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.
2
,
June
2020
,
pp.
792
~
8
0
0
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v11.i
2
.
pp792
-
8
0
0
792
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
A novel
single
-
stage P
W
M mic
roinverter
topolo
gy us
i
ng
two
-
power
switc
hes
A.
R
azi
1
,
M.
Nabil
Hida
y
at
2
,
M
. N. Se
ro
ji
3
,
S.
Z
. Mo
hamm
ad N
oor
4
1
Center
for
Rob
oti
cs
and
Industr
ia
l
Automation
(
CeRIA),
Univ
er
siti
T
ekni
k
al Ma
la
ysia
,
Ma
la
ysia
1,
2
,3,4
Cent
r
e
of
E
le
c
tri
c
al Pow
er Engi
ne
eri
ng
Stu
die
s
(CEPES)
,
U
nive
rsiti T
eknologi
MA
RA
,
Mal
aysia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Oct
20, 201
9
Re
vised Dec
28, 2
019
Accepte
d
Ja
n 1
7,
2020
Thi
s
p
ape
r
pre
s
ent
s
a
novel
sin
gle
-
stag
e
microi
nver
te
r
topo
logy
using
only
two
-
power
sw
it
che
s.
Th
e
nu
mbe
r
of
co
mp
onent
s
count
are
dir
ec
t
ly
proporti
ona
l
to
t
he
power
losses,
weight,
cost
an
d
com
pl
exity
of
the
d
esign.
Now
ada
ys,
conv
ent
ion
al
Microi
n
ver
te
r
wit
hou
t
tr
ansforme
r
hav
in
g
mi
n
im
um
of
six
power
s
witc
hes,
whi
le
only
three
power
sw
itches
inv
olve
d
in
a
Microi
nver
te
r
st
ruc
ture
with
the
pre
senc
e
of
a
tr
ansforme
r.
Thus
,
th
is
pap
er
proposed
a
nov
el
Micro
inve
rt
er
topol
ogy
with
only
two
-
power
sw
it
che
s
to
conve
r
t
DC
-
vol
t
age
from
Photov
olt
aic
(PV
)
mod
ule
to
an
AC
-
out
put.
Modes
of
oper
a
ti
on
an
d
cur
ren
t
flow
during
ea
ch
c
ycl
e
are
be
ing
explaine
d
.
Vari
ation
of
mo
dula
ti
on
inde
x
,
i
rra
dia
n
ce
and
t
e
mpe
ra
ture
of
the
PV
modul
e,
the
sw
itching
fre
quenc
y
and
har
moni
c
content
o
f
the
proposed
Microi
nver
te
r
are
bei
ng
ana
lys
ed.
A
simu
lated
mode
l
of
Microinverte
r
topo
logy
,
em
ploy
ed
only
two
power
sw
it
ch
es
with
a
stand
ard
Unipo
la
r
Sinus
oida
l
P
ulse
Wi
dth
Modulat
ion
(SP
WM)
havi
ng
0.
85%
har
mon
ic
per
ce
n
ta
g
e;
able
to
inject
cur
ren
t
to
th
e
lo
ad;
h
ave
be
en
succ
essfully
bui
lt
and
de
monstra
t
ed
th
rough
simul
ation
base
d
on
MA
TL
AB/S
im
uli
nk
,
thus
pr
ovide
th
eor
etic
al
val
id
at
ion
for
further re
s
ea
r
ch.
Ke
yw
or
d
s
:
Harmo
nic
M
ic
r
oinverter
Photo
vo
lt
ai
c
Sing
le
-
sta
ge
SPWM
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
:
A.
Razi
,
Ce
nter fo
r
R
obotics an
d Ind
ust
rial
A
ut
om
at
io
n (CeR
IA),
Fakult
i Keju
ru
t
eraan
Elektri
k,
Un
i
ver
sit
i Te
knikal
M
al
aysia
M
el
a
ka,
Jala
n Hang
Tua
h
Ja
ya
, 76100
D
ur
ia
n
T
unggal
, Me
la
ka.
Emai
l:
ati
kah@u
te
m
.edu.
m
y
1.
INTROD
U
CTION
M
ic
r
oinverter
i
s
popula
r
am
ong
in
dustria
l
a
nd
researc
h
fie
ld
due
t
o
it
s
gr
eat
ad
va
ntages
in
te
r
ms
of
com
pact
desi
gn,
le
sse
r
nu
mbe
r
of
c
ompone
nts
in
vo
l
ved,
a
nd
ef
fici
ency
-
f
act
or
c
ompare
d
to
oth
e
r
str
uc
ture
of
Photo
vo
lt
ai
c
(
PV
)
s
ys
te
m
[1
-
9].
T
her
e
fore,
the
backg
rou
nd
stu
dy
on
PV
a
pp
li
cat
io
n
(Ce
ntrali
zed,
Stri
ng,
a
nd
M
ic
r
oinverter
)
re
veals
that
the
M
ic
r
oinverter
become
s
the
t
rend
f
or
the
ne
xt
gen
e
rati
on
of
sy
ste
m
dev
el
opment
[1
,
4, 5,
10].
Ther
e
are
t
wo
cl
assifi
cat
ion
of
powe
r
c
onve
rsion
process
in
M
ic
ro
i
nv
e
r
te
r;
Tw
o
-
sta
ge
or
Sin
gle
-
sta
ge.
Cl
assic
a
l
M
ic
ro
i
nv
e
rter
adopted
t
wo
-
s
ta
ge
of
po
wer
co
nve
rsion
w
hi
ch
has
bee
n
br
oad
l
y
u
sed
i
n
the
P
V
sy
ste
m
[
1,
11
-
13].
T
wo
-
sta
ge
M
ic
ro
i
nv
e
rte
r
usual
ly
deal
with
powe
r
i
nterf
ace
chall
e
nge
betwee
n
un
sta
ble
DC
-
vo
lt
age
source
t
o
sta
ble
high
DC
-
volt
a
ge
val
ue
before
trans
formi
ng
into
AC
-
vo
lt
a
ge
outp
ut
[
2,
5,
14].
Fu
rt
hermo
re,
t
wo
-
sta
ge
M
ic
r
oinver
te
r
c
onta
ins
la
rg
e
numb
e
r
of
c
omp
on
e
nts
co
unt
[
2,
15,
16],
i
n
order
t
o
reali
ze
co
nver
te
r
an
d
in
ver
t
er
powe
r
c
onver
si
on
sta
ge
wh
ic
h
i
nclu
de
s
semic
onduct
or
de
vices,
in
du
ct
or,
capaci
tor
,
a
nd/o
r
di
ode.
Higher
co
mpon
e
nts
c
ount
le
a
ds
t
o
higher
s
witc
hing
lo
s
ses
a
nd
pro
du
ct
io
n/mai
ntena
nce
c
os
t
[
16
-
18].
I
n
a
dd
i
ti
on
,
some
of
t
he
c
onve
rter
a
nd
in
duct
or
to
polo
gy
ma
y
c
omp
rise
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 novel
sin
gle
-
stag
e
PWM
mi
croinverter
to
polo
gy usin
g
tw
o
-
powe
r swit
ch
es (
A
. R
az
i)
793
trans
forme
r
[
2,
6,
7,
19
-
22]
t
o
ste
p
-
up
the
vo
lt
age
val
ue.
Con
se
quently
,
the
M
ic
ro
i
nver
te
r
str
uctur
e
be
come
bu
l
ky.
T
he
bes
t
is
to
hav
e
minimu
m
sta
ge
of
po
wer
c
onve
rsion,
hen
ce
Sing
le
-
sta
ge
M
ic
ro
i
nv
e
rter
to
po
logy
,
for
ease
in
modu
le
inte
gr
at
io
n.
T
hus,
it
s
str
ong
to
say
t
ha
t
inv
erte
r
to
pology
is
a
maj
or
area
of
i
nter
est
to
employe
d
le
ss
num
ber
of
co
mpon
e
nts.
T
he
se
num
be
r
of
com
pone
nts
in
side
the
to
pol
ogy
are
sig
nifi
cantl
y
aff
ect
ed
t
he
s
witc
hing
losse
s,
t
he
overall
siz
e,
c
on
t
ro
l
strat
ergy
of
the
powe
r
s
witc
he
s,
a
nd
man
ufa
ct
ur
in
g
cost
of
t
he Mic
ro
i
nv
e
rter.
Sing
le
-
sta
ge
M
ic
r
oinver
ca
n
be
cat
e
gorized
base
d
on
ga
lvanic
is
olati
on
[
23];
T
rans
forme
r
-
base
d
inv
e
rter
or
T
ra
ns
f
ormer
-
le
ss
i
nv
e
rter.
Earl
y
year
s
of
Sin
gl
e
-
sta
ge
M
ic
r
oi
nv
e
rter
histo
ry,
the
to
polo
gy
wer
e
bu
il
d
with
t
he
prese
nt
of
tr
ansfo
rmer.
M
i
cro
i
nv
e
rter
wi
th
cl
assic
al
-
Fl
yb
ac
k
to
po
l
ogy
[7]
with
3
-
powe
r
switc
hes
i
n
19
98
i
n
c
on
j
uction
with
t
he
li
ne
-
fr
e
q
uen
c
y
t
ran
s
f
or
me
r
for
ci
rcu
it
isolat
ion
pur
poses.
Lat
er
in
2015,
a
n
a
ux
il
ia
ry
ci
rcu
it
we
r
e
added
t
o
the
Flyb
ac
k
-
to
po
l
ogy
t
hat
al
lows
the
switc
h
a
nd
diode
at
the
pr
i
mar
y
side
of
t
he
t
ra
ns
f
ormer
c
ould
be
tu
rn
on
usi
ng
s
of
t
-
switc
hing
operati
on.
I
n
20
14,
Atta
n
asi
o
et
.
al
[2]
al
lows
for
AC
-
wa
veform
t
o
be
ge
ne
rated
by
the
us
in
g
of
4
-
po
wer
s
witc
hes
a
nd
the
e
xisti
ng
of
a
li
ne
-
tra
nsfo
rme
r
after
the
filt
er
com
pone
nts
f
or
protect
io
n
plan.
Howe
ver,
Ag
a
nza
-
To
rr
e
s
et
.
al
in
2014
[19]
im
pleme
nt
ed
10
-
powe
r
s
witc
he
s
to
ov
e
r
c
om
e
the
bigger
value
of
dec
oupling
ca
pacit
or.
Lat
er
i
n
2016
[2],
6
-
power
s
witc
he
s
with
se
ries
of
r
eso
nan
t
ta
nk
w
ere
pro
po
se
d
f
or
Zer
o
V
oltag
e
S
witc
hing
(Z
VS
)
th
us
mini
mize
d
t
he
s
witc
hing
loss.
A
Half
-
br
idg
e
M
ic
r
oi
nverter
t
opolog
y
util
iz
ing
4
-
power
switc
he
s
wer
e
pro
pose
d
by
V.
Be
rza
n
et
.
al
in
2016
[
20]
e
m
ployed
an
al
te
rn
at
in
g
c
urren
t
source
(SAC)
to
ge
nerat
ed
AC
-
wav
e
f
or
m
with
s
of
t
s
wi
tc
hin
g
te
chn
iq
ue.
Transf
ormer
-
ba
sed
t
opolog
y
is
on
e
of
maj
or
co
nce
rn
e
d
in
Sin
gle
-
sta
ge
M
ic
ro
i
nv
e
rter
due
t
o
t
he
la
rg
er
s
pac
e
c
ontrib
uted
by
th
e
tran
sf
ormer,
h
ence
a
t
ran
s
f
ormer
-
le
ss
st
ru
c
ture
a
rr
a
ngeme
nt
wa
s
int
rod
uc
ed
t
o
ov
e
rc
om
e
t
he
con
ce
r
n.
Y.
Fa
ng
an
d
X
.
M
a
in
20
10
[
24]
pro
posed
a
c
ou
pled
-
in
du
ct
or
to
a
4
-
po
wer
s
wict
he
s
double
-
boos
t
topolo
gy
to
s
ol
ve
the
vo
lt
a
ge
gain
iss
ue
in
M
ic
r
oinverter
.
Howe
ver,
a
co
mp
le
x
DSP
co
ntr
oller
wer
e
impleme
nted
w
hen
a
si
mp
le
r
di
gital
con
t
ro
ll
er
c
an
be
us
e
d
for
M
ic
ro
i
nv
e
rter
unde
r
300W
a
pp
li
cat
ion
[25].
Anothe
r
te
chn
iq
ue
f
or
s
ing
le
-
sta
ge
M
i
cro
i
nv
e
rter
wa
s
us
i
ng
H
ys
te
r
esi
s
Con
t
ro
ll
er
;
hav
i
ng
cu
rr
e
nt
an
d
vo
lt
age
c
on
tr
ol
le
r
pro
pose
d
by D
. P
et
re
us
et
.
al
in
20
13
[
1].
T
he
Hy
ste
resi
s
Co
ntr
oller we
re
im
plement
ed
int
o
5
-
powe
r
s
witc
hes
of
dual
buck
-
boos
t
M
ic
r
oinverter
to
pol
ogy.
In
2018,
a
Bo
os
t
PWM
I
nv
e
rter
[
26]
wi
th
total
of
4
-
s
witc
hes
with
a
fl
ying
capac
it
or
t
o
el
imi
nate
the
le
akag
e
c
urre
nt.
Howe
ver
,
a
minimu
m
of
7
-
le
vel
microi
nv
e
rter t
opolog
y were
bu
il
d i
n o
rd
e
r
t
o reach
40
0V
DC volt
age
b
e
f
or
e
un
dergone
the in
ver
te
r process.
Con
si
der
i
ng
the
a
bove
as
pects,
t
his
pa
per
prese
nts
a
novel
S
i
ng
le
-
sta
ge
tra
ns
f
o
r
mer
-
le
ss
M
ic
r
oinverter
t
opolog
y
us
i
ng
on
l
y
2
-
po
wer
s
witc
hes
w
hic
h
is
strai
gh
tf
orw
ard
l
y
impleme
nted
with
sin
gle
P
V
modu
le
us
uall
y
ta
rg
et
e
d
f
or
the
re
side
ntial
ap
plica
ti
on
with
le
ss
t
han
1k
W
.
T
he
pr
opos
e
d
M
ic
ro
i
nv
e
rter
topolo
gy
onl
y
us
e
si
ng
le
act
ive
powe
r
dev
i
ces
duri
ng
eac
h
c
ycle.
T
he
tr
end
of
t
he
e
xp
ect
ed
power
de
li
ver
ed
by
th
e
PV
-
m
odule,
t
he
t
rend
of
outp
ut
cu
rrent
a
nd
ha
rm
onic
c
onte
nt
wi
th
respec
t
to
modu
la
ti
on
in
dex
a
nd
switc
hing
fr
e
quenc
y
we
re
a
nalyze
d.
O
veral
l,
the
pro
po
s
ed
Si
ng
le
-
sta
ge
M
ic
ro
i
nv
e
rter
to
polo
gy
usi
ng
2
-
powe
r
s
witc
he
s
producin
g
as
lo
w
as
0.8
5%
harmo
nic
c
on
te
nt
w
hich
su
ccess
fu
ll
y
buil
t
an
d
de
monstrate
d
thr
ough sim
ulati
on
base
d on
M
A
TLAB/Si
m
ulink, th
us p
rovide
t
heoreti
cal
v
al
idati
on fo
r
fur
the
r researc
h
.
2.
PROP
OSE
D MIC
ROIN
VE
RTER T
OPO
LOGY
The
pro
posed
t
opolog
y
is
co
nst
ru
ct
ed
base
d
on
the
idea
of
po
sit
ive
AC
-
c
yc
le
is
act
ivate
d
by
sin
gle
powe
r
s
witc
h
wh
il
e
t
he
oth
e
r
ne
gative
AC
-
c
ycle
is
act
ivate
d
by
a
no
t
her
si
ng
le
po
wer
sw
it
ch.
T
he
uniq
ue
ness
of
this
to
po
l
ogy
unde
rlie
s
i
n
t
he
fact
t
hat
a
s
ine
wav
e
is
ge
ner
at
e
d
by
only
us
i
ng
2
-
pow
er
s
witc
hes
a
nd
us
i
ng
sing
le
PV
m
odule.
T
his
can
be
ac
hieve
d
by
sup
ply
i
ng
on
l
y
on
e
po
w
er
s
ource
w
hich
the
n
c
ha
rg
i
ng
an
d
discha
rg
i
ng
t
he
tw
o
-
pa
rall
el
capaci
tors
a
nd
filt
erin
g
-
i
nduc
tor
co
nnect
ed
acr
os
s
point
-
A
a
nd
point
-
B
of
the
ci
rcu
it
to
po
l
ogy,
a
s il
lustrate
d i
n
Fi
gure
1
.
T
he powe
r
s
witc
hes; S
1
a
nd S
2,
ha
ving
50%
of the
duty
cy
cl
e
.
2.1
Photov
olt
aic (PV)
m
od
ule
Photo
vo
lt
ai
c
modu
le
(
PV)
i
s
a
domina
nt
featur
e
f
or
M
ic
ro
i
nv
e
rter
to
polo
gy
desig
n.
PV
m
odul
e
abs
orb
i
rr
a
dia
nce
fro
m
s
olar
ene
r
gy
a
nd
t
urns
into
el
ect
rici
ty.
N
ormal
ly,
one
P
V
m
odule
has
60
-
ce
ll
per
modu
le
or
up
to
120
-
cel
ls
in
the
same
area
.
N
umber
of
c
el
ls
inside
sin
gle
PV
mod
ule
will
determi
ne
the
modu
le
ef
fici
ency.
Determi
ne
the
P
V
m
odule
c
ould
be
the
very
first
ste
p
i
n
desig
ning
the
P
V
s
ys
te
m
app
li
cat
io
n.
Tr
ina
S
olar
F
ra
med
72
-
cel
l
330W
M
od
ule
[
27]
was
c
hose
n
f
or
this
pa
pe
r
a
nd
it
s
datas
heet
is
sh
ow
n
in
Tabl
e
1;
du
rin
g
ST
C
(Irr
a
diance
1000
2
⁄
,
25℃
)
an
d
dur
ing
NO
C
T
(
Irr
adiance
800
2
⁄
,
20℃
)
.
The
ex
pected
el
ect
rical
pow
er;
ge
ne
rated
f
rom
the
PV
m
odule
wh
e
n
pl
aced
ou
tsi
de
(
on
top
of
the
r
oof
)
,
with
sp
eci
fic
irrad
ia
nce,
G
c
an
be
determin
ed
by
(
1
)
–
(6)
[28]
;
w
he
re
a
nd
a
re
2%
and
1
res
pecti
vely
f
or
a
ne
w
PV
m
odule.
Wh
il
e
the
der
a
ti
ng
fact
or
s
a
r
e;
_
is
total
de
-
rati
ng
factors
relat
ed
to
powe
r,
_
is
de
-
rati
ng
fact
or
du
e
t
o
m
odule
mismat
ch
pow
er,
_
is
de
-
rati
ng
facto
r
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S
N
:
2088
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8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
2
,
J
une
2020
:
79
2
–
8
0
0
794
of
power
du
e
t
o
cel
l
te
mp
e
rat
ur
e
,
is
de
-
rati
ng
factor
due
t
o
dirt,
a
nd
is
de
-
rati
ng
facto
r
of
powe
r
du
e
to
a
gein
g.
All t
hese
de
-
ra
t
ing
factor m
ust
me in decima
l po
i
nt.
C
i
n
D2
C1
C2
+
+
A
B
V
i
n
v
+
-
I
i
n
v
V
g
s
1
V
g
s
2
S1
S2
L
f
+
+
Lc
R
L
L
o
a
d
P
V
m
o
d
u
l
e
Figure
1: P
rop
os
e
d
to
polo
gy
with tw
o pa
rall
el
-
capaci
to
r.
Table
1
:
P
ho
t
ovoltai
c
M
od
ule
datas
heet duri
ng
STC an
d N
OC
T
[
27]
Mod
el
Tr
in
a
So
lar
Framed
72
-
cell 33
0
W
m
o
d
u
le
Du
ring
ST
C (
Ir
radian
ce 10
0
0
2
⁄
,
25℃
)
Peak
Power
,
(W)
d
u
ring
ST
C (
)
330W
Maximu
m
Powe
r
Vo
ltag
e,
(V)
3
7
.4V
Maximu
m
Powe
r
Cu
rr
en
t,
(A)
8
.83
A
Op
en
Circuit Vo
lta
g
e,
(V)
4
5
.8V
Sh
o
rt
Circu
it Cu
rr
en
t,
(A)
9
.28
A
Mod
u
le E
ff
i
cien
cy
,
(%)
17%
Du
ring
NOCT
(I
rr
ad
ian
ce 80
0
2
⁄
,
20℃
)
Maximu
m
Powe
r,
(W) du
ring
NOC
T
245W
Maximu
m
Powe
r
Vo
ltag
e,
(V)
3
4
.6V
Maximu
m
Powe
r
Cu
rr
en
t,
(A)
7
.08
A
Op
en
Circuit Vo
lta
g
e,
(V)
4
2
.4V
Sh
o
rt
Circu
it Cu
rr
en
t,
(A)
7
.49
A
=
_
(1)
_
=
_
_
(2)
_
=
1
−
(3)
_
=
1
+
[
(
100%
)
(
−
)
]
(4)
=
1000
⁄
(5)
=
+
[
(
−
20℃
800
2
⁄
)
]
(6)
=
(
)
(7)
=
(
)
(8)
=
=
2
(
)
(9)
= 0.5
-
0
.5
(
2
)
(10
)
2.2
Pri
ncipl
e of
oper
ati
on
Wh
e
n
the
swit
ch
at
posit
ion
-
1
(
ref
e
rr
i
ng
t
o
Fig
ure
1
)
is
in
high
sta
te
,
the
par
al
le
l
-
ca
pac
it
or
in
gets
connecte
d
t
o
the
input
sup
ply
a
nd
c
harg
e
-
m
ood
O
N
t
hu
s
posit
ive
vo
lt
age
is
obs
erv
e
d
at
the
ou
t
pu
t.
Subseque
ntly,
as
the
s
witc
h
i
n
posit
ion
-
2
tu
rn
s
high,
the
pa
rall
el
-
capaci
tor
te
nds
to
dis
charge
an
d
he
nce
a
neg
at
ive
volt
age
is
ob
se
r
ve
d
at
the
outp
ut.
T
he
a
bove
posit
ion
s
a
re
bein
g
rep
eat
ed
at
hi
gh
s
w
it
ching
fr
e
qu
e
nc
y
to
mainta
in
a
c
onsta
nt
vo
lt
age
acro
s
s
the
l
oad.
P
rinciple
of
il
lustrati
ng
the
c
hargin
g
an
d
discha
rg
i
ng
th
e
pa
rall
el
-
cap
aci
tor
a
re
bei
ng
ma
r
ks
by
bl
ue
-
dott
ed
and
r
ed
-
dott
ed
li
ne
resp
ec
ti
vely
.
Con
cl
us
ively
,
switc
h
S
1
c
ha
r
ges
the
pa
rall
el
-
capaci
to
r
wh
il
e
switc
h
S2
dis
charges
it
the
re
by.
F
rom
the
powe
r
per
s
pecti
ve,
th
e
outp
ut
cu
r
re
nt,
vo
lt
ag
e,
a
nd
powe
r
e
qu
at
i
on
of
t
he
ou
t
put
wa
ve
forms
can
be
ref
e
rr
e
d
in
the
(10)
[
29]
.
W
he
re;
is
the
in
ve
rter
ou
t
pu
t
cu
r
ren
t,
is
the
in
ver
te
r
out
pu
t
l
oad
volt
age
,
w
hile
is
the
in
ver
te
r
outp
ut
powe
r.
Inve
rter
ou
t
put
po
wer
i
n
(
9)
can
be
tran
sf
ormed
i
nto
(
10)
by
us
in
g
M
at
he
mati
cal
t
ran
s
f
or
mati
on.
In
(
10)
,
2
can
be
substi
tuted
with
=
2
;
wh
ere
is
the
gr
i
d
f
requ
ency
of
50Hz.
2.3
Contr
ol
an
d
mod
ul
at
i
on
s
t
rat
e
gy
The
pro
posed
M
ic
r
oi
nve
rter
mod
ulati
on
i
s
ha
nd
le
d
us
i
ng
a
sta
nd
a
rd
unip
olar
Sin
us
oi
dal
P
ulse
Width
Mo
du
la
ti
on
(
SP
W
M
),
as
sho
wn
i
n
Fig
ure
2
.
T
he
un
i
po
la
r
SP
W
M
normall
y
re
qu
i
res
tw
o
si
nuso
i
dal
wav
e
s
w
hich
a
re
of
same
ma
gn
it
ude
a
nd
frequ
e
nc
y
but
180
°
out
of
phas
e
as
dep
ic
te
d
i
n
Fig
ure
2
a.
T
he
t
w
o
modu
la
ti
ng
wa
ves
are
c
ompa
red
with
a
c
ommo
n
tria
ng
ular
ca
rr
ie
r
wa
ve
ge
ne
rati
ng
t
wo
gating
si
gnal
s
f
or
switc
h
S1
an
d
S2
res
pecti
ve
ly.
Her
e
,
s
witc
h
S
1
is
m
odulate
d
i
n
r
efe
r
ence
t
o
the
posit
ive
si
nu
s
oi
dal
to
gen
e
rate
t
he
posit
ive
gri
d
cycl
e
an
d
switc
h
S
2
i
s
m
odulate
d
with
ne
gative
sinu
s
oid
al
re
fe
ren
ce
(
with
phase)
Po
sitio
n
-
1
Po
sitio
n
-
2
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In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
A novel
sin
gle
-
stag
e
PWM
mi
croinverter
to
polo
gy usin
g
tw
o
-
powe
r swit
ch
es (
A
. R
az
i)
795
to
create
the
ne
gative
half
of
the
gr
id
c
ycle.
Hen
ce
,
only
one
s
witc
h
car
ries
the
in
ver
te
r
’
s
cu
rr
e
nt
,
du
ri
ng
the
posit
ive
a
s
well
as
t
he
ne
gative
c
ycle.
T
he
c
hargin
g
of
the
par
al
le
l
-
ca
pacit
or
is
ac
hieved
th
rou
gh
s
witc
h
S1
du
rin
g
posit
ive
cy
cl
e.
T
he
se
tw
o
switc
he
s
e
xp
e
rience
hi
gh
f
reque
nc
y
switc
hing
duri
ng
bo
t
h
t
he
po
sit
ive
and
ne
gative c
ycle, the
reby e
ns
uri
ng
vo
lt
ag
e con
tr
ol ove
r
the capacit
ors.
The
s
witc
hing
seq
uen
ce
for
a
sing
le
-
ph
a
se
c
on
st
ru
c
ti
on
is s
how
n
i
n
Ta
ble
2.
Table
2
: S
witc
hing stat
es
of the
pro
po
se
d M
ic
ro
in
ver
te
r
State
S1
S2
Vlo
ad
Zer
o
state
0
0
0
Po
sitiv
e state
1
0
Vin
/2
Neg
ativ
e state
0
1
-
Vin
/2
Zer
o
state
1
1
~
0
(a)
(b)
(c)
(d)
Figure
2
:
Un
i
pola
r SP
WM fo
r
the
prop
os
e
d mi
cro
i
nv
e
rter t
opolog
y
: (a
)
Si
nu
s
oi
dal & tria
ng
le
ref
e
re
nces
, (b)
Po
sit
ive satt
e S
1,
(c) Ne
gative
S2, (d
)
Ze
ro st
at
e S1
S2
2.4
Modes
of oper
at
i
on
To
sat
isf
y
t
he
po
wer
c
onve
rsion
proce
ss,
t
wo
m
od
e
s
of
op
e
rati
on
ha
ve
bee
n
de
ri
ved
for
this
topolo
gy.
T
he
switc
hing
se
qu
ence
for
a
sin
gl
e
-
phase
c
onstr
uction
is
s
how
n
in
Ta
ble
2
a
nd
Fi
gure
3
sho
w
the
equ
i
valent circ
uit o
f
the
prop
os
e
d
micr
oinve
rter top
ology d
ur
i
ng sw
it
chi
ng stat
es.
C
i
n
D2
C1
C2
+
+
A
B
V
l
o
a
d
+
-
I
i
n
v
V
g
s
1
V
g
s
2
S1
S2
L
f
+
+
Lc
R
L
L
o
a
d
P
V
m
o
d
u
l
e
C
i
n
D2
C1
C2
+
+
A
B
V
l
o
a
d
+
-
I
i
n
v
V
g
s
1
V
g
s
2
S1
S2
L
f
+
+
Lc
R
L
L
o
a
d
P
V
m
o
d
u
l
e
C
i
n
D2
C1
C2
+
+
A
B
V
l
o
a
d
+
-
I
i
n
v
V
g
s
1
V
g
s
2
S1
S2
L
f
+
+
Lc
R
L
L
o
a
d
P
V
m
o
d
u
l
e
(a)
(b)
(c)
Figure
3: E
qu
i
valent circ
uit o
f
the
prop
os
e
d mi
cro
i
nv
e
rter t
opolog
y durin
g swit
chi
ng stat
es:
(
a)
P
os
it
ive stat
e,
(b) Negati
ve
st
at
e, and
(c)
Zer
o
sta
te
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.
2
,
J
une
2020
:
79
2
–
8
0
0
796
2.
4
.1
.
Posi
tive
state
The
posit
ive
modu
la
ti
ng
si
gnal
is
subje
ct
e
d
f
or
co
m
par
is
on
to
a
ref
e
re
nce
tria
ngular
wav
e
f
or
m
in
order
to
genera
te
the
re
qu
i
red
pulse
f
or
s
witc
h
S
1
.
Th
us
,
c
reati
ng
a
gate
pu
lse
f
or
s
witc
h
S1
durin
g
thi
s
sta
te
wh
il
e
s
witc
h
S
2
re
main
OF
F
for
the
c
omplet
e
po
sit
ive
c
yc
le
.
This
en
sure
s
the
pa
rall
el
-
capaci
tor
c
ha
rg
i
ng
i
n
this
sta
ge
.
High
fr
e
quenc
y
s
witc
hing
helps
to
re
du
ce
the
siz
e
of
the
ca
pa
ci
tors.
Th
e
ga
t
e
pulse
f
or
s
w
it
ch
S
1
and the
flo
w of cu
rr
e
nt du
rin
g t
his stat
e are
r
epr
ese
nted
in F
ig
ure
2
b
an
d Fi
gure
3a res
pecti
vely.
2.
4
.2
.
Ne
gativ
e
st
at
e
The
neg
at
ive
modu
la
ti
ng
si
gn
al
with
a
phase
a
ng
le
of
180º
is
s
ubje
ct
ed
f
or
c
omp
ariso
n
to
a
ref
e
ren
ce
tria
ngula
r
wav
e
f
orm
in
or
der
to
gen
e
rate
t
he
re
qu
i
red
pulse
f
or
switc
h
S
2
.
Th
us
,
creati
ng
a
gate
pu
lse
f
or
switc
h
S
2
durin
g
t
hi
s
sta
te
wh
il
e
s
witc
h
S
1
rema
in
O
FF
for
the
com
plete
ne
ga
ti
ve
cycle.
Th
e
gate
pu
lse
f
o
r
s
witc
h
S
2
a
nd
the
flo
w
of
c
urre
nt
duri
ng
this
sta
te
are
re
pr
e
sented
i
n
Fi
g
ure
2c
an
d
Fig
ur
e
3
b
resp
ect
ivel
y.
2.
4
.3
.
Ze
r
o
s
t
ate
Ther
e
a
re
tw
o
zero
-
sta
te
c
ondi
ti
on
s
f
or
this
t
opolog
y.
Fir
st
zero
-
sta
te
c
ondi
ti
on
is
create
d
by
tu
r
ning
OF
F
both
s
witc
hes.
At
this
mo
me
nt,
t
her
e
is
no
outp
ut
coming
out
from
t
he
micr
oi
nv
e
rter.
Both
ou
t
pu
t
current,
an
d
load
volt
age
,
are
e
qu
al
to
zero.
Seco
nd
zero
-
sta
te
c
onditi
on
ha
ppen
s
w
he
n
both
switc
hes
are
a
ct
ive
at
the
sa
me
ti
me.
At
t
hi
s
moment,
both
ou
t
pu
t
c
urre
nt,
an
d
loa
d
volt
age,
are
cancel
li
ng
eac
h
oth
e
r
fro
m
posit
ive
a
nd
ne
gative
sta
te
,
th
eref
or
e
produc
ed
nea
rly
zer
o
outp
ut
,
as
sho
wn
in
Fig
ure
3
c
.
Ba
r
e
in
min
ds
t
hat
,
zer
o
-
sta
te
c
onditi
on
s
f
or
t
his
topolo
gy
only
occ
ur
at
very
sh
ort
ti
me
du
ring
th
e
transiti
ons
between
ne
gative
an
d
po
sit
ive
s
ta
te
.
The
gate
pu
lse
a
nd
the
f
low
of
cu
rr
e
nt
durin
g
ze
ro
sta
te
are
represe
nted
i
n Fi
g
ure
2d a
nd
Figure
3c res
pe
ct
ively.
3.
SIMULATI
O
N RESULTS
N
ume
rical
sim
ulati
on
of
the
pro
po
se
d
M
ic
r
oinverter
is
co
nducted
t
o
veri
fy
the
pe
rfo
r
mance
of
th
e
topolo
gy
.
Sim
ulati
on
wa
s
pe
rformed
by
us
ing
M
A
TLAB/
Simuli
nk,
in
a
detai
le
d
model
.
T
o
de
monstr
at
e
the
ci
rcu
it
pr
inci
pl
e,
the
P
V
m
odule
f
rom
Tri
na
So
la
r
F
ram
ed
72
-
cel
l
Mo
du
le
is
us
e
d.
The
pa
rameter
s
an
d
com
pone
nts r
e
al
ise
d
f
or
MA
TLAB/Si
m
ulin
k
sim
ulati
on
ar
e li
ste
d
in
Tabl
e
3
.
3.1
.
Tr
end
of
and
THD
with re
s
pect
to Fs
The
s
witc
hing
fr
e
qu
e
nc
y,
we
re
va
ried
from
5kHz,
10kHz,
25kHz
an
d
50
kH
z
,
in
orde
r
to
anal
ys
e
the
im
pacts
on
t
he
outp
ut
current,
a
nd
harmo
nic
c
onte
nt,
TH
D
of
the
pro
po
s
ed
Sing
le
-
sta
ge
M
ic
r
oinverter
.
T
he
irra
dia
nc
e
an
d
te
mp
e
r
at
ur
e
of
t
he
P
V
mod
ule
were
fi
xed
acc
ord
ing
to
STC
co
nd
it
io
n
(Irr
a
diance
1000
2
⁄
,
25℃
)
. T
he
m
odula
ti
on
in
de
x was
fixe
d,
M
a =
1.
Figure
4
il
lustrate
s
the
tre
nd
betwee
n
ou
t
put
cu
rr
e
nt,
an
d
T
HD
with
r
espect
to
s
witc
hing
fr
e
qu
e
nc
y,
.
Th
e
switc
hing
f
r
equ
e
nc
y,
aff
e
ct
ed
the
am
plit
ud
e
of
the
outp
ut
cu
rr
e
nt,
as
the
switc
hing
fr
e
quenc
y,
bec
om
e
higher
,
the
am
plit
ud
e
of
outp
ut
cu
rr
e
nt,
decre
ased
si
nce
the
chargi
n
g
and
disc
hargin
g
ti
mes
of
the
par
al
le
l
-
ca
pac
it
or
bec
om
e
sign
i
ficantl
y
s
ho
rter
with
an
i
nc
rease
in
s
witc
hing
fr
e
qu
e
nc
y
,
(chan
ge
from
10kHz,
25kHz
an
d
50kHz).
T
he
ha
rm
on
ic
c
on
te
nt,
TH
D
al
so
de
creases
w
he
n
the
switc
hing
fr
e
quenc
y,
inc
reas
es, since
it
r
e
quires less
ti
me
to complet
e
on
e cycle.
Table
3
:
Pro
posed mi
cro
i
nver
te
r
pa
rameter
s
Para
m
eter
Variable
Valu
e
PV m
o
d
u
le
330W
DC lin
k
capacito
r
400µF
Grid f
requ
en
cy
5
0
Hz
Switch
in
g
f
reqeu
n
cy
5
0
k
Hz
Parallel
-
capacito
r
1
1
20µF
Parallel
-
capacito
r
2
2
20µF
Ind
u
cto
r
filter
1
5
0
m
H
Co
u
p
lin
g
ind
u
cto
r
1
5
0
m
H
Load
,
1
0
Ω,
5
m
H
Po
wer
switch
es
1
,
2
IGBTs
Dio
d
es
1
,
2
-
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 novel
sin
gle
-
stag
e
PWM
mi
croinverter
to
polo
gy usin
g
tw
o
-
powe
r swit
ch
es (
A
. R
az
i)
797
Figure
4: T
rend
of outp
ut c
urren
t,
and TH
D
p
e
rcen
ta
ge wit
h resp
ect
t
o
s
w
it
ching
fr
e
que
nc
y,
3.2
.
Tr
end
of
and
THD
with re
s
pect
to M
a
The
mod
ulati
on
in
de
x,
M
a
f
or
both
SP
W
M
(
∅
=
0
180°
)
we
re
vari
ed
wit
h
the
s
ame
value
s
from
0.1
unti
l
1,
to
a
nalyse
t
he
impact
s
on
the
outp
ut
curr
ent,
and
ha
rm
on
ic
c
on
te
nt,
THD
of
the
pro
po
se
d
Sin
gle
-
sta
ge
M
ic
r
oi
nv
e
rter.
T
he
ir
r
adiance
an
d
te
mp
e
ratur
e
of
t
he
P
V
mod
ule
wer
e
fixe
d
ac
c
ordin
g
to
STC
co
ndit
ion
(Irr
a
diance
1000
2
⁄
,
25℃
)
.
The
s
witc
hing
f
requ
ency,
was
ch
os
e
n
at
50kH
z
since it
prod
uc
ed
lo
we
r harm
on
ic
c
onte
nt
from p
rev
i
ou
s
a
nalysis.
Figure
5
il
lustr
at
es
the
t
rend
of
outp
ut
c
urre
nt,
an
d
T
H
D
pe
rcen
ta
ge
repr
esented
by
the
red
and
blu
e
li
ne
a
ccordin
gly,
with
res
pect
to
m
odulati
on
in
de
x,
M
a
.
It
is
obs
erv
e
d
that
as
modu
la
ti
on
i
nd
ex,
M
a
increase
d,
the
ou
t
pu
t
volt
age
,
al
so
inc
rease
d
.
Wh
e
n
the
m
odulati
on
i
n
dex,
Ma
i
ncr
ease
d,
the
ti
me
f
or
the
switc
h
e
s
s
yn
t
hesized
by
S
PWM
t
o
tu
rn
ON
will
al
so
increase,
res
ulti
ng
in
m
uch
l
onge
r
c
hargin
g
ti
me.
Ther
e
f
or
e,
the
energ
y
st
or
e
d
in
t
he
pa
rall
el
-
capaci
tor
will
increase
d.
In
th
e
ot
her
hand,
a
s
m
odulati
on
i
nd
e
x,
Ma
inc
rea
se
d
,
the
ha
rm
on
ic
pe
rcen
ta
ge,
T
H
D
will
d
ecrea
s
ed
f
rom 5.2
8%
to
0.8
5%,
fo
r mo
du
la
ti
on in
de
x,
M
a
0.1
un
ti
l
0.7
a
ccordin
gly.
Howev
e
r,
ha
rm
onic
con
te
nt,
T
H
D
will
increas
ed
f
r
om
1.0
8%
to
2.0
7%
,
when
the
modu
la
ti
on
in
de
x,
M
a
va
ried
f
rom
0.8
un
ti
l
1
acc
ordin
gly
.
T
he
pro
pose
d
Mi
cro
in
ver
te
r
suc
cessf
ully
f
ollow
e
d
the
IEC
61727
sta
nd
a
rd
f
or
S
ing
le
-
sta
ge
M
ic
ro
i
nv
e
rter
nominal
powe
r
le
ss
than
10kW
and
50Hz
sy
st
em
tha
t
harmo
nic
c
urr
ent’s
c
onte
nt,
THD
m
us
t
be
le
ss
than
4%,
represe
nted
by
the
dott
ed
-
bla
ck
li
ne
in
Fig
ur
e
5.
Th
us
,
f
or
c
ontr
olli
ng
meth
od
i
n
the
f
uture,
th
e
al
gorithm
m
ust
be
ca
refull
y
pick
out
the
m
odulati
on
in
de
x
that
pro
du
ces
h
a
rm
on
ic
c
onte
nt
be
low
t
hat dott
ed
-
blac
k
li
ne o
f 4
% THD sta
nda
rd.
3.3
.
Tr
end
of
of
t
he P
V
wi
th
re
spect t
o
ir
ra
diance
and
amb
ie
nt
t
e
mper
ature
The
ir
rad
ia
nce
an
d
am
bient
t
empe
rature
val
ues
wer
e
va
ried
to
a
naly
se
th
e
impact
on
t
he
ex
pected
powe
r
pro
duce
d
by
th
e
P
V
m
odule,
.
The
e
xpect
ed
powe
r
de
li
ver
ed
by
the
PV
-
m
odule
ca
n
be
cal
culat
ed
by
us
i
ng
(
1
)
.
Figure
6
il
lust
rates
t
he
t
rend
of
ex
pecte
d
powe
r
deli
vered
by
P
V
-
m
odule,
wh
e
n
t
he
irrad
ia
nce
a
nd
am
bient
te
m
per
at
ur
e
we
re
va
ried
f
rom
100
2
⁄
to
1000
2
⁄
and
27℃
unti
l
45
℃
accor
dingly
.
B
oth
blac
k
-
dott
ed
li
ne
s
i
nd
ic
at
e
the
ma
ximum
po
wer
du
rin
g
STC,
a
nd
NOC
T,
with
330W a
nd 24
5W
resp
ect
iv
el
y.
The
bl
ue
an
d
r
ed
li
nes
re
pr
e
s
ent
the
ex
pecte
d
po
wer
,
w
he
n
am
bient
te
m
per
at
ur
e
a
nd
ir
rad
ia
nce
wer
e
fix
ed
at
32
℃
an
d
60
0
2
⁄
accor
dingly
.
It
is
cl
early
sho
w
t
hat,
e
xpect
ed
powe
r
delivere
d
by
the
P
V
-
modu
le
,
pro
du
ci
ng
sli
gh
tl
y
ch
an
ge
of
powe
r
w
he
n
the
ir
rad
ia
nce
is
fixe
d.
T
he
expect
ed
power
eff
ic
ie
nc
y
during
STC
an
d
NO
CT
a
re
ar
ound
ab
out
60.
61%
an
d
81.63
%
at
the
P
V
-
mod
ule
w
he
n
th
e
irrad
ia
nce
is
fixed
at
60
0
2
⁄
wh
i
le
the
am
bient
te
mp
e
ratur
e
is
va
ried
from
27℃
unti
l
45
℃
.
H
oweve
r,
exp
ect
e
d
powe
r
de
li
ver
e
d
by
the
P
V
-
mod
ule,
is
di
rectl
y
a
ffec
te
d
by
t
he
ir
r
adiance
val
ue
r
ecei
ved
by
th
e
PV
m
odule.
T
hu
s
,
it
ca
n
be
co
nclu
de
d
t
ha
t,
irra
diance
giv
e
m
or
e
im
pact
to
ward
e
xp
ect
e
d
powe
r
,
com
par
e
d
t
o
t
he
a
mb
ie
nt
te
mp
e
ratur
e
of
the
s
urr
oundin
g.
If
the
Sin
gl
e
-
sta
ge
M
ic
ro
i
nv
e
rter
is
inte
nd
e
d
t
o
pro
du
ce
powe
r
ap
pro
ximate
ly
or
great
er
tha
n
powe
r
du
rin
g
N
OCT
c
on
diti
on
,
the
700
2
⁄
ir
rad
ia
nce
must
be
achie
ved
for
highe
r
ex
pect
ed
po
wer
e
ff
ic
ie
ncy
.
The
pro
po
s
ed
Si
ng
le
-
s
ta
ge
M
ic
r
oinv
erter
with
700
2
⁄
and
ab
ove
ir
ra
diance
ca
n
be
us
e
fu
l
durin
g
arou
nd
10.
05
am
unti
l
15.
05pm,
M
al
a
ys
ia
n
hour
ba
sed
on
the
sample
daily
s
olar
ir
ra
diance
prof
il
e
giv
e
n
i
n
[23]
.
2
.04
2
.08
2
.12
2
.16
6
1
.
2
6
1
.
4
6
1
.
6
6
1
.
8
62
6
2
.
2
0
10
20
30
40
50
Switch
in
g
f
requ
en
cy
,
Fs (Hz)
Tren
d
of
Iinv
erter
&
THD
with
resp
ect
to
Fs
I inve
rte
r (
m
A
)
TH
D
(%
)
I
in
v
erter (
m
A)
THD
(%)
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.
2
,
J
une
2020
:
79
2
–
8
0
0
798
Figure
5. Tre
nd
of outp
ut c
urren
t,
and
THD pe
rce
ntage wit
h resp
ect
to
m
odulati
on
ind
e
x,
M
a.
Figure
6. Ex
pe
ct
ed
po
wer del
ivere
d by the
PV
-
mod
ule,
w
it
h
res
pect to
Ir
rad
ia
nce a
nd
Ambie
nt tem
pe
ratur
e
.
4.
COMP
AR
I
S
ON
B
ET
WEE
N
P
ROP
OSE
D
MICRO
IN
VERTER
TO
POLOG
Y
A
N
D
OT
HER
TOPOL
OGIE
S
In
this
sect
io
n,
the
propos
ed
Sin
gle
-
sta
ge
M
ic
r
oinvert
er
t
opolog
y
is
co
m
par
e
d
wi
th
hybri
d
of
cl
assic
al
inv
ert
er top
ologies e
xp
la
ine
d
i
n
t
he
Introd
uction s
ect
ion
ea
rlie
r,
as sho
wn in T
a
ble 4.
Ba
se
d
on
the
Table
4,
it
is
cl
early
sho
wing
that
the
pro
po
sed
Sin
gle
-
sta
ge
M
ic
ro
i
nv
e
rt
er
to
po
l
ogy
on
l
y
hav
e
2
-
po
wer
switc
hes
,
and
only
sin
gle
-
po
wer
s
witc
h
is
act
ive
duri
ng
each
cycle.
The
numb
e
r
of
powe
r
switc
hes
hav
e
bigger
im
pa
ct
on
the
c
ost
,
siz
e
and
weig
ht
of
the
M
ic
r
oinverte
r
unit
.
All
of
thi
s
pap
e
rs [
1
-
9,
26
]
s
upporte
d
thi
s r
el
at
ionshi
p o
f numbe
r of sw
it
ches v
e
rs
us
c
os
t/
siz
e of the
inv
e
rter.
F
ur
t
hermo
re,
base
d
on
the
pro
posed
M
ic
r
oi
nv
e
rter’
s
oper
at
ion
m
od
e
s
di
scuss
ea
rlie
r,
only
1
-
powe
r
switc
h
is
act
iv
e
du
rin
g
t
hat
s
ing
le
c
urre
nt
pa
th
durin
g
pos
it
ive
or
ne
gative
sta
te
;
w
hich
le
a
ds
to
re
duce
t
he
powe
r
los
ses.
Since
th
e
pow
er
los
ses
c
om
e
from
the
dy
na
mic
volt
age
a
nd
cu
rr
e
nt
of
the
s
witc
h
duri
ng
th
e
tur
n
-
off
a
nd
t
urn
-
on
tran
sie
nt
s,
th
us
the
sma
ll
er
num
ber
o
f
powe
r
s
witc
he
s
are
re
quire
d
t
o
pro
du
c
e
a
n
outp
ut
vo
lt
age
re
flect
ed
to
le
sse
r
po
wer
l
os
ses
[11,
17,
18
,
26]
.
T
he
pr
opos
e
d
Si
ng
le
-
sta
ge
M
ic
ro
i
nv
e
rter
to
po
logy
wer
e
ver
i
fied
with
di
ff
e
ren
t
analysis
to
obs
erv
e
t
he
tren
d
of
e
xpect
ed
power,
ou
tp
ut
cu
r
re
nt,
and h
a
rm
onic
con
te
nt,
T
H
D.
Table
4.
C
omp
ariso
n of Sin
gl
e
-
sta
ge Micr
oi
nv
e
rter
t
opol
ogie
s
Ref
Micr
o
in
v
erter Top
o
lo
g
y
Po
wer
Switch
es
Tr
an
sfo
r
m
er
Ad
d
itio
n
al Co
m
p
o
n
en
ts
Prop
o
sed
M
icroin
v
erter
w
ith
Para
llel
-
Cap
acito
r
2
-
2
Cap
acito
rs,
2
Di
o
d
es
[19
]
Fu
ll
-
b
ridg
e with p
u
sh
-
p
u
ll & ripp
le
-
p
o
rt
co
n
v
erter
10
Hig
h
-
Frequ
en
cy
-
[2]
Fu
ll
-
b
ridg
e with freq
u
en
cy
con
v
ersio
n
cir
cu
it
6
Hig
h
-
Frequ
en
cy
1
I
n
d
u
cto
r
[20
]
Half
-
b
ridg
e
with
H
F tr
an
sfo
r
m
er
4
Hig
h
-
Frequ
en
cy
2
Cap
acito
rs
[7]
Fly
b
ack au
x
iliary circuit
3
Low
-
Fr
eq
u
en
cy
1
Cap
acito
r,
3 Ind
u
cto
rs,
3
Diod
es
[24
]
Co
u
p
led
-
in
d
u
cto
r
d
o
u
b
le
-
b
o
o
st
4
-
4
Ind
u
cto
rs
[1]
Du
al bu
ck
-
b
o
o
st
5
-
1
I
n
d
u
cto
r,
2 Dio
d
es
[26
]
Bo
o
st PW
M
Inv
ert
er
4
-
1
Cap
acito
r
5.
CONCL
US
I
O
NS
This
pap
e
r
pr
e
sents
a
Si
ng
le
-
sta
ge
M
ic
ro
i
nverter
in
ver
te
r
with
a
new
t
opology,
w
hic
h
use
a
pa
rall
el
-
capaci
tor
,
t
ransforme
r
-
le
ss
a
nd
inte
gr
at
in
g
with
only
tw
o
(2)
-
powe
r
s
wit
ches
.
A
SP
W
M
with
tw
o
sinu
s
oi
dal
wav
e
that
18
0º
a
par
t
are
rea
li
zed
to
init
ia
te
the
switc
hing
se
que
nces.
The
operati
on,
switc
hing
sta
t
e
an
d
ou
t
pu
t
cu
rr
e
nt
f
or
the
pro
po
sed
t
op
olog
y
hav
e
been
dis
cusse
d.
From
t
he
sim
ulati
ons
res
ults,
t
he
propose
d
Sing
le
-
sta
ge
M
ic
r
oinverter
topolo
gy
we
re
su
ccess
fu
ll
y
te
ste
d
to
per
c
ei
ve
the
tre
nd
of
e
xpect
ed
powe
r
delivere
d
by
t
he
PV
-
m
odule
with
res
pect
to
irra
diance
a
nd
am
bient
te
m
pe
ratur
e
,
t
he
tre
nd
of
outp
ut
c
urren
t
and
T
HD
wi
th
re
sp
ect
t
o
m
odulati
on
ind
e
x
a
nd
s
witc
hing
fr
e
quenc
y.
T
he
pro
posed
Si
ng
l
e
-
sta
ge
M
ic
r
oinverter
topolo
gy
has
s
ever
al
ad
va
nta
ges
ove
r
oth
e
r
in
ver
te
r
t
opol
og
ie
s
in
te
r
ms
of
(i)
t
otal
c
ount
of
act
ive d
e
vices,
and (ii) t
he n
umbe
r of
switc
he
s in
c
urre
nt p
a
th which
is
dir
ect
ly r
el
at
ed
t
o p
ow
e
r
l
os
ses.
30
35
40
45
50
55
60
65
1
0
.9
0
.8
0
.7
0
.6
0
.5
0
.4
0
.3
0
.2
0
.1
0
1
2
3
4
5
6
Mod
u
latio
n
ind
ex
,
Ma
Tren
d
of
Iinv
erter
and
THD
with
resp
ect
to
Ma
TH
D
(%
)
Iinve
rte
r (
m
A
)
0
1
0
0
2
0
0
3
0
0
4
0
0
0
1
0
0
2
0
0
3
0
0
4
0
0
P
roc
(W
) w
it
h fix
e
d Ta
mbi
e
nt at
32
ͦ
C
P
roc
(
W
) w
i
th f
i
xe
d Ir
r
a
dianc
e
a
t
600W
/
m2
Trend
of
of th
e PV
with
r
es
pe
ct
to
Irra
diance
or
Ambie
nt
te
m
pe
ratur
e
.
(
I
EC 61727)
TH
Di st
a
nda
rd
P
S
TC = 330W
P
NO
C
T =
245W
I
in
v
erter (
m
A)
THD
(%)
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 novel
sin
gle
-
stag
e
PWM
mi
croinverter
to
polo
gy usin
g
tw
o
-
powe
r swit
ch
es (
A
. R
az
i)
799
ACKN
OWLE
DGE
MENTS
This
w
ork
was
fina
ncial
ly
suppo
rted
by
t
he
M
inist
r
y
of
H
igh
e
r
Ed
ucati
on
(
MoHE
),
M
a
la
ys
ia
.
The
auth
or
s
w
ould
li
ke
to
tha
nk
1
Star
Acc
re
diati
on
U
nde
r
Asea
n
Ene
rgy
M
a
nag
e
men
t
Sche
me
(A
E
M
A
S
)
Pr
oject
N
o.
60
0
-
IRMI/D
ANA
5/3
/B
ES
TA
RI
(
K
Y)
(
001/
2019)
f
or
fina
ncial
s
upportin
g
for
the
pa
pe
r.
The
auth
or
s
al
so
w
ou
l
d
li
ke
t
o
ac
knowle
dge
the
Ce
nter
f
or
R
obotics
a
nd
I
nd
us
tria
l
A
utoma
ti
on
(CeR
IA),
Fakult
i
Keju
ru
te
raa
n
E
le
ktrik
,
Un
i
versi
ti
Tek
nik
al
M
al
aysia
M
el
aka,
76
100,
D
uri
an
T
unggal
,
M
el
aka
,
M
al
a
ysi
a
an
d
Ce
ntre
of
El
ect
rical
Po
we
r
En
gin
ee
rin
g
Stud
ie
s
(CE
PES),
Fa
ku
lt
i
Kejuruteraa
n
Ele
ktrik
,
U
ni
ver
sit
i
Tek
no
l
og
i
MA
RA,
4045
0
S
ha
h Alam,
Sela
ngor,
M
al
a
ys
ia
.
REFERE
NCE
S
[1]
D.
Petre
uş,
S.
Dara
ban
,
I.
Cio
ca
n,
T.
Pat
ara
u,
C.
Morel
,
and
M.
Mac
hmou
m,
“L
ow
Cost
Sin
gle
Stag
e
Micro
-
inve
rt
er
with
M
PP
T
for
Grid
Co
nnec
t
ed
Appli
cat
ions,”
So
lar E
n
e
rgy
,
vol
.
92
,
pp
.
241
–
255,
Jun.
2
013.
[2]
J.
Jana
,
H.
Saha
,
and
K.
Das
B
hat
t
ac
har
y
a,
“A
Rev
ie
w
of
Inve
r
te
r
Topol
ogi
es
f
or
Single
-
Phase
Grid
-
Connec
t
ed
Phtovolt
aic
Sys
t
em
s,”
R
ene
wabl
e
and
Susta
inable
En
ergy
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w
s
,
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[3]
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T.
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rnif
i,
P.
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t
,
G.
B
ac
h
ir,
and
M.
Ail
le
r
ie
,
“Ne
w
Topo
lo
gy
of
Photovolt
a
ic
Micro
inv
er
te
r
base
d
on
Boost
Convert
er
,
”
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gy
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d
ia
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l.
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,
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[4]
H.
A.
Sher
and
K.
E.
Addow
ee
s
h,
“Mic
ro
-
inve
r
t
ers
—
Promisin
g
Solut
ions
in
S
ola
r
Photovolt
aics,”
En
ergy
for
Sustainabl
e
Dev
el
opment
,
vo
l. 1
6,
pp
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–
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[5]
M.
H.
Z
are,
M.
Moham
adi
an
,
and
R
.
B
ei
ran
v
and,
“Single
-
Sta
ge
AC
Modul
e
with
Seri
es
Pow
er
Dec
oup
li
ng
Capa
bility
for
C
onnec
t
ing
PV
to
a
Singl
e
-
Phase
Pow
er
Grid,
”
IE
T
Powe
r
E
le
c
tronic
s
,
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.
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.
517
–
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2017.
[6]
J.
J.
Shriginia
and
V.
Siva
chidhamba
r
ana
th
an
,
“PV
Microi
n
ver
te
r
Topo
logy
base
d
on
Pha
se
Shift
Pow
er
Modulat
ion
T
echnique
using
Fre
quenc
y
Conversi
on
Cir
cui
t
,
”
in
2
016
Se
cond
Int
e
rnational
Confe
r
enc
e
on
S
ci
en
ce
Technol
ogy
Enginee
ring a
nd
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nageme
nt
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NST
EM)
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M.
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il
i
an,
M.
Mal
eka
ne
R
ad,
E.
Adib
,
an
d
H.
I
.
Farz
anehfard,
“Ne
w
Si
ngle
-
Stag
e
Soft
-
Sw
it
chi
ng
Flyb
a
ck
Inve
rte
r
for
AC
Module
Appl
icati
on
with
Si
mp
le
Ci
rcu
i
t.,”
in
The
6th
Powe
r
El
e
ct
ronics,
Dr
iv
es
Syst
ems
&
Technol
ogi
es
Co
nfe
renc
e
(
PE
DS
TC
2015
)
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[8]
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Z
.
Moha
mm
a
d
Noor,
A
.
M.
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,
N.
N
.
Ma
hza
n,
and
I
.
R
.
I
bra
him,
“A
rev
i
e
w
of
Sing
le
-
Ph
ase
Singl
e
St
age
Inve
rte
r
Topo
lo
gie
s
for
Photov
olt
aic
Sys
tem,
”
in
Proc
ee
dings
-
2013
IE
EE
4t
h
Control
and
Syste
m
Gr
aduat
e
Re
search
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ll
oq
uium,
ICSGRC
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S.
Z
.
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ma
d
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,
A
.
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,
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M.
A.
M.
R
adzi,
“Single
-
Ph
ase
Single
St
age
Str
ing
Inve
rte
r
for
Grid
Connec
t
ed
Phot
ovolt
aic
Sys
tem,
”
Journal
of
App
li
ed
Me
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ic
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Mate
ria
ls,
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,
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Kaka
r
,
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.
M.
Ayob,
N
.
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N
ordin,
M.
S.
Ari
f,
A.
Jus
oh,
and
N.
D
.
Muha
mad,
“A
nove
l
sin
gle
-
phase
PWM
a
symme
t
rical
m
ult
ilevel
inve
r
ter
with
nu
mbe
r
of
sem
ic
ondu
ctor
sw
it
ch
es
r
ed
uct
ion
,
”
Int
ernati
onal
Journal
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Powe
r E
le
c
troni
c
and
Dr
ive
S
yst
em
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PE
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l.
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.
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.
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[11]
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R.
Hasan
and
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Mekhi
le
f
,
“
Highly
Eff
ic
i
ent
Flybac
k
Microinve
rte
r
for
Grid
-
conne
c
te
d
Roof
top
PV
Sys
te
m,”
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nergy
,
vo
l.
146
,
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.
511
–
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22,
2017
.
[12]
Te
ch
ina
vo.
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port
-
Glob
al Sola
r
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cro
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e
rte
r
Mark
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16.
[13]
N.
Mohd
Al
i
e
t
al
.
,
“A
r
evi
e
w
of
d
iffe
r
ent
appl
i
ca
t
ions
of
Wi
re
le
ss
Sensor
Network
(W
S
N)
in
monitorin
g
reh
abilitati
on
,
”
J
ournal
of
Te
le
co
mm
unic
ati
on,
Elec
troni
c
and
Co
mputer
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n
ee
r
ing
,
vo
l. 10, no.
1
–
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2018
.
[14]
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Pal
ani
sa
my,
K.
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aya
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ar
,
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Venka
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al
a
m,
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M.
N
a
ray
ana
n
,
D
.
Sar
ava
naku
ma
r
,
an
d
K.
Sar
ava
n
an,
“Sim
ulation
of
var
ious
DC
-
DC
c
onve
rte
rs
for
photovoltaic
s
ystem
,
”
In
te
rnat
ional
Journal
o
f
E
lectric
a
l
and
Computer
Engi
n
ee
ring (
I
JE
C
E)
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.
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.
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17,
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[15]
A.
Raz
i
,
M.
N
.
Hiday
at
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N.
Seroji,
“Mic
roinv
erter
Topol
ogy
bas
ed
Single
-
st
age
Grid
-
connect
e
d
Photovolt
aic
Sys
te
m :
A
Rev
ie
w,
”
Indon
esian
Jo
urnal
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El
e
ct
ri
c
al
Engi
ne
ering
a
nd
Computer
Scienc
e
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JEECS)
,
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d
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l
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ti
le
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d
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e
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rid
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c
te
d
tr
ansforme
rl
ess
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inve
rt
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opo
logies wit
h
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iv
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ca
l
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coup
li
n
g
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tor
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im
izati
on
in
HF
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li
nk
Singl
e
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Phas
e
Cyc
loc
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sed
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n
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”
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t
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te
r
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aic
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the
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e
rnational
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e
renc
e
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po
siti
on
on
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lectri
cal
and
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r
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ne
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pp
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631
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K.
Surap
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A.
K.
Rat
hore
,
“A
Si
ngle
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Stag
e
CC
M
Ze
ta
Microinverte
r
for
Sola
r
Photovolt
a
ic
AC
Module,
”
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EE
E
Ene
rgy
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nve
rs
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ss
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io
n,
ECC
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n
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i,
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n
ver
te
r
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lo
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for
Photovolt
aic
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ration
Sy
stem
s,”
2017.
[2
3
]
SEDA
Mala
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rid
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Connec
te
d
Phot
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c
Sys
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[2
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]
Y.
Fang
and
X.
Ma,
“A
Novel
PV
Microi
nver
te
r
wi
th
Coupl
e
d
Induc
tors
and
Double
-
Boost
Topol
ogy,
”
IE
E
E
Tr
ans
act
ions o
n
Powe
r E
le
c
tron
ic
,
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l. 25, no. 12
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IS
S
N
:
2088
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8
694
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t J
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c
&
D
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-
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e
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Oni,
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it
che
d
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Mult
i
-
Source
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rt
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ogy
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um
Nu
mb
er
of
Us
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it
c
hes,
” in
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EE
PE
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AS Po
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[2
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]
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na
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t
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me
d
7
2
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ce
l
l
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”
2017
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[2
8
]
We
bpag
e
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ww
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a
nd
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cro
-
Photovolt
aic
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r
te
r
,
”
in
2
012
Asia
-
Pacific
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r and Ener
gy
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ine
ering
Confe
renc
e
,
pp.
1
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4
,
2012
.
BIOGR
AP
HI
ES
OF
A
UTH
ORS
Atika
h
Ra
zi
recei
ved
h
er
B
ac
h
e
lor
of
E
lectr
i
ca
l
Engi
ne
eri
ng
in
2
010
from
Univ
e
rsiti
T
eknol
ogi
Mala
ysia
and
M
Sc
Industri
al
E
lectr
oni
cs
&
Cont
rol
fro
m
Univ
er
sity
of
Mal
aya
i
n
2013.
She
is
with
Center
for
Roboti
cs
and
I
ndustria
l
Auto
m
at
ion
(C
eRIA),
Fakult
i
Ke
jurut
e
raa
n
E
le
k
tri
k,
Univer
siti
Te
kni
kal
Mal
aysia
M
el
ak
a,
Ja
la
n
Ha
ng
Tua
h
Jay
a,
7
6100
Duria
n
Tu
nggal
,
Me
la
k
a
(em
a
il
:
a
ti
kah@
ute
m
.
edu
.
my
).
Curre
ntl
y
lectur
er
on
-
l
ea
v
e
pur
suing
PhD
study
in
Cent
r
e
of
El
e
ct
ri
ca
l
Pow
er
Engi
n
ee
ring
Stu
die
s,
Univ
ersit
i
Te
knologi MA
RA,
Shah
Al
am
,
S
el
angor
.
Dr.
M.
Nabi
l
H
id
ayat
re
ce
iv
ed
his
El
e
ct
ri
cal
an
d
El
e
ct
ron
ic
En
gine
er
ing
Ba
chelor’s
Degre
e
,
Master
s
of
Eng
i
nee
ring
and
Ph.
D.
Of
Eng
ine
er
i
ng
in
2006
,
200
8
and
2011
r
espe
ctivel
y
fro
m
th
e
Univer
sity
of
T
ott
ori
Jap
an.
Cu
rre
ntl
y
h
e
is
a
senior
l
ec
tu
rer
in
Univer
sity
T
ek
nologi
M
ARA
,
Mala
ysia
.
He
is
a
m
em
be
r
of
t
he
Instit
u
te
of
El
e
ct
roni
cs,
Inf
orma
ti
on
and
C
omm
unication
Engi
ne
ers
(IE
IC
E)
and
me
mb
er
of
the
The
Ill
u
mi
nating
Eng
ineeri
ng
Insti
tut
e
o
f
Japa
n.
H
e
is
al
so
a
Regi
st
ered
Elec
tr
ical
Energy
Mana
ger
(R
EE
M)
from
Ma
la
ysian
Elec
tr
ic
Comm
ission,
Cert
ified
En
erg
y
Mana
ger
(C
EM)
and
a
C
ertifie
d
Profess
iona
ls
in
Mea
sureme
n
t
an
d
Veri
ficat
ion
(CPM
V) from
AEMA
S.
As
soc.
Prof.
Dr
.
M.
Nawawi
Seroji
is
an
As
socia
t
e
Profess
or
at
th
e
Fa
cul
t
y
of
El
e
ct
ri
cal
Engi
ne
eri
ng
(FK
E),
Ui
TM.
He
r
e
ce
iv
ed
his
fi
rst
d
egr
ee
in
El
e
ct
ri
c
al
Eng
ineeri
ng
f
rom
UiTM
in
2001.
He
pursu
ed
his
Master
’s
degr
e
e
in
Pow
er
Elec
troni
cs
a
nd
Drive
s
at
Th
e
Univer
sity
of
Birm
ingham
and
Th
e
Univ
ersit
y
of
Notti
ngh
am
a
nd
succ
essfully
com
pl
et
ed
th
e
d
oct
ora
l
d
egr
e
e
in
Elec
tr
ic
a
l,
El
e
ct
roni
c
&
Comp
ute
r
Eng
ine
er
ing
in
2008
from
T
he
Univer
sity
of
Birm
ingham,
UK
.
He
has
con
t
ribut
ed
to
the
Fa
cul
ty
and
Ui
TM
through
v
ari
ous
ad
mi
nistr
at
iv
e
p
osts:
Dea
n
of
IPS
is,
Deputy
Dea
n
of
IPS
is,
Hea
d
of
Gr
ad
uat
e
Studie
s
(I
PS
is)
and
Hea
d
of
C
ent
re
for
Pos
tgra
duat
e
Studie
s
(FK
E).
He
is
al
so
a
m
em
b
er
to
I
EEE
Prof
essional
associa
t
ion
since
2003
and
cur
ren
t
ly
i
nvolve
d
activel
y
in
rese
arc
h
works
per
tainin
g
to
Pow
er
E
l
ec
tr
on
ic
High
-
Freque
ncy
Conv
ert
er
.
Ts.
Dr.
S.
Z
ali
ha
ob
ta
in
ed
B
a
che
lor
of
Elec
tr
ic
a
l
Engi
ne
eri
ng
(Hons
)
in
200
5,
MS
c
Pow
er
El
e
ct
roni
cs
in
2
008
and
Ph.D.
in
E
lectr
i
cal
En
gine
er
ing
in
20
18
from
Univer
siti
Te
kno
logi
MA
RA
(UiTM),
Ma
la
ysia
.
She
is
cur
ren
tl
y
a
Senior
L
ecture
r
at
th
e
Faculty
of
Elec
tr
ical
Engi
ne
eri
ng,
Ui
TM.
She
h
as
a
uthore
d
and
co
-
aut
hore
d
over
3
0
technical
pap
ers
in
inde
xed
int
ern
at
ion
al
jo
urna
l
and
conf
ere
nc
es.
H
er
r
e
sea
rch
intere
sts
are
r
ene
wabl
e
ene
rgy
,
powe
r
el
e
ct
roni
cs,
mod
el
ing
t
and
simul
at
ion
,
signa
l
pro
ce
ss
ing
and
e
mb
edde
d
cont
rol
le
r
appl
i
ca
t
ions.
Evaluation Warning : The document was created with Spire.PDF for Python.