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[
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u
t
v
o
ltag
e
w
a
v
e
f
o
r
m
.
I
n
[
9
]
au
th
o
r
s
u
s
ed
t
w
o
s
er
ie
s
s
i
m
ilar
m
o
d
u
les
o
f
th
e
i
n
v
er
ter
p
r
o
p
o
s
ed
in
[
8
]
w
it
h
eq
u
al
d
c
s
o
u
r
ce
s
.
T
h
u
s
t
h
at
to
p
o
lo
g
y
ca
n
g
e
n
er
ate
9
le
v
el
s
(
0
,
V
dc
,
2
V
dc
,
3
V
dc
,
4
V
dc
,
-
V
dc
,
-
2
V
dc
,
-
3
V
dc
,
-
4
V
dc
)
an
d
it
is
co
n
s
id
er
ed
a
s
a
s
y
m
m
e
tr
ic
ML
I
.
I
n
th
is
p
r
o
p
o
s
ed
to
p
o
lo
g
y
an
a
s
y
m
m
etr
ical
C
HB
in
v
er
ter
b
ased
o
n
[
8
]
an
d
[
9
]
is
p
r
esen
t
ed
.
I
n
s
tead
o
f
u
s
i
n
g
eq
u
al
d
c
s
o
u
r
ce
s
,
th
e
ter
tiar
y
r
atio
i
s
e
m
p
lo
y
ed
to
i
n
cr
ea
s
e
th
e
v
o
lta
g
e
le
v
els
w
it
h
th
e
s
a
m
e
n
u
m
b
er
o
f
s
w
itc
h
es.
T
h
e
n
u
m
b
er
o
f
o
u
tp
u
t
v
o
lta
g
e
lev
el
s
is
i
n
cr
ea
s
ed
to
1
7
.
T
h
e
p
r
esen
ted
ML
I
in
th
is
p
a
p
er
is
a
m
o
d
u
la
r
i
n
ad
d
itio
n
t
o
b
o
th
f
u
n
d
a
m
e
n
tal
f
r
eq
u
e
n
c
y
an
d
P
W
M
co
n
tr
o
l
s
ch
e
m
es c
a
n
b
e
e
m
p
lo
y
ed
.
Si
m
u
latio
n
r
es
u
lt
s
ar
e
p
r
o
v
id
ed
t
o
v
er
if
y
t
h
e
v
alid
it
y
o
f
t
h
e
p
r
o
p
o
s
ed
s
y
s
te
m
T
h
e
p
ap
e
r
is
o
r
g
an
ized
as
f
o
l
lo
w
s
:
s
ec
tio
n
2
g
iv
e
s
th
e
o
p
er
atio
n
al
p
r
in
cip
les
o
f
t
h
e
p
r
o
p
o
s
ed
ML
I
to
p
o
lo
g
y
.
T
h
e
Mo
d
u
latio
n
T
ec
h
n
iq
u
es
f
o
r
th
e
p
r
o
p
o
s
ed
ML
I
is
p
r
esen
ted
in
s
ec
ti
o
n
3
.
Su
b
s
eq
u
e
n
tl
y
s
i
m
u
lat
io
n
r
es
u
lt
s
ar
e
p
r
o
v
id
e
d
in
s
ec
tio
n
4
.
Mo
d
u
lar
it
y
o
f
t
h
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
h
a
s
b
ee
n
s
tu
d
ied
i
n
s
ec
tio
n
5
.
Sectio
n
6
p
r
esen
t
s
a
co
m
p
a
r
is
o
n
b
et
w
ee
n
t
h
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
an
d
e
x
is
tin
g
co
u
n
ter
p
a
r
ts
M
L
I
to
p
o
lo
g
ies.
Fin
all
y
co
n
cl
u
s
io
n
is
p
r
ese
n
te
d
in
s
ec
tio
n
7
.
2.
O
P
E
RAT
I
O
NAL P
R
I
NC
I
P
L
E
S O
F
ASYM
M
E
T
RI
CA
L
CASCAD
E
D
M
L
I
T
O
P
O
L
O
G
Y
Fig
u
r
e
1
(
a)
,
(
b
)
an
d
(
c)
s
h
o
w
s
th
e
p
r
o
p
o
s
ed
1
7
lev
els
s
in
g
l
e
p
h
ase
as
y
m
m
etr
ical
ca
s
ca
d
e
d
in
v
er
ter
to
p
o
lo
g
y
a
n
d
its
g
e
n
er
ated
o
u
tp
u
t
v
o
ltag
e
w
a
v
e
f
o
r
m
s
f
o
r
lo
w
an
d
m
ed
i
u
m
m
o
d
u
latio
n
in
d
e
x
(
)
.
T
h
e
p
r
o
p
o
s
ed
in
v
er
ter
co
n
s
i
s
ts
o
f
t
w
o
s
er
ies
co
n
n
ec
ted
m
o
d
u
les
b
ased
o
n
[
9
]
.
E
ac
h
m
o
d
u
le
co
n
s
i
s
ts
o
f
f
i
v
e
I
GB
T
s
w
itc
h
es
as
w
ell
a
s
f
o
u
r
m
a
i
n
d
io
d
es.
E
ac
h
m
o
d
u
le
r
eq
u
i
r
es
t
w
o
eq
u
al
a
n
d
n
o
n
-
is
o
lat
ed
d
c
s
o
u
r
ce
s
.
T
o
in
cr
ea
s
e
t
h
e
le
v
el
s
o
f
o
u
tp
u
t
v
o
ltag
e,
a
ter
tiar
y
r
atio
1
:3
b
etw
ee
n
t
h
e
u
p
p
er
mo
d
u
le
d
c
s
o
u
r
ce
(
)
an
d
t
h
e
lo
w
er
m
o
d
u
le
d
c
s
o
u
r
ce
(
)
is
ad
o
p
ted
.
I
t
ca
n
b
e
n
o
ted
th
at,
th
e
in
p
u
t
v
o
lta
g
e
f
o
r
ea
ch
m
o
d
u
le
is
d
iv
id
ed
in
to
t
w
o
eq
u
al
v
o
ltag
e
s
as
s
h
o
w
n
in
f
i
g
u
r
e
1
.
T
o
o
b
tain
th
i
s
n
u
m
b
er
o
f
lev
el
s
f
r
o
m
th
e
co
n
v
e
n
tio
n
al
to
p
o
lo
g
ies
lik
e
ca
s
ca
d
ed
H
-
b
r
id
g
e
(
C
HB
)
[
10
]
,
n
eu
tr
al
p
o
in
t
cla
m
p
ed
(
NP
C
)
[
11
]
,
o
r
f
ly
in
g
ca
p
ac
ito
r
(
F
C
)
in
v
er
ter
s
[
12
]
,
a
lar
g
e
n
u
m
b
er
o
f
s
w
itc
h
es
a
n
d
d
io
d
es
h
a
v
e
t
o
b
e
u
s
ed
.
T
h
e
m
ai
n
ad
v
a
n
tag
es
o
f
t
h
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
ar
e;
(
1
)
h
ig
h
le
v
el
s
w
itc
h
r
atio
(
L
SR
)
[
13
]
b
ec
au
s
e
o
f
u
s
i
n
g
u
n
eq
u
a
l
D
C
v
o
lt
ag
e
v
al
u
es
(
1
:3
d
c
s
o
u
r
ce
r
atio
)
r
esu
l
tin
g
i
n
r
ed
u
cin
g
th
e
n
u
m
b
er
o
f
co
m
p
o
n
en
ts
u
s
ed
;
(
2
)
th
e
s
w
i
tc
h
es
u
ti
liz
ed
in
u
p
p
er
m
o
d
u
le
w
it
h
lo
w
er
d
c
s
o
u
r
ce
v
alu
e
o
p
er
ate
at
s
w
itc
h
i
n
g
f
r
eq
u
en
c
y
,
w
h
ile
th
e
s
w
itc
h
es
u
t
ilized
i
n
lo
w
er
m
o
d
u
le
w
i
th
h
ig
h
er
d
c
s
o
u
r
ce
v
al
u
e
o
p
er
ate
at
lo
w
f
r
eq
u
e
n
c
y
.
C
o
n
s
eq
u
e
n
t
l
y
th
e
s
w
itc
h
es lo
s
s
es
w
i
ll b
e
r
ed
u
ce
d
.
(
a)
(
b
)
(
c)
Fig
u
r
e
1
.
(
a
)
T
h
e
P
r
o
p
o
s
ed
Si
n
g
le
P
h
a
s
e
A
s
y
m
m
etr
ical
C
a
s
ca
d
ed
Mu
ltil
ev
el
I
n
v
er
ter
; (
b
)
Gen
er
ated
Ou
tp
u
t V
o
ltag
e
f
o
r
L
o
w
Mo
d
u
latio
n
I
n
d
ex
; (
c)
Gen
er
ated
O
u
tp
u
t V
o
lta
g
e
f
o
r
Me
d
iu
m
Mo
d
u
latio
n
I
n
d
e
x
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
7
1
2
–
721
714
T
h
e
g
en
er
ated
o
u
tp
u
t
v
o
lta
g
e
lev
els
o
f
t
h
e
p
r
o
p
o
s
ed
ML
I
ar
e
s
h
o
w
n
in
T
ab
le
1
w
h
er
e
t
wo
m
o
d
u
les
ar
e
co
n
s
id
er
ed
w
it
h
1
0
s
w
itc
h
es
an
d
4
d
io
d
es
th
a
t
ar
e
ab
l
e
to
g
e
n
er
ate
1
7
o
u
tp
u
t
v
o
lta
g
e
le
v
el
s
.
T
h
e
lo
w
er
m
o
d
u
le
d
c
v
o
lta
g
e
s
o
u
r
ce
is
t
h
r
ee
ti
m
es
th
e
u
p
p
er
m
o
d
u
le
d
c
v
o
ltag
e
s
o
u
r
ce
.
Fro
m
T
ab
le
1
,
to
ac
h
ie
v
e
a
n
y
lev
el,
f
o
u
r
s
w
itch
e
s
h
a
v
e
to
b
e
tu
r
n
ed
o
n
.
A
s
a
n
ex
a
m
p
le,
f
o
r
th
e
f
ir
s
t
le
v
el
Q
4
,
Q
a
,
Q
7
,
an
d
Q
8
s
h
o
u
ld
b
e
tu
r
n
ed
o
n
to
g
et
in
th
e
o
u
tp
u
t.
I
n
th
i
s
ca
s
e,
in
v
er
ter
v
o
lta
g
e
=
=
v
o,
1
.
I
t
co
u
ld
b
e
n
o
ticed
f
r
o
m
F
ig
u
r
e
1
(
b
)
an
d
(
c)
th
at
as th
e
m
o
d
u
latio
n
i
n
d
ex
i
n
cr
ea
s
e
s
,
m
o
r
e
le
v
els ar
e
g
en
er
ated
.
T
ab
le
1.
Ou
tp
u
t
Vo
ltag
es o
f
T
w
o
Mo
d
u
les
S
t
a
t
e
s
N
o
.
U
p
p
e
r
mo
d
u
l
e
v
o
l
t
a
g
e
[
]
L
o
w
e
r
mo
d
u
l
e
v
o
l
t
a
g
e
[
]
O
u
t
p
u
t
v
o
l
t
a
g
e
[
]
Q1
Q2
Q3
Q4
QA
Q5
Q6
Q7
Q8
QB
R
a
t
i
o
s:
u
p
p
e
r
mo
d
u
l
e
2V
dc
d
i
v
i
d
e
d
V
dc
&
V
dc
L
o
w
e
r
mo
d
u
l
e
6
V
dc
d
i
v
i
d
e
d
3
V
dc
&
3
V
dc
1
0
0
0
1
1
0
0
0
1
1
0
0
0
2
V
dc
0
V
dc
0
0
0
1
1
0
0
1
1
0
3
2
V
dc
0
2
V
dc
1
0
0
1
0
1
1
0
0
0
4
0
3
V
dc
3
V
dc
1
1
0
0
0
0
0
0
1
1
5
V
dc
3
V
dc
4
V
dc
0
0
0
1
1
0
0
0
1
1
6
2
V
dc
3
V
dc
5
V
dc
1
0
0
1
0
0
0
0
1
1
7
0
6
V
dc
6
V
dc
1
1
0
0
0
1
0
0
1
0
8
V
dc
6
V
dc
7
V
dc
0
0
0
1
1
1
0
0
1
0
9
2
V
dc
6
V
dc
8
V
dc
1
0
0
1
0
1
0
0
1
0
10
-
V
dc
0
-
V
dc
0
1
0
0
1
1
1
0
0
0
11
-
2
V
dc
0
-
2
V
dc
0
1
1
0
0
1
1
0
0
0
12
0
-
3
V
dc
-
3
V
dc
1
1
0
0
0
0
1
0
0
1
13
-
V
dc
-
3
V
dc
-
4
V
dc
0
1
0
0
1
0
1
0
0
1
14
-
2
V
dc
-
3
V
dc
-
5
V
dc
0
1
1
0
0
0
1
0
0
1
15
0
-
6
V
dc
-
6
V
dc
1
1
0
0
0
0
1
1
0
0
16
-
V
dc
-
6
V
dc
-
7
V
dc
0
1
0
0
1
0
1
1
0
0
17
-
2
V
dc
-
6
V
dc
-
8
V
dc
0
1
1
0
0
0
1
1
0
0
3.
M
O
DULAT
I
O
N
T
E
CH
NI
Q
UE
S F
O
R
T
H
E
P
RO
P
O
SE
D
M
LI
Mo
d
u
latio
n
tech
n
iq
u
es
f
o
r
ML
I
ca
n
b
e
d
iv
id
ed
in
to
t
w
o
well
-
k
n
o
w
n
ca
teg
o
r
ies
d
ep
en
d
i
n
g
o
n
t
h
e
s
w
itc
h
in
g
f
r
eq
u
en
c
y
u
s
ed
to
d
r
iv
e
th
e
in
v
er
ter
s
w
itc
h
es
:
(
a)
f
u
n
d
a
m
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tech
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q
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6.
(
1
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I
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I
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I
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I
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6.
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[
9
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.
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RE
F
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R
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NC
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S
[1
]
A
.
Na
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I.
T
a
k
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a
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i,
a
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H.
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n
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tr
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,
1
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[2
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M
.
M
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o
w
sk
i,
K.
G
o
p
a
k
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m
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J.
Ro
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.
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,
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d
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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Mo
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721
[3
]
M
u
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a
m
m
a
d
Ja
m
il
,
“
Co
mp
a
riso
n
o
f
M
u
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v
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In
v
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fo
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mm
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tern
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m (
I
J
PE
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)
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3
,
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l.
3
,
N
o
.
2
,
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7
0
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1
7
8
.
[4
]
J.
W
e
n
a
n
d
K.
M
.
S
m
e
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le
y
,
"
S
y
n
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o
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mu
lt
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,
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,
v
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l.
2
3
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2
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5
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.
[5
]
P.
L
e
za
n
a
a
n
d
G
.
Ortiz,
"
Exte
n
d
e
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f
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sc
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[6
]
Ha
mz
a
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[7
]
W
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wto
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r
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sc
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-
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M
u
lt
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In
v
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r
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ter
n
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ti
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o
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f
P
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Dr
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(
IJ
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0
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7
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l.
8
,
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o
.
3
,
1
1
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3
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1
2
0
2
.
[8
]
R.
S
e
y
e
zh
a
i
,
Ba
n
u
p
a
rv
a
th
y
Ka
lp
a
n
a
,
Je
n
n
if
e
r
V
a
sa
n
th
i,
“
De
sig
n
a
n
d
De
v
e
lo
p
me
n
t
o
f
Hy
b
rid
M
u
l
ti
lev
e
l
In
v
e
rte
r
e
mp
lo
y
in
g
Du
a
l
Refe
re
n
c
e
M
o
d
u
la
ti
o
n
T
e
c
h
n
i
q
u
e
f
o
r
Fu
e
l
Ce
ll
Ap
p
l
ica
ti
o
n
s
,
”
In
ter
n
a
ti
o
n
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l
J
o
u
rn
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l
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f
P
o
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r
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e
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tro
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m (
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)
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1
1
,
V
o
l.
1
,
No
.
2
,
1
0
4
-
1
1
2
.
[9
]
C.
I.
Od
e
h
a
n
d
D.
B.
Nn
a
d
i
,
"
S
in
g
le
-
p
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se
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lev
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l
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y
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d
c
a
sc
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d
e
d
mu
l
ti
lev
e
l
in
v
e
rte
r
,
"
IET
Po
we
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tro
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ics
,
2
0
1
3
,
v
o
l.
6
,
4
6
8
-
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7
7
.
[1
0
]
B.
Dio
n
g
,
H.
S
e
p
a
h
v
a
n
d
,
a
n
d
K.
A
.
Co
rz
in
e
,
"
Ha
rm
o
n
ic
Disto
rtio
n
Op
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miz
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ti
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f
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sc
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rs
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v
ice
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lt
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ro
p
s
a
n
d
No
n
in
te
g
e
r
DC
Vo
lt
a
g
e
Ra
ti
o
s
,
"
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E
T
ra
n
sa
c
ti
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n
s
o
n
In
d
u
stria
l
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e
c
tro
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,
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0
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3
,
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o
l.
6
0
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3
1
0
6
-
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1
4
.
[1
1
]
A
.
Ca
ll
e
-
P
ra
d
o
,
S
.
A
lep
u
z
,
J.
B
o
rd
o
n
a
u
,
J.
Nic
o
las
-
A
p
ru
z
z
e
se
,
P
.
Co
rtes
,
a
n
d
J.
R
o
d
rig
u
e
z
,
"
M
o
d
e
l
Pre
d
ictive
Cu
rr
e
n
t
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n
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id
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n
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ted
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tra
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Cl
a
mp
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d
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o
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v
e
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to
M
e
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t
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o
w
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Vo
lt
a
g
e
Ri
d
e
-
T
h
r
o
u
g
h
Req
u
ire
me
n
ts
,
"
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T
ra
n
s
a
c
ti
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n
s o
n
In
d
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stri
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l
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lec
tro
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,
2
0
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5
,
v
o
l.
6
2
,
1
5
0
3
-
1
5
1
4
.
[1
2
]
V
a
h
i
d
Da
rg
a
h
i
;
A
ra
sh
Kh
o
sh
k
b
a
r
S
a
d
ig
h
;
Ke
it
h
Co
rz
in
e
,
“
En
h
a
n
c
e
d
d
o
u
b
le
fl
y
i
n
g
c
a
p
a
c
it
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mu
lt
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ll
p
o
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r
c
o
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v
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r co
n
tro
ll
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d
wit
h
a
n
e
w
s
wit
c
h
in
g
p
a
tt
e
rn
,
”
I
ET
P
o
we
r E
le
c
tro
n
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,
2
0
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5
,
v
o
l.
8
,
Iss
.
1
2
,
2
3
8
6
–
2
3
9
5
.
[1
3
]
M
.
Ha
ss
a
n
,
S
.
M
e
k
h
e
li
f
,
M
.
A
h
m
e
d
,
“
T
h
re
e
-
p
h
a
se
h
y
b
rid
mu
lt
il
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v
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l
in
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r
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h
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s
p
o
we
r
e
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tro
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ic
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o
m
p
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e
n
ts
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si
n
g
s
p
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c
to
r m
o
d
u
la
ti
o
n
”
,
IET
Po
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lec
tro
n
i
c
s
,
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4
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Vo
l.
7
,
Iss
.
5
,
1
2
5
6
–
1
2
6
5
.
[1
4
]
K.
Ke
e
rth
iv
a
sa
n
,
M
.
Na
ra
y
a
n
a
n
,
V
.
S
h
a
rm
il
a
De
v
e
a
n
d
J.
Je
ro
m
e
,
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Esti
ma
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l
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in
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se
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n
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n
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les
Us
i
n
g
Pa
t
ter
n
S
e
a
rc
h
M
e
th
o
d
”
,
In
ter
n
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ti
o
n
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l
Co
n
fer
e
n
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e
o
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Co
mp
u
ter
C
o
mm
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n
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n
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J.
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[1
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