W
e
n
n
er
’s m
e
t
hod
o
f
m
easuri
n
g s
p
eci
fi
c
Fi
gu
re
3.
Sc
hl
u
m
berger’s
m
e
tho
d
o
f
m
easuri
n
g
resistance
s
p
ecific
resi
stance
Gene
ral m
e
thod
of m
easuring specific
ground
resist
ance
is prese
n
ted
in Figure 4
a
n
d Dipol-Dipol
m
e
t
hod
o
f
m
e
asuri
n
g
sp
eci
fi
c
gr
o
u
n
d
resi
st
an
ce i
s
p
r
ese
n
t
e
d
i
n
Fi
g
u
r
e
5.
b
V
I
P
1
P
2
S
1
S
2
e
f
g
V
b
V
I
P
1
P
2
S
1
S
2
a
na
a
V
Fi
g
u
re
4
.
Ge
neral
m
e
t
hod
o
f
m
easuri
n
g s
p
eci
fi
c
Fi
g
u
r
e
5.
Di
pol
-Di
pol
m
e
t
hod
o
f
m
easuri
n
g s
p
eci
fi
c
resistance
resistance
3-P
r
obe m
e
t
hod
of m
easuri
ng s
p
eci
fi
c
gr
ou
n
d
resi
st
a
n
c
e
i
s
prese
n
t
e
d
i
n
Fi
g
u
re
6.
The m
a
i
n
di
ffe
re
nce f
r
o
m
previ
o
usl
y
el
abo
r
at
ed m
e
t
hods
i
s
t
h
at
i
n
t
h
i
s
m
e
t
hod i
n
s
t
ead o
f
4
pr
o
b
e
s o
n
l
y
3
p
r
o
b
e
s are
use
d
f
o
r det
e
r
m
i
n
i
ng
t
h
e
gr
o
u
n
d
resi
st
ance
.
b
I
P
2
S
1
‐
P
1
S
2
V
b
2
0,
6
2
D
D
d
Fi
gu
re
6.
3
Pr
o
b
e m
e
t
hod
o
f
m
easuri
n
g s
p
e
c
i
f
i
c
gr
o
u
n
d
re
si
st
ance
4.
SOIL MO
DE
LS
Int
e
r
p
ret
a
t
i
on
and
de
vel
o
pm
ent
of a
d
e
quat
e
m
odel
of
t
h
e
soi
l
based
o
n
t
h
e m
easured
val
u
es
of t
h
e
appa
re
nt
speci
fi
c soi
l
resi
st
i
v
i
t
y
i
s
one o
f
t
h
e
m
o
st
chal
l
e
ngi
n
g
pa
rt
s aft
e
r pe
rf
orm
i
ng m
easurem
ent
s
. I
n
p
r
actice, th
e soil is u
s
u
a
lly
mo
d
e
led
as a si
ng
le layer (u
n
i
f
o
rm
), o
r
as a t
w
o
-
lay
e
r an
d
h
o
riz
ontal in
relation t
o
the surface of the soil. In
m
o
re co
m
p
lex configurations, it is necessary
to use horizontal
m
u
lti-l
a
yer soil
m
o
d
e
l [
6
],[
7
].
Th
er
e m
a
y b
e
sp
ecial co
nf
igu
r
ation
s
o
f
th
e so
il, f
o
r
ex
am
p
l
e, w
h
en
ther
e is an
expon
en
tial
ch
ang
e
i
n
sp
ecific so
il resisti
v
ity, v
e
rtical stratificatio
n
,
an
d r
e
g
u
l
a
r
o
r
i
r
r
e
gul
a
r
vol
um
es o
f
s
o
i
l
wi
t
h
d
i
ffere
nt
specific re
sistance of the
surrounding s
o
i
l
.
Ho
we
ver
,
suc
h
con
f
i
g
urat
i
ons
ar
e ve
ry ra
re in practice and
usually
i
n
st
al
l
a
t
i
on o
f
gr
o
u
n
d
i
n
g i
n
s
u
ch
s
o
i
l
t
e
nds
t
o
be a
voi
ded
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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08
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J
ECE
Vo
l. 6
,
N
o
. 4
,
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st 2
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:
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41
–
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455
1
444
4.
1.
Sing
le lay
e
r-unufo
rm so
il mo
dell
Sin
g
l
e-
layer
soil
m
o
d
e
l (
F
i
g
ure 7)
ap
pr
ox
im
a
t
es th
e
g
r
o
und
as ho
m
o
g
e
n
e
ou
s, t
h
at is,
of
co
n
s
tan
t
resistance.
Fi
gu
re
7.
Si
n
g
l
e
-l
ay
er s
o
i
l
m
o
del
Su
ch
m
o
d
e
l o
f
so
il is j
u
stified
to
b
e
u
s
ed
wh
en
it is estab
lish
e
d
b
y
m
eas
u
r
em
en
ts th
at t
h
e app
a
ren
t
resistan
ce of th
e so
il do
es no
t v
a
ry sign
ifi
can
tly with
i
n
creasi
n
g de
pt
h
of m
easuri
n
g
,
or i
f
i
t
i
s
not
abo
u
t
a
m
i
nor
gr
o
u
n
d
i
ng
sy
st
em
, so t
h
at
cert
a
i
n
om
issi
ons
an
d a
p
p
r
o
x
i
m
ati
ons ar
e al
l
o
we
d.
An
app
r
oxi
m
a
t
e
d si
ngl
e
m
odel
of s
o
i
l
,
or
i
t
s
resi
st
a
n
ce, ca
n
be
o
b
t
a
i
n
ed
by
t
a
k
i
ng t
h
e m
ean of al
l
t
h
e
m
e
asure
d
a
p
pare
nt
soi
l
resistances, as
shown in (1).
n
n
a
a
a
a
)
(
)
3
(
)
2
(
)
1
(
...
(1)
whe
r
e
t
h
e nu
m
e
rator rep
r
e
s
ents
th
e su
m of
th
e a
p
p
a
re
n
t
r
e
s
i
s
t
an
c
e
s on
differe
n
t
distances
a
n
d the
den
o
m
i
nat
o
r re
prese
n
t
s
t
h
e t
o
t
a
l
num
ber of m
easurem
ent
s
. An
ot
her m
e
t
hod f
o
r det
e
rm
ini
n
g t
h
e resi
st
ance o
f
a single-layer s
o
il is accordi
n
g to (2).
2
min
max
(2
)
whe
r
e
ρ
m
ax
is
the m
a
xim
u
m
a
ppa
re
nt resistance m
easured
(
Ω
m
)
, and
ρ
mi
n
t
h
e
m
i
nim
u
m
appare
nt
res
i
st
ance
measured (
Ω
m)
.
4.
2.
Two
-
lay
er model of ho
rizo
nta
l
so
il
Tw
o-l
a
y
e
r s
o
i
l
m
odel
consi
s
t
s
o
f
t
h
e
u
ppe
r
l
a
y
e
r of
t
h
e
fi
nal
de
pt
h
h
a
n
d the
speci
fic
ρ
1
resistance
an
d th
e l
o
wer l
a
yer of infin
ite
de
pt
h a
n
d s
p
e
c
i
f
i
c
resi
st
ance
ρ
2
,
[8
],
[9
]
Figu
r
e
8.
Fi
gu
re
8.
Tw
o
-
l
a
y
e
r h
o
ri
zo
nt
a
l
m
odel
Th
e d
i
fficu
lty i
n
u
s
ing
th
is mo
d
e
l is a
m
a
th
e
m
atical
d
e
ter
m
in
atio
n
of th
e d
e
p
t
h
o
f
th
e fi
rst layer d
u
e
to
v
a
riation
s
in
th
e stru
ctu
r
e an
d
p
r
o
p
e
rties o
f
th
e so
il. Meth
od
s u
s
ed
to
d
e
term
in
e t
h
e p
a
ram
e
ters
o
f
two-
layer h
o
rizon
t
al so
il (
ρ
1
,
ρ
2
,
h
) on the ba
sis of m
easuring
specific soil
resistiv
ity can
b
e
classified
in
to
t
w
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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S
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7
0
8
Assessmen
t o
f
S
t
ep
an
d
To
u
c
h
Vo
ltag
e
s
for Differen
t
Mu
lti
la
yer
S
o
il Mo
dels o
f
.... (S
ret
e
Niko
lo
vski)
1
445
gr
o
ups:
em
pi
r
i
cal
and a
n
al
y
t
i
cal
. Det
e
rm
i
n
at
i
on
o
f
t
h
e p
a
ram
e
ters of th
e
ho
rizo
n
t
al two
-
layer so
il is
analytically
ma
de
by applying m
a
the
m
atical
f
o
r
m
u
l
as an
d fu
n
c
tion
s
(3
),
(4)
an
d (5
).
1
2
2
1
2
4
1
2
1
1
4
1
n
n
a
a
h
n
a
h
n
K
(3)
1
2
1
2
K
(
4
)
N
i
mi
mi
i
h
f
1
2
2
2
1
))
(
(
)
,
,
(
(
5
)
whe
r
e
K
is the
reflection coefficient,
ρ
mi
m
e
asure
d
val
u
e of specific soil resistivity and
ρ
(i)
an
esti
m
a
ted
v
a
lue
of speci
fic resi
stance
of t
h
e s
o
il.
An
ot
he
r w
a
y
o
f
pa
ram
e
t
e
r det
e
rm
i
n
at
i
on i
s
by
usi
ng
Su
n
d
e'
s gra
p
hi
cal
m
e
tho
d
(
F
i
g
ure
9)
,
whi
c
h can
roug
h
l
y esti
m
a
te th
e p
a
ram
e
t
e
rs of th
e t
w
o-layer h
o
rizo
n
t
al so
il with
ou
t th
e use of co
m
p
u
t
er or so
ph
isticated
equat
i
o
ns
.
Fi
gu
re 9.
S
u
n
d
e
’s
c
u
r
v
es f
o
r det
e
rm
i
n
i
ng pa
ram
e
ters of tw
o-lay
e
r
h
o
riz
o
n
t
al soil [1
0]
4.
3.
Three-layer m
o
del
of horiz
o
ntal
soil
Horizon
t
al th
ree-layer g
r
ou
nd
m
o
d
e
l is
sh
own
in
Fig
u
re 10
. In
th
is case, the so
il co
n
s
ists o
f
3
layers,
wh
ere each
lay
e
r is ch
aracteri
zed
b
y
th
e acco
m
p
a
n
y
in
g
sp
ecific resistan
ce and
th
ick
n
e
ss
o
f
t
h
e layer
un
til th
e
last 3
th
, wh
ich
is o
f
an
in
fin
i
t
e
th
ick
n
e
ss. [4], Determin
in
g p
a
ram
e
ters o
f
m
u
l
ti-layer
m
o
d
e
ls requ
ires th
e u
s
e
of c
o
m
put
er pr
og
ram
s
and ad
vance
d
m
a
t
h
em
at
i
cal func
t
i
o
ns (c
om
pl
ex fi
gu
re m
e
t
hods,
adva
nce
d
i
n
t
e
g
r
at
ed
Taylor’s
and Sim
p
son’s formulas) beca
use
t
h
e
calculatio
n
in
relation
to th
e si
n
g
l
e
o
r
two layer so
il m
o
d
e
l
becom
e
s signi
ficantly com
p
licated. Th
e
other two m
o
st comm
on
m
odels of s
o
il that occur i
n
real
ity are
v
e
rtical (Figu
r
e 1
1
)
two-layer o
r
m
u
lti-la
yer so
il
m
o
d
e
l an
d
th
e so
il
m
o
d
e
l in
which
th
e sp
ecifi
c so
il
resistiv
ity ch
ang
e
s exp
o
n
e
n
tially with
d
e
p
t
h.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
14
41
–
1
455
1
446
Fi
gu
re
1
0
. T
h
r
ee-l
a
y
e
r s
o
i
l
m
odel
Fi
gu
re
1
1
. T
w
o-l
a
y
e
r
ve
rt
i
cal
soi
l
m
odel
After d
e
term
in
ing
th
e app
a
ren
t
sp
ecific
resis
tiv
ity o
f
each
v
e
rtically o
r
ien
t
ed
layer,
ρ
1
,
ρ
2
, the
equi
val
e
nt
s
p
e
c
i
f
i
c
resi
st
ance
,
ρ
e
,
of the
adja
cent ve
rtical tiers
ca
n be dete
rm
ined
(6
) [9]
.
1
2
2
1
2
1
S
S
S
e
(
6
)
So
il with an ex
pon
en
tial ch
an
g
e
in
sp
eci
fic so
il resistiv
ity with
d
e
p
t
h is
d
e
term
in
ed
b
y
th
e sp
ecific
resistance
on the s
u
rface,
ρ
1
,
specific resistance of
t
h
e de
epest
pa
rt,
ρ
2
,
and the c
o
effi
cient
λ
. T
h
e a
ppa
re
nt
sp
ecific resistiv
ity,
ρ
a
, for s
u
c
h
s
o
il and
We
nner'
s
way
of meas
urem
ent is
calculated acc
ordi
ng to
(7).
)
2
(
)
(
1
2
2
a
a
a
e
e
(
7
)
5.
SIM
U
LATI
O
N
O
F
THE I
N
FLUE
NCE
OF
DIFFE
R
E
NT SO
IL
MO
DELS O
N
G
R
O
U
NDI
NG
SYSTE
M
PE
RFO
R
MANCE
Soft
ware
pac
k
age CDE
G
S i
s
a collection
of i
n
tegr
ated e
ngi
neeri
ng s
o
ftwa
re tools for accurately
anal
y
z
i
ng
pr
ob
l
e
m
s
i
nvol
vi
n
g
gr
ou
n
d
i
n
g, el
ect
rom
a
gnet
i
c
fi
el
ds, el
ect
ro
m
a
gnet
i
c
i
n
t
e
rfere
nces, a
nd
vari
o
u
s
aspect
s o
f
cat
h
odi
c
pr
ot
ect
i
o
n
.
C
D
E
G
S s
o
ft
ware
pac
k
age
no
wa
day
s
co
n
s
i
s
t
s
of ei
g
h
t
e
ngi
neeri
ng m
odul
e
s
,
an
d in
t
h
is stud
y th
e
fo
llowi
n
g
two
are u
s
ed
: RESAP
an
d MALT. RESAP m
o
du
le is
u
s
ed
to
d
e
term
in
e th
e
equi
val
e
nt
m
odel
o
f
t
h
e s
o
i
l
base
d o
n
t
h
e s
e
l
ect
i
on o
f
t
h
e
m
easuri
n
g m
e
tho
d
a
n
d t
h
e m
easuri
n
g
val
u
e
s
of
t
h
e
appa
re
nt resist
ivity
(or
resist
ance)
o
f
the s
o
il. M
A
LT
mo
du
le is
u
s
ed
for th
e an
alysis o
f
low frequ
e
n
c
y
g
r
ou
nd
ing
[
4
].
M
odel
i
n
g
of
t
h
e soi
l
was
per
f
o
rm
ed i
n
R
E
S
A
P m
o
d
u
l
e
. M
easurem
ent
s
d
one
by
We
n
n
er
’s
fo
ur
pr
o
b
e
m
e
t
hod
are ent
e
re
d i
n
R
E
SAP m
odul
e. In t
h
e sel
ect
i
on o
f
soi
l
t
y
pes t
h
at
i
s
t
o
be
m
odel
e
d o
n
t
h
e basi
s
of t
h
e m
easurements is selected.
In t
h
e first
case, the s
o
il is
m
odeled as a
single-layer, in the second cas
e, the
so
il is
m
o
d
e
led
as h
o
rizon
t
al two
-
layer and in
th
ird
case
as horizontal three-layer.
Res
u
lts for all three cases
are pre
s
ent
e
d i
n
Fi
g
u
re
12
, Fi
gu
re 1
3
an
d Fi
gu
re 1
4
. F
o
r m
easurem
ent
of
soi
l
resi
st
i
v
i
t
y
were
used
dat
a
from
[1
1]
.
Tabl
e
1. M
eas
urem
ent
s
o
f
s
o
i
l
resi
st
i
v
i
t
y
us
i
ng
We
nne
r’
s
m
e
t
hod
[
11]
Ti
m
e
Sp
acin
g
(a) [
m
]
Measured resistivity
ρ
[
Ω
m)
1 1
125.
03
54
2 1.
5
108.
66
77
3 2
85.
325
7
4 2.
5
69.
429
2
5 3
55.
417
7
6 4
37.
447
8
7 5
30.
787
6
8 6
26.
012
4
9 7
22.
870
8
10
8
16.
085
0
11
9
17.
530
1
12
10
16.
336
4
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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I
S
SN
:
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8-8
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0
8
Assessmen
t o
f
S
t
ep
an
d
To
u
c
h
Vo
ltag
e
s
for Differen
t
Mu
lti
la
yer
S
o
il Mo
dels o
f
.... (S
ret
e
Niko
lo
vski)
1
447
0
20
40
60
80
100
120
140
0123
4
5
6789
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
A
p
p
a
r
e
n
t
R
e
s
i
st
i
v
i
t
y (
O
h
m
-
m
e
t
er
s)
I
n
t
e
r
-
E
l
ec
t
r
o
d
e S
p
ac
i
n
g
(
m
e
t
er
s
)
Fig
u
re 12
. Simu
latio
n
resu
lts o
f
sing
le-layer so
il
m
o
d
e
l
In t
h
i
s
case acc
or
di
n
g
m
easurem
ent
s
usi
n
g Wen
n
e
r’s m
e
t
hod
, t
h
e s
o
i
l
i
s
m
odel
e
d as a si
ngl
e l
a
y
e
re
d
,
with
th
e
u
n
i
form
so
il resisti
v
ity o
f
ρ
=3
9.
4
25
Ω
m,
wh
ich is
obt
ai
ne
d
u
s
i
ng R
E
AS
P
m
odul
e. De
vi
a
t
i
on o
f
theoretical apparent resistanc
e
from
the
measure
d
ap
pa
r
e
nt
resi
st
ances
i
s
expresse
d by
R
M
S-err
o
r
(ro
ot
-
mean-squa
r
ed
error), RMS error
betwee
n m
easure
d
a
n
d ca
lc
ulated re
sistance in this ca
se
is 36.48 %, which is
a sign
ifican
t error.
Th
is m
o
d
e
l is th
e easiest t
o
u
s
e
bu
t no
t ap
pro
p
r
i
ate b
e
cau
s
e
of s
u
ch h
uge
er
ro
r.
10
30
50
70
90
110
130
01
23
4
5
678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
A
p
p
a
r
e
n
t
R
e
si
s
t
i
v
i
t
y
(
O
h
m
-
m
et
er
s
)
I
n
te
r
-
E
l
e
c
tr
o
d
e
S
p
a
c
i
n
g
(m
e
t
e
r
s
)
Fi
gu
re 1
3
. Si
m
u
l
a
t
i
on res
u
l
t
s
of
t
w
o-l
a
y
e
re
d ho
ri
zo
nt
al
soi
l
m
odel
from
m
easure
d
res
u
l
t
s
Tab
l
e
2
.
Sp
eci
fic resistan
ce and
th
ick
n
e
ss in two-layer so
il
m
o
d
e
l
Nu
m
b
e
r
of
the
layers
Specif
i
c soil resist
ance
ρ
[
Ω
m]
T
h
ickness of the
la
y
e
r [
m
])
1 126.
00
62
1.
8164
45
2 15.
484
84
∞
In t
h
is case a
ccording m
easurem
ents using
Wenn
er’s meth
od
, t
h
e so
il
is
m
o
d
e
led
with
RESAP
m
odul
e as t
w
o
l
a
y
e
red m
odel
.
R
M
S err
o
r w
h
en t
h
e s
o
i
l
i
s
m
odel
e
d as a t
w
o
-
l
a
y
e
r i
s
7
.
4
4
%. B
eca
use
o
f
t
h
e
RMS erro
r
v
a
lu
e, it is o
b
v
i
ou
s th
at two
-
layered
m
o
d
e
l co
rresp
ond
s m
o
re to
th
e m
o
del o
f
th
e
real so
il on
whic
h m
easure
m
ents are pe
rform
e
d than t
o
the previ
ous
case o
f
a sing
le-layer so
il m
o
d
e
l.
Wh
en
th
e
th
ree-
layer
m
o
d
e
l is u
s
ed
, RMS-erro
r is 6.09
%. RMS erro
r is
smaller th
an
in
two-layer so
il m
o
d
e
l. Th
ree-layered
m
odel
corre
sp
on
ds
best
t
o
t
h
e m
odel
of
t
h
e
real
soi
l
on
w
h
i
c
h m
easurem
ent
s
are
pe
rf
o
r
m
e
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
14
41
–
1
455
1
448
0
20
40
60
80
10
0
12
0
14
0
16
0
01
2345
6789
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
A
ppa
re
nt
R
e
s
i
s
t
i
v
i
t
y
(
O
hm
-
m
e
t
e
r
s
)
I
n
t
e
r
-
E
l
ec
t
r
o
d
e S
p
ac
i
n
g
(
m
e
t
er
s
)
Fi
gu
re 1
4
. Si
m
u
l
a
t
i
on res
u
l
t
s
of
t
h
ree
-
l
a
y
e
re
d ho
ri
zo
nt
al
so
i
l
m
odel
fr
om
m
easured
res
u
l
t
s
Tab
l
e
3
.
Sp
eci
fic resistan
ce and
th
ick
n
e
ss in th
ree-layer so
il
m
o
d
e
l
Nu
m
b
e
r
of
the
layers
Specif
i
c soil
resistance
ρ
[
Ω
m]
T
h
ickness of the
la
y
e
r [
m
])
1 150.
84
57
0.
9904
62
2 64.
097
31
1.
6947
74
3 14.
055
51
∞
6.
SIMULATI
O
N
RESULTS
FOR SAMPL
E
CASE
Grounding grid is placed at
a dept
h of 0.8
m
.
It is
meshed gri
d
m
a
de
up
of 12 trans
v
erse a
n
d
9
longitudi
nal grounding stri
ps, whic
h
are
connected t
o
each
othe
r and
form
a network
of
ove
rall 110 ×
80 m
.
[1
2]
The l
e
n
g
t
h
o
f
t
h
e Fe/
Z
n
con
duct
o
r
s
3
0
×
5 m
m
are 19
50 m
.
Ad
di
t
i
onal
l
y
, on t
h
e c
o
n
n
ect
i
n
g g
r
o
u
ndi
ng
gri
d
25 properly distributed
grounding rods are placed in length
of
3 m. The diam
eter of rods is 50.8 mm.
Th
e cu
rren
t th
at is in
j
ected
in
t
o
th
e gro
und
ing
system
is Ik
= 74
80
A.
The g
r
o
u
ndi
n
g
gri
d
f
r
o
m
Fi
g
u
re
15 i
s
b
u
ri
ed i
n
t
h
e de
pt
h o
f
0.
8 m
i
n
a si
ngl
e-l
a
y
e
r
soi
l
m
odel
o
b
t
ain
e
d
b
y
si
m
u
la
tin
g
in
Fig
u
r
e
1
2
. Runnin
g
t
h
e sim
u
la
tio
n
p
r
o
v
i
d
e
s t
h
e fo
llow
i
ng
rep
o
r
t
. Resistance of
sin
g
l
e-layered
so
il is 39
.42
5
Ω
m
.
Resistan
ce of
th
e gr
ound
ing
g
r
i
d
is Ri
=
0.
18
6
7
Ω
.
Th
e
po
ten
tial o
f
t
h
e
g
r
ou
nd
ing
g
r
i
d
is G
P
R= 139
6.8
V
.
Fi
gu
re
1
5
. M
o
del
o
f
t
h
e
gr
ou
nd
sy
st
em
used
i
n
si
m
u
l
a
t
i
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Assessmen
t o
f
S
t
ep
an
d
To
u
c
h
Vo
ltag
e
s
for Differen
t
Mu
lti
la
yer
S
o
il Mo
dels o
f
.... (S
ret
e
Niko
lo
vski)
1
449
Fig
u
r
e
16
.
3
-
D pr
of
ile of
G
P
R f
o
r
a gr
id
i
n
a sing
le-
l
ayer
so
il m
o
d
e
l
According to the selected standa
rds 70KG-IEEE, the body
weight
of 70 kg a
nd fi
brillation curre
nt
according C
3
-IEC,
body res
i
stance acco
rding
IEC that i
s
located
on t
h
e s
u
rface ca
n be e
x
pose
d
t
o
the
m
a
xim
u
m
t
ouch v
o
l
t
a
ge
of
2
9
2
.
2
V a
nd st
e
p
s v
o
l
t
a
ge
of
3
5
8
.
2
V fo
r t
h
e fau
lt clearing
ti
m
e
o
f
0
.
5
s. In
th
is
case there
is
no additional s
u
rface layer on t
h
e soil.
From
Fi
gu
re 1
7
an
d Fi
gu
re 1
8
i
n
s
p
i
t
e
of
r
e
l
a
t
i
v
el
y
hi
gh
GPR
,
t
o
uc
h an
d st
ep
vol
t
a
ge
s are i
n
t
h
e
p
e
rm
issib
l
e secu
rity li
m
its. By p
l
acing
th
e
groun
d
i
n
g
grid
to
a d
e
p
t
h of
0
.
8
m
in
th
e two-layer m
o
d
e
l of so
il,
o
b
t
ain
e
d
b
y
sim
u
la
tio
n
in
Fig
u
re 13
, th
e resu
lt will b
e
a n
e
twork
co
m
p
osed
of co
nn
ecti
n
g
g
r
o
und
strips in
th
e
first layer of
greater resistanc
e
, while rods reach the
sec
o
nd layer of lowe
r resist
ance
. Running the simulation
p
r
ov
id
es
t
h
e f
o
llo
w
i
ng
r
e
po
r
t
.
Fi
g
u
r
e
17
.
To
uch
v
o
l
t
a
ge
fo
r si
ngl
e-l
a
y
e
r
m
odel
Fi
g
u
re
1
8
.
St
e
p
vol
t
a
ge
f
o
r
si
ngl
e
-
l
a
y
e
r m
o
d
e
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
14
41
–
1
455
1
450
Fig
u
r
e
19
.
3
-
D pr
of
ile of
G
P
R f
o
r
a gr
id
i
n
tw
o-
layer
so
il m
o
d
e
l
Th
e
resistan
ce of th
e first layer is
1
5
0
.
84
57
Ω
m
.
Resistan
ce
o
f
th
e seco
nd
layer is
64
.0
973
Ω
m.
Resistan
ce of
t
h
e th
i
r
d layer
i
s
14
.05
5
Ω
m
Th
ickn
ess of
t
h
e
f
i
r
s
t layer
is 0
.
99
046
m
,
thick
n
e
ss of
t
h
e
secon
d
layer
is 1.694
77
4
m
.
Resistan
ce th
e
g
r
ou
nd
i
n
g gr
id is Ri= 0
.
11
294
Ω
. Th
e
p
o
t
en
tial o
f
th
e
g
r
ou
nd
ing gr
i
d
GPR
=
84
4.
7
6
V.
In th
e t
w
o-l
a
yer m
o
d
e
l o
f
th
e so
il, tou
c
h
v
o
ltag
e
and
step
v
o
ltag
e
are
slig
h
tly h
i
gh
er, bu
t
still
in perm
iss
i
ble lim
its since the am
ount
of the m
a
xim
u
m
touch voltage is 340.5
V
and st
e
p
v
o
l
t
a
ge i
s
55
1.
5
V a
n
d
a
r
e
obt
ai
ne
d
fr
o
m
securi
t
y
t
h
reshol
d c
o
m
put
at
i
on
f
o
r
fa
ul
t
cl
eari
n
g t
i
m
e of
0.
5 s.
Figu
r
e
20
.
Tou
c
h vo
ltag
e
f
o
r
two-
layer
m
o
d
e
l
Fi
gure
21.
Step
voltage f
o
r tw
o-layer
m
odel
At
t
h
e e
n
d, t
h
e
gr
o
u
ndi
ng
g
r
i
d
f
r
o
m
Fi
gure
15
i
s
bu
ri
ed i
n
t
h
e
dept
h
of
0
.
8 m
i
n
a t
h
ree
-
l
a
y
e
r s
o
i
l
m
odel
obt
ai
ne
d
by
si
m
u
l
a
ting
i
n
R
E
S
A
P
m
odul
e. T
h
e
resi
st
ance
o
f
t
h
e fi
rst
l
a
y
e
r i
s
1
2
6
.
0
0
6
2
Ω
m.
Resistan
ce o
f
t
h
e seco
nd
layer
is 64
.0
973
Ω
m
.
Res
i
stan
ce o
f
t
h
e th
ird
layer is 15
.4
848
Ω
m
.
Th
ickn
ess o
f
th
e
first layer is 0
.
9
904
6
m
. Th
ick
n
e
ss o
f
th
e seco
nd
layer is 1
.
69
477
m
.
Res
i
stan
ce o
f
th
e g
r
ou
nd
ing
grid is R
i
=
0
.
1
118
4
Ω
. The po
ten
tial of t
h
e
g
r
ou
nd
ing
grid
is
GPR= 836
.5
5
V.
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