In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
2, June
2
01
9, pp.
852~
8
5
9
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
2.pp
8
52-
85
9
852
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
A nine-l
evel hybrid
current
source inverter using common-
em
itter topol
ogy and inductor-cell
Su
ro
s
o
1
, D
aru
Tri N
u
groh
o
2
,
Tosh
ih
iko N
ogu
ch
i
3
1,
2
Dep
a
rt
m
e
nt
o
f Elect
ri
cal
E
ngineerin
g, J
end
e
ral S
o
e
d
irm
a
n
Un
iver
s
i
t
y
,
Indo
nesia
3
De
pa
rtme
n
t
o
f
Ele
c
t
ric
a
l
a
nd
El
e
c
t
ro
nic
s
Eng
ine
e
ring
,
Shiz
uo
ka
Un
iversit
y
, Japan
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
Ju
l
3
1,
201
8
Re
vise
d N
ov
11,
201
8
A
c
c
e
pte
d
F
eb 6,
2019
A
d
i
ff
erent
c
i
rcui
t
st
ruct
ure
o
f
n
ine-l
e
vel
cu
rrent
s
ou
rce
pow
e
r
inverter
i
s
pres
ent
e
d
and
di
scus
sed
in
t
h
i
s
m
a
n
u
scri
pt.
Th
e
prop
os
ed
t
opolo
gy
i
s
based
on
t
he
c
om
m
on-emitt
er
i
nv
ert
e
r
t
o
p
o
l
ogy
e
q
u
i
p
p
e
d
w
i
t
h
a
n
in
d
u
ct
or-cell
c
i
rc
uit.
T
h
e
c
omm
o
n
-
e
m
it
te
r
i
n
v
e
rte
r
w
or
ks
a
s
th
e
ma
in
i
nv
e
r
te
r
c
ircuits
d
e
l
i
v
e
r
i
n
g
a
t
h
r
e
e
-
l
e
v
e
l
A
C
c
u
r
r
e
n
t
w
a
v
e
f
o
r
m
.
T
h
e
i
n
d
u
c
t
o
r
-
c
e
l
l
c
i
r
c
u
i
t
pro
d
u
ces
t
h
e
i
n
t
erm
e
di
ate
ou
tp
u
t
c
urrent
l
ev
els
fo
r
ni
ne-lev
el
cu
rren
t
o
u
t
put
wa
ve
fo
rm
.
Prop
ortion
a
l
in
te
gra
l
c
u
rrent
c
on
trol
le
r w
a
s
a
p
plied
to
r
egu
l
at
e th
e
curren
t
s
tream
ing th
ru
t
he
i
nd
uctor-cell
.
M
ult
i
t
rian
gu
lar
carr
ier si
gnal
s
based
si
nu
soidal
puls
e
w
idth
m
od
u
l
atio
n
m
e
t
h
o
d
w
a
s
u
t
i
l
i
z
e
d
t
o
o
b
t
a
i
n
a
l
o
w
e
r
wav
e
f
o
rm
d
is
to
rti
on.
T
he
p
ro
po
se
d
n
i
n
e
-level
i
nv
erter
circu
it
w
as
t
est
e
d
and
exam
i
n
ed.
T
h
e
tes
t
r
esu
lts
v
erif
ied
t
h
at
t
he
n
ew
n
in
e-lev
e
l
in
v
erter
ci
r
c
uit
wo
rked
w
ell
prod
ucin
g
a
ni
ne-l
evel
c
u
r
ren
t
w
a
v
ef
orm
with
l
ess
l
ow
-
f
r
equ
e
ncy
harm
on
ic
c
o
m
pon
ents.
K
eyw
ord
s
:
Com
m
on-em
itt
er
inverte
r
Cur
r
ent-so
urc
e
c
onver
t
er
Phot
o
v
o
lta
ic
s
Po
wer
g
r
i
d
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Su
r
o
so
,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
Eng
i
ne
eri
ng,
Jen
d
er
al S
oedi
rm
an U
nive
rsit
y,
Jl
.
Ma
yje
n
S
un
gk
o
no km
.
5, Pur
b
a
lin
gga
, Ja
w
a
Tengah,
Indo
ne
sia.
Em
ail:
sur
o
so.
t
e.uns
oed
@
gm
ail.c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
B
a
s
i
c
a
l
l
y
,
elec
tric
a
l
p
ower
c
an
b
e
c
l
a
s
ifi
e
d
in
to
t
wo
m
ai
n
form
s
,
i
.
e
.
D
C
a
n
d
A
C
p
o
w
e
r
.
I
n
m
a
n
y
ca
se
s, t
he
D
C pow
e
r
i
s sim
p
le
r t
h
a
n
the AC
power because
o
f
its
cha
rac
t
e
r
istics.
Tr
a
nsmit
t
i
n
g
o
f
D
C
po
w
e
r i
s
als
o
s
i
m
p
l
er
t
han
the
A
C
p
ow
er
[
1].
T
h
e
r
e
a
r
e
not
p
he
n
o
m
e
na
s
uc
h
as
s
kin
e
f
fe
ct,
o
s
ci
lat
i
on,
o
r
v
o
l
t
a
g
e
un
ba
lanc
e
b
e
t
w
een
phase
s.
F
urther
mor
e
,
there
is
no
r
e
a
c
t
a
n
ce
p
r
op
erty
o
f
t
h
e
co
nduc
t
o
r
in
t
h
e
D
C
p
o
w
er
syste
m
.
The
D
C
p
ow
er
m
ay
b
e
ge
nera
te
d
b
y
a
D
C
p
o
w
e
r
ge
nera
t
i
o
n
syst
e
m
s
uch
a
s
D
C
ge
ne
rat
o
r
m
a
c
h
ine
,
p
hot
ovo
lt
ai
c
m
o
dul
e,
a
n
d
fu
el
c
e
l
l
sy
st
em.
H
o
we
v
e
r,
c
u
rrent
ly
m
os
t
of
p
ower
l
o
a
d
s
n
e
e
d
AC
v
olt
a
g
e
o
r
A
C
curr
ent
e
v
e
n
i
n
som
e
l
oads
t
he
s
up
pl
ie
d
A
C
p
ow
er
m
u
s
t
be
p
r
o
ces
se
d
i
n
t
o
D
C
us
ing
ad
d
iti
ona
l
p
o
w
e
r
con
v
er
t
e
r
circu
i
t
s
[2-
4].
The
pow
er
c
o
nver
t
er
s
are
re
qu
i
r
ed
t
o
proc
eed
t
he
D
C
p
o
w
er
t
o
be
A
C
pow
er,
and
v
i
c
e
ve
rsa.
T
he
con
v
er
t
e
r
use
d
t
o
al
ter
the
D
C
p
ow
er
i
n
t
o
A
C
pow
e
r
i
s
c
a
ll
e
d
p
o
w
e
r
inver
t
e
r
.
I
n
t
he
pow
e
r
i
n
v
erte
r
,
t
he
fre
que
nc
y,
m
a
g
n
i
tu
de,
and
p
h
ase
an
g
l
e
va
lue
s
o
f
A
C
v
o
lta
ge
a
n
d
c
u
rre
nt
c
a
n
b
e
re
gula
t
e
d
a
s
re
quire
d.
Ma
in
ly,
the
r
e
ar
e
tw
o
c
a
t
e
g
o
r
ie
s
o
f
pow
e
r
i
nve
r
t
ers,
i
.e
.
vol
t
a
ge
s
o
u
rce
i
nver
t
e
r
a
n
d
c
urr
e
nt
s
o
u
rc
e
o
n
e
[
5-
8]
.
The
first
ty
pe
p
roce
e
d
s
a
DC
i
n
p
u
t
v
o
lta
g
e
b
ec
o
m
e
a
cer
t
a
i
n
A
C
out
pu
t
vo
lt
ag
e
.
T
he
D
C
in
put
b
u
s
u
ses
ca
paci
t
o
rs
t
o
o
b
ta
i
n
a
s
ta
ble
D
C
i
n
put
v
ol
ta
ge.
H
e
nce,
s
h
o
r
t
c
i
r
c
u
it
co
n
d
i
t
i
o
n
is
p
r
o
hi
bi
te
d
i
n
t
h
i
s
t
ype
o
f
in
verter
,
as
i
t
w
i
l
l
c
a
u
se
l
arg
e
c
urren
t
t
ha
t
wil
l
d
am
age
t
h
e
i
n
v
e
r
ter
c
i
r
c
uits
[
9,
1
0].
In
t
h
e
s
e
c
o
nd
i
nve
r
t
er
t
y
p
e
,
th
e
p
o
w
er
i
nv
ert
e
r
t
r
a
n
sfo
r
ms
t
h
e
D
C
i
nput
c
u
r
re
nt
i
nto
a
d
es
ired
A
C
curr
en
t.
T
hi
s
i
n
ver
t
e
r
u
ti
lize
s
pow
er
i
nd
uc
tor
to
g
ene
r
a
t
e
a
st
a
b
l
e
D
C
i
n
p
u
t
c
urre
n
t
.
D
i
ffe
rent
w
i
t
h
the
vol
ta
ge
s
o
u
r
ce
t
ype
i
nver
t
e
r
,
i
n
t
h
i
s
i
n
v
e
rt
e
r
t
y
p
e
a
n
o
p
e
n
c
i
rcui
t
co
ndi
tion
i
s
f
o
r
bi
d
d
e
n
,
b
ecau
s
e
a
l
ar
ge
v
ol
ta
ge
c
ha
nge
w
il
l
ha
p
p
e
n
i
n
the
in
duc
t
o
r
tha
t
m
ay
d
es
troy t
h
e
circ
u
i
ts [
1
1
, 12
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
A
nine
-
l
eve
l hy
br
id c
u
rr
e
n
t
sourc
e
i
n
v
e
rte
r
u
s
i
ng com
m
o
n
-
e
m
i
t
t
er t
o
p
o
l
ogy
… (
Sur
os
o)
85
3
I
n
o
r
d
er
t
o
obt
a
i
n
hi
gher
p
o
w
er
o
f
i
n
ver
t
e
r
c
ir
cu
its,
a
m
u
lt
ile
v
e
l
inve
r
t
e
r
h
a
s
b
ee
n
i
n
tr
od
uc
e
d
.
This
m
u
lti
le
ve
l
i
n
ve
rter
g
ener
ates
a
m
ultis
tep
A
C
o
u
t
p
u
t
w
a
v
e
f
orm
fr
om
a
s
i
n
g
l
e
or
m
ul
t
i
D
C
i
n
p
u
t
p
ow
e
r
[
13-
16]
.
Whe
n
t
he
i
n
p
u
t
p
o
w
e
r
is
a
s
ing
l
e
or
m
ult
i
pl
e
D
C
v
ol
ta
ge
s
o
u
r
ce
s
a
n
d
th
e
out
pu
t
i
s
a
m
ult
i
s
te
p
AC
vo
l
t
age,
t
he
p
o
w
er
i
nve
r
t
er
i
s
calle
d
a
s
m
ul
t
i
le
ve
l
v
o
lta
ge
s
ou
r
ce
in
ver
t
e
r
[
1
7
,
18]
.
I
n
c
on
t
r
ast,
w
he
n
t
h
e
D
C
in
p
u
t
p
o
w
e
r
is
a
s
in
g
l
e
or
m
ult
i
p
l
e
D
C
c
ur
r
e
nts
a
n
d
the
ou
tpu
t
wa
v
e
form
i
s
a
mu
ltis
tep
AC
c
u
rrent,
th
e
in
ver
t
e
r
i
s
ca
ll
ed
a
s
mul
t
ile
v
e
l
c
u
r
r
ent
so
ur
ce
i
nve
rter
c
irc
u
i
ts
[
19-
22]
.
I
n
s
t
ea
d
o
f
h
ig
h
e
r
pow
e
r
c
a
p
a
b
i
l
i
t
y
,
a
be
tte
r
ou
t
p
u
t
w
ave
f
or
m
c
a
n
be
p
r
o
d
u
c
e
d
usi
ng
m
u
l
til
eve
l
i
nver
t
e
r
cir
c
ui
t
s
[
23]
.
Ref
er
e
n
ce
[
24]
a
nd
[2
5]
p
r
o
p
o
se
d
a
bas
i
c
t
h
r
e
e-
leve
l
c
u
r
r
e
nt
s
o
ur
c
e
i
nve
r
t
er
c
alle
d
as
t
hr
ee
-
l
e
v
e
l
c
o
mm
on-
em
it
te
r
c
u
r
r
e
n
t
s
our
c
e
i
nve
r
t
er
(
CECS
I
)
,
beca
use
of
its
c
o
mmo
n
-
emit
t
e
r
c
o
nf
igu
r
a
t
ion
.
T
his
th
re
e-
leve
l
i
nver
t
er
c
ir
c
u
it
s
i
s
f
ig
ur
ed
i
n
F
i
gur
e
1.
F
our
u
nid
i
r
e
cti
ona
l
co
n
t
ro
lle
d
sw
itc
he
s,
i
.e
.
T
1
,
T
2
,
T
3
a
n
d
T
4
,
w
i
t
h
c
om
mon-
em
i
t
t
e
r
c
o
n
n
ec
ti
o
n
a
r
e
r
equir
e
d
i
n
t
his
c
i
r
c
u
i
t
to
de
l
i
ve
r
a
thr
e
e
-
leve
l
o
u
t
p
ut
c
u
r
r
e
nt
w
av
e
f
or
m
us
in
g
tw
o
D
C
c
ur
r
e
nt
s
o
u
r
c
es
.
To
g
ener
ate
a
ni
nele
ve
l
cur
r
ent
w
ave
f
orm
,
r
efere
n
ce
[
2
6
]
d
i
scuss
e
d
t
h
e
u
s
e
of
in
d
u
ct
or ce
l
l
s
a
nd
a
s
o
l
e thre
e
-
le
ve
l CE
C
S
I as
d
is
pla
y
e
d
in Fig
u
r
e
2
.
T
wel
v
e
c
o
nt
rol
l
e
d
swi
t
c
h
e
s
w
e
r
e
ne
ed
e
d
in
t
h
i
s
n
i
ne-
l
e
v
e
l
i
n
v
er
ter
c
i
r
c
ui
t
s
.
A
n
o
t
her
appr
oa
ch
w
a
s
p
r
o
p
ose
d
i
n
r
e
f
e
r
e
nce
[2
7]
a
nd
[
2
8
]
,
w
her
e
m
ul
ti
D
C
c
ur
r
e
nt
m
odule
s
a
r
e
c
onn
ecte
d
t
o
t
h
e
ba
si
c
t
h
r
e
e-
leve
l
com
m
o
n-
em
itt
er
i
nver
t
e
r
.
Th
is
r
esea
r
c
h
deve
lop
a
n
i
n
e
l
eve
l
i
n
v
er
te
r
c
i
r
c
ui
t
s
u
s
i
n
g
c
om
b
ina
t
ion
of
i
n
d
u
c
t
or-
cell
a
n
d
D
C
c
u
r
r
e
nt
m
odu
le
c
i
r
cui
t
s
co
n
n
e
c
ted
t
o
t
he
m
a
i
n
t
h
r
e
e-
leve
l
com
m
o
n
e
m
it
te
r
circ
ui
t
s
.
Usin
g
t
h
is
n
e
w
n
in
e
-
leve
l
in
ver
t
e
r
,
sw
i
t
c
h
i
n
g
de
vi
c
e
s
a
n
d
the
p
o
w
e
r
sup
p
lie
s
of
d
r
i
vi
n
g
c
ircu
it
s
c
oul
d
be
s
imp
l
i
f
ie
d.
Basic
p
ri
nci
p
le
ope
ra
ti
o
n
o
f
t
h
e
c
i
rcu
its
w
a
s
d
isc
u
sse
d.
T
he
n
i
n
e-le
ve
l
in
ver
t
e
r
ci
rc
ui
ts
w
as
t
e
s
t
e
d
an
d
e
x
a
m
in
ed
u
si
ng
co
mp
ut
e
r
si
m
ul
a
tio
ns.
F
i
gur
e
1.
B
a
s
ic
t
hr
ee
-
l
eve
l
C
E
C
S
I
[
24-
3
0
]
F
i
gur
e
2.
T
r
a
di
t
i
o
n
al
n
ine
-
le
v
e
l
i
n
ve
r
t
er
[
2
6
]
2.
PROPOSED N
I
N
E
-
LEV
EL INVERTER
C
I
RCUITS
Base
d
o
n
t
h
e
ba
sic
thre
e-le
v
e
l
c
o
m
m
on
e
m
itter
c
i
rc
u
it
con
f
ig
ura
tio
n,
a
n
e
w
n
ine-
l
e
vel
i
n
ver
t
e
r
c
i
r
c
u
its
i
s
pr
e
s
ente
d
i
n
F
i
g
ur
e
3.
T
he
c
ir
c
u
i
t
s
c
o
ns
ist
of
t
e
n
con
t
roll
e
d
s
wi
t
c
h
e
s
a
s
s
hown
i
n
t
hi
s
fi
gu
r
e
.
Th
e
c
o
n
t
r
o
lled
sw
i
t
c
h
is
c
o
nne
cte
d
i
n
se
r
i
es
w
i
t
h
a
d
i
ode
t
o
pe
r
f
or
m
a
sing
l
e
d
i
r
e
c
t
i
on
a
l
c
u
r
r
e
n
t
c
on
t
r
o
l
l
e
d
po
wer
sw
itc
h.
T
he
m
ain
in
ve
r
t
er
c
ir
c
u
it
s
c
o
nstr
ucte
d
by
si
x
con
t
r
o
l
l
e
d
sw
i
t
che
s
c
onne
c
t
e
d
i
n
c
o
mm
on-
em
itte
r
c
o
n
f
ig
u
r
at
io
n, he
n
ce
a
si
m
p
le
r
driving
circ
uits c
an be
a
p
pli
e
d
i
n
thi
s
c
i
rc
ui
ts.
The
i
nduc
to
r
c
e
l
l
c
i
r
c
ui
ts
c
o
n
s
i
s
t
of
f
our
c
ontr
o
l
l
e
d
s
w
i
tc
h
e
s,
i
.e.
T
C1
,
T
C2
,
T
C3
a
nd
T
C4
.
T
h
e
p
o
w
e
r
i
ndu
c
t
o
r
i
s
pl
ace
d
a
c
r
o
ss
thi
s
c
ell
.
U
s
i
ng
t
h
e
b
asi
c
c
h
a
rgi
ng
a
nd
d
i
s
c
h
a
r
gin
g
p
r
o
p
e
rti
e
s
of
t
hi
s
i
ndu
ct
o
r
c
e
l
l
,
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
8
5
2
–
8
59
85
4
ni
ne
leve
l
c
u
r
r
e
nt
w
a
v
e
f
or
m
w
i
l
l
b
e
gener
a
te
d
[
2
6]
.
The
ba
s
i
c
op
era
tio
ns
o
f
th
e
ci
rcui
t
s
a
re
s
ho
wn
i
n
Tab
l
e
1
.
F
u
r
t
her
m
or
e
,
F
ig
ur
e
4
is
t
he
i
nver
t
e
r
c
ir
c
u
i
t
i
nc
lud
i
ng
t
h
e
D
C
c
u
r
r
ent
c
o
ntr
o
l
c
i
r
c
ui
ts
w
it
h
D
C
i
np
u
t
i
n
duc
t
o
r
L
1
,
L
2
,
L
3
a
nd
L
4
a
n
d
co
n
t
ro
lle
d
sw
itche
s
T
L1
,
T
L2
,
T
L3
a
nd
T
L4
.
These
dc
i
nd
uc
tor
s
a
nd
sw
itc
he
s
ar
e
uti
l
i
z
e
d
to
g
e
n
er
a
t
e
t
h
e
D
C
c
ur
r
e
nts
f
o
r
inver
t
e
r
.
F
i
gur
e
3
.
P
r
op
ose
d
n
i
n
e-
le
ve
l
hybr
id
i
n
v
e
r
te
r
Tab
l
e
1.
O
per
a
t
i
o
n
m
odes
of
t
he
i
n
v
er
ter
Mode
s
T
1
T
2
T
3
T
4
T
5
T
6
T
C1
T
C2
T
C3
T
C4
I
PW
M
1
0
0
1
1
0
1
1
1
0
0
+
2
I
2
0
0
1
1
0
1
0
1
0
1
+
3
/
2
I
3
0
0
1
1
1
1
0
0
1
1
+
I
4
0
0
1
1
1
1
1
0
1
0
+
I
/2
5
1
1
1
1
1
1
1
1
0
0
0
6
1
1
0
0
1
1
0
1
0
1
-I
/
2
7
1
1
0
0
1
1
1
1
0
0
-I
8
1
1
0
0
1
1
1
0
1
0
-3
I
/
2
9
1
1
0
0
1
0
0
0
1
1
-2
I
F
i
gur
e
4.
N
ine-
le
ve
l
i
n
v
e
r
t
e
r
w
it
h
dc
c
ur
r
e
nt
c
ir
cui
t
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
A
nine
-
l
eve
l hy
br
id c
u
rr
e
n
t
sourc
e
i
n
v
e
rte
r
u
s
i
ng com
m
o
n
-
e
m
i
t
t
er t
o
p
o
l
ogy
… (
Sur
os
o)
85
5
To
r
e
g
u
l
a
t
e
th
e
curre
n
t
i
n
th
e
in
duc
tor
,
a
p
r
o
p
o
r
t
i
o
nal
i
n
t
e
gr
a
l
(
P
I)
c
ur
rent
c
on
tro
lle
r
i
s
a
p
p
l
ie
d
a
s
pr
esen
ted
in
F
i
gur
e
5.
T
he
a
m
p
l
i
t
ude
o
f
in
duc
t
o
r
-
c
ell
c
u
r
r
ent
w
as
d
eter
m
i
ned
a
s
a
h
a
l
f
of
m
a
g
nit
ude
o
f
t
h
e
m
a
in
d
c
in
put
c
ur
r
e
nt
s.
T
hi
s
i
n
d
u
c
t
or
-
c
e
ll
c
i
r
c
u
it
f
unc
t
i
o
n
t
o
cr
e
a
te
t
he
i
nt
e
r
m
e
d
i
ate
l
e
vel
s
o
f
t
h
e
nin
e
-
l
eve
l
c
u
r
r
e
nt
w
a
v
e
f
or
m
.
F
ur
ther
mor
e
,
c
a
rr
i
e
r
base
d
si
n
u
so
ida
l
m
odu
lat
i
o
n
was
ap
pl
i
e
d
t
o
g
e
n
erat
e
a
PWM
AC
c
u
r
r
e
nt
w
ave
f
or
m
w
i
th
l
e
ss
har
m
on
ic
d
is
t
o
r
t
i
on
as
s
h
o
w
n
i
n
F
i
gu
r
e
6
.
Ei
gh
t
tr
ia
n
gula
r
c
arr
i
er
s
w
e
r
e
u
se
d.
Ea
ch
c
a
r
r
i
e
r
h
as
t
he
s
am
e
f
r
eque
nc
y
b
u
t
w
i
t
h
d
i
f
f
e
r
en
t
of
f
s
e
t
v
a
l
ue.
T
h
ese
c
a
r
r
i
e
r
s
w
e
r
e
m
odula
t
e
d
b
y
a
si
ng
le
s
i
n
u
s
o
i
d
a
l
signa
l
t
o
g
en
e
r
ate
P
W
M
dr
i
v
i
n
g
signa
ls
o
f
i
n
v
e
r
ter
power
c
irc
u
i
t
s.
F
i
gur
e
5.
C
ur
r
e
nt
c
o
n
t
r
o
l
l
e
r
[
2
7
,
30]
F
i
gur
e
6.
M
o
d
u
la
t
i
on
me
th
od
[
18,
27]
3.
TE
S
T
RESULTS AND
ANAL
YS
IS
To
t
es
t
t
h
e
bas
i
c
o
p
er
atio
n
a
n
d
c
h
ara
c
ter
i
s
t
ic
o
f
th
e
new
ni
ne
-
le
vel
i
n
ver
t
er
c
ir
cu
its,
s
o
me
c
om
pu
t
e
r
sim
u
la
ti
ons
w
e
r
e
pe
r
f
or
me
d
u
s
i
ng
s
o
f
t
w
a
r
e
o
f
P
o
w
e
r
P
S
I
M
.
The
t
e
st
p
a
r
a
m
e
t
e
r
s
of
t
h
e
p
r
o
p
o
se
d
ne
w
nine
-
leve
l
i
n
ver
t
e
r
c
i
r
cu
its
a
r
e
p
r
e
s
e
nte
d
i
n
Ta
b
l
e
2.
T
he
e
n
o
r
m
it
y
of
d
c
c
u
r
r
e
nt
s
o
u
r
c
e
s
is
se
t to be 5
a
m
pe
r
e
.
F
our
dc
i
n
put
c
ur
r
e
nt
c
ir
c
u
its
w
e
r
e
con
n
ec
t
e
d
t
o
t
he
i
n
v
er
t
e
r
c
i
r
c
ui
ts
a
s
sh
ow
n
i
n
F
ig
ur
e
4.
A
s
ma
l
l
i
nd
uc
t
o
r
0.
3
mH
w
as
u
sed
fo
r
t
h
e
i
ndu
ct
o
r
-c
el
l
ci
rcu
i
t
s
.
T
h
e
fre
qu
en
cy
o
f
t
r
i
a
ngu
l
a
r
c
a
rri
ers
i
s
2
2
kHz
t
o
a
vo
i
d
t
he
n
oi
se
c
a
use
d
b
y
t
h
e
sw
itc
h
i
n
g
ope
r
a
ti
o
n
.
U
s
ing
h
i
gh
s
w
i
tch
i
ng
f
r
e
que
n
cy
,
a
sma
l
l
e
r
o
u
tp
ut
c
a
p
a
c
ito
r
fi
lt
er
(
C
f
)
si
ze
c
a
n
be
ach
ie
ve
d.
I
n
this
e
x
p
er
i
m
ent,
t
he
f
i
l
t
e
r
capa
c
i
t
or
w
as
5
µ
F.
T
h
e
i
n
v
ert
e
r
wa
s
c
o
nne
ct
e
d
t
o
an
e
l
ect
ri
c
a
l
loa
d
,
i.
e
.
pow
er
r
e
s
ist
o
r
12
Ω
and
pow
er
i
n
d
u
c
t
or
1
.
2
m
H
c
o
n
n
e
c
ted
in
s
eries.
F
i
g
u
r
e
7
i
s
t
h
e
simula
tio
n
o
u
t
p
u
t
f
ig
ur
i
ng
t
h
e
w
a
vef
o
r
m
s
of
n
i
n
e
-
le
vel
o
u
t
p
ut
c
ur
r
e
nt,
cur
r
ent
t
h
r
u
e
l
e
c
tr
ica
l
l
oa
d,
a
nd
t
he
c
a
p
a
c
it
or
f
i
l
te
r
c
u
r
r
e
nt.
H
a
r
m
oni
c
spe
c
t
r
a
o
f
t
h
is
n
ine
-
le
vel
curr
ent
wa
veform
i
s
pr
esen
ted
i
n
F
i
g
ur
e
8.
T
he
h
ig
h
e
s
t
a
mp
l
itu
de
o
f
t
h
e
l
o
w
ha
r
m
on
i
c
or
de
r
in
t
h
i
s
f
i
g
u
r
e
i
s
t
h
e
3
rd
h
ar
m
onic
c
o
mpo
n
e
n
t.
I
t
s
am
p
li
tu
de
i
s
0
.
5%,
on
l
y
.
The
har
m
on
ics
o
f
P
W
M
c
u
r
r
ent
f
l
ow
e
d
by w
a
y
of
the
c
apac
ito
r
fi
l
t
e
r
a
s
c
ur
r
e
nt
I
Cf
.
A
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
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Dr
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Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
8
5
2
–
8
59
85
6
Tabl
e 2
.
Paramet
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rs o
f in
v
e
rter
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it
s
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o
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P
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ra
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l
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m
s
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-
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(b
)
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i
gur
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8.
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a
r
monic
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r
e 9
.
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ave
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r
ms
o
f i
nduc
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r
c
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rren
t
s
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A ni
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Trans
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s
4.
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urrent
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rate
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alanc
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erm
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dia
t
e
le
ve
ls
o
f
n
i
ne-l
eve
l
c
u
rre
nt
w
avef
orm.
A
si
m
p
ler
nin
e
-le
v
e
l
i
nve
rter
c
irc
u
it
an
d m
o
re
s
tab
l
e i
n
d
u
c
t
or cu
rre
n
t
s
c
an
b
e
a
c
h
i
ev
ed
in
this new inver
t
er.
REFE
RENCES
[1]
K.
K
uroh
ane,
A
.
Uehara,
T
.
S
enjy
u,
A
.
Yo
na,
N.
U
rasak
i
,
T.
F
u
n
a
bashi,
a
nd
C
.
Kim,
“
Con
t
r
o
l
strategy
f
or
a
di
s
t
ributed
DC
p
o
w
e
r sy
s
t
em
with
renew
a
b
l
e en
e
r
gy
”,
Renewbl
e
Energy
,
v
o
l
.
3
6
,
i
ssue 1
,
p
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2-4
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r
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sco
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quel
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w
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cz,
E
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v
á
n,
R
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C.
P
or
til
l
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G
ui
sado,
Ma.
Ángeles
M
a
rtín
P
ra
ts,
J.
Ign
acio
L
e
ó
n
,
a
n
d
N.
M
oren
o-Alf
o
n
s
o,
“
P
o
wer-elect
ron
i
c
sy
stem
s
f
o
r
t
h
e
grid
i
n
t
eg
rat
i
o
n
o
f
renew
a
ble
en
er
g
y
so
urces:
a s
u
rv
e
y
”,
IEEE T
r
an
sa
c
t
io
ns
on
Ind
u
s
tr
ia
l
E
l
e
c
tron
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3
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“
B
o
ost
current
m
ult
i
leve
l
inverter
a
nd
its
app
l
i
c
a
t
io
n
on
sin
g
l
e
p
h
a
se
g
ri
d
conn
ected
p
ho
tov
o
l
t
a
i
c
s
y
st
em
,
”
IE
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Tr
ans
action
on
Po
wer
El
ectro
n
i
cs
,
vol.
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F
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rg,
Z.
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,
a
n
d
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jaer,
“P
ow
er
e
lect
roni
cs
a
s
e
f
f
icient
i
nterf
a
ce
in
d
i
s
p
e
rsed
p
o
w
er
g
en
e
r
at
ion
syst
e
m
”,
IEEE Tr
an
sactio
ns on
Po
wer Elect
ronics
,
v
o
l
.
19
,
n
o
.
5,
p
.
p
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1
1
8
4
-
11
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Sept
e
m
b
er
2
004
.
[5]
Z
H.
B
a
i
,
and
Z
.
C
.
Z
h
an
g,
“
Con
f
orm
a
ti
on
o
f
mu
ltil
evel
c
u
r
rent
s
ource
con
v
ert
e
r
t
o
p
o
lo
g
i
es
u
s
i
n
g
t
h
e
d
ualit
y
pri
n
ciple,
”
IEE
E
T
r
a
n
s
a
ctio
ns
on Po
we
r Electr
onics
,
vo
l.
23,
p
.
p
.
22
60-2
2
6
7
,
Septem
b
e
r
20
08
.
[6]
B.
P
.
M
c
G
r
a
t
h,
a
n
d
D
.
G.
H
o
l
mes,
“
Natu
ral
curren
t
b
al
ancin
g
o
f
m
u
lti
-cell
curren
t
s
o
u
rce
inv
e
rter,”
IEEE
T
r
a
n
sa
cti
o
n
s
o
n
Power
El
ectr
onics
,
v
o
l
.
23
, n
o.
3
, p
.
p
. 12
3
9
-
12
46
, May 2
00
8
.
[7]
S.
Kwak,
a
nd
H
.
A.
T
oliya
t
,
“Mu
ltilevel
converter
t
o
pology
u
si
n
g
tw
o
ty
pes
of
c
urrent
-so
u
rc
e
i
n
v
e
rters,
”
IE
E
E
Tran
sac
t
io
ns
on
I
n
d
u
c
t
ry
App
lic
a
t
ion
s
, vo
l.
42, n
o
. 6
, p
.
p
.
15
5
8
-
1
5
6
4
,
Nov
e
m
b
er/
D
ecem
ber 2
0
0
6
.
[8]
Suroso
a
nd
T
.
N
o
guchi,
“
Mult
ileve
l
current
w
avef
o
r
m
g
e
n
e
rati
on
u
s
i
ng
in
du
cto
r
cel
ls
a
nd
H
-bri
dge
c
u
rre
n
t
s
o
u
rce
invert
e
r
”,
IEEE T
r
ans
actio
ns
on
Po
wer E
l
ectron
i
cs
, vo
l
. 2
7,
issu
e
. 3,
p.p
.
1
09
0
-
10
98
,
2
0
1
2
.
[9]
D
.
H
.
L
e
e
,
a
n
d
J
.
O
h
n
,
"
A
s
i
m
p
l
e
a
n
d
d
i
r
e
c
t
d
e
a
d
-
t
i
m
e
e
f
f
e
c
t
c
o
mpens
a
tion
schem
e
i
n
PWM-VSI",
IE
EE
Tran
sac
t
io
ns
on
I
n
d
u
stry
Ap
p
lic
a
t
io
n
,
v
o
l
.
5
0
,
n
o.
5
,
p
p
.
3
0
17-3
025,
S
eptem
b
er
2014
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
852
–
8
59
85
8
[10]
L
.
C
h
e
n
,
a
n
d
F
.
Z
.
P
e
n
g
,
"
D
e
a
d
-
t
i
m
e
e
l
i
m
i
n
a
t
i
o
n
f
o
r
v
o
l
t
a
g
e
s
o
u
rce
inv
e
rters
"
,
IEE
E
T
r
an
sa
c
t
io
ns o
n
Powe
r
El
ectro
n
i
cs
,
vol.
2
3
,
no.
2
,
pp.
5
7
4
-580
,
M
arch
2008.
[11]
Y
.
G
e
n
g
,
R
.
D
e
n
g
,
W
.
D
o
n
g
,
K
.
W
a
n
g
,
H
.
L
i
u
,
a
n
d
X
.
W
u
,
“
A
n
o
v
e
r
l
a
p-t
i
m
e
c
om
p
e
nsatio
n
m
e
th
od
f
or
c
urren
t
-
so
urce
s
p
ac
e-v
ect
or
P
W
M
i
nvert
ers,”
IEEE
Tr
a
n
sact
io
n
s
on
P
o
wer
El
ectro
n
i
cs
,
Vo
lum
e
3
3
,
I
ssue
4
,
p.
p
.
3
19
2-
3
2
0
3
, Apr
i
l
2
01
8.
[12]
T. Hal
ko
s
aari, K
. Kuusel
a, an
d
H
.
T
uus
a, “Eff
ect
o
f
no
n-i
d
eali
t
i
e
s on
th
e
perf
orm
a
n
ce of
the
3
-p
hase
c
urrent
so
u
rce
PW
M
co
nv
e
r
t
e
r”,
p
r
oc.
of 20
01
IEEE 3
2
nd
A
n
n
u
a
l
P
o
wer Elect
r
o
ni
cs S
p
ecialists
Co
nf
erence
,
p.
p.
6
54
-659
,
2
0
0
1
.
[13]
N.
V
azqu
e
z,
H
.
L
opez,
C
.
H
e
rnan
dez,
E
.
Vazqu
e
z,
R
.
O
s
orio,
and
J.
A
rau,
“
A
d
i
ff
eren
t
m
u
lti
l
ev
el
c
urren
t
s
o
u
rce
in
verter”,
IEEE T
r
ans
actio
ns
on
Ind
u
s
t
ria
l
E
l
ectron
i
cs
,
vo
.
5
7
,
p.p
.
2
623
–
2
6
32,
Au
g
u
s
t
20
10
.
[14]
F
.
L
.
M
.
A
n
t
u
n
e
s
,
A
.
C
.
B
r
a
g
a
,
a
n
d
I
.
B
a
r
b
i
,
“
A
p
p
l
i
c
a
t
i
o
n
o
f
a
generalized
c
urrent
m
ult
i
leve
l
cell
t
o
c
urrent
s
ource
invert
e
r
s,”
I
EEE Transacti
ons on
P
o
wer El
ectron
i
cs
,” vo
l
.
46
,
n
o
.
1
,
p
.p
. 3
1-3
8
,
F
ebr
u
ary
19
99
.
[15]
Y.
L
.
K
a
m
e
swari
,
an
d
O.
C
.
Sekhar,
"
F
u
zzy
l
o
g
i
c
c
o
n
tro
l
l
e
d
harm
on
ic
s
up
pres
sor
i
n
c
a
s
caded
m
ul
t
ilevel
inverter
",
Int
e
rna
t
i
o
n
a
l
Jo
u
r
n
a
l of Po
wer
E
l
ectr
onics an
d
D
r
i
ve Systems
(
I
JPE
D
S)
,
p
.
p
.
303-31
0,
201
6.
[16]
S
u
r
o
s
o
,
D.
T
.
Nug
r
oh
o,
A
.
N
.
A
z
i
s,
T
.
Noguchi,
“
S
i
m
p
lif
i
ed
f
i
v
e
-lev
el
v
oltag
e
s
o
u
rce
i
nvert
er
w
ith
l
ev
el-ph
a
se-
sh
ift
e
d
carri
ers
b
a
sed
m
o
d
u
l
a
ti
on
tech
ni
que”,
Indon
esi
an Jou
r
n
a
l
of
E
l
ect
rica
l Engi
neeri
n
g
an
d Com
put
er Sci
e
nce
,
vo
l.
13,
n
o
.
2
,
2
0
19
,
p
p.
461
-46
8
,
20
19.
[17]
J.
Rod
igu
ez,
J
.
S.
Lai,
and
F
.
Z.
Peng,
“
M
u
l
t
ilevel
i
nvert
er:
a
su
r
v
e
y of
t
op
o
l
og
i
e
s,
c
on
trol
s,
a
nd
a
pp
li
cati
o
n
,” IE
E
E
Tran
sac
t
io
ns
on
I
n
d
u
str
i
a
l
Ele
c
tr
on
ic
s
,
”
v
o
l
.
4
9
,
no
.
4
,
p
.
p
.
7
24
-7
38
,
A
ug
u
s
t
2
002.
[18]
B.
W
u,
H
ig
h P
o
wer
Co
nv
ert
e
rs
a
n
d
A
C Dri
v
es
. P
i
s
cataw
ay,
NJ
: IEE
E P
r
ess
,
2
00
6
,
ch
. 1
0.
[19]
S
u
ro
so
a
nd
T
.
N
ogu
chi
,
“
A
s
i
n
g
le-p
has
e
m
ul
ti
level
cu
rrent-s
o
u
rc
e
con
v
ert
e
r
us
in
g
H-bri
d
g
e
a
nd
D
C
curr
en
t
mo
du
le
s”
,
Interna
t
i
o
n
a
l
Jou
r
n
a
l
of Po
wer
Elect
ro
n
i
cs
a
nd D
r
ive S
y
stem
(IJ
PEDS
),
v
ol.
2,
n
o
.
4
,
p.
p
.
1
65
-172,
20
14
.
[20]
S
u
ro
so,
and
T.
N
o
g
u
c
hi
.
"No
v
el H-b
ridg
e
m
u
lti
l
ev
el
c
u
rrent
-s
ou
r
ce
P
W
M
i
n
v
e
rter
w
ith
i
nd
ucto
r-cell
s
",
Co
nfer
enc
e
Pr
oceedi
n
g
s
IP
EC
,
p
.
p.
44
5
-
45
0,
2
0
1
0
.
[21]
Suroso
a
nd
T
.
Noguchi,
“
Five
-l
ev
el
c
omm
o
n-e
m
i
t
ter
invert
e
r
u
si
n
g
re
v
e
rse
-
bloc
king
I
GB
Ts”
,
TE
LKO
M
NI
KA
,
v
o
l
.
10
,
n
o.
1
,
p
.
p
.
25-32
,
2
0
1
2
.
[22]
D.
T
amil
arasi
,
a
n
d
T
.
S
.
S
iv
a
kum
aran
,
"An
a
lys
i
s
of
s
ymmetrical
and
as
ym
m
e
tri
c
a
l
c
u
rrent
s
o
u
rce
m
u
lti
l
e
v
el
inverter",
Circ
ui
ts
an
d S
y
ste
m
s
, p
.
p
.
34
69
-348
4
,
20
1
6
.
[23]
S
u
ro
so,
A.
N
.
Aziz,
and
T
.
N
oguch
i
,
"F
iv
e-level
P
W
M
i
n
v
e
rter
w
i
th
a
s
i
ngle
DC
p
o
w
er
s
o
u
rce
fo
r
DC-AC
pow
er
con
v
ersi
on
"
,
In
ter
n
a
t
i
onal Jo
urnal
of
P
o
wer
Elect
ro
n
i
cs
an
d
Dr
ive Sys
t
em
s
(
I
JPE
D
S
)
,
v
o
l.
8
,
p
.
p
.
123
0-1
237,
S
e
pt
emb
e
r
20
17
.
[24]
S
u
ro
so
a
nd
T
.
No
gu
chi
,
”
A
new
th
ree-level
curre
n
t
-s
ou
rce
PWM
i
n
v
e
rter
a
n
d
i
ts
a
pp
li
cati
o
n
for
grid
c
o
nnect
ed
po
wer
co
ndi
ti
oner”,
En
erg
y
Conversi
on
an
d
M
anag
ement
,
v
o
l
.
5
1
,
i
ss
ue
7
,
p
.
p
.
1491
-149
9,
2
0
10.
[25]
Su
roso
,
D.
T
.
N
u
g
r
oh
o,
a
n
d
Wi
na
si
s,
"
A
t
h
ree-lev
e
l
co
mm
o
n
-e
m
i
tt
er
c
u
rrent
s
o
u
rce
inv
e
rter
w
ith
redu
ced
d
ev
ic
e
cou
n
t
"
,
4t
h Inter
n
a
tio
nal Co
n
f
eren
c
e
on
Inf
o
r
m
atio
n Tech
no
lo
gy,
Co
mp
u
t
er,
a
n
d
El
ectric
a
l
E
n
g
i
neer
in
g
(
I
CIT
A
C
EE)
, p
.p
.
7
7
-
8
0
, 2
01
7.
[26]
T.
N
og
uch
i
,
an
d
S
u
ro
so
,
“
N
ew
m
ult
i
l
e
vel
current
-so
u
rce
P
W
M
i
nve
rt
er
w
ith
f
u
l
l
-
bri
dge
i
nduct
o
r
cell
s
”,
IEEJ
T
r
a
n
sa
cti
o
n
s
o
n
In
du
st
ry A
pplicati
ons
,
vol.
1
30,
no.
6
,
p
.
p
.
8
0
8
-815,
2
0
1
0
.
[27]
Suroso,
and
T.
N
oguchi
,
“
C
o
m
m
o
n-emitter
topol
ogy
of
m
ulti
le
vel
current
-S
ou
rce
p
u
ls
e
wid
t
h
m
o
du
la
ti
on
i
nv
erter
with
c
ho
pper
based
DC-cu
rrent
s
o
u
rces”,
IET P
o
wer
Elect
ro
n
i
cs
, v
ol
.
4
,
i
ssu
e
7,
p
.
p
.
7
59
-76
6
,
2
011.
[28]
T.
N
og
uchi
,
and
S
u
ros
o
,
"Revi
e
w
of
n
o
v
el
m
u
l
til
e
v
el
c
urren
t
-s
o
u
rce
i
nvert
ers
wi
th
H
-bri
dg
e
an
d
com
m
o
n-emit
te
r
bas
e
d
t
o
p
o
lo
g
i
es",
IE
EE Energy Conver
si
on
Congres
s and Exposition
, p
.p
. 4
00
6-4
0
1
1
,
2
01
0
.
[29]
K.
I
waya,
and
T
.
N
oguchi
,
“No
v
el
c
urrent
-sour
ce
multilevel
i
n
ve
rt
er
d
ri
ven
by
si
ngle
g
a
te
d
rive
p
o
w
er
s
up
ply
”
,
El
ectr
i
cal
En
gi
n
eer
ing
i
n
Ja
pan
,
v
o
l
.
1
66,
n
o
.
2
,
p.
p.
10-1
6
,
20
09.
[30]
S
u
ro
so,
D
.
T.
N
ugro
ho
and
W
i
na
s
i
s,
“
T
h
ree-lev
e
l
com
m
o
n
-
emitt
e
r
c
urrent
s
ource
pow
e
r
i
nvert
er
w
i
t
h
si
m
p
l
i
fied
d
c
curren
t
s
ource
generat
i
o
n
”,
Jo
urna
l of
E
ngin
e
er
in
g S
c
ien
ce an
d T
ech
nol
og
y
,
v
ol.
1
3
,
n
o
.
2
,
p
.
p
.
4027-4
0
3
8
,
201
8.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
A
nine
-
l
eve
l hy
br
id c
u
rr
e
n
t
sourc
e
i
n
v
e
rte
r
u
s
i
ng com
m
o
n
-
e
m
i
t
t
er t
o
p
o
l
ogy
… (
Sur
os
o)
85
9
BIBLIOGRAPHY
O
F
AUTH
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RS
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ros
o
r
eceiv
e
d
th
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g
r
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n
e
lect
rical
e
n
g
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n
eerin
g
,
f
ro
m
G
a
d
j
ah
M
ada
Un
iv
ersity,
In
do
nes
i
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in
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0
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Un
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ersit
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s
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a
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s
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t
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f
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l
ectri
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ng
in
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ni
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rs
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His
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n
t
eres
t
in
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es
s
tati
c
po
wer
conv
erters
,
and
its
app
l
i
cati
o
n
in
r
enewabl
e
e
nergy
c
o
nv
ersi
on
a
nd
di
s
t
r
ibuted
p
o
w
e
r
g
enerat
io
n.
Daru
T
ri
N
u
g
roho
r
ecei
ved
bac
h
el
or
(
B.E
ng.
)
degree
i
n
e
lect
rica
l
e
n
g
i
n
e
e
r
in
g
fr
o
m
I
n
s
t
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tu
te
Tekn
ol
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epuluh
N
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em
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v
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ect
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ko
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e
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r
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oya
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n
s
tit
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t
e
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f
T
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N
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oya,
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nd
t
h
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n
g
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a
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d
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n
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r
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s
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l
ectri
cal
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nd
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lect
roni
cs
s
yste
m
s
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n
g
i
n
eering
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r
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N
agao
ka
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ni
versity
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f
Technology,
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J
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f
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N
ational
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f
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ec
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ss
oci
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te
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e
l
ect
rical
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nd
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l
ectro
ni
cs
s
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e
m
s
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g
i
n
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994
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5
.
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s
an
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P
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f
e
s
s
o
r
a
t
Na
g
a
ok
a
Univ
e
r
si
ty
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f
Te
c
h
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lo
gy
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96
t
o
20
0
9
.
He
h
a
s
b
e
e
n
a
P
rof
e
ssor
at
S
hi
z
u
oka
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v
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y
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ince
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9.
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is
r
esearch
i
n
t
eres
ts
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re
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tatic
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ow
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co
n
v
erters
a
nd
m
ot
or
d
rives
.
D
r.
No
gu
chi
i
s
a
M
e
m
ber o
f
the
I
E
E
-
J
ap
an an
d
a Sen
io
r
M
e
mber o
f
th
e
I
E
E
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Evaluation Warning : The document was created with Spire.PDF for Python.