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
. 47
1
~
48
5
I
S
SN
: 208
8-8
7
0
8
4
71
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
Effect of
Coatin
g of
Earth
e
d Encl
osure and
Multi-
Cont
aminating P
a
rticl
e
s on B
reakdown Voltage inside Gas
Insulated Bus Duct
M.
A. Ab
d Allah,
S
aye
d A. Ward
, Amr A
.
Y
o
us
sef
Ele
c
tri
cal
Eng
i
n
eering
Depar
t
m
e
nt, F
a
culty
of En
gineer
ing
at
Sho
ubra,
Benha University
, Cairo, Eg
y
p
t
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 28, 2014
Rev
i
sed
Ju
l 1
,
2
014
Accepte
d
J
u
l 15, 2014
Metall
ic
part
icl
e
cont
am
ination
i
s
one of
the
are
a
s of insul
a
tion
design th
at
are cons
ider
ed criti
ca
l. This
p
a
per dem
ons
trat
es
the control
of m
e
talli
c
particles in gas insulated bus duct (GIB
D) by
using dielectric coating on the
ins
i
de s
u
rfa
ce o
f
the ou
ter
encl
os
ure of a
coaxi
a
l e
l
e
c
trode
s
y
s
t
em
. S
e
ver
a
l
m
odels of GIBD with single
and m
u
lti-
conta
m
inating pa
rti
c
l
e
s will b
e
studied.
In
this p
a
per,
th
e Fini
te
Elem
en
ts Me
tho
d
(FEM) is used
to
evalu
a
t
e
the el
ectr
i
c fi
eld
distribution on and around single and m
u
lti-con
t
am
inatin
g
wire par
t
i
c
les w
h
ich
in con
t
a
c
t
with di
ele
c
tri
c
c
o
ating
of
earth
e
d
enc
l
osure
inside GIBD. The effect of changing
the length and the radiu
s
of
middle
parti
c
le
for m
u
l
ti-cont
am
inat
ing
parti
c
l
e
s on th
e el
ec
tric
fi
eld
values
are
studied. Breakd
own Voltage calculations
for g
a
s mixtures with single and
m
u
lti-cont
am
ina
ting wire part
ic
l
e
s are st
udied
. T
h
e effe
cts of gas pressure on
the breakdown
voltage for v
a
rious
fractional concen
trations of SF
6
-gas
mixtures with and without par
t
icle
c
ontamin
atio
n and also with
and withou
t
coating of earth
e
d enclosure ar
e st
udied.
The o
p
timum gas mi
xture which
gives higher dielectr
i
c strength w
ith lower
cos
t
is
als
o
determ
ined
.
The effec
t
of coating
thick
n
ess of earthed
enclosure on the breakdown
voltag
e
for
various fractional c
oncen
trations of SF
6
-gas
mixtures is also studied. Finally
,
the eff
e
c
t
of l
e
ngth and
hem
i
-spheric
a
l r
a
di
us of m
u
lti-co
ntam
inatin
g
particles on
the breakdown vo
ltag
e
with
various SF
6
-gas mi
xtures an
d
var
y
ing g
a
s pressure one time
and an
o
t
her
tim
e with
fixed
pr
essure ar
e
studied.
Keyword:
B
r
eak
do
w
n
Vo
l
t
a
ge
Co
atin
g
Electric Field
Gas M
i
xt
ures
Mu
lti-Particles
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
:
Am
r
A. Yo
uss
e
f,
Electrical Engi
neeri
n
g De
part
ment,
Faculty of E
n
gineering at
Shou
br
a, Benh
a
Un
iv
er
sity,
1
0
8
Shou
br
a Str
eet,
Cair
o,
Egyp
t.
Em
a
il: en
g
_
p
o
wer_
am
r2
01
1@yaho
o.co
m
1.
INTRODUCTION
Several
num
eri
cal
t
echni
ques have
been i
n
creasi
ngl
y
em
pl
oy
ed t
o
sol
v
e such pract
i
cal
probl
em
s
sin
ce th
e av
ailab
ility o
f
h
i
g
h
p
e
rfo
rm
an
ce co
m
p
u
t
ers [1
,
2
]
. Th
e ad
v
a
n
t
ag
e o
f
th
e ap
p
licatio
n
o
f
n
u
m
erical
m
e
thods has
m
a
ny advantages
com
p
ar
ed to
analytical m
e
thods
such as
com
putable
accuracy, sim
p
licity and
lo
w co
st.
The finite
elem
ent
m
e
thod (FEM)
is used in
this
pape
r for its fa
vora
bl
e accuracy,
when a
pplied t
o
hi
g
h
vol
t
a
g
e
pr
obl
em
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
:
47
1
–
48
5
47
2
2.
ELECTRIC FIELD CAL
C
ULATIONS
FEM one
of t
h
e efficient technique
f
o
r s
o
l
v
i
ng
fi
el
d p
r
o
b
l
e
m
s
i
s
used
to determine the electric field
distribution
on the space
r'
s surface. FEM conce
r
ns itself
with m
i
nimiza
tion of the e
n
e
r
gy wit
h
in the
whol
e
fi
el
d re
gi
o
n
o
f
i
n
t
e
rest
, w
h
et
h
e
r t
h
e fi
el
d i
s
e
l
ect
ri
c or m
a
gn
et
i
c
, of La
pl
aci
an o
r
P
o
i
sso
n t
y
pe, by
di
vi
di
n
g
t
h
e
regi
on i
n
t
o
t
r
i
a
ng
ul
ar el
em
ents for t
w
o di
m
e
nsi
o
nal
pr
o
b
l
e
m
s
or t
e
t
r
ahed
r
ons
fo
r t
h
ree di
m
e
nsi
onal
p
r
o
b
l
e
m
s
.
Unde
r steady
state the ele
c
trostatic
field within anis
ot
ropic dielect
ric
m
a
terial, as
sum
i
ng a Cartesian
coo
r
di
nat
e
sy
s
t
em
, and La
pl
aci
an fi
eld, the electrical energy
W stored
wi
t
h
i
n
t
h
e w
hol
e
vol
um
e
U o
f
t
h
e
regi
on
co
nsi
d
e
r
ed
i
s
[
3
,
4
]
:
U
dU
V
grad
W
2
)
(
2
1
(1
)
dxdydz
z
V
y
V
x
V
W
U
z
z
y
y
x
x
2
2
2
2
1
(2
)
Furt
herm
ore,
f
o
r
GI
S ar
ran
g
e
m
e
nt
, whe
n
we co
nsi
d
er t
h
e fi
el
d
be
ha
vi
o
u
r at
m
i
nut
e l
e
vel
t
h
e
p
r
ob
lem
can
be treated
as two
d
i
m
e
n
s
io
n
a
l (2D). Th
e to
ta
l sto
r
ed
en
erg
y
with
in
th
is area-li
m
ited
syst
e
m
i
s
no
w
gi
ve
n acc
or
di
n
g
t
o
[
3
,
4
]
:
dxdy
y
V
x
V
W
y
x
2
2
*
2
1
(3
)
W
h
ere (W
/
) i
s
t
hus an energy
densi
t
y
perel
e
m
e
nt
ary
area dA. B
e
fore appl
y
i
ng any
m
i
ni
m
i
zat
i
on
cri
t
e
ri
a
based upon t
h
e
above equat
i
on, appropri
a
t
e
assu
m
p
t
i
ons
about
t
h
e pot
ent
i
a
l
di
st
ri
but
i
on V(x, y
,
z)
m
u
st
be m
a
de. It
shoul
d be
em
phasi
zed t
h
at
t
h
i
s
func
t
i
on i
s
cont
i
nuous
and a fi
ni
t
e
num
ber of deri
vat
i
v
es
m
a
y exist. As it will be im
possible to find a con
tinuous function for the whole area A, an
adequate
di
scret
i
zat
i
on m
u
st
be
m
a
de. So
al
l
t
h
e area
under consi
d
erat
i
on i
s
subdi
vi
ded
i
n
t
o
t
r
i
a
ngul
ar
el
em
ent
s
hence
[3,4]
:
n
i
i
y
x
A
y
V
x
V
W
1
2
2
*
*
*
2
1
(4
)
W
h
ere n
is the
total num
ber
of elem
ents
and Ai
is th
e
area o
f
th
e ith
tr
iangle
elem
ent. So the
fo
rm
u
l
atio
n
reg
a
rd
in
g
th
e m
i
n
i
m
i
zatio
n
o
f
th
e en
erg
y
with
in
th
e co
m
p
lete system
m
a
y b
e
written
as [3
,4
]:
w
X
Where
y
x
V
X
;
0
,
(5
)
The
resul
t
i
s
an
approxi
m
a
t
i
on for t
h
e el
ect
rost
at
i
c
pot
ent
i
a
l
for t
h
e nodes
at
whi
c
h t
h
e unknown
potentials are
to be
com
puted. W
ithin
each elem
ent
the electric
field strength
is
considered to
be constant and
the electric field strength
is calculated as [3,4]:
y
y
x
V
J
x
y
x
V
I
E
)
,
(
)
,
(
(6
)
The el
ect
ri
c fi
el
d
i
s
cal
cul
a
t
e
d
wi
t
h
usi
ng
t
h
e Fi
ni
t
e
El
em
ent
M
e
t
hod (FEM
)
t
h
roughout
t
h
i
s
work.
The Fi
ni
t
e
El
em
ent
M
e
t
hod M
a
gnet
i
c
s (FEM
M
)
Package i
s
used
t
o
si
m
u
l
a
t
e
t
h
e
probl
em
s and t
o
cal
cul
a
t
e
t
h
e el
ect
ri
c fi
el
d i
n
si
de gas i
n
sul
a
t
e
d swi
t
c
hgear and
gas i
n
sul
a
t
e
d bus duct
s
as di
sscussed i
n
t
h
i
s
paper.
FEMM
is a
finite elem
ent package
for
sol
v
i
ng 2D
pl
anar and
axi
-
sy
m
m
e
t
r
i
c
probl
em
s i
n
el
ect
rost
at
i
c
s and i
n
l
o
w frequency
m
a
gnet
i
c
[5]
.
The
anal
y
s
i
s
i
n
t
h
e paper
i
s
done
by
usi
ng
t
w
o concent
r
i
c
cy
l
i
nder of
i
n
fi
ni
t
e
l
e
ngt
h.
The vol
t
a
ge on
t
h
e i
nner conduct
o
r of
GIB
D
consi
d
ered i
s
t
a
ken
as 1V, For
any
appl
i
e
d vol
t
a
ge t
h
e
val
u
es of t
h
e
el
ect
ri
c
fi
el
ds can be proport
i
oned.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Effect o
f
Coa
tin
g o
f
Ea
rt
h
e
d
En
clo
s
u
r
e and
Mu
lti-
Con
t
amin
a
ting
Pa
rticles on
… (Amr A. Yo
u
s
sef)
47
3
3.
ELEC
TR
OST
A
TIC
M
O
DELIN
G
OF GIBD
WITH PA
R
T
IC
LE C
O
N
T
A
M
IN
A
T
ION
AND
DIELECTRIC COATING OF
ENCLOSURE
The
purpose of
coating the inside
surface of
ga
s insulated bus
duct (GIBD)
enclosure with a
dielectric m
a
terial reduces
the dele
terious effect
of electrode
surface
roughness, increases
the field
required
to
lift p
a
rticles, an
d
red
u
ces th
e ch
arg
e
acq
u
i
red
b
y
p
a
rticles.
Fi
gure 1 shows Gas i
n
sul
a
t
e
d
bus duct
wi
t
h
fi
l
a
m
e
nt
ary
wi
re
cont
am
i
n
at
i
ng part
i
c
l
e
i
n
cont
act
wi
t
h
dielectric coating of earthed enclosure.
In t
h
i
s
fi
gure, (t
) i
s
defi
ned as di
el
ect
ri
c coat
i
ng t
h
i
c
kness and i
t
vari
es
from
200m
i
c
ro-m
et
er t
o
2000m
i
c
ro-m
et
er. The di
el
ect
ri
c m
a
t
e
ri
al
of coat
i
ng can be epoxy
, varni
s
h or
p
o
l
ym
eric film
s.
Fig
u
re
1
.
Gas in
su
lated
b
u
s
du
ct with filam
e
n
t
ary
wi
re co
n
t
a
m
in
atin
g
p
a
rticle in
con
t
act
with
d
i
electric
coating of ea
rt
hed encl
os
ure
3.1. Effect of Dielectric Coating of Earthed Enclosure
The part
i
c
l
e
di
m
e
nsi
ons are t
a
ken as 10m
m
l
e
ngt
h and 0.5m
m
radi
us. The t
h
i
c
kness of
di
el
ect
ri
c
coating for earthed enclosure is taken as 2000 µm
and epoxy m
a
terial of relative perm
ittivity (
є
r=4.5) i
s
used
for coating.
Fi
gure 2
shows t
h
e
el
ect
ri
c fi
el
d
di
st
ri
but
i
on al
ong
gap i
n
si
de
gas i
n
sul
a
t
e
d
bus duct
wi
t
h
wi
re
co
n
t
am
in
atin
g
p
a
rticle in
co
n
t
act w
ith dielectric
coating of
earthed encl
osure. It
can be
observed t
h
at
t
h
e
el
ect
ri
c
fi
el
d i
s
m
i
ni
m
u
m
val
u
e at
l
o
wer
t
i
p
of part
i
c
l
e
and m
a
xi
m
u
m
val
u
e
at
upper t
i
p
of i
t
.
The el
ect
ri
c
field decreases from
upper tip
of wire particle
until it
reach
es a certain
value but
after
that value,
it returns
to
increase till reaches to a certain
value 36V/m
at inner conducto
r of gas insulated bus duct.
Fi
gure
3 shows m
a
gni
t
ude, norm
a
l
and t
a
ngent
i
a
l
com
ponent
s of el
ect
ri
c fi
el
d di
st
ri
but
i
on al
ong
surface
of wire particle.
It can be observed
that the
tangential
com
ponent of elect
ric field
is zero and the
norm
a
l com
ponent of
it increases
gradually from
zer
o until it
reaches the
m
a
xim
u
m
value
at upper
tip
t
h
rough
negat
i
v
e si
de,
so m
a
t
h
em
at
i
cal
l
y
, t
h
e
m
a
gni
t
ude of
el
ect
ri
c fi
el
d i
n
creases
al
so from
zero t
o
99.6V/
m
at upper tip of wire particle through positive side .
Fi
gure
4
shows
m
a
gni
t
ude,
norm
a
l
and t
a
ngent
i
a
l
com
ponent
s of el
ect
ri
c fi
el
d di
st
ri
but
i
on al
ong gap
from
upper t
i
p
of wi
re part
i
c
l
e
up t
o
i
nner
conduct
o
r of
GIB
D
. It
can
be observed t
h
at
norm
a
l
com
ponent
of
el
ect
ri
c
fi
el
d i
s
zero.
The t
a
ngent
i
a
l
com
ponent
and t
h
e m
a
gni
t
ude
of el
ect
ri
c fi
el
d
i
s
m
a
xi
m
u
m
val
u
e
(
≈
99.6V/m
)
at upper tip of wire particle and decreases
gradually along gap until it reaches a certain distance
(7.8m
m
)
from
tip but after
that value up to
inner c
onductor, the electric
field increases gradually until it
reaches a certain value is about 36V/m
.
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
:
47
1
–
48
5
47
4
Fi
gu
re
2.
El
ect
ri
c fi
el
d
di
st
ri
b
u
t
i
o
n
al
o
n
g
g
a
p i
n
si
de
gas i
n
s
u
l
a
t
e
d
bu
s
duct
wi
t
h
wi
re
co
nt
am
i
n
at
i
ng
p
a
rticle in
con
t
act with
d
i
elect
ri
c coat
i
n
g
o
f
e
a
rt
he
d e
n
cl
os
ur
e
Figure
3. Electric fiel
d distri
bution
along
s
u
rface of wire
pa
rticle
Fi
gu
re
4.
El
ect
ri
c fi
el
d
di
st
ri
b
u
t
i
o
n
al
o
n
g
g
a
p
fr
om
uppe
r t
i
p
of
wi
re
pa
rt
i
c
l
e
up
t
o
i
n
n
e
r c
o
n
d
u
ct
o
r
of
G
I
B
D
-
100
-5
0
0
50
100
02
468
1
0
1
2
P
a
r
t
i
c
l
e
Le
ngt
h
(
m
m
)
E
l
ect
r
i
c
F
i
el
d
(
V
/
m
)
IE
I, V
/
m
En
,
V/
m
Et
,
V/
m
-2
0
0
20
40
60
80
100
120
0
1
02
0
3
04
0
U
ppe
r
ga
p s
p
a
c
e
(
m
m
)
E
l
ect
r
i
c
F
i
el
d
(
V
/
m
)
I
E
I, V
/
m
En
,
V/
m
Et
,
V/
m
Half section
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Effect o
f
Coa
tin
g o
f
Ea
rt
h
e
d
En
clo
s
u
r
e and
Mu
lti-
Con
t
amin
a
ting
Pa
rticles on
… (Amr A. Yo
u
s
sef)
47
5
4.
MULTI-CONTAMINATING FI
X
E
D PARTICLES
R
E
STED
ON
EAR
T
HED ENCLOSUR
E
A st
u
d
y
o
f
C
I
GR
E g
r
ou
p s
u
gge
st
s t
h
at
2
0
%
of
fai
l
u
re i
n
G
I
S i
s
due t
o
t
h
e e
x
i
s
t
e
nc
e of
vari
o
u
s
metall
ic co
n
t
amin
atio
n
s
in the fo
rm
o
f
l
o
ose p
a
rticles [6
].
So
, in
t
h
is
p
a
per,
we st
u
d
y
the effect
of m
u
lti-wire
particles on t
h
e
electric field.
Fig
u
r
e
5
sh
o
w
s Gas in
su
lated
b
u
s
d
u
c
t with
m
u
lti-wire co
n
t
am
in
atin
g
fix
e
d
p
a
rticles in
co
n
t
act with
dielectric coating
of earthed
enclosur
e.
The three wire
contam
inating pa
rticles
are id
en
tical
in
len
g
t
h
an
d
radi
us. C
onsi
d
er t
h
at
t
h
e m
i
ddl
e
part
i
c
l
e
l
e
ngt
h (L1)
i
s
t
a
ken
as 5m
m
,
out
erm
o
st
part
i
c
l
e
s (L2)
as 5m
m
and
hem
i
-spherical radius
of particles
(r) are
taken as
0.5m
m
.
The
spacing be
tween m
i
ddle
particle and outerm
o
st
particles is taken as 15m
m
.
Gu1 is defined as uppe
r
gap space from
upper tip
of m
i
ddle particle up to
high
voltage conductor and
Gu2 is define
d
as upper
gap space from
upper tip
of
outerm
o
st particles
up to
high
vol
t
a
ge conduct
o
r.
Fig
u
re
5
.
Gas in
su
lated
b
u
s
du
ct with m
u
lti-
wire con
t
amin
atin
g
fix
e
d
p
a
rt
icles in
contact with di
electric
coa
ting of eart
h
ed enc
l
osure
4.1. For Wi
re Parti
c
l
e
of 5mm L
e
ngth and of 0.5mm Radi
us
Figure 6 shows
the electric
field di
stribution along
gap inside
gas in
sulated bus
duct with
m
u
lti-wire
cont
am
i
n
at
i
ng part
i
c
l
e
s rest
i
ng on
eart
h
ed encl
osure. It
can
be observed t
h
at
t
h
e
electric field is
m
i
nim
u
m
val
u
e at
l
o
wer t
i
p
of m
i
ddl
e and out
erm
o
st
part
i
c
l
e
s and m
a
xi
m
u
m
val
u
e at
upper t
i
p
of i
t
but
t
h
e
m
a
xi
m
u
m
val
u
e of el
ect
ri
c fi
el
d at
upper t
i
p
of out
erm
o
st
part
i
c
l
e
s are sl
i
ght
i
n
creased
from
t
h
at
at
upper t
i
p
of
m
i
ddl
e
particle.
The electric field
decreases
from
upper
tip of wire
particle till reach
es
a certain value
but after this
value, it returns
to increas
e till
reaches to
the m
a
xim
u
m
value of
elect
ric field
at inner
c
onductor of
GIBD in
case of cl
ean gap wi
t
hout
any
part
i
c
l
e
cont
am
i
n
at
i
on.
Figure 7 shows electric fiel
d distribution along surface of m
i
ddle a
nd outerm
o
st particles. It can
be
observed t
h
at
t
h
e el
ect
ri
c
fi
el
d at
upper t
i
p
of out
erm
o
st
part
i
c
l
e
s i
s
sl
i
ght
l
y
great
er t
h
an i
t
at
upper t
i
p
of
m
i
ddle particle and this is because the outerm
o
st partic
les which rested at ground enclosure is nearer to
high
vol
t
a
ge conduct
o
r t
h
an m
i
ddl
e part
i
c
l
e
.
Fi
gure
8 & Fi
gure 9
show m
a
gni
t
ude, norm
a
l
and
t
a
ngent
i
a
l
com
ponent
s of el
ect
ri
c fi
el
d
di
st
ri
but
i
on
al
ong gap from
upper
t
i
p
of m
i
ddl
e and
out
erm
o
st
part
i
c
l
e
s up t
o
hi
gh vol
t
a
ge conduct
o
r. It
can
be
observed t
h
at
norm
a
l
com
ponent
of el
ect
ri
c fi
el
d i
s
about
zero and t
h
e t
a
ngent
i
a
l
com
ponent
of i
t
decreases gradually from
m
a
xim
u
m
value at upper tip of pa
rticle until it reaches a cer
tain value but after that
val
u
e,
i
t
ret
u
rns t
o
i
n
crease t
h
rough negat
i
v
e
si
de, so m
a
t
h
em
at
i
cal
l
y
, t
h
e m
a
gni
t
ude of el
ect
ri
c fi
el
d
decreases gradual
l
y
from
60.14V/
m
and
62.6V/
m
at
upper
t
i
p
of
m
i
ddl
e and
out
erm
o
st
part
i
c
l
e
s
respect
i
v
el
y
until it reaches a certain valu
e but after that value,
it returns to in
crease as it approaches from
high
voltage
conductor through positive side.
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
:
47
1
–
48
5
47
6
Fig
u
re
6
.
Electric field
d
i
stri
bu
tio
n alon
g gap
insid
e
g
a
s i
n
su
lated
b
u
s
d
u
c
t
with
m
u
lti-wire
cont
am
i
n
at
i
ng
part
i
c
l
e
s rest
i
n
g
on
eart
h
ed
en
cl
osu
r
e
Figure
7. Electric fi
eld
distri
bution along s
u
rface
of
m
i
ddle
and outerm
ost particles
Fi
gu
re
8.
El
ect
ri
c fi
el
d
di
st
ri
b
u
t
i
o
n
al
o
n
g
g
a
p
fr
om
uppe
r t
i
p
of
m
i
ddl
e
part
i
c
l
e
u
p
t
o
h
i
gh
v
o
l
t
a
ge c
o
nd
uct
o
r
0
10
20
30
40
50
60
70
02
46
8
Pa
r
t
ic
le
Le
ng
t
h
(
m
m
)
E
l
ect
r
i
c F
i
el
d
(
V
/
m
)
IE
I
_
m
i
d
d
l
e
p
a
r
t
ic
le
, V
/
m
I
E
I_
o
u
t
e
r
-
m
o
s
t
pa
r
t
i
c
le
, V
/
m
-8
0
-6
0
-4
0
-2
0
0
20
40
60
80
0
1
02
0
3
04
0
5
0
Gu
1
(
m
m
)
E
l
ect
r
i
c F
i
el
d
(
V
/
m
)
IE
I, V
/
m
En,
V
/
m
Et
,
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
Effect o
f
Coa
tin
g o
f
Ea
rt
h
e
d
En
clo
s
u
r
e and
Mu
lti-
Con
t
amin
a
ting
Pa
rticles on
… (Amr A. Yo
u
s
sef)
47
7
Fi
gu
re
9.
El
ect
ri
c fi
el
d
di
st
ri
b
u
t
i
o
n
al
o
n
g
g
a
p
fr
om
uppe
r t
i
p
of
o
u
t
e
rm
ost
p
a
r
ticles up
t
o
h
i
gh
v
o
ltage co
ndu
ctor
4.
2.
Effect of
Changing the Length of
Middle
Particle
on
the Electric Field Values
The
vari
at
i
on
of
t
h
e
el
ect
ri
c
fi
el
d
val
u
es at
t
h
e upper t
i
p
of m
i
ddl
e and out
erm
o
st
fi
xed part
i
c
l
e
s wi
t
h
respect
t
o
t
h
e part
i
c
l
e
s
l
e
ngt
hs at
(r1,r2=0.5m
m
)
i
s
shown i
n
Fi
gure 10.
W
h
en t
h
e
di
m
e
nsi
ons of
out
erm
o
st
part
i
c
l
e
s
are const
a
nt
at
5m
m
l
e
ngt
h and 0.5m
m
hem
i
s
pheri
cal
radi
us and change t
h
e l
e
ngt
h of m
i
ddl
e fi
xed
part
i
c
l
e
from
3m
m
t
o
12m
m
at
const
a
nt
0.5m
m
radi
us
, i
t
can be observed t
h
at
as l
e
ngt
h of m
i
ddl
e
fi
xed
part
i
c
l
e
i
n
creases at
const
a
nt
l
e
ngt
h of out
erm
o
st
part
i
c
l
e
s, t
h
e
m
a
xi
m
u
m
el
ect
ri
c fi
el
d at
upper t
i
p
of m
i
ddl
e
part
i
c
l
e
i
n
creases al
so but
i
t
sl
i
ght
l
y
decreased at
upper t
i
p
of out
erm
o
st
part
i
c
l
e
s.
Fi
gu
re
1
0
.
Vari
at
i
on
of
t
h
e el
e
c
t
r
i
c
fi
el
d
val
u
es at
u
p
p
er t
i
p
of
m
i
ddl
e and
out
e
r
m
o
st
part
i
c
l
e
s ver
s
us
p
a
rticles leng
ths at con
s
tan
t
rad
i
u
s
.
4.
3.
Effect of
Changing the
Radius of
Middle
Particle
on
the Electric Field Values
The
vari
at
i
on
of
t
h
e
el
ect
ri
c
fi
el
d
val
u
es at
t
h
e upper t
i
p
of m
i
ddl
e and out
erm
o
st
fi
xed part
i
c
l
e
s wi
t
h
respect
t
o
t
h
e part
i
c
l
e
s
radi
us at
(L1,L2=5m
m
)
i
s
shown i
n
Fi
gure 11.
W
h
en t
h
e di
m
e
nsi
ons of
out
erm
o
st
part
i
c
l
e
s are
const
a
nt
at
5m
m
l
e
ngt
h
and 0.5m
m
hem
i
sphe
ri
cal
radi
us
and change
t
h
e radi
us
of m
i
ddl
e
fi
xed
part
i
c
l
e
from
0.2m
m
t
o
0.7m
m
at
const
a
nt
5m
m
l
e
ngt
h,
i
t
can
be observed t
h
at
as
radi
us of m
i
ddl
e fi
xed
part
i
c
l
e
i
n
creases at
const
a
nt
radi
us
of out
erm
o
st
part
i
c
l
e
s, t
h
e m
a
xi
m
u
m
el
ect
ri
c fi
el
d
at
upper
t
i
p
of
m
i
ddl
e
p
a
rticle
d
ecreases an
d
th
is m
ean
s th
at
th
e electric fiel
d
is m
a
x
i
m
u
m
at
th
in
p
a
rticles b
u
t
it still ap
p
r
o
x
i
m
a
tely
const
a
nt
at
upper t
i
p
of out
erm
o
st
part
i
c
l
e
s.
-8
0
-6
0
-4
0
-2
0
0
20
40
60
80
0
1
02
0
3
04
0
5
0
Gu
2
(
m
m
)
E
l
ect
r
i
c F
i
el
d
(
V
/
m
)
IE
I, V
/
m
En,
V
/
m
Et
,
V
/
m
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
:
47
1
–
48
5
47
8
Fi
gu
re
1
1
.
Vari
at
i
on
of
t
h
e el
e
c
t
r
i
c
fi
el
d
val
u
es at
u
p
p
er t
i
p
of
m
i
ddl
e and
out
e
r
m
o
st
part
i
c
l
e
s
vers
us
pa
rt
i
c
l
e
s ra
di
us
at
co
ns
t
a
nt
l
e
ngt
h.
5.
METHO
D
OL
OGY
FO
R B
R
EAK
D
OWN
VOLT
AGE
CAL
CUL
ATI
O
NS
In
o
r
de
r t
o
st
u
d
y
t
h
e
brea
k
d
o
w
n
v
o
l
t
a
ges
fo
r a
part
i
c
l
e
w
h
i
c
h i
s
re
prese
n
t
e
d
by
a hem
i
-sphe
ri
cal
t
i
p
wi
t
h
di
am
et
er
(2
r) a
nd l
e
ngt
h
(L) w
h
i
c
h i
s
c
ont
am
i
n
at
i
ng i
n
si
de
gas i
n
s
u
l
a
t
e
d b
u
st
d
u
ct
fo
r SF
6
-g
as m
i
x
t
ur
e
u
n
d
e
r
DC vo
ltag
e
.
Th
e electric field
aroun
d
p
a
rticles is sati
sfied
i
n
th
is p
a
p
e
r b
y
u
s
ing
fi
n
ite elem
en
t
meth
od
.
W
i
t
h
a
n
a
p
pl
i
e
d el
ect
ri
c
fi
el
d
,
di
sc
har
g
es
i
n
t
h
e
gas
occ
u
r
as a
res
u
l
t
of
i
oni
zat
i
o
n,
w
h
i
c
h l
e
a
d
t
o
stream
er fo
rmatio
n
and
u
ltimatel
y to
b
r
eak
down
of th
e g
a
s mix
t
u
r
e. On
e way to
p
r
edict b
r
eak
down
v
o
ltage
of
t
h
e
gas m
i
xt
ure
i
s
, t
h
e
r
ef
o
r
e, by
k
n
o
w
ing
its effective i
o
nization
coe
ffi
cients (
)[
7-
1
1
]
.
In
a non
-un
i
fo
rm
field
g
a
p, co
ron
a
d
i
scharg
es
will o
ccu
r
wh
en
th
e
co
nd
itio
ns fo
r a strea
m
er
form
at
io
n
in
t
h
e g
a
s are fu
lfilled
.
Stream
er
form
at
i
o
n
is b
o
t
h
pressu
re
an
d
field
d
e
p
e
n
d
e
n
t
, an
d
therefo
r
e
d
e
p
e
nd
s
o
n
t
h
e electro
d
e
pro
f
ile,
g
e
o
m
etry o
f
th
e con
t
amin
atin
g
p
a
rticle, its p
o
s
ition
in
th
e
g
a
p
between
electrodes if it
is free, and
on the i
n
stant
a
neous
va
lue
of the am
bient field. The c
o
ndition
for stream
e
r
fo
rm
ati
on i
s
gi
ven
by
;
(7
)
Whe
r
e,
(x
)=
α
(x)
-
η
(x)
,
α
(x
) an
d
η
(x
)are t
h
e first ionizatio
n
coefficie
n
t and the coe
fficie
n
t of attachm
e
nt,
respect
i
v
el
y
;
b
o
t
h
bei
n
g f
unct
i
ons
o
f
fi
el
d
a
n
d
t
h
us
o
f
geom
et
ry
.
Th
e d
i
stan
ce (x
c) fro
m
th
e
particle’s
tip
o
r
trip
le
jun
c
tio
n
p
o
i
n
t
is wh
ere
th
e n
e
t i
o
n
i
zatio
n is zero
,
no
rmall
y
k
now
n as th
e io
n
i
zation
b
ound
ar
y.
Th
er
e is
so
m
e
co
n
t
ro
v
e
r
s
y ov
er th
e
v
a
lu
e of
K
,
t
h
e
disch
a
rg
e co
nstan
t
.
In
th
is stud
y fo
r breakdo
wn
vo
ltag
e
s
we tak
e
the v
a
lu
e of
K =
1
8
.42
fo
r
SF
6
gas
and
SF
6
-
g
as m
i
xt
ure
[
1
2]
.
6.
BREAK
D
O
W
N V
O
LTAGE
CAL
CUL
AT
IONS
FO
R G
A
S
MI
X
T
U
R
E
S WITH SI
NGLE WI
RE
CO
NTA
M
I
N
ATIN
G P
A
R
T
ICLE
Fi
gu
re 1
2
sh
o
w
s t
h
e effect
of gas p
r
ess
u
re o
n
t
h
e b
r
eakd
o
w
n
vol
t
a
ge fo
r va
ri
o
u
s fract
i
o
nal
conce
n
t
r
at
i
o
ns
of SF
6
-N
2
-Ai
r
gas m
i
xtures without coating of inne
r s
u
rface of eart
h
e
d
enclos
ure
.
We fixed
th
e
fraction
a
l co
n
c
en
tration
o
f
SF
6
gas at
5% in these m
i
xtures with
va
ri
o
u
s f
r
act
i
ona
l
conce
n
t
r
at
i
o
n
s
of
N
2
and
Ai
r t
o
a
v
oi
d di
sa
dva
nt
a
g
e
s
of S
F
6
gas s
u
ch as hi
gh c
o
st
s and al
s
o
o
b
t
a
i
n
t
h
e o
p
t
i
m
u
m
gas
m
i
xt
ure.
From
this figure, it
can
be
obse
rved
t
h
at
,
t
h
e
brea
k
d
o
w
n
vo
l
t
a
ge f
o
r
(S
F
6
-N
2
-
A
ir
) i
n
cre
a
ses w
h
e
n
fra
ctional
conce
n
t
r
at
i
o
n of SF
6
gas i
s
c
onst
a
nt
at
5%
and
wi
t
h
i
n
cre
a
si
ng
fract
i
o
na
l
conce
n
t
r
at
i
o
n
of
N
2
g
a
s an
d with
decreasi
n
g
f
r
a
c
t
i
onal
co
nce
n
t
r
at
i
on
of
Ai
r.
Al
so
, t
h
e
bre
a
kd
o
w
n
v
o
l
t
a
g
e
fo
r m
i
xt
ure i
s
i
n
crease
d
by
abo
u
t
50
0% as
t
h
e
p
r
essu
re
of m
i
xt
ure i
n
c
r
eases
fr
om
100
Kpa to 700Kpa. From these
m
i
xt
ures, t
h
e o
p
t
i
m
u
m
gas
m
i
xt
ure i
s
ob
se
rve
d
at
5%S
F
6
-8
0%N
2
-15
%
A
i
r
.
Fi
gu
re 1
3
sh
o
w
s t
h
e effect
of gas p
r
ess
u
re o
n
t
h
e b
r
eakd
o
w
n
vol
t
a
ge fo
r va
ri
o
u
s fract
i
o
nal
conce
n
t
r
at
i
o
ns
of
SF
6
-g
as m
i
x
t
u
r
es with
an
d
withou
t p
a
rticle c
o
n
t
am
i
n
atio
n. Fro
m
th
is figure, it
can
b
e
obs
er
ved t
h
at
,
t
h
e brea
k
d
o
w
n
vol
t
a
ge f
o
r a m
i
xt
ure of (
5
%SF
6
-8
0%N
2
-1
5%Air) in
case o
f
g
a
p
with p
a
rticle
()
0
xc
x
dx
K
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Effect o
f
Coa
tin
g o
f
Ea
rt
h
e
d
En
clo
s
u
r
e and
Mu
lti-
Con
t
amin
a
ting
Pa
rticles on
… (Amr A. Yo
u
s
sef)
47
9
co
n
t
am
in
atio
n d
e
creased
to abou
t 43
% fro
m
its v
a
lu
e in
case
o
f
clean
g
a
p,
i.e with
ou
t an
y
particle
cont
am
i
n
at
i
on.
Al
so, t
h
e
bre
a
k
d
o
w
n
vol
t
a
ge
for a m
i
xt
ure
of (
5
%
S
F
6
-80%CO
2
-15%Air) in case of ga
p with
part
i
c
l
e
co
nt
a
m
i
n
at
i
on d
ecre
a
sed t
o
a
b
o
u
t
4
0
%
fr
om
i
t
s
val
u
e i
n
ca
se
of
c
l
ean ga
p.
Fi
gu
re
1
2
.
Effe
ct
of
gas
p
r
ess
u
re
o
n
t
h
e
brea
kd
o
w
n
v
o
l
t
a
ge
f
o
r
va
ri
o
u
s
fra
ct
onal
c
o
n
cent
r
at
i
ons
of
SF
6
-N
2
-
A
i
r
gas
m
i
xt
ures
Fi
gu
re
1
3
.
Effe
ct
of
gas
p
r
ess
u
re
o
n
t
h
e
brea
kd
o
w
n
v
o
l
t
a
ge
f
o
r
va
ri
o
u
s
fra
ct
onal
c
o
n
cent
r
at
i
ons
of
SF
6
-g
as
m
i
x
t
u
r
es with
and
with
ou
t p
a
rticle
con
t
am
in
atio
n
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
:
47
1
–
48
5
48
0
0
100
200
300
400
500
600
100
200
300
400
500
600
700
Breakdo
w
n
Voltage
(KV)
Pressure (kPa)
5%
SF6+80
%
N
2+1
5
%
AIR
(W
ith coating)
5%
SF6+80
%
C
O2+15
%
A
I
R
(W
ith coating)
5%
SF6+80
%
N
2+1
5
%
AIR
(W
ithout coating)
5%
SF6+80
%
C
O2+15
%
A
I
R
(W
ithout coating)
430
440
450
460
470
480
490
500
00
.
5
11
.
5
2
Breakdow
n Voltage
(KV)
Coating Thickness
(mm)
(5%
S
F6+80
%
N2+15
%
A
I
R)
(5%
S
F6+80
%
CO2+15
%
A
IR)
Fi
gu
re 1
4
sh
o
w
s t
h
e effect
of gas p
r
ess
u
re o
n
t
h
e b
r
eakd
o
w
n
vol
t
a
ge fo
r va
ri
o
u
s fract
i
o
nal
co
n
c
en
tration
s
of SF
6
-
g
as m
i
xt
ures
wi
t
h
a
n
d
wi
t
h
o
u
t
c
o
at
i
ng
of
i
n
ner
su
rface
o
f
ea
rt
he
d e
n
cl
os
ur
e. T
h
e
m
a
t
e
ri
al
whi
c
h
pre
f
er
re
d f
o
r c
o
at
i
n
g
o
f
ea
rt
h
e
d e
n
cl
os
ur
e is Epo
x
y
with
20
00
µm
th
ick
n
e
ss. Fro
m
th
is fi
g
u
re,
it can be
observed t
h
at, the
breakdow
n
v
o
l
t
a
ge f
o
r
a m
i
xt
ure of
(
5
%SF
6
-8
0%N
2
-15%
Air) in case
of coa
ting
of
inne
r surface
of ea
rthe
d enc
l
osure inc
r
eas
ed to a
b
out
102% from
its
value in ca
se
of
unc
oating e
a
rthe
d
encl
os
ure
.
Al
s
o
, t
h
e
brea
k
d
o
w
n
v
o
l
t
a
ge f
o
r
a
m
i
xt
ure o
f
(5%
S
F
6
-80
%
CO
2
-
15%
Ai
r
)
i
n
case of c
o
at
i
ng
o
f
inne
r surface
of ea
rthe
d enc
l
osure inc
r
eas
ed to a
b
out
102% from
its
value in ca
se
of
unc
oating e
a
rthe
d
enclos
ure
.
From this figure,
it can
be deduced that the optim
u
m
case is
with coating the inner s
u
rface of
ear
th
ed
en
cl
o
s
u
r
e
w
ith
2
000micr
o
-
m
eter
t
h
ickn
ess
o
f
ep
ox
y m
a
ter
i
al
an
d
w
ith
(
5
%SF
6
-8
0%N
2
-1
5%A
i
r)
m
i
xt
ure
whi
c
h
i
t
gi
ves t
h
e
hi
g
h
er
b
r
eak
d
o
w
n
v
o
l
t
a
ge t
h
an
o
t
her case
s
.
Fig
u
re
1
5
shows th
e effect
of co
ating
th
ickn
ess
of ea
rt
he
d encl
os
ure
o
n
t
h
e br
eakdo
wn
vo
ltag
e
f
o
r
vari
ous
f
r
act
i
o
nal
co
nce
n
t
r
at
i
ons
o
f
SF
6
-
g
as
m
i
xt
ures.
T
h
e
gas
p
r
ess
u
re i
s
t
a
ke
n as c
o
n
s
t
a
nt
val
u
e
60
0k
Pa.
Fro
m
th
is fig
u
re, it can
b
e
ob
serv
ed
th
at, th
e b
r
eakdo
wn
v
o
ltag
e
is sligh
tly in
creased
as co
atin
g
th
ick
n
e
ss
increase
d
from zero i.e. (without c
o
a
ting) to 2mm
.
The effect of coatin
g
thickne
ss is s
m
all because c
h
arge
accum
u
lation on coating
doe
s
n'
t effect on
fi
eld in case
of
c
o
axial
gas
gap. From
this figure, the optim
um
gas
m
i
xt
ure i
s
(5%
S
F
6
-
80%
N
2
-15%A
i
r)
at
d
i
f
f
e
ren
t
th
ickn
ess of
co
atin
g.
Fi
gu
re
1
4
.
Effe
ct
of
gas
p
r
ess
u
re
o
n
t
h
e
brea
kd
o
w
n
v
o
l
t
a
ge
f
o
r
va
ri
o
u
s
fra
ct
onal
c
o
n
cent
r
at
i
ons
of
SF
6
-g
as m
i
x
t
u
r
es
with
and
with
ou
t co
a
ting
o
f
e
a
r
th
ed
enc
l
o
s
ur
e
Fig
u
r
e
15
. Ef
f
e
ct o
f
co
ating
t
h
ick
n
e
ss of
ear
t
h
e
d en
cl
o
s
u
r
e
o
n
th
e
br
eakdow
n vo
ltag
e
fo
r
v
a
r
i
o
u
s
fractonal c
o
nce
n
trations
of SF
6
-gas
m
i
xt
ures
Evaluation Warning : The document was created with Spire.PDF for Python.