TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 5071 ~ 50
7
7
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.579
7
5071
Re
cei
v
ed Fe
brua
ry 4, 201
3; Revi
se
d Ma
rch 13, 201
4
;
Accepte
d
March 30, 201
4
Effect of Conta
m
ination on Electric Field Distribution of
DC Voltage Divider
Liao Caibo*,
Ruan Jia
ngjun, Du Zhiy
e
, Liu Chao
Schoo
l of Elect
r
ical En
gin
eeri
ng, W
uhan U
n
i
v
ersit
y
, W
u
h
a
n
4300
72, Hu
bei
Province, Ch
in
a
No.8, South R
oad of Easter
n Lake, 43
00
72, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: lcb17
52@
12
6.com
A
b
st
r
a
ct
In order to res
earch th
e influ
ence of the c
o
ntam
in
ation
ar
oun
d the exter
nal i
n
sul
a
tin
g
surface o
f
DC voltag
e div
i
der w
i
th differe
nt types in the electic fi
el
d dis
t
ributio
n by usi
ng the finite e
l
ement metho
d
, a
tw
o dime
nsio
n
a
l axisy
m
metri
c
mod
e
l of th
e DC volta
ge
divid
e
r in L
o
n
gqu
an co
nvert
o
r station is b
u
ilt.
T
h
roug
h the c
a
lcul
atio
n co
mparis
on i
n
e
l
e
c
trostatic and
quas
i-el
ectrostatic fiel
d, the
relativ
e
di
el
ectri
c
constant
of the
dry, moist a
n
d
t
he n
on-u
n
ifor
m
mix
ed c
onta
m
i
nati
on l
a
yer
i
s
discuss
ed
un
der the
con
d
iti
o
n
of the mater
i
al par
a
m
eters
is k
now
n in quas
i-el
ectrostatic field.
Analys
is sho
w
s that for
dry
conta
m
i
natio
n
，
the field
type
has
no
infl
ue
n
c
e o
n
the
el
ectric
fiel
d d
i
strib
u
t
ion w
h
e
n
th
e
para
m
eters of
the
mater
i
als
ar
e
same. W
h
il
e f
o
r
moist c
onta
m
i
nati
o
n
，
the r
e
lativ
e
d
i
el
ectri
c
consta
nt in
electrostatic
fi
eld
shou
ld
be s
e
t
accord
ing
to th
e
materi
al r
e
si
stivity in
qu
asi-
electrostatic
fie
l
d a
n
d
the
actu
al co
nd
ition. T
h
e
calcul
atio
n of t
he
non-
unif
o
rm c
onta
m
i
nati
on pr
ove
that t
he
mat
e
ria
l
s p
a
ra
meters
in
e
l
ectrostatic fil
e
d i
s
reaso
nab
le.
Ke
y
w
ords
: DC
voltage d
i
vsid
e
r, conta
m
in
ati
on, elec
trostati
c field, quas
i-el
ectrostatic field
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
As o
ne
of th
e impo
rtant
device
in
DC co
nver
te
r
station, the i
n
sulation
de
sig
n
of
DC
voltage divide
r is extremely
important. In case of
bad
weath
e
r, the insul
a
tion pe
rforma
nce of DC
voltage divider with serve
contamin
atio
n will signifi
cantly redu
ced
,
which
will result in pollut
i
on
flashove
r
a
ccident. Du
rin
g
2004
an
d 2
009, poll
u
tion
flashove
r
a
c
cide
nts of
DC voltage
div
i
der
occurre
d
in
seque
nce in
Ji
anglin
g, Tian
she
ng
Qi
ao a
nd Lo
ngq
uan
conve
r
ter
st
ation, and
ha
ve
cau
s
e
d
se
rio
u
s con
s
eq
ue
nce
s
[1]. Therefore, the st
u
d
y of surface electri
c
field d
i
stributio
n of DC
voltage divide
r with contam
ination is very
nece
s
sary.
Corre
s
p
ondin
g
ly, the study on surfa
c
e
electri
c
field
distributio
n of DC voltag
e divider
with
contami
nation at
ho
me an
d ab
ro
ad up
to
n
o
w
is rare.
While ma
ny scholars
had
st
udied
electri
c
field
distrib
u
tion a
r
oun
d poll
u
te
d insulators,
whi
c
h h
ad
achi
eved frui
tful results,
and
accumul
a
ted
a lot of experien
c
e. T
he num
eri
c
a
l
comp
utatio
n method
s
of electri
c
fi
eld
distrib
u
tion
o
f
AC
pollute
d
insul
a
tors has been rel
a
tively
maturity,
including finite
differen
c
e
method [2, 3]
, finite eleme
n
t method [4
-6], cha
r
ge
si
mulation m
e
thod [7] a
nd b
ound
ary ele
m
ent
method [8-10
], while a lot
of rese
arch o
n
DC poll
u
ted
insulato
rs
were ba
se
d on
measu
r
em
en
t o
f
potential distribution,
exp
e
rimental
re
sult
s h
ad
sh
own
that pote
n
tia
l
distri
bution
of DC p
o
llute
d
insul
a
tors de
pend o
n
cont
amination
co
mpositio
n an
d distrib
u
tion
[11]. Rese
arch on elect
r
ic f
i
eld
distrib
u
tion i
s
extremely li
mited, and
el
ectri
c
fi
eld
di
stributio
n of
DC in
sulato
rs und
er unifo
rmity
and n
o
n
-
unif
o
rmity conta
m
ination
wa
s cal
c
ulate
d
in
[12] and
[13]
, the co
ncl
u
si
on that exi
s
te
nce
of contami
nat
ion on th
e insulators result in loca
l extre
m
ums
of ele
c
tric field
wa
s
prop
osed, wh
ile
the influen
ce
of contamin
ation on ele
c
tri
c
fi
eld distribution a
r
o
und pollute
d
insulato
rs a
nd
nume
r
ical si
mulation of contaminatio
n were ra
rely di
scusse
d [14-20].
In the
ca
se
of moi
s
t
contaminatio
n, t
here
was
leakage
current in
semi
condu
ctor
contami
natio
n layer outsi
de DC voltag
e divider, an
d
the cal
c
ulat
ion of electri
c
field distribut
ion
can n
o
t be
simplified a
s
an elect
r
o
s
tatic problem.
While a
c
cording to the relation bet
we
en
electrostati
c
and q
u
a
s
i-el
ectro
s
tati
c problem, it
ca
n be a
pproximated by el
ectro
s
tati
c field
analysi
s
met
hod. A 2
D
axis-symme
tric finite
el
ement mo
de
l of DC voltage divide
r in
con
s
id
eratio
n
of uniformity
contami
natio
n wa
s b
u
ilt
in
the pap
er. B
y
contra
sting
the cal
c
ul
ation
results
of qu
a
s
i-el
ect
r
o
s
tatic a
nd
ele
c
tro
s
tatic fiel
d, p
a
ram
e
ters of
contami
natio
n in
ele
c
tro
s
tatic
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5071 – 50
77
5072
field were
co
nfirmed.
The
n
, the i
n
fluen
ce
of thr
ee d
i
fferent kind
s
of contami
n
ation
o
n
el
ectric
field distrib
u
tion wa
s di
scu
s
sed in the p
aper.
2. Rese
arch
Metho
d
As the m
a
jo
r paramete
r
s
of DC voltag
e divide
r an
d
co
ntaminatio
n in el
ect
r
o
s
tatic field
cal
c
ulatio
n were diel
ectric con
s
tant, leakage
cu
rre
nt in co
ntamination l
a
yer ca
n not
be
cal
c
ulate
d
. After introd
ucin
g of condu
cti
v
ity in
quas
i
-
electrostati
c field, its influence o
n
elect
r
ic
field distrib
u
tion is con
s
ide
r
ed.
In quasi
-
el
ect
r
ostati
c field,
oulombi
an fie
l
d
E
c
is mu
ch
greate
r
than i
ndu
ced el
ect
r
ic field
E
i
, which me
ans that
E
i
ca
n be negl
ecte
d. The total electri
c
field is i
rrotatio
nal, an
d satisfie
s:
()
0
ci
c
EE
E
E
(
1
)
Therefore, th
e differential form
s of Maxwell’
s equatio
ns for q
uasi
-
e
l
ectro
s
tatic fie
l
d are:
0
0
E
D
HJ
t
D
B
(
2
)
Whe
r
e,
E
is electri
c
field i
n
tensity,
H
magneti
c
field intensity,
B
magneti
c
flux density,
J
electric
c
u
rrent dens
i
ty,
ρ
electric d
ensity. The re
lationship
s
be
tween differe
nt param
eters are:
D
E
B
H
J
E
(
3
)
In which,
ε
is diele
c
tri
c
consta
nt,
μ
permeability,
σ
con
d
u
c
tivity.
For isotro
pic
medium, the
s
e
para
m
eters a
r
e scala
r
, co
rresp
ondi
ng to tenso
r
for ani
sotro
p
ic m
edi
um.
Therefore, th
e ele
c
tric fie
l
d equ
ation
s
in
qua
si
-ele
ctro
static fiel
d are the
same for
electrostati
c field, and ma
king use of additional
mag
n
e
tic field equ
ations, ele
c
tri
c
and ma
gne
tic
field equatio
n
s
are d
e
coupl
ed.
3. Calculatio
n Model
3.1. DC Volta
g
e Div
i
der
(a) Whol
e
mo
del
(b) L
o
c
a
l mod
e
l
Figure 1. The
Model of DC
Voltage Divid
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Effect of Contam
ination on Electri
c
Field
Di
stri
bution of
DC Voltage
Divi
der
(Liao
Caib
o)
5073
In this pap
er, a 2D axis-symmetri
c
finite
eleme
n
t model of DC voltage di
vider in
Long
quan
co
nverter statio
n is intro
d
u
c
e
d
, as di
sp
lay
ed in
Figu
re
1. The
main
para
m
eters
o
f
DC
voltage divid
e
r a
r
e a
s
foll
ows. The tot
a
l height
of v
o
ltage divide
r is 5.060
m, a
nd the
comp
osite
bushing
co
nsi
s
ts of
93 bi
g
and 9
2
small
insul
a
tor
u
m
b
r
ella ski
rts, corres
pon
dingl
y diameters a
r
e
573mm an
d 5
33mm. The e
x
ternal diame
t
er of gradi
n
g
ring is 1.340
m, internal di
ameter 12
4m
m,
and the centre distan
ce of
two gra
d
ing
ri
ng is 1.4m.
Due to th
e a
c
tual in
stallati
on lo
cation, f
ound
ation of
DC volta
ge d
i
vider is
also
built in
the model, wi
th its potentia
l set to be ze
ro in cal
c
ulatio
n.
3.2. Contamination Mod
e
l
The u
n
iformi
ty contamin
ation of
DC voltage div
i
der i
n
finite
eleme
n
t m
odel i
s
approximated
by a thin l
a
yer on
the
surface of in
sulator
umb
r
el
la skirt
s
, wh
ose t
h
ickne
s
s i
s
1mm, as di
sp
layed in Figu
re 2.
Figure 2. Con
t
amination of the DC Volta
ge Divide
r
To en
su
re th
at conta
m
ina
t
ion co
nsi
s
ts of at lea
s
t two tie
r
gri
d
s after di
scret
i
zation,
contami
natio
n layer i
s
partitioned to b
e
two laye
rs with sam
e
thi
c
kne
s
s. At the
sam
e
time, t
h
e
junctio
n
s of
contami
natio
n layers are
curve
d
, so
a
s
to re
du
ce the influen
ce
of model o
n
the
cal
c
ulatio
n re
sults.
3.3. Parameters of Ma
teri
als
In finite element analysi
s
,
potential di
stribution
de
pen
ds on
relative
dielect
r
ic
con
s
tant of
material
s in
electrostati
c f
i
eld, whil
e in
qua
si-ele
ctrostatic field, i
t
is
codete
r
m
i
ned by
rel
a
tive
diele
c
tric con
s
tant a
nd
re
si
stivity. Makin
g
u
s
e
of
the
p
r
eviou
s
re
sea
r
ch
in [1
4], the pa
ram
e
ters of
material
s in q
uasi
-
ele
c
trost
a
tic field is shown in
Tabl
e 1. The feature of differe
nt contamin
ation
is ch
ara
c
te
ri
zation by di
fferent para
m
eter,
and
the thickne
s
s of conta
m
ination re
ma
ins
unchan
ged d
u
ring
cal
c
ulati
on.
Table 1. Para
meters of Material
s in Qua
s
i-ele
c
tro
s
tatic Field
Material
Relative
Permittivity
Resistiv
ity
Air 1
10
15
Insulation 3.5
10
12
Dr
y
cont
amination
2.8
10
10
Moist contamination
20
0.9754
4. Finite Element An
aly
s
is
In order to
g
e
t the
app
ro
priate
pa
ram
e
ters
that
re
pre
s
ent
different contami
n
ation in
electrostati
c field, the potential and
electri
c
field
distributio
n
are compa
r
ed with q
u
a
si-
electrostati
c field by finite element an
al
ysis meth
o
d
. Thre
e differe
nt kind
s of co
ntamination,
dry,
moist and mi
xed are di
scu
s
sed in the p
aper.
4.1. Dr
y
Contamination
For d
r
y co
nta
m
ination, lea
k
ag
e cu
rrent
on the
surfa
c
e of DC volta
ge is
so
small
that can
be negl
ecte
d
beca
u
se of its high re
si
stivity. Therefore, the pot
e
n
tial distrib
u
tion still depe
nds
mostly on rel
a
tive dielectri
c
co
nsta
nt in quasi
-
ele
c
tro
s
tatic field. Accordi
ng to Table 1, relati
ve
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5071 – 50
77
5074
diele
c
tric
of d
r
y conta
m
inat
ion is
set to b
e
2.8 in
el
ect
r
ostati
c field.
The ele
c
tri
c
fi
eld di
stributio
n
results in qu
a
s
i-el
ect
r
o
s
tatic and el
ectro
s
tatic field are displ
a
yed in
Figure 3.
(a) Elec
tros
tatic
(b) Quas
i-elec
tros
tatic
Figure 3. Electri
c
al Field
Distributio
ns
Result
s in
Electrostati
c Field
and Qua
s
i-el
ectro
s
tati
c Field
The cal
c
ul
ation re
sults
ind
i
cate
th
at
for dry c
ontami
n
ation with a
h
i
gh re
sistivity,
ele
c
tri
c
field distri
buti
on in q
u
a
s
i-el
ectro
s
tati
c fie
l
d is
con
s
i
s
te
nt with ele
c
trostatic fiel
d for
same
relat
i
ve
diele
c
tric
con
s
tant. The m
a
ximum ele
c
tric fiel
d inten
s
ity are 13.6
k
V/cm, app
e
a
rs
at the rig
h
t
surfa
c
e of lo
wer g
r
a
d
ing ri
ng.
The ele
c
tri
c
field inten
s
ity results alo
n
g
t
he path o
n
the su
rface
of contami
nation in
electrostati
c and qua
si
-el
e
ctro
stati
c
field are di
sp
la
yed in Figure
4, which sh
ows that electri
c
field intensity in electrostati
c field is sli
g
h
t
ly larger than
quasi
-
ele
c
tro
s
tatic field.
Figure 4. Electri
c
al Field
Distributio
ns of
t
he Contami
nation in Electrostati
c Field
and Qua
s
i-
electrostati
c Field
The results
of dry conta
m
ination in
di
cate t
hat
hig
h
re
si
stivity
has little infl
uen
ce o
n
electri
c
field
distrib
u
tion
in qua
si-el
e
ctro
stati
c
field calcul
ation, and the
relative diel
ectri
c
c
o
ns
tant in elec
tros
tatic
field s
h
ould set to be 2.
8, sam
e
as that in q
uasi
-
ele
c
trost
a
tic field.
4.2. Moist Contamination
Moist contam
ination on the su
rface of DC voltage divider
will form a semiconductor
layer, which
will lead to a subs
tantial i
n
crease i
n
le
akage
current. As the
resi
stivity of moist
contami
natio
n is very sma
ll in quasi-ele
c
tro
s
tati
c fiel
d, its influence on
the potential distrib
u
tion
can n
o
t be negle
c
ted. T
he elect
r
ic fi
eld distri
butio
n results wit
h
the same
relative diele
c
tri
c
con
s
tant in el
ectro
s
tati
c an
d qua
si-el
e
ct
rostatic field a
r
e sh
own in F
i
gure 5.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Effect of Contam
ination on Electri
c
Field
Di
stri
bution of
DC Voltage
Divi
der
(Liao
Caib
o)
5075
(a) Elec
tros
tatic
(b) Quas
i-elec
tros
tatic
Figure 5. Electri
c
al Field
Distributio
ns
Result
s in
Electrostati
c Field
and Qua
s
i-el
ectro
s
tati
c Field
The re
sults d
i
splaye
d in Figure 5 indi
ca
te that
the same relative
diele
c
tric
con
s
tant in
qua
si-el
e
ct
ro
static an
d ele
c
tro
s
tatic fiel
d lead to gr
e
a
t diversity in
electri
c
field
distrib
u
tion. T
h
e
maximum val
ue of ele
c
tri
c
field inten
s
ity in qua
si-ele
ctrostati
c
field
is 16.7
k
V/cm,
co
rre
sp
ondi
ng
to 13.6kV/cm
in electrostati
c field, and th
e
maximum value
s
app
ear
at different po
sition.
In ele
c
tro
s
tati
c field
calcula
t
ion, the
relati
ve diele
c
tri
c
consta
nt of m
o
ist contamin
a
t
ion is
increa
sed f
r
o
m
10
4
to 10
8
in se
quen
ce
, the potenti
a
l and el
ect
r
i
c
field di
strib
u
tion curve
of
contami
natio
n comp
ared
with qua
si-ele
ctro
static field
are displaye
d as Figu
re 6.
Electric Potential/V
(a) Ele
c
tri
c
Potential
(b) Ele
c
tri
c
Fi
eld
Figure 6. Electri
c
Potential
and Electri
c
Fiel
d Di
strib
u
tions of Moi
s
t Contami
natio
n in
Electro
s
tatic
Field and Q
u
asi-ele
c
tro
s
ta
tic Field
The re
sult
s show that wh
en the relativ
e
diel
e
c
tric
consta
nt of moist co
ntamin
ation is
betwe
en 10
5
and
1
0
7
, the potential an
d
electri
c
field
distri
b
u
tion curves on
the surfa
c
e of
m
o
ist
contami
natio
n in
ele
c
tro
s
t
a
tic field
a
r
e
in g
ood
ag
reement
with
qua
si-el
e
ct
ro
static fiel
d. T
h
e
curve
indi
cat
e
s that
potent
ial dist
ribution
is line
a
r,
a
n
d
the potential
distrib
u
tion in
elect
r
o
s
tatic
is
smalle
r
th
an that
in qua
si-electrostati
c
whe
n
relative
diele
c
tri
c
co
nstant i
s
bel
ow
10
5
. Whil
e
if
relative diele
c
tri
c
con
s
tant
set to be 10
8
in electrostat
i
c field, there
will be oscillations in electric
field distrib
u
tion cu
rve just
as sho
w
n in
Fig.6(b)
. Co
nse
que
ntly, a
ppro
p
ri
ate rel
a
tive dielectri
c
con
s
tant of m
o
ist co
ntamin
ation in
ele
c
trostatic field
should
set to be 10
6
.
4.3. Mixed Contamina
t
io
n
For
mixed
co
ntamination
d
i
scusse
d in
th
e
pa
per,
the t
h
ickne
s
s rem
a
ins 1.0mm,
and th
e
contami
natio
n is divide
d
into th
ree
parts.
Two
end
s of
co
n
t
amination
are set to
be
dry
contami
natio
n be
cau
s
e
of heating, the
middle p
a
rt
i
s
moist. Th
e relative diele
c
t
r
ic
co
nsta
nts
of
dry and moi
s
t
contamin
atio
n are ba
se
d o
n
previou
s
re
sea
r
ch in ch
a
p
ter 4.1 and
4.2. The elect
r
ic
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TELKOM
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KA
Vol. 12, No. 7, July 201
4: 5071 – 50
77
5076
field distri
buti
ons in
qua
si-electrostati
c
and ele
c
trost
a
tic field a
r
e
displaye
d in
Figure 7. T
h
e
maximum ele
c
tri
c
field intensity appe
ars at t
he junctio
n
of dry and
moist contam
ination.
(a) Elec
tros
tatic
(
b
)
Qu
as
i-
e
l
ec
tr
os
ta
tic
Figure 7. Electri
c
al Field
Distributio
ns in
El
ectro
s
tatic
Field and Q
u
asi-ele
c
tro
s
ta
tic Field
The
potentia
l and
ele
c
tri
c
field
di
stri
but
ion
cu
rve
s
al
ong
the
su
rfa
c
e
of mixed
contami
natio
n are
shown as
Figu
re
8. The el
e
c
tro
s
tatic
cal
c
ulatio
n re
su
lts are in g
ood
agre
e
me
nt wi
th that in
qu
a
s
i-el
ect
r
o
s
tatic field.
The
p
o
tential di
stri
bution
cu
rve
s
indi
cate
that
for
qua
si-el
e
ct
ro
static fiel
d, as th
e resi
stivity
of moist contamin
ation is far less tha
n
dry
contami
natio
n, the voltage drop in
moist cont
a
m
ination al
m
o
st eq
ual
s to 0. Whil
e
for
electrostati
c field, the sam
e
result can
be obt
aine
d becau
se of the huge dive
rsity in relati
ve
dielectric constant.
The el
ectri
c
field di
stribution
curve shows t
hat there
will be distortions at t
he
junctio
n
of dry and moist contaminatio
n.
(a) Ele
c
tri
c
Potential
(b) Ele
c
tri
c
Fi
eld
Figure 8. Electri
c
Potential
and Electri
c
Fiel
d Di
strib
u
tions of Mixed
Contamin
ation in
Electro
s
tatic
Field and Q
u
asi-ele
c
tro
s
ta
tic Field
The
potential
and
ele
c
tri
c
f
i
eld
cal
c
ulatio
n result
s
are
also
in
goo
d
agre
e
me
nt fo
r mixed
contami
natio
n, which indi
cate that the
param
et
ers of dry and moist co
ntamin
ation obtaine
d in
the pape
r are
valid and fea
s
ible.
5. Conclusio
n
Makin
g
u
s
e
of 2D
axis-sy
mmetry finite
elem
e
n
t mo
del of
DC vol
t
age, the infl
uen
ce of
contami
natio
n on it
s
su
rfa
c
e
elect
r
ic fie
l
d dist
ri
butio
n
is di
scu
s
sed
in this pa
per. By compa
r
i
n
g
the ele
c
tro
s
ta
tic cal
c
ul
ation
re
sults
with
qua
si-el
e
ct
ro
static field, th
is pa
per stu
d
i
es the
rel
a
tive
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TELKOM
NIKA
ISSN:
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046
Effect of Contam
ination on Electri
c
Field
Di
stri
bution of
DC Voltage
Divi
der
(Liao
Caib
o)
5077
diele
c
tric
co
n
s
tant of d
r
y, moist an
d mi
xed co
nt
amin
ation in el
ectrostatic fiel
d. The
con
c
lu
si
ons
are as
follows.
1) Fo
r dry
co
ntamination,
becau
se of
it
s high
re
si
st
iv
it
y
,
t
y
pe of field ha
s little influen
ce
on ele
c
tri
c
field di
stributio
n. The ap
pro
p
riate
relati
ve
diele
c
tric
co
nstant in
ele
c
tro
s
tatic fiel
d is
same a
s
the
value in qua
si
-ele
ctro
static
field.
2) F
o
r moi
s
t
contami
natio
n, the a
pprop
riate
rela
tive
diele
c
tric con
s
tant in
ele
c
trostatic is
10
6
, which is
much la
ge
r than qua
si-ele
ctrostati
c
field.
3) Fo
r id
eal
mixed co
nta
m
ination di
scussed i
n
the
pape
r, the rel
a
tive diele
c
tri
c
con
s
tant
prop
osed is v
a
lid and fea
s
i
b
le.
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