Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 75
2
~
76
1
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p75
2-7
61
7
52
Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
A new multilevel DC-AC conver
ter topology with
reduced
switch
using multicarrier sinu
so
idal pu
lse
w
i
d
t
h
m
o
dulation
R.
Pal
a
ni
sa
m
y
, S.
Vi
dy
as
a
g
a
r,
V.
K
a
ly
an
asun
dar
a
m
,
D
.
K
a
r
t
hi
ke
y
a
n
,
K
.
Se
lv
ak
um
ar
,
D
.
S
e
lv
abha
rat
h
i,
K.
Vija
ya
k
u
ma
r
De
p
a
rtm
e
nt
of
ele
c
t
ri
c
a
l a
n
d e
l
ec
tro
n
i
c
s
e
ngin
e
e
r
ing
,
SRM
In
st
it
u
t
e
of
Sci
e
nc
e a
n
d T
e
c
h
no
lo
gy,
In
d
i
a
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
Se
p 9
,
20
19
Re
vise
d N
o
v
8
,
20
19
A
c
ce
p
t
ed
Jan
3,
202
0
M
u
ltilev
el
con
v
e
rters
h
a
v
e
a sig
n
i
fic
a
nt
ro
le
in
p
o
w
e
r pro
ces
sing
con
t
rol
in
th
e
p
o
w
e
r
s
y
ste
m
, which h
a
s
s
o
me in
h
e
rent
f
e
a
t
ures like r
e
du
c
e
d
harmon
ics
,
high
p
o
wer
&
med
i
um
vo
lt
age
,
redu
ced
v
o
lta
ge
stress.
In
th
is
p
r
op
osed
pap
e
r, a
no
vel
multi
l
ev
e
l
inv
e
r
t
er
with
red
u
c
e
d
numb
e
r
o
f
sw
itches
an
d
with
ou
t
p
a
ss
iv
e
comp
on
e
n
ts
.
Th
e prop
os
ed inv
e
r
t
er
g
e
n
e
rat
e
s
1
5
leve
l
o
u
t
put
vo
ltag
e w
ith
sui
t
ab
le
s
w
itch
ing
p
u
lse g
e
nera
tion
us
in
g
multic
a
rri
e
r
sinu
soidal
p
u
l
s
e
wid
t
h
m
o
d
u
l
a
ti
on (MSPW
M
)
a
n
d
d
i
ffere
nt
l
e
v
e
l
of v
o
l
t
a
g
e
s
a
r
e
o
b
t
a
ine
d
wit
h
v
a
ria
t
io
n
o
f
m
o
d
u
l
a
t
io
n
i
nde
x. Al
so c
o
u
p
le
d in
duc
to
r is use
d
t
o
min
i
m
i
ze
th
e h
a
rm
o
n
ic
co
nten
t
and
smo
o
thing
ou
tp
ut
curren
t
.
Th
e s
c
h
e
me
wh
ich
in
clu
d
e
s
differen
t
r
a
ng
e
of un
equ
a
l
v
o
lta
ge so
urc
e
s.
As
a resul
t
,
th
e
pro
p
o
s
ed
sy
ste
m
it
redu
ces
s
w
i
tching
contro
l
comp
lexi
ty
an
d
th
er
e is
no
vo
ltag
e
b
a
lan
c
ing
p
r
ob
le
m.
T
h
is paper
eluc
i
d
ates the
oper
a
tin
g
mo
des
,
vo
ltag
e
s
t
res
s
minim
i
satio
n
an
d harmon
ic red
u
ctio
n are d
i
s
c
us
sed.
Th
e
re
sul
t
s of t
h
e
p
r
op
ose
d
m
u
lti
le
v
e
l d
c
-a
c c
onv
e
r
te
r a
r
e
ve
rifi
e
d
u
s
i
n
g
mat
l
ab/si
m
u
l
ink
.
The
si
mulati
on
& hard
wa
re
re
su
l
t
s o
f
t
h
e
pro
p
o
se
d
in
ve
rte
r
were
v
e
rif
i
ed
u
s
i
n
g
m
a
tl
ab
s
i
mu
li
nk
and
ds
P
I
C
co
n
t
ro
ller
r
e
spec
tiv
e
ly
, w
h
ich
was
analys
ed
w
ith d
i
ff
erent
vo
lta
ge l
e
vel
and
diff
erent
modu
latio
n
ind
e
x
.
Ke
yw
ords:
Co
up
le
d i
n
d
u
c
to
r
(
C
I)
D
C
-A
C c
onv
erte
r
Mult
i
c
a
r
ri
er si
n
u
s
o
i
d
al
p
u
l
s
e
w
i
d
t
h mo
du
la
tio
n
(M
S
P
WM
)
M
u
l
tile
v
e
l inv
e
rt
er
(
M
LI)
To
ta
l h
a
rmon
ic
d
i
s
t
or
tio
n
(TH
D
)
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
D.K
a
rt
hi
ke
yan
,
Asst.
p
rof, De
p
a
rt
ment
of el
ec
tri
cal
a
n
d
e
l
e
c
t
r
o
n
i
c
s
e
ngi
ne
eri
ng,
SR
M In
st
i
t
ut
e of Sc
ie
nce
an
d T
ech
nol
og
y,
Kat
t
a
nk
ul
at
h
u
r, C
h
e
n
nai
,
In
di
a.
Emai
l:
kart
hi
p
n
c
l
@
g
ma
il
.co
m
1.
IN
TR
O
DUCTION
As
a o
u
t
co
me o
f
h
i
g
h
te
c
hnolo
g
i
es gr
ow
th,
t
h
e p
o
w
e
r
re
qu
ir
em
e
n
t
and
q
u
a
l
i
ty
of
po
wer
a
r
e
b
e
tt
er
t
h
an e
a
r
l
i
e
r. B
eca
use
of
e
vol
u
t
i
on i
n
p
o
w
er
semi
co
nd
uct
o
r de
v
i
c
e
s an
d
p
o
w
e
r c
o
n
v
ers
i
on met
h
o
d
s
[1]. The
scheme
whi
c
h
is used
t
o
tr
ansfe
r
DC
so
urce t
o
AC
s
o
u
r
c
e
is ca
ll
ed i
n
v
e
rt
er
. T
h
e
l
e
ve
l
of t
h
e
i
nve
rte
r
in
c
r
ea
se
s to st
a
b
ilis
e th
e
v
o
lt
a
g
e
a
nd
r
e
du
ces r
i
p
p
l
e c
o
n
t
e
n
t
[
2
]
.
G
e
n
e
r
a
lly
mu
lti
l
e
v
el
i
n
v
e
r
t
e
r
s
ar
e
u
s
e
d
fo
r
hi
gh
p
o
w
e
r
m
e
d
i
um
v
o
l
t
a
g
e
a
ppli
c
a
t
i
o
n
s
,
b
y
c
o
nnec
t
i
n
g
serie
s
of p
o
w
e
r swi
t
c
h
es
wi
t
h
l
o
we
r vol
t
a
ge
dc
so
ur
c
e
s
to
g
e
ne
ra
te
sta
i
r
c
a
s
e
o
u
t
p
u
t
vo
lt
ag
e
.
Mu
l
tile
v
e
l in
ve
rt
er
ac
ts a
s
inte
r
m
ed
iat
e
d
e
vic
e
,
w
h
i
c
h
t
r
a
n
smi
t
po
we
r t
o
el
e
c
t
r
i
cal
unit
s
l
i
ke
gri
d
s
y
ste
m
,
UP
S, F
A
CTS
de
vi
c
e
s,
el
ec
tri
cal
dri
v
e
s
a
n
d
ot
he
rs [
3
].
A
m
on
g
vari
o
u
s
mul
t
i
l
e
vel
i
n
verte
r
t
o
pol
ogi
es l
i
k
e n
e
utral
p
o
int
c
l
a
m
pe
d, c
a
p
ac
it
o
r
c
l
a
m
pe
d a
n
d
ca
sc
ade
d
H
-
b
r
i
dge
, w
h
i
c
h a
r
e
most
ly
pre
p
a
r
ed st
an
dar
d
t
opol
ogi
es
[4
, 5
]
. The
u
n
e
qua
l
volt
a
ge
bal
a
nc
ing i
n
th
e
D
C
link
c
a
p
a
c
ito
rs
lea
d
t
o
in
cre
a
s
e
o
f
cla
m
p
i
ng
d
i
od
es a
s
th
e
vo
l
t
ag
e l
e
v
e
l in
cr
ease
s
,
wh
ic
h is l
i
mit
a
t
i
o
n
of
ne
ut
ra
l cl
a
m
pe
d i
n
ve
rt
e
r
[6
]. A
nd i
n
fl
yin
g
ca
paci
t
o
r inve
rt
er,
capa
c
i
t
ors
a
c
t
as cl
ampi
ng
di
o
d
es
an
d it
bec
o
me
mo
re
com
p
l
e
x
d
u
e
nu
mbe
r
of
ca
p
a
ci
t
o
r a
n
d
t
o
t
a
l
harmo
n
i
c
di
st
ort
i
o
n
i
n
c
r
e
a
s
e
ba
se
d
o
n
le
vel
o
f
i
nve
rt
er.
In
ca
scade
d
H
-
bri
d
ge i
n
vert
e
r
, t
h
e ut
il
i
s
at
ion n
u
m
b
er o
f
dc
sou
r
ce i
n
c
r
ease
s
, d
u
e t
o
tha
t
vol
t
a
ge
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
A
n
e
w mu
ltil
ev
e
l
D
C
-AC
con
vert
e
r
to
po
l
o
g
y
wi
th
redu
c
e
d
swit
ch
u
s
ing
multi
c
a
r
r
i
e
r
…
(
R
.
Pa
lan
i
s
a
my
)
7
53
bal
a
nc
in
g
pro
b
l
em, u
n
e
q
ua
l
s
w
i
t
c
hi
n
g
,
v
o
l
t
a
g
e st
ress
an
d re
du
nda
nc
y
p
h
a
s
e v
o
l
t
a
ge i
n
c
r
e
a
ses [7]. To
reduc
e
t
h
e
T
H
D of t
h
e ab
o
v
e c
o
nve
nt
i
o
na
l
m
u
lt
i
l
evel
in
ve
rt
ers, e
i
t
h
er s
w
i
t
c
h
in
g
fre
q
ue
ncy
of t
h
e s
y
ste
m
.
B
u
t
t
h
e
sy
st
em ou
tcome
le
a
d
s to in
cre
a
s
e
sw
itc
h
in
g
d
e
v
i
c
e
s, c
ond
uc
ti
o
n
l
o
ss a
n
d
mi
ni
mi
se
rel
i
ab
i
l
i
t
y
of
t
h
e
s
y
st
em [8].
To
o
v
erc
o
me
t
h
e
a
b
o
v
e
-
me
nti
one
d
l
i
mi
ta
t
i
ons,
t
h
e
rese
arc
h
m
o
ved
t
o
wa
rds
t
o
ge
nera
te
mul
t
i
l
e
vel
o
u
t
p
u
t
vo
l
t
a
g
e wi
th
r
e
du
ced
nu
mb
e
r
of
sw
itc
h
es
. Th
e m
a
jo
r
ob
je
ct
iv
e
o
f
wo
rk
is
to
in
cr
e
a
se
t
h
e vo
lta
g
e
l
e
v
e
l
wi
th a s
m
a
l
l
e
r nu
mbe
r
of po
w
e
r se
mi
c
ond
uc
tor swi
t
c
hes
[9].
In mul
t
i
l
e
vel
i
nve
rt
er, t
h
e
rat
i
o o
f
out
put
v
o
l
ta
ge
le
v
e
ls
and
re
qu
ir
ed
p
o
w
e
r sw
it
ch
e
s
i
s
terme
d
as S
L
R
(sw
i
tc
h
lev
e
l ra
tio
)
,
wh
ic
h
i
s
u
s
ed
to
d
e
sign
th
e
mini
mu
m
sw
it
che
d
ML
I. Th
e
S
L
R
deci
de
s
t
h
e
n
u
m
be
r of s
w
it
c
h
e
s
us
ed, co
st
of th
e
sy
st
e
m
a
n
d out
put
vol
ta
ge
l
e
vel
s
[10
]
. Cost
o
f
s
y
ste
m
de
pe
nds,
t
h
e
usage
nu
mbe
r
o
f
swi
t
c
he
s an
d
passi
ve
e
l
e
m
ent
s
l
i
k
e
i
n
d
u
ct
o
r
& la
rg
e cap
a
c
i
t
o
r
s
[1
1,
1
2
]
.
N
u
mer
o
us
m
o
dula
t
i
o
n
st
ra
t
e
gi
es w
e
re
de
v
e
lope
d
t
o
co
nt
rol
c
o
n
v
e
r
t
e
r
p
o
we
r
swi
t
c
hes.
I
n
t
h
at
, t
h
e
con
v
e
r
te
r wi
t
h
hi
g
h
fre
q
ue
nc
y P
W
M met
h
o
d
s li
ke
car
ri
er-
b
ase
d
m
o
d
u
l
a
t
i
on, t
r
ape
z
o
i
d
a
l
met
h
o
d
, si
nu
soi
d
a
l
PW
M
,
s
p
ace
vect
o
r
mo
d
u
l
a
t
i
on
a
n
d mul
t
ic
arrie
r
base
d
PWM use
d
[1
3-
1
5
]. Mo
re
ove
r, se
l
ect
i
v
e
&
act
i
v
e
harmo
n
i
c
el
im
i
n
at
i
o
n
nea
r
est
ve
ct
o
r
c
ont
ro
l
me
th
od
an
d s
ync
h
r
o
nous
o
p
t
i
mal
P
W
M a
r
e
use
d
fo
r c
o
n
v
e
r
t
e
r
wi
th l
o
w freq
u
e
nc
y
P
W
M t
e
c
hni
que
s [16
,
1
7
]
.
Re
d
u
ce
d
s
w
i
t
c
hes
MLIs are p
r
e
domi
n
a
n
t
l
y u
s
ed
ne
are
s
t
st
at
e
cont
rol
a
n
d m
u
lt
i
c
a
rri
er ba
se
d
SP
WM
sc
hem
e
s [
18-
20
].
In t
h
is
pro
p
o
s
e
d
w
o
rk,
syst
e
m
ge
ne
rat
e
s
15
l
e
vel
o
u
t
p
ut
vol
ta
ge
wi
t
h
re
duce
d
nu
mbe
r
swi
t
c
hes
.
It
pro
v
i
d
es
be
tt
er
fe
at
u
r
es
co
mpa
r
e
c
o
n
v
e
n
t
i
o
n
a
l
sche
me
s
l
i
k
e
mini
mise
d
T
H
D, l
o
w v
o
l
t
a
g
e st
re
ss,
c
o
nt
rol
l
e
d
out
put
c
u
rre
nt
a
nd re
duce
s
co
st
o
f
t
h
e s
y
ste
m
. P
o
we
r se
mi
c
o
n
d
u
c
t
o
r
s
w
i
t
ches
used
in t
h
is prop
ose
d
sy
st
em i
s
cont
rol
l
e
d
by
mult
i
c
a
rri
er
ba
se
d
si
n
u
s
o
ida
l
pul
se
w
i
dt
h mod
u
l
a
t
i
on
,
whi
c
h
a
v
oi
ds t
h
e
sho
o
t
th
ro
u
gh
p
r
o
b
l
e
m.
In t
h
at
sec
t
i
o
n
-
2 de
al
s ab
o
u
t
mode
s
of
o
p
er
at
ion
of
pr
o
p
o
s
ed sc
he
me
, se
c
t
ion-
3 e
x
pl
ai
ns a
b
o
u
t
mul
t
i
c
a
rri
e
r
S
P
WM
me
thod
a
n
d se
ct
ion
-
4
disc
us
s sim
u
lation
r
e
sults.
2.
POW
E
R S
T
AG
E
2.1 Ci
rcu
i
t
C
o
n
f
i
g
ur
ati
o
n
Fig
u
r
e
1
s
hows th
e
pr
opo
sed
n
o
v
e
l
topo
l
ogy
fo
r
15
l
e
v
e
ls
in
v
e
rt
er
. It
c
o
n
s
ist
s
of
thr
e
e
d
c
so
ur
ce
v
o
l
t
a
g
e
s ar
e
10V
, 20V
& 40V.
Th
e
M
O
SF
ET
p
o
w
e
r sw
it
ch
e
s
S1
,
S
2
, S
3
, S4
, S5 &
S
6
co
nn
e
c
t
e
d
d
i
re
ctly
t
o
dc sou
r
ces, w
h
i
c
h deci
de t
h
e l
e
vel
o
u
t
p
ut v
o
lt
a
g
e
f
r
om
t
h
e pro
pose
d
sc
he
me
. The
n
swi
t
c
he
s S
7
, S
8
, S9
&
S
1
0
p
e
r
f
o
r
ming
a V
S
I
b
r
i
d
ge
ci
rcu
i
t
,
w
h
ich
d
e
cid
e
s
t
h
e
po
s
itiv
e
and
n
e
g
a
ti
v
e
r
a
n
g
e
o
f
ou
t
p
u
t
vo
lt
ag
e
le
v
e
l
s
wi
th R
l
o
a
d
i
s
con
n
ec
te
d
a
c
ro
ss b
r
i
d
ge
net
w
ork. The
p
r
o
p
o
s
e
d
s
y
st
em
ge
n
e
ra
te
s
1
5
l
e
vel
out
put
v
o
lt
a
g
e
wi
th
su
i
t
a
b
le g
a
te
pu
lse
g
e
n
e
r
a
tion
.
N
u
mb
er
sw
i
t
c
h
es
u
s
ed
in
th
is pr
opo
sed
me
th
od
d
e
c
i
d
e
d
by
SLR
ra
tio
, wh
ic
h
cont
ai
n
s
tot
a
l
l
y
1
0
po
wer s
w
i
t
ches.
Do
es
n’t
n
e
e
d
of a
n
y ad
di
t
i
ona
l c
onve
rt
er
l
i
ke b
oost
c
o
n
v
e
r
t
e
r or a
n
y
re
so
na
nt co
n
v
e
r
te
r
t
o
bo
ost
vo
l
t
a
ge o
r
to
bal
a
nce
t
h
e
v
o
lt
a
g
e
.
F
i
gu
re
1. Ci
rcu
i
t
di
agra
m fo
r 15
-l
eve
l
i
nve
rt
er wi
t
h
re
d
u
ce
d sw
it
che
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
7
5
2
–
761
75
4
2.2. Mo
d
e
s o
f
O
p
e
r
a
t
i
o
n
The
prop
ose
d
syst
em ge
ne
ra
t
e
s
1
5
l
e
ve
l o
u
t
put
vol
t
a
g
e
s
(
+V
dc
, +
6
/
7
V
dc
, +5
/7
V
dc
, +
4
/
7
V
dc
, +
3
/
7
V
dc
, +2/
7
V
dc
, +1
/7 V
dc
, 0,
-
1
/
7
V
dc
, -
2
/7
V
dc
, -3/7
V
dc
, -4/
7
V
dc
, -5/7 V
dc
, -
6
/
7
V
dc
,
-V
dc
) ar
e e
x
p
l
a
i
n
e
d
as foll
ows,
1)
T
o
obt
ai
n
o
u
t
p
ut
v
o
l
t
age
of
V
0
= +
1
/7
V
dc
,
s
w
i
t
c
hes S
2
,
S
3
& S
5
kept
O
N
t
o
get
1/
7
th
vo
l
t
a
g
e fr
om th
e
p
o
wer
c
i
r
c
u
it
a
n
d
sw
itc
h
e
s S7
& S10
ar
e turn
e
d
O
N
t
o
g
e
t
p
o
s
it
iv
e le
ve
l.
F
i
g
u
r
e
2(
a) show
s t
h
e
c
u
rr
e
n
t
fl
ow
pat
h
fo
r
t
h
i
s
m
o
de a
n
d
Ta
ble
1 sho
w
s
vari
ous
swi
t
c
h
i
ng co
mbi
n
at
io
ns
fo
r 15
l
e
vel
out
put
v
o
l
t
a
g
e.
2)
T
o
a
c
q
u
i
r
e
out
put
v
o
l
t
a
ge
of V
0
= +2
/7
V
dc
,
sw
it
c
h
e
s
S
1
, S
4
&
S
5
ke
pt
ON
t
o
fi
n
d
2/
7
th
vo
lt
ag
e from
t
h
e
p
o
we
r c
i
rc
ui
t
a
n
d
fr
o
m
bri
dge
ci
rc
ui
t
swi
t
c
h
es
S
7
&
S
10
a
r
e
tu
rne
d
O
N
t
o
g
e
t
p
o
si
ti
ve
le
vel
.
F
i
gu
re
2(
b
)
s
h
ows
the
c
u
rre
n
t
fl
o
w
pat
h
fo
r
thi
s
m
ode
.
3)
To
at
ta
in
ou
tp
u
t
vo
lt
ag
e
of
V
0
= +
3
/
7
V
dc
, s
w
it
c
h
e
s
S
2
, S
4
& S5
ke
pt
O
N
to ge
t 3/
7
th
v
o
l
t
a
ge fr
om t
h
e
po
w
e
r
c
i
rc
ui
t
and
f
r
o
m
bri
d
ge
c
i
rc
ui
t
s
w
it
c
h
es S
7
& S
1
0
a
r
e tu
r
n
ed
O
N
to
get
p
o
sit
i
ve le
vel
.
F
i
gur
e
2(c
)
s
h
ows
t
h
e
curre
n
t
fl
o
w
pa
th for t
h
is
mo
d
e
.
4)
T
o
ac
hi
eve
o
u
t
put
v
o
l
t
a
g
e of
V
0
= +
4
/
7
V
dc
,
swi
t
c
h
es
S
1
, S3 &
S
6
ke
pt
ON
t
o
get
4/
7
th
vo
l
t
ag
e
f
r
o
m
th
e
pow
er c
i
r
c
u
i
t a
n
d
f
r
o
m
br
idg
e
ci
rcu
i
t
sw
itc
h
e
s
S7
&
S1
0
a
r
e
turn
e
d
ON
to ge
t posi
tiv
e
ou
tp
u
t
l
e
vel
.
Fi
g
u
r
e
2(d) sho
w
s t
h
e
c
u
rre
n
t
fl
o
w
pa
t
h
fo
r thi
s
m
ode
.
5)
T
o
ac
co
mpli
s
h
o
u
t
p
ut
v
o
l
t
a
g
e o
f
V
0
= +5
/
7
V
dc
,
s
w
i
t
c
hes
S2,
S
3
&
S
6
k
e
pt
ON
t
o
ge
t
5/
7
th
vo
lt
ag
e
from
t
h
e
p
o
we
r
c
i
rcui
t a
nd
from
bri
d
ge
c
i
rc
ui
t
swi
t
ches S
7
& S
10 a
r
e tu
rne
d
O
N
t
o
ge
t
posi
t
i
v
e
o
u
t
put
l
e
vel
.
Fi
g
u
r
e
2(e)
s
h
o
w
s
t
h
e c
u
rrent
flo
w
pat
h
fo
r
t
h
i
s
m
o
de
.
6)
T
o
re
al
i
ze
o
u
t
p
ut
volt
a
ge
o
f
V
0
= +6
/
7
V
dc
, s
w
i
t
c
hes
S1
, S
4
&
S
6
ke
pt
O
N
to
get
6/7
th
vo
l
t
a
g
e fro
m
t
h
e
po
w
e
r c
i
rcui
t
and
from
bri
d
ge c
i
rc
ui
t
swi
t
c
h
es S
7
& S
1
0
are
t
u
rned
O
N
t
o
get
po
si
t
i
ve
o
u
t
put
l
e
vel
.
F
i
gu
re
2(
f)
s
h
o
w
s
t
h
e c
u
r
r
e
n
t
fl
o
w
pa
t
h
fo
r
t
h
is
m
o
de
.
7)
T
o
achi
e
ve
o
u
t
p
ut
vol
t
a
ge
of V
0
= +
V
dc
, sw
i
t
c
h
es S
2
,
S
4
& S6
ke
pt
ON
t
o
get
V
dc
v
o
lt
a
g
e
f
r
o
m
th
e
po
w
e
r ci
rc
ui
t a
nd f
r
o
m
bri
dge
ci
rc
ui
t
swi
t
c
h
es S
7
& S
1
0 are
t
u
rne
d
ON t
o
get
ma
xi
mu
m
posit
i
v
e
out
put
l
e
ve
l.
F
i
gu
re
2(
g
)
s
h
o
w
s
the
c
u
r
r
e
n
t
fl
ow
pat
h
fo
r t
h
i
s
m
ode
.
Tabl
e.
1.
Swi
t
c
hi
n
g
C
o
mbi
n
at
i
ons
o
f
P
r
op
os
ed
S
y
st
em
for
15
-Le
v
el
O
u
t
p
ut
V
o
l
t
a
ge
L
e
ve
l
Out
p
u
t
voltage
Sw
itc
hes O
N
1 +
V
dc
S2
, S4
, S
6
,
S
7
, S1
0
2 +6/7
V
dc
S1
, S4
,
S
6
, S
7
,S1
0
3 +5/7
V
dc
S2
, S3
, S
6
,
S
7
, S1
0
4 +4/7
V
dc
S1
, S3
, S
6
,
S
7
, S1
0
5 +3/7
V
dc
S2
, S4
, S
5
,
S
7
, S1
0
6 +2/7
V
dc
S1
, S4
, S
5
,
S
7
, S1
0
7 +1/7
V
dc
S2
, S3
, S
5
,
S
7
, S1
0
8 0
S7,
S9
9 -1/7
V
dc
S2
, S3
,
S
5
, S
8
,
S9
10
-2/7
V
dc
S1
, S4
,
S
5
, S
8
,
S9
11
-3/7
V
dc
S2
, S4
,
S
5
, S
8
,
S9
12
-4/7
V
dc
S1
, S3
,
S
6
, S
8
,
S9
13
-5/7
V
dc
S2
, S3
,
S
6
, S
8
,
S9
14
-6/7
V
dc
S1
, S4
,
S
6
, S
8
,
S9
15
-
V
dc
S2
, S4
,
S
6
, S
8
,
S9
8)
T
o
obt
ai
n
o
u
tp
ut
v
o
l
t
a
g
e
of
V0 =
0, al
l
swi
t
che
s
a
r
e
ke
pt OF
F t
o
get
0 vol
t
a
ge
f
r
o
m
th
e
po
w
e
r ci
rc
ui
t
a
nd from bri
d
ge ci
rc
ui
t swi
t
c
h
es S
7
& S
9
(o
r) S
8
& S
1
0 are tu
r
n
ed
O
N
to get
ze
ro out
put
vol
t
a
ge
l
e
vel
.
Fi
g
u
r
e
2(h) sho
w
s t
h
e
c
u
rre
n
t
fl
o
w
pa
t
h
fo
r thi
s
m
ode
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
o
w
Elec &
Dri Sy
st
I
SSN
: 2
0
8
8
-8
69
4
A n
e
w
mu
lt
ile
ve
l D
C
-
A
C c
o
n
v
e
r
te
r
t
o
po
log
y
w
ith
re
du
ce
d swit
ch
u
s
ing
mult
ic
a
r
rie
r
…
(
R
. Pa
lan
i
sam
y
)
7
55
(a)
(b
)
(c)
(d
)
(e)
(f)
(g) (
h
)
F
i
gu
r
e
2.
M
o
d
e
s o
f
ope
rat
i
o
n
-
posi
t
i
ve
a
nd z
e
r
o
l
e
ve
l
,
(
a
)+
1/
7 V
dc
(b
) +
2
/
7
V
dc
(c
) +
3
/
7
V
dc
(d
) +4
/
7
V
dc
(e
)
+5
/7
V
dc
(
f)
+
6
/7
V
dc
(g
)
V
dc
(h
) 0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
7
5
2
–
761
75
6
G
e
ne
ra
l
l
y,
vol
t
a
ge
bal
a
nc
i
n
g
p
r
obl
ems
a
r
ise
s
d
u
e
t
o
no
n-
uni
fo
rm s
w
i
t
c
hi
ng
, n
o
n
-i
d
e
a
l
dc
l
i
n
k
ca
paci
t
o
rs
, u
n
e
qual
c
o
mm
ut
at
i
on o
f
se
mi
c
ond
uc
to
r
de
vi
ce
s, u
n
sy
mmet
r
i
cal
cu
rre
nt a
n
d
inj
e
c
t
io
n
of
c
u
rrent
fl
o
w
.
It
e
f
fect
s
on
perfo
rma
n
c
e
o
f
i
nve
rt
er
de
gra
d
es,
i
n
c
r
eas
e
o
f
v
o
l
t
a
g
e st
re
ss, a
d
dit
i
onal
h
a
rmo
n
ic
di
st
o
r
t
i
on
and
i
n
crea
se
i
n
l
o
a
d
c
u
rre
nt
ma
g
n
it
ude
.
B
u
t
thi
s
p
r
o
p
o
sed
syst
em
a
v
oids
ab
o
v
e
me
nt
i
o
n l
i
mi
t
a
t
i
on
s,
due
t
o
th
a
t
vo
lt
ag
e
b
a
la
n
c
in
g no
t
re
qu
ir
ed
.
2.3.
T
o
p
o
l
o
g
y
comp
ari
s
o
n
The
p
r
o
p
o
sed
syste
m
c
o
mpa
r
ed
wit
h
cl
assi
c t
o
pol
ogi
e
s
l
i
k
e
di
o
d
e c
l
a
m
pe
d
,
fl
yi
n
g
ca
pa
ci
t
o
r an
d
ca
sc
ade
d
H
-
bri
dge i
nve
rt
er. A
m
o
n
g
t
h
at
p
r
o
pos
ed sc
he
me
req
u
i
r
es
mi
n
i
m
u
m nu
m
b
er of po
w
e
r swi
t
ch
e
s
an
d
doe
sn
’t
ne
e
d
o
f
a
n
y pa
ssi
v
e
el
ement
s
. Ta
bl
e 2
s
h
ows
e
q
u
i
p
m
e
n
ts
c
o
m
p
a
r
i
s
o
n
o
f
va
rio
u
s
to
pol
ogie
s
for
15
le
v
e
ls inv
e
rt
er.
Tabl
e
2. E
q
uip
m
ent
s
C
o
mpa
r
i
s
on o
f
Vari
o
u
s To
pol
ogie
s
for
1
5
-Le
v
el
Out
p
ut
V
o
l
t
a
ge
Fe
atur
e
s
/T
opo
l
ogies P
r
opose
d
Diode
cl
am
pe
d
H
-
b
r
i
dge
Flying
c
a
pa
cit
o
r
D
C
sour
ce
3
1
7
1
DC l
i
nk ca
pac
itor
s
0
14
7
14
Pow
e
r
swi
t
che
s
10
128
28 128
Fr
ee
whe
e
l
i
n
g
(or)
c
l
a
m
pin
g
diodes
0
14
0
0
3.
MUL
T
I
C
A
R
RIER
SI
NU
S
O
ID
A
L
P
U
LS
E WIDT
H M
O
D
U
L
AT
ION
To
a
m
al
ga
ma
t
e
t
h
e
m
u
l
t
i
l
e
ve
l
A
C
o
u
t
put
vol
t
a
ge
wit
h
di
ffere
nt
l
e
ve
l
s
of
d
c
i
n
p
u
t, t
h
e
se
mi
con
d
u
c
tor
pow
er swi
t
c
h
es
mu
st
sw
i
t
ch
ed
t
o
ON
and
O
FF s
t
at
e
i
n
su
c
h
th
a
t
d
e
s
i
r
e
d
fu
nd
am
e
n
t
i
on
a
l
i
s
ac
hie
v
e
d
wi
t
h
mini
mu
m
ha
rmo
n
ic
di
storti
on
[2
1-
2
3
]. T
h
e
r
e a
r
e
seve
ral
a
p
proac
h
e
s
ar
e
a
v
ai
la
bl
e
t
o
sel
e
c
t
a
P
W
M
str
a
te
gy f
o
r
mu
ltil
ev
el
in
v
e
rt
ers
lik
e
b
a
se
d
on
low
/
h
i
gh
fr
e
q
u
e
n
c
y,
nu
mb
e
r
o
f
sw
it
ch
e
s
u
s
e
d
a
n
d
v
o
l
t
a
g
e
s
t
r
e
ss
[
2
4
-
27
].
F
o
r
c
l
a
ssic
a
l
mu
l
tile
v
e
l t
o
po
log
i
es to
g
e
t
b
e
t
t
e
r
per
f
o
r
ma
n
c
e
mo
stly
p
r
e
p
a
r
e
d
sp
a
c
e
vec
t
o
r
mo
d
u
la
ti
on t
h
e
a
m
on
g
va
ri
o
u
s
m
o
dula
t
io
n
te
ch
n
i
ques
.
B
u
t
SV
M
is
not
poss
i
bl
e w
h
e
n
mi
ni
mum
nu
mbe
r
o
f
s
w
i
t
c
hes
use
d
,
bec
a
u
se
i
t
cann
o
t
ge
ne
ra
t
e
si
mul
t
a
n
e
o
us
swit
chi
n
g
p
u
l
s
es
for
mul
t
i
p
l
e
nu
mbe
r
of
s
w
i
t
c
hes.
Thi
s
p
r
op
ose
d
scheme i
m
pl
e
m
e
n
t
a
t
e
d
usi
ng
M
u
l
t
i
c
a
rri
e
r
Si
n
u
s
o
ida
l
P
u
lse
Wi
d
t
h
Mo
d
u
la
ti
on
(M
SP
WM
).
A si
n
u
soi
d
al
(re
f
ere
n
ce
) wave
f
o
rm i
s
c
o
mpa
r
ed
wi
th
nu
merous
t
r
ia
n
g
ul
a
r
(car
ri
er)
wa
ve
for
m
s
are
sc
at
te
red
u
s
ing
p
h
a
s
e di
sposit
i
o
n
met
h
o
d
. T
h
e pe
ak t
o
peak
am
pli
t
u
d
e
of
t
r
i
a
n
gul
ar signa
l
i
s
Vt
ag
,
an
d
pea
k
t
o
pea
k
a
m
pl
i
t
ude
o
f
si
n
e
si
g
n
al
i
s
V
s
i
n
.
T
h
en
t
h
e
mo
dul
a
t
i
on i
n
d
e
x
M
i
is
defi
ned
a
s
,
M
∗
(1)
The
n
t
h
e
o
u
t
put
v
o
l
t
a
ge
o
f
pro
pose
d
syste
m
ba
sed
o
n
t
h
e a
p
p
l
i
e
d i
n
p
u
t
volt
a
ge
a
n
d
mo
dula
t
io
n
i
nde
x,
w
h
ic
h i
s
de
fi
ne
d a
s
,
V
M
∗
V
(2)
F
i
gure
3
s
h
o
w
s the
Mul
t
i
c
a
rri
er
S
i
n
u
s
o
i
d
al
Pul
s
e
Wi
dth
Mo
dul
at
i
on w
i
t
h
re
fe
re
n
c
e si
gna
l,
c
a
rrie
r
signa
l a
n
d gat
e
p
u
l
s
es. Ba
se
d
on
t
h
e
s
e
c
o
m
p
ariso
n
ga
te
p
u
lse
ge
ne
rat
e
d
for
the
p
o
w
er sw
it
che
s
o
f
pro
pos
ed
in
v
e
r
t
e
r
,
th
is is d
e
fin
e
d
as
,
(a
)
V
si
n
<
0 a
n
d
V
si
n
> V
tag1
= S1 s
w
it
c
h
ed
O
N
(b
)
V
si
n
>
0 a
n
d
V
si
n
< V
tag2
=
S2
sw
itch
ed
O
N
(c
)
V
si
n
>
V
tag4
= S4 sw
it
che
d
ON
and
V
si
n
< V
ta
g
= S3 sw
itch
e
d
O
N
(d
)
V
si
n
>
V
tag5
=
S5 s
w
it
c
h
e
d
ON
and
V
si
n
< V
tag
4
= S6
sw
it
che
d
ON
(e
)
V
si
n
>
V
tag6
= S7 sw
it
che
d
ON
(f
)
V
si
n
>
V
tag3
= S8 sw
it
che
d
ON
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
A
n
e
w mu
ltil
ev
e
l
D
C
-AC
con
vert
e
r
to
po
l
o
g
y
wi
th
redu
c
e
d
swit
ch
u
s
ing
multi
c
a
r
r
i
e
r
…
(
R
.
Pa
lan
i
s
a
my
)
7
57
Fi
gu
re
3. M
S
P
W
M
- re
fere
nc
e si
gna
l
,
c
a
rri
e
r
si
g
n
al
& gat
e
p
u
lses
4.
SIM
U
LAT
I
O
N
RE
SUL
T
S
The
p
r
o
pose
d
15
l
e
vel
in
ve
rt
er t
o
p
o
lo
gy
is
si
mul
a
t
e
d
usi
ng
mat
l
ab /
si
mul
i
n
k
20
1
6
a.
T
h
e
si
m
u
la
t
i
o
n
r
e
s
u
lts ar
e ob
ta
in
e
d
w
ith swi
t
c
h
in
g fr
e
q
u
e
nc
y
o
f
10 kH
z
an
d
gate
pu
l
s
e
s
ar
e g
e
n
e
r
a
t
e
d
u
s
ing
m
u
ltica
r
r
i
e
r
sinus
oi
dal
p
u
l
s
e
w
i
dt
h
m
o
d
u
l
a
t
i
on
wi
th
pha
se di
s
posit
i
o
n met
h
od
.
Pro
pos
ed
syst
em c
o
n
s
ist
s
o
f
thr
ee dc
vol
ta
ge
s
o
u
r
c
e
s
a
r
e
V
1
=
1
0
V
, V
2
=
2
0V
&
V
3
=40
V
.
T
h
e si
mul
a
t
i
on p
r
o
p
o
s
e
d syst
em ha
s
t
h
e
fol
l
o
w
i
n
g m
e
rit
s
,
(a
)
It
d
o
e
s
ha
ve
di
ode
s
a
n
d
ca
pac
i
t
o
rs,
w
h
en
n
u
mbe
r
l
e
ve
l i
n
cre
a
se, usage
o
f
dio
d
e
wi
l
l
i
n
cre
a
se.
(b
)
C
o
mp
le
x
i
t
y
of
th
e c
o
n
t
ro
lle
r
i
s
mo
re
, wh
en
nu
mb
er of le
v
e
l
i
n
cr
e
a
se
.
(c
)
Vol
t
a
g
e
st
re
ss
& v
o
l
t
a
ge
b
a
l
a
nci
n
g
i
ssue
ca
n be rec
t
i
f
i
e
d
base
d o
n
t
h
e pe
rfor
ma
nc
e
o
f
t
h
e
cont
rol
l
e
r
.
Th
e
pr
opo
sed
1
5
-
l
ev
e
l
ou
t
put
vo
lta
g
e
wi
th 6
9
.5
6 V,
w
h
ich
is sh
own
in
Fig
u
r
e
4. I
n
Fi
g
u
r
e
s
5
& 6
sho
w
s
vol
ta
ge
a
c
ross
s
w
i
t
ch
S
8
&
S
9
re
spe
c
t
i
vel
y
.
T
o
t
a
l
ha
rm
o
n
ic
di
st
orti
o
n
for
o
u
t
p
ut
v
o
l
t
a
g
e
an
d
cont
rol
l
e
d c
u
rrent
o
f
p
r
op
ose
d
1
5
l
e
ve
l
s
sc
heme i
s
10
.3
8
%
a
n
d
6.3
6
%
re
spect
i
v
el
y,
whi
c
h
is e
x
p
o
s
e
d
in
Fi
gu
re
s
7
(
a
)
& 8(
b).
Fi
gu
re
4. p
r
o
p
o
se
d 15
le
vel
o
u
t
p
ut
v
o
l
t
a
g
e
w
a
ve
form
Fi
gu
re
5. Vol
t
a
g
e ac
ross swit
ch S8
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
7
5
2
–
761
75
8
Fi
gu
re
6. Vol
t
a
g
e ac
ross swit
ch S7
(a
)
(b
)
F
i
gure
7. TH
D
a
n
al
y
s
i
s
(a
)
O
u
t
put
v
o
lt
age
(b)
C
o
ntr
o
ll
ed
c
u
rrent
F
i
gure
8 sh
ow
s p
r
o
p
o
se
d in
v
e
rt
er
out
put
v
o
l
ta
ge wi
th
co
u
p
l
e
d i
nduc
t
o
r,
whi
c
h is
use
d
to sm
o
o
th
out
put
vol
ta
ge
and c
u
r
r
e
n
t
& a
l
so e
l
i
m
ina
t
es the
usa
g
e t
r
a
n
sfo
r
me
r t
h
at
ca
n mi
nimi
se c
o
st
of the
syst
e
m
an
d
le
a
k
ag
e c
u
r
r
ent
p
r
ob
lem
.
Th
e
mo
du
la
tio
n
ind
e
x
w
i
l
l
d
e
ci
de
th
e ou
tpu
t
volt
a
g
e
le
v
e
l.
Whe
n
m
odu
la
tio
n in
d
e
x
Mi i
s
0.6
wi
t
h
vo
l
t
a
ge
of
4
9
.2
V
an
d
Mi
is
0
.
8
wi
t
h
v
o
lt
age
o
f
65
.2
V
a
n
d
Mi
i
s
0
.
9
9
w
i
t
h
out
p
u
t
v
o
l
t
a
g
e
o
f
69
.5
6
V
,
w
h
i
c
h i
s
s
h
o
w
n i
n
F
i
gu
res
9
,
1
0
&
11
respec
ti
vel
y
.
T
h
e
o
u
t
p
ut
c
u
rre
n
t
of t
h
e
p
r
o
p
o
sed
i
nve
rt
e
r
wi
tho
u
t
c
o
upl
e
d
i
n
d
u
ct
o
r
sho
w
n i
n
Fi
gu
re
1
2
.
T
h
e
o
u
tp
ut
current
is c
o
nt
rol
l
e
d
wi
t
h
he
l
p
o
f
c
o
up
l
e
d i
n
duct
o
r
wi
th
4.2
A i
s
e
x
p
o
se
d i
n
F
i
gu
re
13
.
Fi
gu
re
8. Inve
r
t
e
r
out
p
u
t
vol
t
a
ge
wi
th c
o
u
p
l
e
d
i
n
d
u
ct
o
r
Fi
gu
re
9. O
u
t
p
ut v
o
lt
a
g
e
wi
t
h
M
I
=
0
.7
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
A
n
e
w mu
ltil
ev
e
l
D
C
-AC
con
vert
e
r
to
po
l
o
g
y
wi
th
redu
c
e
d
swit
ch
u
s
ing
multi
c
a
r
r
i
e
r
…
(
R
.
Pa
lan
i
s
a
my
)
7
59
F
i
gure 10.
O
u
t
put
v
o
l
t
age wi
th M
I
=
0
.
8
In
cl
ass
i
ca
l mult
ile
v
e
l in
v
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Int
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c
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r
i
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y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
7
5
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–
761
76
0
5.
CO
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U
S
I
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N
Thi
s
pa
pe
r est
a
bl
ishe
d a n
o
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e
l
15
l
e
ve
l dc
-a
c co
nve
rte
r
w
i
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h
red
u
ce
d
s
w
i
t
c
h
es. Ba
sed on t
h
e
S
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R
ra
ti
o t
h
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u
m
b
er
o
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d
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verte
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ca
n
be
a
c
h
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e
ve
d.
Prop
ose
d
i
nve
rte
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p
o
we
r sw
i
t
c
hes
cont
rol
l
e
d b
y
MS
P
W
M me
t
h
o
d
,
a
n
d
w
i
t
h
he
lp
of
c
o
u
p
l
e
d in
duc
t
o
r w
h
i
c
h of
fer hig
h
co
nsist
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y out
put
vol
ta
ge
a
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o
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ac
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p
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fi
ci
ency
, l
o
w syst
em
c
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s
t
and
hi
ghe
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i
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ty.
The
p
r
op
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d
s
y
st
e
m
ge
ne
rat
e
s 1
5
l
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l
out
put
vol
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wit
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of
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we
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w
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wit
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9 a
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ffere
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f
out
put
v
o
lt
ag
e
s
are
obt
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d wi
t
h
va
ria
t
i
on of
Mi
.
A
cco
mpl
i
s
h
ed
be
tt
e
r
cu
rre
n
t
cont
rol
a
nd
v
o
l
t
a
ge c
o
ntrol
o
f
1
5
-l
e
v
el
p
r
o
p
o
se
d i
n
verte
r
s
c
he
me
wi
th
THD
o
f
6.
3
6
%
& 10
.3
8%
res
p
ect
i
v
el
y
.
RE
FERE
NC
E
S
[1]
J.
S
.
Lai
an
d F
.
Z. P
e
ng
,
“M
ulti
lev
e
l Conv
erters
- A new Br
eed o
f
P
o
w
e
r Con
v
ert
e
rs,”
IEE
E
T
r
an
s.
In
d.
Ap
plicat
.,
vo
l.3
2
,
pp
.
5
09-
5
1
7
,
M
a
y/Ju
ne
2
0
1
4
.
[2]
K.C.A. De
Sou
za,
M.R.T. De
Castro
,
and
M
.
R An
tu
nes
,
“D
C-AC con
v
erter
of sing
le-ph
a
s
e
grid-
c
on
ne
cte
d
ph
otov
olta
ic
s
y
s
t
em”
,
In
:
IECON
Pro
ceed
in
gs
,
vol.
4, p
p
.
32
68
-3
2
7
3,
20
1
3
.
[3]
T.
Kerek
e
s,
R.
T
e
od
ores
c
u
,
an
d M
.
Lis
e
rre
,
“Eva
luation
of th
re
e
-
p
h
a
s
e t
r
a
n
sfo
r
m
e
rl
e
ss p
hot
ov
ol
tai
c
i
n
v
e
rter
to
po
lo
gies
,”
IEEE Trans. P
o
wer
El
ectron
.
,
v
o
l
.
2
4
,
no
.
9
,
pp
. 2
2
0
2
-
22
11,
S
e
p
.
20
13.
[4]
Xiao, H.,
Xi
e, S.
:
“A ZVS
bid
i
re
ctio
n
a
l DC-D
C
con
v
ert
e
r
for
ph
as
e-sh
ift
plus
P
W
M
con
t
ro
l s
c
h
e
me
”,
IEE
E
Tr
ans.
Po
w
e
r E
l
ec
t
r
on
.
,
Vo
l 23,
No
.
2
,
pp
. 8
1
3
-
82
3, 2
013.
[5]
J.
Ro
drigu
ez, S.
Bern
et, P
.
K
.
S
t
eim
e
r, I.
E.
Li
z
a
ma
, “A s
u
rvey
on n
e
utra
l po
in
t
cla
m
p
e
d inv
e
rt
er
s,”
IEEE T
r
ans
.
Ind.
E
l
ect
r
on
.
,
v
o
l. 5
7
,
no
.
7
,
pp
.
22
19
-22
30,
Ju
l.
20
10.
[6]
Xu
, D., Zh
ao, C
.
, F
a
n,
H
.
: “A P
W
M
plu
s
ph
ase-
shi
f
t control bi
directio
n
a
l DC–D
C
co
nv
erter”
,
I
E
EE
T
r
an
s.
Po
w
e
r
El
e
c
tr
on
.
,
Vo
l. 19,
No
. 3, pp
.
6
66-6
7
5
,
2
0
0
8
.
[7]
Ino
u
e, S
., Ak
ag
i,
H.
“A bid
i
re
ctio
nal
D
C
–DC c
o
n
v
erter
for
the
energ
y
s
t
o
r
ag
e
sys
t
em with
gal
v
an
ic
iso
l
a
t
io
n”
,
I
E
E
E
Tra
n
s
.
Pow
e
r E
l
e
c
t
ro
n
.
,
Vo
l.
22
, N
o
. 6
,
p
p
.
229
9-2
3
0
6
,
201
1.
[8]
M
a
dawala
, U.K
.
,
Thrim
a
w
i
th
ana
,
D
.
J.: “A
b
i
d
i
r
ectional
in
d
u
ct
iv
e pow
er
inte
rf
ace fo
r
ele
c
tri
c
v
e
hicles
in
V2
G
systems”,
IEEE
Tran
s. In
d.
El
e
c
tro
n
.
,
Vo
l.
58,
No
. 1
0
,
pp.
47
89
-47
9
6
,
20
13.
[9]
Rod
r
ig
uez
,
A
.
,
V
azqu
e
z
,
A.,
La
mar,
D.G
.
: “D
if
ferent
p
u
rpo
s
e
d
e
sign
str
a
teg
i
es
an
d
techn
i
q
u
es
with
impro
v
e
th
e
perfo
rm
an
ce of
a d
u
al
ac
tive b
r
idg
e
with
ph
ase
-
sh
ift con
t
ro
l”
,
I
E
EE
T
r
a
n
s.
Po
w
e
r E
l
e
c
tr
on
.,
Vo
l
.
3
0
,
No. 2,
p
p
.
79
0-8
04,
20
14
.
[10]
Fan,
H.
,
Li, H.: “H
i
g
h-frequency
transformer i
s
ol
at
ed
bi
direct
ional D
C
-DC
c
o
nver
t
e
r
m
o
dules
w
i
th hi
gh
eff
i
ciency
ov
er
w
i
d
e
lo
ad r
a
ng
e o
f
20
k
V
A
s
o
lid
-
s
t
ate
t
r
ansfo
r
mer”
,
I
E
EE
T
r
a
n
s
.
Pow
e
r
E
l
ect
ro
n
.,
Vo
l.
26
,
No
.
1
2
,
pp.
35
99
-360
8
,
20
12.
[11]
R.
Pa
la
n
i
sa
m
y
an
d
K.
Vija
ya
k
u
m
a
r, “
M
a
x
im
um
Bo
ost
Co
nt
rol for
7-l
e
ve
l z
-
so
u
r
c
e
c
a
s
ca
d
e
d
h-bri
d
g
e
in
ve
rte
r
,”
In
te
rna
t
io
na
l J
ourna
l o
f
P
o
we
r
El
ec
tro
n
i
c
s a
nd
Driv
e
S
y
ste
m
s (IJ
P
EDS)
, vo
l.8
,
No
. 2
,
pp
.
73
9-7
4
6
20
17
.
[12]
R
.
A. Ah
me
d
,
S. Me
k
h
ile
f,
a
nd
W
.
P.
He
w, “
N
ew m
u
lt
ile
v
e
l i
nve
rte
r
t
o
p
o
l
o
g
y
wit
h
m
i
nim
u
m
num
be
r
o
f
swit
c
h
es,
”
in
Pr
oc
. I
E
EE
R
e
gio
n
10
Conf
.
(
T
ENCO
N)
,
pp
.
18
62
-18
6
7
,
20
12.
[13]
M
.
R. Ban
a
e
i
an
d E. S
a
lary
,
“N
e
w
multi
l
ev
e
l
in
v
e
rter
w
ith redu
ction
o
f
sw
itch
es an
d gat
e
driv
er,” in
P
r
oc
.
IE
EE
18
th
Ira
n
.
Conf.
Ele
c
t.
En
g
.
(I
EC
C)
,
p
p
.
784
-78
9
,
201
2.
[14]
R.
Pa
la
ni
sa
m
y
and
K.
Vi
ja
y
a
kum
a
r
,
“
A
3
D
-spa
c
e
v
e
c
t
or m
o
dula
t
io
n
a
l
go
rith
m
for th
re
e
pha
se
f
o
u
r
wi
re
n
e
u
t
ral
po
in
t cla
m
ped
in
v
e
rter
s
y
s
t
ems
a
s
p
o
w
e
r
qu
a
l
ity
compen
sa
tor”
.
E
n
er
gies
1
0
:
17
92
,
20
17
.
[15]
R. P
a
lanisa
my
,
C.
S
.
Bo
opath
i,
K. S
e
lv
aku
m
ar
,
“S
w
itch
i
n
g
pu
ls
e
g
e
n
e
ra
tion
f
o
r
D
C
-DC bo
os
t con
v
e
rter us
in
g
Xil
i
n
x
-I
SE wit
h
FPGA p
r
oc
e
s
sor”
,
I
n
t
e
rn
at
io
na
l
Jo
ur
nal
o
f
E
l
ec
tr
ica
l
a
n
d
C
o
m
p
u
t
er
Eng
i
n
e
eri
n
g
(
I
J
EC
E)
, Vo
l.
1
0
,
No
. 2, pp
.
1
722
-17
2
7
,
Ap
ril
20
20
.
[16]
W.
Li an
d X
.
H
e
, “A
n
inter
l
e
a
v
e
d
w
i
nd
in
g-co
u
p
led
bo
os
t conv
e
r
ter with passive
l
o
ss
less
cla
m
p circuits,
”
IE
E
E
Trans. Power Electron
.,
v
o
l
.
22
,
n
o
.
4, p
p
.
14
99
-1
50
7,
Ju
ly
20
07.
[17]
P
a
lan
i
s
a
my
, R
.
,
Vi
jay
a
ku
mar
,
K.
, S
e
l
v
abh
a
r
a
th
i,
D,
“MS
P
W
M
bas
e
d i
m
pl
e
m
en
tat
i
o
n
of
n
o
v
e
l 5
-
le
v
e
l i
n
v
e
r
t
er
w
i
t
h
ph
otov
olta
ic
s
y
stem
”,
Int
e
rna
t
io
n
a
l Jo
ur
na
l o
f
Power
Electro
nic
s
an
d D
r
iv
e
S
y
stem
s (IJ
EPDS
),
Vol. 8
,
pp.
149
4
-
15
02
, 2
017
.
[18]
N. A
.
Rahim,
K
.
Chani
a
go
, a
nd J
.
S
e
lvar
aj,
“S
ing
l
e-p
h
a
se s
e
ven-l
e
vel
g
r
id
-
c
onn
ec
ted
inv
e
r
t
er for
ph
otov
olt
a
ic
system,”
IEEE
T
r
an
s. In
d.
Ele
c
tr
o
n
.
,
vo
l.
58
,
n
o
.
6
,
p
p
.
243
5-2
4
4
3
,
Jun
e
20
11
.
[19]
K.
Ha
se
ga
wa a
n
d
H.
Ak
a
g
i,
“
A
n
e
w d
c
-vo
l
t
a
ge
-ba
l
a
n
c
i
ng
c
i
rc
ui
t in
c
l
u
d
in
g a si
ngl
e
c
o
u
p
l
e
d
i
nduc
t
o
r
fo
r a
fiv
e
-
l
e
vel
di
ode
-cl
a
mpe
d
PWM i
nve
rte
r
,”
IEEE T
r
ans
. In
d.
App
l
.
,
vo
l.
47
, n
o
.
2
,
p
p
.
84
1
-
85
2,
M
a
r/Ap
r
.
2
015
.
[20]
Chen
g-Han
H
s
ie
h, Ts
orn
g
-J
uu Liang
,
“Design
an
d Impl
eme
n
tati
o
n
of a
Novel Mu
ltilevel
D
C
–A
C
In
verter
”,
IE
E
E
Tran
sac
t
io
ns on
Ind
u
stry
Ap
plic
at
io
ns
,
Vo
l
.
5
2
,
N
o
. 3
,
M
a
y/
Ju
ne
2
016
.
[21]
Gn
ana P
r
ak
ash
,
M., Ba
l
a
muru
gan,
M
,
Umas
h
a
n
k
ar, S
.
“A n
e
w mul
t
ilev
e
l in
verter
with
re
d
u
ced n
u
m
ber
of
sw
itches”,
In
te
rn
ation
a
l Jou
r
n
a
l of Power
Ele
ctro
nics a
n
d
Dr
ive S
y
st
ems
(IJ
EP
D
S
)
,
vol 5
,
N
o
.
1,
p
p
.
63
-70,
Se
ptem
b
e
r
2
0
14.
[22]
R. Anton
y
Raja
S
e
kar, D.
A
r
un
P
r
asad
, “I
mprov
e
d Tran
sform
e
rl
ess Invert
er for
PV
GridCon
n
ect
ed P
o
wer S
y
s
t
em
by
us
in
g IS
P
W
M
Techn
i
q
u
e
”
IJ
E
T
T
– V
o
l.
4
(
5
)- M
a
y
20
14
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
A
n
e
w mu
ltil
ev
e
l
D
C
-AC
con
vert
e
r
to
po
l
o
g
y
wi
th
redu
c
e
d
swit
ch
u
s
ing
multi
c
a
r
r
i
e
r
…
(
R
.
Pa
lan
i
s
a
my
)
7
61
[23]
Ali
s
h
a
h, R.
S.,
Hosse
i
ni
, S.
H. “
A
ne
w m
u
lt
ile
ve
l
i
n
v
e
rte
r
st
ru
c
t
ure
for h
i
g
h
-
po
wer
a
ppli
c
ation
s
u
s
ing mu
lti-
carr
i
er
PW
M swi
t
c
h
i
ng st
ra
te
gy
”,
In
tern
atio
na
l
Jou
r
na
l o
f
Po
we
r
Electr
o
nics an
d Dr
iv
e
Sys
t
em
s (IJEPD
S
)
,
vo
l 6, No
. 2,
p
p
.
31
8-3
2
5
,
1
Jun
e
20
15
.
[24]
T
.
It
o,
M
.
Ka
ma
ga
, Y.
Sato
,
a
nd H.
Oh
a
s
h
i
,
“An in
ve
sti
g
a
t
i
on
o
f
v
o
l
t
a
g
e
ba
lan
c
in
g
c
i
rc
u
i
t for
d
c
c
a
p
a
c
ito
rs in
diode-clamped mul
tilevel
inver
t
ers t
o
r
eal
i
z
e
high
output
po
wer densi
t
y
converters,” i
n
P
r
o
c
. I
EEE
Ener
gy
Convers. Congr
.
E
x
po.
(
E
CCE
)
,
pp
.
3
675
-36
8
2
,
20
12
.
[25]
R.
Pa
la
n
i
sa
m
y
,
A.
Vel
u
,
K. Se
l
v
a
k
u
m
a
r
, D. Ka
rth
i
k
e
ya
n
,
“
A
S
u
b
-
Re
gi
on B
a
se
d S
p
a
c
e
Vec
t
or
Modu
la
t
i
o
n
Sc
he
me
for
Dual 2-
L
e
vel
Invert
e
r
Sys
t
em
”,
In
ter
n
a
t
i
ona
l
Jou
r
na
l of
El
e
c
t
r
ica
l
a
n
d
C
o
mpu
t
er
E
ngi
n
eer
in
g (
I
J
E
C
E)
, Vol
.
8,
No.
6, p
p
. 49
02
-4
91
1,
Dec
e
m
b
e
r 2
0
1
8
.
[26]
V. T
.
S
o
mas
e
k
h
ar,
et
al.,
“
A
s
p
ace v
ecto
r
b
a
sed
P
W
M
sw
itch
in
g s
c
h
e
me
fo
r th
e
redu
ctio
n
o
f
c
o
mmon
-
m
o
d
e
vo
ltag
es
for a
d
u
a
l inv
e
rter
fed
op
en-end
w
i
nd
in
g
ind
u
ct
io
n mo
to
r drive
,
”
I
EEE
-PESC-20
05
, R
e
cif
e
,
B
r
a
z
il
, p
p
.
81
6-8
21,
20
05
.
[27]
S.
S.
Ki
m
,
D
.
K. C
h
o
i
,
S.
J.
Ja
ng,
T
.
W
.
L
e
e
,
C
.
Y
.
Wo
n
.
“Th
e
act
iv
e c
l
amp
S
E
P
I
C-fly
b
ack
con
v
ert
e
r”,
Po
w
e
r
Ele
c
tr
onics Sp
ec
ialis
t
s Con
f
eren
c
e
,
2005
.
PE
SC’
0
5. IEEE 36th
,
pp. 1
2
0
9
-
1
2
12,
2
005
.
Evaluation Warning : The document was created with Spire.PDF for Python.