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3
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,
[
1
4
]
.
2.
DE
S
I
G
N
O
F
SYM
M
E
T
RI
CAL
M
UL
T
I
L
E
VE
L
I
NVE
RT
E
R
S
T
RUC
T
UR
E
WI
T
H
RE
DUC
E
D
NUM
B
E
R
SWI
T
CH
I
NG
D
E
VIC
E
S
Fig
u
r
e
1
s
h
o
w
s
t
h
e
s
y
m
m
et
r
ical
m
u
lti
lev
el
i
n
v
er
ter
s
tr
u
ctu
r
e
cir
cu
it
w
i
th
r
ed
u
ce
d
n
u
m
b
er
o
f
s
w
itc
h
in
g
d
ev
ice
s
.
W
ith
t
h
is
s
tr
u
ctu
r
e,
t
h
e
s
w
itc
h
i
n
g
d
ev
ices
ar
e
r
ed
u
ce
d
w
it
h
o
u
t
a
f
f
ec
ti
n
g
th
e
o
u
tp
u
t
v
o
ltag
e
lev
els
a
s
co
m
p
ar
ed
to
th
e
co
n
v
e
n
tio
n
al
s
tr
u
ct
u
r
e.
I
t
is
d
em
o
n
s
tr
ated
th
at
t
h
i
s
s
tr
u
ctu
r
e
co
m
p
r
is
e
s
o
f
t
w
o
ess
e
n
tial
p
ar
ts
,
i.e
.
,
DC
s
o
u
r
c
es,
H
-
b
r
id
g
e
s
tr
u
ct
u
r
e
f
o
r
cr
e
atin
g
p
o
s
iti
v
e
an
d
t
h
e
n
e
g
ati
v
e
o
u
tp
u
t
v
o
ltag
e
s
.
T
h
e
o
u
tp
u
t v
o
lta
g
e
lev
el
s
ca
n
b
e
in
cr
ea
s
e
as c
o
n
v
en
t
io
n
al
s
tr
u
ctu
r
e
as
w
e
ll.
Fig
u
r
e
1
.
T
h
e
Sy
m
m
etr
ical
Str
u
ctu
r
e
o
f
M
u
lt
ilev
e
l I
n
v
er
ter
T
h
e
lev
el
n
u
m
b
er
o
f
o
u
tp
u
t
v
o
ltag
e
is
d
eter
m
in
ed
b
y
r
ef
er
r
in
g
E
q
u
atio
n
(
1
)
.
Me
an
w
h
ile,
t
h
e
s
w
itc
h
in
g
d
e
v
ices
n
u
m
b
er
u
s
ed
in
th
e
s
tr
u
c
tu
r
e
i
s
d
eter
m
i
n
ed
b
y
r
e
f
er
r
in
g
E
q
u
atio
n
(
2
)
.
B
esid
es,
th
e
m
ax
i
m
u
m
an
d
m
i
n
i
m
u
m
v
al
u
es
o
f
th
e
g
e
n
er
ated
o
u
tp
u
t
v
o
ltag
e
ar
e
esti
m
ated
b
y
r
ef
er
r
i
n
g
E
q
u
atio
n
(
3
)
an
d
E
q
u
atio
n
(
4
)
.
N
level
= 2
k
+ 1
(
1
)
S
number
=
k
+ 4
(
2)
V
L_max
= k
V
dc
(
3
)
V
L_min
=
-
kV
dc
(
4
)
w
h
er
e
k
is
th
e
n
u
m
b
er
o
f
s
o
u
r
ce
.
3.
DE
S
I
G
N
O
F
ASYM
M
E
T
RI
CAL M
UL
T
I
L
E
VE
L
I
NV
E
RT
E
R
ST
RUCT
URE B
AS
E
D
Fig
u
r
e
2
s
h
o
w
s
t
w
o
ca
s
ca
d
ed
s
tr
u
ct
u
r
es
o
f
t
h
e
m
u
l
tile
v
el
i
n
v
er
ter
.
I
t
co
n
s
is
ts
o
f
eig
h
t
n
u
m
b
er
s
o
f
s
w
itc
h
in
g
d
ev
ices
a
n
d
th
e
o
u
t
p
u
t
v
o
ltag
e
le
v
el
ca
n
b
e
7
-
lev
el
an
d
to
9
-
lev
el
f
o
r
as
y
m
m
etr
ical
b
ase
d
s
tr
u
ctu
r
e.
T
h
e
n
u
m
b
er
o
f
s
w
i
tch
i
n
g
d
ev
ices
u
s
ed
i
n
t
h
e
s
tr
u
ct
u
r
e
ca
n
b
e
esti
m
ated
b
y
r
e
f
er
r
in
g
E
q
u
atio
n
(
5
)
.
Me
an
w
h
ile,
t
h
e
m
a
x
i
m
u
m
a
n
d
m
i
n
i
m
u
m
o
f
o
u
tp
u
t
v
o
lta
g
es
g
en
er
ated
ca
n
b
e
es
ti
m
ated
b
y
r
ef
er
r
in
g
E
q
u
at
io
n
(
6
)
an
d
E
q
u
atio
n
(
7
)
,
r
esp
ec
tiv
el
y
.
S
numb
er
= 4
k
(
5
)
V
L_max
= k
V
dc
+ V
dc1
(
6
)
V
L_min
=
-
kV
dc
-
V
dc1
(
7
)
S
1
S
2
S
3
V
dc
1
V
dc
2
V
dc
3
D
1
D
2
S
A
S
C
S
B
S
D
L
o
a
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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2
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Sci,
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1
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ly
201
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4
4
–
151
146
S
11
S
13
S
12
S
14
V
dc
1
S
21
S
23
S
22
S
24
V
dc
2
L
o
a
d
Fig
u
r
e
2
.
T
h
e
A
s
y
m
m
etr
ical
S
tr
u
ctu
r
e
o
f
M
u
lti
lev
el
I
n
v
er
ter
4.
E
XP
E
R
I
M
E
NT
A
L
RE
SUL
T
S
T
h
is
s
ec
tio
n
a
n
al
y
ze
s
t
h
e
r
esu
lts
f
r
o
m
s
i
m
u
latio
n
an
d
ex
p
er
i
m
en
t.
T
h
e
s
i
m
u
latio
n
a
n
d
ex
p
er
i
m
en
tal
r
esu
lt
s
ar
e
an
al
y
ze
d
to
co
n
f
ir
m
th
e
d
esi
g
n
ed
p
ar
a
m
eter
s
an
d
s
tr
u
ctu
r
es
o
f
t
h
e
s
y
m
m
etr
ic
al
an
d
as
y
m
m
etr
ica
l
s
tr
u
ct
u
r
es o
f
m
u
ltil
e
v
el
i
n
v
er
t
er
.
4
.
1
.
Co
nv
ent
io
na
l In
v
er
t
er
T
h
e
s
tr
u
ctu
r
e
u
s
ed
f
o
u
r
s
w
it
ch
es
an
d
t
h
e
o
u
tp
u
t
v
o
ltag
e
lev
el
f
o
r
th
i
s
s
tr
u
ctu
r
e
is
3
-
l
ev
el.
T
w
o
d
if
f
er
e
n
t
m
o
d
u
la
tio
n
tech
n
iq
u
es
ar
e
u
s
ed
in
th
e
ex
p
er
i
m
e
n
t,
i.e
.
,
m
o
d
if
ied
s
q
u
ar
e
p
u
ls
e
w
id
th
m
o
d
u
latio
n
(
MP
W
M)
an
d
s
in
u
s
o
id
al
p
u
l
s
e
w
id
t
h
m
o
d
u
latio
n
(
SP
W
M)
.
Fig
u
r
e
3
s
h
o
w
s
t
h
e
s
w
itc
h
in
g
p
atter
n
b
y
u
s
i
n
g
MP
W
M.
Fo
r
s
w
itc
h
i
n
g
p
atter
n
,
s
w
i
tch
e
s
S1
a
n
d
S4
u
s
ed
s
a
m
e
s
w
itc
h
in
g
p
atter
n
an
d
a
n
o
t
h
er
s
w
itc
h
e
s
S2
a
n
d
S3
w
it
h
1
8
0
o
f
p
h
ase
-
s
h
if
ted
an
d
eq
u
iv
ale
n
t
to
ti
m
e
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d
ela
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ed
o
f
1
0
m
s
.
T
h
e
s
w
itch
in
g
f
r
eq
u
en
c
y
i
s
5
0
Hz.
Fig
u
r
es
4
(
a)
an
d
4
(
b
)
s
h
o
w
a
g
o
o
d
ag
r
ee
m
en
t
b
et
w
ee
n
s
i
m
u
latio
n
a
n
d
ex
p
er
i
m
en
ta
l
r
esu
lt
s
.
Fro
m
t
h
es
e
r
esu
lt
s
,
th
e
d
esi
g
n
p
r
i
n
cip
le
is
co
n
f
ir
m
ed
f
o
r
th
e
co
n
v
e
n
tio
n
a
l in
v
er
ter
s
tr
u
ct
u
r
e
w
it
h
MP
W
M.
S
1
S
4
S
2
S
3
34
%
34
%
20
mS
28
V
28
V
10
ms
/
di
v
10
V
/
di
v
Fig
u
r
e
3
.
S
w
i
tch
i
n
g
P
atter
n
f
o
r
C
ascad
ed
I
n
v
er
ter
Stru
ct
u
r
e
b
y
U
s
i
n
g
MP
W
M
V
ol
t
a
ge
C
ur
r
e
nt
20
mS
120
V
90
mA
50
V
/
di
v
50
mA
/
d
i
v
4
ms
/
di
v
(
a)
E
x
p
er
im
e
n
t
20
mS
120
V
(
b
)
Sim
u
latio
n
Fig
u
r
e
4
.
Ou
tp
u
t
W
av
e
f
o
r
m
f
r
o
m
C
ascad
ed
Stru
c
tu
r
e
b
y
U
s
i
n
g
MP
W
M
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
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n
J
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S
ymm
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s
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r
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tr
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ctu
r
e
s
w
ith
R
ed
u
ce
d
N
u
mb
er
o
f .
.
.
(
M.
H.
Ya
tim)
147
Me
an
w
h
ile,
Fi
g
u
r
e
5
s
h
o
w
s
s
w
itc
h
i
n
g
p
atter
n
o
f
SP
W
M.
T
h
e
r
ef
er
e
n
ce
f
r
eq
u
en
c
y
i
s
5
0
Hz
an
d
t
h
e
ca
r
r
ier
f
r
eq
u
en
c
y
i
s
3
0
k
Hz.
T
h
e
SP
W
M
tech
n
iq
u
e
u
s
ed
is
p
h
ase
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
(
P
OD)
.
Fig
u
r
es
6
(
a)
an
d
6
(
b
)
s
h
o
w
th
e
o
u
tp
u
t
v
o
lt
ag
e
w
a
v
ef
o
r
m
s
o
f
t
h
e
ex
p
er
i
m
en
tal
a
n
d
s
i
m
u
latio
n
r
e
s
u
l
ts
,
r
esp
ec
tiv
el
y
.
B
o
th
r
esu
lt
s
s
h
o
w
a
g
o
o
d
ag
r
ee
m
en
t b
et
w
ee
n
ex
p
er
i
m
en
tal
a
n
d
s
i
m
u
latio
n
r
es
u
lt
s
.
S
1
S
2
S
4
S
3
20
V
/
d
i
v
2
.
5
ms
/
di
v
Fig
u
r
e
5
.
S
w
i
tch
i
n
g
P
atter
n
f
o
r
C
ascad
ed
I
n
v
er
ter
Stru
ct
u
r
e
b
y
U
s
i
n
g
SP
W
M
V
ol
t
a
ge
C
ur
r
e
nt
20
mS
120
V
91
mA
50
V
/
di
v
100
mA
/
di
v
4
ms
/
di
v
(
a)
E
x
p
er
im
e
n
t
20
mS
120
V
88
mA
(
b
)
Sim
u
latio
n
Fig
u
r
e
6
.
Ou
tp
u
t
W
av
e
f
o
r
m
f
r
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m
C
ascad
ed
Stru
c
tu
r
e
b
y
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s
i
n
g
SP
W
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4
.
2
.
Sy
mm
et
rica
l 7
-
lev
el
M
ultilev
el
I
nv
er
t
er
T
h
e
s
elec
ted
s
tr
u
ctu
r
e,
Fig
u
r
e
1
,
is
c
o
n
s
id
er
ed
in
th
e
s
y
m
m
etr
ica
l
7
-
lev
e
l
m
u
ltil
e
v
e
l
in
v
er
ter
s
tr
u
ct
u
r
e.
T
h
e
in
v
er
ter
s
tr
u
ctu
r
e
is
co
n
s
id
er
ed
f
o
r
t
w
o
m
o
d
u
latio
n
tech
n
iq
u
es,
i.e
.
,
MP
W
M
an
d
SP
W
M.
T
h
e
s
tr
u
ct
u
r
e
o
n
l
y
u
s
ed
s
e
v
e
n
s
witch
es
i
n
o
r
d
er
to
p
r
o
d
u
ce
7
-
L
e
v
el
o
f
th
e
o
u
tp
u
t
v
o
ltag
e.
Fig
u
r
e
7
s
h
o
w
s
t
h
e
s
w
itc
h
in
g
p
atter
n
i
n
MP
W
M.
S
w
itc
h
i
n
g
s
i
g
n
als
f
o
r
S1
,
S2
an
d
S3
u
s
e
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
o
f
1
0
0
Hz.
T
h
e
d
u
t
y
c
y
cle
f
o
r
S1
i
s
0
.
3
.
Me
a
n
w
h
ile,
t
h
e
d
u
t
y
c
y
cle
s
f
o
r
S
2
an
d
S3
is
0
.
1
5
,
r
esp
ec
tiv
el
y
.
Fo
r
th
e
s
w
itc
h
i
n
g
s
ig
n
al
s
S
A
,
SB
SC
a
n
d
SD,
th
e
s
w
itc
h
i
n
g
f
r
eq
u
e
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RE
F
E
R
E
NC
E
S
[1
]
A
.
B.
P
o
n
n
iran
,
e
t
a
l
.
,
“
M
i
n
im
u
m
F
l
y
in
g
Ca
p
a
c
it
o
r
f
o
r
N
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L
e
v
e
l
Ca
p
a
c
it
o
r
DC/DC
Bo
o
st
Co
n
v
e
rter,”
IEE
E
T
ra
n
s
.
In
d
.
Ap
p
l.
,
v
o
l
/i
ss
u
e
:
52
(
4
)
,
p
p
.
3
2
5
5
-
3
2
6
6
,
2
0
1
6
.
[2
]
J.
Ro
d
rig
u
e
z
,
e
t
a
l.
,
“
M
u
lt
il
e
v
e
l
in
v
e
rters
:
a
su
rv
e
y
o
f
to
p
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o
g
ies
,
c
o
n
tro
ls,
a
n
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a
p
p
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c
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ti
o
n
s,”
IE
EE
T
ra
n
s.
In
d
.
El
e
c
tro
n
.
,
v
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l/
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49
(
4
)
,
p
p
.
7
2
4
-
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3
8
,
2
0
0
2
.
[3
]
A
.
B.
P
o
n
n
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n
d
M
.
A
.
N.
B.
Ka
sira
n
,
“
P
a
ra
m
e
ters
d
e
sig
n
e
v
a
l
u
a
ti
o
n
in
3
-
lev
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l
f
l
y
in
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c
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p
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o
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”
in
2
0
1
7
IE
EE
S
y
m
p
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m
o
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Co
m
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ter
A
p
p
li
c
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ti
o
n
s &
In
d
u
stria
l
E
lec
tro
n
ics
(
IS
CAIE
)
,
p
p
.
1
9
5
-
1
9
9
,
2
0
1
7
.
[4
]
A
.
B
.
P
o
n
n
iran
,
e
t
a
l.
,
“
M
in
im
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ti
o
n
o
f
P
a
ss
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Co
m
p
o
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e
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ts
in
M
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lt
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-
lev
e
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F
ly
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Ca
p
a
c
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o
r
DC
-
DC
Co
n
v
e
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IEE
J
J
.
In
d
.
A
p
p
l
.
,
v
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l
/
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:
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1
)
,
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,
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0
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.
[5
]
J
.
S
.
L
a
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a
n
d
F
.
Z
.
P
e
n
g
,
“
M
u
lt
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a
n
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w
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re
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f
p
o
w
e
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,
”
IAS
’9
5
.
C
o
n
f
.
Rec
.
1
9
9
5
IEE
E
In
d
.
Ap
p
l.
C
o
n
f
.
T
h
irti
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th
IAS
An
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u
.
M
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.
,
v
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e
:
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(
3
)
,
p
p
.
2
3
4
8
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2
3
5
6
,
1
9
9
6
.
[6
]
S
.
G
h
o
sh
a
n
d
S
.
M
a
h
a
n
ty
,
“
S
in
g
le
P
h
a
se
M
u
lt
i
le
v
e
l
In
v
e
rters
w
it
h
S
im
p
le
Co
n
tro
l
S
trate
g
y
Us
in
g
M
AT
LAB,
”
In
t.
Res
.
J
.
En
g
.
T
e
c
h
n
o
l
.
,
v
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l
/
issu
e
:
2
(
7
)
.
[7
]
A
.
P
ra
y
a
g
a
n
d
S
.
Bo
d
k
h
e
,
“
No
v
e
l
Ba
sic
Blo
c
k
o
f
M
u
lt
il
e
v
e
l
In
v
e
rt
e
r
Us
in
g
Re
d
u
c
e
d
Nu
m
b
e
r
o
f
On
-
S
tate
S
w
it
c
h
e
s
a
n
d
Ca
sc
a
d
e
d
Circu
it
T
o
p
o
lo
g
y
,
”
v
o
l.
2
0
1
7
,
2
0
1
7
.
[8
]
M
.
M
a
rc
h
e
so
n
i
,
e
t
a
l
.
,
“
A
n
o
n
c
o
n
v
e
n
ti
o
n
a
l
p
o
w
e
r
c
o
n
v
e
rter
f
o
r
p
las
m
a
sta
b
il
iza
ti
o
n
,
”
in
P
o
we
r
El
e
c
tro
n
ics
S
p
e
c
ia
li
sts C
o
n
fer
e
n
c
e
,
1
9
8
8
.
PE
S
C
’8
8
Rec
o
rd
,
1
9
t
h
An
n
u
a
l
I
EE
E
,
v
o
l.
1
,
p
p
.
1
2
2
-
1
2
9
,
1
9
8
8
.
[9
]
S
.
N.
Ra
o
,
e
t
a
l.
,
“
Im
p
le
m
e
n
tatio
n
o
f
Ca
sc
a
d
e
d
b
a
se
d
Re
v
e
rsin
g
Vo
lt
a
g
e
M
u
lt
il
e
v
e
l
In
v
e
rter
u
sin
g
M
u
lt
i
Ca
rrier
M
o
d
u
latio
n
S
trate
g
ies
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
i
c
s
a
n
d
Dr
ive
S
y
ste
m
(
IJ
PE
DS
)
,
v
o
l
/i
ss
u
e
:
9
(
1
)
,
p
p
.
2
2
0
-
2
3
0
,
2
0
1
8
.
[1
0
]
S
.
M
a
lath
y
,
“
A
Ne
w
S
in
g
le
P
h
a
se
M
u
lt
il
e
v
e
l
In
v
e
rter
T
o
p
o
lo
g
y
w
i
th
Re
d
u
c
e
d
Nu
m
b
e
r
o
f
S
w
it
c
h
e
s,”
In
t.
Co
n
f
.
El
e
c
tr.
En
e
rg
y
S
y
st
.
,
v
o
l.
3
,
p
p
.
1
-
6
,
2
0
1
6
.
[1
1
]
S
.
N.
Ra
o
,
e
t
a
l
.
,
“
In
teg
ra
ti
o
n
o
f
Re
v
e
rsin
g
V
o
lt
a
g
e
M
u
lt
i
lev
e
l
In
v
e
rter
T
o
p
o
lo
g
y
w
it
h
Hig
h
V
o
l
tag
e
G
a
in
Bo
o
st
Co
n
v
e
rter
f
o
r
Distrib
u
ted
G
e
n
e
ra
ti
o
n
,
”
I
n
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
I
J
PE
DS
)
,
v
o
l
/i
ss
u
e
:
9
(
1
)
,
p
p
.
2
1
0
-
2
1
9
,
2
0
1
8
.
[1
2
]
O.
L
.
Jim
e
n
e
z
,
e
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