Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
5
,
No
. 3,
J
une
2
0
1
5
,
pp
. 39
1~
40
2
I
S
SN
: 208
8-8
7
0
8
3
91
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
Modelling of the AC Breakdown
Voltage of Point-Plane Air
Gaps with Insulating Barrier
Abdel
g
ha
ni Ro
uini, Djilla
li
Mahi
Laborator
y
of
studies and
Development of Semic
onductor
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
Ja
n 20, 2015
Rev
i
sed
Mar
31
, 20
15
Accepte
d April
15, 2015
High voltag
e
device d
i
mensioning require
s the predic
tion
of th
e
withstand
voltag
e
for test
conditions like impulse
s, surges
and AC voltage. There is a
large need
of
designer
to hav
e
relia
bl
e
de
si
gn
c
r
i
t
e
r
ia
a
n
d
we
l
l
-
d
e
fi
n
e
d
simulation procedure for dev
i
ce
developmen
t.
T
h
i
s
p
a
r
a
me
t
r
ic
st
udy
i
s
ba
se
d
on the methodo
log
y
of
experim
e
ntal
designs. This method allo
wed us to
propose a mathematical poly
n
o
m
ial model.
The objectiv
e of this paper is to
stud
y
the disch
a
rge phenomena for a point–plan
e air interv
al with insulating
barrier b
e
tween them. Firstly
on experime
ntal stud
y
of
a laborator
y setup that
we designed to
carr
y
out th
e inf
l
uence
of param
e
ters (geometr
ical) involv
e
d
in the pro
cess of breakdown.
The dist
an
ce b
e
tween electrodes
and differ
e
nt
parameters of
th
e barrier such as
its position between electrodes
dimension
and its
holes
is
studied
. The barri
er acts
as
a geom
etrica
l obs
tacl
e agains
t th
e
direct propagation of discharge. Sec
ondly
,
using results obtained b
y
the
experimental setup, we
have experiments design
methodolog
y
of techniq
u
e
to pred
ict th
e br
eakdown threshold voltage.
Keyword:
B
r
eak
do
w
n
vol
t
a
ge
Geom
etrical obstacle
Hi
g
h
vol
t
a
ge
d
e
vi
ce
In
su
latin
g b
a
rri
er
Poi
n
t
-
pl
a
n
e ga
p
Copyright ©
201
5 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
:
Ab
del
g
ha
ni
R
o
ui
ni
,
Lab
o
rat
o
ry
of st
udi
es
a
n
d De
vel
o
pm
ent
of S
e
m
i
conductor and
Dielectric
Materials, LeDMaScD,
Uni
v
ersity
Am
ar
Telidji of La
ghouat, Alge
ria
Em
ail
:
a.ro
ui
n
i
@u
ni
v-
d
j
el
fa.
d
z
1.
INTRODUCTION
Th
e barriers are wid
e
ly used
in
m
a
n
y
h
i
gh
vo
lta
ge
devi
ces. It is well known t
h
at the dielectric
streng
th
of long
air
g
a
p
is si
g
n
i
fican
tly in
creased b
y
t
h
e in
sertion
o
f
an
in
su
lating
b
a
rrier. Th
e
i
n
su
latin
g
st
ruct
u
r
e i
s
di
ffe
rent
st
ress
and
part
i
c
ul
arl
y
t
o
t
h
e di
scharge p
h
e
n
om
ena [1]
,
[
2
]
.
T
h
e k
n
o
w
l
e
d
g
e
of t
h
e
co
nd
itio
n of i
o
n
i
sation
an
d
p
r
op
ag
ation
o
f
electrical d
i
sch
a
rg
e is
o
f
great in
terest to well un
d
e
rstan
d
t
h
e
mecanis
m
leading t
o
brea
kdown
[3].
Two
cond
itio
ns m
u
st b
e
si
mu
ltan
e
ou
sly fulfielled
in
order fo
r an
im
p
u
l
se d
i
sch
a
rg
e to
o
c
cu
r i
n
gases: there s
h
oul
d be at least one s
u
itably located free
electron close to the stresse
d electrode and the electric
field
stress shou
ld
b
e
su
fficien
tly h
i
g
h
with
i
n
th
e critical v
o
l
u
m
e o
f
th
e stressed
electrod
e
.
Wh
en
th
ese two
co
nd
itio
ns are satisfied
, th
e electro
n
p
r
odu
ces a seq
u
e
n
ce o
f
av
alan
ch
es and
streamers th
at lead
to
a
b
r
eakd
own
[4
], [5
].
In
th
e absen
c
e o
f
an
in
itiato
ry electro
n
in
th
e critical v
o
l
u
m
e, n
o
sin
g
l
e av
alan
ch
e can
lead
to
a
brea
kdown, e
v
en if t
h
e electric fiel
d exceeds the
brea
kdown field
strength
of the
gas
medium
[6]. Whe
n
t
h
e
discha
rge
develops
, the accum
u
lation of charges on th
e
surface
of the barrie
r
f
acing the sha
r
p electrode
m
a
kes t
h
e
bar
r
i
e
r t
o
be
ha
ve
as a
fl
ot
i
n
g
p
l
an el
ect
ro
de,
and the electri
c field
betwee
n the
ba
rrie
r
a
n
d the
electro
d
e
will b
e
u
n
i
form
[7
].
The insulating barriers i
n
fl
ue
nce
on t
h
e
dielectric st
reng
th o
f
arrang
em
e
n
t po
in
t-p
l
an.
It is sho
w
n
t
h
at
t
h
e di
el
ect
ri
c
st
re
ngt
h of
suc
h
us
i
n
sul
a
t
i
ng st
r
u
ct
ur
es i
s
th
e im
p
r
ov
ed wh
en th
e b
a
rrier is in
serted
n
ear
t
h
e shar
p el
ect
r
ode
. The ef
fect
i
v
eness
of t
h
e
bar
r
i
e
r de
pe
nd
s on t
h
e ge
om
et
ry
(t
he di
m
e
nsi
on an
d t
h
e p
o
s
i
t
i
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mo
del
l
i
ng
of
t
h
e AC
Break
d
o
w
n V
o
l
t
age
of
Poi
n
t
-
Pl
a
n
e
A
i
r Ga
ps
w
i
t
h
I
n
sul
a
t
i
n
g B
a
rri
e
r
(
A
. Ro
ui
ni
)
39
2
o
f
th
e b
a
r
r
i
er)
,
and
th
e physical n
a
tu
r
e
o
n
th
e
b
a
rr
ier [
8
]-
[10
]
. The in
v
e
stig
ation
h
a
v
e
b
e
en d
o
n
e
expe
ri
m
e
nt
al
ly and
si
m
u
l
a
t
e
d i
n
o
r
de
r t
o
st
udy
t
h
e
b
r
eak
do
w
n
p
h
e
nom
ena o
f
s
o
l
i
d
di
el
ect
ri
c barri
e
r
. Th
e
prese
n
ce of a hole withi
n
the barrie
r
signi
ficantly redu
ce
s the dielectric strengt
h of the syste
m
. Tests are
conducted t
o
measure th
e
5
0
H
z
AC
b
r
ea
kd
ow
n
v
o
l
t
a
ge
of
sm
all
ai
r ga
p.
Ener
gi
zed
ro
d and
gr
ou
n
d
ed
pl
an ga
ps are
st
udi
e
d
wi
t
h
t
h
e fl
at
i
n
sul
a
t
i
ng
bar
r
i
e
rs t
h
a
t
have t
h
ree
di
ffe
re
nt
di
am
et
ers [
1
1]
, [
1
2]
. T
h
e re
sul
t
s
o
f
t
h
e
t
e
st
seri
es
sh
ow
ho
w t
h
e
b
r
eak
d
o
w
n
v
o
l
t
a
ge va
ri
es
wi
t
h
t
h
e
d
i
stan
ce
b
e
tween
th
e electrodes, th
e size an
d th
e m
a
terial
o
f
b
a
rrier, th
e rel
a
tiv
e po
sitio
n
o
f
th
e electrodes and
the ba
rrie
r
between them
.
As a result, al
l three
m
a
terials show n ea
rly sa
m
e
effect when they a
r
e use
d
as a barrier, the
brea
kdown vol
t
age va
ries
due to th
e size
of the
barriers
a
n
d the m
a
xi
m
u
m
fl
asho
ver
vol
t
a
ge
s are
o
b
ser
v
e
d
wh
en
th
e b
a
rri
ers are po
sition
e
d
at th
e n
e
arest p
o
i
n
t
to
th
e electrod
e
an
d
th
e sm
all s
i
zed
b
a
rriers beco
m
e
effect
i
v
e
o
n
l
y
i
n
ve
ry
sm
all
ai
r ga
ps [
1
3]
-[
19]
.
A
n
anal
y
s
i
s
based
o
n
e
x
peri
m
e
nt
al
desi
gn m
e
t
hod
ha
s bee
n
devel
ope
d
w
h
i
c
h i
n
di
cat
es t
h
at
m
easurem
ent
s
d
o
c
ont
ai
n
som
e
rel
e
vant
i
n
f
o
rm
at
i
on t
e
st
at
earl
y
st
ages i
n
red
u
ce
d tim
e fram
e
.
The
hi
st
ory
of
desi
g
n
of e
x
p
e
ri
m
e
nt
s st
art
e
d i
n
t
h
e
19
3
0
i
n
En
gl
an
d wi
t
h
M
.
Fi
she
r
[
20]
,
whi
c
h i
s
a
useful statistic
al approac
h
that woul
d
lead
t
o
a reliab
l
e and
sign
ifican
t interp
retation
o
f
th
e d
i
fferen
t ord
e
ri
ng
param
e
ters of the ins
u
lation a
g
eing proce
ss but it kne
w
an accelerating de
velopm
ent
since the publication
of
som
e
prede
f
i
n
ed t
a
bl
es
by
T
a
guc
hi
[
2
1]
. T
h
e
pri
n
ci
pl
e o
f
t
h
i
s
m
e
t
hodol
ogy
i
s
t
o
car
r
y
out
a
sche
d
u
l
e
o
f
expe
rim
e
nts designe
d to
obtai
n the m
o
st accurate inform
ation
for a s
p
eci
fi
c problem
with a
m
i
nim
u
m
num
ber
of e
xpe
ri
m
e
nts [2
2]
, [
2
3]
. It
s ad
vant
a
g
es
were
pr
o
v
ed
i
n
di
f
f
ere
n
t
areas o
f
ap
pl
i
cat
i
on, es
peci
al
l
y
i
n
chem
istry and m
echanic
s, w
h
ere
a l
a
r
g
e
n
u
m
b
er o
f
para
m
e
t
e
rs ha
ve t
o
be
o
p
t
i
m
i
zed sim
u
l
t
a
neousl
y
[
24]
.
Di
ffe
re
nt
desi
gns
exi
s
t
i
n
o
r
de
r t
o
g
o
wi
t
h
a l
a
r
g
e
n
u
m
b
er
o
f
a
ppl
i
cat
i
ons
. I
n
or
de
r
t
o
pe
rf
orm
a desi
g
n
m
e
t
hod i
t
i
s
ne
cessary
t
o
de
fi
ne t
h
e p
r
obl
em
and c
h
o
o
se t
h
e vari
abl
e
s
,
w
h
i
c
h are cal
l
e
d f
act
ors
or
para
m
e
t
e
rs
by
t
h
e e
x
peri
m
e
nt
al
desi
gne
r
[2
5]
.
A
d
e
sign
sp
ace, orreg
i
on
of
in
terest, m
u
st b
e
d
e
fi
n
e
d, th
at is, a rang
e
o
f
v
a
riab
ility
m
u
st b
e
set
for
each varia
b
le. The num
ber of
the variables
values
c
a
n
a
s
s
u
m
e
in design
m
e
thod is
re
stricted and
gene
rally is
sm
a
ll [2
6
]
-[28]. Th
erefore,
we can
d
eal eith
er with
qu
alitativ
e d
i
screte v
a
riab
les, or q
u
a
n
titativ
e discrete
v
a
riab
les. Qu
an
titativ
e co
n
tinu
o
u
s
v
a
riab
les
are d
i
screti
zed
with
in
th
eir ran
g
e
. At first there is n
o
kno
wled
g
e
on t
h
e sol
u
tion space, a
nd it
may happe
n that the regi
on
of
interest excludes the
optim
um design.
If t
h
is is
co
m
p
atib
le with
d
e
sign
req
u
i
re
m
e
n
t
s, th
e regio
n
of in
tere
st
can
be a
d
justed later on
, as so
on
as th
e
w
r
on
gn
ess
of t
h
e c
h
oi
ce
i
s
percei
ve
d.
The de
si
g
n
m
e
t
hod t
ech
ni
que a
n
d t
h
e
n
u
m
b
er of l
e
ve
l
s
are t
o
be s
e
l
ect
ed
according to the num
ber of experim
e
nts
whi
c
h can
be afforded
[29]. By th
e ter
m
levels
we m
ean the num
be
r
of different
val
u
es a
va
riable
can ass
u
m
e
according t
o
its
discretization. The num
b
er
of
levels us
ually
is
the
sam
e
for al
l
vari
abl
e
s,
ho
we
ver s
o
m
e
t
ech
ni
q
u
es al
l
o
w t
h
e di
f
f
ere
n
t
i
a
t
i
on
of t
h
e
num
ber
of l
e
vel
s
f
o
r eac
h
vari
a
b
l
e
. I
n
e
x
peri
m
e
nt
al
desi
gn,
t
h
e
ob
ject
i
v
e f
u
nct
i
o
n
an
d t
h
e
set
o
f
t
h
e per
f
o
rm
ed expe
ri
m
e
nt
s are cal
l
e
d
response
varia
b
le and
sam
p
le
space
res
p
ectively.
In
t
h
i
s
pa
per
w
o
r
k
,
i
n
o
r
de
r t
o
m
odel
l
i
ng t
h
e
AC
brea
kd
o
w
n
v
o
l
t
a
ge i
n
p
o
i
n
t
-
pl
an
ga
ps a
r
ran
g
em
ent
i
n
pre
s
ence
of
bar
r
i
e
r, t
h
e ex
peri
m
e
nt
s desi
gn m
e
t
hod i
s
u
s
ed. T
h
e car
ri
e
d
o
u
t
ex
peri
m
e
nt
al
resul
t
s
are
t
a
ke
n
to
bu
ild
a m
o
d
e
l wh
ich tak
e
s in
to con
s
ideratio
n
d
i
ffer
en
t p
a
ram
e
ters such
as (the relativ
e po
sitio
n of the
bar
r
i
e
r,
i
t
s
h
o
l
e
an
d t
h
e
wi
dt
h
of
t
h
e
bar
r
ier) t
h
at affect the
breakdown phenom
ena.
2.
E
X
PERI
MEN
T
AL SETUP
Th
e exp
e
rim
e
n
t
al set-u
p
con
s
ists o
f
a h
i
g
h
-vo
ltag
e
test tran
sform
e
r 1
0
0kV/5
kVA/
5
0
Hz, a cap
acitiv
e
vol
t
a
ge
di
vi
de
r
.
Fi
gu
re 1 an
d Fi
gu
re 2 (t
he
expe
ri
ences
ha
ve bee
n
per
f
o
r
m
e
d
i
n
t
h
e
l
a
bo
rat
o
ry
of
hi
gh
v
o
l
t
a
g
e
Un
i
v
ersity
o
f
Bisk
ra) sh
ows th
e a
rra
ngement of electrodes
and
i
n
s
u
latin
g
ba
rri
e
r
i
t
c
ont
ai
n
s
a
p
o
i
n
t
–pl
a
n
el
ect
rode
ar
ran
g
em
ent
m
ount
ed vert
i
cal
.
The
HV electrode
s consist a
steel needle
point on c
opper
of conical in s
h
a
p
e
30°. T
h
e
grounded pl
a
n
el
ect
rode i
s
a
ci
rcul
ar st
eel
pl
at
e of
30 c
m
l
ong,
2.
8 c
m
di
am
et
er. The pl
e
x
i
g
l
a
s b
a
rri
ers
(
3
.
3
are
squ
a
res o
f
di
f
f
ere
n
t
wi
dt
h
s
(5 cm
, 10 cm
, 15 cm
) and di
ffe
re
nt
hol
es
(4m
m
, 8
m
m
and
12m
m
)
and i
t
s
t
h
i
c
kne
sses i
s
1m
m
,
an al
u
m
i
num
pl
an g
r
o
u
nde
d. T
o
chan
ge t
h
e p
o
s
i
t
i
ons fo
r seve
ral
barri
e
r
s, c
a
rri
er
s
Bak
e
lite are
u
s
ed
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I
S
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:
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08
IJEC
E V
o
l
.
5, No
. 3,
J
u
ne 2
0
1
5
:
39
1 – 4
0
2
39
3
Fi
gu
re
1.
C
i
rcu
i
t
pr
obat
i
o
na
ry
i
n
d
u
st
ri
al
real
i
zes a f
r
e
que
nc
y
Fi
gu
re
2.
Vi
e
w
o
f
real
t
e
st
cel
l
and
t
h
e
hi
gh
vol
t
a
ge
l
a
b
o
rat
o
ry
c
o
nt
rol
pa
n
e
l
The
barrier is
m
ounted vertically between the elect
rode
s Fi
gure
2. Its s
u
rfaces are c
h
ecked after eac
h
b
r
eakd
own
.
The po
sitio
n
o
f
the b
a
rrier is
d
e
fi
n
e
d
b
y
th
e ratio
a /d
, wh
ere a is th
e po
in
t
–
barrier d
i
stan
ce
and
d
i
s
t
h
e
poi
nt
–
p
l
a
n el
ect
r
ode
ga
p.
3.
MODELLING AND PRE
D
ICTION BY
E
X
PERIME
NTS
DESIGN METHOD
3.1 Principles
and Interests
The
pri
n
ci
pl
e o
f
t
h
e t
e
c
hni
cal
desi
g
n
of e
x
pe
ri
m
e
nt
s consi
s
t
s
i
n
va
ry
i
n
g l
e
vel
s
o
f
one
o
r
m
o
re fact
ors
sim
u
l
t
a
neous
(
w
hi
c
h
a
r
e
vari
abl
e
,
di
scret
e
o
r
c
ont
i
n
u
ous
) i
n
eac
h t
e
st
.
Th
is
will h
e
lp to
redu
ce
sign
ifican
tly th
e
n
u
m
b
e
r
o
f
exp
e
rim
e
n
t
s to
be p
e
rfo
r
m
e
d
.
Wh
ile i
n
creasi
n
g th
e
num
ber
of
st
u
d
i
e
d
fact
o
r
s,
d
e
t
ect
i
ng i
n
t
e
r
a
ct
i
ons
bet
w
ee
n
t
h
e
fact
o
r
s a
n
d
opt
i
m
al
co
m
p
are
d
t
o
a
r
e s
p
o
n
se
,
th
at is to
say
aq
u
a
n
tity u
s
ed
as stand
a
rd
and
allo
wing
to easily
m
o
d
e
llin
g
resu
lts.
Th
e d
e
licate po
in
t in
th
e u
s
e o
f
exp
e
rim
e
n
t
al d
e
sig
n
will
b
e
min
i
m
i
zed
as
m
u
ch
as possib
l
e th
e
n
u
m
b
e
r
o
f
experim
e
n
t
s to
b
e
carried ou
t
with
ou
ts a crificing
accu
r
acy
resu
lts.
To
o
b
t
a
i
n
rel
e
v
a
nt
i
n
fo
rm
at
i
o
n, a
m
e
t
hodol
o
g
i
cal
ap
pr
oac
h
sho
u
l
d
be as
f
o
l
l
o
wed
[
3
0]
:
Defi
nitions of objectives
and criteria,
Defi
ni
t
i
on of
f
act
ors st
u
d
i
e
d and
ex
pe
ri
m
e
n
t
al
fi
el
d,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
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208
8-8
7
0
8
Mo
del
l
i
ng
of
t
h
e AC
Break
d
o
w
n V
o
l
t
age
of
Poi
n
t
-
Pl
a
n
e
A
i
r Ga
ps
w
i
t
h
I
n
sul
a
t
i
n
g B
a
rri
e
r
(
A
. Ro
ui
ni
)
39
4
C
onst
r
uct
i
o
n
o
f
t
h
e
ex
peri
m
e
nt
al
desi
gn
,
Ex
péri
m
e
nt
at
ion
,
Analy
s
is,
Co
ndu
ct an
y ad
d
ition
n
e
l testi
n
g,
Valid
atio
n,
Co
n
c
l
u
sion
o
f
th
e
stud
y.
Th
e trad
ition
a
l
m
e
th
o
d
o
l
og
y
fo
r an
exp
e
ri
m
e
n
t
al d
e
sign
co
nsists of fo
ur
(4) step
s: fi
rst th
e
p
r
ep
aration
stud
y in
clu
d
i
n
g
the d
e
fin
ition
o
f
respon
ses ch
aracterizin
g
th
e
o
b
j
ectiv
es, wh
ich
is th
e
m
a
in
scop
e
of
t
h
i
s
pa
per
a
n
d
t
h
e
det
e
rm
inat
i
o
n
of
fact
o
r
l
e
vel
s
, t
h
e
n
t
h
e c
hoi
ce
o
f
fa
ct
ors a
n
d e
x
per
i
m
e
nt
al
dom
ain i
n
t
h
e
secon
d
step
, the propo
sed m
o
d
e
l it self and
fin
a
lly, th
e m
a
t
h
em
at
ical
m
o
d
e
l.
a.
Step A: Defini
tion
of
res
ponses
charac
teri
z
i
ng the
objec
t
ives
W
e
want to
m
e
asure the influe
nce of
the following factors Where:
P (cm
)
i
s
t
h
e rel
a
ti
ve posi
t
i
on
of t
h
e
barri
er.
L (cm
)
i
s
t
h
e wi
dt
h of t
h
e
barr
i
e
r.
T (mm) is th
e
h
o
l
e in
th
e b
a
rrier.
b.
S
t
e
p
B:
C
h
o
i
ce
of
fa
ct
o
r
s
and experimental dom
a
in
Det
e
r
m
i
n
i
ng the fi
el
d of study
i
s
cl
osel
y rel
a
t
e
d
t
o
t
h
e i
n
i
t
i
a
l
know
l
e
dge hel
d
on
t
h
e phy
si
cal
phenom
e
non under study, but also to th
e objectives of the experim
e
nt.
In
addition, ca
re m
u
st be tak
e
n to
m
i
nim
i
ze t
h
e cost
of t
h
e st
u
d
y
,
exp
r
essed as
num
ber of t
e
st
s.
W
e
defi
ne t
h
e
fi
el
d of st
u
d
y
and
val
i
d
i
t
y
o
f
t
h
e expe
rim
e
nt
consi
d
eri
n
g
t
h
e possi
bl
e l
i
m
it
s t
o
t
h
e vari
ati
o
n
fact
ors. Fo
r t
h
i
s
, we refe
rred t
o
t
h
e p
r
el
im
i
n
ary
st
udy
on t
h
e
i
n
fl
uence o
f
v
a
ri
ous pa
ram
e
ters.
W
e
recall n
o
w
th
at th
e resu
lt
s o
f
th
e stu
d
y
will b
e
v
a
lid
o
n
l
y o
n
th
e range o
f
v
a
riatio
n
o
f
th
e facto
r
s
considered. The
m
a
in factors consider
ed in this plan experiments are:
Tabl
e
1. L
e
vel
s
o
f
f
act
or
s st
u
d
i
e
d
F
a
c
t
o
r
P
(
c
m)
L
(
c
m)
T
(
m
m)
L
e
vel – 1
0
5
4
L
e
vel 0
2
10
8
L
e
vel +1
4
15
12
c.
Step C: A
Pr
oposed
m
o
del:
Our choice fel
on c
o
m
posite f
ace-centered pl
ans fo
r the study of
response
surfaces.
A
face-centered
com
posite design is defined
by: two
start points by para
mete
rs and positioned don each of the axes. These
p
o
i
n
t
s con
t
rib
u
te to
th
e ev
aluatio
n
.
Th
e
q
u
a
d
r
atic ter
m
s o
f
th
e po
lyn
o
m
ia
l
m
o
d
e
l, i.e., th
ey g
i
v
e
in
fo
rmat
io
n
about the c
u
rva
t
ure of the s
u
rface of response
:
a ful
l
fact
ori
a
l
desi
gn
2k
n
0
rep
e
titio
n
s
at th
e cen
ter o
f
th
e ex
p
e
ri
m
e
n
t
a
l
d
o
m
a
i
n
,
d
e
d
i
cated
to
th
e stati
s
tica
l
an
alys
is
Two start points by param
e
ter and
positioned
don each of the
axes.
These poi
nt
s cont
ri
but
e t
o
t
h
e eval
uat
i
on.
The quad
r
at
i
c
t
e
r
m
s of t
h
e pol
y
nom
ial
m
odel
,
i
.
e., t
h
ey
gi
ve
inform
ation about the curvatur
e of the s
u
rface of res
p
onse.
Th
e to
tal nu
mb
er
o
f
tests to
b
e
cond
u
c
ted
,
N
, d
e
p
e
nd
s
on
th
e nu
m
b
er
of
facto
r
s
k
stud
ied
and
th
e
nu
mb
er
of
rep
e
titio
n
s
in th
e cen
t
er
o
f
the do
m
a
in
,
n
N2
2
.
K
n
(1
)
n
3
W
ith
N2
2
.
3
3
1
7
(2
)
The last three rows
of Ta
ble 2 co
rresponds
to a test center consid
ere
d
experi
m
e
nt
al
fi
el
d, whi
c
h
shoul
d be
repe
at
ed
n
ti
mes to
e
n
su
re certain
p
r
o
p
e
rties th
e ma
trix
ex
p
e
rim
e
n
t
s.
So t
h
at
i
t
m
e
et
s t
h
e requi
rem
e
nt
of uni
form
preci
si
on,
ensuring a nearly cons
tan
t
v
a
rian
ce with
in
th
e
experi
m
e
nt
al
range.
The used
plan is a co
m
posite face-centered plan
allowing
m
odel the evolution of a criterion using
fo
rm
an
aly
tica
l
co
n
s
id
eratio
n
s
tak
i
n
g
in
to
3
para
m
e
ters.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 3,
J
u
ne 2
0
1
5
:
39
1 – 4
0
2
39
5
Tabl
e
2. C
o
m
posi
t
e
pl
a
n
f
o
r t
h
e st
udy
ce
nt
er
ed
on
t
h
ree Fac
t
ors
N °
E
xper
i
m
e
nts
Factor
U
(k
V)
P (c
m
)
L(c
m
)
T (
m
m
)
1
-1
-1
-1
3
0
,
1
2
-
1
-
1
1
31,
08
3
-
1
1
-
1
29,
89
4
-
1
1
1
29,
26
5
1
-
1
-
1
45,
08
6
1
-
1
1
43,
68
7
1
1
-
1
43,
89
8
1
1
1
37,
94
9
0
0
-
1
35,
84
1
0
0
0
1
31,
64
1
1
0
1
0
34,
025
1
2
0
1
0
34,
025
1
3
-
1
0
0
29,
26
1
4
1
0
0
42,
84
1
5
0
0
0
33,
76
1
6
0
0
0
33,
74
1
7
0
0
0
33,
72
Whet
her t
h
e v
ect
or of m
odel coeffi
ci
ent
s
anal
y
t
i
cal sough
t
:
It
is defi
ned by
The coef
fi
ci
ent
s
vect
or
of t
h
e
anal
y
t
i
cal
m
odel
i
s
defi
ned as
fol
l
o
w:
a
X
X
X
y
(3
)
Where
X
are the matrix
ex
p
e
ri
m
e
n
t
,
X
are the
transpose
m
a
trix expe
rim
e
nt,
y
th
e b
r
eak
dow
n vo
ltag
e
(
t
he
response).
The n
u
m
b
er of
un
kn
ow
n para
m
e
ters (
a
o
f
th
e
p
o
l
yn
o
m
ia
l is
d
e
ter
m
in
ed
from th
e fo
llo
win
g
fo
rm
u
l
a
A
!
!!
⇒a
!
!
!
1
0
(4)
Fi
nal
l
y
,
t
h
e
m
odel
i
s
gi
ven by
equat
i
on (
5
)
y
a
a
X
a
X
a
(5)
Or:
ya
a
.x
a
.x
a
.x
a
.x
a
.x
a
.x
a
.x
a
.x
a
.x
(6)
d.
Step D
:
Ma
th
ematic
a
l
m
o
d
e
l
Esti
mat
i
o
n
o
f
m
o
d
e
l co
effic
i
en
ts. To
esti
mate th
e
math
e
m
at
ica
l
m
o
d
e
ls
co
efficien
ts, we h
a
v
e
u
s
ed
Matlab program
,
which gives an
analytical for
m
of
the response
studied surface and they are calculated
by
usi
n
g
eq
uat
i
on (3)
.
So
we can
write th
e
m
a
th
e
m
at
ical
m
o
d
e
l (ex
p
eri
m
en
tal d
o
m
ain
)
as fo
llo
ws:
U
33,97567
568
6
,
384
.
P
1
,12
.
T
1,0075
.
L
0
,9625
.
.
0,6125
.
.
0,77.
T.
L
1,
8975.
P
0
,4124
.
T
0,9483
.
L
(7
)
The obt
ai
ned r
e
sul
t
s
can be pl
ot
t
e
d t
o
co
m
p
are t
h
e m
easured
responses
with
th
e esti
mated
o
n
e
. For
this, it is
nece
ssary to plot
the
adequacy of the
m
odel.
Measured re
sponses are placed on the absc
issa and
est
i
m
a
t
e
d responses are on t
h
e ordi
nat
e
Fi
gure 3. The cl
oud
poi
nt
s i
s
al
i
gned wi
t
h
t
h
e li
ne y
= x, whi
c
h m
eans
that accuracy of the m
odel is pretty good.
The descriptive quality of the
m
odel
is illustrated here but a second
analysis of variance will possible
to
v
e
rify th
is co
n
c
lu
sio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mo
del
l
i
ng
of
t
h
e AC
Break
d
o
w
n V
o
l
t
age
of
Poi
n
t
-
Pl
a
n
e
A
i
r Ga
ps
w
i
t
h
I
n
sul
a
t
i
n
g B
a
rri
e
r
(
A
. Ro
ui
ni
)
39
6
Figure
3. Graph m
odel adequacy
e.
Stati
s
ti
cal
an
a
l
ysi
s
of the m
o
del
Th
e eq
u
a
tio
n
of th
e e
m
p
i
ric
a
l
m
o
d
e
l is
o
n
l
y
ap
p
r
ox
im
a
tio
n
o
f
reality.
Th
e esti
ma
ted
co
efficien
ts o
f
the polynom
ia
l
m
odel of second
degree is
based on test results that are,
for each
of the
experim
e
nta
l
design
treatments, specific values of
a random
varia
b
le.
The im
pl
em
entat
i
on of st
at
i
s
t
i
cal
t
e
st
s
m
u
st
al
l
o
w a j
u
d
g
m
e
nt
on
t
h
e res
u
l
t
s
obt
ai
ned,
na
m
e
ly
a
m
odel
descri
bi
ng t
h
e
vari
at
i
on of t
h
e
respo
n
se i
n
t
h
e experi
m
e
ntal
dom
ain. This
step of the statistica
l
analys
is
results
in
th
e con
s
tructio
n
o
f
Tab
l
e o
f
regressio
n
an
alysis an
d
d
e
ter
m
in
in
g
th
e d
e
scrip
tiv
e
q
u
a
lity o
f
th
e
m
o
d
e
l.
Reg
r
essio
n
an
alysis
is
to
ex
p
l
ain
th
e to
ta
l ch
an
g
e
in
t
h
e respo
n
se from
t
h
e defi
ned sum
of square
d di
ffe
rences
between the re
sults testing and their avera
g
e:
The statistical
analysis
of the
m
odel
as a whol
e i
s
fol
l
o
wed by
t
h
e const
r
uct
i
on of a st
ati
s
t
i
cal t
e
st,
wh
ich
is to
say th
at th
e
m
o
d
e
l d
o
e
s no
t all
o
w
d
e
scrib
e
the
α
equal
t
o
5
%
:
Tabl
e regressi
on anal
y
s
i
s
Tabl
e 3
in
clu
d
e
s d
i
fferen
t
step
s fo
r lead
calcu
latin
g
t
h
e p
r
o
b
a
b
ilit
y t
h
at.
The regression
analysis
table is used to achie
ve i
mmediately calculate the c
o
e
fficien
t d
e
termin
at
io
n
o
f
R
²
, R
²
and Q² ajust
t
e
:
t
h
e
descri
pt
i
v
e qu
al
it
y
of t
h
e
m
odel wi
ll
be eval
uat
e
d
average coefficients of
d
e
ter
m
in
at
io
n
,
R
2
and R
2
adj
.e
t Q² These are
values following:
Tab
l
e 3
.
Determin
in
g
th
e co
efficien
ts o
f
d
e
scrip
tiv
e q
u
a
lity
o
f
th
e m
o
d
e
l
R
R
Q
0,
991 0,
979
0,
986
W
ith the coefficients R²
and R²
adj
> 0
.
9
clo
s
e to
u
n
ity,
a g
o
o
d
d
e
scrip
tiv
e q
u
a
lity
is assu
red
.
W
e
ca
n there
f
ore say that the
m
odels obtained can
u
s
ed
to
p
r
ed
i
c
t th
e re
sponse values and the
d
e
ter
m
in
in
g
facto
r
v
a
lu
es
R² are clo
s
e to
1, reflectin
g
th
e g
o
o
d
qu
ality
o
f
m
o
d
e
l. Si
milarl
y, v
a
lu
es o
f
the
co
efficien
t ad
ju
sted
d
e
termin
atio
n
in
d
i
cate t
h
at th
e
m
o
d
e
l i
s
also
ap
p
lied
pro
p
e
rly fitted
.
Ju
st as o
n
e
h
a
s p
r
ev
iou
s
ly defin
e
d
th
e d
e
scrip
tiv
e
m
o
d
e
l
q
u
a
lity, it
is p
o
ssib
l
e to
now d
e
fin
e
th
e
p
r
ed
ictiv
e q
u
a
lity
o
f
th
e
m
o
d
e
l to
fro
m
th
e co
efficien
t
Q², th
e
m
o
re its v
a
lu
e i
s
cl
o
s
e to
u
n
ity, a g
o
o
d
d
e
scrip
tiv
e q
u
a
lit
y is assu
red
.
So
we can
say th
at th
e two
mo
d
e
ls ob
tain
ed
h
a
v
e
a go
od
d
e
scrip
tiv
e q
u
a
lit
y.
Anot
her step in the statistica
l analys
is of the
m
odel concerns the statisti
cal analys
is o
f
coefficients
based
stat
ist
i
cal
ly
test
<< ti >> Stu
d
e
n
t:
Th
e test u
s
ed
is th
e "t" t
e
st o
f
Stu
d
e
n
t
. effect wil
l
b
e
said
to
b
e
sig
n
i
fican
t (th
a
t is to
say th
at
th
e
vari
abl
e
or i
n
t
e
ract
i
on associ
at
ed t
h
ere wi
th i
n
fl
uences re
sponse
)
, i
f
, fo
r
a gi
ven ri
sk si
gni
fi
cant
l
y
di
f
f
erent
fro
m
0
.
Th
erefo
r
e will b
e
tested
assu
m
i
n
g
:
H
0
= << ai=0>>
count
er hy
pot
h
e
si
s:
H
0
= << ai
≠
0>>
(8)
28,
80
30,
80
32,
80
34,
80
36,
80
38,
80
40,
80
42,
80
44,
80
28,
8
30,
8
32,
8
34,
8
3
6
,
8
38,
8
40,
8
42,
8
44,
8
v
ex
p
v
mo
d
è
l
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 3,
J
u
ne 2
0
1
5
:
39
1 – 4
0
2
39
7
Fo
r th
is,
we calcu
late :
|
|
(9
)
St
ude
nt
t
a
bl
e
g
i
ves f
o
r
α
=
5
%
ris
k
,
N
-
p =
1
7
-1
0 =
7
Fro
m
th
e St
u
d
en
t tab
l
e: t
crit
=(
0,
00
5
,7
)
=2
.3
7
An effect will
b
e
si
g
n
i
fican
t
at th
e 5% risk
if h
i
s "t
i
" an
d abo
v
e
2,37
.
The fol
l
o
wi
n
g
t
a
bl
e
we
re obt
a
i
ned:
Tabl
e 4. Test
o
f
si
gni
fi
cance of the coefficients
Facto
r
s
Ef
f
ect
t
2
.
3
7
results
Constante 33,
975676
179,
16
significant
P 6,
384
33,
66
significant
T -
1
,
1
2
5,
91
significant
L -
1
,
075811
5,
67
significant
P.
T -
0
,
9625
5,
08
significant
P.
L -
0
,
6125
3,
23
significant
T
.
L -
0
,
7
7
4,
06
significant
P
1,
8975676
10,
01 significant
T
-
0
,
412432
2,
17 not
significant
L
0,
9483784
5,
00 significant
Fro
m
Tab
l
e 4
,
o
n
l
y th
e co
effi
cien
ts p
r
o
v
i
d
i
ng
d
e
scrip
tiv
e qu
alit
y o
f
m
o
d
e
l
will b
e
p
r
eserved
.
That is to reject the coefficients (
T
) t
h
e red
u
ce
d m
odel
equat
i
on
becom
e
s:
U
3
3
,
97567
568
6
,
384.
P
1,12
.
T
1,0075
.
L
0,9625
.
P
.
T
0,6125
.
P
.
L
0,77.
T.
L
1,8975.
P
0
,9483
.
L
(10)
In
th
is case th
e
co
n
f
id
en
ce in
terv
al o
f
an
effect is g
i
v
e
n
b
y
:
a
1
,96.0,189
lo
w
e
r
bo
un
d,
a
1
,96.
0,189
Hi
gher
bo
un
d
.
Table 5. Confidence interv
al
of 5%
ri
sk
z
o
n
e
Facto
r
s
Ef
f
ect
interva
l
lower bound
Higher bound
Constante 33,
9756757
33,
60
34,
35
P
6,
384
6,
01 6,
76
T
-1
,1
2
-1
,4
9
-0
,7
5
L
-
1
,
07581081
-1
,4
5
-0
,7
0
P
.
T
-
0
,
9625
-1
,3
3
-0
,5
9
P
.
L
-
0
,
6125
-0
,9
8
-0
,2
4
T.
L
-0
,7
7
-1
,1
4
-0
,4
0
P
1,
89756757
1,
53 2,
27
T
0,
94837838
0,
58 1,
32
4.
R
E
SU
LTS AN
D ANA
LY
SIS
Th
e v
a
lid
atio
n o
f
th
e resu
lts g
i
v
e
n b
y
th
e m
o
d
e
l is to
ch
eck
wh
eth
e
r th
e assu
m
p
ti
o
n
s
m
a
d
e
in
depart
ure
of e
x
perim
e
nt
s are wel
l
veri
fi
ed.
Val
i
d
at
i
on can be car
ri
ed pe
rfo
rm
i
ng t
e
st
com
p
lem
e
ntary
out
si
de t
h
e t
e
st
i
ng pl
an ex
perim
e
nt
s t
o
val
i
d
at
e t
h
e
m
o
del
behavi
o
r
o
b
t
a
i
n
ed by
t
h
e
experi
m
e
nt
al
desi
gn.
In o
u
r case st
u
d
y
,
we t
ook t
h
e
m
a
de t
e
st
t
o
st
udy
t
h
e i
n
fl
uence of pa
ram
e
t
e
rs Apart
fro
m
t
e
st
i
ng t
h
e
experi
m
e
nt
al
desi
gn. The
resu
l
t
s
of t
h
ese t
e
sts are
co
m
p
ared
with
resu
lts o
f
th
e
m
a
th
e
m
at
ic
al
m
o
d
e
l
4.
1. I
n
fl
ue
nce
of
the
Wi
d
t
h
o
f
t
h
e B
a
rrier on the
Breakdown Voltage
In th
is test shou
ts, t
h
e
d
i
fferen
t
d
i
stan
ces
b
e
tw
een electrodes
and ba
rrier
(0cm
, 2 cm
and
4cm
)
, the
hol
e i
n
t
h
e m
i
ddl
e
of t
h
e ba
r
r
i
e
r f
o
r
(
4
m
m
),
di
ffe
rent
wi
dt
h
of t
h
e ba
rr
i
e
r (5cm
, 1
0
c
m
and 1
5
cm
) we see
cl
earl
y
, t
h
e bre
a
kd
o
w
n
vol
t
a
g
e
i
s
very
l
o
w w
i
t
h
t
h
e i
n
creasi
ng
of l
a
r
g
e wi
d
t
hs of t
h
e ba
rri
er an
d ve
ry
bi
g
wi
t
h
t
h
e dec
r
easi
n
g
of
t
h
em
. Thi
s
c
a
n
be e
xpl
ai
ne
d
by
t
h
e
fact that the scre
en pl
ay
s in a
ge
om
e
t
ric opstacle.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mo
del
l
i
ng
of
t
h
e AC
Break
d
o
w
n V
o
l
t
age
of
Poi
n
t
-
Pl
a
n
e
A
i
r Ga
ps
w
i
t
h
I
n
sul
a
t
i
n
g B
a
rri
e
r
(
A
. Ro
ui
ni
)
39
8
Fr
o
m
Figu
r
e
6
,
t
h
e
br
eakdo
wn
voltage
decrease
s
with i
n
creasi
n
g
of the
ba
rrier widt
hs. T
h
e
pre
d
iction val
u
es
are situat
ed
betw
ee
n the two boundaries of the a
r
ea
of
risk
o
f
5
%
. Th
is m
ean
s th
at the
m
odel
fo
un
de
d
by
t
h
e
ex
pe
ri
m
e
nt
al
desi
g
n
m
e
t
hod i
s
pe
rf
ect
.
Fi
gu
re 6.
I
n
fl
u
e
nce of
t
h
e wi
d
t
h
o
f
t
h
e bar
r
i
e
r on
t
h
e
b
rea
k
d
o
w
n
v
o
l
t
a
ge:
di
ffe
re
nt
rel
a
t
i
v
e po
si
t
i
on of
t
h
e bar
r
i
e
r
4.
2. I
n
fl
ue
nce
of
the
H
o
l
e
i
n
th
e B
a
rrier on the
Breakdown Voltage
-1
-0
.
8
-0
.
6
-0.
4
-0
.
2
0
0.
2
0.
4
0.
6
0.
8
1
25
26
27
28
29
30
31
32
33
34
35
w
i
dt
h of
t
he bar
r
i
e
r
(a
)
B
r
ea
k
dow
n v
o
l
t
age (k
V
)
H
i
ghe
r l
i
m
i
t
L
o
w
e
r
lim
it
P
r
edi
c
t
Me
s
u
r
e
d
-1
-0
.
8
-0.
6
-0
.
4
-0
.
2
0
0.
2
0.
4
0.
6
0.
8
1
26
27
28
29
30
31
32
33
34
35
W
i
d
t
h o
f
t
h
e ba
r
r
i
e
r
(b)
B
r
ea
k
dow
n
v
o
l
t
a
ge (
k
V
)
H
i
g
h
e
r
lim
it
L
o
w
e
r
lim
it
Pr
e
d
i
t
M
eas
u
r
ed
-1
-0.
8
-0
.
6
-0.
4
-0
.
2
0
0.
2
0.
4
0.
6
0.
8
1
25
26
27
28
29
30
31
32
33
34
35
W
i
d
t
h of
t
he b
a
r
r
i
er
(c
)
B
r
eak
dow
n v
o
l
t
age
(
k
V
)
H
i
gher l
i
m
i
t
Low
er l
i
m
i
t
Pr
e
d
i
t
M
eas
ur
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 3,
J
u
ne 2
0
1
5
:
39
1 – 4
0
2
39
9
In
th
is test, a ho
le in
th
e mid
d
l
e o
f
th
e
b
a
rri
e
r v
a
ries
(4
m
m
,
8
m
m
an
d
1
2
m
m
)
. Th
e relativ
e p
o
s
ition
of t
h
e
bar
r
i
e
r v
a
l
u
es fo
r 4 cm
, di
ffe
rent
wi
dt
h (5
cm
, 10 cm
and 1
5
cm
). In
revi
ewi
ng fi
g
u
res
,
we o
b
se
r
v
e t
h
at
th
e d
e
cr
ease of
th
e br
eak
dow
n vo
ltag
e
w
i
th
th
e
increa
se
of the
holes i
n
m
i
ddle of the ba
rrier
.
Th
is resu
lt
co
u
l
d
b
e
i
n
terpreted
b
y
th
e fact th
at th
e electric ch
ar
ge
that
passe
s through the
hole is
low.
When a
dia
m
eter
of hole is
greater, a
large
part
of the
c
h
arging s
p
ace
pa
sse
s
through t
h
e
hole as
well. T
h
is can
be
interprete
d
by the
fact that increasing t
h
e
diam
et
er of
t
h
e
hol
e.
The
pre
d
i
c
t
i
o
n
va
lues
are situate
d
betwee
n the
t
w
o
bo
u
nda
ri
es of
t
h
e
a
r
ea of ri
sk
of
5%
.
Fig
u
r
e
5
.
In
f
l
uen
ce
o
f
th
e
ho
le in
th
e m
i
d
d
l
e of
th
e b
a
r
r
i
er
o
n
th
e
br
eakdow
n vo
ltag
e
:
diffe
re
nt wi
dth
(a)
5cm
,
(
b
)
1
0
cm
and
(c)
1
5
cm
).
4.
3 In
fl
uence
of
the
Rel
a
ti
v
e
Posi
ti
on
B
a
r
r
i
er on
the
B
reakd
ow
n
V
o
l
t
age
Fi
gu
re 4 s
h
o
w
s t
h
e expe
ri
m
e
nt
al
and
pre
d
i
c
t
e
d brea
kd
o
w
n
vol
t
a
ge as
a funct
i
o
n o
f
t
h
e rel
a
t
i
v
e
p
o
s
ition
of th
e
b
a
rrier v
a
l
u
es o
f
th
e
b
a
rrier fo
r
d
i
fferen
t
wid
t
h
(5
cm
, 1
0
cm an
d
15
cm
) o
f
th
e b
a
rrier. Th
e ho
le
i
n
t
h
e
ba
rri
er
i
s
(
4
m
m
). Di
ffe
rent
di
st
ances
bet
w
ee
n t
h
e
p
o
i
nt
an
d t
h
e
bar
r
i
er (
0
t
o
5
cm
) were
st
u
d
i
e
d.
Th
e in
sertion
o
f
the b
a
rrier
h
a
s a sign
ifican
t in
f
l
u
e
n
ce on
th
e b
r
eakd
ow
n
vo
ltag
e
.
Th
e
pr
ed
ictio
n
values
are
situated betwee
n t
h
e two
bo
u
n
d
a
r
i
e
s o
f
t
h
e a
r
ea
o
f
ri
s
k
of
5%.
Thi
s
m
eans t
h
at
t
h
e f
o
un
de
d
m
odel
by
t
h
e e
x
peri
m
e
nt
al
desi
gn
m
e
t
h
o
d
i
s
per
f
ec
t
.
-1
-0
.
8
-0
.
6
-0
.
4
-0.
2
0
0.
2
0.
4
0.
6
0.
8
1
42
42
.
5
43
43
.
5
44
44
.
5
45
45
.
5
46
46
.
5
47
H
o
l
e
i
n
t
he m
i
dd
l
e
o
f
t
he ba
r
r
i
e
r
(a
)
B
r
e
a
k
dow
n v
o
l
t
age (
k
V
)
H
i
g
her
l
i
m
i
t
Lo
w
e
r l
i
m
i
t
Pr
e
d
i
t
M
e
as
u
r
ed
-1
-0
.
8
-0
.
6
-0
.
4
-0
.
2
0
0.
2
0.
4
0.
6
0.
8
1
38
39
40
41
42
43
44
45
H
o
l
e
i
n
t
he m
i
d
d
l
e
of
t
he ba
rr
i
e
r
(b
)
B
r
eak
d
o
w
n
v
o
l
t
age (
k
V
)
H
i
g
her
l
i
m
i
t
Lo
wer
l
i
m
i
t
P
r
edi
t
M
e
as
ur
ed
-1
-0.
8
-0
.
6
-0.
4
-0
.
2
0
0.
2
0.
4
0.
6
0.
8
1
34
36
38
40
42
44
46
H
o
l
e
i
n
t
he m
i
ddl
e of
t
he bar
ri
er
(c
)
B
r
eak
do
n v
o
l
t
a
ge (k
V
)
H
i
g
her l
i
m
i
t
Low
er
l
i
m
i
t
Pr
e
d
i
t
M
eas
ur
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mo
del
l
i
ng
of
t
h
e AC
Break
d
o
w
n V
o
l
t
age
of
Poi
n
t
-
Pl
a
n
e
A
i
r Ga
ps
w
i
t
h
I
n
sul
a
t
i
n
g B
a
rri
e
r
(
A
. Ro
ui
ni
)
40
0
Fig
u
re
4
.
In
fl
uen
ce
o
f
th
e
relativ
e po
sitio
n of b
a
rrier on
t
h
e
b
r
eakd
own
v
o
l
tag
e
:
diffe
re
nt wi
dth
(a)
5
cm
, (b)
1
0
cm
and
(c)
1
5
cm
, the h
o
le
(4
m
m
).
Th
e i
n
terv
al
between
t
h
e
u
p
p
e
r li
m
it an
d
th
e li
m
it lo
wer is called
con
f
i
d
en
ce in
terv
al (zon
e
of
co
nfid
en
ce i
n
terv
al estim
atio
n
will b
e
sm
al
l t
o
g
r
eat co
efficien
t confid
en
ce).
-1
-0
.
8
-0
.
6
-0
.
4
-0
.
2
0
0.
2
0.
4
0.
6
0.
8
1
28
30
32
34
36
38
40
42
44
46
48
R
e
l
a
t
i
v
e
pos
i
t
i
on of
t
he bar
r
i
er
(a
)
B
r
e
a
k
dow
n v
o
l
t
ag
e (
k
V
)
H
i
gher
l
i
m
i
t
Low
er
l
i
m
i
t
pr
edi
t
M
eas
ur
ed
-1
-0
.
8
-0
.
6
-0
.
4
-0
.
2
0
0.
2
0.
4
0.
6
0.
8
1
28
30
32
34
36
38
40
42
44
46
R
e
l
a
t
i
v
e
pos
i
t
i
on of
t
he bar
r
i
er
(b
)
B
r
ea
k
d
ow
n v
o
l
t
a
g
e
(
k
V
)
H
i
gher
l
i
m
i
t
Low
er
l
i
m
i
t
P
r
edi
t
M
eas
uer
d
-1
-0.
8
-0.
6
-0
.
4
-0
.
2
0
0.
2
0.
4
0.
6
0.
8
1
30
32
34
36
38
40
42
44
46
R
e
l
a
t
i
v
e
po
s
i
t
i
on
o
f
t
h
e
ba
r
r
i
e
r
(c
)
B
r
eak
down v
o
l
t
age (
k
V
)
H
i
g
h
e
r
lim
it
L
o
w
e
r
lim
it
Pr
e
d
i
t
M
e
as
ur
ed
Evaluation Warning : The document was created with Spire.PDF for Python.