Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
4, N
o
. 4
,
A
ugu
st
2014
, pp
. 48
6
~
49
7
I
S
SN
: 208
8-8
7
0
8
4
86
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
Capaciti
ve Interf
erences Mode
ling and Optimization between
HV Power Lines and Aerial Pipelines
Rabah
Djekidel, Djilla
li Mahi
Laborator
y
of
studies and
Development of Se
miconductor
and
Dielectr
i
c
Mater
i
als, LeDMaScD,
University
Amar
Telidji of
Lagho
uat, BP
37G route of Gh
ardaïa
, Laghouat 03000,
Algeria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 7, 2014
Rev
i
sed
Jun
4
,
2
014
Accepted
Jun 26, 2014
Metal p
i
pe
lines
are wid
e
l
y
used
for th
e tr
ansport of flu
i
ds and
liquid
an
d
gaseous h
y
drocarbons. When these pipe
lin
es are installed near overhead
power transm
ission lines, AC interfe
r
e
nce can occur between the high
voltag
e
power
li
nes
and p
i
pel
i
ne
s
.
This
interf
eren
ce
can
caus
e
the
appear
anc
e
of induced voltages that pres
en
t
a risk of
electric
shock to th
e op
erator saf
e
ty
,
di
re
ct
e
f
fe
ct
s on t
h
e pi
pel
i
n
e,
suc
h
as
corros
i
on of th
e co
at
i
ng and s
t
eel
.
Evalu
a
tion of
this coupling is n
e
cessar
y
to ensure
the safety
of p
e
r
s
onnel and
equipm
ent conn
ect
ed to th
e pip
e
lin
e. In
th
is paper, an
optimization method
combining PSO with CSM is p
r
oposed
to simu
late the capacitive coupling
between th
e HV power lines
and aeria
l pipe
line
s
and anal
yz
e
th
e differe
n
t
factors
that aff
e
ct th
e level of
this
coupling, the simulation
r
e
sults were
compared with a previous stud
y
of specialty
,
th
e results are fou
nd in good
agreem
ent
.
Keyword:
Adm
i
ssi
bl
e bo
dy
cu
rre
nt
Aeri
al
pi
pel
i
n
e
cap
acitiv
e co
up
lin
g
C
h
ar
ge si
m
u
l
a
ti
on m
e
t
hod
Particle swarm op
ti
m
i
zatio
n
Copyright ©
201
4 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
:
Ra
b
a
h Dj
ek
id
el,
Lab
o
rat
o
ry
of st
udi
es
a
n
d De
vel
o
pm
ent
of S
e
m
i
cond
uct
o
r and
Di
el
ect
ri
c M
a
t
e
ri
al
s,
Uni
v
ersity
Am
ar
Telidji of La
ghouat, Alge
ria
Em
a
il: d
j
ek
id
el
@m
ai
l.lag
h
-
univ
.
d
z
1.
INTRODUCTION
Because of the
continuous
growt
h
of ene
r
gy
cons
um
ption a
nd
of t
h
e incre
a
se
d tendency
to locate the
hi
g
h
v
o
l
t
a
ge e
l
ect
ri
c t
r
ansm
issi
on l
i
n
es
, an
d pi
pel
i
nes al
o
ng t
h
e sam
e
cor
r
i
d
ors
,
t
h
e
m
e
t
a
l
l
i
c
pi
pel
i
nes are
gene
ral
l
y
bu
ri
ed at
shal
l
o
w
dept
hs b
u
t
t
h
e
y
can al
so
b
e
aer
ial [
1
]-
[3
].
Th
e pr
ese
n
ce of a HV powe
r
line
parallel or clos
e to the pipeline can
be a source
of
dang
erous electrical interfe
re
nce
fo
r th
is str
u
ctur
e, u
n
d
e
r
no
rm
al
and post
-
faul
t
co
nd
i
t
i
ons of
po
w
e
r sy
st
em
operat
i
o
n
.
The
r
e
are t
h
ree p
r
edom
i
n
ant
t
y
pes o
f
electr
o
m
a
g
n
e
tic in
terf
er
en
ce
su
ch
as cap
acit
i
v
e
, i
n
du
ctiv
e,
an
d condu
ctiv
e. Each
o
f
th
ese ph
eno
m
en
a ind
u
c
es
vol
t
a
ge
o
n
t
h
e
pi
pel
i
n
e, ca
us
i
ng ha
rm
ful
effect
s. Thes
e effects
m
a
y present a risk of electric shoc
k to the
o
p
e
rator safety
. Th
ey can
also
threaten
th
e
in
teg
r
ity o
f
cath
od
ic pro
t
ectio
n
equ
i
p
m
en
t, th
e p
i
p
e
lin
e coatin
g,
an
d th
e
p
i
p
e
line steel [
4
]-[6
].
Seve
ral interna
tional standards provide a m
e
thod
for dete
rmining the m
a
xim
u
m
acceptable contact
and
t
h
e m
easur
ed
vol
t
a
ge
s t
o
pr
ot
ect
w
o
r
k
e
r
s pi
pel
i
ne. T
h
e
y
are al
l
base
d
on
t
h
e m
i
nim
u
m
current
re
q
u
i
red t
o
in
du
ce v
e
n
t
ricu
lar fibrillatio
n (VF). In
th
e no
rm
al o
p
e
ra
ting
con
d
ition
s
in IEC 6
0
4
79-1
:
2
005
for adu
lt males,
a curre
n
t avail
a
ble greater t
h
an
or
e
q
ual to 10 (m
A)
would ge
ne
rally
be conside
r
ed unaccepta
ble from
the
poi
nt
o
f
vi
ew
o
f
pers
o
n
al
safet
y
[7]
.
In
t
h
is con
t
ex
t
,
th
is stud
y presen
ts th
e simu
latio
n
an
d
m
o
d
e
ling
o
f
a cap
acitiv
e couplin
g
b
e
t
w
een
aeri
a
l
pi
pel
i
n
e
and
p
o
we
r l
i
n
e, o
p
erat
i
n
g i
n
t
h
e st
eady
st
a
t
e, usi
n
g c
h
ar
g
e
sim
u
l
a
t
i
on m
e
t
hod c
o
upl
e
d
wi
t
h
st
ochast
i
c
opt
i
m
i
zat
i
on t
echn
i
ques
(P
SO
)
fo
r t
h
e
o
p
t
i
m
i
zat
ion
o
f
t
h
e
pr
obl
em
param
e
t
e
rs.
In this m
e
thod, the
fictitious li
near cha
r
ges a
r
e use
d
for the
m
odeling
of the line
c
o
nductors; whic
h a
r
e
placed
in
sid
e
con
d
u
c
t
o
rs;
t
h
e v
a
lu
es o
f
t
h
ese fictitio
u
s
ch
arg
e
s
are d
e
term
in
ed
b
y
satisfyin
g
t
h
e b
oun
d
a
ry
co
nditio
n
s
o
n
th
e con
d
u
c
t
o
rs’ surfaces [6
] , [8
]-[11
], it is v
e
ry i
m
p
o
r
t
a
n
t
to
d
e
term
i
n
e th
e op
tim
a
l
p
o
s
ition
and
nu
m
b
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
48
6
–
49
7
4
87
of
fictitious charges, especially with
respect to the realized
accuracy a
nd
c
o
nve
r
ge
nce
with the num
b
er
of t
h
e
fictitio
u
s
ch
arges.
Th
e cho
i
ce o
f
th
e p
o
s
itio
n
an
d
th
e
o
p
timal n
u
m
b
e
r o
f
fictitio
u
s
ch
arg
e
s was b
e
en carried
out
em
pi
ri
cal
l
y
by
usi
n
g t
h
e assi
g
n
m
e
nt
fact
or
[
12]
,
o
r
acc
or
di
ng
t
o
t
h
e e
x
p
e
r
i
ence o
f
t
h
e i
n
vest
i
g
at
o
r
[1
3]
.
Recently a genetic algorithm
s
(GAs
) as a se
a
r
ch m
e
t
hod has
bee
n
used t
o
determine the arrangem
ent
of
fictitious c
h
arges in c
h
a
r
ge si
m
u
lation m
e
thod
[14]-[16].
Sim
i
lar
to Ge
netic algorithm
s
(GAs) and
evol
ut
i
ona
ry
al
go
ri
t
h
m
s
(EAs
), P
S
O
i
s
a
po
pul
at
i
o
n-
base
d
o
p
t
i
m
i
zat
i
on t
ool
,
w
h
i
c
h
sea
r
ches
f
o
r
o
p
t
i
m
a by
up
dat
i
n
g ge
ner
a
t
i
ons.
Ho
we
v
e
r, u
n
l
i
k
e
GA
s and E
A
s,
PS
O d
o
es n
o
t
ne
ed ev
ol
ut
i
o
na
r
y
operat
o
rs s
u
ch as
cross
o
ver
an
d
m
u
t
a
t
i
on [
1
7]
,
[1
8]
.
2.
CAP
A
C
ITI
V
E CO
UPLI
N
G
F
R
O
M
P
O
WER LI
NES
TO PIPELI
N
E
S
Th
e
p
i
p
e
lin
es in
stalled
abov
e eart
h
are su
bj
ect to
cap
a
citiv
e co
up
ling
fro
m
th
e con
d
u
c
tors
o
f
o
v
e
rh
ead lin
es. Th
e electric
fi
eld
of th
e h
i
g
h
vo
ltag
e
tran
smissio
n
lin
e
gen
e
rates t
h
e cap
acitiv
e coup
lin
g b
y
in
du
cing
electric ch
arg
e
s in th
e aerial p
i
pelin
es. Th
is rep
r
esen
ts a fo
rm o
f
cap
acitive co
up
ling
operatin
g
acros
s the ca
pacitance betwe
e
n the
ov
erh
e
ad
p
o
wer lin
es and
th
e p
i
p
e
lin
e, in
series
with
th
e cap
acitan
ce
bet
w
ee
n t
h
e
pi
pel
i
n
e a
n
d
t
h
e
adjace
nt
ea
rt
h
as sh
o
w
n
i
n
Fi
gu
re
1.
Fig
u
re
1
.
Cap
a
citiv
e cou
p
ling fro
m
a p
o
wer
lin
e to
a
p
i
p
e
lin
e
Th
e i
n
du
ced
vo
ltag
e
b
e
tween th
e
p
i
p
e
lin
e and
th
e
eart
h
,
due to
cap
acitiv
e
co
up
ling
is equal to
:
12
12
2
.
p
c
C
VV
CC
(1
)
Buried pi
pelines are
not e
x
posed to ca
pacitive c
o
up
ling from the powe
r line b
ecause
the
earth acts a
s
an electrostatic shield [6], [19].
3.
C
A
P
AC
ITIVE C
O
U
P
LING CA
LCU
L
ATION
The c
h
arge
sim
u
la
tion m
e
thod is used to
calcula
t
e
t
h
e e
l
ect
ri
c fi
el
d
di
st
ri
but
i
o
n a
n
d
t
h
e i
n
duc
e
d
v
o
ltag
e
on
aerial p
i
p
e
lin
e due to
h
i
gh
v
o
ltag
e
tran
sm
issio
n
lin
e, th
e tran
sm
issio
n
lin
es co
ndu
ctors an
d
t
h
e
p
i
p
e
lin
e are
rep
r
esen
ted b
y
in
fi
n
ite lin
e charg
e
s. Ea
c
h
t
r
ansm
i
ssi
on l
i
n
e p
h
ase c
o
nd
u
c
t
o
r i
s
m
odel
e
d
by
a
num
ber n
c
infin
ite lin
e ch
arges k
e
p
t
slig
h
t
l
y
in
sid
e
th
e p
e
r
i
ph
er
y of
th
e co
ndu
ctor
/w
ire, p
i
p
e
lin
e is mo
d
e
led
by
a num
ber
n
p
in
fin
ite lin
e charg
e
s also
k
e
p
t
slig
h
tly in
sid
e
th
e p
e
ri
p
h
e
ry o
f
th
e
p
i
p
e
line [10
]
, th
e sim
u
l
a
tion
charges a
nd t
h
e contour points are equally
arrang
ed
on th
e circles with
rad
i
u
s
r
2
a
nd
r
1
res
p
ectively.
Sim
u
l
a
t
i
on c
h
a
r
ges
f
o
r
l
i
n
e c
o
nd
uct
o
rs a
n
d t
h
e
pi
pel
i
n
e
i
s
s
h
o
w
n i
n
Fi
g
u
r
e
2.
The c
o
or
di
nat
e
s o
f
t
h
e
si
m
u
l
a
t
i
on c
h
ar
ges a
n
d
co
nt
o
u
r
p
o
i
n
t
s
i
n
t
h
e c
r
os
s sect
i
o
n
o
f
t
h
e co
nd
uct
o
r
and
t
h
e pi
pel
i
n
e
are gi
ve
n by
[2
0]
-[
2
2
]
.
Pipeline
C
12
C
1
C
2
V
P
V
c
Power line
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ca
pa
citive
In
terferen
ces
Modelin
g
a
n
d
Op
timiza
tion
b
e
tween
HV
Po
wer Lin
e
s an
d
…
(Rab
ah
Djekid
e
l
)
48
8
0
0
.c
o
s
.s
i
n
kk
kk
xx
R
k
yy
R
k
(2
)
Whe
r
e:
R= {r1 if k=i, r2
if k=j
};
y
0
: h
e
igh
t
s of
co
ndu
ctor
s an
d
p
i
p
e
lin
e
abov
e
g
r
ou
nd
;
x
0
:
ho
ri
zo
nt
al
c
o
o
r
di
nat
e
s
of
c
o
n
d
u
ct
o
r
s a
n
d
pi
pel
i
n
e.
Fi
gu
re
2.
A
rra
ngem
e
nt
o
f
t
h
e
si
m
u
l
a
ti
on c
h
a
r
ges
an
d t
h
e c
o
nt
o
u
r
p
o
i
n
t
s
(
C
on
du
ctor
/ Pi
p
e
lin
e)
Th
e
p
o
t
en
tial resu
ltin
g
fro
m
a set o
f
fictiti
o
u
s
ch
arg
e
s of
m
a
g
n
itud
e
(Qj
)
can
b
e
co
mp
u
t
ed
easily
u
s
ing
t
h
e su
p
e
rp
o
s
ition
p
r
i
n
ci
p
l
e [20
]
, [21
]
, is g
i
v
e
n at po
in
t
(i) as:
1
n
ii
j
j
j
VP
Q
(3
)
Wh
ere: n is th
e to
tal n
u
m
b
e
r
of fictitio
u
s
ch
arg
e
s an
d
(P
ij
) called
th
e po
ten
tial co
efficien
t; mean
s th
e
p
o
t
en
tial
at
poi
nt
(i
) ca
u
s
ed
by
a u
n
i
t
c
h
ar
ge
of
(
Q
j
).
I
t
depe
n
d
s
onl
y
on
t
h
e t
y
pe
o
f
t
h
e c
h
ar
ge a
n
d
t
h
e rel
a
t
i
v
e
di
st
ance
bet
w
ee
n
(i
) a
n
d c
h
ar
ge
(Q
j
) [
20]
,
[
21]
.
22
22
0
1
ln
2.
.
ij
i
j
ij
ij
i
j
xx
y
y
P
xx
y
y
(4
)
Whe
r
e:
(x
i
, y
i
): co
ord
i
nates o
f
th
e con
t
o
u
rs
po
in
t;
(x
j
, y
j
):
c
o
o
r
di
n
a
t
e
s of
t
h
e
si
m
u
l
a
t
i
ons
cha
r
ge
s.
Th
e D
i
r
i
ch
let b
oun
d
a
r
y
co
nditio
n
is satisf
i
e
d
at th
e b
o
undar
y
p
o
i
n
t
s cho
s
en
on
th
e p
h
a
se co
nd
u
c
t
o
r
s
and the
ground wires
.
T
h
e
val
u
es
of the
sim
u
lation char
ges
are calculated
by the
res
o
luti
on of t
h
e syste
m
:
1
.
j
ij
c
i
QP
V
(5
)
Whe
r
e:
P
ij
: Th
e
po
ten
t
ial co
efficien
ts m
a
trix
;
Q
j
: The
col
u
mn
vector for si
m
u
la
tion c
h
arges;
V
ci
: Th
e v
a
l
u
es of th
e po
ten
t
i
a
l are
k
now
n valu
es at th
e con
t
ou
r po
in
ts.
Aft
e
r
ha
vi
n
g
det
e
rm
i
n
ed t
h
e val
u
es
of
t
h
e sim
u
l
a
t
i
on char
ges
we ch
o
o
se t
h
e
n
n ot
her c
h
ec
ki
n
g
poi
nt
s pl
ace
d
on t
h
e c
ont
ou
r o
f
t
h
e c
o
nd
uct
o
rs, a
n
d
w
e
cal
cul
a
t
e
t
h
e
new
p
o
t
e
nt
i
a
l
s
(V
vi
) gi
ven
by
t
h
e
sim
u
l
a
t
i
on cha
r
ges
(
Q
j
).
.
vi
v
i
j
VP
Q
(6
)
: Contour
point
:
Charg
e
s
i
m
u
lation
: Check poin
t
r
1
: Real radius o
f
the condu
ctor/p
ipelin
e
r
2
: Fictitious radius of
the condu
ctor/pipelin
e
r
1
r
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
48
6
–
49
7
4
89
The
differe
n
ce
betwee
n t
h
e
new
pote
n
tial calculated (V
vi
) and the
exact
pote
n
tial (V
ci
)
to
wh
ich is
su
bj
ected
th
e co
ndu
ctor
r
e
pr
esen
t th
e pr
ecisio
n
of
calcu
latio
n [20
]
, [21
]
.
1
.1
0
0
n
vi
c
i
i
vi
VV
V
(7
)
Whe
r
e:
n i
s
t
h
e t
o
t
a
l
num
ber
of c
o
nt
o
u
r
poi
nt
s (
n
= 3
.
nc+
2
.n
g+ n
p
)
.
Al
s
o
nc i
s
t
h
e
num
ber o
f
t
h
e i
n
fi
ni
t
e
l
i
n
e
charges for ea
ch transm
issio
n
line ph
ase (f
or
t
h
ree phase
s)
co
n
duct
o
r, ng
is th
e
nu
mb
er
o
f
t
h
e in
fi
n
ite lin
e
charges
for ea
ch eart
h
wire
(for two wires)
and
np is
th
e
nu
m
b
er o
f
t
h
e in
fi
n
ite lin
e ch
arg
e
s
for th
e
p
i
p
e
lin
e
(f
or
o
n
e
pi
pel
i
ne)
.
The e
q
uat
i
o
n
(
7
)
m
u
st
be m
i
n
i
m
i
zed ove
r
nc
, n
g
,
n
p
,
rc
, r
g
and
r
p
.
Whe
r
e: rc
,
r
g
an
d r
p
are t
h
e fi
ctitio
u
s
rad
i
u
s
o
f
ph
ase con
duc
to
r, earth wi
re and
p
i
p
e
lin
e resp
ectiv
ely.
Fi
gu
re
3.
Si
n
g
l
e
h
o
ri
z
ont
al
c
o
nfi
g
u
r
at
i
o
n
wi
t
h
a
b
o
v
e
pi
pel
i
ne
The el
ect
ri
c
fi
e
l
d (Ei
)
at
poi
nt
co
nt
o
u
r
i
s
t
h
e
sum
of t
h
e
el
e
c
t
r
i
c
fi
el
d c
o
nt
ri
b
u
t
i
ons
o
f
al
l
si
m
u
l
a
ti
on
char
ges (
Q
j)
. The h
o
r
i
z
o
n
t
a
l
and
vert
i
cal
com
pone
nt
s o
f
t
h
e el
ect
ri
c fi
el
d i
n
t
e
nsi
t
y
at
any
p
o
i
n
t
(
x
, y
)
f
o
r
a
num
ber of
cha
r
ges (Q
j
)
ca
n be
cal
cul
a
t
e
d by
t
h
e fol
l
o
wi
n
g
e
quat
i
o
ns:
1
1
i
i
n
ij
xj
j
n
ij
yj
j
P
EQ
x
P
EQ
y
(8
)
The
res
u
lting e
l
ectric field at t
h
e
c
ont
ou
r
p
o
i
n
t
i
s
e
x
p
r
esse
d
by
:
22
ii
ix
y
E
EE
(9
)
In
th
e p
r
esen
ce o
f
a p
o
wer lin
e p
a
rallel to
o
n
aerial p
i
p
e
line, th
e v
o
ltag
e
s are in
du
ced
in
th
e p
i
p
e
line
t
h
r
o
u
g
h
t
h
e el
ect
ri
c fi
el
ds pr
od
uce
d
by
hi
g
h
v
o
l
t
a
ge po
w
e
r t
r
ansm
i
ssi
on l
i
n
es. The i
n
d
u
ce
d v
o
l
t
a
g
e
on t
h
e
metall
ic p
i
p
e
li
n
e
lo
cated
at (x
p, yp
)
d
u
e
to
cap
acitiv
e coup
lin
g
with
th
e
p
o
wer lin
es u
n
d
e
r
n
o
rm
al s
t
e
a
d
y
state
al
on
g t
h
e
ri
gh
t
-
of
-
w
ay
ha
ve
bee
n
cal
c
u
l
a
t
e
d
usi
n
g t
h
e
char
ge si
m
u
l
a
t
i
on m
e
t
hod
(
C
SM
). T
h
i
s
i
n
d
u
ce
d
vol
t
a
ge
i
s
gi
ve
n
by
t
h
e e
x
pres
si
on
[
10]
:
Radius
19.
05
m
m
0.
46 m
Radius
7.
5 m
m
10.
4 m
12.
2
m
20.
3 m
Radius
r
p
=0
.
3
m
25 m
h
p
=1 m
15.
9 m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ca
pa
citive
In
terferen
ces
Modelin
g
a
n
d
Op
timiza
tion
b
e
tween
HV
Po
wer Lin
e
s an
d
…
(Rab
ah
Djekid
e
l
)
49
0
'
'
1
1
ˆ
..
.
l
n
2
rD
n
in
d
i
r
j
j
o
rD
D
VE
r
a
Q
D
Whe
r
e:
'
D
is the distance from
the im
age
o
f
co
ndu
ctor
to
pip
e
lin
e,
D
is the distance fro
m
co
ndu
ctor
to
pi
pel
i
n
e. T
h
e e
a
rt
h i
s
assum
e
d t
o
be a pe
rfe
ct
cond
uct
o
r, s
o
that the im
ages are
the same distance below the
earth as
are
the
conductors a
b
ove
the ea
rth.
If a pers
o
n
t
o
u
c
hes a pi
pel
i
n
e
who
s
e v
o
l
t
a
ge
i
s
Vi
nd, t
h
e di
schar
g
e cu
rre
n
t
t
h
at
woul
d fl
ow t
h
ro
u
g
h
hi
s bo
dy
i
s
gi
v
e
n by
[
6
]
,
[2
3]
:
..
.
.
.
p
pp
i
n
d
Ij
C
L
V
(1
3)
Whe
r
e: L
p
is t
h
e len
g
t
h
o
f
th
e
p
i
p
e
lin
e
expo
sed
to cap
acitiv
e cou
p
ling
.
C i
s
th
e
p
i
p
e
lin
e’s cap
acitiv
e.
If t
h
e curre
nt is above the a
d
m
i
ssibl
e limit, the earth
resi
stance re
qui
re
d R
E
to reduce
the current
bel
o
w t
h
e a
d
m
i
ssi
bl
e l
i
m
i
t
,
appl
y
i
n
g
t
h
e
rel
a
t
i
ons
hi
ps ci
rc
ui
t
sy
st
em
sho
w
n i
n
Fi
g
u
r
e
4
,
we
have t
h
e e
quat
i
o
n
[6]
:
1
c
E
R
R
(1
4)
Whe
r
e: R
E
the
earth
resistanc
e
re
quire
d; R
c
i
s
th
e
bo
d
y
resi
stan
ce; ß is th
e ratio
.
I/
I
pa
d
m
ß
Fi
gu
re
4.
Tech
ni
cal
m
i
t
i
g
at
i
on:
g
r
ou
n
d
i
n
g
p
i
pel
i
n
e f
o
r
p
e
rs
onal
secu
ri
t
y
4.
PARTICLE SWARM OPTIMIZ
A
TION
PSO
o
p
t
i
m
i
zes an
o
b
j
ect
i
v
e
f
unct
i
o
n
by
un
de
rt
ak
ing
a
p
opu
latio
n-
b
a
sed
sear
ch
. The po
pu
lation
co
nsists o
f
po
ten
tial so
lu
tions, n
a
m
e
d
p
a
rti
c
les, wh
ich
are
a
m
e
taphor of birds in fl
oc
ks. Thes
e pa
rticles are
random
l
y initialized and
fre
ely fly acr
oss the m
u
ltidim
e
n
sional searc
h
space. During flight, eac
h particle
u
p
d
a
tes
its o
w
n
v
e
lo
city
and
p
o
s
ition
b
a
sed
o
n
th
e b
e
st
exp
e
rien
ce o
f
its o
w
n
and
th
e
en
tire p
opu
latio
n
.
The
up
dat
i
n
g
pol
i
c
y
dri
v
es t
h
e
pa
rt
i
c
l
e
swarm
t
o
m
ove t
o
war
d
t
h
e
regi
on
wi
t
h
t
h
e hi
gh
er
o
b
je
ct
i
v
e f
unct
i
o
n
val
u
e
,
an
d
ev
en
t
u
ally all p
a
rticles
will g
a
th
er aro
und
th
e
po
int with
th
e h
i
gh
est o
b
j
ectiv
e v
a
lu
e. Th
e
detailed
ope
rat
i
o
n
of
pa
rt
i
c
l
e
swarm
o
p
t
i
m
i
zat
i
on i
s
gi
ve
n
bel
o
w:
Step
1
:
In
itiali
zatio
n
.
Th
e v
e
lo
city an
d po
si
tio
n
o
f
a
ll p
a
rticles are rand
omly set to
with
in
pre-d
e
fi
ned
ran
g
es.
Step
2
:
Vel
o
city u
p
d
a
ting
at each
iteration
;
th
e
v
e
lo
cities of all p
a
rticles are up
d
a
ted
accord
i
n
g
to
:
11
,
2
2
,
.
.
.(
)
.
.(
)
ii
i
b
e
s
t
i
i
i
b
e
s
t
i
i
VW
V
c
R
P
P
c
R
g
P
(1
5)
Whe
r
e: P
i
a
n
d
are V
i
th
e
po
sitio
n
an
d v
e
l
o
city o
f
p
a
rticle i, resp
ectiv
ely; P
i,best
and g
i,best
, is th
e
p
o
sitio
n wit
h
th
e ‘b
est’ obj
ectiv
e v
a
lu
e
foun
d
so
far
b
y
particle i
an
d
the en
tire pop
u
l
atio
n
resp
ectiv
ely; W
is a p
a
rameter
co
n
t
ro
lling
th
e flyin
g
d
y
n
a
mics; R
1
and R
2
are ra
ndom
variables in t
h
e
range [0,
1]; c
1
and c
2
a
r
e factors
co
n
t
ro
lling
th
e related
weigh
t
in
g
o
f
correspon
d
i
n
g
term
s. Th
e in
cl
u
s
ion
o
f
rando
m
v
a
riables end
o
ws t
h
e PSO
with
th
e ab
ility o
f
sto
c
h
a
stic sear
ch
ing
,
t
h
e weigh
ting
facto
r
s, c
1
and
c
2
;
co
m
p
ro
m
i
se th
e in
ev
itab
l
e trad
e-o
ff
bet
w
ee
n ex
pl
o
r
at
i
on a
nd e
x
pl
oi
t
a
t
i
o
n
.
Aft
e
r u
pdat
i
n
g V
i
should
be checke
d
a
nd se
cure
d withi
n
a pre
-
speci
fi
ed
ra
n
g
e
t
o
a
voi
d
vi
ol
e
n
t
ra
n
dom
wal
k
i
n
g.
Step
3
:
Po
sition
Upd
a
ting
.
Assu
m
i
n
g
a
u
n
i
t
ti
m
e
in
terv
al
b
e
tween
su
ccessiv
e
iteration
s
, th
e
po
sitio
n
s
o
f
all p
a
rticles are up
d
a
ted
acco
r
d
i
ng
to
:
I
S
Z
P
R
E
V
P
R
C
I
c
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
48
6
–
49
7
4
91
1
ii
PP
V
(1
6)
After upd
atin
g, P
i
sh
ou
ld b
e
ch
eck
ed
and
limited
to
the allowed rang
e.
St
ep
4:
M
e
m
o
ry
up
dat
i
n
g.
U
p
dat
e
P
i,best
and g
i,best
, wh
en
con
d
ition
is m
e
t.
,,
,,
()
(
)
()
(
)
i
b
e
s
ti
i
i
i
b
e
s
ti
i
b
es
t
i
i
i
i
b
es
t
i
P
P
i
f
fP
fP
g
g
i
f
fg
fg
(1
7)
Wh
ere: f(x
) is th
e
o
b
j
ectiv
e fun
c
tio
n su
bj
ect t
o
m
i
n
i
mizatio
n
.
Step
5
:
Term
i
n
atio
n Ch
eck
i
n
g
. Th
e algorith
m
rep
eats Step
s
2
to 4
un
til certain
term
in
atio
n
co
nd
itio
ns
are m
e
t
,
such
a
s
a
pre
-
de
fi
ne
d
n
u
m
b
er o
f
i
t
e
r
a
t
i
ons
or
a
fai
l
u
re
t
o
m
a
ke
pr
og
ress
f
o
r
a ce
rt
ai
n
num
ber
o
f
iteratio
n
s
.
On
ce term
in
ated
, th
e algorith
m
rep
o
rts th
e v
a
l
u
es of
g
i,best
and f
(
g
i,best)
as its so
lutio
n
.
Est
i
m
a
t
i
on t
h
e num
ber o
f
ch
arges
usi
n
g P
S
O t
ech
ni
q
u
e
PSO m
e
nt
i
one
d ab
o
v
e i
s
use
d
t
o
sel
ect
param
e
ters of
CSM: the
Num
b
er of cha
r
ges,
whic
h a
r
e attrib
u
t
es o
f
each
p
a
rticle. In
PSO o
p
e
ratio
n,
t
h
e
fitn
ess fun
c
tion
o
f
th
e p
a
rticl
e
s
group
with
t
e
st cases
was e
v
aluated using
the E
q
.
(7).
C
onsi
d
er
fo
r t
h
e case st
udy
a
si
ngl
e ci
rc
ui
t
t
r
ansm
i
ssi
on l
i
n
e a 40
0 k
V
,
fre
que
ncy
o
f
t
h
e s
y
st
em
i
s
50
H
z
, t
h
e
p
h
a
se
co
ndu
ctor
s an
d gr
oun
d w
i
r
e
s
ar
e assu
m
e
d
par
a
llel to
a larg
e
f
l
at con
d
u
c
t
i
n
g
gr
oun
d p
l
an
e, t
h
e
geom
et
ri
cal
param
e
t
e
rs of t
h
e
l
i
n
e con
f
i
g
ura
t
i
on are s
h
ow
n
i
n
Fi
gu
re
3, t
h
e l
e
ngt
h
of
par
a
l
l
e
l
expos
ure
of t
h
e
metall
ic p
i
p
e
lin
e and
power l
i
n
e
is 4
k
m
, th
ick
n
e
ss of th
e i
n
su
lating
co
v
e
ring
of th
e p
i
pelin
e is co
n
s
i
d
ered
to
b
e
0
.
0
0
4
m
,
the relativ
e
p
e
rm
ittiv
ity o
f
th
e i
n
su
lating
cov
e
rin
g
is equ
a
l to
5
.
5.
R
E
SU
LTS AN
D ANA
LY
SIS
To ch
o
o
se the
better param
e
ters fo
r the P
S
O alg
o
ri
t
h
m
,
we have ca
rr
i
e
d out
m
a
ny
expe
ri
m
e
nt
s
rando
m
l
y, th
e p
a
ram
e
ters which
m
a
d
e
th
e fitn
ess v
a
lu
e
b
e
th
e sm
a
llest a
r
e cho
s
en
to
use in
th
is p
a
p
e
r, th
e
o
p
tim
u
m
p
a
rameters u
s
ed
in
th
e nu
m
e
rical calcu
latio
n
are
sh
own
in Tab
l
e 1
.
Tabl
e
1. C
h
ar
g
e
si
m
u
l
a
ti
on m
e
t
h
o
d
a
n
d
PS
O
Param
e
t
e
rs
m
e
thod Par
a
m
e
ter
s
PSO
nu
m
b
er of optim
ization var
i
ables (
6
var
i
ables )
N=20,
C
1
=C
2
=2, w
ma
x
=1.
40,
w
mi
n
=0.
20,
k
ma
x
=250.
CSM
range of fictitious
charges :2–30
r
a
nge for
R(
phase)
: 0.
01–0.
084
range for
R(
wir
e
)
:0.
001–0.
006
8
range for
R(
pipe)
:0.
1–0.
27
Fi
gu
re
5.
Ev
ol
vi
n
g
pr
ocess
o
f
PS
O al
g
o
r
i
t
h
m
wi
t
h
opt
i
m
um
param
e
t
e
rs
0
20
40
60
80
10
0
12
0
14
0
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
x 1
0
-1
3
It
e
r
at
i
o
nn nu
m
b
e
r
F
i
tn
e
ss v
a
lu
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ca
pa
citive
In
terferen
ces
Modelin
g
a
n
d
Op
timiza
tion
b
e
tween
HV
Po
wer Lin
e
s an
d
…
(Rab
ah
Djekid
e
l
)
49
2
The fi
t
n
ess
val
u
e nam
e
l
y
(Fg
)
gi
ven i
n
eq
u
a
t
i
on (
7
)
va
ri
es wi
t
h
t
h
e i
t
e
ra
t
i
on n
u
m
b
er as
sh
ow
n i
n
Fig
u
re
5
.
Th
e
ap
p
lication
resu
lts in
v
a
l
u
es
th
at fin
a
lly con
v
e
rg
e to
t
h
e
o
p
tim
u
m
v
a
lu
es are
d
e
tailed
in
the
Tabl
e
2.
Tabl
e
2. T
h
e
o
p
t
i
m
u
m
val
u
es
o
f
t
h
e
C
S
M
conductor
Fictitious
charges nu
m
b
e
r
Fictitious radius
[m
]
Fg
Phase conducto
r
3 0.
0716
1.
4422e-
0
1
6
Gr
ound wir
e
7
0.
0026
Pipeline
14
0.
2493
Th
e sim
u
latio
n resu
lts are sho
w
n
i
n
Figu
res 6 and
7
,
whe
r
e i
t
be
com
e
s ob
vi
ous
that t
h
e algorithm
con
v
e
r
ges
ra
pi
dl
y
t
o
t
h
e
s
e
val
u
es.
The
C
S
M
and
PS
O m
ode
l
were
co
nst
r
uc
t
e
d i
n
M
A
TL
A
B
7.
8
(R
0
0
9
a).
Figure
8 s
h
ows the c
o
m
puted elect
r
i
c f
i
eld p
r
of
iles at 1
m
abo
v
e
gr
oun
d
lev
e
l, w
ithou
t
an
d w
ith
t
h
e
prese
n
ce
of a
metal pipeline. We can
see from
the graph that the electric
field increases
from
the center point
of t
h
e line and it reaches its maxim
u
m
value at a trans
v
ers
e
distance e
q
ual
to 13 m
from this point.
Furt
her,
from
the conductors, the electric fiel
d st
rengt
h dec
r
eases
rapi
dl
y
wi
t
h
d
i
stance. The presence of the pipeline
h
a
s a si
g
n
i
fican
t effect on
the v
a
lu
e of th
e
electric field
at th
e po
sitio
n
wh
ere th
e p
i
p
e
lin
e is lo
cated. Th
is
fi
g
u
re s
h
o
w
s h
o
w a pi
pel
i
n
e
pert
ur
bs t
h
e electric field beneath a
power line. T
h
e field is reduced at the
top
of
th
e p
i
p
e
lin
e, bu
t in
creased aro
und
its sid
e
s.
Fig
u
re
6
.
Con
v
erg
e
n
ce
o
f
th
e
o
p
tim
u
m
v
a
lu
es of fictitio
u
s
ch
arg
e
s
nu
m
b
er (n
c,
ng
,n
p)
The
pert
urbed
electric field on the
pi
pel
i
ne l
o
cat
ed
at
di
ffe
rent
di
st
ances fr
om
t
h
e
t
r
ans
m
i
ssi
on
l
i
n
e
i
s
sho
w
n i
n
Fi
gu
re 9. It
can
be seen t
h
at
t
h
e
m
a
xim
u
m
elect
ri
c fi
el
d i
s
nearl
y
unde
r t
h
e
si
de con
duct
o
rs fo
r a
separat
i
o
n
di
st
ance eq
ual
t
o
13 m
.
Th
e e
l
ectric field unde
r the m
i
ddle
c
o
n
d
u
c
to
r
is
l
e
s
s
t
h
a
n
th
e
s
i
d
e
conductors.
The electric field
decr
ease
s
ra
pidly with the
dist
ance.
In
d
u
ced
v
o
l
t
a
g
e
s o
n
t
h
e
pi
pe
l
i
n
e l
o
cat
ed at
di
f
f
ere
n
t
di
st
a
n
ces
fr
om
t
h
e m
i
dpoi
nt
o
f
t
h
e l
i
n
e ha
ve
b
een calcu
lated
an
d th
e
resu
lt is g
i
v
e
n in
Figu
re 10
.
Th
e lateral d
i
stribu
tio
n
o
f
th
e
Indu
ced
v
o
ltage is b
r
o
a
d
l
y similar to
th
at o
f
th
e electric fie
l
d
sho
w
n
in
Fig
u
re
9
.
For t
h
is ex
am
p
l
e, th
e Ind
u
c
ed
vo
ltag
e
on
t
h
e
p
i
pelin
e du
e to the vo
ltag
e
4
0
0
KV on
th
e power line
is equ
a
l to
1
.
91
KV.
We can
also
o
b
s
erv
e
th
at th
e ind
u
c
ed
v
o
ltage
b
e
co
m
e
s al
m
o
st n
e
g
lig
ib
le at a critical
distance. It is
suggeste
d t
h
at the
pi
pel
i
n
e c
oul
d
be l
o
cat
e
d
cl
ose t
o
t
h
e
cr
itical distanc
e
so that t
h
e i
n
duce
d
vol
t
a
ge
w
o
ul
d
be cl
o
s
e t
o
zer
o.
The b
o
d
y
cur
r
e
nt
of i
n
fl
ue
nc
e i
n
a pers
on t
ouc
hi
n
g
t
h
e
pi
pel
i
n
e l
o
cat
ed
at
di
ffere
nt
di
s
t
ances fr
om
t
h
e m
i
dpoi
nt
o
f
t
h
e l
i
n
e i
s
sh
ow
n i
n
Fi
g
u
r
e
11
.
We n
o
t
i
ced f
r
om
t
h
e res
u
l
t
i
f
t
h
e i
n
d
u
c
e
d
vol
t
a
ge
bec
o
m
e
s
v
e
ry in
tense in
th
e p
i
p
e
lin
e, so
th
e indu
ced
curren
t
also increa
ses. T
h
e curre
nt on the pipeline
by the
cap
acitiv
e co
up
lin
g
is 71
.1
6
(m
A) , th
is v
a
lu
e is
m
u
ch
h
i
g
h
e
r th
an
th
e
p
e
rm
issib
l
e safety v
a
lu
e wh
ich
can
flow th
rou
g
h
t
h
e bod
y of a
p
e
rson
in
con
t
act with
th
e
p
i
p
e
lin
e
u
n
d
e
r stead
y state con
d
ition
s
wh
ich is 1
0
(m
A) fo
r adu
lt males.
There
f
ore, t
h
e
pi
pel
i
n
e m
u
st
be g
r
o
u
n
d
e
d t
h
ro
u
gh a
d
e
quat
e
st
ren
g
t
h
t
y
pi
cal
l
y
of t
h
e o
r
der
of a
few
hundre
d
ohm
s
.
Acc
o
rding t
o
t
h
e
Am
erican standa
rd I
EEE
80:2000, the
overall resistance
of the
hum
a
n body
0
20
40
60
80
10
0
12
0
14
0
0
5
10
15
20
25
30
35
40
45
Fi
c
t
i
t
i
o
us
c
h
a
r
g
e
num
be
r
I
t
e
r
at
i
o
n num
be
r
n (
p
ha
s
e
)
n (
w
i
r
e
)
n (
p
i
p
e
)
n(
t
o
t
a
l
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
48
6
–
49
7
4
93
is u
s
u
a
lly tak
e
n
equ
a
l to
1
000
Ω
[2
1]
, i
n
t
h
i
s
exam
pl
e
t
h
e pi
pel
i
n
e w
oul
d ge
neral
l
y
be
eart
h
ed t
h
r
o
u
gh a
n
resistance
equal to:
1000
71.
16
10
1
163.
5
g
R
Fig
u
re
7
.
Con
v
erg
e
n
ce
o
f
th
e
o
p
tim
u
m
v
a
lu
es of fictitio
u
s
rad
i
u
s
(rc,
rg,rp)
Fi
gu
re 8.
Electric Field
p
r
ofile at 1
m
ab
ov
e
th
e gro
und
with
an
d withou
t th
e
p
i
p
e
lin
e
Fi
gu
re 9.
Pert
u
r
be
d
Electric
Field
on
th
e
p
i
pelin
e
R
e
si
st
ance of
gr
o
u
n
d
i
n
g (Ea
r
t
h
i
n
g
)
t
h
e
pi
pe
l
i
n
e as a fu
nct
i
on
of t
h
e h
o
ri
z
ont
al
p
r
o
x
i
m
i
t
y
di
st
ance of
p
i
p
e
lin
e is show
n in
Figu
r
e
12
.
0
20
40
60
80
10
0
12
0
14
0
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
I
t
e
r
at
i
o
n num
be
r
F
i
c
t
itio
u
s
r
a
d
i
u
s
R (
p
h
a
s
e
)
R (
w
i
r
e
)
R (
p
ip
e
)
0
10
20
30
40
50
60
70
80
90
10
0
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
L
a
te
ra
l
d
i
s
t
a
n
c
e
(x
)
[
m
]
E
l
e
c
tr
ic field
[K
V
/
m
]
W
i
tho
u
t p
i
p
e
l
i
ne
Wit
h
p
i
p
e
l
i
n
e
0
10
20
30
40
50
60
70
80
90
10
0
0
0.
5
1
1.
5
2
2.
5
P
i
p
e
lin
e
p
o
s
i
t
i
o
n
f
r
o
m
t
h
e
c
e
n
t
e
r
o
f
t
r
a
n
s
m
is
s
i
o
n
lin
e
[
m
]
E
l
ect
ri
c F
i
el
d
[
K
V
/
m
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ca
pa
citive
In
terferen
ces
Modelin
g
a
n
d
Op
timiza
tion
b
e
tween
HV
Po
wer Lin
e
s an
d
…
(Rab
ah
Djekid
e
l
)
49
4
Fo
r safety p
r
ob
lem
s
d
u
r
in
g
p
i
p
e
lin
e co
n
s
t
r
u
c
tio
n, th
e imp
o
rtan
t p
a
rameter is th
e cu
rren
t p
a
ssing
th
ro
ugh
th
e
human
bo
d
y
i
n
case of
a direct contact with
the
pipeline
,
the
adm
i
ssible body current i
n
ste
a
dy-
st
at
e operat
i
o
n
as defi
ne
d by
t
h
e nat
i
o
nal
re
gul
at
i
o
ns.
In
o
r
de
r t
o
ens
u
re t
h
ere i
s
n
o
ri
sk
of el
ect
ri
c sh
o
c
k, a
safe se
paration
distance
bet
w
een the
pipeline and th
e po
wer lin
e is req
u
i
red, the min
i
m
u
m
d
i
stan
ce
recom
m
ended
by
IPS
st
an
dar
d
[
24]
,
fo
r a t
r
ansm
i
ssi
on l
i
n
e of
40
0
kV si
ngl
e ci
rc
ui
t
s
;
t
h
i
s
di
st
ance i
s
equal
t
o
60
M
e
t
e
r.
Fig
u
re
10
.
Indu
ced vo
ltag
e
on
an
insu
lated
p
i
p
e
lin
e
Fig
u
r
e
11
. C
u
rr
en
t i
n
th
e body d
u
r
i
ng
a con
t
act w
ith
the
p
i
p
e
lin
e
Fig
u
re 12
.
Cal
c
u
l
atio
n
of
th
e earth
ling
resistan
ce
0
10
20
30
40
50
60
70
80
90
10
0
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
Pi
p
e
l
i
n
e
p
o
s
i
ti
on
f
r
om
t
h
e
m
i
d
p
o
i
n
t
of
t
r
a
n
sm
i
s
si
on
l
i
n
e
[
m
]
I
n
d
u
ced
vo
l
t
age
[k
V
]
0
10
20
30
40
50
60
70
80
90
10
0
0
20
40
60
80
10
0
12
0
14
0
16
0
18
0
P
i
pe
l
i
ne
p
o
s
i
t
i
o
n
f
r
o
m
t
h
e
m
i
d po
i
n
t
o
f
t
r
ans
m
i
s
s
i
o
n
l
i
ne
[
m
]
Cu
r
r
e
n
t
[
m
A]
0
5
10
15
20
25
30
35
40
45
0
10
00
20
00
30
00
40
00
50
00
60
00
70
00
80
00
90
00
100
00
X:
2
5
Y
:
16
3.
5
P
i
pe
l
i
ne
p
o
s
i
t
i
o
n
f
r
o
m
t
h
e
m
i
d po
i
n
t
o
f
t
r
ans
m
i
s
s
i
o
n
l
i
ne
[
m
]
E
a
rth
i
n
g
resi
s
tan
c
e of
t
h
e P
i
p
e
l
i
n
e [
O
h
m
s]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 4
,
Au
gu
st 2
014
:
48
6
–
49
7
4
95
Fi
gu
re 1
3
s
h
o
w
s t
h
e si
m
u
l
a
t
i
on res
u
l
t
s
o
b
t
ai
ned f
o
r t
h
e
val
u
es
of m
i
nim
u
m
di
st
ances fr
om
t
h
i
s
app
r
oach
, m
i
n
i
m
u
m
val
u
es of
di
st
ance i
n
di
cat
ed i
n
t
h
i
s
fi
gu
re t
e
n
d
t
o
ra
nge
fr
om
45 t
o
6
5
M
e
t
e
r;
t
h
e
m
i
nim
u
m
di
st
ance
recom
m
ended
by
t
h
i
s
st
a
nda
r
d
i
s
l
o
cat
e
d
i
n
t
h
i
s
ran
g
e.
To
v
a
lid
ate the m
o
d
e
llin
g
in
th
is
stud
y, th
e sim
u
latio
n
resu
lts are com
p
ared
with
ex
p
e
rim
e
n
t
al
resul
t
s
p
ubl
i
s
h
e
d
by
t
h
e
I
n
t
e
r
n
at
i
onal
C
I
GR
E
Wor
k
i
n
g
G
r
ou
p
3
6
.
0
2
[
6
]
.
We
hav
e
s
h
o
w
n i
n
Fi
gure
14
,
a b
e
st
agreem
ent bet
w
een the
res
u
lts obta
i
n
e
d
by
C
S
M
-
PS
O m
odel
an
d t
h
e
CI
GRE Gr
ou
p
.
We can t
h
ere
f
ore c
o
nclude that the propos
ed m
odel has
been
succes
sfully used t
o
sim
u
la
te and
m
o
d
e
l b
o
t
h
the co
nd
ucto
rs of th
e tran
sm
issio
n
lin
es and
t
h
e pipelines, a
l
so as to
evaluate the calculation of
th
e electric field
,
th
e cap
acitiv
e coup
lin
g
b
e
tween
th
e el
ectrical p
o
wer li
n
e
s an
d
p
i
p
e
li
n
e
s sh
ari
n
g
t
h
e same
corridor.
Fi
gu
re
1
3
. M
i
n
i
m
u
m
hori
z
ont
al
spaci
n
g
bet
w
een
pi
pel
i
n
e
and
pa
ral
l
e
l
o
v
e
rhea
d
p
o
we
r l
i
ne
(a)
(b
)
Fig
u
re
14
. C
o
m
p
ariso
n
o
f
the resu
lts b
e
t
w
een
th
e CSM-PSO m
o
d
e
l an
d
th
e CIGRE m
e
th
od
Ref.
[6
]
a:
B
ody
c
u
r
r
e
n
t
per
km
a per
s
on
t
o
uchi
ng
t
h
e pi
pel
i
n
e,
b:
I
n
d
u
ce
d
vol
t
a
ge
o
n
t
h
e
pi
pel
i
n
e
6.
CO
NCL
USI
O
N
In
th
is p
a
p
e
r, a PSO techn
i
qu
e is u
s
ed
to
d
e
term
in
e th
e
ap
pro
p
riate arran
g
e
m
e
n
t
o
f
fictitio
u
s
charges in charge sim
u
lati
on m
e
thod (CSM
), thus the CSM
-
PS
O m
odel is
propose
d
to est
i
m
a
te the capacitive
co
up
ling
o
n
aerial
m
e
tall
ic
p
i
p
e
lin
es op
erati
n
g
n
e
ar po
wer lin
es.
Fro
m
th
e calcu
latio
n
resu
lts, we no
ticed
th
at th
e p
r
o
f
ile
of the field electric with
the presence of the
pipeline
has
bee
n
m
odi
fied c
o
m
p
ared
to the
origi
n
al
figure. It is
cle
a
r that
the
pres
ence
of
th
e p
i
pelin
e in
t
h
e
v
i
cin
i
t
y
of
powe
r line
causes the
di
stortion of the
electric fi
eld on t
h
e pipeline surfac
e
due to electric charges
accum
u
lated in the
pipeline
.
Th
e indu
ced
v
o
ltag
e
s du
e to
cap
acitiv
e co
up
ling
on
aerial
m
e
tall
ic p
i
p
e
lin
es h
a
v
e
been
co
m
p
u
t
ed
using t
h
e CSM
-
PSO m
odel.
It
is seen that t
h
e induce
d
vo
ltag
e
is
propo
rtio
n
a
l t
o
t
h
e electrical field
.
Ind
u
c
ed
45
50
55
60
65
5
6
7
8
9
10
11
12
13
14
15
V
a
l
u
e
s
o
f
mi
n
i
mu
m d
i
s
t
a
n
c
e
s
[
m
]
M
a
x
i
m
u
m
pe
r
m
i
s
s
i
bl
e
bo
dy
c
u
r
r
e
nt
[
m
A
]
-10
0
-90
-8
0
-70
-6
0
-50
-4
0
-3
0
-2
0
-1
0
0
0
5
10
15
20
25
30
35
Pi
p
e
l
i
n
e
p
o
s
i
ti
on
f
r
om
t
h
e
a
x
i
s
of
t
h
e
l
i
n
e
[
m
]
B
o
d
y
cu
rr
en
t p
e
r K
m
o
f
i
n
fl
u
e
n
c
e
a
t
50
H
z
[m
A
/
k
m
]
CS
M
-
P
S
O
CI
G
R
E
0
10
20
30
40
50
60
70
80
90
10
0
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
Pi
p
e
l
i
n
e
p
o
s
i
t
i
on
f
r
om
th
e c
e
n
t
er
of
t
r
a
n
s
m
i
s
s
i
on
l
i
n
e
[
m
]
I
nduc
e
d
v
o
l
t
a
g
e
[
K
V
]
CS
M
-
P
S
O
CI
G
R
E
Evaluation Warning : The document was created with Spire.PDF for Python.