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.
4, D
e
c
e
m
ber
201
9,
pp.
2013~
20
20
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp2013-2020
2013
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
Grid tied PV system usi
n
g
modular multilevel inverter
S
u
jit
h
a
N
.
, Pa
r
t
h
a
S
a
ra
th
i Subu
d
h
i,
K
ri
t
h
iga
S
.
,
S. Ang
a
l
a
e
swa
r
i,
T. Deep
a,
D
.Su
bbu
lek
s
h
m
i
S
c
ho
ol
o
f Elect
rical
E
ngin
eering
,
V
ell
o
re Inst
itute
o
f
Technolo
gy,
I
nd
ia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Mar
12,
2
0
1
9
Re
vise
d A
p
r
20,
201
9
A
c
c
e
pte
d
J
u
n
4
,
2019
A grid
tied ph
otovo
lt
a
i
c
s
y
s
t
e
m
u
si
ng
m
od
ul
ar
m
ul
tilevel
i
nvert
e
r
t
op
olog
y
is
pro
p
o
s
ed
i
n
this
p
aper.
Basi
c
u
n
it
s
tructure
o
f
modular
mul
t
i
l
e
v
e
l
in
ve
r
t
e
r
us
ed
i
n
t
h
i
s
s
ystem
is
cap
abl
e
o
f
co
nvert
in
g
DC
pow
er
f
ro
m
P
V
a
rray
to
A
C
po
wer
f
o
r
f
eed
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t
o
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h
e
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ous
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l
d
l
o
ads
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r
u
ti
lity
g
ri
d.
T
h
e
p
r
o
p
o
s
e
d
modul
a
r
mu
ltile
vel
i
n
verter
s
tr
uc
ture
h
a
s
l
esser
power
elect
r
o
n
i
c
d
evices
com
p
are
d
t
o
the
exi
s
ti
ng
m
ulti
level
inv
e
rter
t
op
o
l
og
ies.
T
h
e
p
r
oposed
s
y
st
e
m
g
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ra
te
s
a
n
e
a
r
ly
s
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o
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o
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a
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o
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tion.
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im
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rop
o
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e
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y
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m
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s
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ATLAB
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i
mu
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t
w
a
re a
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h
e
resu
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s
a
r
e
p
resented.
K
eyw
ord
s
:
Phot
o
v
o
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ic
Ar
r
ay
Mo
du
la
r Mu
lti
leve
l
Inver
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e
r
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tili
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y
gri
d
To
tal H
a
rm
o
n
i
c
D
ist
o
r
t
i
on
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:
K
r
ith
iga
S
.
,
S
c
hoo
l
o
f
Ele
c
t
rica
l
En
gine
erin
g,
V
e
ll
ore
Instit
ut
e
of Te
c
hn
o
l
o
g
y
, Che
nna
i
,
V
a
nda
l
u
r
-
K
e
la
m
b
akka
m
Roa
d
, Che
nna
i
-
6
0
012
7,
Ta
m
il Na
du, I
nd
i
a
.
Em
ail:
s_kr
i
t
h
i
ga@
y
a
h
o
o
.
c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
P
hoto
v
o
l
tai
c
(
P
V
)
system
s
are
b
oom
i
n
g
in
t
he
r
enew
a
b
l
e
e
ne
rg
y
m
a
r
k
e
t
d
u
e
t
o
i
t
s
c
l
e
a
n
a
n
d
abu
n
d
an
t
l
y
a
v
a
ila
b
l
e
n
a
t
u
re
[
1
,
2
].
A
lso,
s
ola
r
e
ner
gy
i
s
e
a
s
i
l
y
tap
p
e
d
a
nd
c
onve
rte
d
i
n
t
o
e
l
e
c
tr
ici
t
y
w
h
ic
h
is
the
ad
de
d
a
dva
nta
g
e
o
f
P
V
arr
a
y
o
v
er
o
the
r
r
e
n
ew
a
b
l
e
e
ne
rgy
s
o
u
rce
s
[
3].
D
u
e
t
o
t
he
i
n
t
erm
itten
t
n
a
t
u
r
e
o
f
the
P
V
a
rr
ay,
power
e
lectr
o
n
i
c
i
n
ter
f
ac
e
is
n
ee
de
d
i
n
t
he
s
ta
nd
a
l
one
a
n
d
gri
d
tie
d
P
V
s
ystem
s
f
or
o
bta
i
n
i
ng
the
des
i
red
o
u
t
p
u
t
[4].
F
or
g
rid
t
i
e
d
P
V
syst
e
m
,
po
w
e
r
ele
c
tro
n
ic
i
n
v
e
r
t
e
rs
a
r
e
u
ti
l
i
ze
d
a
s
t
he
i
nterf
ace
t
o
con
v
er
t
t
h
e ge
nera
t
e
d dc
pow
er
fr
o
m
t
h
e
P
V
a
rra
y
into
ac
p
ow
er
to feed
t
h
e
uti
li
ty gri
d
[5
-9].
Bas
i
c
in
verte
r
g
ener
a
t
es
a
s
q
u
ar
ewa
v
e
ou
tp
ut
w
h
i
ch
i
s
co
ns
i
d
e
r
e
d
to
h
av
e
h
i
gh
e
r
h
armo
n
i
c
c
ont
e
n
t
.
Th
us,
large
s
i
ze
f
il
ter
ha
s
t
o
b
e
e
m
pl
o
y
e
d
t
o
o
b
ta
i
n
p
ure
si
n
u
s
o
i
dal
w
a
ve
form
i
n
o
rde
r
t
o
fe
ed
t
he
P
V
gene
ra
ted
p
o
w
e
r
to
t
he
g
r
i
d.
A
lso,
t
h
i
s
i
n
ve
rter
h
as
h
i
g
h
d
v
/
d
t
s
tress
an
d
ha
rm
o
n
ic
d
is
tort
io
n
in
t
he
o
ut
pu
t
w
a
ve
form
.
To ove
rc
om
e the
s
e
prob
lem
s
, mult
ile
ve
l i
nver
t
e
r
s w
e
re
d
eve
l
ope
d
.
M
u
lti
l
e
v
e
l
i
nve
rt
e
r
(
M
L
I)
i
s
p
opu
l
a
r
amo
n
g
i
ndu
st
ri
al
a
nd
r
e
s
e
a
rch
sec
t
or
s
d
u
e
t
o
i
ts
a
dv
a
n
t
a
ges
l
i
k
e
i
m
p
r
ov
ed
out
pu
t
vol
t
a
g
e
p
rofi
l
e
w
it
h
lo
w
d
v
/
d
t
and
l
o
w
c
o
mmo
n
m
ode
v
ol
t
a
ges
[1
0,
1
1
]
.
The
o
u
t
p
ut
v
ol
ta
ge
of
M
LI
has
l
o
w
dist
o
rt
io
n a
n
d
low
ha
rmon
i
c
co
n
te
n
t
w
hic
h
re
d
u
c
e
s t
h
e
si
z
e
an
d c
o
st
of
t
h
e
fil
t
e
r an
d
the
l
e
v
e
l
o
f
e
l
ect
ro
ma
gne
t
i
c
i
n
t
e
r
fe
re
n
ce
(E
MI)
[
12].
The
three
ba
sic
MLI
t
op
o
l
ogie
s
a
re
d
io
de
c
la
mpe
d
M
LI,
fly
i
ng
ca
paci
t
o
r
M
L
I
an
d
ca
sca
d
e
d
M
LI
[
1
3
-1
5].
A
s
t
he
n
um
b
e
r
of
l
e
v
e
l
s
o
f
out
put
v
olt
a
g
e
i
n
c
re
as
es,
th
e
s
e
to
pol
o
g
ie
s
re
q
u
i
r
e
incre
a
se
d
num
ber
of
s
w
i
tche
s,
d
io
de
s
a
n
d
ca
p
ac
i
t
ors
w
h
ic
h
e
v
en
t
u
a
lly
i
ncr
ease
s
t
h
e
c
os
t,
vo
lum
e
a
nd
co
ntr
o
l com
p
le
xi
ty
[
1
6
-2
0].
To o
verc
ome
t
h
ese
d
i
sad
v
a
n
t
a
ge
s,
m
od
u
l
ar mult
i
l
e
v
el
i
n
v
e
r
te
rs
(
M
M
LI)
a
r
e deve
l
ope
d [21, 22] w
it
h
two pa
rts v
i
z. l
evel ge
n
er
at
or
a
nd p
o
lar
i
t
y
ch
a
nge
r. Leve
l
g
ene
ra
to
r
c
r
ea
t
e
s
u
n
ip
ol
a
r
m
u
l
ti
l
e
v
e
l
out
put
v
o
l
t
a
ge
w
a
ve
form
s
usi
ng
h
i
g
h
f
re
qu
e
n
cy
s
w
i
tc
hes
a
nd
po
lar
i
t
y
c
han
g
e
r
c
o
nv
e
r
ts
t
his
uni
p
o
l
a
r
w
a
ve
form
i
nt
o
a
bi
pola
r
w
a
v
e
f
o
r
m
usi
ng
l
o
w
fr
eque
nc
y
sw
i
t
ches
a
t
li
ne
f
r
e
que
nc
y
.
In
t
h
i
s
M
M
LI
,
t
h
e
num
ber
o
f
s
w
itc
he
s,
con
d
u
ct
i
on
lo
ss
a
nd
swi
t
c
h
in
g
l
o
ss
ar
e
re
du
ce
d
com
p
are
d
t
o
t
h
a
t
o
f
th
e
co
nv
en
ti
o
n
a
l
mu
lti
l
ev
e
l
i
nv
erte
r
f
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
2
0
1
3
– 2
020
2
014
the
sa
me
ou
t
pu
t
le
vels
[23]
.
Thus, the
m
o
d
u
la
r mult
ile
ve
l
i
n
verter
is
e
m
p
l
o
y
ed
i
n
t
h
e
pr
o
p
o
s
e
d
sy
st
em
t
o
f
e
ed
the
P
V
a
rr
ay
p
ow
er
t
o
th
e
ut
il
it
y
gri
d
.
T
h
e
c
o
n
t
ri
b
u
t
i
ons
o
f
th
e
pr
opo
se
d
gri
d
t
ie
d
P
V
s
y
s
tem
a
r
e
s
u
mmar
i
z
e
d
a
s
fo
l
lo
ws:
Th
i
s
p
a
p
er
p
r
o
pose
s
a
n
im
prove
d
sys
t
em
w
hic
h
e
m
p
l
o
ys
m
odula
r
m
u
l
t
i
l
e
vel
in
ver
t
e
r
t
op
o
l
o
g
y
i
n
or
de
r
t
o
f
ee
d P
V
array
gene
ra
ted
p
o
w
er
t
o
util
it
y g
r
id w
it
h lesse
r nu
m
b
er
o
f
com
p
o
n
e
n
ts
a
nd r
e
duce
d
l
osse
s.
The
p
r
o
p
o
se
d
in
ver
t
e
r
o
pe
rat
e
s
w
ith
l
esser
vo
l
t
a
g
e
a
nd
c
u
rre
nt
TH
D
i
n
o
rde
r
t
o
fac
i
l
i
t
a
te
s
moo
t
h
gr
i
d
i
n
te
gr
at
ion
o
f
t
he
sys
t
e
m.
2.
WO
R
K
ING OF TH
E
P
ROPO
S
E
D
GRID CONNECTED
S
YS
T
E
M
The
b
l
oc
k
d
i
a
g
r
a
m
of
t
he
p
r
opose
d
s
ys
te
m
show
n
i
n
F
igure
1
c
ons
i
s
t
s
o
f
P
V
a
r
r
a
y
,
m
o
d
u
l
a
r
mult
i
l
e
v
el
i
nve
rter,
c
ontro
lle
r
and
u
til
i
t
y
gri
d
.
Basic
u
n
it
s
t
ruct
ure
o
f
M
M
L
I
show
n
i
n
F
i
gure
2(
a)
c
ons
i
s
t
s
o
f
Leve
l
ge
nera
tor
and
P
o
lari
t
y
c
han
g
e
r
.
Th
i
s
b
a
s
ic
u
n
it
s
t
ru
cture
c
a
n
b
e
e
xpa
n
d
ed
t
o
t
h
e
m
o
d
u
lar
s
t
ruc
t
ur
e
a
s
show
n
i
n
F
i
gur
e
2(b)
t
o
i
n
c
r
e
a
s
e
the
n
u
m
b
er
o
f
ou
t
p
u
t
v
ol
ta
ge
l
ev
e
l
s.
T
h
e
l
ev
el
g
e
n
e
r
at
or
o
f
t
h
e
MM
LI
b
a
s
i
c
un
it co
ns
ist
s
of
3 P
V
a
r
r
ay source
s,
V
PV1
,
V
PV
2
an
d
V
PV3
an
d
4
p
ow
e
r
s
w
i
t
c
he
s,
S
1
,
S
2
, S
3
and S
4
. The
pola
r
ity
cha
nge
r
i
s
a
n
H
-
bridge
i
n
v
erter
c
ons
is
tin
g
of
4
s
w
i
tc
hes,
S
5
,
S
6
,
S
7
a
nd
S
8
.
The
c
o
nt
r
o
ller
i
n
t
he
p
ro
pos
ed
sy
st
em
g
e
n
era
t
es
t
h
e
g
at
e
p
u
l
s
e
s
t
o
t
h
e
swi
t
ch
e
s
o
f
l
e
v
e
l
ge
n
e
r
at
or
t
o
pro
duce
a
u
n
i
p
o
l
a
r
s
tairc
a
se
w
a
v
efor
m
and
gener
a
tes
the
gate
p
u
l
se
s
to
t
he
p
ol
a
r
it
y
cha
nger
sw
it
c
h
e
s
t
o
c
o
nver
t
t
he
u
ni
p
o
l
a
r
si
gna
l
in
to
a
b
ip
o
l
ar
s
i
g
n
a
l
.
B
a
s
i
c
s
t
r
u
c
t
u
r
e
o
f
M
M
L
I
w
i
t
h
3
s
y
m
m
e
t
r
i
c
a
l
v
o
l
t
a
g
e
s
o
u
r
c
e
s
gener
a
tes
t
h
e
ou
tpu
t
w
ave
f
o
r
m
w
i
t
h
seve
n l
e
ve
ls of eq
ua
l w
i
dths.
Th
e
swi
t
c
h
i
n
g
o
f
l
ev
e
l
g
en
erat
o
r
i
s
e
x
p
la
i
n
e
d
in
th
is se
c
t
i
o
n for
differ
en
t vo
l
t
ag
e
leve
ls.
F
i
gure
1. Bl
o
c
k
d
ia
gram
of th
e pr
op
ose
d
s
ys
t
e
m
2.1.
Leve
l
0
I
n
t
h
i
s
l
e
v
e
l
,
a
l
l
t
h
e
s
w
i
t
c
h
e
s
i
n
t
h
e
l
e
v
e
l
g
e
n
e
r
a
t
o
r
a
r
e
i
n
O
FF
c
o
n
d
i
t
i
o
n
an
d
th
e
swit
ch
es,
S
5
a
nd
S
7
are
O
N
i
n
t
he
p
olar
it
y
c
h
a
n
ger
r
e
sul
t
i
ng
a
ze
ro
l
e
v
e
l
o
u
t
pu
t
a
n
d
he
nce,
t
he
re
i
s
n
o
f
l
o
w
o
f
c
ur
rent
i
n
t
h
e
syste
m
.
The
equi
va
len
t
c
ircu
i
t
for
thi
s
l
eve
l
i
s show
n
in
F
ig
ur
e 3
(
a).
2.2.
Leve
l
1
I
n
t
h
i
s
le
ve
l,
s
w
itc
hes
S
4
,
S
5
&
S
8
a
re
t
urned
O
N
,
k
eepin
g
ot
her
sw
i
t
c
h
e
s
O
FF
a
nd
t
he
d
c
vo
ltage
,
V
PV
3
a
p
p
ear
s
acr
oss
the
ou
t
p
ut
t
e
r
m
i
na
l
an
d
t
h
e
curr
ent
fl
ows
from
V
PV
3
t
o
t
h
e
o
u
t
p
ut
t
e
r
m
i
na
ls
t
hro
u
gh
the
pat
h
S
5
,
S
8
and
S
4
a
s
show
n
i
n
F
igure
3(b)
.
2.3.
Leve
l
2
Sw
i
t
ch
e
s
S
2
,
S
3
,
S
5
a
nd
S
8
a
re
t
ur
ne
d
O
N
and
t
h
e
o
t
he
r
sw
itc
hes
a
r
e
turne
d
O
F
F
i
n
t
h
i
s
l
e
ve
l.
A
s
a
resul
t
,
the
in
v
e
rter
out
p
u
t
vo
lt
a
g
e
t
e
rm
ina
l
i
s
(
V
PV
2
+
V
PV
3
).
T
he
c
urrent
f
lows
f
r
o
m
V
PV
2
an
d
V
PV3
t
o
t
h
e
ou
tpu
t
t
e
r
m
i
na
l
thro
ug
h t
h
e pa
th S
2
, S
3
, S
5
a
nd S
8
as
show
n i
n
F
i
gur
e 3(
c).
2.4.
Leve
l
3
Sw
i
t
ch
e
s
S
1
,
S
5
&
S
8
a
re
t
ur
ne
d
O
N
,
k
ee
pin
g
o
t
h
er
s
w
itc
hes
O
F
F
in
t
h
i
s
le
ve
l.
A
s
sh
own
in
F
i
gure
3(d)
,
(
V
PV
1
+
V
PV
2
+
V
PV
3
)
a
ppe
ars
acr
oss
ou
tpu
t
t
er
minal
o
f
t
he
i
n
v
erter
an
d
the
c
u
rren
t
flows
f
r
o
m
V
PV
1
,
V
PV2
and V
PV
3
to t
h
e
ou
t
p
u
t
te
r
mina
l
thr
o
u
g
h
t
h
e
sw
itche
s
S
1
,
S
5
a
nd S
8
.
After
ac
h
i
ev
i
ng
t
h
e
pe
a
k
v
o
l
t
a
ge
o
f
(V
PV1
+
V
PV2
+
V
PV3
),
t
he
v
o
lta
ge
l
e
v
e
l
s
a
r
e
gra
d
ual
l
y
de
cre
a
sed
from
l
e
v
e
l
3
to
leve
l
0
to
g
en
e
r
ate
seve
n
le
v
e
l
o
u
tp
ut vol
ta
ge
w
a
vefor
m
a
t
inp
u
t
t
e
r
m
i
na
l
s
o
f
p
o
l
a
r
ity
c
ha
n
g
er
w
ith
s
te
p
vo
l
t
a
g
es
o
f
0,
V
PV
3
,
(
V
PV
2
+
V
PV
3
),
(
V
PV1
+
V
PV
2
+
V
PV3
),
(
V
PV
2
+
V
PV3
),
V
PV
3
a
n
d
0
.
Th
e
pol
a
r
i
t
y
cha
nge
r
swi
t
c
h
es,
S
6
a
nd
S
7
a
re
t
urne
d
O
N
a
nd
S
5
&
S
8
a
re
t
u
r
ne
d
OF
F
t
o
c
h
a
ng
e
t
h
e
pol
a
r
it
y
o
f
t
h
i
s
dc
l
i
nk
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
G
r
id
t
i
e
d
PV
sy
st
e
m
usi
n
g m
o
d
u
l
a
r
m
u
l
tile
v
e
l inv
e
r
ter (S
uj
it
ha
N
.
)
2
015
vo
lta
ge,
V
dcl
i
nk
r
esul
t
i
n
g
i
n
a
n
a
lter
n
a
t
i
n
g
per
i
o
d
ic
s
t
a
ir
-
case
w
a
ve
form
a
s
sh
ow
n
i
n
F
i
gure
4
a
n
d
th
e
corr
espo
n
d
in
g
sw
it
c
h
i
n
g
st
a
t
e
s
o
f
t
h
e
M
M
L
I
a
re
s
how
n
in
T
able
1
.
The
num
ber
o
f
o
utpu
t
l
e
ve
ls
i
ncre
ase
s
w
ith
t
he i
ncr
e
a
s
e
in n
um
ber
of th
i
s ba
sic
u
n
i
t
o
f MM
LI.
F
i
gure
2.
S
chem
atic
d
i
a
gram
of M
L
I
(a
)
Basic un
i
t
struc
t
u
re
(b)
M
od
ul
ar s
t
r
u
c
t
u
re
Ta
ble
1.
S
w
itc
hi
n
g
S
tates of
M
MLI
S
1
S
2
S
3
S
4
S
5
S
6
S
7
S
8
V
ou
t
OF
F
OF
F
O
F
F
O
N
O
N
O
FF
OF
F
ON
V
PV
3
OF
F
ON
O
N
O
FF
O
N
O
FF
OF
F
ON
(
V
PV2
+ V
PV3
)
ON
OF
F
O
F
F
O
FF
O
N
O
FF
OF
F
ON
(
V
PV1
+ V
PV2
+
V
PV
3
)
OF
F
OF
F
O
F
F
O
FF
O
N
O
FF
ON
OF
F
0
OF
F
OF
F
O
F
F
O
N
O
FF
O
N
ON
OF
F
-
V
PV3
OF
F
ON
O
N
O
FF
O
FF
O
N
ON
OF
F
-
(
V
PV2
+
V
PV3
)
ON
OF
F
O
F
F
O
FF
O
FF
O
N
ON
OF
F
-
(
V
PV1
+
V
PV2
+
V
PV
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
2
0
1
3
– 2
020
2
016
F
i
gure
3.
E
qui
vale
n
t
c
irc
u
it o
f
MM
L
I ba
si
c
un
i
t
for
(
a
)
lev
e
l
0
; (b)
leve
l
1
;
(
c) leve
l
2
; (d
)
level
3
F
i
gure
4.
O
ut
p
u
t
vo
lta
ge
w
av
e
f
orm
of M
ML
I ba
sic
un
it
3.
SIMU
L
A
TION STUDIES
S
i
mulat
i
o
n
mode
l
of
t
he
p
r
o
p
o
se
d
syste
m
s
how
n
i
n
F
igur
e
5
is
c
o
ns
truc
t
e
d
us
i
n
g
p
o
w
e
r
MO
S
F
ET
sw
it
c
h
es,
p
u
l
s
e
g
e
n
e
r
at
or
a
nd
u
til
i
t
y
g
r
id
a
va
ila
b
l
e
in
t
he
S
im
P
o
w
e
rS
yst
e
m
B
l
oc
kse
t
l
ib
rary
o
f
MA
TLA
B/s
i
mul
i
nk s
o
ftw
a
re and P
V
a
rra
y
is m
odele
d
usi
n
g the
cla
s
sic
a
l
e
qua
t
i
o
n
a
s
fo
l
l
ow
s [24]
:
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
G
r
id
t
i
e
d
PV
sy
st
e
m
usi
n
g m
o
d
u
l
a
r
m
u
l
tile
v
e
l inv
e
r
ter (S
uj
it
ha
N
.
)
2
017
ℎ
0
e
x
p
ℎ
1
(
1
)
wher
e,
I
ph
i
s
t
h
e
li
g
h
t
ge
nera
te
d
cur
r
en
t,
I
0
i
s
th
e
reverse
saturation
curre
nt
o
f
t
h
e
P
V
a
r
r
ay,
R
se
i
s
t
h
e
s
e
r
i
e
s
resista
n
ce
of
t
h
e P
V
arra
y and
V(th)
i
s
t
h
e
t
h
e
r
m
a
l
volta
ge.
Th
e
p
r
op
o
s
e
d
7
l
e
v
el
s
y
s
t
e
m
i
s
s
i
m
ul
at
e
d
w
it
h
t
h
e
sy
mmet
ri
c
a
l
P
V
ar
ray
source
s
a
t
a
n
irra
dia
t
i
o
n
o
f
90
0
W/m
2
(
ea
ch
s
ourc
e
i
s
c
ons
ti
tu
te
d
w
i
t
h
2
s
e
r
i
e
s
c
o
n
n
e
cted
P
V
mod
u
le
s
e
ac
h
r
a
te
d
25
0
W
w
i
t
h
o
pen
circ
u
i
t
vo
l
t
age
,
V
oc
of
3
7.8
V
and
s
hort
c
i
rc
uit
curr
en
t,
I
sc
of
8
.
8
A
)
.
F
igure
6
sh
ow
s
t
h
e
w
a
veform
s
o
f
P
V
arr
a
y
vo
l
t
a
g
e
s
,
V
PV
1
,
V
PV2
&
V
PV
3
o
f
6
2
.08
V
,
61.9
6
V
&
62.8
2
V
r
e
s
pect
i
v
e
l
y
a
nd
t
h
e
ge
ne
rate
d
d
c
lin
k
vo
lta
ge,
V
dcli
n
k
of 8
5
.1
4
V
a
nd dc
l
i
n
k
curr
en
t
,
I
dcli
nk
of
5.33
A
.
F
i
gure
5.
S
imulat
i
on m
o
d
e
l o
f
the
p
ro
pose
d
s
ys
tem
F
i
gur
e 6.
Wav
efo
r
ms
o
f P
V
arra
y
vol
tage
s a
nd dc
l
ink
v
o
l
t
a
ge
a
n
d cur
r
en
t
U
n
i
p
o
l
ar
d
c
li
n
k
v
o
l
ta
ge
i
s
c
o
n
v
erte
d
in
to
a
7
l
e
v
e
l
s
te
ppe
d
b
i
p
o
lar
a
c
v
o
l
tage
by
t
h
e
H
-
brid
ge
po
lari
t
y
c
ha
n
g
e
r
a
nd
t
h
is
s
te
p
p
e
d
w
a
v
efor
m
is
f
il
tere
d
u
s
i
n
g
L
C
L
fi
l
t
er
o
f
85
µ
H
a
n
d
1
25
µ
F
a
nd
fe
d
t
o
t
he
11
0
V
sin
g
le
pha
se
u
ti
li
ty
g
rid.
W
a
v
e
f
orm
s
o
f
dc
l
in
k
vol
ta
ge
,
7
l
e
v
e
l
in
v
e
rt
er
out
pu
t
vol
t
a
g
e
,
V
out
,
grid
vo
lta
ge,
V
gr
i
d
a
nd
gri
d
c
ur
rent,
I
gr
i
d
i
s
sh
o
w
n
i
n
F
ig
ure
7.
T
he
t
o
t
al
h
a
r
m
oni
c
dis
t
ortio
n
(TH
D
)
o
f
i
nv
ert
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
2
0
1
3
– 2
020
2
018
ou
tpu
t
v
ol
t
a
ge
a
nd
c
urren
t
w
i
t
h
out
f
il
ter
i
s
f
ou
n
d
t
o
be
22.
16
%
an
d
2.7
%
an
d
TH
D
o
f
t
he
g
r
i
d
v
o
l
t
a
g
e
a
n
d
curr
ent
w
ith
f
il
ter
is
r
educ
e
d
t
o
1.74
%
a
nd
2.
18
%
respec
tive
l
y
which
is
w
ell
w
i
thin
t
he
I
EEE
519
s
t
a
ndar
d
as show
n
in
F
igure
8.
The
pro
p
o
se
d
sys
t
em
i
s
simu
late
d
an
d
a
n
a
l
yze
d
f
or
v
ari
o
us
i
rra
d
ia
ti
on
c
o
n
d
i
t
i
o
n
s
o
f
P
V
a
rra
y
and
the
c
o
rre
sp
ond
in
g
pow
er
f
e
d
t
o
the
gri
d
a
n
d
e
ff
i
c
ie
nc
y
i
s
p
l
o
tt
e
d
i
n
F
i
gur
e
9.
F
rom
F
i
gur
e
9,
i
t
is
e
v
i
de
nt
t
ha
t
t
h
e
g
r
i
d
p
o
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er
a
n
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ffi
c
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enc
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i
s
i
n
cre
a
si
n
g
w
it
h
t
h
e
in
c
r
ea
se
i
n
PV
a
rray
i
r
ra
di
a
t
i
o
n
s
.
Th
us,
mo
dul
ar
mu
l
til
e
v
e
l
i
n
v
ert
e
r
t
opol
og
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fe
ed
t
h
e
m
a
x
imu
m
p
o
w
er
t
o
th
e
ut
il
it
y
gri
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f
rom
t
h
e
P
V
a
rra
y
e
f
fic
i
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n
tl
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t
hi
ghe
r ir
radiat
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n
d
i
t
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o
ns
w
i
t
h
l
o
w
v
o
lta
ge a
nd cur
r
en
t TH
D
.
A
c
o
mpa
r
sio
n
b
e
t
w
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e
n
t
he
c
o
m
pone
n
t
s
c
o
u
n
t
o
f
t
h
e
e
x
i
s
t
i
n
g
t
o
p
o
l
og
ies
a
nd
t
h
e
m
o
d
u
l
a
r
m
ul
t
ile
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l
in
verter
t
o
p
l
og
y
pre
s
e
n
t
e
d
i
n
t
h
i
s
pa
per
a
r
e
pro
v
i
d
e
d
i
n
Ta
ble
2.
F
rom
th
e
ta
ble,
i
t
is
e
v
i
de
n
t
t
ha
t
t
h
e
m
odu
lar
mult
i
l
e
v
el
t
o
p
l
og
y
prese
n
te
d
in
t
h
i
s
pa
per
h
a
s
less
n
u
mbe
r
o
f
c
o
m
po
n
e
nts
wh
i
c
h
re
du
c
e
s
t
h
e
c
o
st
a
nd
s
i
z
e
of
the s
y
stem
.
F
i
gure
7.
Wa
v
efor
ms
o
f dc
li
n
k
v
o
l
ta
ge,
V
dc
link
,
out
put
v
olt
a
ge
w
it
ho
ut
f
i
l
t
e
r,
V
in
v
, grid voltage,
V
gr
i
d
a
nd gri
d
curren
t
,
I
gr
i
d
Figure
8.
TH
D
w
ave
f
orm
s
of
(a) grid
vol
ta
g
e
w
ith
out
f
ilte
r
(b)
grid
c
urre
n
t
w
itho
u
t
fi
lter
(c
) gr
i
d
v
olta
ge
w
ith
f
ilt
er (
d)
gr
i
d
cu
rr
ent with filter
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
G
r
id
t
i
e
d
PV
sy
st
e
m
usi
n
g m
o
d
u
l
a
r
m
u
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v
e
l inv
e
r
ter (S
uj
it
ha
N
.
)
2
019
F
i
g
u
r
e
9
.
Rela
t
i
ve
v
ar
iat
i
on o
f
outp
u
t
pow
er
a
nd e
f
fic
i
e
n
c
y
of
t
h
e pr
o
p
o
s
e
d
sys
t
e
m
w
i
t
h
r
espe
c
t
to P
V
arra
y
irra
di
a
tio
ns
Tab
l
e
2
.
Com
pa
riso
n of
s
eve
n
l
e
v
el t
o
p
o
l
ogi
e
s
Topology
D
iode
cl
a
m
p
e
d
MLI
C
a
p
aci
to
r
cl
a
m
p
e
d
M
L
I
Cas
cad
e
d
H
-
brid
ge
M
LI
Re
v
e
rse
volta
ge
M
L
I
[25]
P
r
opo
se
d
M
o
dul
a
r
MLI
C
o
m
pone
nts
Sourc
e
s
1
1
3
3
3
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i
ode
s
16
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Ca
p
a
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r
s
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6
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w
itc
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s
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1
2
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1
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4.
CONCL
U
S
ION
G
r
i
d
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ie
d
p
h
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t
ov
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t
a
i
c
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te
m
usi
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mod
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l
ar
m
ult
ile
ve
l
inve
r
t
er
i
s
pro
p
o
se
d
i
n
t
hi
s
pa
per.
M
M
L
I
use
d
i
n
t
h
e
pr
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ose
d
s
y
s
tem
prod
uces
a
7
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eve
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t
p
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t
w
it
h
m
i
n
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m
u
m
num
ber
o
f
s
w
i
t
c
hes
ac
t
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ve
a
t
an
y
in
sta
n
t.
G
ener
ati
on
of
o
u
t
p
u
t
l
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l
s
are
e
x
pla
i
ned
w
i
t
h
t
he
c
or
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spo
n
d
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q
u
i
va
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i
n
t
h
i
s
paper
.
MA
TLA
B/S
i
mul
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nk
s
o
f
t
w
a
re
i
s
us
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f
or
t
h
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im
ula
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pose
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ys
te
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a
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h
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re
s
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e
furn
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d.
F
rom
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i
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lat
i
o
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su
lts,
it
i
s
e
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d
e
n
t
tha
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t
he
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opose
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y
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tem
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capa
b
le
o
f
fe
e
d
in
g
p
o
w
e
r
to
gri
d
f
r
o
m
the
symm
etric
a
l
P
V
a
r
r
ay
s
ourc
e
s
w
i
t
h
l
ow
v
ol
ta
ge
a
n
d
c
urre
nt
T
H
D
of
1
.74
%
a
n
d
2.
18
%
respe
c
t
i
ve
l
y
.
The
n
u
mbe
r
o
f
out
pu
t
l
e
ve
ls
c
an
a
ls
o
be
i
nc
r
ease
d
,
if
m
ore
number
o
f
b
a
s
ic
u
n
i
t
s
o
f
th
is
M
MLI
i
s
a
dd
ed
.
ACKNOW
LEDG
E
MEN
T
S
The
a
u
th
ors
w
o
u
l
d
li
ke
t
o
th
ank
Mr.
Sw
ith
i
n
A
b
n
e
r
,
Mr.
Sum
i
t
P
a
nj
a
a
n
d
M
r
.
Ri
sh
i
Raj
Gupt
a
,
B.
Tec
h
.
S
t
u
d
e
n
t
s
,
S
c
hoo
l
of
E
le
c
t
rica
l
E
n
g
i
neer
ing,
V
el
lor
e
I
ns
t
itu
te
o
f
T
e
c
h
n
o
l
o
g
y
,
C
h
enna
i
,
I
nd
ia
f
o
r
t
he
ir
con
t
ri
b
u
ti
ons
i
n the
s
i
mula
t
i
o
n
st
u
d
y
of
sta
nd-
al
one
m
od
u
l
ar mu
ltil
evel inver
t
e
r.
REFE
RENCES
[1]
N.
T.
,Z
han
g
C
.
,
M
ah
mu
d
M
.
A.
,
“
O
p
t
im
al
C
oo
rdin
ati
o
n
o
f
G
2V
a
nd
V
2
G
to
S
uppo
rt
P
ower
G
rids
w
ith
H
ig
h
P
e
net
r
atio
n
o
f
Renew
abl
e
En
e
rgy,
”
IEE
E
Tr
ans.
T
r
an
sp.
El
ectr
i
f
.
,
v
o
l
.
1,
p
p
.
18
8–19
5,
2
01
5.
[2]
D.
S
atti
anadan
,
K.
S
arav
anan
,
S
.
M
urug
an,
N.
H
ari
,
P
.
Ven
k
ad
e
s
h
,
“
I
m
p
lem
e
ntati
o
n
of
q
u
a
si
-z
s
ou
rce
i
n
v
e
rter
f
o
r
g
r
id
c
on
nected
P
V
bas
e
d
chargin
g
s
tatio
n
of
e
lect
ric
v
e
hi
c
l
e,”
In
ter
natio
nal Jo
ur
na
l
of P
o
wer
El
ectro
n
i
cs
an
d D
r
i
ve Sys
t
e
m
, v
o
l
. 1
0,
n
o.
1,
pp
. 36
6
–
3
7
3
,
M
arch
20
1
9
.
[3]
Basm
adjian
R.,
M
eer
H
,
“
A
H
euri
s
t
ics-Bas
e
d
Pol
i
cy
t
o
Red
u
ce
th
e
C
urt
a
ilm
e
nt
o
f
S
o
lar-P
ower
G
en
e
r
at
io
n
Empo
we
re
d b
y
E
ne
rg
y-Sto
r
a
g
e
Sy
ste
m
s,”
El
ectron
i
cs
, Vo
l
.
7
,
n
o.1
2
, p
p
. 34
9
,
N
o
v
.
2
01
8.
[4]
S
.
N
a
g
a
r
a
j
a
R
a
o
,
D
.
V
.
A
s
h
o
k
K
u
m
a
r
,
C
h
.
S
a
i
B
a
b
u
,
“
G
r
i
d
C
o
n
n
e
c
t
ed
D
i
s
tri
buted
G
e
n
erati
o
n
S
y
s
t
emw
i
th
H
ig
h
Vol
t
age
Gai
n
C
ascaded
D
C-DC
C
on
vert
e
r
F
ed
A
symmetric
M
u
ltil
evel
I
nvert
er
T
o
pol
og
y
”
,
International
Jou
r
n
a
l
o
f
El
ectri
cal
an
d
Comp
u
t
er E
n
g
i
neerin
g (
I
JE
CE)
,
vo
l. 8
,
no
.6, p
p
.
40
47
-4
0
5
9
, Decem
ber 20
18.
[5]
S.
K
r
ithiga,
N
.
Ammasai
Goun
den,
“
A
n
I
m
p
roved
P
o
wer
E
l
ectroni
c
Con
t
roller
w
i
t
h
U
n
i
t
y
P
ower
F
acto
r
f
o
r
a
S
i
ng
le
-
S
ta
g
e
G
r
i
d-
T
i
e
d
P
V
S
y
s
t
e
m
”,
Arab
J
o
u
r
na
l S
c
i.
En
gg
., v
ol
.
3
9
,
p
p
.
7
1
7
3
–
7
1
8
2, 20
1
4
.
[6]
K.
R
a
j
a
s
e
k
h
a
ra
R
e
d
dy
,
V.
N
a
g
a
b
ha
ska
r
R
e
ddy,
M
.
V
i
ja
ya
K
u
m
a
r
,
“
C
on
tro
l
o
f
S
i
ng
le
S
ta
ge
G
rid
T
i
e
d
Ph
otov
o
l
ta
ic
I
nv
e
r
te
r
Using
Inc
r
em
ental
Co
nd
uctan
ce
M
e
th
od
,”
In
ter
n
a
t
io
nal Jou
r
na
l o
f
P
o
wer
Electr
oni
cs an
d
Dr
ive S
y
s
t
em,
v
o
l
. 9
,
n
o. 4
, p
p
.
1702–
17
08
, Decem
b
e
r
20
18.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
2
0
1
3
– 2
020
2
020
[7]
H.
E
.
G
e
lani
a
nd
F
.
Dastg
eer,
“
E
ff
ici
e
ncy
An
aly
s
es
o
f
a
DC
R
esi
den
t
ial
P
o
wer
Di
st
rib
u
ti
on
S
yst
e
m
f
o
r
t
h
e
Mo
de
rn
Ho
m
e
,
”
A
d
v. Electr.Com
p
ut
.En
g
.
,
vol.
15
,
no
.
1
,
p
p
.
1
35
–
1
42,
2
0
1
5
.
[8]
Krith
iga
S.
,
Amm
a
sai
G
o
u
n
d
e
n
N.
,
“
I
nves
t
i
g
ations
o
f
a
n
i
m
p
rov
e
d
P
V
sy
st
em
t
o
p
ol
og
y
us
in
g
mul
t
ilev
e
l
bo
os
t
con
v
ert
e
r
and
line
com
m
u
t
a
ted
in
verter
w
ith
s
olut
ions
t
o
grid
i
ssu
es”,
S
i
mu
l
a
tion
Mo
de
l
l
ing
Prac
tic
e
a
n
d
Th
e
o
ry
, vo
l
.
42
,
p
p
. 1
47
–1
59
,
20
14
.
[9]
Ma
rio
Nor
m
a
n
S
y
a
h
a
n
d
Su
biy
a
nto
Su
biya
n
t
o,
“
Pe
rfo
r
ma
nc
e
e
n
ha
nc
e
me
n
t
o
f
ma
x
i
mu
m
po
we
r
p
o
in
t
tr
a
c
k
ing
f
o
r
g
r
id
-conn
ected
p
h
o
t
ovo
lt
aic
s
y
s
t
em
u
n
d
er
v
ario
us
g
radi
ent
o
f
i
rrad
i
ance
chan
ges
,
”
TE
L
K
O
M
N
I
K
A
T
e
leco
mmu
ni
cation
,
Co
mputi
ng,
E
l
ectr
onics an
d
Co
nt
ro
l
,
v
o
l.
1
7
,
n
o.
4
,
A
ug
ust
201
9.
[10]
Bh
agwat
P.M
.,
Ste
f
an
ov
i
c
V
.R
.,
“
Gen
e
ral
i
zed
S
t
r
uctu
re
o
f
a
Mu
lt
ilevel
PW
M
Inverter,
”
IEEE
Tr
a
n
s
.
I
n
d.
App
l
.
,
IA-1
9,
p
p
.
1
0
57–10
69
,
1
983
.
[11]
Carrara
G
.,
Gardella
S
.,
M
arches
oni
M.
,
Salutar
i
R
.,
Sci
u
tto
G
.
,
“A
n
ew
m
ulti
l
e
vel
P
W
M
method:
a
t
he
oreti
cal
anal
ys
is
,
”
I
E
EE
Tra
n
s
.
Po
w
e
r E
l
e
c
t
ro
n
.
,
v
ol.
7
,
p
p
.
4
9
7
–
5
0
5
,
1
992.
[12]
Beigi
L.
M.
A.
,
Azl
i
N
.
A
.
,
K
ho
sravi
F
.,
Naj
a
fi
E
.
,
K
aykhosravi
A
.
,
“A
n
e
w
m
u
ltil
e
vel
in
vert
er
t
opolo
g
y
wit
h
redu
ced
n
u
m
b
e
r
o
f
p
ow
er
s
witches
,
”
i
n
P
r
oce
e
di
ng
s
of
t
h
e
2
0
1
2
IEEE
In
ter
nationa
l Con
f
er
ence o
n
Po
wer an
d
Ene
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i
q
u
e
f
o
r
F
i
ve
L
ev
el
Inv
e
rter
C
o
n
n
ected
t
o
t
h
e
G
r
id
,”
In
ter
natio
nal Jo
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r
na
l o
f
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e
l
evel
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g
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s
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a
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d
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t
i
mi
sation
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)
a
l
gori
t
h
m
with
r
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Nu
m
b
er
o
f
switch
e
s
in
m
u
l
til
evel
i
nvert
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(
ML
I),”
In
do
nes
i
an
Jour
na
l o
f
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n
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t
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l
eti
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h
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mmet
r
i
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Li
nk
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e
vel
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t
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u
l
t
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evel
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n
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lo
g
i
es
w
i
t
h
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u
ced
D
ev
ice
Co
un
t
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A Rev
i
e
w,”
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6
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ara
n
N
.
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alani
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a
m
y
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“
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m
p
r
ehens
i
v
e
r
evi
e
w
on
r
edu
c
e
d
swi
t
ch
m
ulti
level
i
n
verter
t
opologies,
mo
du
la
tion
te
c
h
niqu
e
s
a
n
d
a
p
p
l
i
c
a
tion
s
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”
Re
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Su
sta
i
n
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r
g
y
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v
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Gaddal
a
Jayaraj
u
a
nd
G
udapati
Sa
mbasi
v
a
Rao,
“
Intelligent
c
ont
r
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bas
e
d
po
wer
qu
ali
t
y
impro
v
em
ent
of
m
i
cro
g
ridinteg
ratio
n
o
f
p
hot
ov
o
l
tai
c
po
w
er s
ys
tem
us
in
g n
e
w cas
cade
multi
level i
n
verter,”
Inter
n
a
t
i
onal Jour
na
l
of
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i
cal a
nd Comp
u
t
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E
n
g
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n
eerin
g (IJE
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a
n
d
L.
Z
ho
u
,
“
Con
t
rol
l
e
r
a
r
chit
e
c
t
u
re
d
es
ign
f
o
r
M
M
C-H
VDC
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”
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El
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t
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o
d
u
lar
hy
bri
d
e
n
e
rg
y
concep
t
em
p
l
o
y
in
g
a
no
vel
cont
rol
st
ruct
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bas
e
d
o
n
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s
im
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g
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a
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“N
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id
irectio
nal
m
u
lti
lev
e
l
i
n
v
e
rt
er
t
op
ol
og
y
with
s
t
a
i
r
case
cascad
ing
f
o
r symm
e
t
ric an
d as
y
m
m
e
tri
c
st
r
uc
t
u
res,
”
IET
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o
wer
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f
igu
r
ati
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n
f
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r
t
he
operat
i
o
n
of
PV
s
y
s
tem
i
n
c
om
bi
ned
gri
d
-
con
n
ect
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d
s
tand
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H
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M
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Y
atim
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ig
n
and
Im
pl
em
entatio
n
o
f
a
N
ew
M
ul
til
e
vel
In
verter
T
o
p
o
l
o
gy,
"
IEEE
T
r
a
n
s
a
cti
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n
s
o
n
Indu
st
r
i
a
l
El
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