Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
(I
J
PE
D
S
)
Vo
l.
11
,
No.
4
,
Decem
be
r 202
0
, p
p.
1866
~
1871
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v11.i
4
.
pp1
866
-
1871
1866
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
A narrat
ive 3
-
ph
ase 9
-
lev
el volta
ge so
urce
inverter
M.
Selv
ap
eru
mal
1
,
D.
Kiru
ba
k
ar
an
2
1
Depa
rt
me
nt
of
El
e
ct
ri
ca
l
and
E
l
ec
tron
ic
s E
ng
ineeri
ng,
Sathy
abama
Univ
ersit
y
,
I
ndia
.
2
Depa
rtment
of Electrical a
nd
E
l
ec
tron
ic
s E
ng
ineeri
ng,
St.
Jos
ph’s
Instit
ut
e
of
Tec
hnology,
Ind
ia.
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Dec
4
, 2
01
9
Re
vised
Feb
2
2
, 2
0
20
Accepte
d
J
un
18
, 20
20
A
tale
t
ec
hniqu
e
for
a
3
-
st
age
nine
-
l
eve
l
vol
tage
sourc
e
inve
r
t
er
u
ti
l
iz
ing
sixte
en
sw
it
ch
es
is
pr
ese
nte
d
.
T
he
giv
en
sys
tem
ut
il
i
ze
s
ord
in
ary
3
-
stag
e
sca
ffolds
of
two
-
le
ve
l
as
a
d
iod
e
br
aced
mode
l
.
A
DC
interfa
ce
voltage
is
provide
d
so
that
the
f
el
l
H
-
con
nec
t
produc
es
t
he
nin
e
vo
ltage
le
v
el
s.
Th
e
exc
hang
ing
d
esi
gns
are
expr
esse
d
as
th
e
le
v
el
s
e
xpand
the
n
th
e
exa
mp
le
is
har
d
to
create
thre
e
-
st
age
y
iel
ds
with
key
ba
la
nc
e
proc
edur
e
s.
Here
an
answer
for
an
a
-
l
eve
l
inve
r
te
r
to
c
rea
t
e
r
equi
red
vo
lt
ag
e
-
le
v
el
with
l
ess
power
el
e
ct
roni
c
par
ts
by
setting
up
in
th
e
look
-
in
to
t
abl
es.
Thi
s
in
vesti
gation
dia
gra
ms
th
e
c
orre
lations
bet
w
ee
n
nin
e
-
le
v
el
volt
ag
e
sour
ce
inve
rt
ers
in
var
ious
arr
ang
e
me
nts
and
propo
sed
novel
,
si
x
tee
n
sw
it
ch
three
-
st
age
inv
ert
er
struct
ure
d
with
a
sma
ll
er
numb
e
r
of
in
te
nsity
e
lectr
oni
c
pa
rts
an
d
ree
n
acte
d
in
MA
TL
AB/S
i
mul
ink.
Ke
yw
or
d
s
:
Bi
directi
on
al
s
witc
hes
M
A
TLAB
Sim
ulink
M
ulti
le
vel in
ve
rters
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
M
. Sel
va
peru
mal
,
Re
search
schol
ar, De
par
tme
nt
of Elect
rical
a
nd Elec
tro
nics
En
gin
eeri
ng,
Sathy
a
bama
Unive
rsity
Chen
nai,
India
.
Emai
l:
pons
el
va
.eee@
gm
ai
l.c
om
1.
INTROD
U
CTION
The
sta
ndar
d
volt
age
source
i
nv
e
rter
co
nnec
ts
with
the
ble
nd
of
sin
usoida
l
yield
volt
age
from
tw
o
or
three
pe
rio
ds
of
vo
lt
a
ges.
T
he
w
ord,
ast
ound
ed
has
begu
n
with
t
he
t
hr
ee
-
le
vel
co
nverte
r
lo
ok
e
d
f
or
a
fter
by
change
d
daze
d
co
nverte
r
topolo
gies.
A
wide
de
gr
ee
of
t
opologies
and
co
ntr
ol
strat
egies
a
ppear
i
n
the
f
ormin
g
[
1
-
3].
A
heap
of
ast
onis
hing
in
ve
rter
modu
le
s
is
no
rm
al
for
acc
omp
li
sh
ing
lo
w
D
V/DT
char
act
e
risti
cs,
low
exc
ha
nging
misf
or
t
unes
lo
w
s
ound
s
in
t
he
yield
vo
lt
age
,
a
nd
pr
ese
nt
a
nd
bette
r
el
ect
ro
ma
gn
et
i
c
im
ped
a
nce.
Takin
g
into
a
ccount
a
fe
w
decen
t
c
onditi
on
s
,
dazzli
ng
inv
e
rters
ha
ve
be
en
app
li
ed
in
different
a
pp
li
cat
ion
fiel
ds
[4
-
8]
.
The
fell
sta
ggered
i
nv
e
rter
is
made
by
va
rio
us
sin
gle
-
orga
nize
H
-
par
t
ner
i
nv
e
rte
rs
a
nd
is
ment
ion
e
d
int
o
s
ymmet
ric
a
n
d
T
op
s
y
t
urv
y
de
pende
nt
on
t
he
essenti
al
s
of
t
he
DC
vo
lt
age
s
ource
s.
I
n
t
he
s
ymmet
ric
fla
bb
e
r
gasted
in
ver
te
r
,
the
pro
portio
ns
of
the
DC
vo
lt
age
s
a
re
a
relat
iv
e
wh
il
e,
the
l
op
s
ided
par
al
yzed
inv
erte
r,
the
e
sti
mati
on
s
of
the
DC
vo
lt
age
s
are
cl
ashin
g.
Be
ginni
ng
la
te
,
Hilt
e
r
kilt
er
ast
ou
nd
e
d
in
ve
rter
a
nd
mix
mu
lt
ist
age
topolo
gies
a
re
getti
ng
on
e
of
the
mo
st
intri
gu
i
ng
ex
amina
ti
on
zon
e
s.
T
his
to
po
l
ogy
diminis
hes
the
ex
pe
nse
an
d
siz
e
of
t
he
in
ver
te
r
a
nd
im
prov
e
s
rel
entle
ssn
ess
sin
ce
the
base
num
ber
of
power
el
ect
ronic
se
gm
e
nts,
capaci
tors,
a
nd
DC
s
upplies
ut
il
iz
ed.
The
hal
f
a
nd
hal
f
m
ulti
sta
ge
conve
rters
i
nclud
e
di
ver
se
da
zzl
ing
game
-
pl
ans
with
cl
as
hi
ng
DC
vo
lt
a
ge
supp
li
es.
Wi
th
suc
h
co
nver
te
rs,
unquest
io
nab
le
cha
nge
strat
e
gies,
a
nd
forc
e
el
ect
ronic
pa
rts
a
dv
a
nces
are
re
qu
i
red
[
9
-
15].
Re
ga
rd
le
ss
,
the
cl
arifica
ti
on
be
hind
im
prov
i
ng
t
he
pre
sentat
ion
of
t
he
sta
ndar
d
si
ng
le
a
nd
t
hr
e
e
-
co
mpose
in
ve
rters,
var
i
ou
s
t
opol
ogie
s
util
iz
ed
with
va
rio
us
s
or
ts
of
bid
i
rec
ti
on
al
switc
he
s
has
i
ntrod
uc
ed.
B
y
se
par
at
ing
th
e
un
i
directi
onal
and
bid
i
recti
onal
switc
hes
,
a
bid
irect
io
nal
switc
h
ca
n
le
ad
the
c
urren
t
and
withsta
nding
the
vo
lt
age
in
t
w
o
-
ha
bits.
F
or
accom
plishin
g
the
higher
volt
age
le
ve
ls,
bid
irect
io
nal
s
witc
hes
with
a
fitt
ing
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
A narr
ative
3
-
phas
e
9
-
le
vel
voltage
s
ou
rce
invert
er (
M
. Se
lv
ap
er
umal
)
1867
even
i
ng
out
f
r
amew
ork
ca
n
impro
ve
the
s
howcase
of
vo
lt
age
source
i
nv
e
rter
t
o
the
degree,
re
du
ci
ng
t
he
semi
-
co
nduct
or
par
ts
an
d
li
mit
ing
t
he
withstan
ding
volt
ages.
I
n
the
c
on
te
xt
of
the
par
ti
cula
r
fou
ndat
ion,
this
pa
pe
r
e
ndor
ses
a
novel
topolo
gy
f
or
a
three
-
ar
ra
ng
e
ni
ne
-
le
vel
vo
lt
age
sou
rce
i
nv
e
rter
with
s
i
xteen
switc
hes.
In
add
it
io
n,
a
n
exten
ded
st
ruct
ur
e
f
or
N
-
l
evel
is
a
pp
e
ared
a
nd
i
nspect
ed
by
c
ha
ng
e
d
glidin
g
to
polo
gi
es [
16
-
26]
.
2.
PROP
OSE
D MET
HO
D
2.1.
Model
ing
The
pro
pose
d
ni
ne
-
le
vel
volt
age
s
ource
i
nv
e
rter
co
ntains
t
hr
ee
-
bid
ire
ct
ion
al
s
witc
he
s
(
S1
-
S
6),
two
diodes
(
D
a1
-
Da
2)
,
are
a
dd
e
d
t
o
th
e
st
and
a
r
d
th
ree
-
c
ompose
tw
o
-
le
vel
gr
ow
t
h
(
Q
1
-
Q6)
a
s
a
pp
e
ared
in
Fig
ure
1.
T
he
r
est
rict
ion
of
t
he
se
bid
irect
io
na
l
switc
hes
is
to
f
or
est
al
l
the
higher
vo
lt
age
and
ease
the
c
urrent
stream
to
an
d
from
the
mi
dpoin
t
(
o).
As
s
uc
h,
V
SI
is
bol
ste
red
wit
h
a
f
ixed
vo
lt
age
of
4Vdc
a
nd
t
w
o
fell
sy
ste
ms
are
c
on
ti
nu
ing
wit
h
cl
as
hing
vo
lt
ages
V
dc
an
d
2Vdc
are
c
onnected
with
(+,
-
,
o)
te
r
mina
ls.
Accor
dingly,
t
he
dem
onstrat
ed
VSI
is
e
ndeav
ored
to
c
onve
y
nin
e
re
la
ti
ve
an
d
sp
e
ci
fic
volt
age
l
evels,
the
force
ci
rcu
i
t
of
t
he
fell
H
-
par
t
ner
util
iz
es
tw
o
a
ppr
oac
he
s
cel
ls
ha
ving
cl
ashi
ng
vo
lt
a
ge
sup
plies.
In
eve
r
y
cel
l, two
switc
hes
a
re tur
ned
On and
OFF
unde
r
c
ha
ng
e
d
c
onditi
ons to
y
i
el
d
tw
o vo
lt
a
ge
levels.
Fig
ure
1. Ci
rcui
t diagr
a
m
for pr
opos
e
d
si
xte
en
s
witc
h nine
-
le
vel volt
age s
ource i
nv
e
rter
A
ti
tl
e
of
the
arti
cl
e
ough
t
t
o
be
t
he
le
ast
po
te
ntial
words
that
preci
sel
y
with
co
ntras
ti
ng
volt
ages
Vd
c
,2V
dc,3Vd
c,4Vd
c
.0
–
Vdc,
-
2V
dc,
T
he
essenti
al
cel
l
dc
vo
lt
age
grace
fu
ll
y
V
dc
is
co
ns
oli
dated
if
s
witc
h
T1
is
t
urne
d
O
N
in
duci
ng
V
mg
=
Vd
c
w
he
r
e
Vmg
is
t
h
e
volt
age
at
th
e
m
idd
le
po
i
nt
(
m)
with
reg
a
rd
to
inv
e
rter
gro
und
(g)
or
dodge
i
f
s
witc
h
T2
is
tu
r
ned
ON
dri
vi
ng
to
Vmg=
0.
Als
o,
the
se
co
nd
ce
ll
dc
vo
lt
age
fl
exibly
2Vdc
is
joine
d
wh
e
n
s
witc
h
T3
is
tur
ne
d
ON
ha
pp
e
ning
in
Vom=+
2Vdc
w
her
e
V
om
is
the
vo
lt
age
at
the
midpoint
(o)
con
ce
rn
i
ng
fo
c
us
(
m)
or
ci
rcu
m
ve
nt
wh
e
n
s
witc
h
T4
is
tur
ne
d
O
N
co
min
g
ab
out
com
pensat
ion
=
0.
T
he
pinnacl
e
volt
age
rati
ng
of
t
he
s
witc
hes
of
t
he
sta
ndar
d
tw
o
-
le
vel
gro
wth
(Q1
–
Q6)
is
4Vdc
wh
e
reas
t
he
bid
irect
io
na
l
switc
hes
(S1
–
S
6)
ha
ve
a
pe
ak
vo
lt
age
rati
ng
of
3Vdc
.In
CHBce
ll
s,
the
su
m
mit
vo
lt
age
rati
ng
of
sec
ond
cel
l
switc
hes
(T
3
a
nd
T
4)
is2
V
dc
wh
il
e
t
he
ze
nith
vo
lt
a
ge
rati
ng
of
T
1
a
nd
T
2
in
t
he
basic
cel
l
is
V
dc.
B
y
preemi
nen
t
Va
b,
V
bc
,
Vca
wit
h
rel
at
ing
volt
ages
V
dc,2Vdc,
3V
dc,4Vdc.
0
–
Vd
c
,
-
2Vdc,
-
3V
dc,
-
4Vdc
as
appe
ared i
n
Fig
ur
e
2.
The
se
ns
i
ble
weig
ht
volt
age
s
can
be
pract
ic
ed
if
t
he
pro
po
s
ed
in
ver
te
r
chip
s
a
way
at
the
tra
ding
sta
te
s
dep
ic
te
d
in
Ta
ble
1
.
Th
e
inv
e
rter
may
inco
rpo
rate
24
unmist
aka
ble
modes
in
side
a
patte
rn
of
the
yield
wav
e
f
or
m
.
Th
e
in
ver
te
r
li
ne
-
to
-
li
ne
volt
age
wav
e
f
or
m
s
Va
b,
V
bc,
a
nd
V
c
a
with
relat
in
g
tradin
g
do
or
sign
al
s
are
portra
yed in Ta
ble
1
.
[
]
=
[
1
−
1
0
0
1
−
1
−
1
0
1
]
∗
[
]
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
4
,
D
ecembe
r
2020
:
1866
–
1871
1868
Fig
ure
2. Sim
ul
at
ed
wa
veforms
of
Va
b,
V
bc
, V
ca
Table
1
.
L
oo
kup
ta
bles
seque
nc
e of the
prop
ose
d nine
-
le
vel i
nnve
rter
S
Q1
Q2
Q3
Q4
Q5
Q6
S1
S2
S3
S4
S5
S6
T1
T2
T3
T4
VA
VB
VC
t1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
4
0
0
t2
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
4
1
0
t3
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
4
2
0
t4
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
4
3
0
t5
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
4
4
0
t6
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
3
4
0
t7
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
2
4
0
t8
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
4
0
t9
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
4
0
t
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
4
1
t
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
4
2
t
1
2
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
4
3
t
1
3
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
4
4
t
1
4
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
3
4
t
1
5
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
2
4
t
1
6
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
4
t
1
7
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
4
t
1
8
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
4
t
1
9
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
2
0
4
t
2
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
3
0
4
t
2
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
4
0
4
t
2
2
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
4
0
3
t
2
3
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
4
0
2
t
2
4
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
4
0
1
It
is
importa
nt
that
every
ree
na
ct
ed
wa
veform
is
go
tt
en
at
t1=t
2
=
•
••=t
24=
0.02
/
24
s
.
S
o
as
to
plo
t
the
sp
ace
ve
ct
or
gr
a
ph
of
the
pro
po
se
d
in
ve
rter
in
a
sta
ti
on
a
r
y
d
–
q
refe
ren
ce
outl
ine,
the
acco
mp
a
ny
i
ng
conditi
ons ca
n be
util
iz
ed
to
de
te
rmin
e
d
a
nd
q
volt
ag
e
par
ts
for
all
in
ve
rter
v
ect
ors:
=
4
√
3
(
−
1
)
(
−
)
(2)
V
=
V
q
−
J
V
d
(3)
Perce
ntage of
t
total
h
a
rm
on
ic
d
ist
ort
ion
dete
rmin
e
d
t
he valve
%
=
√
∑
2
∞
=
2
1
∗
100%
(4)
3.
SWITC
HING
A
LG
ORI
T
H
M
The
ca
rr
ie
r
bas
ed
is
the
le
ast
com
plex
t
weak
proce
dure
f
or
inco
ns
ist
ent
volt
age
sources
.
Be
arer
with
Sele
ct
ive
s
ympho
nious
is
t
he
m
os
t
widel
y
rec
ognize
d
re
gu
la
ti
on
strat
e
gy
us
e
d
t
o
co
ntr
ol
the
ce
ntr
al
yield
vo
lt
age
j
us
t
as
to
dispose
of
t
he
unwa
nte
d
c
on
s
on
a
nt
se
gme
nts
from
the
yield
volt
ages.
N
otwith
sta
nding,
a
n
it
erati
ve
te
ch
ni
qu
e
,
f
or
e
xam
ple,
t
he
Ne
wton
-
Ra
pson
strat
egy
is
ty
pical
ly
us
e
d
to
disc
ov
e
r
the
an
sw
ers
f
or
(N
-
1)
nonlinea
r
s
up
e
rn
at
ur
al
conditi
ons.
T
he
troub
le
s
om
e
fig
ur
in
gs
a
nd t
he
re
quireme
nt
f
or
a
n
el
it
e co
ntr
oller
for
the
g
e
nuine
appli
cat
ion
a
r
e the
fun
dame
ntal i
mp
e
dime
nts
of
s
uc
h
a
techn
i
qu
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
A narr
ative
3
-
phas
e
9
-
le
vel
voltage
s
ou
rce
invert
er (
M
. Se
lv
ap
er
umal
)
1869
Th
us
ly,
an
el
ect
ive
proce
dure
is
pro
po
se
d
t
o
conve
y
the
in
ve
rter's
e
xc
hang
ing
door
si
gn
al
s.
It
is
le
ss
perplexi
ng
to
c
on
t
ro
l
t
he
pro
pose
d
in
ver
te
r
a
nd
acc
ompli
sh
the
basic
yield
vo
lt
a
ge
waveforms
to
t
he
degree
Sa,
Sb,
a
nd
Sc
as
ap
pea
red
F
ig
ure
3.
T
he
r
easo
n
of
th
e
pro
posed
strat
e
gy
ca
n
be
e
xp
l
ai
ned
as
see
ks
after:
Fo
r
a
giv
e
n
e
s
ti
mati
on
of
pa
rity
rec
ord
M
a
an
d
insi
de
a
f
ull
cy
cl
e
of
th
e
act
ivit
y
of
th
e
pr
o
pose
d
i
nv
erter,
the ex
c
ha
ng
i
ng
stat
es Sa, Sb
, a
nd Sca
re
pick
ed
imme
diate
ly.
Fig
ure
3. Exc
ha
ng
i
ng stat
es ve
ct
or
s
of the
pr
opos
e
d
DC
to
ac in
d
–
q refe
r
ence
ou
tl
ine
4.
EXTE
ND
E
D ST
RUC
UTR
E
We
ca
n
see
t
ha
t
there
is
a
li
ke
li
ho
od
to
la
nd
at
a
yield
vo
lt
age
with
a
higher
num
be
r
of
ste
ps
i
n
t
he
pro
po
se
d v
oltage s
ource i
nv
e
r
te
r
by c
onso
li
da
ti
ng
fell
H
-
pa
rtner in a
cou
rs
e of acti
on as
a
pp
ea
re
d
in
Fig
ure
4.
So
as
to
acc
ompli
sh
the
i
de
al
numb
e
r
of
volt
age
le
vels
,
go
i
ng
with
a
f
r
amew
ork
for
t
he
degrees
of
D
C
volt
age
supp
li
es a
re:
By
ma
king
t
he
twof
old
rela
ti
on
s
hip
betwe
en
the
DC
supp
li
es
of
the
f
el
l
h
-
inte
rf
ace
struct
ur
e
as
looks
f
or
a
fter
the
MATL
AB/Si
mu
li
nk
m
odel
of
the
pr
opose
d
in
ver
te
r
a
ppeare
d
in
Fi
g.
1
has
bee
n
ma
de
to
consi
der
c
onduct
ion
a
nd
ex
c
hangin
g
impac
t
dif
ficult
ie
s.
The
pro
posed
inv
e
rter
is
reli
ed
upon
t
o
pa
ss
on
a
yield
po
wer
of
Pout=1
890wa
tt
s.
Thr
ee
-
s
or
t
ou
t
a
str
at
eg
y
resist
ive
–
i
nduc
ti
ve
(23
Ohm
–
3
m
H/Ph
a
se)
i
n
sta
r
al
li
ance
is
util
iz
ed
as
a
sto
r
e.
T
he
stu
nne
d
DC
-
inte
rf
ac
e
is
set
tl
ed
as
V
dc=75
V,
2Vdc=
150
V
,
a
nd
V
cons
=
4V
dc
=
30
0
V
an
d
the
propose
d
tran
spo
rt
c
hange
st
r
uc
ture
at
M
a=
1
i
s
ac
knowle
dge
d
t
o
ma
ke
t
he
mo
st
ideal
ex
cha
nging
e
ntr
y
si
gn
al
s.
T
hree
s
pecif
ic
sorts
of
se
m
ic
ondu
ct
or
par
t
s
are
picke
d
to
ma
ke
t
he
m
odel
of
the
pro
posed
inv
e
rter
c
ontrol
ci
rcu
it
as
f
ollow
i
ng
:
IG
BT
(
HG
T
G
20N
60B3D)
60
0
V/
40
A
f
or
t
he
tw
o
-
le
ve
l
Bridg
e
a
nd
C
HB
s
witc
hes
,
I
GBT
(
IRG
4B
C40W)
600
V/
20
A
f
or
bi
directi
onal
s
witc
hes,
a
nd
Di
od
e
(RHRP
1540)
440 V/
15 A f
or
instal
le
d
di
od
e
s in bidirect
i
onal
sw
it
ches a
nd
f
ree
w
heeli
ng
diodes.
Fig
ure
4. Ci
rcui
t gr
a
ph of th
e
pro
po
se
d
t
hr
ee
-
sta
ge N
-
le
vel
vo
lt
age
s
ource
inv
e
rter.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
4
,
D
ecembe
r
2020
:
1866
–
1871
1870
5.
COMP
AR
I
SI
ON
STU
DY
In
view
of
the
examinati
on
c
onve
yed
a
mon
g
t
he
pr
opos
e
d
te
ch
nique,
th
e
acc
ompan
ying
pe
rce
ptions
are
ta
ke
n.
Co
mp
a
red
to
eve
ry
one
of
t
he
pe
rspect
ives,
the
propose
d
t
hr
ee
-
sta
ge
volt
age
s
ource
in
ver
te
r
requires
fe
we
r
powe
r
gadgets
segme
nts
a
nd
l
ess
siz
e
with
lo
w
volt
age
ta
kin
g
car
e
of
pr
es
su
re
T
he
n
a
gai
n,
the
vo
lt
age
a
nd
c
urren
t
exa
min
at
ion
s
of
t
he
f
or
ce
portions
influ
e
nce
the
cost
a
nd
a
ff
ir
mati
on
of
the
vo
lt
age
so
urce
i
nv
e
rter
.
T
olerati
ng
th
at
al
l
fo
rc
e p
art
s
ha
ve
a
co
mpa
rab
le
c
urre
nt
r
at
ing
w
hic
h
is t
hen
a
ssesse
d
c
urrent
of
the
st
or
e
(
I
L),
the
vo
lt
age
exa
minati
ons
of
these
fr
a
gme
nts
de
pend
upon
the
sig
nifi
cance
of
DC
volt
ag
e
su
ppli
es,
volt
age stre
ss,
a
nd s
tructu
re
of the
inv
e
rter.
Con
si
der
i
ng
th
at
al
l
in
ver
te
rs
ha
ve
a
co
mp
a
rab
le
data
DC
-
inter
face
w
hich
a
scen
ds
to
(N
–
1)
V
dc
.
The
pro
pose
d
i
nv
e
rter
is
e
xpe
ct
ed
t
o
pass
on
a
yield
powe
r
of
P
out=
1900
WATTS.
3
-
sta
ge
co
urse
of
act
ion
R
-
L
(
23ohm
–
3
mil
li
hen
try/P
ha
se)
in
sta
r
a
ffi
li
at
ion
is
us
e
d
as
a
sto
re.
Th
e
amaze
d
DC
-
associat
e
is
set
tl
ed
as
Vd
c=
75V
,
2Vdc=15
0V,
a
nd
Fix
=
4
V
dc
=
300V
an
d
t
he
pro
po
s
ed
tran
spor
te
r
bala
nce
pro
cedure
at
Mo
dula
ti
on
ind
e
x=1
is
e
xe
cuted
t
o
make
the
fitt
ing
tra
din
g
ent
rywa
y
si
gn
al
s
.
T
hr
ee
e
xtra
ordina
ry
sorts
of
se
mico
nduct
or
par
ts
a
re
pick
ed
to
colle
ct
the
pr
o
pose
d
inv
e
rter
c
on
t
r
ol
ci
rc
uit
as
fo
ll
owin
g:
I
nsula
te
d
gate
bip
ola
r
transisto
r(H
GT
G20
N60B3D
)
.600
V/40
A
f
or
t
he
t
wo
-
le
vel
Bridg
e
a
nd
C
H
B
switc
he
s,
I
G
BT
(
IRG
4BC4
0W)
600
V/
20
A
for
bid
i
recti
onal
switc
hes
,
a
nd
Diode
(R
HRP15
40)
44
0
V/12
A
f
or
introd
uced
diodes
in
bid
irect
io
nal s
witc
hes
a
nd fre
ewh
eel
in
g di
odes.
Table
2.
C
omp
ariso
n of i
nvert
ers wit
h
the
pr
opos
e
d
i
nv
e
rter
Top
o
lo
g
y
Clamped
Dio
d
es
Fly
in
g
Cap
acito
rs
Cas
caded
H
-
b
ridg
e
Prop
o
sed
Po
wer
Se
m
ico
n
d
u
cto
r
Switch
es
4
8
S
4
8
S
4
8
S
16S
Clamped
Diod
es
t
h
ree
p
h
ases
8
0
0
12
DC b
u
s cap
acito
r
8
8
4
3
Balan
cin
g
capacito
rs
0
28
0
0
Vo
ltag
e un
b
alan
ce
Av
erage
Hig
h
Very sm
all
Sm
all
6.
CONCL
US
I
O
N
In
this
pa
per
,
a
novel
co
ntr
ol
sy
ste
m
pro
per
for
hi
gh
force
l
ow
tra
di
ng
repea
t
sixtee
n
swi
tc
hes
three
-
ph
a
se
nin
e
-
le
ve
l
inv
e
rter
is
intr
oduce
d.
So
as
to
li
mit
th
e
exc
ha
ng
i
ng
ga
dg
et
s
di
ver
se
volt
age
sourc
es
a
s
desig
ne
d
by
co
nn
ect
ci
rc
uits
a
nd
cl
as
ped
by
t
he
di
od
e
.
Alon
g
t
hese
li
nes,
t
he
pro
pose
d
t
opol
ogy
br
in
gs
about
a
de
crease
in
est
ablishme
nt
te
rr
it
ory
an
d
c
os
t.
The
ce
ntr
al
rec
urren
ce
adjustme
nt
wa
s
easi
ly
util
iz
e
d
a
n
d
dem
onstrat
ed
high
ve
rsati
li
ty
and
ease
i
n
co
ntr
ol.
Like
wise
,
the
pro
pose
d
sy
ste
m
was
co
nn
ect
e
d
with
N
-
le
vel
with
diff
e
ren
t
proce
dures.
Th
e
pro
posed
t
opology
was
co
nt
rasted
a
nd
the
var
i
ou
s
ty
pes
of
meth
ods
in
w
riti
ng
from
va
rio
us
pe
rsp
ect
ive
s.
As
pe
r
t
he
e
xa
minati
on
resu
lt
s,
the
pro
po
se
d
topolo
gy
re
qu
ir
es
a
le
sse
r
nu
mb
e
r
of
powe
r
diodes,
IG
BTs
,
dr
i
ver
ci
rcu
it
s,
a
nd
D
C
volt
age
s
our
ces.
T
he
i
ntr
oductio
n
preci
sion
of
t
he
pro
pose
d
sixtee
n
s
witc
he
s thr
ee
-
ph
ase
ni
ne
-
le
vel i
nv
e
rt
er
was
c
onfirm
ed
th
r
ough the
M
A
TLAB
r
ec
r
eat
ion
.
REFERE
NCE
S
[1]
Mohs
en
Alee
n
ejad,
Seyyedmahd
i
Jaf
ari
shiad
eh,
Hami
d
M
ahm
ou
di,
Rez
a
Ahmad
i,
“Re
du
ce
d
nu
mbe
r
of
auxi
l
ia
r
y
H
-
bridge
power
ce
l
ls
for
post
-
fa
ult
oper
at
ion
o
f
thre
e
ph
ase
c
asc
ade
d
H
-
bridg
e
i
nver
te
r
,
”
I
ET
Po
wer
El
e
ct
ronics
,
v
ol.
12
,
n
o
.
11
,
p
p.
2923
-
2931
,
A
ug.
2019
.
[2]
M.
Selva
per
u
mal,
D.
ki
ruba
kar
an
,
“PV
Based
As
ymm
et
r
ical
Casc
ade
Thr
ee
Phase
Nine
Le
v
el
Mul
ti
L
eve
l
Inv
erte
r
Fed
Induc
t
ion
M
otor,
”
Int
ernati
o
nal
Journal
of
E
ngine
ering
and
Adv
anc
ed
Te
chn
ology
,
vol
.
8
,
no
.
6,
2019.
[3]
Nira
j
Rana,
Mukesh
Kumar
,
Arn
ab
Ghos
h,
Subra
ta
B
ane
r
jee.
"A
Novel
In
te
rl
ea
v
e
d
Tri
-
State
Boos
t
Conver
te
r
with
Lowe
r
R
ipple
a
nd
Improv
ed
Dynamic
R
esponse,
”
I
EE
E
Tr
ansacti
ons
on
Indu
strial
El
e
ct
ronic
s
,
v
ol
.
65,
n
o
.
7
,
pp.
5456
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5465
2
018,
[4]
R.
B
arzega
rkho
o,
M
.
Moradz
ad
eh,
E
.
Z
am
ir
i,
H.
Mad
adi
Koja
badi
and
F.
Bl
a
abj
erg
,
“
A
New
Boost
S
witc
h
e
d
-
Capa
c
it
or
Multi
le
ve
l
Conv
ert
e
r
with
Redu
ce
d
Circ
uit
Dev
ic
es
,
”
in
I
EEE
Tr
an
sacti
ons
on
Po
wer
E
le
c
troni
cs
,
v
ol.
33
,
n
o
.
8
,
pp
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6738
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6754
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18.
[5]
A.
Ta
ghv
aie,
J.
Adabi
and
M.
Rezane
j
ad,
“
A
Self
-
Ba
la
nc
ed
Step
-
Up
Multi
l
e
vel
Inv
ert
e
r
Bas
ed
on
Sw
itched
-
Ca
pacitor
Stru
cture,
”
IE
EE Tr
ansacti
ons on Pow
er
Elec
troni
cs
,
v
ol.
33
,
no
.
1
,
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R.
Shalc
h
i
Alish
ah,
S.
H
.
Hos
seini
,
E
.
Bab
aei,
M
.
Sabahi
and
G.
B.
Ghare
hp
et
i
an
,
“
New
High
St
e
p
-
Up
Multi
le
v
el
Convert
er
Topo
l
ogy
with
Self
-
V
olt
ag
e
B
al
an
ci
ng
Abil
i
ty
and
Its
Optim
izati
o
n
An
al
ysis,
”
in
IE
EE
Tr
ansacti
ons
on
Industrial
E
le
c
tronic
s
,
vo
l. 64, n
o.
9
,
pp
.
7060
-
7
070,
2017
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[7]
Kumar
,
G
K
Na
vee
n,
and
Yash
Pal
,
“
A
new
sw
i
tc
hing
sch
em
e
f
or
fu
el
c
el
l
supp
orte
d
red
u
ce
d
s
witc
h
thr
ee
phas
e
mul
tilevel
inve
r
te
r
topol
og
y
,
”
2015
Inte
rnat
io
nal
Conf
ere
nc
e
on
Ene
rg
y
Po
wer
and
Env
ir
onment
Tow
ards
Sustainabl
e
Gr
owth
(ICE
PE
)
,
pp
.
1
-
4
,
2015
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
A narr
ative
3
-
phas
e
9
-
le
vel
voltage
s
ou
rce
invert
er (
M
. Se
lv
ap
er
umal
)
1871
[8]
J.
Li
u,
J
.
Wu
a
nd
J.
Ze
ng,
“Sy
mm
et
r
ic/As
ymmetric
Hybrid
Multi
l
eve
l
Inve
rt
ers
Inte
gra
ti
ng
Sw
i
tc
hed
-
C
apa
c
it
or
Te
chn
ique
s,
”
I
EE
E
Journal
of
Eme
rging
a
nd
Selec
te
d
Topics
in
Pow
e
r
El
e
ct
ronics
,
v
ol.
6
,
n
o.
3,
pp.
1616
-
1626
,
2018.
[9]
S.
Lee,
“
Singl
e
-
Stage
Sw
itched
-
Capa
c
it
or
Modu
le
(S3CM
)
Top
ology
for
C
asc
a
ded
Mult
il
ev
el
I
nver
te
r
,
”
IEEE
Tr
ansacti
ons on Power
E
le
c
troni
cs
,
v
ol
.
33
,
n
o
.
1
0,
pp
.
8204
-
820
7,
2018
.
[10
]
Hos
sein
Ardi,
Ali
Aja
mi
,
Meh
ra
n
Sabahi
,
“
A
no
vel
high
st
ep
-
up
DC
–
DC
conve
rte
r
with
cont
inu
ous
input
cur
ren
t
int
egr
at
ing
coup
le
d
indu
ct
or
for
ren
ewa
bl
e
en
er
gy
appl
i
ca
t
ions,
”
IEEE
Tr
ansacti
ons
on
Industrial
Elec
tronic
s
,
v
ol.
65
,
n
o
.
2
,
pp
.
1306
-
1315
,
20
17.
[11
]
Mojta
ba
Forouz
esh,
Yam
P.
S
iwakot
i
,
Sam
an
A.
Gorji
,
Fre
de
Bl
aa
bj
erg
,
Brad
L
ehm
an
,
“
Step
-
up
DC
–
D
C
conve
rt
ers:
a
c
ompre
hensiv
e
r
evi
ew
of
vo
lt
a
ge
-
boosting
t
echnique
s,
topo
lo
gie
s,
and
appli
ca
t
ions,”
IEEE
transacti
ons on power e
l
ec
troni
c
s
,
v
ol.
32,
n
o.
12
,
pp
.
9143
-
9178
,
2017.
[12
]
Minh
-
Khai
Ngu
yen,
Truong
-
Du
y
Duong,
Youn
g
-
Cheol
Li
m
,
“
Sw
it
che
d
-
c
apaci
tor
-
base
d
du
al
-
s
witc
h
h
igh
-
boost
DC
–
DC c
onver
t
er,
”
IE
EE t
rans
act
ions o
n
power
el
e
ct
ronics,
v
ol
.
33,
n
o
.
5
,
pp
.
41
81
-
4189,
2017
.
[13
]
Sathya
n,
She
la
s,
H.
M.
Su
rya
wa
nshi,
Maka
ra
nd
Sudhakar
Ballal,
and
Amar
de
ep
B.
Shitol
e
,
“
Soft
-
sw
it
chi
ng
DC
–
DC
conve
rt
er
fo
r
distri
bu
te
d
en
e
rgy
source
s
wi
th
high
step
-
up
vol
ta
ge
c
apa
bi
li
ty
,
”
IEE
E
Tr
ansacti
o
ns
on
Industrial
El
e
ct
ronics
,
v
ol
.
62,
n
o.
11,
pp.
7
039
-
7050,
2015
.
[14
]
K.
I.
Hw
u
,
W
.
Z.
Ji
ang,
L.
C
.
Yang.
"
A
novel
vol
ta
ge
-
boo
sting
conve
r
te
r
with
leaka
ge
in
duct
an
ce
ene
rgy
rec
yc
li
ng
,
”
201
5
9th
Inte
rnat
i
onal
Conf
ere
nc
e
on
Powe
r
Elec
troni
cs
and
ECCE
Asia
(IC
PE
-
ECCE
Asia
)
,
pp.
1297
-
1302
2
015.
[15
]
P.
Sung
-
Jun
et
al.
,
“A
n
ew
sin
gle
-
phase
f
ive
-
l
e
vel
PWM
inv
erter
em
ploy
ing
a
dea
dbe
at
con
trol
sche
me,”
IE
EE
Tr
ansacti
ons on power e
l
ec
troni
c
s
,
v
ol. 18,
n
o.
3,
pp.
831
–
843
,
20
03.
[16
]
Mekhil
ef
and
A.
Masaoud,
“Xi
linx
FP
GA
base
d
mul
tilevel
PWM
single
ph
ase
in
ver
te
r
,
”
2006
IE
EE
In
te
rnat
ional
Confe
renc
e
on
I
ndustrial
Techno
logy
,
pp.
259
–
26
4,
2006
.
[17
]
C.
Klumpn
er
an
d
F.
B
la
ab
je
rg
,
“Using
rev
erse
-
bloc
king
IGBTs
in
power
converte
rs
for
ad
justable
-
spee
d
driv
es,
”
IEE
E
Tr
ansacti
o
ns on
Industry A
ppli
cations
,
v
o
l.
42,
n
o
.
3
,
pp
.
80
7
–
816,
2006
.
[18
]
E.
A
.
Mahrous
e
t
al
.
,
“
T
hre
e
-
pha
se
three
-
l
eve
l
vo
lt
ag
e
sourc
e
inv
ert
er
with
low
s
witc
hing
fre
qu
e
ncy
bas
ed
on
th
e
two
-
le
ve
l
inv
erte
r
topol
ogy
,
”
IET
Elec
tri
c Powe
r
Appl
ic
a
ti
ons
,
v
o
l.
1
,
n
o
.
4
,
pp
.
63
7
–
641,
2007
.
[19
]
E.
A.
M
ahr
ous
and
S.
Mekhi
lef,
“De
sign
and
im
plementat
ion
of
a
mu
lt
i
l
ev
el
thre
e
-
phase
inv
ert
er
w
it
h
l
ess
sw
it
che
s a
nd
lo
w qut
put
vo
lt
ag
e
distort
ion
,
”
Jou
rnal
of Powe
r
Elec
troni
cs
,
v
o
l. 9,
n
o.
4,
pp.
593
–
6
03,
2009
.
[20
]
H.
W.
Ping,
N
.
A.
Rahim,
and
J.
Jam
al
udin
,
“N
ew
three
-
phase
mul
tilevel
inve
rt
er
with
share
d
p
ower
sw
it
che
s
,
”
Journal
of
Power
El
e
ct
ronics
,
v
o
l.
13
,
n
o
.
5
,
pp
.
7
87
–
797,
2013
.
[21
]
S.
Suros
o
and
T
.
Noguchi
,
“Mult
ilevel
cur
r
ent
wave
form
g
ene
r
at
ion
using
indu
ct
or
ce
l
ls
and
H
-
bridge
cur
ren
t
-
source
inv
erter
,”
IEE
E trans
act
io
ns on
power
el
e
c
tronic
s
,
v
o
l. 27,
n
o.
3
,
pp
.
1090
–
1098,
2012
.
[22
]
M.
F.
Kanga
r
l
u
and
E
.
B
abaei
,
“A
gen
erali
ze
d
ca
sc
ade
d
mul
tilevel
in
ver
te
r
using
s
eri
es
connect
ion
of
submult
ilevel i
n
ver
te
rs,
”
I
EEE
tr
ansacti
ons on
po
wer
elec
troni
cs
,
v
ol.
28
,
n
o
.
2
,
pp
.
625
–
636
,
2013
.
[23
]
C.
Govind
araju
and
K.
B
aska
r
an,
“
Eff
icien
t
s
eque
nt
ia
l
sw
it
ch
ing
hybr
id
-
mod
ula
ti
on
te
chn
iqu
es
for
c
asc
ad
ed
mul
tilevel
inve
rt
ers,
”
IEEE
Tr
ansacti
ons on Pow
er
Elec
troni
cs
,
v
ol.
26
,
n
o
.
6
,
pp
.
1639
–
1648,
201
1.
[24
]
A.
Nam
i
et
al.
,
“
A
hybri
d
ca
sc
ad
e
conv
erter
topo
logy
with
seri
es
-
conne
c
te
d
symm
et
ri
ca
l
and
asym
me
trica
l
d
iode
-
cl
a
mpe
d
H
-
br
idg
e
c
el
ls
,
”
IEEE
tr
ansacti
ons on
po
wer
elec
troni
cs
,
v
ol.
26
,
n
o
.
1
,
pp
.
51
–
65
,
2011
.
[25
]
S.
Mekhi
le
f
et
al.
,
“Digi
t
al
co
ntrol
of
thr
ee
p
hase
three
-
stag
e
hybrid
mul
t
il
e
vel
inv
ert
er
,
”
I
EE
E
Tr
ans.
Ind
.
El
e
ct
ron.
IEEE T
rans
act
ions o
n
Industrial
Infor
matic
s
,
vo
l. 9, n
o.
2
,
pp
.
719
–
72
7,
2013
.
[26
]
J.
Mathe
w
et
al.
,
“A
hybrid
multi
le
ve
l
inve
r
te
r
sy
stem
base
d
on
d
odec
agon
al
spa
c
e
vectors
for
medium
voltage
IM
drive
s,”
IE
EE t
r
ansacti
ons on
po
wer
elec
troni
cs
,
vol.
28
,
no
.
8
,
pp
.
3723
–
3732
,
20
13.
BIOGR
AP
H
I
ES
OF
A
UTH
ORS
M.Sel
vape
ru
ma
l
has
done
her
B.
E
E
EE
fro
m
Madra
s
Univer
sity
,
in
th
e
ye
ar
20
02
and
M.E
i
n
Pow
er
El
e
ct
roni
cs
and
Industr
ial
Drive
s
fro
m
S
at
hyab
am
a
Univ
ersit
y,
Tamil
Na
du
in
th
e
y
ea
r
2005.
He
is
by
and
by
a
r
ese
arc
h
Schol
ar
at
Sathy
aba
m
a
Univer
sity
Chenn
ai
,
Indi
a.
His
exa
m
in
ation
in
tr
igue
inc
orpor
at
e
s
Pv
Based
As
ymm
et
r
ical
C
asc
ade
Thr
ee
Pha
se
Nine
Le
v
el
Multi
L
evel
Inv
e
rte
r
Fed
Induc
ti
o
n
Motor.
D.
Kiruba
kar
an
has
gott
en
his
P
h.
D.
from
Anna
Univer
sity
in
2
010
and
an
M.E
.
Degre
e
fro
m
Bhara
th
ida
san
Univer
sity
in
200
0.
His
te
rr
it
ory
of
int
r
igue
is
A
C
-
AC
conve
rt
er
s
for
a
ccept
an
ce
warm
ing,
non
-
tr
adi
ti
on
al
v
it
a
li
ty
source
s.
By
an
d
by
cont
rol
li
ng
in
excess
of
ten
expl
ora
ti
on
rese
arc
h
ers
at
d
iffe
ren
t
Univer
s
it
ie
s
and
h
as
di
stribut
ed
in
excess
of
20
p
ape
r
s
in
the
f
il
ed
J
ourna
ls.
He
ha
s
ta
ken
an
in
te
r
est
as
a
keynote
spea
ke
r,
and
a
s
a
com
m
ent
a
to
r
in
nu
me
rous
Inte
rna
ti
ona
l
ga
t
her
ings.
He
h
as
15
yea
rs
of
sho
wing
expe
ri
ence
and
by
and
by
he
is
Profess
o
r
and
Hea
d
of
EEE,
St
.
Jos
eph‟
s
I
nstit
ute of Te
chn
ology,
Ch
enna
i
–
119.
Evaluation Warning : The document was created with Spire.PDF for Python.