TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3381 ~ 33
9
1
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.5151
3381
Re
cei
v
ed
No
vem
ber 1
5
, 2013; Re
vi
sed
De
cem
ber 3,
2013; Accept
ed De
cem
b
e
r
21, 2013
Magnetic Field Calculation under Normal and Abnormal
Conditions of Overhead Transmission Lines
Naga
t M. K. Abdel
-
Ga
w
a
d
1
, Adel Z. El
Dein*
2
, Mohamed Magdy
1
1
F
a
cult
y
of Eng
i
ne
erin
g at Sho
ubra, Ben
ha U
n
iversit
y
, Ca
iro
,
Eg
y
p
t
2
F
a
cult
y
of Ene
r
g
y
E
ngi
ne
erin
g, As
w
a
n Un
iv
ersit
y
, As
w
a
n, Eg
ypt
*Corres
p
o
ndi
n
g
author, em
ail
:
azeinm2
0
0
1
@
hotmai
l
.com
Ab
stra
ct
Ground lev
e
l magn
etic
fie
l
d
fro
m
overh
e
a
d
tra
n
smi
ssio
n
l
i
nes
(OHT
Ls) is of i
n
creas
ing
l
y i
m
portan
t
consi
derati
ons
in severa
l res
earch ar
eas d
ue to their h
a
r
m
ful
effect on hu
ma
n he
alth
and e
n
vir
o
n
m
e
n
t.
T
h
is p
aper
co
mp
utes th
e
gr
oun
d l
e
ve
l
ma
gnetic
fiel
d, u
n
der
nor
ma
l
an
d a
b
n
o
rmal
co
nditi
ons
of Egy
p
tia
n
500-kV si
ngl
e circuit trans
mi
ssion li
ne, in t
h
ree d
i
m
ens
io
n (3-D) coord
i
nates by usi
n
g 3-D inte
grati
o
n
techni
qu
e. Ab
nor
mal c
o
n
d
iti
ons inc
l
u
de sy
mmetric fa
ul
t, un-sy
mmetric f
aults, dire
ct st
roke, and indir
e
ct
stroke o
n
th
e
OHT
L
. W
here,
AT
P softw
are
is
use
d
to
si
mu
late
the
OH
T
L
un
der
al
l f
aulty
an
d l
i
g
h
tnin
g
cond
itions. V
a
rying ti
me
ma
gnetic fi
elds
u
nder
nor
ma
l a
nd a
b
n
o
rmal c
ond
itions,
at certain
poi
nts that
locate
d at mid-
span, tow
e
r he
ight an
d rig
h
t-of-w
ay (R
OW
), are also c
o
mputed th
at to indic
a
te the w
o
rst
case.
Ke
y
w
ords
: ma
gnetic fie
l
d, ov
erhe
ad trans
mi
ssion li
ne, n
o
rma
l
an
d ab
nor
ma
l con
d
itio
ns, right-of-w
a
y.
Copy
right
©
2014 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
Con
s
id
era
b
le
rese
arch a
nd publi
c
attention trigg
e
r
ed a we
alth
of resea
r
ch
efforts
focu
sed
on
th
e evalu
a
tion
of mag
netic fields p
r
o
d
u
c
e
d
b
y
o
v
er
he
ad
tr
an
s
m
iss
i
on
lin
es
(
O
H
T
L
s
)
to insu
re
the
safety for h
u
man
health
whi
c
h i
s
re
comm
end
ed
by wo
rld h
e
a
lth organi
za
tion
(WHO
) a
nd A
m
eri
c
an
conf
eren
ce
of g
o
vernm
ental
in
d
u
strial
hygie
n
i
s
ts
(ACGIH) [1-4]. There are
many
researche
s
deal with
the calcu
l
ation
of
the
magn
etic fi
eld un
de
r n
o
rmal
ope
rat
i
ng
con
d
ition
of the O
H
T
L
. An
analytical
cal
c
ulatio
n
of th
e ma
gnetic fi
eld p
r
od
uced
by OHTL
s, which
is suita
b
le fo
r flat, vertical, or delta a
rrangem
ent co
mputed by complex vecto
r
method
wa
s
prod
uced i
n
[
5
-6]. Th
e e
s
ti
mation
of the
mag
netic fiel
d de
nsity at
points lo
cate
d un
der a
nd
far
from the t
w
o
parall
e
l tra
n
smissi
on lin
es
with diffe
rent desi
gn config
uration
s
wa
s pre
s
ente
d
in
[
7
-
8]. In this pa
per, th
e time
varying m
agn
etic fiel
d
s
at
spe
c
ific poi
nts a
r
e
calculat
ed u
nde
r
normal
and ab
normal
conditio
n
s of
Egyptian 500
kV OHTL.
Und
e
r n
o
rm
a
l
con
d
ition
s
, the effect of
different p
e
rcenta
g
e
s
of
load
curre
n
t on the
cal
c
ulate
d
m
agneti
c
field
i
s
inve
stigate
d
. As
well
a
s
, unde
r
abn
o
r
mal
co
nditio
n
s, the
different
type of faults and lightni
ng,
such as:
sin
g
le pha
se to
grou
nd fault, doubl
e pha
se
to groun
d fault,
pha
se to ph
ase fault, three
-
ph
ase to groun
d f
aul
t, direct stro
ke, and in
di
rect
stro
ke
are
investigated.
In this pape
r, the time varying magn
etic
fields
are cal
c
ulate
d
at three different p
o
ints: 1)
unde
r mi
d-sp
an, 2
)
u
nde
r
tower h
e
ight,
and
3
)
at
rig
h
t-of-way, tha
t
to e
s
timate
the worst
ca
se.
Also in
this p
aper,
the
3-D integration t
e
ch
niqu
e
i
s
u
s
ed
[9], wh
ere the
effect o
f
the cond
uct
o
r’
s
sag i
s
take
n into con
s
id
era
t
ion.
2. Magne
tic
Fie
l
d
Calculati
ons
By using
the
3-D Integ
r
atio
n Te
chni
que,
whi
c
h
explain
ed in
detail
in
[9] and
is re
viewe
d
here, the m
a
gnetic field, p
r
odu
ce
d by a
multipha
se condu
ctors (
M
) and thei
r im
age
s, in su
pp
ort
stru
ctures
at any field poi
nt
P(x
o
,y
o
,z
o
)
sho
w
n in
Fig
u
re 1,
can b
e
obtaine
d b
y
using the
Biot-
Savart law as follow [9-10]:
The
exact
sh
ape
of a
co
n
ducto
r
su
spe
nded
bet
wee
n
two
towers
of equ
al h
e
ig
ht ca
n b
e
descri
bed by
such param
eters; a
s
the distan
ce bet
wee
n
the poi
nts of su
spe
n
sio
n
spa
n
L
, the
sag of the co
ndu
ctor
S
, the height of the lowe
st poin
t
above the groun
d
h
, and
the height of the
highe
st point above the gro
und hm, wh
ere
h
m
–
h
=
S
.
Only two parameter
s are need
ed in order
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3381 – 33
91
3382
to define the shape of the catena
ry (
S
and
L
), while the third
one (
h
or
h
m
), determine
s its
locatio
n
in rel
a
tion to the ground
surfa
c
e.
Figure 1. Application of Bio
t
-S
avart Law i
n
Thre
e Dime
nsio
ns
Figure 2 sho
w
s the ba
si
c caten
a
ry geo
metry for
a si
ngle co
ndu
ct
or line, this g
eometry is
descri
bed by
the followin
g
equatio
n:
α
z
α
h
y
2
sinh
2
2
(1)
Whe
r
e
α
is the sol
u
tion of
the transcen
dental eq
uati
on:
α
L
α
h
h
4
sinh
2
2
m
The pa
ram
e
ter
α
is al
so a
s
soci
ated wit
h
the mechan
ical pa
ram
e
te
rs of the lin
e,
α
= T
h
/
w
wh
ere
T
h
is the cond
ucto
r tensio
n at mid-span a
nd
w
is the weig
ht per-unit len
g
th of the line.
M
K
N
N
n
L
L
z
k
z
y
k
y
x
k
x
o
dz
a
H
a
H
a
H
H
1
2
/
2
/
)
(
)
(
)
(
4
1
(2)
Whe
r
e,
k
o
k
k
o
k
k
o
k
k
o
k
k
x
d
y
y
z
nL
z
z
I
d
y
y
z
nL
z
z
I
H
`
)
2
(
)
sinh(
)
(
)
(
)
sinh(
)
(
)
(
(3)
k
o
k
k
k
o
k
k
k
y
d
x
x
I
d
x
x
I
H
`
)
(
)
(
)
(
(4)
k
k
o
k
k
k
k
o
k
k
k
z
d
z
x
x
I
d
z
x
x
I
H
`
)
sinh(
)
(
)
sinh(
)
(
)
(
(5)
2
/
3
2
2
2
)
(
)
(
)
(
nL
z
z
y
y
x
x
d
o
o
k
o
k
k
(6)
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TELKOM
NIKA
ISSN:
2302-4
046
Magneti
c
Fiel
d Cal
c
ulation
unde
r No
rm
al
and Abno
rm
al… (Nagat
M.
K. Abdel-Gawad)
3383
2
/
3
2
2
2
`
)
(
)
2
(
)
(
nL
z
z
y
y
x
x
d
o
o
k
o
k
k
(7)
x
a
Unit vector in
X-dire
ction,
y
a
Unit vector in
Y-dire
ction,
z
a
Unit vector in
Z-dire
ction.
The
ζ
is the
compl
e
x de
pth of ea
ch
co
ndu
ctor
’
s
ima
ge current which ca
n
b
e
f
ound as
given in [10-1
1
].
4
/
2
j
e
,
f
503
Whe
r
e:
δ
is the skin d
epth of the ea
rth,
ρ
is the re
si
stivity of the earth, and
f
is the freque
ncy of the so
urce cu
rrent in Hz
The p
a
ra
met
e
r
(
N
) in E
q
u
a
tion (2)
re
prese
n
ts th
e n
u
mbe
r
of
spa
n
s to th
e
righ
t and to
the left from the gen
eri
c
on
e whe
r
e
n
=0
as sho
w
n in
Figure 2.
Figure 2. Line
ar Dim
e
n
s
ion
s
whi
c
h
Determine Para
me
ters of the Ca
tenary
3. Resul
t
s
and
Discus
s
ion
The d
a
ta u
s
e
d
in the
calcu
l
ation of the
magneti
c
fiel
d de
nsity at p
o
ints
one
met
e
r a
bove
grou
nd level
(field poi
nts), unde
r Egypti
an 50
0-kV tra
n
smi
ssi
on
-lin
e sin
g
le
circu
i
t are p
r
e
s
ent
ed
in appe
ndix (A).
Figure 3. Three Phase 50
Hz Sinu
soi
dal
Current
s und
er No
rmal
Co
ndition
0
0.
0
2
0.
0
4
0.
0
6
0.
08
0.
1
0.
1
2
-
1
000
-500
0
500
1
000
V
a
r
i
at
i
o
n
of
t
i
m
e
(
S
ec.
)
P
has
e cu
r
r
e
nt
s
(
A
)
pha
s
e
A
pha
s
e
B
pha
s
e
C
X
Original span
L2
L
L1
n
=
-1
n
=
0
P1
P2
n
=
1
h
s
Y
h
m
-L/2
L/
2
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3381 – 33
91
3384
The pha
se
-condu
ctor
cu
rrents
are defi
ned by a bal
anced direct
-seq
uen
ce three-p
h
a
s
e
set
of 50 Hz
sin
u
soidal currents, with 665-A
rm
s, a
r
e
sho
w
n
in
Figure 3
and
define
d
by t
h
e
followin
g
equ
ation:
3
/
2
3
/
2
;
;
1
665
j
j
p
e
e
I
A
(8)
3.1. Case (A): Magne
tic Field Under
Normal Condi
tion
Figure 4 and
5 sho
w
s the
effect of the variati
on
of the load capa
city
of the OHTL
system
(
I
p
) on th
e calcul
ated ma
gnetic fiel
d d
ensity un
der mid-spa
n
a
nd un
der to
wer heig
h
t a
nd a
distan
ce
awa
y
from the
ce
nter p
h
a
s
e, resp
ective
ly. It is n
o
tice
d th
at, the magn
etic field
den
sity
decrea
s
e
s
wit
h
the decrea
s
e of the load cap
a
city.
Figure 4. Effect of Load Cu
rre
nt on the Magneti
c
Fiel
d Den
s
ity at Point (P1) un
der Mid
-
span
Acco
rdi
ng to
[12], the valu
e of ma
gneti
c
field
den
sit
y
at right
-of-way i
s
ta
ken
to be
in
rang
e from 6.
5 to 1.7 µ.T.
In this pape
r, the
RO
W is a
s
sumed to be
equal 25 m from the cent
er
pha
se [13]. From Fig
s
. 4 and 5 it is noticed that
the magneti
c
field den
sity at
RO
W equ
als
5.3
µ.T under mi
d-span a
nd 4.
55 µ.T unde
r tower h
e
ight, respe
c
tively.
Figure 5. Effect of Load Cu
rre
nt on the Magneti
c
Fi
el
d Den
s
ity at Point (P2) un
der To
we
r He
ight
Figure 6 sho
w
s the time v
a
riation
of the cal
c
ulate
d
magneti
c
fiel
d den
sity at mid-p
o
int
unde
r the
ce
nter p
h
a
s
e
a
nd at
RO
W,
unde
r the
mi
d-span
(point
P1)
and
und
er the
tower
height
(point P2
). It is noti
c
ed th
at the maximu
m values
of the calculated
magneti
c
fiel
d den
sitie
s
o
c
cur
unde
r the mid
-
sp
an.
-5
0
-4
0
-30
-2
0
-1
0
0
10
20
30
40
50
0
5
10
15
20
D
i
s
t
an
ce f
r
om
t
h
e
c
e
n
t
er
ph
as
e
(
m
)
M
a
g
net
i
c
f
i
e
l
d de
ns
i
t
y
(
µ
.
T
)
P
1
-
f
u
ll
lo
a
d
P
1
-
90%
f
u
l
l
l
oad
P
1
-
70%
f
u
l
l
l
oad
P
1
-
hal
f
l
oad
-5
0
-40
-3
0
-20
-1
0
0
10
20
30
40
50
0
2
4
6
8
10
D
i
st
an
c
e
f
r
om
t
h
e c
e
n
t
er
ph
ase (
m
)
M
agn
et
ic
f
i
eld
dens
it
y
(
µ
.
T
)
P
2
-
f
u
ll
lo
a
d
P
2
-
9
0
%
f
u
ll
lo
a
d
P
2
-
7
0
%
f
u
ll
lo
a
d
P
2
-
h
a
lf
lo
a
d
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Magneti
c
Fiel
d Cal
c
ulation
unde
r No
rm
al
and Abno
rm
al… (Nagat
M.
K. Abdel-Gawad)
3385
Figure 6(a
)
. Varying Time
Magneti
c
Fiel
d
Den
s
ity unde
r Mid-spa
n
(p
oint P1) und
e
r
Normal Condi
tion
Figure 6(b
)
. Varying Time
Magneti
c
Fiel
d
Den
s
ity unde
r Tower
Heig
ht (point P2)
and at
RO
W (p
oint P1, P2) unde
r No
rmal Con
d
ition
3.2. Case (B): Magne
tic Field under Fa
ult Condi
tions
In ca
se
(B),
the ATP
so
ftware i
s
used to
simul
a
te the O
H
TL
unde
r
different fault
c
o
nditions
[14]. The fault is
c
l
eared after the time
th
at is taken
by t
he p
r
ote
c
tion
device.
The
time
of the protecti
on device is
divided into h
i
gh voltage SF
6
circuit bre
a
ke
r brea
king
time that equals
40 mse
c
. (2
cycle
)
[15], and the nume
r
ical dista
n
ce relay time, which eq
ual
s 1
2
mse
c
[16]. So,
the total fault
cle
a
rin
g
tim
e
eq
ual
s 5
2
mse
c
.
Hen
c
e
,
the fault i
s
assume
d to
be o
c
curre
d
at
instant
equ
al
s 0.0
3
se
con
d
an
d i
s
clea
red afte
r the
time that i
s
ta
ken by th
e p
r
ot
ection
devi
c
e,
at
instant equ
al
s 0.082 seco
nd. The effects of various
types of faults on the time varying mag
n
e
t
ic
field den
sity are studi
ed in this sectio
n.
3.2.1. Single
Phase to G
r
ound Fault
Figure 7 sho
w
s th
e thre
e pha
se si
nu
so
idal
cu
rrents
unde
r si
ngle
pha
se to g
r
o
und fault
on pha
se A, [0.03:0.082] sec, wh
ere, th
e maximu
m value of the fault current ten
d
s to be 11
kA.
Figure 8
sh
o
w
s th
e time
varying ma
g
netic fi
eld
de
nsitie
s, du
rin
g
the
singl
e
pha
se to
grou
nd fa
ult, at mid-p
o
int (unde
r the
ce
nter p
h
a
s
e)
a
nd at
RO
W u
nder both
mid-span
(p
oint
P1)
and tower
he
ight (poi
nt P2), re
spe
c
tivel
y
. It is seen that the maxi
mum value o
f
magnetic fi
eld
den
sity, durin
g the fault period [0.03:0.08
2] se
c., und
er mid-span (po
i
nt P1), equal
s 170 µ.T.
Figure 7. Three Phase Sin
u
soi
dal Curre
n
ts
unde
r Single
Phase to G
r
o
und Fault
Figure 8. Time Varying Ma
gnetic Fiel
d Density
at Mid-poi
nt and at RO
W u
nder Mi
d-spa
n
and
unde
r To
wer
Heig
ht (point
P1, P2) unde
r
Single Pha
s
e
to Groun
d Fault
3.2.2. Doubl
e Phase to G
r
ound Faul
t
Figure 9 sh
o
w
s the th
ree
pha
se si
nu
so
idal
cu
rrents
unde
r dou
ble
phase (A an
d B) to
grou
nd fault, [0.03:0.082] sec, wh
ere, th
e maxi
mum value of fault current tend
s to be 20
kA.
0
0.
02
0.
04
0.
06
0.
08
0.
1
0.
1
2
16
16
.
5
17
17
.
5
18
18
.
5
19
V
a
ri
a
t
i
o
n
o
f
ti
me
(S
e
c
.)
M
a
gne
t
i
c
f
i
el
d
de
ns
i
t
y
(
µ
.
T
)
P
1
at
m
i
d-s
p
an
0
0.
02
0.
04
0.
06
0.
08
0.
1
0.
12
0
2
4
6
8
10
V
a
r
i
at
i
o
n
of
t
i
m
e
(
S
ec
.
)
M
a
gne
t
i
c
f
i
el
d
de
ns
i
t
y
(
µ
.
T
)
P
2
at
t
o
w
e
r
hei
ght
P1
a
t
R
O
W
P2
a
t
R
O
W
0
0.
02
0.
04
0.
06
0.
08
0.
1
0.
1
2
-15
-10
-5
0
5
10
15
V
a
ri
a
t
i
o
n
o
f
ti
me
(S
e
c
.)
P
h
as
e c
u
r
r
ent
s
(
k
A
)
ph
as
e A
ph
as
e B
ph
as
e C
0
0.
02
0.
0
4
0.
0
6
0.
08
0.
1
0.
12
0
50
10
0
15
0
20
0
V
a
r
i
at
i
o
n
of
t
i
m
e
(
S
ec
.
)
M
agne
t
i
c
f
i
el
d d
ens
i
t
y
(
µ
.
T
)
P
1
at m
i
d-
s
pan
P
2
at t
o
w
e
r
he
i
g
ht
P1
a
t
R
O
W
P2
a
t
R
O
W
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3381 – 33
91
3386
Figure 1
0
sh
ows the
time
varying
mag
netic
fiel
d de
nsitie
s, du
rin
g
the
doubl
e
pha
se to
grou
nd fa
ult, at mid-p
o
int
(unde
r the
ce
n
t
er ph
ase)
an
d
at
ROW, un
der bot
h mi
d-spa
n
(point P
1
)
and tower
he
ight (poi
nt P2), re
spe
c
tivel
y
. It is seen that the maxi
mum value o
f
magnetic fi
eld
den
sity, durin
g the fault period [0.03:0.08
2] se
c, un
der
mid-spa
n
(poi
nt P1), equal
s 430µ.T.
Figure 9. Three Phase Sin
u
soi
dal Curre
n
ts
unde
r Do
uble
Phase to Ground Fa
ult
Figure 10. Time Varying
Magneti
c
Fiel
d
Den
s
ity at Mid-poi
nt and at
ROW u
nde
r
Mid-
spa
n
and u
n
d
e
r To
wer
Hei
ght (point P1,
P
2)
unde
r Do
uble
Phase to Ground Fa
ult
3.2.3. Phase to Phase F
a
ult
Figure
11
sh
ows the
thre
e ph
ase
sinu
soid
al
curre
n
ts u
nde
r
pha
se to p
h
a
s
e
(A and
B)
fault, for a period [0.03:0.0
82] se
c, whe
r
e, the
maximum value of fault curre
n
t tends to be 1
8
kA.
Figure 12 sh
ows the time varying mag
n
e
tic fi
eld den
sities, du
ring
pha
se to pha
se fault,
at mid-point
(unde
r the
ce
nter p
h
a
s
e) a
nd at
RO
W,
unde
r b
o
th m
i
d-span
(p
oin
t
P1) an
d to
wer
height
(poi
nt P2), respe
c
tively. It is se
en that th
e
maximum val
ue of m
agn
e
t
ic field
den
sity,
durin
g the fau
l
t period [0.03
:
0.082] se
c,
under mi
d-spa
n
(point P1),
equal
s 36
0µ.T.
Figure 11. Th
ree Pha
s
e Si
nusoidal
Currents
unde
r Pha
s
e
to Phase Fa
u
l
t
Figure 12. Time Varying
Magneti
c
Fiel
d
Den
s
ity at Mid-poi
nt and at
ROW u
nde
r
Mid-
spa
n
and u
n
d
e
r To
wer
Hei
ght (point P1,
P2)
unde
r Pha
s
e
to Phase Fa
u
l
t
3.2.4. Three
Phase to G
r
ound Fault
Figure 13
sho
w
s the th
ree
pha
se si
nu
soi
dal cu
rrents,
unde
r thre
e p
hase to gro
u
n
d
fault,
for a peri
od [0.03:0.082] sec, wh
ere, th
e maxi
mum value of fault current tend
s to be 21
kA.
0
0.
0
2
0.
04
0.
06
0.
08
0.
1
0.
12
-2
0
-1
5
-1
0
-5
0
5
10
15
20
V
a
r
i
at
i
o
n
of
t
i
m
e
(
S
ec
.
)
P
has
e c
u
r
r
ent
s
(
k
A
)
pha
s
e
A
pha
s
e
B
pha
s
e
C
0
0.
02
0.
04
0.
06
0.
08
0.
1
0.
1
2
0
100
200
300
400
500
V
a
r
i
at
i
o
n
of
t
i
m
e
(
S
ec
.
)
M
agn
et
i
c
f
i
el
d
den
s
i
t
y
(
µ
.
T
)
P
1
at
m
i
d
-
s
pan
P
2
at
t
o
wer
hei
ght
P1
a
t
R
O
W
P2
a
t
R
O
W
0
0.
0
2
0.
04
0.
06
0.
0
8
0.
1
0.
1
2
-20
-15
-10
-5
0
5
10
15
20
V
a
r
i
at
i
o
n
of
t
i
m
e
(
S
ec
.
)
P
has
e c
u
r
r
e
n
t
s
(
k
A
)
ph
as
e A
ph
as
e B
ph
as
e C
0
0.
02
0.
04
0.
06
0.
08
0.
1
0.
1
2
0
50
100
150
200
250
300
350
400
V
a
r
i
at
i
o
n
of
t
i
m
e
(
S
e
c
.
)
M
agn
et
i
c
f
i
e
l
d
d
ens
i
t
y
(
µ
.
T
)
P
1
at m
i
d-
s
pan
P
2
at tow
e
r
hei
ght
P1
a
t
R
O
W
P2
a
t
R
O
W
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Magneti
c
Fiel
d Cal
c
ulation
unde
r No
rm
al
and Abno
rm
al… (Nagat
M.
K. Abdel-Gawad)
3387
Figure 13. Th
ree Pha
s
e Si
nusoidal
Currents
unde
r Three
Phase to G
r
o
und Fault
Figure 14. Time Varying
Magneti
c
Fiel
d
Den
s
ity at Mid-poi
nt and at
ROW u
nde
r
Mid-
Span and u
n
der To
we
r He
ight (point P1
, P2)
unde
r Three
Phase to G
r
o
und Fault
Figure 14
sh
ows the time
varying ma
g
netic fi
eld
de
nsitie
s, duri
n
g the three p
hase to
grou
nd fa
ult, at mid-p
o
int
(unde
r the
ce
n
t
er ph
ase)
an
d
at
ROW, un
der bot
h mi
d-spa
n
(point P
1
)
and tower
he
ight (poi
nt P2), re
spe
c
tivel
y
. It is seen that the maxi
mum value o
f
magnetic fi
eld
den
sity, durin
g the fault period [0.03:0.08
2] se
c, un
der
mid-spa
n
(poi
nt P1), equal
s 400µ.T.
From
case
(B
), the
wo
rst
e
ffect of fault o
n
the time
va
rying m
agn
etic field
de
nsit
y is the
doubl
e ph
ase
to groun
d fa
ult, whe
r
e th
e maximum
value of the
magneti
c
fiel
d de
nsity, du
ring
the fault pe
riod [0.03:0.08
2] se
c un
der mid-spa
n
(p
oint P1) e
q
u
a
ls 4
30µ.T. F
o
llowed by th
re
e
pha
se to g
r
o
und fault, which
have a
maximum v
a
lue of the
magneti
c
fiel
d den
sity eq
uals
400µ.T. Th
en
pha
se to
ph
ase fa
ult, whi
c
h h
a
ve a
m
a
ximum valu
e of the m
a
g
netic field
de
nsity
equal
s 360µ.
T
. Finally, single ph
ase t
o
grou
nd fau
l
t, which hav
e a maximu
m value of the
magneti
c
fiel
d den
sity equ
als 1
70µ.T.
Also, it is
n
o
ticed th
at, for
each ki
nd of t
he faults th
at are
studie
d
und
er case (B) a
n
d
also un
de
r n
o
rmal
co
n
d
ition of ca
se (A
), the maximum value of the
magneti
c
field den
sity occurs
und
er the
mid-span,
where th
e cle
a
r
an
ce b
e
twee
n the con
d
u
c
to
rs
and the grou
nd level ha
s its minimum v
a
lue.
3.3. Case (C): Magne
tic Field under Li
ghtning
Con
d
ition
In ca
se (C), a
l
so ATP software is
used
to simulate th
e OHT
L
un
de
r lightnin
g
co
ndition
s.
The lightnin
g
impulse is
assume
d to have the
followin
g
param
eters: pe
ak
value of 100
kA,
cha
nnel re
sistance equal
s 1M
Ω
, front ti
me equ
als
4
µse
c
an
d tail time equal
s 5
0
µse
c
[17]. The
effects of va
riou
s type of lightning (di
r
ect a
nd indi
rect
) on the
time varying
magneti
c
field
den
sities a
r
e
studie
d
in this sectio
n.
3.3.1. Direct
Stroke on P
h
ase (B)
Figure 15(a).
Thre
e Phase Curre
n
ts un
d
e
r
Dire
ct Stro
ke
on Phase B
Figure
15(b). Grou
nd Wire Curre
n
ts
un
d
e
r
Dire
ct Stro
ke
on Phase B
0
0.
02
0.
04
0.
0
6
0.
0
8
0.
1
0.
12
-3
0
-2
0
-1
0
0
10
20
30
V
a
r
i
a
t
i
o
n
o
f
ti
me
(
S
e
c
.)
P
h
as
e c
u
r
r
e
nt
s
(
k
A
)
pha
s
e
A
pha
s
e
B
pha
s
e
C
0
0.
02
0.
04
0.
0
6
0.
08
0.
1
0.
12
0
50
10
0
15
0
20
0
25
0
30
0
35
0
40
0
V
a
r
i
a
t
i
o
n
o
f
ti
m
e
(
S
e
c
.)
M
a
g
net
i
c
f
i
e
l
d
den
s
i
t
y
(
µ
.
T
)
P
1
at
m
i
d-
s
pan
P
2
at
t
o
wer
height
P1
a
t
R
O
W
P2
a
t
R
O
W
0
0.
0
2
0.
0
4
0.
0
6
0.
0
8
0.
1
0.
12
-2
0
-1
0
0
10
20
30
40
50
V
a
r
i
at
i
o
n
of
t
i
m
e
(
S
ec.
)
P
h
as
e c
u
r
r
e
n
t
s
(
k
A
)
p
has
e A
p
has
e B
p
has
e C
0
0.
0
2
0.
04
0.
0
6
0.
08
0.
1
0.
12
-600
0
-400
0
-200
0
0
200
0
400
0
600
0
V
a
ri
a
t
i
o
n
o
f
t
i
me
(S
e
c
.
)
P
h
a
s
e
c
u
rre
n
t
s
( A
)
G.
W
1
=
G
.
W
2
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3381 – 33
91
3388
Figure 15 sh
ows the thre
e pha
se sin
u
s
oid
a
l
cu
rre
nts and g
r
ou
nd
wire current
s und
er
dire
ct stroke
on ph
ase (B
), wh
e
r
e the
currents i
n
the
two g
r
ou
nd
wire
s
are
eq
ual, due to
th
eir
relative p
o
siti
on with
re
sp
ect to p
h
a
s
e
(B). It is n
o
ticed th
at the
maximum val
ue of the
stroke
curre
n
t tends
to be 50kA wi
thin the first 4
µ
se
c.
Figure 16 sh
ows the time
varying mag
netic fi
eld de
nsitie
s, durin
g the dire
ct lightning
stro
ke o
n
ph
ase B, at mid-poi
nt (un
d
e
r
the
ce
nter
pha
se)
and a
t
ROW, un
de
r both mid
-
sp
an
(point P1) a
nd towe
r hei
ght (point P2
), respecti
vel
y
. It is seen
that the ma
ximum value of
magneti
c
field den
sity, under mid
-
span
(point P1), eq
uals 6
80µ.T.
Figure 16. Time Varying
Magneti
c
Fiel
d Den
s
ity
at Mid-p
o
int and
at ROW un
d
e
r Mid-sp
an a
nd
unde
r To
wer
Heig
ht (point
P1, P2) unde
r Direct Stro
ke on Phase B
3.3.2. Indirect Strok
e
on Ground
Wire
(1)
Figure 17 sh
ows the thre
e pha
se sin
u
s
oid
a
l
cu
rre
nts and g
r
ou
nd
wire current
s und
er
indire
ct stro
ke
on groun
d wire
(1
). It is noticed that
the maximu
m
value of
the stro
ke cu
rrent
tends to be 5
0
kA within th
e first 4µsec.
Figure 17(a).
Thre
e Phase and G.W2 Cu
rre
nts
unde
r Indirect
Stroke on G.
W1
Figure
17(b). Grou
nd Wire (1) Curre
n
t
under
Indire
ct Stroke on G.W1
Figure 18 sh
ows the time varying mag
netic fiel
d de
nsitie
s, durin
g the indire
ct lightning
stro
ke
on
gro
und wire (1
), at
mid-point (unde
r
th
e ce
nter pha
se
) a
nd at
ROW,
unde
r
both m
i
d-
spa
n
(point
P1) and
tower height (poi
nt P2),
resp
ec
tively. It is
seen that the maximum value
of
magneti
c
field den
sity, under mid
-
span
(point P1), eq
uals 4
60µ.T.
0
0.
0
2
0.
0
4
0.
0
6
0.
0
8
0.
1
0.
12
0
10
0
20
0
30
0
40
0
50
0
60
0
70
0
V
a
r
i
at
i
o
n
of
t
i
m
e
(
S
ec.
)
M
a
gn
et
i
c
f
i
e
l
d
de
n
s
i
t
y
(
µ
.
T
)
P
1
at
m
i
d-
s
p
a
n
P
2
at
t
o
w
e
r
he
i
ght
P1
a
t
R
O
W
P2
a
t
R
O
W
0
0.
02
0.
04
0.
0
6
0.
08
0.
1
0.
1
2
-6
00
0
-4
00
0
-2
00
0
0
200
0
400
0
600
0
V
a
r
i
a
t
i
o
n
o
f
ti
m
e
(
S
e
c
.)
P
h
a
s
e
c
u
rre
n
t
s
( A
)
phas
e A
phas
e B
phas
e C
G.
W
2
0
0.
02
0.
0
4
0.
0
6
0.
0
8
0.
1
0.
12
-2
0
-1
0
0
10
20
30
40
50
60
V
a
r
i
a
t
i
o
n
o
f
ti
me
(
S
e
c
.)
P
h
as
e c
u
r
r
ent
s
(
k
A
)
G.
W
1
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TELKOM
NIKA
ISSN:
2302-4
046
Magneti
c
Fiel
d Cal
c
ulation
unde
r No
rm
al
and Abno
rm
al… (Nagat
M.
K. Abdel-Gawad)
3389
Figure 18. Time Varying
Magneti
c
Fiel
d Den
s
ity
at Mid-p
o
int and
at ROW un
d
e
r Mid-sp
an a
nd
unde
r To
wer
Heig
ht (point
P1, P2) unde
r Indire
ct Stro
ke on G
r
ou
nd
Wire (1)
4. Conclu
sion
In this p
ape
r the time va
rying ma
gnet
ic field
den
si
ties a
r
e
cal
c
ulated a
nd
a
nalyze
d
unde
r three
different ca
se
s of the OHT
L
nam
el
y: normal operatin
g, fault, and lightning
conditions.
At normal op
erating
con
d
ition, the mag
netic fi
eld de
nsity varie
s
with the dista
n
ce fro
m
the center ph
ase
for
differe
nt perce
ntage
of load
curre
n
t. Also, the
d
e
crea
se i
n
th
e load
capa
ci
ty
decrea
s
e
s
th
e mag
netic field d
e
n
s
ity. Due
to the
sag effe
ct, the
gro
und
level
magn
etic fie
l
d
den
sity has its maximum
value unde
r the mid-
sp
an, whe
r
e, the cle
a
ra
nce
betwee
n
the
con
d
u
c
tors a
nd the gro
u
n
d
level has its minimum v
a
lue. But under tower h
e
ight, the grou
nd
level magneti
c
field den
sit
y
has its mini
mum value d
ue to the ma
ximum clea
ra
nce b
e
twe
en
the
c
o
nd
uc
to
rs
an
d
th
e
g
r
ou
nd
le
ve
l.
Und
e
r differe
nt faulty conditions, it is obs
erved tha
t
the highest
values of the time
varying mag
netic field d
ensitie
s at certain
p
o
ints (mid-sp
an,
tower
heig
h
t, and RO
W) are
obtaine
d firstl
y under dou
bl
e pha
se to
ground fa
ult, then un
der t
h
re
e pha
se to
ground fa
ult, then
unde
r ph
ase to phase fault
,
and finally u
nder
sin
g
le
p
hase to grou
nd fault, whi
c
h has th
e lo
west
value.
Und
e
r li
ghtni
ng conditio
n
s, it is cl
ear that
the
cal
c
u
l
ated value
s
of the time v
a
rying
magneti
c
fiel
d de
nsitie
s
a
t
ce
rtain p
o
in
ts for
direct l
i
ghtning
stroke are m
o
re
dang
ero
u
s th
an
those of indi
rect lightnin
g
stroke a
nd of d
i
ffer
ent faulty con
d
ition
s
, even if, it is rare
ly happen.
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ces
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a
w
i
a, K
Y
oussef, AA
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a
tio
n
of
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e
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ealth
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m
a
gneti
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i
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o
w
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ilippo
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w
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hai
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act p
a
rall
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e
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n
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i
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r
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n
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e
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alistic
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e
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22
22.
0
0.
02
0.
0
4
0.
0
6
0.
08
0.
1
0.
12
0
10
0
20
0
30
0
40
0
50
0
V
a
r
i
a
t
i
o
n
o
f
ti
m
e
(
S
e
c
.
)
M
a
g
net
i
c
f
i
el
d dens
i
t
y
(
µ
.
T
)
P
1
at
m
i
d
-
s
pan
P
2
at
t
o
w
e
r hei
ght
P1
a
t
R
O
W
P2
a
t
R
O
W
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3381 – 33
91
3390
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udr
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ile
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ans
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