I
nte
rna
t
io
na
l J
o
urna
l o
f
Adv
a
nces in Applie
d Science
s
(
I
J
AAS)
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
2
0
1
7
,
p
p
.
2
0
3
~
2
1
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I
SS
N:
2252
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8814
203
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Co
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©
201
7
In
s
t
it
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te o
f
A
d
v
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n
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i
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.
Al
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C
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p
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A
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r
:
Mo
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a
m
m
ad
B
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ip
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,
De
p
a
rtme
n
t
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El
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c
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En
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b
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co
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1.
I
NT
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D
UCT
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in
d
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g
s
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cir
cu
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lts
[
1
]
.
I
n
th
is
v
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w
p
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in
t,
t
h
is
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s
i
m
p
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f
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s
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g
e,
o
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b
in
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o
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all
t
h
e
m
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tio
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ed
r
ea
s
o
n
s
[
2
-
3
]
.
T
h
e
tr
an
s
f
o
r
m
er
m
o
d
els
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s
ed
i
n
m
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t
p
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n
s
id
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ex
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f
au
l
t
[
4
-
5
]
.
I
n
[
6
-
8
]
,
b
y
m
a
k
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n
g
s
h
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t
cir
cu
it
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a
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n
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w
p
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tectio
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t
cir
cu
it
f
au
lts
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an
s
f
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r
m
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s
.
I
n
[
9
]
,
an
ad
v
a
n
ce
d
al
g
o
r
ith
m
is
p
r
o
p
o
s
ed
in
w
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th
e
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w
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f
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m
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s
p
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tectio
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s
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in
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le
-
p
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f
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m
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y
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eq
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t
cir
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f
i
n
v
er
s
e
i
n
d
u
cta
n
ce
s
.
I
n
[
1
0
-
1
1
]
,
o
n
e
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f
th
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m
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s
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p
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tan
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m
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r
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tan
ce
m
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s
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I
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2
2
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8814
IJ
AA
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Vo
l.
6
,
No
.
3
,
Sep
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b
er
201
7
:
2
0
3
–
2
1
2
204
to
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h
is
m
o
d
el
e
m
p
lo
y
s
th
e
w
i
n
d
in
g
l
in
k
a
g
e
f
lu
x
es
a
s
s
o
lu
tio
n
v
ar
iab
les.
A
n
o
t
h
er
r
esear
ch
u
s
es
T
r
an
s
m
i
s
s
io
n
L
i
n
e
Me
t
h
o
d
(
T
L
M)
an
d
f
u
zz
y
lo
g
ic
an
al
y
s
is
b
ased
o
n
d
y
n
a
m
ic
p
r
in
cip
le
c
o
m
p
o
n
en
t
an
a
l
y
s
is
i
n
m
o
d
ellin
g
o
f
tr
a
n
s
f
o
r
m
er
b
eh
av
io
r
f
o
r
in
ter
n
al
s
h
o
r
t c
ir
cu
it st
u
d
ies [
1
6
]
.
Fin
ite
E
le
m
e
n
t
An
al
y
s
is
(
FE
A)
is
an
o
t
h
er
tech
n
iq
u
e
f
o
r
p
r
ec
is
e
m
o
d
elli
n
g
o
f
ele
m
e
n
t
s
b
eh
av
io
r
s
u
c
h
as p
o
w
er
tr
an
s
f
o
r
m
er
s
w
h
ic
h
h
av
e
n
o
n
li
n
ea
r
ch
ar
ac
ter
i
s
tics
lik
e
m
ag
n
etic
s
atu
r
atio
n
[
1
9
-
2
0
]
.
I
n
[
1
8
]
,
th
e
t
w
o
d
i
m
e
n
s
io
n
al
m
o
d
el
o
f
f
in
i
te
ele
m
e
n
t
m
e
th
o
d
is
p
r
esen
ted
f
o
r
in
v
e
s
ti
g
ati
n
g
t
h
e
b
eh
av
io
r
o
f
tr
an
s
f
o
r
m
er
.
I
n
t
h
is
m
o
d
el,
d
u
e
to
eli
m
i
n
ati
n
g
o
n
e
d
i
m
e
n
s
io
n
,
in
o
r
d
er
to
p
r
o
p
er
ap
p
r
o
x
i
m
atio
n
,
th
e
lo
s
t
v
a
lu
e
o
f
co
il
s
h
o
u
ld
b
e
ap
p
lied
in
elec
tr
ical
m
o
d
el
o
f
tr
a
n
s
f
o
r
m
er
.
So
t
h
i
s
m
o
d
el
c
an
n
o
t b
e
co
n
s
id
er
ed
as a
n
a
cc
u
r
ate
m
o
d
el
f
o
r
tr
an
s
f
o
r
m
er
.
I
n
th
is
p
ap
er
,
b
y
u
s
in
g
elec
tr
o
m
a
g
n
etic
co
u
p
li
n
g
m
o
d
el
an
d
th
r
ee
-
d
i
m
e
n
s
io
n
a
l
s
tr
u
ct
u
r
al
f
i
n
ite
ele
m
e
n
t,
a
p
o
w
er
tr
a
n
s
f
o
r
m
e
r
m
o
d
ellin
g
is
p
r
esen
ted
i
n
d
if
f
er
e
n
t
co
n
d
itio
n
s
i
n
cl
u
d
in
g
n
o
r
m
al
co
n
d
itio
n
,
m
ag
n
etiz
in
g
i
n
r
u
s
h
a
n
d
in
ter
n
al
s
h
o
r
t c
ir
cu
it
f
a
u
lt c
ase
s
.
I
n
th
i
s
ap
p
r
o
ac
h
,
a
m
u
lti
-
co
il
f
o
r
m
i
s
co
n
s
id
er
ed
f
o
r
th
e
tr
a
n
s
f
o
r
m
er
a
n
d
w
ith
elec
tr
o
m
a
g
n
et
ic
an
d
elec
tr
ic
co
u
p
le
b
et
w
ee
n
co
ils
;
a
p
h
y
s
ical
a
n
d
g
eo
m
etr
ic
m
o
d
el
o
f
tr
an
s
f
o
r
m
er
is
co
n
s
tr
u
c
ted
.
A
ls
o
,
d
if
f
er
en
t
f
ield
a
n
d
ter
m
i
n
al
p
ar
a
m
e
ter
s
o
f
tr
an
s
f
o
r
m
er
in
t
h
e
n
o
r
m
a
l
co
n
d
itio
n
a
n
d
i
n
ter
n
al
s
h
o
r
t
cir
cu
it
ca
s
e
s
,
ar
e
o
b
tain
ed
v
er
y
ac
cu
r
atel
y
w
i
th
ev
a
l
u
ati
n
g
d
o
n
e
b
y
ti
m
e
s
tep
m
et
h
o
d
.
T
h
is
m
o
d
el
also
co
n
s
id
er
s
th
e
tr
an
s
f
o
r
m
er
n
o
n
li
n
ea
r
ch
ar
ac
te
r
is
tic.
2.
I
NT
E
RNA
L
F
AU
L
T
S IN
T
RANSF
O
RM
E
RS
I
n
ter
n
al
s
h
o
r
t
cir
c
u
it
f
a
u
lts
ar
e
k
n
o
w
n
a
s
m
o
s
t
i
m
p
o
r
tan
t
r
e
aso
n
s
o
f
i
n
ap
p
r
o
p
r
iaten
ess
p
e
r
f
o
r
m
an
ce
in
p
o
w
er
tr
an
s
f
o
r
m
er
s
.
A
l
s
o
,
d
is
tin
g
u
is
h
i
n
g
th
e
f
au
l
t
f
r
o
m
m
ag
n
etiz
in
g
i
n
r
u
s
h
e
f
f
ec
t
o
f
t
h
e
tr
a
n
s
f
o
r
m
er
i
s
s
o
s
ig
n
i
f
ica
n
t
to
g
u
ar
an
tee
t
h
e
r
o
b
u
s
t
p
r
o
tectio
n
o
f
w
i
n
d
to
w
i
n
d
f
au
lt
i
n
th
e
p
r
i
m
ar
y
p
h
a
s
e
an
d
at
last
,
it
d
ep
icts
th
e
p
r
i
m
ar
y
to
s
ec
o
n
d
ar
y
w
i
n
d
in
g
f
a
u
lt.
I
n
g
r
o
u
n
d
f
a
u
lts
,
t
h
e
w
i
n
d
i
n
g
is
d
iv
id
ed
in
to
t
wo
-
N1
a
n
d
N2
-
p
ar
ts
[
1
1
]
.
Fig
u
r
es
1
(
a)
,
1
(
b
)
,
1
(
c)
,
an
d
1
(
d
)
d
ep
ict
eq
u
iv
ale
n
t
c
ir
cu
its
s
ta
tes
o
f
t
h
e
tr
a
n
s
f
o
r
m
er
n
o
r
m
al
co
n
d
itio
n
,
s
h
o
r
t
cir
c
u
it
f
a
u
lt
in
p
r
i
m
ar
y
p
h
ase,
t
u
r
n
to
t
u
r
n
f
a
u
lt
in
p
r
im
ar
y
p
h
ase
an
d
p
r
i
m
ar
y
p
h
a
s
e
tu
r
n
to
s
ec
o
n
d
ar
y
p
h
ase
tu
r
n
f
a
u
lt,
r
esp
ec
ti
v
el
y
.
On
t
h
e
o
th
er
h
an
d
,
i
n
tu
r
n
to
tu
r
n
f
a
u
lts
,
t
h
e
w
i
n
d
i
n
g
i
s
d
i
v
id
ed
to
th
r
ee
–
N1
,
N2
an
d
N3
-
p
ar
ts
.
Fin
all
y
in
t
w
o
w
in
d
i
n
g
f
a
u
lt
s
,
ea
ch
w
i
n
d
in
g
is
d
iv
id
ed
t
o
t
w
o
p
ar
ts
.
A
ll
t
h
e
m
e
n
tio
n
ed
f
au
l
ts
s
h
all
b
e
co
n
s
id
er
ed
f
o
r
3
p
h
ases
.
A
l
s
o
,
th
e
s
i
m
u
lta
n
eit
y
p
r
o
b
ab
ilit
y
o
f
t
h
e
f
a
u
lt
s
is
p
o
s
s
ib
le.
No
w
,
t
h
e
m
o
s
t
i
m
p
o
r
ta
n
t
p
r
o
b
lem
i
s
ev
a
lu
at
in
g
a
n
d
o
b
tain
i
n
g
th
e
r
elatio
n
s
h
ip
s
o
f
tr
a
n
s
f
o
r
m
er
in
th
e
s
e
co
n
d
itio
n
s
(
i
n
ter
n
al
f
au
l
ts
)
w
h
ile
co
n
s
id
er
in
g
tr
a
n
s
f
o
r
m
er
c
h
ar
ac
ter
i
s
tics
s
u
ch
as
lea
k
ag
e
an
d
m
u
tu
a
l
i
n
d
u
cta
n
ce
s
a
n
d
th
e
ir
m
u
t
u
al
i
m
p
ac
ts
,
n
o
n
li
n
ea
r
B
-
H
c
u
r
v
e,
ch
a
n
g
e
i
n
lo
ad
an
d
ch
an
g
e
o
f
s
o
u
r
ce
i
m
p
ed
a
n
ce
.
Du
r
in
g
n
e
t
w
o
r
k
r
ec
o
n
f
ig
u
r
ati
o
n
,
th
e
p
o
w
er
f
lo
w
an
a
l
y
s
is
s
h
o
u
ld
b
e
p
er
f
o
r
m
ed
.
Fo
r
ea
ch
p
r
o
p
o
s
ed
co
n
f
i
g
u
r
atio
n
,
t
h
e
p
o
w
er
f
lo
w
an
al
y
s
i
s
s
h
o
u
ld
b
e
i
m
p
le
m
en
ted
to
ev
alu
a
te
th
e
n
o
d
al
v
o
ltag
e,
p
o
w
er
lo
s
s
o
f
s
y
s
te
m
a
n
d
cu
r
r
en
t
o
f
ea
ch
b
r
an
ch
.
D
u
e
to
s
ev
er
al
ad
v
a
n
ta
g
es
o
f
th
e
f
o
r
w
ar
d
/b
ac
k
w
ar
d
s
w
ee
p
tech
n
iq
u
e
s
u
c
h
as.
Nee
d
in
g
lo
w
m
e
m
o
r
y
,
h
i
g
h
co
m
p
u
tatio
n
a
l
p
er
f
o
r
m
a
n
c
e,
s
i
m
p
le
s
t
r
u
ct
u
r
e,
h
ig
h
co
n
v
er
g
e
n
ce
ca
p
ab
ilit
y
,
an
d
ap
p
licab
ilit
y
to
u
tili
za
ti
o
n
in
u
n
b
alan
ce
d
s
y
s
te
m
s
,
th
is
p
o
w
er
f
lo
w
m
et
h
o
d
h
a
s
b
ee
n
s
elec
ted
in
th
is
s
t
u
d
y
[1
0
].
3.
P
O
WE
R
T
R
ANSF
O
RM
E
R
M
O
DE
L
I
N
G
B
AS
E
D
O
N
F
I
NIT
E
E
L
E
M
E
NT
M
E
T
H
O
D
3
.
1
.
G
ener
a
l P
rinci
ples
Fin
ite
ele
m
en
t
m
e
th
o
d
is
a
n
u
m
er
ical
tec
h
n
iq
u
e
to
o
b
tain
a
p
p
r
o
x
im
a
te
s
o
l
u
tio
n
s
i
n
b
o
u
n
d
ar
y
v
al
u
e
p
r
o
b
lem
s
a
n
d
b
ec
au
s
e
o
f
its
h
ig
h
ab
ilit
y
i
n
an
a
l
y
s
is
o
f
s
o
-
co
m
p
lica
ted
g
eo
m
e
tr
ic
an
d
c
o
m
p
o
s
i
te
p
r
o
b
lem
s
,
th
is
m
et
h
o
d
is
an
i
m
p
o
r
tan
t to
o
l in
s
o
lv
i
n
g
elec
tr
o
m
a
g
n
etic
p
r
o
b
lem
s
.
Ge
n
e
r
al
p
r
in
cip
les i
n
th
r
ee
-
d
i
m
e
n
s
io
n
al
f
i
n
ite
ele
m
e
n
t
an
a
l
y
s
is
f
o
r
tr
an
s
ien
t
as
s
es
s
m
e
n
t
o
f
t
h
e
p
o
w
er
tr
an
s
f
o
r
m
er
b
eh
av
io
r
w
it
h
co
u
p
led
elec
tr
ical
an
d
elec
tr
o
m
ag
n
etic
f
ield
ar
e
b
ased
o
n
Ma
x
w
ell
’
s
eq
u
at
io
n
s
(
1
-
2
)
.
*
(
1
*
⃗
)
+
(
⃗
+
V
)
=
J
s
(
1
)
.
A
=
0
(
2
)
[E
m
]
=[
R
m
]
[
I
m
]
+N
[
m
]
+[
L
m
]
[I
m
]
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
AA
S
I
SS
N:
2252
-
8814
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d
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g
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in
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205
N
th
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eq
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atio
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σ
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ep
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tr
ical
co
n
d
u
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elate
d
d
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ag
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ili
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,
m
a
g
n
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p
o
ten
tial
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to
r
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s
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r
r
en
t
s
o
u
r
ce
d
en
s
it
y
a
n
d
V
is
th
e
elec
tr
i
ca
l
s
ca
lar
p
o
ten
tial
w
h
o
s
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g
r
ad
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h
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b
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v
al
u
ated
if
th
e
i
n
j
ec
ted
elec
tr
ical
v
o
lta
g
e
to
th
at
s
u
r
f
ac
e
h
as
b
ee
n
d
eter
m
i
n
ed
.
T
h
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[
21
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2
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.
(
a)
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1
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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IJ
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201
7
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0
3
–
2
1
2
206
E
ac
h
s
et
o
f
t
h
e
elec
tr
ical
an
d
m
ag
n
etic
eq
u
at
io
n
s
o
f
tr
an
s
f
o
r
m
er
i
n
th
e
ab
o
v
e
eq
u
atio
n
s
m
ak
e
s
its
o
w
n
co
r
r
esp
o
n
d
in
g
m
atr
ic
eq
u
atio
n
a
n
d
w
ith
co
u
p
li
n
g
th
e
s
e
eq
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atio
n
s
an
d
s
o
lv
in
g
t
h
em
b
y
d
is
cr
et
io
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s
p
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o
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l
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m
i
n
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w
co
m
p
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n
e
n
t
s
k
n
o
w
n
as
m
e
s
h
(
Fig
u
r
e
2
)
an
d
ca
lc
u
lati
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th
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p
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ten
tial
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to
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in
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ch
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o
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e,
t
h
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p
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Ma
x
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s
a
n
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in
all
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m
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av
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[
2
0
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.
3
.
2
.
M
o
delin
g
a
nd
Si
m
ula
t
io
n o
f
T
ra
ns
f
o
r
m
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3
.
1
.
1
.
M
o
delin
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M
a
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net
I
n
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er
to
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t
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ep
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in
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.
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f
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Mu
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I
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4
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F
ig
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4
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Fig
u
r
e
3
.
P
h
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s
ical
Vie
w
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Stu
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ied
T
r
an
s
f
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Fig
u
r
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4
.
Fin
ite
E
le
m
e
n
t M
o
d
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o
f
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St
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T
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an
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1
.
C
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ied
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3
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ults M
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3
.
3
.
1
.
M
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M
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del
Fig
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5
ill
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ates
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o
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at
p
r
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ted
in
[
1
2
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in
w
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1
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
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S
I
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N:
2252
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8814
Mo
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207
Fig
u
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5
.
Fin
ite
E
le
m
e
n
t M
o
d
el
o
f
th
e
St
u
d
ied
T
r
an
s
f
o
r
m
er
.
(
A
)
C
o
r
e
,
(
B
)
P
r
im
ar
y
C
o
il,
(
C
)
Hea
lth
y
P
ar
t o
f
Fau
lt
y
C
o
il a
n
d
Sh
o
r
t C
ir
cu
it
P
ar
t o
f
T
h
e
Fau
lt
y
C
o
il
(
D)
I
t
m
ea
n
s
in
s
h
o
r
t
cir
cu
it
f
a
u
lt
co
n
d
itio
n
,
th
e
f
a
u
lt
y
w
in
d
i
n
g
h
as
c
u
r
r
en
t
d
en
s
it
y
a
n
d
t
h
e
o
th
er
s
b
ec
o
m
e
o
p
en
cir
c
u
it.
W
it
h
k
n
o
w
i
n
g
th
e
v
al
u
e
o
f
d
e
n
s
it
y
c
u
r
r
en
t,
elec
tr
o
m
a
g
n
et
ic
eq
u
atio
n
s
h
a
v
e
b
ee
n
s
o
lv
ed
.
B
u
t
b
ec
au
s
e
t
h
e
f
o
llo
w
in
g
ele
ctr
ical
cu
r
r
en
t
d
en
s
it
y
i
n
th
e
c
o
n
n
ec
tio
n
m
e
s
h
es
is
a
f
u
n
c
tio
n
o
f
to
tal
w
i
n
d
i
n
g
d
en
s
it
y
cu
r
r
e
n
t
an
d
f
a
u
lt
co
n
d
itio
n
(
lo
ca
tio
n
a
n
d
n
u
m
b
er
o
f
co
n
tain
i
n
g
t
u
r
n
s
)
,
also
cu
r
r
en
t
an
d
to
tal
m
a
g
n
etic
m
o
tiv
a
tio
n
f
o
r
ce
(
MM
F)
o
f
w
in
d
i
n
g
ar
e
d
ep
en
d
e
n
t
on
th
e
f
a
u
lt
co
n
d
itio
n
,
s
o
th
ese
m
o
d
el
s
co
u
ld
n
o
t b
e
p
r
ac
tical.
A
l
s
o
,
it
s
h
o
u
ld
b
e
n
o
ted
th
at
in
th
is
p
ap
er
,
w
it
h
u
tili
z
in
g
f
i
n
ite
ele
m
e
n
t
ap
p
r
o
ac
h
,
d
if
f
er
en
t
f
ield
p
ar
am
eter
s
an
d
ter
m
i
n
al
b
eh
a
v
io
r
o
f
tr
an
s
f
o
r
m
er
in
th
e
w
i
n
d
in
g
s
h
o
r
t
cir
cu
it
co
n
d
itio
n
ar
e
ca
lcu
lated
th
r
o
u
g
h
C
OM
SO
L
Mu
ltip
h
y
s
ic
s
s
o
f
t
w
a
r
e
[
2
3
]
.
I
n
ad
d
itio
n
to
h
a
v
in
g
an
ab
ilit
y
o
f
ca
lcu
lati
on
an
d
in
v
e
s
tig
a
ti
o
n
o
f
m
ag
n
etic
ch
ar
ac
ter
i
s
tics
o
f
th
e
s
t
u
d
ied
m
o
d
el,
t
h
is
s
o
f
t
w
ar
e
ca
n
s
i
m
u
late
t
h
e
ter
m
i
n
al
q
u
an
titi
e
s
b
eh
a
v
io
r
o
f
th
e
m
o
d
el.
T
h
u
s
,
u
s
i
n
g
a
n
cill
ar
y
s
o
f
t
w
ar
e
to
co
n
n
ec
t
elec
t
r
ical
cir
c
u
it
s
(
i
n
cl
u
d
in
g
s
u
p
p
l
y
a
n
d
lo
ad
in
g
)
a
n
d
m
ag
n
etic
cir
cu
it
s
u
s
ed
i
n
p
r
ev
io
u
s
s
tu
d
ie
s
o
f
f
i
n
ite
e
le
m
e
n
t
m
et
h
o
d
is
n
o
t
r
eq
u
ir
ed
.
W
h
en
th
e
d
i
m
en
s
io
n
s
an
d
ch
ar
ac
ter
is
tic
s
o
f
co
r
e
is
d
ef
in
ed
,
th
e
n
o
n
lin
ea
r
ch
ar
ac
ter
i
s
tics
o
f
co
r
e
,
w
h
ich
ar
e
d
ep
en
d
en
t
on
its
m
a
ter
ial,
ar
e
ad
d
ed
to
th
e
m
o
d
el.
W
it
h
t
h
e
d
ef
in
i
tio
n
o
f
t
h
e
co
r
e
m
o
d
el
an
d
it
s
m
ater
ial,
w
i
n
d
in
g
s
a
n
d
b
o
u
n
d
ar
y
co
n
d
itio
n
s
,
as
w
el
l a
s
i
n
ter
esti
n
g
elec
tr
ical
cir
c
u
it,
t
h
e
d
esire
d
m
o
d
el
is
p
r
o
v
id
ed
.
4.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
Firstl
y
,
th
e
n
o
r
m
al
w
o
r
k
i
n
g
co
n
d
itio
n
o
f
t
r
an
s
f
o
r
m
er
is
s
i
m
u
lated
.
Fi
g
u
r
e
6
s
h
o
w
s
t
h
e
n
o
r
m
a
l
w
o
r
k
i
n
g
cu
r
r
en
t
o
f
tr
a
n
s
f
o
r
m
e
r
an
d
Fig
u
r
e
7
d
ep
icts
tr
an
s
f
o
r
m
er
m
a
g
n
et
izin
g
i
n
r
u
s
h
at
th
e
s
tar
tin
g
ti
m
e.
I
t
is
o
b
v
io
u
s
t
h
at
m
a
g
n
etizi
n
g
i
n
r
u
s
h
at
s
tar
ti
n
g
ti
m
e
i
s
cr
ea
te
d
d
u
e
to
n
o
n
-
li
n
ea
r
n
at
u
r
e
o
f
th
e
co
r
e
an
d
af
ter
p
ass
in
g
a
s
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o
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t ti
m
e,
m
ag
n
etiz
in
g
i
n
r
u
s
h
b
ec
o
m
es a
tte
n
u
ated
an
d
r
ea
ch
es to
a
s
tead
y
s
ta
te.
P
h
a
se
A
P
h
a
se
B
P
h
a
se
C
Fig
u
r
e
6
.
C
u
r
r
en
t V
a
lu
e
i
n
th
e
T
r
an
s
f
o
r
m
er
No
r
m
al
W
o
r
k
in
g
C
o
n
d
it
io
n
Evaluation Warning : The document was created with Spire.PDF for Python.
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SS
N
:
2
2
5
2
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AA
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Vo
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6
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3
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201
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h
ase
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P
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ase
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ase
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Fig
u
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7
.
Ma
g
n
etiz
in
g
I
n
r
u
s
h
I
n
t
h
is
p
ap
er
,
th
r
ee
t
y
p
e
s
o
f
s
i
m
u
latio
n
i
n
clu
d
i
n
g
1
-
p
r
i
m
ar
y
to
s
ec
o
n
d
ar
y
p
h
a
s
e
w
i
n
d
i
n
g
f
au
lt,
t
u
r
n
to
tu
r
n
f
a
u
lt
a
n
d
s
i
m
u
lta
n
eo
u
s
tu
r
n
to
tu
r
n
f
au
l
t
i
n
t
w
o
p
h
a
s
e
an
d
th
r
ee
p
h
ase,
ar
e
s
tu
d
ied
.
B
ec
au
s
e
t
h
e
s
u
p
p
l
y
is
an
id
ea
l
s
in
u
s
o
id
al
,
th
e
v
al
u
e
o
f
in
it
ial
v
o
lta
g
e
is
s
a
m
e
as
th
e
s
u
p
p
l
y
v
al
u
e.
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ec
au
s
e
t
h
e
s
ec
o
n
d
ar
y
s
id
e
is
an
o
p
en
cir
c
u
it,
t
h
e
v
alu
e
o
f
t
h
e
s
ec
o
n
d
ar
y
s
id
e
c
u
r
r
en
t
is
e
q
u
al
to
ze
r
o
.
T
h
er
ef
o
r
e,
o
n
l
y
th
e
s
ec
o
n
d
ar
y
s
id
e
cu
r
r
en
ts
ar
e
ill
u
s
tr
ated
.
T
h
e
s
h
o
r
t c
ir
cu
it
f
au
lt o
cc
u
r
r
en
ce
ti
m
e
in
al
l t
y
p
e
s
o
f
s
i
m
u
latio
n
i
s
co
n
s
id
er
ed
as 1
s
ec
an
d
th
e
s
h
o
r
t c
ir
cu
it r
esi
s
ta
n
ce
is
0
.
3
o
h
m
w
h
ic
h
d
escr
ib
es s
w
itc
h
r
esi
s
ta
n
ce
an
d
co
n
tacto
r
b
lad
es r
esis
tan
ce
.
W
h
en
a
an
i
n
ter
n
al
s
h
o
r
t
cir
c
u
it
f
a
u
lt
o
cc
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r
s
in
s
ec
o
n
d
ar
y
w
i
n
d
i
n
g
o
f
tr
a
n
s
f
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m
er
,
b
o
th
in
tu
r
n
to
ea
r
th
s
h
o
r
t
cir
cu
it
f
a
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n
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tu
r
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to
t
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f
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er
w
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ld
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a
n
d
a
h
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y
c
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r
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t
i
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n
n
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tio
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es
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w
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ld
f
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w
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Fi
g
u
r
e
8
s
h
o
w
s
t
u
r
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s
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it
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ase
a
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h
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9
8
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n
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d
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a
n
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ar
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i
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Fig
u
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ates
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n
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h
ase
B
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
AA
S
I
SS
N:
2252
-
8814
Mo
d
elin
g
o
f Ma
g
n
etiz
in
g
I
n
r
u
s
h
a
n
d
I
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l F
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Tr
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fo
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F
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md
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Fig
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r
es
u
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o
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e
p
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tical
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y
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e
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a
n
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o
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er
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e
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i
n
T
ab
le.
2
.
I
n
tab
le
2
an
d
at
th
e
f
ir
s
t
co
l
u
m
n
,
P
m
ea
n
s
p
r
i
m
ar
y
s
id
e
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th
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n
u
m
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e
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e
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P
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r
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s
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ch
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th
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d
A
,
B
,
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d
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u
s
tr
ate
t
h
e
co
r
r
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g
f
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h
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s
.
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h
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o
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lts
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ea
l
w
h
en
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ter
n
al
f
au
lt
o
cc
u
r
s
i
n
t
h
e
tr
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s
f
o
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er
,
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u
p
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s
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tan
t
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e
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n
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m
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er
o
f
t
u
r
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s
s
h
o
u
ld
p
r
o
v
id
e
th
e
s
a
m
e
m
ag
n
etic
m
o
ti
v
atio
n
f
o
r
ce
(
MM
F),
th
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Mo
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mers
(
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211
A
ll
t
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n
u
m
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ical
r
esu
lts
in
t
h
e
tab
le
ar
e
b
ased
o
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d
o
m
ai
n
.
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h
e
co
m
p
ar
is
o
n
b
et
w
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n
s
i
m
u
lat
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esu
lt
s
s
h
o
w
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a
t
m
o
s
t
o
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ti
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e,
th
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a
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o
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g
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in
ter
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al
s
h
o
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t
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it
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d
itio
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u
s
in
g
3
D
s
tr
u
ct
u
r
al
f
in
i
te
ele
m
en
t
m
et
h
o
d
p
r
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ts
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i
g
h
ac
c
u
r
ac
y
o
f
tr
an
s
f
o
r
m
er
b
e
h
av
io
r
.
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,
th
e
p
er
f
o
r
m
a
n
ce
o
f
p
o
w
er
tr
an
s
f
o
r
m
er
i
n
p
r
o
tecti
o
n
s
t
u
d
ies
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d
e
s
p
ec
iall
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n
t
er
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al
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au
lts
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it
h
h
i
g
h
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eliab
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it
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is
p
r
o
v
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b
y
u
s
i
n
g
3
D
s
tr
u
ct
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f
in
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te
ele
m
en
t
m
e
th
o
d
w
h
ic
h
i
s
p
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p
o
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ed
an
d
in
v
esti
g
ated
i
n
th
i
s
co
n
tr
i
b
u
tio
n
.
5.
CO
NCLU
SI
O
N
I
n
th
is
p
ap
er
,
an
ap
p
r
o
ac
h
-
b
ased
o
n
s
tu
d
y
o
f
in
t
er
n
al
w
i
n
d
in
g
s
h
o
r
t
cir
cu
it
f
au
l
ts
o
f
t
h
r
ee
p
h
ase
tr
an
s
f
o
r
m
er
w
it
h
u
s
i
n
g
3
D
f
i
n
ite
ele
m
e
n
t
m
e
th
o
d
is
i
n
v
esti
g
ated
.
B
ased
o
n
p
r
ac
tical
in
f
o
r
m
atio
n
o
f
tr
an
s
f
o
r
m
er
,
t
h
e
f
in
ite
ele
m
e
n
t
m
o
d
el
f
o
r
in
ter
n
al
s
h
o
r
t
cir
cu
it
f
au
lt
co
n
d
itio
n
is
ca
r
r
ied
o
u
t
b
y
u
s
i
n
g
CO
MSO
L
M
u
ltip
h
y
s
ics
s
o
f
t
w
ar
e.
B
ased
o
n
th
is
m
o
d
el,
b
y
d
eter
m
in
i
n
g
th
e
d
i
m
e
n
s
io
n
s
,
th
e
m
ater
ial
o
f
p
r
o
d
u
ce
r
elem
e
n
ts
a
n
d
elec
tr
ical
co
n
n
ec
tio
n
s
b
et
w
ee
n
tr
an
s
f
o
r
m
er
co
m
p
o
n
e
n
ts
a
n
d
w
it
h
n
u
m
er
ical
s
o
l
u
tio
n
in
m
ag
n
etic
ar
ea
an
d
o
b
tain
i
n
g
t
h
e
f
lo
w
f
lu
x
,
t
h
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v
a
lu
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s
o
f
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r
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en
t
a
n
d
v
o
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g
es
in
tr
an
s
f
o
r
m
er
ar
e
ca
lcu
lated
.
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l
s
o
,
f
o
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d
eter
m
i
n
i
n
g
t
h
e
f
a
u
l
ts
in
tr
an
s
f
o
r
m
er
,
af
ter
en
ter
in
g
th
e
ch
ar
ac
ter
i
s
tics
a
n
d
d
iv
id
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g
t
h
e
f
a
u
lt
y
co
i
l
in
to
s
o
m
e
p
ar
ts
,
t
h
e
e
x
is
ti
n
g
f
au
lts
ar
e
ap
p
lied
in
t
h
e
tr
an
s
f
o
r
m
er
an
d
w
it
h
t
h
e
m
e
n
tio
n
ed
n
u
m
er
ical
ap
p
r
o
ac
h
,
th
e
p
r
o
b
lem
h
as b
ee
n
s
o
lv
ed
.
A
l
s
o
i
n
o
r
d
er
to
h
a
v
e
m
o
r
e
s
tu
d
ie
s
ab
o
u
t
th
e
e
f
f
ic
ien
c
y
o
f
p
r
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p
o
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ed
ap
p
r
o
ac
h
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d
s
h
o
w
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g
it
s
r
o
b
u
s
tn
es
s
,
d
i
f
f
er
e
n
t
co
n
d
itio
n
s
o
f
in
ter
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al
f
a
u
lt
s
ar
e
s
i
m
u
lat
ed
an
d
v
ar
io
u
s
p
r
ac
tical
test
s
ar
e
p
er
f
o
r
m
ed
o
n
a
t
y
p
ical
tr
an
s
f
o
r
m
er
i
n
th
e
la
b
o
r
ato
r
y
.
W
ith
en
ter
in
g
th
e
t
r
an
s
f
o
r
m
er
ch
ar
ac
ter
is
tic
s
in
t
o
th
e
p
r
o
g
r
am
an
d
m
ak
in
g
t
h
e
tr
a
n
s
f
o
r
m
er
m
o
d
el,
th
e
c
u
r
r
en
t
a
n
d
v
o
ltag
e
v
alu
e
s
ar
e
a
s
s
es
s
ed
.
T
h
e
co
m
p
ar
i
s
o
n
b
et
w
ee
n
s
i
m
u
lat
io
n
r
es
u
lts
a
n
d
o
b
tain
ed
ex
p
er
i
m
en
tal
r
es
u
lt
s
r
ev
ea
ls
th
at
t
h
e
m
o
d
eli
n
g
o
f
tr
an
s
f
o
r
m
er
b
y
u
s
i
n
g
3
D
f
i
n
ite
ele
m
e
n
t
m
et
h
o
d
p
r
esen
ts
an
ac
cu
r
ate
ap
p
r
o
x
i
m
atio
n
o
f
ter
m
i
n
al
v
al
u
es
o
f
tr
a
n
s
f
o
r
m
er
i
n
t
h
e
n
o
r
m
al
co
n
d
itio
n
,
m
ag
n
etizi
n
g
i
n
r
u
s
h
an
d
i
n
ter
n
al
f
a
u
lt
s
.
T
h
is
m
o
d
el
ca
n
b
e
u
s
ed
i
n
d
i
f
f
er
e
n
t
al
g
o
r
i
th
m
s
w
h
ich
ar
e
n
ee
d
ed
f
o
r
u
tili
z
i
n
g
p
r
o
tectio
n
o
f
p
o
w
er
tr
an
s
f
o
r
m
er
s
.
RE
F
E
R
E
NC
E
S
[
1
]
F
ra
n
k
li
n
,
A
rth
u
r
Ch
a
rles
,
a
n
d
Da
v
id
P
e
ter
F
ra
n
k
li
n
.
T
h
e
J
&
P
tra
n
sfo
rm
e
r
b
o
o
k
:
a
p
ra
c
ti
c
a
l
tec
h
n
o
l
o
g
y
o
f
t
h
e
p
o
we
r tra
n
sfo
rm
e
r
.
El
se
v
ier,
2
0
1
3
.
[
2
]
Oliv
e
ira,
L
u
ís
M
R.
"
A
p
e
r
m
e
a
n
c
e
-
b
a
se
d
tran
sf
o
r
m
e
r
m
o
d
e
l
a
n
d
it
s
a
p
p
li
c
a
ti
o
n
to
w
in
d
i
n
g
in
tert
u
rn
a
rc
in
g
f
a
u
lt
stu
d
ies
.
"
Po
we
r De
li
v
e
ry
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
on
2
5
.
3
(
2
0
1
0
)
:
1
5
8
9
-
1
5
9
8
.
[
3
]
G
.
Eas
o
n
,
B.
No
b
le,
a
n
d
I.
N.
S
n
e
d
d
o
n
,
“
On
c
e
rta
i
n
in
teg
ra
ls
o
f
L
i
p
sc
h
it
z
-
Ha
n
k
e
l
typ
e
i
n
v
o
lvin
g
p
r
o
d
u
c
ts
o
f
Bes
se
l
fu
n
c
ti
o
n
s,
”
P
h
il
.
T
ra
n
s.
R
o
y
.
S
o
c
.
L
o
n
d
o
n
,
v
o
l.
A
2
4
7
,
p
p
.
5
2
9
-
5
5
1
,
A
p
ril
1
9
5
5
.
[
4
]
P
e
d
ra
,
Jo
a
q
u
i
n
,
e
t
a
l.
"
Ha
r
m
o
n
ic
n
o
n
li
n
e
a
r
tran
sf
o
r
m
e
r
m
o
d
e
li
n
g
.
"
Po
we
r
De
li
v
e
ry
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
1
9
.
2
(2
0
0
4
):
8
8
4
-
8
9
0
.
[
5
]
G
re
e
n
e
,
J.
Da
v
id
,
a
n
d
C
h
a
rles
G
ro
ss
.
"
No
n
li
n
e
a
r
m
o
d
e
li
n
g
o
f
tran
sf
o
r
m
e
rs."
In
d
u
stry
Ap
p
li
c
a
ti
o
n
s,
IE
EE
T
ra
n
sa
c
ti
o
n
s
on
2
4
.
3
(1
9
8
8
):
4
3
4
-
4
3
8
.
[
6
]
M
o
rc
h
e
d
,
A
.
,
L
.
M
a
rti
,
a
n
d
J.
Ot
tev
a
n
g
e
rs.
"
A
h
ig
h
f
re
q
u
e
n
c
y
tran
sf
o
rm
e
r
m
o
d
e
l
f
o
r
th
e
EM
T
P
.
"
P
o
w
e
r
De
li
v
e
r
y
,
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
8
,
n
o
.
3
(
1
9
9
3
):
1
6
1
5
-
1
6
2
6
.
[
7
]
P
h
a
d
k
e
,
A
.
G
.
,
T
h
o
rp
,
J.
S
.
(
1
9
8
3
).
“
A
n
e
w
c
o
m
p
u
ter
-
b
a
se
d
f
lu
x
-
re
stra
in
e
d
c
u
rre
n
t
-
d
if
fe
re
n
ti
a
l
re
la
y
f
o
r
p
o
w
e
r
tran
sf
o
r
m
e
r
p
ro
tec
ti
o
n
”
.
IEE
E
T
ra
n
s.
o
n
Po
we
r A
p
p
.
S
y
ste
m,
V
o
l
.
P
A
S
-
1
0
2
,
n
o
.
1
1
,
p
p
.
3
6
2
4
-
3
6
2
9
.
[
8
]
Ra
h
m
a
n
,
M
.
,
a
n
d
B.
Je
y
a
su
r
y
a
.
"
A
sta
te
-
of
-
th
e
-
a
rt
re
v
ie
w
o
f
tran
s
f
o
r
m
e
r
p
ro
tec
ti
o
n
a
lg
o
rit
h
m
s."
IE
EE
tra
n
s
a
c
ti
o
n
s
o
n
p
o
we
r d
e
l
ive
ry
3
,
n
o
.
2
(1
9
8
8
)
:
5
3
4
-
5
4
4
.
[
9
]
L
a
rso
n
,
R.
R.
,
A
.
J.
F
lec
h
sig
,
a
n
d
E.
O.
S
c
h
w
e
it
z
e
r.
"
T
h
e
d
e
sig
n
a
n
d
tes
t
o
f
a
d
ig
it
a
l
re
l
a
y
f
o
r
tran
s
f
o
rm
e
r
p
ro
tec
ti
o
n
.
"
Po
we
r A
p
p
a
ra
t
u
s a
n
d
S
y
ste
ms
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
3
(1
9
7
9
):
7
9
5
-
8
0
4
.
[
1
0
]
In
a
g
a
k
i,
Ke
izo
,
M
a
sa
ru
Hig
a
k
i
,
Yo
sh
iak
i
M
a
tsu
i,
Ke
n
taro
Ku
rit
a
,
M
a
m
o
ru
S
u
z
u
k
i,
Ka
z
u
y
o
sh
i
Yo
sh
id
a
,
a
n
d
T
a
k
a
f
u
m
i
M
a
e
d
a
.
"
Dig
it
a
l
p
ro
tec
ti
o
n
m
e
th
o
d
f
o
r
p
o
w
e
r
tran
sf
o
rm
e
rs
b
a
se
d
o
n
a
n
e
q
u
iv
a
len
t
c
ircu
it
c
o
m
p
o
se
d
o
f
in
v
e
rse
in
d
u
c
tan
c
e
.
"
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o
w
e
r
De
li
v
e
r
y
,
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
3
,
n
o
.
4
(1
9
8
8
):
1
5
0
1
-
1
5
1
0
.
[
1
1
]
Be
rtran
d
,
P
.
,
A
.
De
v
a
ll
a
n
d
,
a
n
d
P
.
Ba
sta
rd
.
"
A
si
m
u
latio
n
m
o
d
e
l
f
o
r
tran
sf
o
rm
e
r
in
tern
a
l
f
a
u
lt
s
b
a
se
f
o
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th
e
stu
d
y
o
f
p
ro
tec
ti
o
n
a
n
d
m
o
n
it
o
ri
n
g
s
y
ste
m
s."
In
El
e
c
tricity
Distrib
u
ti
o
n
,
1
9
9
3
.
CIR
ED.
1
2
th
I
n
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
,
p
p
.
1
-
2
1
.
IET
,
1
9
9
3
.
[
1
2
]
Ba
sta
rd
,
P
a
u
ick
,
P
ierre
Be
rtran
d
,
a
n
d
M
ich
e
l
M
e
u
n
ier.
"
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tran
sf
o
r
m
e
r
m
o
d
e
l
f
o
r
w
in
d
in
g
f
a
u
lt
stu
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ies
.
"
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o
w
e
r
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li
v
e
r
y
,
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T
ra
n
sa
c
ti
o
n
s
o
n
9
,
n
o
.
2
(1
9
9
4
):
6
9
0
-
6
9
9
.
[
1
3
]
W
a
n
g
,
Hu
i
f
a
n
g
,
a
n
d
K.
L
.
Bu
tl
e
r.
"
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in
it
e
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le
m
e
n
t
a
n
a
l
y
s
is
o
f
in
tern
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l
w
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d
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g
fa
u
lt
s
in
d
istri
b
u
ti
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n
tran
sf
o
r
m
e
rs."
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we
r De
li
v
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ry
,
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E
T
ra
n
sa
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ti
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n
s
o
n
16
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n
o
.
3
(
2
0
0
1
):
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2
2
-
4
2
8
.
[
1
4
]
W
a
n
g
,
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a
n
g
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e
ter
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a
lm
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r
-
Bu
c
k
le,
a
n
d
Ka
re
n
L
.
Bu
tl
e
r.
"
T
ra
n
s
fo
rm
e
r
m
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e
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f
o
r
d
e
tec
t
io
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o
f
i
n
c
ip
ien
t
i
n
tern
a
l
w
in
d
in
g
f
a
u
lt
s."
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Pro
c
e
e
d
in
g
s
o
f
th
e
3
0
th
N
o
rth
Ame
ric
a
n
p
o
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sy
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m
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to
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d
,
OH
,
p
p
.
9
0
-
9
8
.
1
9
9
8
.
[
1
5
]
L
iu
,
Z.
,
S
.
L
iu
,
a
n
d
O.
A
.
M
o
h
a
m
m
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d
.
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p
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se
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sf
o
rm
e
r
s f
o
r
d
y
n
a
m
ic si
m
u
latio
n
s
."
M
a
g
n
e
ti
c
s,
IE
EE
T
r
a
n
sa
c
ti
o
n
s o
n
43,
n
o
.
4
(2
0
0
7
):
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7
6
1
-
1
7
6
4
.
[
1
6
]
L
iu
,
S
.
,
Z.
L
iu
,
a
n
d
O.
A
.
M
o
h
a
m
m
e
d
.
"
F
E
-
b
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se
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m
o
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li
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le
-
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se
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istri
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u
ti
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tran
sf
o
rm
e
rs
w
it
h
w
in
d
in
g
sh
o
rt
c
ircu
i
t
f
a
u
lt
s."
M
a
g
n
e
ti
c
s,
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
4
3
,
n
o
.
4
(
2
0
0
7
):
1
8
4
1
-
1
8
4
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8814
IJ
AA
S
Vo
l.
6
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No
.
3
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tem
b
er
201
7
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0
3
–
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1
2
212
[
1
7
]
Oz
g
o
n
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e
l,
Ok
a
n
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a
n
d
Erd
a
l
Kil
ic.
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o
d
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a
n
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re
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ti
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e
f
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u
l
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ti
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ica
ti
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tra
n
sf
o
rm
e
rs
."
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o
u
rn
a
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o
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n
k
li
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sti
tu
te
3
4
5
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o
.
3
(
2
0
0
8
):
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0
5
-
2
2
5
.
[
1
8
]
S
re
lath
a
,
G
.
,
M
.
Ra
jk
u
m
a
r,
Y.
S
u
d
h
a
k
a
r,
a
n
d
T
.
K.
G
a
n
g
u
l
y
.
"
I
m
p
ro
v
e
m
e
n
ts
in
In
tern
a
l
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n
su
lati
o
n
De
sig
n
o
f
P
o
w
e
r
T
ra
n
s
f
o
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m
e
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u
sin
g
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e
c
tri
c
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ield
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n
a
l
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sis
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h
ro
u
g
h
F
in
i
te
El
e
m
e
n
t
M
e
t
h
o
d
."
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we
r
E
n
g
in
e
e
r
J
o
u
rn
a
l
1
6
,
n
o
.
2
(
2
0
1
4
):
56
-
6
0
.
[
1
9
]
d
a
S
il
v
a
,
Ju
li
a
n
o
Rica
rd
o
,
Jo
a
o
P
.
Ba
sto
s,
Ne
lso
n
S
a
d
o
w
sk
y
,
a
n
d
Je
a
n
V.
L
e
it
e
.
"
El
e
c
tro
m
a
g
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e
t
ic
a
n
d
t
h
e
rm
a
l
sim
u
latio
n
o
f
a
n
o
il
in
su
late
d
p
o
w
e
r
tran
sf
o
r
m
e
r
.
"
In
El
e
c
trica
l
Ap
p
a
ra
t
u
s
a
n
d
T
e
c
h
n
o
l
o
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ies
(
S
IEL
A),
2
0
1
4
1
8
th
In
ter
n
a
t
io
n
a
l
S
y
mp
o
si
u
m o
n
,
p
p
.
1
-
4
.
IEE
E,
2
0
1
4
.
[
2
0
]
Be
h
jat,
V
.
,
V
a
h
e
d
i
,
A
.
“
Nu
m
e
ric
a
l
m
o
d
e
li
n
g
o
f
tran
s
f
o
r
m
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rs
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n
tu
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f
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h
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ra
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teriz
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th
e
f
a
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lt
y
tran
s
f
o
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m
e
r
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a
v
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u
n
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e
r
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rio
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s f
a
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lt
s an
d
o
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e
ra
ti
n
g
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o
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d
it
i
o
n
s”
.
I
ET
E
lec
ti
c
Po
we
r A
p
p
,
Vo
l.
5
,
(
2
0
1
1
)
p
p
.
4
1
5
-
4
3
1
.
[
2
1
]
P
ir
io
u
,
F
.
,
a
n
d
A
.
Ra
z
e
k
.
"
Nu
m
e
rica
l
si
m
u
latio
n
o
f
a
n
o
n
c
o
n
v
e
n
t
io
n
a
l
a
lt
e
rn
a
t
o
r
c
o
n
n
e
c
ted
to
a
r
e
c
ti
f
ier.
"
En
e
rg
y
Co
n
v
e
rs
io
n
,
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
5
,
n
o
.
3
(1
9
9
0
):
5
1
2
-
5
1
8
.
[
2
2
]
Bo
u
isso
u
,
S
.
,
F
.
P
iri
o
u
,
C.
Kie
n
y
,
a
n
d
G
.
T
a
n
n
e
a
u
.
"
Nu
m
e
rica
l
si
m
u
latio
n
o
f
a
p
o
w
e
r
tran
sf
o
r
m
e
r
u
sin
g
3
D
f
in
it
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le
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e
n
t
m
e
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o
d
c
o
u
p
le
d
t
o
c
ircu
i
t
e
q
u
a
ti
o
n
.
"
M
a
g
n
e
ti
c
s,
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
3
0
,
n
o
.
5
(1
9
9
4
):
3
2
2
4
-
3
2
2
7
.
[
2
3
]
COMS
OL
,
M
ULT
IP
HA
S
ICS
©
(F
EM
L
A
B),
[
o
n
l
in
e
]
.
h
tt
p
:/
/w
ww
.
c
o
m
so
l.
c
o
m
Evaluation Warning : The document was created with Spire.PDF for Python.