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o
u
p
lin
g
c
o
ef
f
icien
t
th
r
o
u
g
h
f
in
ite
elem
en
t
an
aly
s
i
s
s
im
u
latio
n
f
o
r
m
o
d
elin
g
,
d
e
s
ig
n
in
g
,
an
d
an
al
y
zin
g
th
e
I
P
T
s
y
s
tem
u
s
in
g
th
e
ANSYS
Ma
x
well
to
o
l.
T
h
e
d
e
s
ig
n
o
f
th
e
cir
c
u
lar
ch
a
r
g
in
g
p
ad
s
co
n
s
is
ts
o
f
a
f
lat
h
elica
l
c
o
il
with
f
er
r
ite
an
d
alu
m
in
u
m
s
h
ield
s
to
p
r
o
tect
ag
ain
s
t
m
ag
n
etic
f
lu
x
leak
a
g
e.
T
h
is
d
esig
n
was
r
ea
lized
u
s
in
g
ANSYS
Ma
x
well
-
3
D,
as
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
e
d
esig
n
p
ar
a
m
eter
s
wer
e
s
elec
ted
as
s
h
o
wn
in
T
ab
le
1
.
T
h
e
co
il
p
ar
am
eter
s
wer
e
ex
tr
ac
ted
f
r
o
m
th
e
f
in
ite
elem
en
t
an
aly
s
is
(
FEA)
an
d
u
s
ed
in
a
cir
cu
it
m
o
d
el
in
A
NSYS
Simp
lo
r
er
to
an
aly
ze
th
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
en
tire
s
y
s
tem
[
8
]
,
[
1
1
]
.
Fi
g
u
r
e
4
d
is
p
lay
s
th
e
FEA
o
f
t
h
e
s
lack
ly
c
o
u
p
le
d
tr
an
s
f
o
r
m
er
.
T
h
e
s
im
u
latio
n
o
u
tco
m
es
ex
p
o
s
e
th
at
t
h
e
s
elf
-
i
n
d
u
ctan
ce
o
f
th
e
p
r
im
ar
y
a
n
d
th
e
s
elf
-
in
d
u
cta
n
ce
o
f
th
e
s
ec
o
n
d
ar
y
c
o
ils
ar
e
1
2
2
.
7
7
7
µH
an
d
1
3
9
.
9
5
3
µH
,
r
esp
ec
tiv
ely
,
an
d
th
e
m
u
tu
al
i
n
d
u
ctan
ce
b
etwe
en
th
ese
co
ils
is
7
7
.
6
4
1
3
µH
[
7
]
,
as sh
o
wn
in
T
ab
le
2
.
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
am
o
f
I
P
T
s
y
s
tem
[
1
3
]
(
a)
(
b
)
Fig
u
r
e
3
.
C
h
ar
g
in
g
p
ad
m
o
d
el
in
ANSYS M
ax
well:
(a
)
3
D
-
v
iew
an
d
(
b
)
t
o
p
v
iew
T
ab
le
1
.
Simu
latio
n
d
esig
n
o
f
th
e
cir
cu
lar
ch
a
r
g
in
g
p
ad
p
ar
a
m
eter
s
D
e
si
g
n
p
a
r
a
me
t
e
r
s
V
a
l
u
e
I
n
n
e
r
r
a
d
i
u
s
I
n
t
e
r
-
t
u
r
n
se
p
a
r
a
t
i
o
n
C
r
o
ss
-
se
c
t
i
o
n
a
l
a
r
e
a
o
f
t
h
e
c
o
n
d
u
c
t
o
r
N
o
.
o
f
t
u
r
n
s
F
e
r
r
i
t
e
s
A
l
u
m
i
n
u
m
s
h
i
e
l
d
2
5
0
m
m
0
.
1
mm
6
.
3
mm
2
11
2
8
5
×
50
×
5
mm
6
8
0
×
6
8
0
×
1
0
mm
T
ab
le
2
.
T
h
e
s
im
u
latio
n
r
esu
lt
s
o
b
tain
ed
f
r
o
m
ANSYS M
ax
well
P
a
r
a
me
t
e
r
s
V
a
l
u
e
L
p
L
s
M
K
1
2
2
.
7
7
7
µ
H
1
3
9
.
9
5
3
µ
H
7
7
.
6
4
1
3
µ
H
0
.
5
9
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2453
-
2
4
6
3
2456
Fig
u
r
e
4
.
I
PT
Sy
s
tem
in
ANS
YS
Ma
x
well
Simp
lo
r
er
3.
M
E
T
H
O
D
C
o
m
p
en
s
atio
n
n
etwo
r
k
s
ar
e
a
n
im
p
o
r
ta
n
t
co
m
p
o
n
e
n
t
o
f
a
n
I
PT
s
y
s
tem
,
r
ed
u
cin
g
th
e
s
y
s
tem
v
o
ltag
e
r
atin
g
an
d
im
p
r
o
v
in
g
p
o
wer
tr
an
s
m
is
s
io
n
ca
p
ac
ity
.
Mo
r
eo
v
e
r
,
th
e
eq
u
iv
alen
t lo
ad
o
f
th
e
b
a
tter
y
d
if
f
er
s
d
u
r
in
g
th
e
ch
ar
g
in
g
p
e
r
io
d
,
af
f
ec
tin
g
th
e
in
p
u
t
im
p
ed
an
ce
v
alu
e
a
n
d
,
co
n
s
eq
u
e
n
tly
,
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
en
tire
s
y
s
tem
.
C
o
m
p
en
s
atio
n
to
p
o
lo
g
ies
ar
e
o
f
two
ty
p
es:
b
asic
a
n
d
h
y
b
r
i
d
.
T
h
er
e
a
r
e
f
o
u
r
b
as
ic
to
p
o
lo
g
ies
b
ased
o
n
th
e
lo
ca
tio
n
o
f
th
e
ca
p
ac
itiv
e
co
m
p
en
s
atio
n
:
s
er
ies
-
s
er
ies
(
SS
)
,
p
ar
allel
-
p
ar
allel
(
PP
)
,
p
ar
allel
-
s
er
ies
(
PS
)
,
an
d
s
er
ies
-
p
ar
allel
(
SP
)
,
as
s
h
o
wn
in
Fig
u
r
e
5
.
Am
o
n
g
th
e
f
o
u
r
b
asic
to
p
o
l
o
g
ies,
th
e
SS
to
p
o
lo
g
y
is
th
e
m
o
s
t
wid
ely
u
s
ed
d
u
e
to
its
s
im
p
le
d
esig
n
an
d
in
d
e
p
en
d
e
n
ce
o
f
th
e
co
u
p
lin
g
co
e
f
f
icien
t
(
k
)
a
n
d
lo
ad
.
Ho
wev
er
,
its
m
ain
d
r
awb
a
ck
is
th
e
lar
g
e
c
u
r
r
en
t
s
u
r
g
e
wh
en
th
e
s
ec
o
n
d
ar
y
cir
cu
it
is
s
u
d
d
en
ly
clo
s
ed
[
9
]
.
T
h
is
r
esu
lts
in
a
s
ig
n
if
ican
t
in
cr
ea
s
e
in
th
e
in
d
u
ce
d
cu
r
r
e
n
t
with
in
th
e
p
r
im
a
r
y
win
d
in
g
s
,
lead
in
g
to
s
ev
er
e
s
h
o
r
t
cir
cu
its
th
at
d
am
ag
e
th
e
p
r
im
a
r
y
cir
cu
it.
As
a
r
esu
lt,
h
y
b
r
id
r
eso
n
an
t
co
m
p
en
s
atio
n
cir
cu
its
co
n
s
is
t
o
f
m
u
ltip
le
p
ass
iv
e
elem
en
ts
,
s
u
ch
as
th
e
L
C
/L
C
an
d
L
C
C
/L
C
C
[
1
]
,
[
1
5
]
.
T
h
ese
to
p
o
lo
g
ies
ar
e
ty
p
ic
ally
co
n
s
id
er
ed
to
ac
co
m
p
lis
h
a
co
n
s
tan
t
v
o
ltag
e
o
u
tp
u
t,
co
n
s
tan
t
cu
r
r
en
t
o
u
tp
u
t,
o
r
b
o
t
h
[
2
1
]
.
I
n
th
is
p
ap
e
r
,
we
will
d
is
cu
s
s
two
ty
p
es o
f
to
p
o
lo
g
ies
:
L
C
C
/S co
m
p
en
s
atio
n
an
d
L
C
C
/LC
C
co
m
p
en
s
atio
n
.
Fig
u
r
e
5
.
B
asic c
o
m
p
en
s
atio
n
to
p
o
lo
g
y
3
.
1
.
Ana
ly
s
is
o
f
L
CC/S
co
mp
ens
a
t
io
n t
o
po
lo
g
y
Fig
u
r
e
6
illu
s
tr
ates
an
I
PT
s
y
s
tem
with
an
L
C
C
/
S
co
m
p
en
s
atio
n
to
p
o
lo
g
y
.
V
in
r
ep
r
esen
t
s
th
e
A
C
in
p
u
t
v
o
ltag
e,
wh
ile
V
o
an
d
I
o
r
ep
r
esen
t
th
e
DC
o
u
tp
u
t
v
o
lta
g
e
an
d
cu
r
r
e
n
t,
r
esp
ec
tiv
ely
.
T
h
e
h
ig
h
-
f
r
e
q
u
en
c
y
in
p
u
t
an
d
o
u
tp
u
t
v
o
ltag
es
ar
e
r
ep
r
esen
ted
b
y
V
P
an
d
V
S
,
wh
ile
I
P
an
d
I
S
r
ep
r
esen
t
th
e
h
i
g
h
-
f
r
e
q
u
en
c
y
in
p
u
t
an
d
o
u
tp
u
t
cu
r
r
en
ts
.
T
h
e
f
u
ll
-
b
r
id
g
e
in
v
e
r
ter
co
n
s
is
ts
o
f
f
o
u
r
p
o
wer
tr
an
s
is
to
r
s
,
Q
1
−Q
4
,
u
s
ed
to
co
n
v
er
t
th
e
DC
v
o
ltag
e
(
V
DC
)
in
to
a
s
q
u
ar
e
-
wav
e
v
o
ltag
e.
Du
e
t
o
th
e
m
u
ltip
le
h
ar
m
o
n
ics
g
en
e
r
ate
d
b
y
t
h
e
in
v
e
r
ter
,
f
u
n
d
am
e
n
tal
h
ar
m
o
n
ic
an
aly
s
i
s
(
FHA)
is
u
s
ed
f
o
r
q
u
alitativ
e
an
aly
s
is
in
W
PT
s
y
s
tem
s
[
2
3
]
.
L
P
an
d
L
S
d
en
o
te
th
e
s
elf
-
in
d
u
ctan
ce
s
o
f
t
h
e
p
r
i
m
ar
y
an
d
s
ec
o
n
d
ar
y
win
d
in
g
s
,
r
esp
ec
tiv
ely
.
M
s
ig
n
if
ies
th
e
m
u
tu
al
in
d
u
cta
n
ce
b
etwe
en
th
e
p
r
im
a
r
y
a
n
d
s
ec
o
n
d
ar
y
win
d
in
g
s
,
wh
ich
ca
n
b
e
ca
lcu
lated
u
s
in
g
(
1
)
.
=
√
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Desig
n
a
n
d
s
imu
la
tio
n
o
f in
d
u
ctive
p
o
w
er tr
a
n
s
fer s
y
s
tem
u
s
in
g
h
yb
r
id
…
(
N
o
o
r
S
a
mi
)
2457
T
h
e
r
eso
n
an
t
n
etwo
r
k
s
co
n
s
is
t
o
f
o
n
e
i
n
d
u
cto
r
,
L
P
1
,
an
d
th
r
ee
ca
p
ac
ito
r
s
,
C
P
1
,
C
P
,
an
d
C
S
.
A
b
r
id
g
e
r
ec
tifie
r
co
n
s
is
tin
g
o
f
4
d
io
d
es,
D
1
to
D
4
,
is
u
s
ed
to
ad
j
u
s
t
th
e
o
u
tp
u
t
v
o
ltag
e
V
o
to
t
h
e
b
atter
y
c
h
ar
g
i
n
g
v
o
ltag
e
V
b
,
wh
er
e
I
o
is
t
h
e
o
u
t
p
u
t
cu
r
r
en
t,
I
b
is
th
e
b
atter
y
c
h
ar
g
in
g
cu
r
r
en
t
,
th
ese
ca
n
b
e
ca
lcu
lated
u
s
in
g
th
e
(
2
)
,
an
d
(
3
)
,
C
o
is
th
e
o
u
tp
u
t f
ilter
ca
p
ac
ito
r
,
an
d
R
L
is
th
e
o
u
tp
u
t lo
ad
, R
o
is
th
e
eq
u
iv
alen
t A
C
lo
ad
r
esis
tan
ce
an
d
ca
n
b
e
ca
lcu
lated
b
y
(
4
)
[
4
]
,
[
2
4
]
.
=
√
2
4
(
2
)
=
2
√
2
(
3
)
=
8
2
(
4
)
Fig
u
r
e
6
s
h
o
ws
th
e
cir
cu
it
d
ia
g
r
am
o
f
th
e
L
C
C
/S
co
m
p
en
s
ated
to
p
o
lo
g
y
.
T
h
e
I
PT
ch
ar
g
i
n
g
s
y
s
tem
an
d
th
e
co
m
p
e
n
s
atio
n
to
p
o
lo
g
y
co
m
p
o
n
en
ts
wer
e
d
esig
n
ed
b
ased
o
n
u
s
in
g
(
5
)
,
(
6
)
,
(
7
)
,
a
n
d
(
8
)
to
o
b
tain
th
e
elec
tr
ical
p
ar
am
eter
s
.
L
P1
=
V
S
M
V
P
(
5
)
C
P1
=
1
ω
2
L
P1
(
6
)
C
P
=
1
ω
2
(
L
1
−
L
P1
)
(
7
)
C
S
=
1
ω
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2
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8
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Fig
u
r
e
6
.
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h
e
cir
cu
it d
ia
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o
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th
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L
C
C
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en
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ated
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y
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.
2
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ly
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L
CC/L
CC
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o
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e
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m
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r
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ilter
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icate
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n
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Fig
u
r
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7
[
2
5
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.
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h
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aly
tical
ap
p
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ar
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[
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PT
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as
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
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s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
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2453
-
2
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=
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1
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u
r
e
7
.
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h
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cir
cu
it d
ia
g
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am
o
f
th
e
L
C
C
/LCC
co
m
p
en
s
ated
to
p
o
lo
g
y
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
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T
h
e
FEA
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im
u
latio
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o
llo
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d
esig
n
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d
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al
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is
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f
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n
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tific
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ar
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eter
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(
L
P
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M,
an
d
K)
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ted
in
T
ab
l
e
2
.
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h
e
th
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o
r
etica
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m
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m
th
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im
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g
en
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ated
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y
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Ma
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well
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D
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s
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th
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ap
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o
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iate
eq
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atio
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s
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e
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ted
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d
a
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im
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latio
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o
f
a
3
.
7
k
W
W
PT1
ch
ar
g
in
g
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y
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tem
with
a
m
ag
n
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ap
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p
er
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o
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ac
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e
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5
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ch
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r
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g
s
tan
d
ar
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with
MA
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AB
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m
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f
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4
.
1
.
L
CC/S
c
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m
pens
a
t
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esu
lt
Af
ter
co
m
p
letin
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th
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d
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ANSYS
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x
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o
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twar
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d
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aly
s
in
g
t
h
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cu
it
f
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r
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to
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e
I
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ch
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tem
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d
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s
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n
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k
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en
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to
o
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lectr
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ar
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eter
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h
ich
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a
b
le
3
.
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h
ese
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p
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s
ar
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esig
n
ed
to
o
p
er
ate
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n
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ce
with
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e
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im
ar
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n
d
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r
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s
elf
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u
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ce
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ab
le
3
.
R
esu
lts
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f
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C
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p
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g
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a
r
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me
t
e
r
s
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a
l
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in
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P
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1
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1
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8
5
k
H
z
1
0
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m
F
i
g
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r
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8
s
h
o
w
s
t
h
a
t
t
h
e
p
r
i
m
a
r
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v
o
l
t
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g
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(
V
P
)
,
r
e
p
r
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s
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n
t
s
t
h
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t
p
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f
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n
v
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r
t
e
r
a
s
a
s
q
u
a
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w
a
v
e
.
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n
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n
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c
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t
e
m
u
s
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h
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h
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u
r
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d
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lti
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t
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u
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r
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t
h
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m
p
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d
a
n
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e
m
i
s
m
a
t
c
h
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n
c
r
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as
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c
a
u
s
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h
e
c
u
r
r
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n
t
t
o
d
e
c
r
e
a
s
e
t
o
it
s
o
p
ti
m
a
l
v
al
u
e.
T
h
e
s
e
c
o
n
d
a
r
y
v
o
l
t
a
g
e
(
V
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)
,
r
e
p
r
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s
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n
t
i
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p
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n
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a
t
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n
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i
r
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u
i
t
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n
d
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n
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u
t
o
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t
h
e
b
r
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d
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e
r
e
ct
i
f
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e
r
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i
s
al
s
o
a
s
q
u
a
r
e
w
a
v
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,
as
s
h
o
w
n
i
n
F
i
g
u
r
e
9
.
T
r
a
n
s
m
is
s
i
o
n
s
y
s
t
e
m
u
s
i
n
g
a
h
y
b
r
i
d
L
C
C
/
S
c
o
m
p
e
n
s
a
ti
o
n
to
p
o
l
o
g
y
,
t
h
e
p
r
i
m
a
r
y
c
u
r
r
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n
t
ty
p
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c
a
l
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x
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i
b
it
s
a
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i
g
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it
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ta
t
e
,
a
s
s
h
o
w
n
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n
F
i
g
u
r
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8
.
I
n
ad
d
itio
n
,
t
h
e
p
r
im
ar
y
v
o
lta
g
e
an
d
cu
r
r
en
t
a
r
e
in
p
h
ase,
lik
e
th
e
s
ec
o
n
d
ar
y
v
o
ltag
e
an
d
cu
r
r
en
t,
s
o
th
e
s
y
s
tem
wo
r
k
s
at
a
r
eso
n
an
t
f
r
eq
u
e
n
cy
,
an
d
th
e
p
r
im
a
r
y
an
d
s
ec
o
n
d
ar
y
cu
r
r
e
n
t
(
I
P
,
I
S
)
ar
e
s
in
e
wav
es
as
s
h
o
wn
in
Fig
u
r
e
1
0
.
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h
e
s
ec
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n
d
ar
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cu
r
r
en
t
in
c
r
ea
s
es
b
ec
au
s
e
th
e
s
er
ies
r
eso
n
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t
co
m
p
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ig
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if
ican
tly
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th
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f
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r
e
n
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m
ain
tain
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p
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ase
alig
n
m
en
t
with
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Desig
n
a
n
d
s
imu
la
tio
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f in
d
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p
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2459
p
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I
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8
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4
I
n
t J Po
w
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lec
&
Dr
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16
,
No
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4
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Dec
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b
er
20
25
:
2453
-
2
4
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n
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3
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1
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r
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1
5
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ag
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ield
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h
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r
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1
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r
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ase,
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ase
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r
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ase
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n
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u
r
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1
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r
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L
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r
e
.
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4
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I
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&
Dr
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s
t
I
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m
en
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u
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n
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en
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in
d
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en
t
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P
A
f
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r
o
m
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g
r
esu
lts
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is
s
tu
d
y
r
em
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ased
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is
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ea
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wo
r
ld
f
ac
to
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s
s
u
ch
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m
ag
n
etic
co
u
p
lin
g
v
ar
iatio
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E
MI
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p
ar
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ic
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s
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s
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d
th
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m
al
co
n
s
tr
ain
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n
o
t
co
n
s
id
er
ed
.
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s
u
ch
,
f
u
tu
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e
wo
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k
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h
o
u
ld
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clu
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e
h
ar
d
war
e
p
r
o
to
t
y
p
in
g
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p
er
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tal
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alid
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d
ad
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d
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o
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s
tr
ateg
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am
ically
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s
t
to
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lo
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m
en
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itio
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x
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tio
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PT,
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o
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ed
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o
l,
a
n
d
r
en
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r
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ial
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licatio
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n
f
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k
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th
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p
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o
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ty
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es
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e
im
p
lem
e
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ted
i
n
th
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n
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t
v
er
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n
.
T
h
is
wo
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k
will
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clu
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e
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n
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u
ctio
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L
C
C
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S.
T
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e
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ig
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etr
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s
; a
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o
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ACK
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DG
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Nin
ev
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Un
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lectr
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F
UNDING
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No
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.
AUTHO
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h
is
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C
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to
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ax
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(
C
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tio
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h
ip
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is
p
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tes,
an
d
f
ac
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co
llab
o
r
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2453
-
2
4
6
3
2462
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
No
o
r
Sam
i
✓
✓
✓
✓
✓
✓
✓
✓
✓
Har
ith
Al
-
B
ad
r
an
i
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
o
l
o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
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o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
n
O
:
W
r
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t
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n
g
-
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n
a
l
D
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a
f
t
E
:
W
r
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e
v
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&
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d
i
t
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g
Vi
:
Vi
su
a
l
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z
a
t
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o
n
Su
:
Su
p
e
r
v
i
s
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o
n
P
:
P
r
o
j
e
c
t
a
d
mi
n
i
st
r
a
t
i
o
n
Fu
:
Fu
n
d
i
n
g
a
c
q
u
i
si
t
i
o
n
CO
NF
L
I
C
T
O
F
I
N
T
E
R
E
S
T
ST
A
T
E
M
E
NT
T
h
e
au
th
o
r
s
d
ec
lar
e
th
at
th
ey
h
av
e
n
o
k
n
o
w
n
co
m
p
u
tin
g
f
i
n
an
cial
in
ter
ests
o
r
p
er
s
o
n
al
r
el
atio
n
s
h
ip
s
th
at
co
u
ld
h
av
e
ap
p
ea
r
ed
t
o
in
f
lu
en
ce
th
e
wo
r
k
r
e
p
o
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te
d
in
t
h
is
p
ap
er
.
DATA AV
AI
L
AB
I
L
I
T
Y
T
h
e
d
ata
th
at
s
u
p
p
o
r
t th
e
f
in
d
i
n
g
s
o
f
th
is
s
tu
d
y
a
r
e
av
ailab
le
f
r
o
m
th
e
co
r
r
esp
o
n
d
in
g
au
th
o
r
.
RE
F
E
R
E
NC
E
S
[
1
]
W
.
L
i
,
W
.
M
e
i
,
Q
.
Y
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Y
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,
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.
D
o
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y
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d
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D
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a
o
,
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D
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r
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s,
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o
rl
d
El
e
c
t
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c
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h
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o
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n
a
l
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v
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l
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1
6
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9
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5
.
[
3
]
J.
Y
a
n
g
,
R
.
Li
u
,
Q
.
T
o
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g
,
X
.
Y
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g
,
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u
,
a
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d
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p
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[
4
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J.
Y
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,
X
.
Z
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a
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g
,
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,
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i
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,
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sat
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[
5
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.
W
u
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t
a
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.
,
“
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c
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c
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,
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[
7
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L.
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,
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.
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n
g
,
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.
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i
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