I
n
t
e
r
n
at
ion
al
Jou
r
n
al
of
P
owe
r
E
lec
t
r
on
ics
an
d
Dr
ive
S
ys
t
e
m
s
(
I
JP
E
DS)
Vol.
13
,
No.
1
,
M
a
r
c
h
20
2
2
,
pp.
500
~
508
I
S
S
N:
2088
-
8694,
DO
I
:
10
.
11591/i
jpeds
.
v
13
.i
1
.
pp
500
-
508
500
Jou
r
n
al
h
omepage
:
ht
tp:
//
ij
pe
ds
.
iaes
c
or
e
.
c
om
S
t
u
d
y of
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ove
l
p
ar
al
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l
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-
b
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i
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om
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itt
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s
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p
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si
on
syst
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r
os
o,
Hari
S
is
want
or
o
D
e
pa
r
tm
e
nt
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E
le
c
tr
ic
a
l
E
ngi
ne
e
r
in
g, J
e
nde
r
a
l
S
oe
di
r
ma
n U
ni
ve
r
s
it
y, P
ur
ba
li
ngga
,
I
ndone
s
ia
Ar
t
icle
I
n
f
o
AB
S
T
RA
CT
A
r
ti
c
le
h
is
tor
y
:
R
e
c
e
ived
J
ul
26,
2021
R
e
vis
e
d
F
e
b
8
,
202
2
Ac
c
e
pted
F
e
b
15
,
2022
A
n
o
v
el
o
p
erat
i
o
n
o
f
t
h
ree
-
l
ev
e
l
H
-
b
r
i
d
g
e
an
d
c
o
mmo
n
-
e
mi
t
t
er
cu
rren
t
s
o
u
rce
i
n
v
ert
er
s
(CSIs
)
p
ro
p
o
s
ed
f
o
r
p
h
o
t
o
v
o
l
t
a
i
c
p
o
w
er
c
o
n
v
ert
ers
i
s
p
res
e
n
t
e
d
i
n
t
h
i
s
p
a
p
er.
T
w
o
p
h
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o
v
o
l
t
a
i
c
s
y
s
t
em
s
w
i
t
h
t
w
o
d
i
fferen
t
i
n
v
er
t
er
ci
rc
u
i
t
s
,
i
.
e.
H
-
b
r
i
d
g
e
an
d
co
mm
o
n
-
em
i
t
t
er
CSIs
,
w
ere
c
o
n
n
ect
e
d
i
n
p
aral
l
el
t
o
s
u
p
p
l
y
a
s
h
ar
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n
g
ac
p
o
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l
o
a
d
.
In
o
rd
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o
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g
u
l
at
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h
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p
o
w
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s
u
p
p
l
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eac
h
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n
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er
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er
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s
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em,
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ro
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o
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t
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o
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l
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t
e
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ral
cu
rre
n
t
co
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r
o
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ere
emp
l
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d
.
T
ri
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g
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l
ar
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d
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s
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al
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l
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b
as
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mo
d
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l
at
i
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ch
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es
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i
mp
l
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t
ed
t
o
b
o
t
h
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v
er
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So
me
p
arame
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ers
s
u
c
h
as
l
o
ad
cu
rre
n
t
,
i
n
v
er
t
er’s
o
u
t
p
u
t
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rren
t
,
t
o
t
a
l
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armo
n
i
c
s
d
i
s
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o
rt
i
o
n
(T
H
D
),
an
d
effi
c
i
e
n
cy
w
ere
t
e
s
t
e
d
an
d
an
al
y
zed
.
T
es
t
res
u
l
t
s
s
h
o
w
ed
t
h
at
i
n
t
h
e
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aral
l
el
o
p
era
t
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o
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o
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t
h
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n
v
er
t
ers
,
t
h
e
av
era
g
e
T
H
D
p
ercen
t
ag
e
o
f
t
h
e
l
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r
ren
t
w
as
0
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3
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fo
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l
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o
r
0
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9
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n
d
0
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6
2
%
fo
r
l
o
ad
p
o
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er
fact
o
r
0
.
7
8
2
.
M
i
n
i
m
u
m
w
a
v
efo
rm
d
i
s
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o
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t
i
o
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c
u
rren
t
s
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i
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p
aral
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el
o
p
erat
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o
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ca
n
b
e
ach
i
ev
e
d
i
f
t
h
e
c
u
rren
t
mag
n
i
t
u
d
es
o
f
b
o
t
h
i
n
v
er
t
ers
w
ere
s
e
t
t
h
e
s
ame.
In
t
h
e
cas
e
o
f
effi
ci
e
n
cy
,
t
h
e
ma
x
i
m
u
m
effi
c
i
en
c
y
o
f
t
h
e
s
y
s
t
em
w
a
s
8
9
.
0
7
%
.
O
p
erat
i
n
g
t
h
e
H
-
b
r
i
d
g
e
C
SI
w
i
t
h
a
h
i
g
h
er
mag
n
i
t
u
d
e
o
f
t
h
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t
p
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t
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t
w
i
l
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res
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l
t
i
n
h
i
g
h
er
effi
c
i
en
c
y
o
f
t
h
e
s
y
s
t
em.
K
e
y
w
o
r
d
s
:
I
nve
r
ter
P
a
r
a
ll
e
l
ope
r
a
ti
on
P
hotovol
taic
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
r
t
i
c
l
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e.
C
or
r
e
s
pon
din
g
A
u
th
or
:
S
ur
os
o
De
pa
r
tm
e
nt
of
E
lec
tr
ica
l
E
nginee
r
ing,
E
ng
inee
r
ing
F
a
c
ult
y,
J
e
nde
r
a
l
S
oe
dir
man
Unive
r
s
it
y
M
a
yjen
S
ungkono
S
t.
km.
5,
B
late
r
,
P
ur
ba
li
ngga
,
C
e
ntr
a
l
J
a
va
53371,
I
ndone
s
ia
E
mail:
s
ur
os
o.
te@u
ns
oe
d.
a
c
.
id
1.
I
NT
RODU
C
T
I
ON
R
e
c
e
ntl
y,
the
a
ppli
c
a
ti
on
of
r
e
ne
wa
ble
e
ne
r
gy
s
our
c
e
s
e
s
pe
c
i
a
ll
y
photovol
taic
s
ys
tems
h
a
s
be
e
n
incr
e
a
s
ing
in
many
c
ountr
ies
a
r
ound
the
wor
ld
.
I
t
is
be
c
a
us
e
of
s
ome
mer
it
s
int
r
oduc
e
d
by
the
pho
tovol
taic
s
ys
tem,
s
uc
h
a
s
r
e
duc
ing
e
nvir
onmenta
l
poll
u
ti
on,
low
ope
r
a
ti
ng
c
os
t,
a
nd
a
va
il
a
bil
it
y
f
r
om
a
f
e
w
wa
tt
powe
r
to
a
lar
ge
r
mega
wa
tt
-
s
c
a
le
s
ys
t
e
m
[
1]
−
[
4]
.
S
im
pli
c
it
y
in
ins
tallation
s
uc
h
a
s
on
r
oof
top
is
a
f
e
a
tur
e
tha
t
a
tt
r
a
c
ts
mor
e
int
e
r
e
s
t
to
photovol
taic
f
or
r
e
s
idential
a
ppl
ica
ti
on
[
5
]
−
[
7]
.
E
ve
n
mo
r
e
s
o,
s
ome
gove
r
nment
s
is
s
ue
d
poli
c
ies
givi
ng
ince
nti
ve
s
f
or
the
de
ve
lopm
e
nt
o
f
r
e
ne
wa
ble
e
ne
r
gy
s
our
c
e
s
s
uc
h
a
s
photovol
tai
c
powe
r
ge
ne
r
a
tor
to
incr
e
a
s
e
it
s
a
ppli
c
a
ti
on
in
their
c
ou
ntr
ies
.
F
or
tunate
ly,
the
late
s
t
e
f
f
icie
nc
y
of
a
pho
tovol
taic
modul
e
ha
s
a
c
hieve
d
47.
1%
,
r
e
a
li
z
e
d
by
us
ing
mul
ti
-
junction
c
onc
e
ntr
a
tor
s
olar
c
e
ll
s
[
8]
.
I
t
wil
l
boos
t
the
tot
a
l
e
f
f
icie
nc
y
of
s
olar
e
ne
r
gy
c
onve
r
s
ion
in
to
e
lec
tr
ica
l
e
ne
r
gy.
M
or
e
ove
r
,
the
a
va
il
a
bil
it
y
of
s
uppor
ti
ng
tec
hnologi
e
s
s
uc
h
a
s
photovol
taic
powe
r
c
onve
r
ter
s
is
a
ls
o
an
other
im
por
tant
f
a
c
tor
to
incr
e
a
s
e
the
wide
r
a
ppli
c
a
ti
on
of
the
photovol
taic
s
ys
tem.
P
owe
r
e
lec
tr
onic
c
onve
r
ter
s
a
r
e
e
s
s
e
nti
a
l
pa
r
ts
of
the
de
ve
lopm
e
nt
o
f
r
e
ne
wa
ble
e
ne
r
gy
a
ppli
c
a
ti
ons
[
9]
−
[
11]
.
S
ome
r
e
ne
wa
ble
e
ne
r
gy
s
our
c
e
s
ge
ne
r
a
te
e
lec
tr
ica
l
e
ne
r
gy
in
t
he
f
o
r
m
of
dc
powe
r
,
s
uc
h
a
s
photovol
taic
s
ys
tems
,
a
nd
f
ue
l
c
e
ll
s
.
T
he
ge
ne
r
a
ted
powe
r
of
other
e
ne
r
gy
s
our
c
e
s
s
uc
h
a
s
mi
c
r
o
hydr
o
powe
r
,
wind
powe
r
s
ys
tem,
ti
da
l,
a
nd
s
e
a
wa
ve
e
ne
r
gies
a
r
e
c
omm
only
in
the
f
or
m
of
a
c
po
we
r
.
T
he
y
us
e
a
n
a
c
mac
hine
ge
ne
r
a
tor
to
pr
oduc
e
e
lec
tr
ica
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
Study
of
nov
e
l
par
all
e
l
H
-
br
idge
and
c
omm
on
-
e
mit
ter
c
ur
r
e
nt
-
s
ou
r
c
e
inve
r
t
e
r
s
for
…
(
Sur
os
o
)
501
e
ne
r
gy.
F
o
r
the
dc
load
s
ys
tem,
the
ge
ne
r
a
ted
dc
p
owe
r
c
a
n
be
us
e
d
to
s
upply
powe
r
load
a
f
ter
p
r
oc
e
s
s
e
d
by
the
dc
-
dc
c
onve
r
ter
to
ha
ve
s
table
dc
volt
a
ge
a
nd
c
ur
r
e
nt
a
s
r
e
quir
e
d.
I
n
the
c
a
s
e
of
a
n
a
c
load
s
ys
tem,
the
dc
powe
r
s
hould
b
e
c
onve
r
ted
int
o
a
c
powe
r
by
uti
li
z
ing
dc
to
a
c
powe
r
c
onve
r
ter
or
powe
r
inver
ter
[
12]
−
[
14]
.
T
he
powe
r
inver
te
r
ge
ne
r
a
tes
a
c
powe
r
with
a
dju
s
table
f
r
e
que
nc
y,
magnitude,
a
nd
pha
s
e
a
ngle
o
f
i
ts
output
volt
a
ge
a
nd
c
ur
r
e
nt.
I
n
c
a
s
e
the
input
of
the
inver
t
e
r
is
dc
volt
a
ge
,
a
nd
the
ou
tput
is
a
c
ontr
oll
a
ble
a
c
volt
a
ge
,
the
inver
ter
is
c
las
s
if
ied
a
s
a
volt
a
ge
s
our
c
e
inver
te
r
(
VSI
)
.
How
e
ve
r
,
i
f
the
input
is
in
dc
c
ur
r
e
nt
f
or
m
,
a
nd
the
output
is
c
ontr
oll
a
ble
a
c
c
ur
r
e
nt
,
the
inver
ter
is
c
a
ll
e
d
a
c
ur
r
e
nt
s
our
c
e
inver
te
r
(
C
S
I
)
[
15]
−
[
17
]
.
T
he
s
e
two
kinds
of
inver
te
r
s
a
r
e
a
ppli
c
a
ble
f
o
r
photovo
lt
a
ic
e
ne
r
gy
c
onve
r
s
ion
s
ys
tems
.
A
s
ingl
e
-
pha
s
e
powe
r
inver
ter
is
s
uit
a
ble
to
be
us
e
d
in
a
r
e
s
idential
P
V
s
ys
tem,
i.
e
.
r
oof
top
ins
talled
photovol
taic
,
whe
r
e
mos
t
r
e
s
idential
loads
a
r
e
s
ingl
e
-
pha
s
e
s
ys
tem
s
.
F
or
a
s
ingl
e
-
pha
s
e
gr
id
-
ti
e
d
inver
ter
a
ppli
c
a
ti
on,
the
c
ur
r
e
nt
s
our
c
e
inver
ter
int
r
oduc
e
d
s
ome
f
e
a
tur
e
s
c
ompar
e
d
to
volt
a
ge
s
our
c
e
inver
ter
s
uc
h
a
s
mor
e
im
mune
to
s
hor
t
c
i
r
c
uit
f
a
ult
,
longer
li
f
e
ti
me
of
it
s
powe
r
inducto
r
s
than
c
a
pa
c
it
or
s
,
a
nd
be
tt
e
r
q
ua
li
ty
of
a
c
output
c
ur
r
e
nt
[
18]
−
[
22]
.
M
or
e
ove
r
,
s
ome
c
ir
c
uit
topol
ogies
of
the
c
ur
r
e
nt
s
our
c
e
inver
ter
ha
ve
inher
e
nt
boos
t
-
up
volt
a
ge
c
a
pa
bil
it
y.
He
nc
e
,
it
will
e
li
mi
na
t
e
the
ne
e
d
f
or
a
powe
r
tr
a
ns
f
or
mer
to
r
a
is
e
the
output
volt
a
ge
of
the
inver
ter
[
23]
−
[
25
]
.
F
o
r
a
higher
powe
r
r
e
s
i
de
nti
a
l
photovol
taic
s
ys
tem,
a
s
ingl
e
inver
ter
ma
y
not
be
e
nough
to
pr
oc
e
e
d
with
the
tot
a
l
ge
ne
r
a
ted
powe
r
.
T
he
c
a
pa
c
it
y
of
a
c
omm
e
r
c
ially
a
va
il
a
ble
s
ing
le
-
pha
s
e
inver
ter
is
li
mi
ted.
M
or
e
ove
r
,
a
s
ingl
e
inver
te
r
s
y
s
tem
is
we
a
k
in
r
e
li
a
bil
it
y
is
s
ue
s
.
He
nc
e
,
ope
r
a
ti
ng
s
ome
powe
r
inver
ter
s
in
pa
r
a
ll
e
l
is
a
r
e
a
li
s
ti
c
opti
on
to
a
ddr
e
s
s
thes
e
is
s
u
e
s
.
I
n
f
a
c
t,
pa
r
a
ll
e
l
ope
r
a
ti
on
of
many
inver
ter
s
is
a
n
una
voidable
s
it
ua
ti
on
whe
n
many
r
e
s
idential
photovol
taic
s
ys
tems
a
r
e
ope
r
a
ted
in
gr
id
-
ti
e
d
ope
r
a
ti
on.
T
he
s
e
inver
ter
s
c
a
n
be
many
types
with
dif
f
e
r
e
nt
c
i
r
c
uit
s
a
nd
c
ha
r
a
c
ter
is
ti
c
s
[
26]
−
[
34
].
T
he
ba
s
ic
c
onc
e
pt
o
f
pa
r
a
ll
e
li
ng
inver
ter
s
is
s
hown
in
F
igur
e
1.
As
s
hown
in
thi
s
f
igu
r
e
,
N
nu
mber
of
photovol
taic
s
ys
tems
with
N
nu
mber
of
inver
ter
s
wor
k
in
pa
r
a
ll
e
l
.
A
s
tudy
of
ope
r
a
ti
on
pa
r
a
ll
e
l
be
t
we
e
n
two
H
-
br
idge
c
ur
r
e
nt
s
our
c
e
inver
te
r
s
ha
s
be
e
n
dis
c
us
s
e
d
in
[
1
7
]
.
How
e
ve
r
,
powe
r
tr
a
ns
f
or
mer
s
we
r
e
a
ppli
e
d
in
thi
s
s
ys
tem,
a
nd
the
inver
ter
c
ir
c
uit
s
we
r
e
the
s
a
me
type.
T
his
pa
pe
r
inves
ti
ga
tes
a
nd
pr
e
s
e
nts
a
nove
l
photovol
taic
s
ys
tem
c
ons
tr
uc
ted
by
two
dif
f
e
r
e
nt
types
of
c
ur
r
e
nt
s
our
c
e
powe
r
inver
ter
s
,
i.
e
.
H
-
br
idge
a
nd
c
omm
on
-
e
mi
tt
e
r
c
ur
r
e
nt
s
our
c
e
inver
ter
s
.
E
a
c
h
i
nve
r
ter
is
c
onne
c
ted
with
a
dif
f
e
r
e
nt
photovol
tai
c
s
ys
tem
wor
king
in
pa
r
a
ll
e
l
to
s
upply
a
c
omm
on
a
c
powe
r
l
oa
d.
T
he
p
r
opos
e
d
s
ys
tem
int
r
oduc
e
s
s
ome
f
e
a
tur
e
s
s
uc
h
a
s
mor
e
im
mune
to
s
hor
t
c
ir
c
uit
f
a
ult
,
h
ighe
r
powe
r
c
a
pa
c
it
y,
the
pos
s
ibi
li
ty
of
ba
c
kup
ope
r
a
ti
on
mode,
a
nd
be
tt
e
r
qua
li
ty
of
load
c
ur
r
e
nt
.
C
omput
e
r
s
im
ulation
tes
ts
we
r
e
pe
r
f
or
med
to
inves
ti
ga
te
the
pe
r
f
o
r
manc
e
of
t
he
s
ys
tem.
F
igur
e
1
.
P
a
r
a
ll
e
l
ope
r
a
ti
on
o
f
inve
r
ter
s
f
o
r
photov
olt
a
ic
s
ys
tems
2.
P
ROP
OS
E
D
P
HO
T
OVOL
T
AI
C
S
YST
E
M
F
igur
e
2
pr
e
s
e
nts
c
ir
c
uit
s
of
a
th
r
e
e
-
leve
l
H
-
br
idge
c
ur
r
e
nt
s
our
c
e
inver
ter
.
T
he
powe
r
inductor
(
L
)
is
uti
li
z
e
d
to
ge
ne
r
a
te
dc
c
ur
r
e
nt
s
our
c
e
f
r
o
m
the
in
put
powe
r
(
V
in
)
f
o
r
inve
r
ter
c
i
r
c
uit
s
.
T
otal
f
ive
c
ontr
oll
e
d
powe
r
s
witche
s
with
f
our
is
olate
d
ga
te
d
r
ive
c
i
r
c
uit
s
a
r
e
r
e
quir
e
d
,
including
the
s
witch
f
or
dc
c
ur
r
e
nt
g
e
ne
r
a
tor
c
ir
c
uit
Q
c
.
T
a
ble
1
is
the
s
witching
c
ombi
na
ti
on
of
powe
r
s
witche
s
Q
1
,
Q
2
,
Q
3
,
a
nd
Q
4
to
pr
oduc
e
a
thr
e
e
-
leve
l
output
c
ur
r
e
nt
,
i
.
e
.
+
I
,
0,
a
nd
–
I
c
u
r
r
e
nts
.
M
or
e
ove
r
,
F
igur
e
3
is
a
th
r
e
e
-
leve
l
c
omm
on
-
e
mi
tt
e
r
c
ur
r
e
n
t
s
our
c
e
inver
ter
c
i
r
c
uit
.
I
t
is
a
ls
o
c
ompos
e
d
of
f
ive
c
ontr
ol
led
powe
r
s
witche
s
.
T
he
powe
r
inducto
r
s
L
1
a
nd
L
2
in
th
is
c
ir
c
uit
a
r
e
e
mpl
oye
d
to
c
r
e
a
te
two
dc
c
ur
r
e
nt
s
our
c
e
s
of
the
inver
ter
.
T
he
s
e
two
inducto
r
s
ha
ve
a
c
omm
on
c
or
e
a
s
s
hown
in
the
f
igu
r
e
.
F
our
powe
r
s
witche
s
a
r
e
c
on
ne
c
ted
togethe
r
o
f
their
e
mi
tt
e
r
ter
mi
na
l
a
t
a
c
omm
on
point
,
he
nc
e
a
s
ingl
e
is
olate
d
powe
r
s
upply
c
a
n
be
a
ppli
e
d
to
s
upply
f
our
ga
te
d
r
ive
c
ir
c
uit
s
of
the
inver
ter
’
s
s
witche
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
500
-
508
502
M
or
e
o
ve
r
,
b
e
c
a
us
e
o
f
th
e
c
o
mm
on
-
e
m
it
te
r
c
on
ne
c
t
i
on
of
i
ts
po
we
r
s
w
i
tch
e
s
,
a
l
ow
e
r
g
r
a
die
n
t
vo
l
tage
c
a
n
be
a
c
h
ie
ve
d
.
He
nc
e
t
hi
s
i
nv
e
r
t
e
r
is
a
ls
o
m
or
e
s
ui
ta
ble
f
or
h
i
gh
e
r
s
p
e
e
d
s
w
it
c
h
in
g
ope
r
a
t
io
n
,
c
om
pa
r
e
d
to
t
he
H
-
b
r
i
dg
e
c
ur
r
e
nt
s
our
c
e
inver
ter
.
B
oth
inver
ter
s
ne
e
d
only
a
s
ingl
e
dc
c
ur
r
e
nt
s
e
ns
or
f
or
c
u
r
r
e
nt
c
ontr
oll
e
r
f
un
c
ti
on
a
s
s
hown
in
F
igur
e
2
a
nd
F
igur
e
3
.
T
a
ble
2
is
the
s
witching
ope
r
a
ti
on
of
thi
s
th
r
e
e
-
leve
l
c
omm
on
-
e
mi
tt
e
r
c
ur
r
e
nt
s
our
c
e
inver
ter
c
ir
c
uit
.
F
igur
e
2
.
H
-
br
idge
c
ur
r
e
nt
s
o
ur
c
e
inver
ter
[
3
5
]
F
igur
e
3.
T
h
r
e
e
-
leve
l
c
omm
on
-
e
mi
tt
e
r
c
ur
r
e
nt
-
s
our
c
e
inver
ter
[
3
6
]
,
[
3
7
]
T
a
ble
1.
S
witching
modes
of
H
-
br
idge
C
S
I
Q
1
Q
2
Q
3
Q
4
I
out
ON
O
F
F
ON
O
F
F
+I
ON
O
F
F
O
F
F
ON
0
O
F
F
ON
ON
O
F
F
0
O
F
F
ON
O
F
F
ON
-
I
T
a
ble
2.
Ope
r
a
ti
on
mode
of
c
omm
on
-
e
mi
tt
e
r
C
S
I
[
18]
Q
1
Q
2
Q
3
Q
4
I
out
O
F
F
O
F
F
ON
ON
+I
ON
O
F
F
O
F
F
ON
0
ON
ON
O
F
F
O
F
F
-
I
In
thi
s
pa
pe
r
,
the
th
r
e
e
-
leve
l
H
-
br
idge
a
nd
c
omm
on
-
e
mi
tt
e
r
inver
ter
c
ir
c
uit
s
a
r
e
a
ppli
e
d
togethe
r
to
pr
oc
e
e
d
the
dc
powe
r
de
li
ve
r
e
d
by
two
photovo
lt
a
i
c
s
ys
tems
to
be
tr
a
ns
f
or
med
int
o
a
c
powe
r
to
s
uppl
y
powe
r
load
a
s
de
picte
d
in
F
igur
e
4.
T
he
pr
opos
e
d
pa
r
a
ll
e
l
ope
r
a
ti
on
of
thes
e
c
ir
c
uit
s
is
s
hown
in
F
igur
e
4
(
a
)
.
I
t
c
a
n
be
a
ne
w
a
lt
e
r
na
ti
ve
ope
r
a
ti
on
of
inver
ter
s
to
pr
oc
e
e
d
with
two
photovol
taic
s
ys
tems
.
T
e
n
photovol
taic
modul
e
s
with
a
tot
a
l
c
a
pa
c
it
y
1
kW
p
we
r
e
a
ppli
e
d
a
s
dc
powe
r
s
our
c
e
of
e
a
c
h
inver
ter
c
ir
c
u
it
.
T
wo
a
r
r
a
ys
of
pho
tovol
taic
s
ys
tems
we
r
e
de
s
igned
in
the
s
ys
tem.
F
ive
phot
ovolt
a
ic
modul
e
s
we
r
e
c
onne
c
ted
in
s
e
r
ies
to
c
o
ns
tr
uc
t
a
photovol
taic
a
r
r
a
y
a
s
s
hown
in
F
igur
e
4
(
b
)
.
A
mor
e
number
of
photovol
taic
s
ys
tems
of
c
our
s
e
will
ne
e
d
mor
e
inver
ter
c
ir
c
u
it
s
to
a
c
hieve
higher
powe
r
.
A
c
omm
on
a
c
powe
r
load
is
c
onne
c
ted
to
both
inver
ter
s
.
T
he
c
ur
r
e
nt
c
ontr
oll
e
d
ope
r
a
ti
on
mode
wa
s
uti
l
ize
d
to
r
e
gulate
the
powe
r
de
li
ve
r
e
d
by
photovol
taic
via
inver
ter
s
to
the
load.
P
r
opo
r
ti
ona
l
int
e
gr
a
l
(
P
I
)
c
ur
r
e
nt
c
ontr
oll
e
r
s
we
r
e
a
ppli
e
d
to
both
inver
ter
s
a
s
s
hown
in
F
igur
e
5
a
nd
F
igu
r
e
6.
T
he
s
e
c
ontr
oll
e
r
s
will
a
djus
t
the
output
c
ur
r
e
nt
a
nd
powe
r
o
f
e
a
c
h
inver
te
r
.
I
n
the
c
a
s
e
of
a
c
omm
on
-
e
mi
tt
e
r
inver
ter
,
two
powe
r
ind
uc
tor
s
with
a
s
ingl
e
c
or
e
we
r
e
i
mpl
e
mente
d
to
ge
n
e
r
a
te
tw
o
dc
input
c
ur
r
e
nt
s
our
c
e
s
f
o
r
inve
r
ter
c
i
r
c
uit
s
.
How
e
ve
r
,
e
ve
n
two
inductor
s
we
r
e
us
e
d,
only
a
s
ingl
e
s
e
ns
or
wa
s
a
ppli
e
d
to
r
e
gulate
the
c
ur
r
e
nts
in
inductor
1
a
nd
i
nduc
tor
2
a
s
s
hown
in
F
igur
e
5
.
He
nc
e
it
c
a
n
s
im
pli
f
y
the
r
e
quir
e
d
s
e
ns
or
number
.
I
n
the
c
a
s
e
of
the
H
-
br
idg
e
C
S
I
,
the
dc
c
ur
r
e
nt
s
our
c
e
wa
s
c
r
e
a
ted
by
a
s
ingl
e
powe
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
Study
of
nov
e
l
par
all
e
l
H
-
br
idge
and
c
omm
on
-
e
mit
ter
c
ur
r
e
nt
-
s
ou
r
c
e
inve
r
t
e
r
s
for
…
(
Sur
os
o
)
503
inductor
.
He
nc
e
,
a
s
ingl
e
s
e
ns
or
wa
s
r
e
quir
e
d
to
s
e
ns
e
the
inductor
c
ur
r
e
nt
f
or
c
ontr
ol
pur
pos
e
.
T
he
a
c
ti
on
of
a
c
ur
r
e
nt
c
ontr
ol
s
ignal,
a
nd
maximum
powe
r
po
int
t
r
a
c
king
(
M
P
P
T
)
wa
s
r
e
a
li
z
e
d
by
powe
r
s
witch
Q
c
t
ha
t
will
r
e
gulate
the
magnitude
of
dc
c
ur
r
e
nt
th
r
u
c
ha
nging
it
s
duty
c
yc
le.
Diode
D
F
wa
s
r
e
qui
r
e
d
to
e
ns
ur
e
th
e
c
ur
r
e
nt
pa
th
f
or
the
inductor
’
s
c
ur
r
e
nt
dur
ing
s
witch
Q
c
tur
n
-
of
f
.
T
o
g
e
n
e
r
a
t
e
a
p
u
ls
e
wi
d
th
m
od
ul
a
t
io
n
(
P
W
M
)
a
c
c
u
r
r
e
n
t
,
tw
o
t
r
ia
ng
u
la
r
c
a
r
r
ie
r
s
i
gn
a
ls
w
i
th
o
pp
os
i
te
o
f
f
s
e
t
va
lu
e
p
lu
s
a
s
in
g
le
s
in
us
o
id
a
l
s
i
gn
a
l
we
r
e
a
pp
l
ie
d
t
o
th
e
m
od
u
lat
o
r
s
ys
t
e
m
a
s
s
how
n
in
F
ig
u
r
e
7
.
T
he
s
e
s
ignals
f
e
e
d
in
two
c
ompar
a
tor
s
to
ge
ne
r
a
te
P
W
M
s
witching
s
ignals
.
T
he
f
r
e
que
nc
y
o
f
c
a
r
r
ier
s
ignal
pr
ovides
the
wor
king
f
r
e
que
nc
y
of
the
inve
r
ter
’
s
powe
r
s
witche
s
,
a
nd
the
main
f
r
e
que
nc
y
of
a
c
c
ur
r
e
nt
is
a
s
s
igned
by
the
f
r
e
que
nc
y
of
modul
a
ti
ng
s
ignal.
T
he
s
inus
oidal
modul
a
ti
ng
s
ignal
will
wor
k
a
ls
o
to
s
ync
hr
onize
the
f
r
e
que
nc
y
of
the
two
inver
ter
s
.
T
he
c
ompar
a
tor
s
w
il
l
pr
oduc
e
P
W
M
s
ignals
f
r
om
the
c
ompar
is
on
be
twe
e
n
the
c
a
r
r
ier
a
nd
modul
a
t
ing
s
ignals
.
T
he
p
r
oduc
e
d
P
W
M
s
ignals
will
be
a
mpl
i
f
ied
by
ga
te
d
r
ive,
a
n
d
on
-
of
f
c
ontr
oll
e
r
c
ir
c
uit
s
to
ope
r
a
te
powe
r
s
witche
s
tur
n
-
on
a
nd
tur
n
-
of
f
.
(
a
)
(
b)
F
igur
e
4
.
P
r
opos
e
d
inve
r
ter
s
ys
tem
(
a
)
pr
opos
e
d
pa
r
a
ll
e
l
s
ys
tem
of
H
-
br
idge
a
nd
c
omm
on
-
e
mi
tt
e
r
inv
e
r
ter
s
a
nd
(
b)
c
onf
igur
a
ti
on
of
pho
tovol
taic
s
ys
tem
f
or
e
a
c
h
inver
ter
F
igur
e
5.
C
ontr
ol
of
C
E
-
C
S
I
F
igur
e
6.
C
ontr
ol
of
H
-
br
idge
C
S
I
F
igur
e
7.
P
W
M
modul
a
ti
on
s
tr
a
tegy
of
inver
ter
s
3.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ON
T
o
inves
ti
ga
te
the
pe
r
f
o
r
manc
e
of
the
p
r
opos
e
d
inver
ter
s
ys
tem,
c
omput
e
r
s
im
ulation
tes
ts
we
r
e
pe
r
f
or
med
us
ing
P
S
I
M
s
of
twa
r
e
.
T
he
tes
ted
inver
ter
c
ir
c
uit
s
a
nd
P
V
s
ys
tem
is
s
hown
in
F
igur
e
4
.
T
a
ble
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
500
-
508
504
pr
e
s
e
nts
tes
t
pa
r
a
mete
r
s
of
the
c
omm
on
-
e
mi
tt
e
r
i
nve
r
ter
c
ir
c
uit
,
whi
le
T
a
ble
4
l
is
ts
tes
t
pa
r
a
mete
r
s
of
the
H
-
br
idge
inver
ter
c
ir
c
uit
.
T
he
c
omm
on
-
e
mi
tt
e
r
inv
e
r
ter
uti
l
ize
s
a
t
r
a
ns
f
or
mer
with
the
s
a
me
winding
number
on
both
s
ides
f
unc
ti
one
d
a
s
powe
r
inductor
s
.
T
h
e
pr
im
a
r
y
winding
o
f
a
t
r
a
ns
f
or
mer
is
a
ppli
e
d
a
s
th
e
f
ir
s
t
inductor
L
1
,
while
the
s
e
c
onda
r
y
winding
is
s
e
t
a
s
the
s
e
c
ond
inductor
L
2
.
T
he
inducta
nc
e
of
inducto
r
L
1
a
nd
L
2
a
r
e
the
s
a
me
a
s
0.
01
mH
with
a
winding
r
e
s
is
tanc
e
va
lue
of
0
.
1
mΩ
.
T
he
magne
ti
z
ing
inducta
nc
e
of
thi
s
tr
a
ns
f
or
mer
is
0
.
5
mH
.
I
n
the
c
a
s
e
of
H
-
br
idge
C
S
I
,
a
s
ingl
e
powe
r
inductor
0.
01
mH
wa
s
a
ppli
e
d
to
ge
ne
r
a
te
the
input
dc
c
u
r
r
e
nt.
T
he
s
witching
ope
r
a
ti
on
of
both
inver
te
r
s
wa
s
s
e
t
t
he
s
a
me
a
s
20
kHz
,
while
the
modul
a
ti
on
index
in
thi
s
tes
t
wa
s
a
djus
ted
a
t
a
va
lue
of
0.
9
.
A
f
il
te
r
c
a
pa
c
it
o
r
10
µ
F
wa
s
c
onne
c
ted
to
e
a
c
h
inver
ter
’
s
output
ter
mi
na
l
to
f
il
te
r
the
ha
r
moni
c
s
c
omponents
of
it
s
P
W
M
a
c
c
ur
r
e
nt.
T
he
two
inver
ter
s
s
ha
r
e
d
a
c
omm
on
inducti
ve
powe
r
load
with
r
e
s
is
tanc
e
a
nd
inducta
nc
e
c
onne
c
ted
in
s
e
r
ies
.
T
o
inves
ti
ga
te
dif
f
e
r
e
nt
load
powe
r
f
a
c
tor
op
e
r
a
ti
ons
,
two
inductor
s
with
dif
f
e
r
e
nt
va
lues
we
r
e
tes
ted
with
inducta
nc
e
1
mH
a
nd
10
mH.
T
he
s
e
induct
or
s
we
r
e
c
onne
c
ted
with
r
e
s
is
tor
4
Ω
whic
h
ga
ve
load
pow
e
r
f
a
c
tor
s
of
0.
996
a
nd
0
.
782,
r
e
s
pe
c
ti
ve
ly.
M
or
e
ove
r
,
the
s
pe
c
if
ica
ti
on
of
a
photovol
t
a
ic
modul
e
is
ind
ica
ted
in
T
a
ble
5.
T
e
n
pho
tovol
taic
modul
e
s
with
a
c
a
pa
c
it
y
pe
r
modul
e
of
100
W
p
we
r
e
uti
l
ize
d
f
or
e
a
c
h
inver
ter
s
ys
tem.
A
c
ons
tant
li
gh
t
int
e
ns
it
y
of
1000
W
/m
2
wa
s
a
ppli
e
d
to
a
ll
photovol
taic
modul
e
s
.
T
a
ble
3.
P
a
r
a
mete
r
s
of
c
omm
on
-
e
mi
tt
e
r
inver
ter
P
a
r
a
me
te
r
s
V
a
lu
e
I
nduc
ta
nc
e
L
1
a
nd L
2
0.01 mH
R
e
s
is
ta
n
c
e
of
i
nduc
to
r
s
0.1 mΩ
M
a
gne
ti
z
in
g i
nduc
ta
nc
e
0.5 mH
F
il
te
r
A
C
c
a
pa
c
it
or
10 µF
W
or
ki
ng f
r
e
que
nc
y of
pow
e
r
s
w
it
c
he
s
20 kHz
M
odul
a
ti
on i
nde
x
0.9
M
a
in
out
put
f
r
e
que
nc
y
50 H
z
L
oa
d
R
=
4 Ω
, L
=
1 mH, a
nd 10 mH
T
a
ble
4.
P
a
r
a
mete
r
s
of
H
-
br
idge
inver
ter
P
a
r
a
me
te
r
s
V
a
lu
e
P
ow
e
r
i
nduc
to
r
0.01 mH
F
il
te
r
A
C
c
a
pa
c
it
or
10 µF
W
or
ki
ng f
r
e
que
nc
y of
pow
e
r
s
w
it
c
he
s
20 kHz
M
odul
a
ti
on i
nde
x
0.9
M
a
in
out
put
f
r
e
que
nc
y
50 H
z
L
oa
d
R
=
4 Ω
, L
=
1 mH, a
nd 10 mH
T
a
ble
5.
P
a
r
a
mete
r
s
of
P
V
s
ys
tem
P
a
r
a
me
te
r
s
V
a
lu
e
L
ig
ht
i
nt
e
ns
it
y
1000 W
/m
2
T
e
mpe
r
a
tu
r
e
25
0
C
S
e
r
ie
s
r
e
s
is
ta
nc
e
0.0032 Ω
P
a
r
a
ll
e
l
r
e
s
is
ta
nc
e
2000 Ω
S
hor
t
c
ir
c
ui
t
c
ur
r
e
nt
12.14 A
N
umbe
r
of
modul
e
s
10
C
a
pa
c
it
y pe
r
modul
e
100 W
p
T
he
s
ys
tem
wa
s
tes
ted
by
va
r
ying
the
c
ur
r
e
nt
c
ontr
oll
e
r
r
e
f
e
r
e
nc
e
va
lue
of
the
inve
r
ter
’
s
output
c
ur
r
e
nts
f
r
om
1
A
to
9
A
,
ba
s
e
d
on
the
photovol
ta
ic
s
ys
tem
c
a
pa
c
it
y.
T
hr
e
e
pos
s
ibl
e
ope
r
a
ti
ng
c
ondit
ions
of
the
inver
ter
s
ys
tem
we
r
e
e
va
luate
d
to
a
ppr
oa
c
h
the
r
e
a
l
pr
oba
ble
ope
r
a
ti
on
a
s
f
oll
ow:
−
T
he
c
ur
r
e
nt
magnitude
of
H
-
br
idge
C
S
I
wa
s
lowe
r
than
the
c
omm
on
-
e
mi
tt
e
r
C
S
I
,
I
c
s
i
1
<I
c
s
i
2
.
−
T
he
magnitude
o
f
two
inver
ter
c
ur
r
e
nts
we
r
e
the
s
a
me,
i
.
e
.
I
c
s
i
1
=I
c
s
i
2
−
T
he
c
ur
r
e
nt
magnitude
of
H
-
br
idge
C
S
I
wa
s
higher
than
the
c
omm
on
-
e
mi
tt
e
r
C
S
I
,
I
c
s
i
1
>I
c
s
i
2
.
F
igur
e
8
pr
e
s
e
nts
the
inj
e
c
ted
c
ur
r
e
nt
by
H
-
br
idge
C
S
I
(
I
c
s
i
1
)
,
c
omm
on
-
e
mi
tt
e
r
inver
ter
(
I
c
s
i
2
)
,
a
nd
load
c
ur
r
e
nt
(
I
L
o
a
d
)
wa
ve
f
or
ms
whe
n
the
r
e
f
e
r
e
nc
e
magn
it
ude
of
H
-
br
idge
C
S
I
c
ur
r
e
nt
wa
s
lowe
r
than
the
c
omm
on
-
e
mi
tt
e
r
C
S
I
,
I
c
s
i
1
<I
c
s
i
2
,
i
.
e
.
1
A
a
nd
9
A
.
As
c
a
n
be
obs
e
r
ve
d,
the
output
c
ur
r
e
nts
of
the
two
inve
r
ter
s
a
r
e
s
inus
oidal
c
ur
r
e
nts
.
High
-
f
r
e
que
nc
y
r
ippl
e
s
we
r
e
m
or
e
vis
ibl
e
f
or
c
omm
on
-
e
mi
tt
e
r
inver
ter
c
ur
r
e
nt
(
I
c
s
i
2
)
whe
r
e
it
s
magnitude
is
lowe
r
than
I
c
s
i
1
.
F
igu
r
e
9
s
hows
the
c
ur
r
e
nt
wa
ve
f
or
ms
of
H
-
br
idge
C
S
I
(
I
c
s
i
1
)
,
c
omm
on
-
e
mi
tt
e
r
inver
ter
(
I
c
s
i
2
)
,
a
nd
load
c
ur
r
e
nt
(
I
L
o
a
d
)
whe
n
the
ma
gnit
ude
of
two
inver
ter
c
u
r
r
e
nts
wa
s
a
djus
ted
the
s
a
me,
i.
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
Study
of
nov
e
l
par
all
e
l
H
-
br
idge
and
c
omm
on
-
e
mit
ter
c
ur
r
e
nt
-
s
ou
r
c
e
inve
r
t
e
r
s
for
…
(
Sur
os
o
)
505
I
c
s
i
1
=I
c
s
i
2
.
T
he
c
ur
r
e
nt
wa
ve
f
or
m
of
I
c
s
i
1
wa
s
a
s
in
us
oidal
c
ur
r
e
nt
with
a
s
maller
dis
tor
t
ion
than
the
f
ir
s
t
tes
t
c
ondit
ion.
F
ur
ther
mo
r
e
,
c
ur
r
e
nt
wa
ve
f
o
r
ms
whe
n
the
c
ur
r
e
nt
magnitude
of
H
-
br
idge
C
S
I
is
highe
r
than
the
c
omm
on
-
e
mi
tt
e
r
C
S
I
,
I
c
s
i
1
>I
c
s
i
2
we
r
e
de
picte
d
in
F
i
gur
e
10.
T
he
high
-
f
r
e
que
nc
y
c
ur
r
e
nt
r
ippl
e
s
a
ppe
a
r
e
d
in
the
c
ur
r
e
nt
ge
ne
r
a
ted
by
H
-
br
idge
C
S
I
(
I
c
s
i
2
)
.
C
ur
r
e
nt
wa
ve
f
or
ms
of
I
c
s
i
1
a
nd
load
c
ur
r
e
nt
(
I
L
o
a
d
)
we
r
e
c
los
e
ly
s
inus
oidal
c
ur
r
e
nt
wa
ve
f
or
ms
.
F
igur
e
8.
I
njec
ted
c
u
r
r
e
nt
by
H
-
br
idge
C
S
I
(
I
c
s
i
1
)
,
c
omm
on
-
e
mi
tt
e
r
inver
ter
(
I
c
s
i
2
)
,
a
nd
load
c
ur
r
e
nt
(
I
L
o
a
d
)
wa
ve
f
or
ms
whe
n
I
c
s
i
1
<I
c
s
i
2
F
igur
e
9
.
I
njec
ted
c
u
r
r
e
nt
by
H
-
br
idge
C
S
I
(
I
c
s
i
1
)
,
c
omm
on
-
e
mi
tt
e
r
inver
ter
(
I
c
s
i
2
)
,
a
nd
load
c
ur
r
e
nt
(
I
L
o
a
d
)
wa
ve
f
or
ms
whe
n
I
c
s
i
1
=I
c
s
i
2
F
igur
e
10.
I
njec
ted
c
u
r
r
e
nt
by
H
-
br
idge
C
S
I
(
I
c
s
i
1
)
,
c
omm
on
-
e
mi
tt
e
r
inver
ter
(
I
c
s
i
2
)
,
a
nd
load
c
ur
r
e
nt
(
I
L
o
a
d
)
wa
ve
f
or
ms
whe
n
I
c
s
i
1
>I
c
s
i
2
T
o
ma
ke
a
m
or
e
de
ta
i
led
a
n
a
l
ys
is
o
f
t
he
w
a
v
e
f
o
r
m
d
is
to
r
ti
on
,
F
ig
ur
e
1
1
p
r
e
s
e
n
ts
t
he
ha
r
mo
nics
p
r
o
f
il
e
o
f
c
u
r
r
e
n
ts
I
c
s
i
1
,
I
c
s
i
2
,
a
nd
l
L
o
a
d
f
or
d
i
f
f
e
r
e
nt
mag
n
it
ude
s
a
t
l
oa
d
pow
e
r
f
a
c
t
o
r
0
.
9
96
.
As
c
a
n
be
no
ti
c
e
d
in
F
i
g
ur
e
11
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
500
-
508
506
in
the
c
a
s
e
of
a
n
H
-
br
idge
inver
ter
,
if
the
magnitud
e
of
output
c
ur
r
e
nt
i
nc
r
e
a
s
e
s
,
the
T
HD
o
f
ou
tput
c
ur
r
e
nt
wi
ll
de
c
r
e
a
s
e
.
T
he
mi
nim
um
T
HD
va
lue
of
H
-
br
idge
C
S
I
wa
s
0.
50
%
a
t
ou
tput
c
ur
r
e
nt
5A,
a
nd
it
s
maxim
um
va
lue
wa
s
21.
27%
a
t
output
c
ur
r
e
nt
1
A.
I
n
c
ont
r
a
s
t,
in
t
he
c
a
s
e
of
a
c
omm
on
-
e
mi
tt
e
r
inver
ter
,
if
the
magn
it
ude
of
outp
ut
c
ur
r
e
nt
incr
e
a
s
e
s
,
the
T
HD
will
incr
e
a
s
e
.
T
he
mi
nim
um
T
HD
va
lue
of
I
c
s
i
2
wa
s
0.
81%
C
S
I
a
t
output
c
ur
r
e
nt
5A,
a
nd
it
s
maximum
va
lue
wa
s
21.
3%
a
t
output
c
ur
r
e
nt
9
A
.
How
e
ve
r
,
a
s
c
a
n
be
s
e
e
n
in
the
gr
a
ph,
the
T
HD
va
lues
of
load
c
u
r
r
e
nt
we
r
e
a
lm
os
t
c
ons
tant
a
t
a
r
ound
0.
34%
.
E
ve
n
the
T
HD
va
lue
of
both
inver
ter
s
va
r
ied,
the
T
HD
va
lue
of
the
load
c
ur
r
e
nt
d
id
not
c
h
a
nge
.
F
igur
e
12
is
the
T
HD
p
r
of
il
e
f
or
di
f
f
e
r
e
nt
magnitudes
of
a
c
c
ur
r
e
nt
a
t
powe
r
f
a
c
tor
0.
782
.
T
he
mi
ni
mum
T
HD
va
lue
o
f
load
c
ur
r
e
nt
wa
s
0.
617
%
whe
n
ou
tp
ut
c
ur
r
e
nt
H
-
br
idge
a
nd
c
omm
on
-
e
mi
tt
e
r
C
S
I
s
we
r
e
1
A
a
nd
9
A,
r
e
s
pe
c
ti
ve
ly.
T
otal
ha
r
moni
c
s
dis
tor
ti
on
(
T
HD
)
pr
of
il
e
f
or
d
if
f
e
r
e
nt
load
c
ondit
ions
with
the
s
a
me
c
ur
r
e
nt
magnitudes
of
c
omm
on
-
e
mi
tt
e
r
a
nd
H
-
br
idge
C
S
I
s
,
i.
e
.
5
A,
is
de
s
c
r
ibed
in
F
igur
e
13
.
As
c
a
n
be
view
e
d
in
the
f
igur
e
,
if
the
r
e
s
is
tanc
e
of
load
incr
e
a
s
e
s
,
the
T
HD
of
the
inver
te
r
’
s
output
c
u
r
r
e
nt
will
a
ls
o
incr
e
a
s
e
.
T
he
lowe
s
t
T
HD
va
lue
o
f
load
c
ur
r
e
nt
wa
s
0
.
38%
whe
n
the
l
oa
d
wa
s
4
Ω
,
a
nd
the
maximum
T
HD
wa
s
0
.
51%
whe
n
the
load
wa
s
8
Ω
.
M
or
e
ove
r
,
the
e
f
f
icie
nc
y
p
r
of
il
e
of
th
e
inver
ter
s
ys
tem
f
or
dif
f
e
r
e
nt
c
u
r
r
e
nt
magnitude
op
e
r
a
ti
ons
is
s
hown
in
F
igur
e
14.
T
he
powe
r
inductor
s
a
nd
di
ode
s
c
ount
of
c
omm
on
e
mi
tt
e
r
C
S
I
is
lar
ge
r
than
H
-
br
idge
C
S
I
.
I
t
will
c
a
us
e
mor
e
powe
r
los
s
e
s
in
the
c
ir
c
ui
ts
.
He
nc
e
,
the
e
f
f
icie
nc
y
of
c
omm
on
-
e
mi
tt
e
r
C
S
I
is
ba
s
ica
ll
y
lowe
r
than
H
-
br
idge
C
S
I
.
Ope
r
a
ti
ng
the
H
-
br
idge
C
S
I
in
a
la
r
ge
r
c
ur
r
e
nt
magnitude
wi
ll
give
h
igher
e
f
f
icie
nc
y
to
the
s
ys
tem.
C
ompar
e
d
to
the
s
ys
tem
a
pplyi
ng
v
olt
a
ge
s
our
c
e
inver
ter
s
,
a
lowe
r
e
f
f
i
c
ienc
y
is
a
li
mi
tation
of
the
pr
opos
e
d
c
ur
r
e
nt
s
our
c
e
inver
ter
s
ys
tem.
F
r
o
m
the
da
ta,
the
mi
ni
mum
wa
ve
f
or
m
dis
tor
ti
on
of
in
ve
r
ter
a
c
c
ur
r
e
nts
dur
ing
pa
r
a
ll
e
l
ope
r
a
ti
on
c
a
n
be
a
c
hieve
d
i
f
the
c
ur
r
e
nt
magnitudes
o
f
both
inver
te
r
s
we
r
e
s
e
t
t
he
s
a
me.
F
igu
re
11
.
T
HD
ve
r
s
us
output
c
ur
r
e
nt
of
inver
ter
s
f
or
powe
r
load
R
4
Ω
,
L
1
mH
F
igur
e
12
.
T
HD
ve
r
s
us
output
c
ur
r
e
nt
of
inver
ter
s
f
or
powe
r
load
R
4
Ω
,
L
10
mH
F
igur
e
13
.
T
HD
pr
of
il
e
f
o
r
di
f
f
e
r
e
nt
powe
r
load
F
igur
e
14.
E
f
f
icie
nc
y
p
r
of
il
e
f
or
dif
f
e
r
e
nt
load
r
e
s
is
tanc
e
a
nd
magnitude
of
output
c
ur
r
e
nt
4.
CONC
L
USI
ON
A
nove
l
photovol
taic
e
ne
r
gy
c
onve
r
s
ion
s
ys
tem
c
ons
tr
uc
ted
us
ing
H
-
br
idge
a
nd
c
omm
on
-
e
mi
tt
e
r
c
ur
r
e
nt
s
our
c
e
inver
ter
c
ir
c
uit
s
c
onne
c
ted
in
pa
r
a
ll
e
l
ha
s
be
e
n
p
r
opos
e
d
a
nd
p
r
e
s
e
nted.
I
n
t
he
c
a
s
e
of
d
c
c
ur
r
e
nt
s
our
c
e
ge
ne
r
a
ti
on,
the
H
-
br
idge
C
S
I
c
ir
c
uit
is
les
s
c
ompl
e
x
than
the
c
omm
on
-
e
mi
tt
e
r
C
S
I
be
c
a
us
e
it
ne
e
ds
a
s
ingl
e
powe
r
inductor
only.
How
e
ve
r
,
f
or
ga
te
d
r
i
ve
c
ir
c
uit
r
e
quir
e
ments
,
the
c
omm
on
-
e
mi
tt
e
r
C
S
I
i
s
s
im
pler
be
c
a
us
e
of
the
c
omm
on
-
e
mi
tt
e
r
c
onne
c
ti
on
of
it
s
po
we
r
s
witche
s
.
T
he
pr
opos
e
d
s
ys
tem
c
a
n
be
a
ne
w
a
lt
e
r
na
ti
ve
f
or
a
photovol
taic
s
ys
tem
with
a
high
-
qua
li
ty
load
c
ur
r
e
nt
wa
ve
f
or
m.
T
e
s
t
r
e
s
ult
s
ha
ve
s
hown
that
the
d
is
tor
ti
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
Study
of
nov
e
l
par
all
e
l
H
-
br
idge
and
c
omm
on
-
e
mit
ter
c
ur
r
e
nt
-
s
ou
r
c
e
inve
r
t
e
r
s
for
…
(
Sur
os
o
)
507
of
load
c
ur
r
e
nt
wa
s
les
s
than
1%
.
Highe
r
e
f
f
icie
nc
y
o
f
the
inver
ter
s
ys
tem
c
a
n
be
a
c
hieve
d
by
ope
r
a
ti
n
g
the
H
-
br
idge
C
S
I
wi
th
a
highe
r
magnitude
of
ou
tput
c
ur
r
e
nt
than
the
c
omm
on
-
e
mi
tt
e
r
C
S
I
.
AC
KNOWL
E
DGE
M
E
NT
S
T
his
wor
k
wa
s
f
unde
d
by
r
e
s
e
a
r
c
h
gr
a
nt
pr
ovided
by
J
e
nde
r
a
l
S
oe
dir
man
Unive
r
s
it
y
,
I
ndone
s
ia
.
RE
F
E
RE
NC
E
S
[
1]
J
.
J
ur
a
s
z
,
F
.
A
.
C
a
na
le
s
c
,
A
.
K
ie
s
d,
M
.
G
ue
z
gouz
e
,
a
nd
A
.
B
e
lu
c
of
,
“
A
r
e
vi
e
w
on
th
e
c
ompl
e
me
nt
a
r
it
y
of
r
e
ne
w
a
bl
e
e
ne
r
gy
s
our
c
e
s
:
C
onc
e
pt
,
me
tr
ic
s
,
a
ppl
ic
a
ti
on
a
nd
f
ut
ur
e
r
e
s
e
a
r
c
h
di
r
e
c
ti
ons
,”
Sol
ar
E
ne
r
gy
,
vol
.
195,
pp.
703
-
724,
2020,
doi
:
10.1016/j
.s
ol
e
ne
r
.2019.11.087.
[
2]
S
.
W
a
ng,
“
C
ur
r
e
nt
s
t
a
tu
s
of
P
V
in
C
hi
na
a
nd
it
s
f
u
tu
r
e
f
or
e
c
a
s
t,
”
C
SE
E
J
our
nal
of
P
ow
e
r
and
E
ne
r
g
y
Sy
s
t
e
m
s
,
vol
.
6,
no.
1,
pp.
72
-
82, 2020, doi:
10.17775/C
S
E
E
J
P
E
S
.2019.03170.
[
3]
A
.
G
hol
a
mi
,
M
.
A
me
r
i,
M
.
Z
a
ndi
,
R
.
G
.
G
hoa
c
ha
ni
,
S
.
E
s
la
mi
a
nd
S
.
P
ie
r
f
e
de
r
ic
i,
“
P
hot
ovol
ta
ic
P
ot
e
nt
ia
l
A
s
s
e
s
s
m
e
nt
a
nd
D
us
t
I
mpa
c
ts
on
P
hot
ovol
ta
ic
S
ys
te
ms
in
I
r
a
n:
R
e
vi
e
w
P
a
pe
r
,”
I
E
E
E
J
our
nal
of
P
hot
ov
ol
ta
ic
s
,
vol
.
10,
no.
3,
pp.
824
-
837,
2020,
doi
:
10.1109/J
P
H
O
T
O
V
.2020.2978851.
[
4]
J
.
C
.
B
la
ke
s
le
y,
T
.
H
ul
d,
H
.
M
ül
le
ja
ns
,
A
.
G
r
a
c
ia
-
A
mi
ll
o, G
.
F
r
ie
s
e
n,
T
.R
.
B
e
tt
s
,
a
nd
W
.
H
e
r
ma
nn,
“
A
c
c
ur
a
c
y,
c
o
s
t
a
nd
s
e
ns
it
i
vi
ty
a
na
ly
s
is
of
P
V
e
ne
r
gy r
a
ti
ng,”
Sol
ar
E
ne
r
g
y
, vol
. 203, pp. 91
-
100, 2020, doi:
10.1016/j
.s
ol
e
ne
r
.2020.03.0
88
.
[
5]
F
.
L
uo, G
.
R
a
nz
i,
C
.
W
a
n,
Z
.
X
u
a
nd
Z
.
Y
.
D
ong,
“
A
M
ul
ti
s
ta
g
e
H
ome
E
ne
r
gy
M
a
na
ge
me
nt
S
ys
te
m
W
it
h
R
e
s
id
e
nt
ia
l
P
hot
ovol
ta
ic
P
e
ne
tr
a
ti
on,”
I
E
E
E
T
r
ans
ac
ti
ons
on I
ndus
tr
ia
l
I
nf
or
m
at
ic
s
, vol
.
15, no. 1, pp. 116
-
126, 2019, doi:
10.1109/T
I
I
.2018.2871159.
[
6]
L
.
C
a
ll
e
ga
r
o,
G
.
K
ons
ta
nt
in
ou,
C
.
A
.
R
oj
a
s
,
N
.
F
.
A
vi
la
a
nd
J
.
E
.
F
le
tc
he
r
,
“
T
e
s
ti
ng
E
vi
de
nc
e
a
nd
A
n
a
ly
s
is
of
R
oof
to
p
P
V
I
nve
r
te
r
s
R
e
s
pons
e
to
G
r
id
D
is
tu
r
ba
nc
e
s
,”
I
E
E
E
J
our
nal
of
P
hot
ov
ol
ta
ic
s
,
vol
.
10,
no.
6,
pp.
1882
-
1891,
2020,
doi
:
10.1109/J
P
H
O
T
O
V
.2020.3014
873.
[
7]
R
.
P
a
ni
gr
a
hi
,
S
.
K
.
M
is
hr
a
,
S
.
C
.
S
r
iv
a
s
ta
va
,
A
.
K
.
S
r
iv
a
s
ta
va
a
nd
N
.
N
.
S
c
hul
z
,
“
G
r
id
I
nt
e
gr
a
ti
on
o
f
S
ma
ll
-
S
c
a
le
P
hot
ovol
t
a
ic
S
ys
te
ms
in
S
e
c
onda
r
y
D
is
tr
ib
ut
io
n
N
e
twor
k
-
A
R
e
vi
e
w
,”
I
E
E
E
T
r
ans
ac
ti
ons
on
I
ndus
tr
y
A
ppl
ic
at
io
ns
,
vol
.
56,
no.
3,
pp.
3178
-
31
95, 2020, doi:
10.1109/T
I
A
.2020.2979789.
[
8]
J
.
F
.
G
e
is
z
, M
.
A
.
S
te
in
e
r
, N
.
J
a
in
,
K
.
L
.
S
c
hul
te
,
R
. M
.
F
r
a
nc
e
,
W
.
E
.
M
c
M
a
hon,
E
.
E
.
P
e
r
l,
a
nd
D
. J
.
F
r
ie
dma
n,
“
B
ui
ld
in
g
a
s
ix
-
ju
nc
ti
on
in
ve
r
te
d
me
ta
mor
phi
c
c
onc
e
nt
r
a
to
r
s
ol
a
r
c
e
ll
,”
I
E
E
E
J
our
nal
of
P
hot
ov
ol
ta
ic
s
,
vol
.
8,
no.
2,
pp.
626
-
632,
2018,
doi
:
10.1109/J
P
H
O
T
O
V
.2017.2778567
.
[
9]
S
. B
. K
ja
e
r
, J
. K
. P
e
de
r
s
e
n a
nd F
.
B
la
a
bj
e
r
g, “
A
r
e
vi
e
w
of
s
in
gl
e
-
pha
s
e
gr
id
-
c
onne
c
te
d i
nve
r
te
r
s
f
or
photovo
lt
a
ic
modul
e
s
,”
I
E
E
E
T
r
ans
ac
ti
ons
on I
ndus
t
r
y
A
ppl
ic
at
io
ns
, vol
. 41, no. 5, pp. 1292
-
1306, 2005, doi:
10.1109/T
I
A
.2005.853371.
[
10]
K
.
A
ll
uha
ybi
,
I
.
B
a
ta
r
s
e
h
a
nd
H
.
H
u,
“
C
ompr
e
he
ns
iv
e
R
e
vi
e
w
a
nd
C
ompa
r
is
on
of
S
in
gl
e
-
P
ha
s
e
G
r
id
-
T
ie
d
P
hot
ovol
t
a
ic
M
ic
r
oi
nve
r
te
r
s
,”
I
E
E
E
J
our
nal
of
E
m
e
r
gi
ng
and
Se
le
c
te
d
T
opi
c
s
in
P
ow
e
r
E
le
c
tr
oni
c
s
,
vol
.
8,
no.
2,
pp.
1310
-
1329,
2020,
doi
:
10.1109/J
E
S
T
P
E
.2019.2900413.
[
11]
J
.
M
.
C
a
r
r
a
s
c
o
e
t
al
.,
“
P
ow
e
r
-
E
le
c
tr
oni
c
S
ys
te
ms
f
or
th
e
G
r
id
I
nt
e
gr
a
ti
on
o
f
R
e
ne
w
a
bl
e
E
ne
r
gy
S
our
c
e
s
:
A
S
ur
ve
y,”
I
E
E
E
T
r
an
s
ac
ti
ons
on I
ndus
t
r
ia
l
E
le
c
tr
oni
c
s
, vol
. 53, no. 4, pp. 1002
-
1016, 2006, doi:
10.1109/T
I
E
.2006.878356.
[
12]
S
.
W
.
S
hne
e
n,
F
.
N
.
A
bdul
la
h,
a
nd
D
.
H
.
S
ha
ke
r
,
“
S
im
ul
a
ti
on m
ode
l
of
s
in
gl
e
pha
s
e
P
W
M
in
ve
r
te
r
by
us
in
g
M
A
T
L
A
B
/S
im
ul
in
k”
,
I
nt
e
r
na
ti
ona
l
J
our
na
l
of
P
ow
e
r
E
le
c
tr
oni
c
s
a
nd
D
r
iv
e
S
ys
te
ms
,
v
ol
.
12,
no.
1,
pp.
212
-
216,
2021,
doi
:
10.11591/i
jp
e
ds
.v12.i1.pp212
-
216.
[
13]
Z
.
B
a
i
a
nd
Z
.
Z
ha
ng,
“
C
onf
or
ma
ti
on
of
M
ul
ti
le
ve
l
C
ur
r
e
nt
S
our
c
e
C
onve
r
te
r
T
opol
ogi
e
s
U
s
in
g
th
e
D
u
a
li
ty
P
r
in
c
ip
le
,”
I
E
E
E
T
r
ans
ac
ti
ons
on P
ow
e
r
E
le
c
tr
oni
c
s
, vol
. 23, no. 5, pp. 2260
-
22
67, 2008, doi:
10.1109/T
P
E
L
.2008.2001893.
[
14]
N
. V
a
z
que
z
,
H
. L
ope
z
,
C
. H
e
r
na
nde
z
,
E
. V
a
z
que
z
, R
. O
s
or
io
a
n
d J
. A
r
a
u, “
A
D
if
f
e
r
e
nt
M
ul
ti
le
ve
l
C
ur
r
e
nt
-
S
our
c
e
I
nve
r
te
r
,”
I
E
E
E
T
r
ans
ac
ti
ons
on I
ndus
t
r
ia
l
E
le
c
tr
oni
c
s
, vol
. 57,
no. 8, pp. 2623
-
2632, 2010, doi:
10.1109/T
I
E
.2009.2030814.
[
15]
N
.
F
.
N
.
I
s
ma
il
,
N
.
A
.
R
a
hi
m,
S
. R
.
S
.
R
a
ih
a
n,
a
nd
Y
.
A
l
-
T
ur
ki
,
“
P
a
r
a
ll
e
l
in
duc
to
r
mul
ti
le
ve
l
c
ur
r
e
nt
s
our
c
e
in
ve
r
te
r
w
it
h e
ne
r
gy
-
r
e
c
ove
r
y s
c
he
me
f
or
i
nduc
to
r
c
u
r
r
e
nt
s
ba
la
nc
in
g”
, I
E
T
P
ow
e
r
E
le
c
tr
oni
c
s
, vol
. 9, i
s
s
ue
11, pp.
2298
-
2304, 2016,
doi
:
10.1049
/i
e
t
-
pe
l.
2015.0909.
[
16]
K
.
G
na
na
s
a
mba
nda
m,
A
.
K
.
R
a
th
or
e
,
A
.
E
dpuga
nt
i,
D
.
S
r
in
iv
a
s
a
n,
a
nd
J
.
R
odr
ig
ue
z
,
“
C
ur
r
e
nt
-
f
e
d
mul
ti
le
ve
l
c
onve
r
te
r
s
:
a
n
ove
r
vi
e
w
of
c
ir
c
ui
t
t
opol
ogi
e
s
, modul
a
ti
on
te
c
hni
que
s
, a
nd
a
ppl
ic
a
ti
ons
,”
I
E
E
E
T
r
a
ns
a
c
ti
ons
on P
ow
e
r
E
le
c
tr
oni
c
s
, vol
.
32, no
. 5,
pp. 3382
-
3401, 2016, doi:
10.1109/T
P
E
L
.2016.2585576.
[
17]
S
ur
os
o,
D
.
T
.
N
ugr
oho,
A
mr
a
n,
a
nd
T
.
N
oguc
hi
,
“
P
a
r
a
ll
e
l
ope
r
a
ti
on
of
c
ur
r
e
nt
-
s
our
c
e
in
ve
r
te
r
f
or
lo
w
-
vol
ta
ge
hi
gh
-
c
ur
r
e
nt
gr
id
-
c
onn
e
c
te
d
phot
ovol
ta
ic
s
y
s
te
m,”
I
nt
e
r
nat
io
nal
J
our
nal
of
E
le
c
tr
ic
al
and
C
om
put
e
r
E
ngi
ne
e
r
in
g
,
vol
.
9,
no.
4,
pp.
2220
-
2229,
20
19,
doi
:
10.11591/i
je
c
e
.v9i
4.pp2220
-
2229
.
[
18]
S
ur
os
o
a
nd
T
.
N
oguc
hi
,
“
A
ne
w
th
r
e
e
-
le
ve
l
c
ur
r
e
nt
-
s
our
c
e
P
W
M
in
ve
r
te
r
a
nd
it
s
a
ppl
ic
a
ti
on
f
o
r
gr
id
c
onne
c
te
d
pow
e
r
c
ondi
ti
o
ne
r
,”
E
ne
r
gy
C
onv
e
r
s
io
n and M
anage
m
e
nt
, vol
. 51, no. 7, pp. 1491
-
1
499, 2010, doi:
doi
.or
g/
10.1016/j
.e
nc
onma
n.2010.02.007
.
[
19]
E
.
L
o
r
e
nz
a
ni
,
F
.
I
mm
ovi
ll
i,
G
.
M
ig
li
a
z
z
a
,
M
.
F
r
ig
ie
r
i,
C
.
B
ia
nc
hi
ni
a
nd
M
.
D
a
vol
i,
“
C
S
I
7:
A
M
odi
f
ie
d
T
hr
e
e
-
P
ha
s
e
C
ur
r
e
nt
-
S
ou
r
c
e
I
nve
r
te
r
f
or
M
odul
a
r
P
hot
ovol
ta
ic
A
ppl
i
c
a
ti
ons
,”
I
E
E
E
T
r
ans
ac
ti
ons
on
I
ndus
tr
ia
l
E
le
c
t
r
oni
c
s
,
vol
.
64,
no.
7,
pp.
5449
-
5459,
20
17,
doi
:
10.1109/T
I
E
.2017.2674595.
[
20]
X
.
G
uo,
N
.
W
a
ng,
J
.
Z
ha
ng,
B
.
W
a
ng
a
nd
M
.
N
guy
e
n,
“
A
N
o
ve
l
T
r
a
ns
f
or
me
r
le
s
s
C
ur
r
e
nt
S
our
c
e
I
nve
r
te
r
f
or
L
e
a
ka
ge
C
ur
r
e
nt
R
e
duc
ti
on,”
I
E
E
E
A
c
c
e
s
s
, vol
. 7, pp. 50681
-
50690, 2019, doi:
10.1109/AC
C
E
S
S
.2019.2908287.
[
21]
H
.
K
e
yha
ni
,
a
nd
H
.
A
.
T
ol
iy
a
t,
"
S
in
gl
e
-
s
ta
ge
mul
ti
s
tr
in
g
P
V
in
ve
r
te
r
w
it
h
a
n
is
ol
a
te
d
hi
gh
-
f
r
e
que
nc
y
li
nk
a
nd
s
of
t
-
s
w
it
c
h
in
g
ope
r
a
ti
on"
, I
E
E
E
T
r
a
ns
a
c
ti
ons
on P
ow
e
r
E
le
c
tr
oni
c
s
, vol
. 29, no. 8, pp. 3919
-
3929, 2014, doi:
10.1109/T
P
E
L
.2013.2288361.
[
22]
S
.
V
.
A
r
a
uj
o,
P
.
Z
a
c
ha
r
ia
s
a
nd
R
.
M
a
ll
w
it
z
,
“
H
ig
hl
y
E
f
f
ic
i
e
nt
S
in
gl
e
-
P
ha
s
e
T
r
a
ns
f
or
me
r
le
s
s
I
nve
r
te
r
s
f
or
G
r
id
-
C
onne
c
te
d
P
hot
ovol
ta
i
c
S
ys
te
ms
,”
I
E
E
E
T
r
ans
ac
ti
ons
on
I
ndus
t
r
ia
l
E
le
c
tr
oni
c
s
,
vol
.
57,
no.
9,
pp.
3118
-
3128,
2010,
d
oi
:
10.1109/T
I
E
.2009.2037654.
[
23]
P
.
G
.
B
a
r
bos
a
,
H
.
A
.
C
a
r
va
lh
o
B
r
a
ga
, M
.
D
.
C
a
r
mo B
a
r
bos
a
R
odr
ig
ue
s
a
nd
E
.
C
.
T
e
ix
e
ir
a
,
“
B
oos
t
c
ur
r
e
nt
mul
ti
le
ve
l
in
v
e
r
te
r
a
nd
it
s
a
ppl
ic
a
ti
on on s
in
gl
e
-
pha
s
e
gr
id
-
c
onne
c
te
d photovol
ta
ic
s
ys
t
e
ms
,”
I
E
E
E
T
r
ans
ac
ti
ons
on P
ow
e
r
E
le
c
tr
oni
c
s
, vol
. 21, no. 4,
pp.
1116
-
1124, 2006, doi:
10.1109/T
P
E
L
.2006.876784.
[
24]
L
.
S
.
G
a
r
c
ia
,
G
.
M
.
B
ui
a
tt
i,
L
.
C
.
de
F
r
e
it
a
s
,
E
.
A
.
A
.
C
oe
lh
o,
V
.
J
.
F
a
r
ia
s
a
nd
L
.
C
.
G
ome
s
de
F
r
e
it
a
s
,
“
D
ua
l
T
r
a
ns
f
or
me
r
le
s
s
S
in
gl
e
-
S
ta
ge
C
ur
r
e
nt
S
our
c
e
I
nve
r
te
r
W
it
h E
ne
r
gy M
a
na
ge
me
n
t
C
ont
r
ol
S
tr
a
te
gy,”
I
E
E
E
T
r
ans
ac
ti
ons
on P
ow
e
r
E
le
c
tr
oni
c
s
,
vol
.
28, no. 10, pp. 4644
-
4656, 2013, doi:
10.1109/T
P
E
L
.2012.2234
139.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
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I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
500
-
508
508
[
25]
S
. A
na
nd, S
. K
. G
undl
a
p
a
ll
i
a
nd B
. G
. F
e
r
na
nde
s
, “
T
r
a
ns
f
or
me
r
-
L
e
s
s
G
r
id
F
e
e
di
ng C
ur
r
e
nt
S
our
c
e
I
nve
r
te
r
f
o
r
S
ol
a
r
P
hot
ovol
t
a
ic
S
ys
te
m,”
I
E
E
E
T
r
ans
ac
ti
ons
on I
ndus
tr
ia
l
E
le
c
tr
oni
c
s
, vol
. 61,
no. 10, pp. 5334
-
5344, 2014, doi:
10.1109/T
I
E
.2014.2300038.
[
26]
A
.
M
ohda
,
E
.
O
r
tj
oha
nna
,
D
.
M
or
to
nb,
a
nd
O
.
O
ma
r
ic
,
“
R
e
vi
e
w
of
c
ont
r
ol
te
c
hni
que
s
f
or
in
ve
r
te
r
s
pa
r
a
ll
e
l
ope
r
a
ti
on,”
E
le
c
tr
ic
P
ow
e
r
Sy
s
te
m
s
R
e
s
e
a
r
c
h
, vol
. 80, pp. 1477
-
1487, 2010, doi:
doi
.or
g/
10.1016/j
.e
ps
r
.2010.06.009
.
[
27]
Z
.
L
iu
,
J
.
L
iu
,
X
.
H
ou,
Q
.
D
ou,
D
.
X
ue
a
nd
T
.
L
iu
,
“
O
ut
put
I
mpe
da
nc
e
M
ode
li
ng
a
nd
S
ta
bi
li
ty
P
r
e
di
c
ti
on
of
T
hr
e
e
-
P
ha
s
e
P
a
r
a
ll
e
le
d
I
nve
r
te
r
s
W
it
h
M
a
s
te
r
–
S
la
ve
S
ha
r
in
g
S
c
he
me
B
a
s
e
d
on
T
e
r
mi
na
l
C
ha
r
a
c
te
r
is
ti
c
s
of
I
ndi
vi
dua
l
I
nve
r
te
r
s
,”
I
E
E
E
T
r
ans
ac
ti
ons
on
P
ow
e
r
E
le
c
tr
oni
c
s
, vol
. 31, no. 7, pp. 53
06
-
5320, 2016, doi:
10.
1109/T
P
E
L
.2015.2483741.
[
28]
Y
.
Q
i,
J
.
F
a
ng,
J
.
L
iu
a
nd
Y
.
T
a
ng,
“
C
oor
di
na
te
d
c
ont
r
ol
f
o
r
ha
r
moni
c
mi
ti
ga
ti
on
o
f
pa
r
a
ll
e
l
vol
ta
ge
-
s
our
c
e
in
ve
r
te
r
s
,”
C
E
S
T
r
ans
ac
ti
ons
on E
le
c
tr
ic
al
M
ac
hi
ne
s
and Sy
s
te
m
s
, vol
. 2, no. 3,
pp. 276
-
283, 2018, do
i:
10.30941/C
E
S
T
E
M
S
.2018.00034.
[
29]
X
.
Z
ou,
X
.
D
u
a
nd
G
.
W
a
ng,
“
M
ode
li
ng
a
nd
s
ta
bi
li
ty
a
na
ly
s
is
f
or
mul
ti
pl
e
pa
r
a
ll
e
l
gr
id
-
c
onne
c
te
d
in
ve
r
te
r
s
s
ys
te
m,”
I
E
E
E
A
pp
li
e
d
P
ow
e
r
E
le
c
tr
oni
c
s
C
onf
e
r
e
nc
e
and E
x
pos
it
io
n (
A
P
E
C
)
, 2018, p
p. 2431
-
2436, doi:
10.1109/AP
E
C
.2018
.8341357.
[
30]
S
. D
. P
a
nj
a
it
a
n, R
. K
ur
ni
a
nt
o, B
.
W
. S
a
nj
a
ya
a
nd
M
. C
.
T
ur
ne
r
,
“
C
ont
r
ol
of
P
a
r
a
ll
e
l
I
nve
r
te
r
s
f
or
H
ig
h P
ow
e
r
Q
ua
li
ty
a
nd S
ha
r
in
g
A
c
c
ur
a
c
y i
n
S
in
gl
e
-
P
ha
s
e
A
C
M
i
c
r
ogr
id
s
,”
U
K
A
C
C
12t
h I
nt
e
r
n
at
io
nal
C
onf
e
r
e
nc
e
on
C
ont
r
ol
(
C
O
N
T
R
O
L
)
, 2018, pp. 50
-
55, d
oi
:
10.1109/C
O
N
T
R
O
L
.2018.8516761.
[
31]
J
.
Y
u,
L
.
D
e
ng,
D
.
S
ong,
a
nd
M
.
P
e
i,
“
W
id
e
ba
ndw
id
th
c
ont
r
ol
f
or
mul
ti
-
pa
r
a
ll
e
l
gr
id
-
c
onne
c
te
d
in
ve
r
te
r
s
w
it
h
ha
r
moni
c
c
ompe
ns
a
ti
on,”
E
ne
r
gi
e
s
, vol
. 12, no. 3, pp. 1
-
22, doi:
10.3390/e
n12030571
.
[
32]
Z
.
W
a
ng,
Z
.
Z
ou
a
nd
Y
.
Z
he
ng,
“
D
e
s
ig
n
a
nd
C
ont
r
ol
o
f
a
P
ho
to
vol
ta
ic
E
ne
r
gy
a
nd
S
M
E
S
H
ybr
id
S
ys
te
m
W
it
h
C
ur
r
e
nt
-
S
ou
r
c
e
G
r
id
I
nve
r
te
r
,”
I
E
E
E
T
r
ans
ac
ti
ons
on
A
ppl
ie
d
Sup
e
r
c
on
duc
ti
v
it
y
,
vol
.
23,
no.
3,
pp.
5701505
-
5701505,
2013,
doi
:
10.1109/T
A
S
C
.2013.2250172.
[
33]
A
.
A
.
A
.
R
a
dw
a
n
a
nd
Y
.
A
.
I
.
M
oha
me
d,
“
P
ow
e
r
S
ync
hr
oni
z
a
ti
on
C
ont
r
ol
f
or
G
r
id
-
C
onne
c
te
d
C
ur
r
e
nt
-
S
our
c
e
I
nve
r
te
r
-
B
a
s
e
d
P
hot
ovol
ta
ic
S
ys
te
ms
,”
I
E
E
E
T
r
ans
ac
ti
ons
on
E
ne
r
gy
C
onv
e
r
s
io
n
,
vol
.
31,
no.
3,
pp.
1023
-
1036,
2016,
doi
:
10.1109/T
E
C
.2016.2533630.
[
34]
B
.
W
e
i,
J
.
C
.
V
á
s
que
z
,
J
.
M
.
G
ue
r
r
e
r
o
a
nd
X
ia
oqi
a
ng G
uo,
“
C
ont
r
ol
a
r
c
hi
te
c
tu
r
e
f
or
pa
r
a
ll
e
le
d
c
u
r
r
e
nt
-
s
our
c
e
-
in
ve
r
te
r
(
C
S
I
)
ba
s
e
d
uni
nt
e
r
r
upt
ib
le
pow
e
r
s
ys
te
ms
(
U
P
S
)
,”
I
E
E
E
8
th
I
nt
e
r
nat
io
nal
P
ow
e
r
E
le
c
tr
oni
c
s
and
M
ot
io
n
C
ont
r
ol
C
onf
e
r
e
nc
e
(
I
P
E
M
C
-
E
C
C
E
A
s
ia
)
, 2016, pp. 151
-
156, doi:
10.1109/I
P
E
M
C
.2016.7512278.
[
35]
S
ur
os
o,
W
in
a
s
is
,
a
nd
T
.
N
oguc
hi
,
“
O
ve
r
la
p
-
ti
me
c
ompe
n
s
a
ti
on
te
c
hni
que
f
or
c
ur
r
e
nt
-
s
our
c
e
pow
e
r
in
ve
r
te
r
,”
I
E
T
P
o
w
e
r
E
le
c
tr
oni
c
s
, vol
. 13, no. 4, pp. 854
-
862, 2020, doi:
10.1049/i
e
t
-
pe
l.
2019.0503
.
[
36]
S
ur
os
o,
D
.
T
.
N
ugr
oho,
a
nd
W
in
a
s
is
,
“
T
hr
e
e
-
le
ve
l
c
omm
on
-
e
mi
tt
e
r
c
ur
r
e
nt
-
s
our
c
e
pow
e
r
in
ve
r
te
r
w
i
th
s
im
pl
if
ie
d
D
C
c
ur
r
e
nt
-
s
our
c
e
ge
ne
r
a
ti
on,”
J
ou
r
nal
of
E
ngi
ne
e
r
in
g Sc
ie
nc
e
and T
e
c
hn
ol
ogy
, vol
. 13, no. 12, pp. 4027
-
4038, 2018.
[
37]
S
ur
os
o,
H
.
S
is
w
a
nt
or
o,
a
nd
T
.
N
oguc
hi
,
“
R
ip
pl
e
r
e
duc
ti
on
of
D
C
c
ur
r
e
nt
s
our
c
e
s
in
th
r
e
e
-
le
ve
l
C
E
-
C
S
I
c
ir
c
ui
ts
us
in
g
s
in
gl
e
c
or
e
in
duc
to
r
s
,”
J
our
nal
of
P
hy
s
ic
s
:
C
onf
e
r
e
n
c
e
Se
r
ie
s
, vol
. 1367
, n
o. 1, pp. 1
-
8, 2019, doi:
10.1088/1742
-
6596/1367/
1/
012057
.
B
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