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ties
.
2.
P
RO
P
O
SE
D
T
O
P
O
L
O
G
Y
2
.
1
.
Sy
mm
et
rica
l C
o
nfig
ura
t
io
n
I
n
s
y
m
m
etr
ical
co
n
f
i
g
u
r
at
io
n
,
m
ag
n
it
u
d
e
o
f
ea
ch
d
c
v
o
lta
g
e
s
o
u
r
ce
s
is
eq
u
al.
C
a
s
ca
d
ed
co
n
n
ec
tio
n
o
f
p
r
o
p
o
s
ed
ML
I
in
cr
ea
s
es
t
h
e
o
u
tp
u
t
v
o
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g
e
le
v
els.
T
h
e
t
o
tal
o
u
tp
u
t
v
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g
e
i
s
th
e
s
u
m
m
atio
n
o
f
i
n
d
iv
id
u
a
l
p
r
o
p
o
s
ed
ML
I
s
o
u
tp
u
t
v
o
lta
g
e.
P
r
o
p
o
s
ed
m
u
lti
lev
el
i
n
v
er
t
er
co
n
s
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t
s
o
f
f
o
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r
d
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v
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r
ce
s
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h
ic
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h
o
w
n
in
th
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F
ig
u
r
e
1
.
Ou
r
p
r
o
p
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ed
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y
ca
n
g
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er
ate
9
lev
els
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n
o
u
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t
v
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g
e.
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y
p
r
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p
er
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r
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d
o
f
f
s
w
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h
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r
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t
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n
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e
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.
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h
er
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r
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in
p
r
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p
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ed
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g
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r
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ased
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ca
n
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e
f
i
n
d
i
n
g
o
u
t b
y
u
s
in
g
M
=
4
n+
1
(
1
)
w
h
er
e
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n
u
m
b
er
o
f
o
u
tp
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t v
o
lta
g
e
lev
els
n
=
n
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m
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s
ca
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lo
ck
s
Fro
m
t
h
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ab
o
v
e
ex
p
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es
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io
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o
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g
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er
atin
g
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lev
el
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n
o
u
tp
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t
v
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t
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s
y
m
m
etr
ic
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s
ca
d
ed
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ee
d
ed
w
h
ic
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ar
e
s
h
o
w
n
i
n
F
i
g
u
r
e
1
.
V
d
c
V
d
c
S
a
S
b
S
c
S
d
S
e
S
f
V
d
c
V
d
c
S
a
1
S
b
1
S
c
1
S
d
1
S
e
1
S
f
1
L
O
A
D
+
-
V
0
Fig
u
r
e
1
.
P
r
o
p
o
s
ed
ML
I
to
p
o
l
o
g
y
i
n
S
y
m
m
etr
ical
co
n
f
i
g
u
r
at
io
n
T
h
e
o
u
tp
u
t
v
o
lta
g
e
w
av
e
f
o
r
m
co
n
s
is
t
s
o
f
n
in
e
lev
el
s
±
4
Vd
c,
±
3
Vd
c,
±
2
Vd
c,
±
Vd
c
an
d
0
.
T
h
e
s
w
itc
h
in
g
p
atter
n
f
o
r
th
e
p
r
o
p
o
s
ed
in
v
er
ter
in
s
y
m
m
etr
ical
c
o
n
f
i
g
u
r
atio
n
is
s
h
o
w
n
i
n
b
elo
w
T
ab
le
1
.
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
.
4
,
Dec
em
b
er
2
0
1
8
:
1616
–
1
6
2
3
1618
T
ab
le
1.
Sw
itch
in
g
s
tate
s
an
d
Ou
tp
u
t v
o
lta
g
es
f
o
r
S
y
m
m
etr
i
ca
l Co
n
f
ig
u
r
atio
n
2
.
2
.
Asy
mm
et
rica
l C
o
nfig
ura
t
io
n
I
n
th
i
s
co
n
f
i
g
u
r
atio
n
,
d
c
v
o
lta
g
e
s
o
u
r
ce
s
ar
e
d
i
f
f
er
i
n
g
in
t
h
e
ir
m
ag
n
it
u
d
es.
T
h
er
ef
o
r
e,
th
e
d
if
f
er
e
n
ce
in
th
e
d
c
v
o
ltag
e
s
o
u
r
ce
s
en
h
a
n
ce
s
th
e
o
u
tp
u
t
v
o
lta
g
e
lev
el
s
.
Du
e
to
in
cr
ea
s
e
o
f
th
e
v
o
ltag
e
th
e
o
u
tp
u
t
v
o
lta
g
e
lev
els
ar
e
i
n
cr
ea
s
e
f
r
o
m
9
to
1
3
.
I
n
th
e
s
e
m
o
d
e
s
i
x
p
o
s
iti
v
e
v
o
lta
g
es,
s
ix
n
e
g
ati
v
e
v
o
lta
g
es
a
n
d
ze
r
o
ca
n
b
e
p
r
o
d
u
ce
d
.
T
h
e
d
if
f
er
en
t
o
u
tp
u
t
v
o
ltag
e
le
v
els
ar
e
±
6
Vd
c,
±
5
Vd
c,
±
4
Vd
c,
±
3
Vd
c,
±
2
Vd
c,
±
Vd
c
an
d
0
an
d
th
e
co
r
r
esp
o
n
d
in
g
s
w
itc
h
i
n
g
s
t
ates a
r
e
s
h
o
w
n
in
T
ab
le
2
.
T
ab
le
2.
Sw
itch
in
g
p
atter
n
a
n
d
Ou
tp
u
t
v
o
ltag
e
s
f
o
r
A
s
y
m
m
etr
ical
C
o
n
f
i
g
u
r
atio
n
3.
CO
M
P
ARIS
O
N
O
F
P
RO
P
O
SE
D
M
L
I
T
O
P
O
L
O
G
Y
W
I
T
H
CO
NV
E
N
T
I
O
NAL
M
L
I
T
O
P
O
L
O
G
I
E
S
T
h
e
f
o
llo
w
i
n
g
T
ab
le
3
an
d
T
ab
le
4
illu
s
tr
ate
t
h
e
co
m
p
a
r
is
o
n
b
et
w
ee
n
e
x
i
s
ti
n
g
to
p
o
lo
g
ies
a
n
d
p
r
o
p
o
s
ed
to
p
o
l
o
g
y
in
s
y
m
m
etr
ical
an
d
as
y
m
m
etr
ical
co
n
f
i
g
u
r
atio
n
.
T
ab
le
3
.
C
o
m
p
ar
is
o
n
o
f
o
th
er
to
p
o
lo
g
ies
w
i
th
p
r
o
p
o
s
ed
to
p
o
lo
g
y
f
o
r
s
y
m
m
etr
ical
co
n
f
i
g
u
r
atio
n
Ty
p
e
o
f
M
L
I
N
o
o
f
M
a
i
n
S
w
i
t
c
h
e
s
N
o
o
f
D
i
o
d
e
s
N
o
o
f
D
C
B
u
s
C
a
p
a
c
i
t
o
r
s
D
i
o
d
e
C
l
a
me
d
M
L
I
16
16
8
F
l
y
i
n
g
C
a
p
a
c
i
t
o
r
M
L
I
16
16
8
C
a
sc
a
d
e
d
H
-
b
r
i
d
g
e
M
L
I
16
16
4
P
r
o
p
o
se
d
M
L
I
12
16
0
T
ab
le
4.
C
o
m
p
ar
is
o
n
o
f
o
th
er
to
p
o
lo
g
ies
w
i
th
p
r
o
p
o
s
ed
to
p
o
lo
g
y
f
o
r
a
s
y
m
m
etr
ical
co
n
f
i
g
u
r
atio
n
Ty
p
e
o
f
M
L
I
N
o
o
f
M
a
i
n
S
w
i
t
c
h
e
s
N
o
o
f
D
i
o
d
e
s
N
o
o
f
D
C
B
u
s
C
a
p
a
c
i
t
o
r
s
D
i
o
d
e
C
l
a
me
d
M
L
I
24
24
12
F
l
y
i
n
g
C
a
p
a
c
i
t
o
r
M
L
I
24
24
12
C
a
sc
a
d
e
d
H
-
b
r
i
d
g
e
M
L
I
24
24
12
P
r
o
p
o
se
d
M
L
I
12
16
0
Fro
m
T
ab
le
3
an
d
4
,
th
e
Pr
o
p
o
s
ed
I
n
v
er
ter
u
s
es
le
s
s
n
u
m
b
er
o
f
p
o
w
er
elec
tr
o
n
ic
co
m
p
o
n
en
ts
co
m
p
ar
ed
to
co
n
v
e
n
tio
n
a
l
M
L
I
to
p
o
lo
g
ies
an
d
h
e
n
ce
s
w
itc
h
in
g
lo
s
s
e
s
as
w
ell
as
co
s
t
f
o
r
i
m
p
le
m
e
n
ti
n
g
it
i
s
r
ed
u
ce
d
.
S
a
S
b
S
c
S
d
S
e
S
f
S
a
1
S
b
1
S
c
1
S
d
1
S
e
1
S
f
1
V
o
l
t
a
g
e
L
e
v
e
l
0
0
1
1
0
0
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1
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0
0
+
4
V
DC
0
0
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1
0
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+
3
V
DC
0
0
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+
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V
DC
0
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+V
DC
0
1
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4V
DC
1
0
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0
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0
1
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3V
DC
1
0
0
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1
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0
0
1
0
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2V
DC
0
1
0
0
0
1
0
1
0
0
1
0
-
V
DC
S
a
S
b
S
c
S
d
S
e
S
f
S
a
-
1
S
b
1
S
c
1
S
d
1
S
e
1
S
f
1
V
o
l
t
a
g
e
L
e
v
e
l
0
0
1
1
0
0
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1
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0
+
6
V
d
c
0
0
1
0
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1
1
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+
5
V
d
c
0
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1
0
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1
0
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1
+
4
V
d
c
0
0
1
1
0
0
0
0
0
0
1
1
+
3
V
d
c
0
0
0
1
1
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1
1
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+
2
V
d
c
0
0
0
1
1
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1
1
+
V
d
c
0
0
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1
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1
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0
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1
-
V
d
c
0
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1
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1
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2
V
d
c
1
0
0
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1
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1
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1
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3
V
d
c
0
1
0
0
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1
0
0
1
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-
4
V
d
c
0
1
0
0
1
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1
1
0
0
0
0
-
5
V
d
c
1
1
0
0
0
0
1
1
0
0
0
0
-
6
V
d
c
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
Gri
d
I
n
terco
n
n
ec
tio
n
o
f P
V
S
y
s
tem
Usi
n
g
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ymm
etri
c
a
n
d
A
s
ymm
etri
c
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LI
To
p
o
lo
g
y
(
V
S
P
r
a
s
a
d
a
r
a
o
K
)
1619
4.
SI
M
UL
I
NK
M
O
DE
L
L
I
NG
AND
RE
SUL
T
S
T
h
e
F
ig
u
r
e
3
d
ep
icts
t
h
e
M
AT
L
A
B
/
SIM
U
L
I
NK
d
iag
r
a
m
o
f
th
e
p
r
o
p
o
s
ed
5
lev
el
M
L
I
t
o
p
o
lo
g
y
.
I
t
u
s
e
s
s
i
x
s
w
itc
h
es
a
n
d
eig
h
t
d
i
o
d
es
to
g
et
f
iv
e
lev
el
o
u
tp
u
t
w
a
v
e
f
o
r
m
.
T
h
e
o
u
tp
u
t
v
o
lta
g
e
o
b
tain
ed
f
r
o
m
t
h
e
s
y
m
m
etr
ical
co
n
f
ig
u
r
atio
n
co
n
tai
n
s
f
iv
e
le
v
el
(
Fig
u
r
e
4
)
.
C
o
m
p
a
r
ed
to
ca
s
ca
d
e
H
-
b
r
id
g
e
ML
I
it
u
s
es
les
s
s
w
itc
h
es
an
d
h
e
n
ce
th
e
s
w
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h
in
g
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s
s
e
s
ar
e
r
ed
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ce
d
.
Fr
o
m
th
e
Fi
g
u
r
e
5
an
d
6
,
as
th
e
lev
el
o
f
th
e
i
n
v
er
te
r
in
cr
ea
s
es T
HD
co
n
ten
t r
ed
u
ce
s
.
Fig
u
r
e
3
.
MA
T
L
A
B
/ SI
MU
L
I
NK
d
iag
r
a
m
o
f
th
e
p
r
o
p
o
s
ed
5
lev
el
M
L
I
to
p
o
lo
g
y
Fig
u
r
e
4
.
O
u
tp
u
t
v
o
ltag
e
o
f
p
r
o
p
o
s
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1623
RE
F
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NC
E
S
[1
]
M
.
H
.
Ra
sh
i
d
,
“
P
o
w
e
r
El
e
c
tro
n
ics
:
c
ir
c
u
it
s,
De
v
ice
s an
d
A
p
p
li
c
a
ti
o
n
s
,
”
P
e
a
rso
n
E
d
u
c
a
ti
o
n
,
T
h
ird
E
d
it
io
n
,
2
0
0
4
.
[2
]
M
.
Ca
lais,
e
t
a
l.
,
“
In
v
e
rter
f
o
r
sin
g
lep
h
a
se
g
rid
c
o
n
n
e
c
ted
p
h
o
to
v
o
lt
a
ic
sy
ste
m
s
-
A
n
o
v
e
rv
ie
w
,
”
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c
.
P
o
we
r
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e
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tro
n
.
S
p
e
c
.
C
o
n
f
.
,
v
o
l.
4
,
p
p
.
1
9
9
5
-
2
0
0
0
,
2
0
0
2
.
[3
]
J.
S
.
L
a
i
a
n
d
F
.
Z.
P
e
n
g
,
“
M
u
lt
il
e
v
e
l
Co
n
v
e
rters
-
A
n
e
w
b
re
e
d
o
f
p
o
w
e
r
c
o
n
v
e
rters
,
”
Co
n
fer
e
n
c
e
Rec
o
rd
o
f
th
e
IEE
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-
lA
S
An
n
u
a
l
M
e
e
ti
n
g
,
p
p
.
2
3
4
S
-
2
3
5
6
,
1
9
9
5
.
[4
]
K.
Din
g
,
e
t
a
l.
,
“
A
n
a
l
y
sis,
o
f
a
n
a
s
y
m
m
e
tri
c
m
o
d
u
lati
o
n
m
e
th
o
d
s
f
o
r
c
a
sc
a
d
e
d
m
u
lt
il
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in
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IET
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o
we
r
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tro
n
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:
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(
1
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p
.
7
4
–
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5
,
2
0
1
2
.
[5
]
J.
Na
p
o
les
,
e
t
a
l
.
,
“
S
e
lec
ti
v
e
h
a
r
m
o
n
ic
m
it
ig
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ti
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n
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e
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h
n
o
n
e
q
u
a
l
d
c
li
n
k
v
o
lt
a
g
e
s,”
IEE
E
T
ra
n
s.
I
n
d
.
El
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c
t
ro
n
.
,
v
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ss
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e
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,
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.
1
9
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0
1
3
.
[6
]
N.
F
a
ro
k
h
n
ia,
e
t
a
l.
,
“
M
in
im
isa
ti
o
n
o
f
to
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h
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rm
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n
ic
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n
in
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c
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sc
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m
u
lt
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in
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y
re
g
u
latin
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o
f
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s,”
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.
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–
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4
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0
1
2
.
[7
]
S
.
M
e
k
h
il
e
f
,
e
t
a
l.
,
“
Dig
it
a
l
c
o
n
tro
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th
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se
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re
e
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sta
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y
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rid
m
u
lt
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e
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e
l
in
v
e
rter,”
IE
EE
T
ra
n
s.
In
d
.
In
fo
rm
a
t
.,
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l
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ss
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e
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(
2
)
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p
p
.
7
1
9
–
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2
7
,
2
0
1
3
.
[8
]
J.
Ew
a
n
c
h
u
k
a
n
d
J.
S
a
lm
o
n
,
“
T
h
re
e
-
li
m
b
c
o
u
p
le
in
d
u
c
t
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r
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p
e
r
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ti
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n
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o
r
p
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ra
ll
e
l
m
u
lt
i
-
lev
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th
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e
-
p
h
a
se
v
o
lt
a
g
e
so
u
rc
e
d
i
n
v
e
rters
,
”
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T
ra
n
s.
I
n
d
.
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c
tro
n
.
,
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l
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ss
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e
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)
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p
.
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9
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–
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8
,
2
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1
3
.
[9
]
E.
Ba
b
a
e
i,
e
t
a
l.
,
“
Ex
ten
d
e
d
m
u
lt
il
e
v
e
l
c
o
n
v
e
rters
:
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n
a
tt
e
m
p
t
to
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d
u
c
e
t
h
e
n
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m
b
e
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f
in
d
e
p
e
n
d
e
n
t
d
c
v
o
lt
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g
e
so
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rc
e
s in
c
a
sc
a
d
e
d
m
u
lt
il
e
v
e
l
c
o
n
v
e
rters
,
”
IET
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we
r E
lec
tro
n
.
,
v
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l
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ss
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:
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p
p
.
1
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.
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d
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ra
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.
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.
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ter
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ti
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p
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(
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N
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ter
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p
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1
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.
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