Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 2, No. 1,
April 201
6, pp. 11 ~ 22
DOI: 10.115
9
1
/ijeecs.v2.i1.pp11
-22
11
Re
cei
v
ed
Jan
uary 21, 201
6
;
Revi
sed Ma
rch 1, 2
016;
Acce
pted Ma
rch 1
3
, 2016
The Influence of Moisture and Temperature on the
Behavior of Soil Resistivity in Earthing Design Using
Finite Element Method
Sajad Samadinasab*, Fa
rhad Namda
r
i, Mohammad Bak
h
ship
our
Dep
a
rtment of Electrical E
ngi
neer
ing, L
o
rest
an Un
iversit
y
,
Dan
e
shg
ah Str
eet, 712
34-9
8
6
53, Khorram
a
b
ad, Loresta
n, Iran
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: sajad.sam
adi
nasa
b
@gm
a
il.
com
A
b
st
r
a
ct
Protection
of e
qui
p
m
ent, safe
ty of perso
ns a
nd co
nt
in
uity of
pow
er su
pply
are the
mai
n
o
b
jectiv
e
s
of the
grounding system
. For
its accur
a
te
design, it is
ess
ential to
deter
m
i
ne
the potentia
l distribution on
the earth surfa
c
e and th
e eq
u
i
vale
nt resistan
ce of
the system. The know
le
dge of suc
h
pa
rameters al
low
s
checking the s
e
curity offered
by t
he gr
ounding system
when there
is a fa
ilure in the
power
system
s. A
new
m
e
thod
to design an earthing
system
s
us
ing Finite Elem
ent Method (FE
M) is pr
esented in this
article.In
this ap
pro
a
ch,
the infl
ue
nce
of the
moist
u
re a
nd
te
mp
erature
on th
e
beh
avior
of soil
res
i
stivity are
considered in
EARTHING system
DESIGN
. The
earthing s
ystem
is consider
ed to
be a r
od
electrode and
a
plate type e
l
ec
trode bur
ied ve
rtically
in the g
r
oun
d.The resi
st
ance of the system w
h
ich is
a very import
a
nt
factor in the d
e
sig
n
process i
s
calcul
ated us
ing F
i
ni
t
e
Ele
m
ent Method. F
i
nite Ele
m
ent Method is us
ed t
o
estimate the s
o
lution of the
partial differential
equation t
hat gov
er
ns the system
behavior. COMSOL
Multip
hysics 4
.
4
w
h
ich is o
ne of
the
p
a
c
k
ages
that
w
o
rk w
i
th the F
E
M is
used
a
s
a to
ol
in
th
is
desi
gn.F
i
na
lly the
val
ues of the
resista
n
ce
obtai
ne
d by
COMSOL Mult
iphysics
are
c
o
mpar
ed w
i
th
the
prove
n
an
alytic
al for
m
ul
a val
u
es for the gr
ou
nd resist
ance, i
n
ord
e
r to prov
e the w
o
rk do
n
e
w
i
th COMSOL
Multiphysics.
Ke
y
w
ords
: F
i
n
i
te Ele
m
e
n
t Method (F
EM), earthi
ng d
e
sig
n
,
groun
di
ng g
r
ids, soil resisti
v
ity, soil mo
isture
,
soil T
e
mp
eratu
r
e
Copy
right
©
2016 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Grou
ndin
g
gri
d
s a
r
e, with
o
u
t doubt, the
most im
p
o
rta
n
t part of an
electri
c
al
syst
em from
the point of view of the safety of peo
ple
and e
qui
pment. The
safety, reliabi
lity, and correct
operation
of electri
c
al po
wer system
s depe
nd
on
th
e quality of the de
sign
an
d con
s
tructio
n
of
their g
r
ou
ndi
ng g
r
id
s [1]. Earthing i
s
th
e art of m
a
ki
ng a
co
nne
ction to e
a
rth i
n
ord
e
r to
protect
the po
wer sy
stem’s equi
p
m
ents
and th
e pe
rso
nnel
who
wo
rk in i
t
from the d
a
nger of ele
c
trical
sho
c
ks.
A
c
o
mplet
e
g
r
o
u
n
d
ing
sy
st
em
might
in
clu
d
e
only o
ne
eart
h
ele
c
tro
de, a
n
entire g
r
o
u
p of
electrode
s
with a g
r
oun
d
i
ng g
r
id, o
r
anythi
ng i
n
betwe
en
a
nd beyo
nd.
In many of
th
e
appli
c
ation
s
of
groundi
ng
,
low ground
ing resi
stan
ce
is e
s
senti
a
l to m
eet
electri
c
al
safety
stand
ard
s
[2]. The grou
n
d
resi
stan
ce
for a gi
ven fault current
deter
min
e
s what
ha
za
rd
ous
voltages exist insid
e
o
r
a
r
ound
the
sub
s
tation
or
ge
neratin
g
station. Con
s
equ
ently, the gro
und
resi
stan
ce i
s
an impo
rtan
t techni
cal p
a
ram
e
ter
whi
c
h i
s
rel
a
ted
to the safet
y
of people
and
equipm
ent. If the gro
und
resi
stan
ce i
s
too hig
h
and
an ea
rth fault
occurs, pe
rsonnel m
a
y b
e
killed
or inj
u
red a
nd e
q
u
i
pment may
be dam
age
d [3]. The e
a
rth mu
st b
e
treated
as a
semi
con
d
u
c
tor, while the
grou
ndin
g
ele
c
trod
e itse
lf is a
pure
con
ducto
r. Kno
w
l
edge
of the l
o
ca
l
soil
con
d
ition
s
is man
dato
r
y and i
s
the fi
rst
step in
the
desi
gn p
r
o
c
e
ss. An A
c
curate de
sign
of
a
grou
ndin
g
system
requi
re
s an
a
c
curat
e
asse
ssme
n
t
of the site’
s
soil
co
nditio
n
s. Th
ese fa
ctors
make the d
e
sign of a grou
n
d
ing sy
stem complex [4].
One im
porta
nt step i
n
d
e
sig
n
ing
a
grou
ndin
g
system i
s
to
estimate th
e
gro
und
resi
stan
ce of
the grou
ndin
g
grid. The di
fferent
cal
c
ul
ating method
s the gro
und
resi
stan
ce of
the
grou
ndin
g
g
r
i
d
s
are
ba
sed
on the
dete
r
mination
of
g
r
id voltag
e o
r
grid
capa
citance. The
first
method i
s
ba
sed o
n
dete
r
mining the g
r
oundi
ng g
r
id
potential, usu
a
lly by
mean
s of the imag
e
method [5]. The se
co
nd m
e
thod is b
a
se
d on dete
r
mi
n
i
ng the ele
c
trode capa
cita
nce o
n
the ba
sis
of the relatio
n
betwe
en el
ectri
c
ch
arge and potentia
l,
once the ele
c
tri
c
field in the soil ha
s b
een
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 1, April 2016 : 11 – 22
12
cal
c
ulate
d
. O
n
ce
were
obt
ained
the
groundi
ng
gr
id
potential
an
d the
ea
rth f
ault current,
the
grou
nd re
si
stance of the groun
ding g
r
id
is calcul
ated
by applying Ohm’s la
w. Simple formul
a
s
for calcul
atin
g gro
und
re
si
stan
ce in
sq
u
a
re g
r
o
undi
n
g
grid
s h
a
ve
been
pro
p
o
s
e
d
by Dwight e
t
al.
[6–9], in re
cta
ngula
r
g
r
id
s b
y
Schwarz [1
0], and in
g
r
o
undin
g
gri
d
s
of any sh
ape
by Thapa
r et
al.
[11]. Current
grou
ndin
g
gri
d
cal
c
ulatio
n method
s dete
r
mine g
r
ou
nd
resi
stan
ce a
nd the step
a
nd
touch volta
g
e
s u
s
in
g diff
erent m
a
the
m
atical te
ch
nique
s. Th
ese tech
niqu
es are
use of
the
hypothe
se
s that allow
us to model th
e real
sy
ste
m
in theoretical sy
stem
s
with co
mpa
r
able
results. The
s
e
stu
d
ie
s are
pe
rform
ed g
enerally
for symmetrical
g
r
oun
ding
g
r
id
s with uniform,
two-laye
r, or
multilayer soil
s [12–1
5].
Re
cently, stu
d
ies
ba
sed
on the finite
-e
lem
ent me
thod (FEM)
have be
en
use
d
to
cal
c
ulate g
r
o
und resi
stan
ce of g
r
ou
n
d
ing g
r
id
s. The FEM all
o
ws obtaini
n
g
the groun
ding
resi
stance as a function of
the resi
stivity
of soil. Th
en,
it will be
possible to
justify the use
of finite
element met
hod in dime
nsio
ning of the gro
undi
ng
system
s. The first sim
u
l
a
tion studi
es of
grou
ndin
g
g
r
id beh
avior u
s
ing th
e FE
M we
re b
a
se
d on
cal
c
ulat
ing groun
d resi
stan
ce for an
arbitrary g
r
id
potential
(on
c
e the
grid
current i
s
kn
ow
n)
. T
h
e gr
id
c
u
r
r
e
n
t
fo
r th
e
gr
id
po
te
n
t
ia
l
se
t
is dete
r
mine
d by mean
s
of a cu
rre
nt flow anal
y
s
is. Once th
e current is
cal
c
ulated, groun
d
resi
stan
ce
is
determi
ned
a
s
the q
uotient
betwe
en
the
voltage set a
nd the
cu
rre
n
t
calculated [
1
].
Model
si
ze
selectio
n was
difficult in thi
s
method,
and
this
con
d
itio
ned the
value
of the
cal
c
ul
ated
grou
nd
re
sist
ance. To
de
crea
se th
e e
r
ror of th
e g
r
o
und
re
sista
n
ce calcul
ated,
electri
c
al
po
wer
engin
eers we
re forced to a
nalyze mo
del
s of different sizes
with a high numb
e
r o
f
nodes. Due to
the low level
s
of accu
ra
cy
of the results and th
e lo
ng
cal
c
ulatio
n ti
mes
re
quired
,
this meth
od
is
not very fea
s
i
b
le. As a
re
sult of the difficultie
s of the
method o
u
tlin
ed ab
ove, a
new
method
to
desi
gn an e
a
r
thing
system
s usi
ng Finite
Element
Method (FEM
) is pre
s
ente
d
in
this pape
r. In
this metho
d
, from the finite element
method i
s
used to estima
te the solutio
n
of the part
i
al
differential
eq
uation th
at go
verns the
sy
stem be
hav
ior.
In p
r
op
osed
method, th
e i
n
fluen
ce
of th
e
moistu
re
and
tempe
r
ature
on the
be
ha
vior of
so
il
resi
stivity is consi
dered i
n
earthin
g
syst
em
desi
gn. Th
e
earthin
g
syst
em is con
s
id
ered
to b
e
a
rod
ele
c
tro
d
e
an
d a
plat
e type ele
c
trode
burie
d verti
c
a
lly in the gro
und. Also the
gro
und
re
sistance to
be
d
e
termin
ed by
usin
g the fini
te
element
met
hod
and
with
cal
c
ul
ate the
dissip
ated
p
o
we
r or
f
r
om
the stored e
nergy.
T
hen
with
integratio
n of
the su
rface
den
sity
is cal
c
ulate
d
the
size of the
cu
rre
nt pa
ssi
ng
throug
h of the
grou
nde
d ro
d
or regi
on. Fi
nally, the gro
und resi
st
an
ce is dete
r
min
ed as the
qu
otient betwe
en
the voltage and the current cal
c
ulate
d
. This
meth
od ha
s the addition
al ad
vantage of b
e
ing
indep
ende
nt
of the b
oun
d
a
ry conditio
n
,
sha
pe, a
n
d
si
ze
of the
grid
and
soil
structu
r
e. T
h
e
method
pre
s
ented in thi
s
pape
r p
r
ov
es hi
ghly u
s
eful in dete
r
mining p
r
e
c
i
s
e fo
rmula
s
for
cal
c
ulatin
g g
r
ound
re
si
sta
n
ce
in diffe
re
nt kin
d
s of g
r
oun
ding
gri
d
, with n
o
ne
ed to
build
a
n
d
measure larg
e numbe
rs of grou
ndin
g
gri
d
s or
study scale mo
del
s.
2. Earthing Sy
stems
Earthing
or
grou
ndin
g
m
a
y be d
e
scri
bed
as
syste
m
of ele
c
tri
c
al conne
ctio
n to the
gene
ral ma
ss of earth. This sy
stem o
f
electric
al conne
ction co
nsi
s
ts of co
mpone
nts of
an
electri
c
al
syst
em and meta
l works a
s
so
ciated
with equipme
n
t, apparatu
s
an
d applia
nce
s
. T
h
is
system p
r
ovi
des p
r
ote
c
tio
n
to personn
e
l
, equipment
and buil
d
ing
s
.
2.1. Require
ment of Ear
t
hing Sy
stems Design
A good g
r
ou
nding
system
-also kn
own
as an e
a
rth
electrode
system -is imp
o
rtant for
the prote
c
tio
n
of an overall system fa
cility.
Therefo
r
e, a safe groundi
ng gri
d
design h
a
s
the
following main objec
tives
[1]:
To prote
c
t p
e
rsonn
el aga
inst ele
c
trical
risk
s by limi
t
ing the touches a
nd ste
p
voltages to
safe value, f
o
r a
s
surin
g
that if grou
nd
faults
occu
r
in sub
s
tation
s or
gen
erati
ng station
s
,
a
person
in the
vicinity of ground
ed fa
cilities i
s
n
o
t ex
posed to th
e
dang
er
of critical el
ect
r
i
c
sho
c
k;
Electrom
agnetic
compatibility
(EMC), limitation of
electrom
agnetic
disturbances of the
electri
c
ity su
pply network and to
en
sure
sa
fety, g
ood
power q
uality and
continuity of
electri
c
al
eq
u
i
pment by lim
iting the ove
r
vo
ltages that
can
ap
pea
r
unde
r extre
m
e ope
ratio
n
con
d
ition
s
or
in ca
se of an
accide
nt;
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
The Influen
ce
of Moisture a
nd Tem
perat
ure on the Be
havi
o
r of Soil Re
sisti
v
ity …
(Sajad S.)
13
to ensu
r
e
co
rre
ct ope
rati
on of equi
p
m
ent and el
ectri
c
al p
r
ote
c
tion devi
c
e
s
by enabling
grou
nd
faults
to be
dete
c
te
d an
d
action
s sel
e
ct
e
d
to
d
i
sconn
ect th
o
s
e
zo
ne
s
of the el
ect
r
ical
installatio
n
where fault
s
occur;
To provid
e m
ean
s to ca
rry
electri
c
curre
n
ts
into the e
a
rth un
der n
o
r
mal an
d fault conditio
n
s,
without excee
d
ing any op
erating and e
q
u
i
pment limits.
Provide prote
c
tion of buildi
ng and in
sul
a
tion again
s
t lightning.
2.2. Compon
ents a
nd Par
a
meter
s
of E
a
rthing Sy
stems Design
The main
Co
mpone
nts of a safe g
r
oun
d
i
ng grid d
e
si
g
n
are [16]:
Earth: The lo
cation to be
grou
nde
d mu
st firs
t be an
alyzed to det
ermin
e
the soil stru
cture,
type, depth
a
nd
re
sistivity of ea
ch l
a
yer of th
e
soil, a
nd to
have
a
backg
rou
nd i
n
vestigatio
n
of any buried
cabl
es, metall
ic pipe
s, etc.
Earth ele
c
tro
de: a metal condu
ctor
or a
system
of int
e
rconn
ecte
d
metal co
ndu
ctors, or
other
metal pa
rts a
c
ting i
n
the
same m
anne
r
embed
ded
in
the g
r
ou
nd
a
nd el
ectri
c
ally
co
nne
cted
to it.
Earth
re
sistiv
i
t
y
(
ρ
): the
re
sista
n
ce m
e
a
s
ured
betwee
n
two
op
po
site faces of
a
one
meter
cub
e
of eart
h
whi
c
h is e
x
presse
d in unit of
Ω
.m. Soil resi
stivity is the key factor that
determi
ne
s what the resi
st
ance
of the chargi
ng ele
c
trode will be a
nd to what d
epth it must
be d
r
iven to
o
b
tain lo
w g
r
o
und
re
sista
n
ce. The
re
sisti
v
ity of soil varies
widely th
rough
out the
worl
d and
ch
ange
s sea
s
o
nally. The lower the
re
sist
ivity
the fewe
r the elect
r
od
es re
qui
red t
o
achi
eve the d
e
sired ea
rth resi
stan
ce val
ue.
It is an advantage to
kno
w
the re
si
stivity valu
e
at the
plan
ning
stage
a
s
it give
s a
n
indication fo
r ho
w m
u
ch
electrode
i
s
l
i
kely to
be
requi
re
d. Usu
a
lly there a
r
e
seve
ral
soil l
a
yers e
a
ch h
a
ving diffe
ren
t
re
sistivity in
whi
c
h
ca
se
the soil is
sa
id to be non
-uniform. Th
u
s
, uniform
so
il is the soil
that has o
n
e
layer with
con
s
tant val
u
e of resi
stivity. Measureme
n
ts h
e
lp
defin
e the l
a
yers o
f
the soil an
d
they sh
ow
that the resi
st
ivity is a
function of the dep
th [16].
Earthing resi
stance: Since soil ex
hibit
s
a resi
stan
ce to
the flow
of an electri
c
al
cu
rre
nt and is
not an “ideal” conductor,
there will al
way
s
be some resist
ance (can never be zero) between
the
ea
rth ele
c
trod
e and
“true
Ea
rth”. Th
e
resi
stan
ce
betwe
en
th
e earth
ele
c
tro
de
a
nd “tru
e
Earth” i
s
known as the E
a
rth
Resistance
of
an
electrode, and i
t
will depend on the soi
l
resi
stivity, the type and size of the electr
ode an
d the d
epth to whi
c
h
it is buried.
Table 1 sho
w
s the value
s
of the resi
stivity for various
types of soil [5].
Table 1. Example of re
sist
ivit
y
value for variou
s soil types
T
y
pe of grou
nd
Grou
nd
re
sisti
v
i
t
y
ρ
[
Ω
.m]
Range
of v
a
lues
A
v
e
r
age v
a
lues
Bogg
y
g
r
ound
2-50
30
Adobe Cla
y
2-200
40
Slit and sand-clay gro
und, humus
20-260
100
Sand and sand
y
ground
50-3000
200 (moist)
Peat >1200
200
Gravel (moist)
50-3000
1000 (moist)
Ston
y
,
and
rock
y ground
100-8000
2000
Concrete: 1 p
a
rt
cement+3 parts
sand
50-300
150
1 part cement+5
parts gravel
100-8000
400
3. Finite Element Me
tho
d
In mathem
atics finite el
e
m
ent meth
o
d
(FEM
) i
s
a num
eri
c
al
techni
que
for finding
approximate
solutio
n
s to
boun
dary
value p
r
o
b
lem
s
. Thi
s
m
e
tho
d
is
similar t
o
the
idea
t
hat
con
n
e
c
ting m
any tiny strai
ght line
s
ca
n
approx
imate
a larg
er
circl
e
. FEM enco
m
passe
s all t
h
e
method
s fo
r
con
n
e
c
ting m
any sim
p
le
el
ement
e
quati
ons over ma
ny small
Sub
domain,
nam
ed
finite element
s, to app
roxi
mate a mo
re
compl
e
x equ
ation over a l
a
rge
r
d
o
main
[17]. In gene
ral,
the FEM con
s
ist of three
main matri
c
e
s
, whi
c
h ar
e: the prop
erty matrix, the behavior matrix
and
the action ma
trix.
.
K
uF
(1)
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02-4
752
IJEECS
Vol.
2, No. 1, April 2016 : 11 – 22
14
Whe
r
e: {K
} i
s
the p
r
op
erty
matrix, {u}
is
the
be
havior
matrix an
d {F
} is the
action
matrix.
In ele
c
trical
appli
c
ation
s
,
{K} can
re
prese
n
t the
dielectri
c
pe
rm
ittivity, {u} ca
n re
present t
h
e
electri
c
al p
o
tential and {F
}
can re
pr
esen
t the electri
c
a
l
charge [18].
-1
uF
K
(2)
FEM is use
d
to study the behavior of ma
ny el
ectri
c
al systems, by finding the sol
u
tion of
the uppe
r eq
uation.
3.1. Laplace’
s Equation
For ste
ady direct cu
rrent, the different
ial relation is d
e
fined a
s
follows [19]:
. J
0
(3)
Whe
r
e: J i
s
the curre
n
t den
sity. Ohm’s L
a
w at a point
is:
J E
(4)
Whe
r
e: E is the electri
c
field and
σ
is th
e electri
c
al condu
ctivity of the media or material.
The ele
c
tri
c
field E can be
obtaine
d as t
he neg
ative gradie
n
t of the electri
c
pote
n
t
ial:
E -
.
V
(5)
Whe
r
e: V is the ele
c
tri
c
p
o
tential. Fro
m
Equation
s
(3) and (5
),
the
follo
wing equatio
n
s
are obtai
ned:
.V
E
(6)
.(
.V
)
0
(7)
Finally, the Lapla
c
e eq
uati
on is obtai
ne
d as follo
ws:
V
2
V
= 0
(8)
To determine
spe
c
ific di
st
ribut
ion
of the elect
r
ic fiel
d, i.e., to determin
e
uniq
u
e
ly the
solutio
n
of the differentia
l equation, the boun
da
ry condition
s
given
at the bounda
ry of the
resea
r
ch regi
on are n
eed
e
d
. There a
r
e t
w
o ki
nd
s of bound
ary co
nd
itions:
Bounda
ry whi
c
h is far a
w
a
y
from the cu
rre
nt
sou
r
ce, introdu
ce
s Di
richlet bou
nda
ry conditio
n
[20]:
V =
0
(9)
Or
V =
V
0
(10
)
Whe
r
e: V is the ele
c
tric p
o
t
ential and V
0
is a kno
w
n v
a
lue.
Insulatin
g
su
rface (i.e., gro
und), which is Neuma
nn bo
unda
ry con
d
ition [20]:
0
n
V
(11
)
Whe
r
e: n is t
he normal ve
ctor to the bo
unda
ry.
3.2. Finite Element Gr
ou
nding Meth
o
d
s
The Mo
st re
cent
studie
s
about g
r
ou
ndi
ng
analysis are ba
se
d on Finite
Elemen
t
Method
s
(FE
M
). FEM
use
d
to d
e
termi
n
e groun
ding
resi
stan
ce of a
de
sig
n
o
r
a
grou
nde
d reg
i
on
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
The Influen
ce
of Moisture a
nd Tem
perat
ure on the Be
havi
o
r of Soil Re
sisti
v
ity …
(Sajad S.)
15
They give m
o
re a
c
curate
results
comp
ared to
co
nventional g
r
o
u
nding m
e
tho
d
s [21]. Old
FEM
method
s a
r
e
comp
osed
of
curre
n
t flow a
nalysi
s
by
usi
ng el
ectrode
potential. After the
current
is
comp
uted,
ground
re
si
stan
ce
ca
n b
e
fo
und
by divi
di
ng voltag
e by
cu
rrent. In th
is m
e
thod, m
a
in
disa
dvantag
e
is sele
cting
the size of the model
su
ch a
s
earth
distan
ce to b
e
con
s
ide
r
e
d
is
starting
fro
m
the g
r
oun
din
g
ele
c
trode.
Since
analy
s
i
s
of
ea
ch
pot
ential in
the
soil for a
sel
e
cted
point is con
s
i
dere
d
from g
r
oundi
ng ele
c
t
r
ode to the p
o
int.
Ne
w FEM method
s are d
e
velope
d by resea
r
c
hers, su
ch a
s
mai
n
disa
dvanta
ge of old
FEM method
is overcome
. In the first step, t
hey assume th
at groundi
ng re
si
stance i
s
such
a
para
m
eter th
at does
not d
epen
d on pot
ential or
curr
ent in the ele
c
trod
e. Seco
nd assu
mptio
n
is
that, the regio
n
is an infinite
flat surface. Model
st
ru
ctu
r
e for this
sol
u
tion is given
in Figure 1.
Figure 1. Ne
w finite eleme
n
t model of soil
Whe
r
e: d
1
i
s
the dista
n
ce
from ele
c
trod
e to t
he p
o
in
ts wh
ere se
mi-sphe
rical
model
of
equip
o
tent surface di
sturb. d
2
is the
distan
ce fro
m
elect
r
od
e
to the point
s whe
r
e el
ect
r
ical
potential g
o
e
s
to
ze
ro. Te
chni
cally, this point i
s
at in
finity. R
1
is t
h
e re
si
st
an
ce i
n
sid
e
t
he
se
mi-
sph
e
ri
cal surf
ace a
nd R
2
is the resi
stan
ce outsid
e
the semi
-sphe
rical surfa
c
e.
From t
e
st
s of
v
a
riou
s de
sig
n
s,
d
1
can b
e
determi
ned b
y
:
30
2
D
1
d
(12
)
Where: D is the diagon
al
distan
ce of gr
ou
ndin
g
el
ectro
de. Re
si
stan
ce of gro
undin
g
electrode
can
be derived from Figure 1:
2
R
1
R
R
(13
)
R
2
is co
mput
ed from the followin
g
equ
a
t
ion:
1
d
2
2
R
(14
)
Whe
r
e:
s t
h
e soil re
si
st
iv
it
y
.
Determina
t
ion of R
1
, is
not as sim
p
le
as R
2
. This i
s
wh
ere
finite element
analysi
s
exa
c
tly takes it
s place. In gen
eral, R
1
can
be cal
c
ul
ated
from dissipat
ed
power given i
n
the followin
g
equatio
n:
power
disspeated
2
)
(
1
R
voltage
(15
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 1, April 2016 : 11 – 22
16
R
1
can b
e
det
ailed by repl
a
c
ing the term
s as in Equ
a
tion (15
)
[1]:
dV
2
E
2
)
(
1
R
V
B
V
G
V
(16
)
Whe
r
e: V
G
i
s
the pote
n
tial i
n
the g
r
o
undi
ng ele
c
trode,
V
B
is the
pote
n
tial in the
bo
unda
ry
d1, E is the
electri
c
field, d
V
is the volume element
and
σ
is the
electri
c
al
con
ductivity. In this
new m
e
thod,
which ha
s
been d
e
velo
ped, the e
n
a
b
les g
r
o
und
resi
stan
ce to
be determin
e
d
starting from the dissi
pate
d
powe
r
,
or from the store
d
energy (by t
he electri
c
field) in the model
[1].
4. Ne
w
FEM
Metho
d
for the Earthing
Sy
stem Desi
gn
In this sectio
n, the Earthin
g
syste
m
de
sign an
d imple
m
entation
wil
l
be p
r
esente
d
. The
desi
gn ha
s b
een divide
d into two pa
rts:
the electrod
e desi
gn an
d the soil de
sig
n
. Each of th
ese
parts
ha
s
its own de
sign criteria,
p
a
ra
m
e
ters,
and
co
nstrai
nts. Th
e
De
sign
and I
m
pleme
n
tatio
n
wa
s m
ade
u
s
ing
a
sp
eci
a
l FEM
soft
ware
pack
age
n
a
me
d as C
O
MSO
L
Mu
ltip
h
y
s
i
c
s
4
.
4
,
provide
d
with
built-in
drawi
ng toolb
o
x to
help the
de
si
gner to d
r
a
w
the sim
u
lated
model
with t
r
ue
scale
s
. A two and three di
mensi
onal fiel
d comp
ut
er p
r
og
ram (COM
SOL Multiphy
sics 4.4)
can
be
use
d
to
solv
e FEM
pro
b
l
e
ms. It p
r
ovi
des autom
atic m
e
sh g
ene
ration fo
r
sol
v
ing ele
c
tro
s
t
a
tic
and ele
c
tro
m
agneti
c
pro
b
l
e
ms, by differential ope
rato
r Finite Elem
ent Method. It is also p
r
ovid
e
d
with po
we
rful
postp
ro
ce
ssor techniq
u
e
s
to
help th
e de
signe
r t
o
analyze th
e re
sults, m
a
ke
comp
ari
s
o
n
s
and even
cha
nge
s in the d
e
sig
n
whi
c
h a
r
e mad
e
very quickly and e
a
sily.
When solving the PDEs,
COMSOL M
u
ltiphysi
cs
uses
the prove
n
finite eleme
n
t method
(FEM). Thi
s
software
run
s
the finite element
analysi
s
togethe
r wit
h
adaptive m
e
shi
ng and e
rro
r
control usi
n
g
a variety of numeri
c
al solvers.
Th
e De
signi
ng pl
an start
s
wit
h
determini
n
g
the
Space
Dime
n
s
ion, which is a 3D Spa
c
e,
then dete
r
min
i
ng the ro
d ra
dius, the rod l
ength, the soil
radiu
s
an
d the soil len
g
th. This idea i
s
to design a
model that si
mulates a
n
y desi
r
ed type
of
grou
ndin
g
sy
stem
s su
ch
as a vertical
grou
ndin
g
ro
d, a horizo
n
tal grou
nding
rod, a plate type
electrode
o
r
a
he
misp
he
ri
cal ele
c
trod
e type,
driv
en
i
n
to the
soil,
to an
alyze
the
voltage
gradi
ent
arou
nd it a
n
d
on the
su
rf
ace
of the
soil. Also to
calcul
ate
the resi
stan
ce of
the entire m
ode
l
con
s
i
s
ting of
the elect
r
od
e
,
the soil and
the c
onta
c
t resi
stan
ce bet
wee
n
the ele
c
trod
e an
d the
soil i
s
used
of the FEM
concept. The
desi
gn m
ade
simul
a
tes a
vertical
grou
nding
ro
d a
n
d
a
plate type el
ectro
de
drive
n
into a
volu
me of u
n
if
orm soil
with
consta
nt
resi
stivity. The ini
t
ial
model wa
s d
e
sig
ned usi
n
g
the
b
a
si
c concepts
a
s
in
[1] and [1
7]
whi
c
h
will b
e
discu
s
sed in
th
e
following.
4.1. The con
cept o
f
Sphe
re of Influen
c
e
Determinin
g how effici
entl
y
groundi
ng
electr
ode
s di
scharge ele
c
t
r
on
s into the earth an
importa
nt co
nce
p
t is the
“sp
h
e
r
e
of
influence”.
The
sphe
re of influence is the volume of soil
throug
hout which the ele
c
trod
e disch
a
rge
s
curr
en
t into the soil. The gre
a
ter the volume
comp
ared
wit
h
the vol
u
me
of the el
ect
r
o
de, the
mo
re
efficient i
s
th
e ele
c
tro
de. L
ong
ele
c
trod
e
s
,
su
ch
as g
r
ou
nding
ro
ds,
are the
mo
st eff
i
cient.
T
he
su
rface
a
r
ea
of
the ele
c
trode
determi
ne
s th
e
cap
a
city of t
he devi
c
e, b
u
t doe
s n
o
t
affect “the
sp
here
of influe
nce
”
. Th
e g
r
eater th
e
surface
area i
s
, the greate
r
the
conta
c
t with
the soil
an
d
the more el
ectri
c
al e
nergy that can
be
discha
rge
d
p
e
r unit of time [16]. Thus the sph
e
re of influen
ce ca
n
be taken to be gre
a
ter th
a
n
1.1 times the
rod len
g
th, in this area n
o
other
rod
s
must exist, to
avoid interfe
r
en
ce b
e
twe
e
n
sph
e
re
of influen
ce of ea
ch rod, a
nd to
hav
e the ma
ximum efficie
n
cy of the g
r
oundi
ng sy
st
em.
Figure 2 sh
o
w
s the
sph
e
re of influenc
e
for a vertical
grou
ndin
g
ro
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
The Influen
ce
of Moisture a
nd Tem
perat
ure on the Be
havi
o
r of Soil Re
sisti
v
ity …
(Sajad S.)
17
Figure 2. The
sphe
re of influen
ce
4.2. The Gro
unding Rod
Design
The rod, is d
e
sig
ned a
s
a
cylindri
c
al
sh
aped el
eme
n
t with ra
diu
s
r
r
, and len
g
th
r
l
, and
made of co
p
per with
con
ductivity of coppe
r that is
1
7
)
.
(
10
99
.
5
m
r
or resi
stivity of coppe
r
whi
c
h is
m
r
.
10
66
.
1
8
. The rod i
s
drive
n
vertically int
o
the soil. Co
nsid
erin
g a ro
d elect
r
ode
of a diameter d and length
L as sh
own in figure 2,
with the assu
mptions that
the curre
n
t flow
outwa
rd
s fro
m
the vertica
l
secti
on i
s
horizontal an
d
from the lower h
e
misph
e
re en
d is ra
dial
outwa
rd
s. Th
e rod resi
stan
ce is give
n in [16] as follows:
8
R[
l
n
1
]
2
L
L
d
(17
)
Whe
r
e: L
is
the bu
ried l
e
ngth of the
electr
ode
(m
), d is th
e di
ameter of th
e bu
ried
electrode (m),
ρ
is the soil resi
stivity (
Ω
.m) and
R is the ele
c
trod
e resi
stan
ce (
Ω
).
4.3. The Gro
unding Soil Design
The soil in g
r
oundi
ng
syst
ems i
s
thou
g
h
t to be a
s
a
con
d
u
c
tive medium. Th
e soil in the
desi
gne
d mo
del is assu
med to be uniform h
a
ving a con
s
ta
nt resi
stivity
s
, or a con
s
ta
nt
c
o
nd
uc
tivity
s
.
The soil i
s
d
e
sig
ned a
s
a
cylindri
c
al el
ement su
rrou
nding the g
r
oundi
ng ro
d
having a radi
us
s
r
, an
d a
le
ngth o
r
heig
h
t
s
l
, with th
e
ro
d d
r
iven ve
rti
c
ally into
the
cente
r
of the
soil.
This mo
del was de
sign
ed
usin
g the basic co
ncepts a
s
in [1] and [16]. The soil
radiu
s
is
taken to
be
2.5 times th
e
rod l
ength t
o
obtain
suffi
cient volu
me
of the soil that gua
ra
nte
e
s
effective cu
rrent discha
rg
e. The rod l
engt
h
s
and
radiu
s
e
s
de
si
gned
were 1
m
, 2m, 3m,
and
0.025m, 0.00
8m re
spe
c
tively. Table 2 shows the
soil radiu
s
for the
variou
s lengt
hs of ro
d.
Table 2. Soil radiu
s
for e
a
ch value of rod
length
Rod le
ng
th
(m
)
Soil radiu
s
(
m
)
1 2.5
2 5
3 7.6
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752
IJEECS
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2, No. 1, April 2016 : 11 – 22
18
In the pro
p
o
s
ed metho
d
, the soil aroun
d the ro
d is
d
i
vided into three cylind
r
i
c
al
sha
ped
parts,
as is shown in
Figu
re 3.
The
first cyli
nde
r whi
c
h
i
s
calle
d
t
he soil
g
r
o
u
n
d
ing system
i
s
taken to be with a radiu
s
2.5 times the rod lengt
h
to obtain sufficient volume
of the soil that
guarantee
s ef
fective curre
n
t
disch
arg
e
. The se
co
nd cyl
i
nder i
s
call
ed
the effective soil, usually is
con
s
id
ere
d
wi
th a radiu
s
an
d a height of
10 m. T
he ne
xt layer or third cylinde
r, wit
h
a height an
d
radiu
s
of m
o
re than 1
0
me
ters,
whi
c
h d
oes
not
have
signifi
cant ef
fect on the
soil re
sistivity are
assume
d as i
n
finite.
Figure 3. The
propo
se
d Ea
rthing de
sig
n
Table
s
3
an
d
4 a
r
e
sh
ows soil
re
si
stivity ch
a
nge
s
a
s
functio
n
s of soil
tem
p
e
r
at
ure and
s
o
il mois
ture c
ontent, res
p
ec
tively.
Table 3. Soil resi
stivity cha
nge
s as a fun
c
tion of soil te
mperature
Resisti
v
i
t
y
(
Ω
.m
)
Tem
p
erat
ure
°F
°C
7.2
68
20
9.9
50
10
13.8
32 (
w
ate
r
)
0 (
w
ate
r
)
30
32 (ice)
0 (i
c
e
)
79
23
-5
330
14
-15
Table 4. Soil resi
stivity cha
nge
s as a fun
c
tion of soil m
o
isture
Resisti
v
i
t
y
(
Ω
.m
)
Moisture
Con
t
en
t (
%
b
y
w
e
ight)
Sand
y
Loa
m
Top S
o
il
6
10
1000
6
10
1000
0
150
250
2.5
43
165
5
18.5
53
10
10.5
19
15
6.3
12
20
4.2
6.4
30
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IJEECS
ISSN:
2502-4
752
The Influen
ce
of Moisture a
nd Tem
perat
ure on the Be
havi
o
r of Soil Re
sisti
v
ity …
(Sajad S.)
19
4.4. COMSO
L
Multiph
y
sics 4.4 Bou
n
dar
y
Setting
s
Bounda
ry co
ndition
s defi
ne the interfac
e bet
wee
n
the mode
l geometry
and its
surro
undi
ngs.
Interface
co
ndition
s on i
n
terio
r
bo
und
arie
s in mo
d
e
l geom
etry
can
also be
set.
Also diffe
rent
bou
nda
ry condition
s
can
be
set fo
r
each b
ound
a
r
y. For the
rod, the
ele
c
tric
potential bo
u
ndary is
set o
n
V0 =100 vo
lts. For
the so
il, the bounda
ries a
r
e
sele
cted as follo
ws:
From Conditi
ons Sho
w
n in
figure 3, the four
sid
e
s, an
d the bottom of the soil cylinder
were
set to Gro
und
Bounda
ry co
ndition.
The top of the soil cylin
der was
set to Electri
c
al Insula
tion Bounda
ry.
No
w the mo
del is compl
e
tely desig
ne
d as
requi
re
d, all the Subdomai
n we
re defined
along
with the boun
dary condition
s for
each bou
nda
ry of the model.
5. Simulation Resul
t
s an
d Discus
s
io
n
After the m
o
d
e
l was de
sig
n
ed, in
order to obt
ai
n the
solution
of the
Lapla
c
e
eq
ua
tion, it
must be solv
ed. This mod
e
l is the mod
e
l govern
ed b
y
Laplace e
q
uation, whi
c
h
is the govern
i
ng
equatio
n
for the
Earthi
ng system und
e
r
de
sig
n
.
De
pend
ent Vari
able i
s
by
de
fault set to
1
0
0
volts, whi
c
h i
s
the be
havi
o
r pa
ram
e
ter to
be studi
e
d
and a
nalyzed. The L
apl
ace
equatio
n
is
written in the
Subdom
ain Settings dial
og
box in the Following F
o
rm:
j
Q
)
e
J
-
V
(
(18
)
Whe
r
e: V
is
the ele
c
tri
c
al
potential,
σ
is
the elec
tric
Conduc
tivity, J
e
is the
external
Curre
n
t Den
s
ity and
j
Q
is the curre
n
t Source Den
s
ity.
FEM is kno
w
n with its u
n
i
que T
r
iangl
e
s
. Initialize th
e Mesh allo
ws the de
sig
n
e
r
to se
e
the triangle
s
made by the COMSO
L
Mu
ltiphysi
cs 4.4
solver, which sho
w
n in figu
re 4.
Figure 4. Initialize
d
Mesh Model
The results
are o
b
taine
d
by con
s
ide
r
i
ng effect of
temperature
and moi
s
ture
on the
resi
st
iv
it
y
soil
.
Figur
e 5
sh
ow
s t
h
e
pote
n
tial di
stributi
on o
n
the
so
i
l
su
rface a
n
d
also in
a pl
a
t
e
surfa
c
e
with
a depth of 0.
5 m (groun
di
ng gri
d
pl
ate). As can b
e
seen t
he mo
st
of the potential
distrib
u
tion is on the su
rfa
c
e of the cop
per plat
e
and
whateve
r
be
come
s farth
e
r
from the co
pper
plate su
rface,
the potentia
l distrib
u
tion b
e
com
e
s lo
we
r. Figure
6 sh
ows the pote
n
tial distrib
u
tion
on the
soil
surface an
d al
so in
a rod
surface
with
a
depth of 1
m. Here al
so
the mo
st of the
potential
dist
ribution
is o
n
the
co
ppe
r rod
surf
a
c
e
and
whatev
er b
e
come
s
farther from
the
cop
per
rod, the potential d
i
stributio
n be
come
s lo
we
r.
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752
IJEECS
Vol.
2, No. 1, April 2016 : 11 – 22
20
Figure 5. The
potential dist
ribution o
n
the soil
surfa
c
e
and in a plat
e with a dept
h of 0.5 m
Figure 6. The
potential dist
ribution o
n
the soil su
rfa
c
e
and in a rod
surfa
c
e
with a depth of 1 m
Usi
ng the e
q
uation (15)
a
nd with
solvin
g
the Lapl
ace
equation
(1
7
)
, the value o
f
groun
d
resi
stan
ce of
the earthin
g system for the cop
per pl
ate is obtain
ed a
s
follows:
8951
.
1
7666
.
52
100
dV
E
voltage
V
2
2
R
Also, the val
ue of g
r
ou
n
d
re
si
stan
ce
of
the e
a
rth
i
ng sy
stem f
o
r the
co
ppe
r rod i
s
obtaine
d as f
o
llows:
4407
.
3
064
.
29
100
dV
E
voltage
V
2
2
R
As ca
n be
se
en, the value
of grou
nd re
sista
n
ce for t
he coppe
r ro
d is g
r
eate
r
from the
value of g
r
ou
nd resi
stan
ce
for the
cop
p
e
r
plate.
T
o
sol
v
e this p
r
obl
e
m
, usu
a
lly instead of u
s
ing
a
singl
e rod, fro
m
a netwo
rk i
s
used which con
s
i
s
ts of se
veral pa
rallel
rod
s
.
Table 5
sho
w
s
the gro
und resi
stan
ce
va
lues
obtain
e
d
with the
met
hod expl
aine
d in thi
s
pape
r and th
ose
cal
c
ulate
d
in [1] and [11] us
ing the method
s
develop
ed b
y
Thapar et al.
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