Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 70
2
~
71
0
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p70
2-7
10
7
02
Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
A performance comparison of tr
ansform
e
r-less grid ti
ed P
V
system using diode clam
ped and
neutral point shorted inverters
Suros
o
, H
a
ri
Siswa
n
tor
o
De
p
a
rt
me
nt
o
f
Ele
ct
rica
l En
g
i
ne
erin
g,
Jenderal Soedirman Un
iv
ers
ity
,
In
do
nesi
a
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
Ju
l
17
,
20
19
Rev
i
sed
No
v 22
, 20
19
Acc
e
pt
e
d
Fe
b 1, 2
0
2
0
Grid
ti
ed p
h
o
t
o
v
o
l
ta
i
c
(P
V
)
s
y
stem
is
a
n
o
p
er
ation
mo
de
of
P
V
s
y
stem
working t
o
gether wi
th utili
ty power
s
uppl
y
to
provi
d
e power
t
o
the
power
lo
ad. Con
v
ent
i
o
n
ally
,
tran
sfo
r
m
e
r is
u
s
ed
to
geth
er
w
i
th the po
w
e
r
inver
t
er
.
T
h
e
po
we
r tra
n
sform
e
r work
s a
s
gal
v
a
n
ic i
n
sol
a
tio
n a
m
on
gst PV
syste
m
a
n
d
power gri
d
.
It w
o
rks
al
s
o
to raise the
v
o
lta
ge
o
f
po
we
r i
n
v
e
rte
r
.
Howe
ve
r,
use
of trans
f
orm
e
r
will add
sys
t
em
co
mple
x
i
ty
, pr
ice, weig
ht
and
size
of th
e
entir
e
s
y
stem. Tran
sfo
r
m
e
r-l
ess
sy
stem is an
alt
e
rn
ative
to
mak
e
the
s
y
s
t
em
sim
p
le
r
a
nd
m
o
re
p
r
a
c
ti
ca
l
in
u
s
e
.
T
h
e pa
p
e
r d
i
sc
usse
s p
e
rfor
m
a
nce
of
tran
sfo
r
m
e
r-
less
g
r
id
tied P
V
s
y
stems us
in
g diod
e
cl
a
m
p
e
d and
n
e
utral point
sh
orted in
v
e
rter
s
.
Eff
ects
of
tra
n
sforme
r
eli
m
in
atio
n
to
th
e feat
o
f
the
grid
tied P
V
s
y
s
t
em
e
s
peci
ally
h
a
r
m
on
ics con
t
en
t
an
d leakag
e c
u
rren
t of PV
sy
stem
were
ex
amin
ed and
an
a
l
yzed
.
Th
e p
e
rf
ormanc
e was
als
o
comp
a
r
ed
wit
h
the
t
r
a
d
iti
ona
l
system
usin
g
H-bri
d
ge
in
v
e
rter.
The
leak
ag
e
cu
rrents
did
n
o
t
fl
ow i
n
th
e
syst
e
m
a
p
pl
y
i
ng d
i
od
e
c
l
am
pe
d i
n
ve
rte
r
, a
n
d
n
e
u
t
ral
p
o
i
n
t
sho
r
te
d
i
nve
rte
r
. In
ca
se
o
f
ha
rm
on
ic
s
c
o
nt
e
n
t, t
h
e
di
ode
cl
amp
e
d
in
v
e
rt
er
i
n
j
e
c
t
e
d
le
ss h
a
rm
on
ic
s c
o
m
p
o
n
e
n
ts th
a
n
t
h
e ne
ut
ra
l poi
nt
sho
r
te
d in
v
e
rte
r
.
T
h
e
ne
u
t
ra
l
poin
t
sho
r
te
d
provi
d
e
s a sim
p
ler i
nve
rt
er
c
i
rcu
it i
n
t
h
e
tran
sfo
r
m
e
r
l
ess
s
y
stems.
Ke
yw
ords:
Gri
d
t
i
e
d
p
hot
o
vol
ta
i
c
H-bri
dge
i
n
vert
er
Tr
ansf
orm
e
r-
les
s
sys
t
em
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
Sur
o
so,
Depa
rt
me
nt o
f
Ele
c
t
r
i
c
a
l
Engi
ne
eri
n
g
,
Jen
d
eral
S
o
e
d
i
r
ma
n
Un
i
v
e
r
sit
y
,
Jl.
Ma
y
j
e
n
S
u
n
g
k
o
n
o
k
m
. 5,
Bl
at
e
r
, Pu
r
b
a
l
ing
g
a
,
Ja
wa Te
nga
h
5
337
1, In
do
ne
si
a
.
Emai
l:
sur
o
so.t
e@u
n
s
o
ed
.a
c.i
d
1.
IN
TR
O
DUCTION
Pho
t
ov
o
lta
ic
(PV
)
c
e
ll
s a
r
e ap
p
lie
d t
o
cap
t
u
re
an
d pr
o
c
e
e
d th
e
li
gh
t en
e
r
gy
o
f
th
e
sun
in
to
e
l
ec
tr
ic
a
l
ene
r
g
y
. To
g
e
nera
t
e
hi
ghe
r
out
put
p
o
w
er
,
some
s
o
l
a
r
cel
l
s
are
c
onst
r
uc
te
d t
o
fo
rm
a
PV
mod
u
l
e
.
T
h
ese
P
V
modul
es
are
li
nke
d a
n
d c
o
ns
truct
e
d
in
seri
es an
d
pa
ra
ll
e
l
t
o
a
c
q
uire la
rger
o
u
t
p
ut
vol
t
a
ge
or cu
rre
nt
[1-3]
.
Th
e g
e
n
e
r
a
t
e
d
p
o
w
e
r
of
PV sy
ste
m
s is
i
n
t
h
e for
m
of d
c
vo
lta
g
e
or d
c
cu
rre
n
t
. To
su
pp
ly ac pow
er l
o
a
d
,
a
po
we
r
i
n
verte
r
i
s
ne
e
d
e
d
.
T
h
e
inve
rt
er
p
r
oc
eeds t
h
e
dc
po
wer o
f
P
V
s
y
st
e
m
t
o
be ac
p
o
w
e
r
wi
th
co
nt
rol
l
a
bl
e
mag
n
i
t
ude
, fre
que
nc
y
a
n
d
p
h
a
se an
gl
e
of it
s
c
u
rre
nt
an
d v
o
l
t
a
ge [4-8]
.
In
ge
ne
ral
,
tw
o
ope
ra
ti
o
n
t
y
pes
of
p
h
o
to
vo
l
t
ai
c syst
em w
e
re
int
r
o
duc
e
d
a
nd
use
d
.
T
h
e
fi
rst
t
y
pe
is
sta
n
d
-
al
o
n
e
o
p
e
rat
i
o
n
.
In
t
h
i
s
sta
n
d-al
one
o
p
erat
i
on,
t
h
e
p
hot
ov
ol
t
a
i
c
s
u
ppl
ie
s
el
ect
ric
a
l
ene
r
g
y
t
o
t
h
e
p
o
w
e
r
lo
a
d
[9-
1
0
]
. Pow
e
r co
nv
er
te
rs
ar
e
n
eed
e
d
t
o
ma
k
e
th
e ou
tpu
t
po
w
e
r
su
i
t
ab
le
f
o
r
th
e
load
s,
i.e
.
d
c
o
r
a
c
l
o
ad
s.
I
n
the
sec
ond
o
p
e
r
a
ti
on
typ
e
, th
e
PV
sy
s
t
em is c
o
nn
ec
ted to
th
e
a
c
powe
r
gr
id
,
wo
rk
i
n
g
tog
e
th
er t
o
co
mp
ly
p
o
w
e
r
t
o
t
h
e ac
pow
e
r
lo
ad
. In
th
is c
a
s
e, th
e
pow
er in
v
e
r
t
er
is u
t
ili
ze
d
as
in
t
e
r
f
a
c
e
a
m
ong
th
e PV sy
s
t
em an
d
ac
po
we
r g
r
i
d
[1
1-1
3
].
He
n
c
e, i
t
cha
n
ges
t
h
e
dc
vol
t
a
g
e
of
p
h
ot
ov
ol
ta
ic
syst
em i
n
t
o
ac
v
o
l
t
a
g
e.
Po
w
e
r
in
v
e
r
t
e
r
a
l
so
reg
u
l
a
t
e
s
th
e pow
e
r
th
a
t
w
i
ll
be
se
n
t
i
n
to
th
e
p
o
w
e
r g
r
i
d
. In
th
e
seco
nd
op
era
tio
n
typ
e
, th
e p
o
we
r
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
o
w
Elec &
Dri Sy
st
I
SSN
: 2
0
8
8
-8
69
4
A Pe
rf
or
m
ance
c
o
m
p
ari
s
on
of
t
r
a
n
sfor
me
r-l
e
ss gri
d
t
i
e
d
PV
syst
em
usi
n
g
di
ode
cl
am
pe
d
…
(S
ur
os
o)
7
03
tr
an
sfor
mer
i
s
co
nv
en
ti
o
n
a
lly emp
l
oy
e
d
to
ra
ise
th
e
ou
t
p
u
t
vo
lta
g
e
of PV syst
em
. I
t
wo
rk
s a
l
so
a
s
g
a
lv
a
n
ic
in
su
la
ti
on
b
e
tw
ee
n P
V
sy
ste
m
an
d ac powe
r
g
r
i
d
[1
4-
16].
N
e
v
e
rt
h
e
le
ss, a
p
p
lic
at
io
n of low
f
r
e
qu
e
n
cy pow
er
tr
an
sfor
mer
w
i
l
l
a
d
d t
h
e w
e
i
g
h
t
,
vo
lu
me
,
co
st
a
n
d
po
w
e
r lo
sses
o
f
sy
ste
m
[
1
7
-
19
]. Mo
r
e
o
v
e
r
,
th
e ex
ist
e
n
c
e
of
dc
c
u
r
r
e
n
t c
o
mp
one
nt i
n
th
e
syst
e
m
wi
l
l
c
a
use
co
r
e
s
a
t
u
rat
i
o
n
of
p
o
we
r
t
r
a
n
s
f
or
mer.
It
ma
y
r
e
sul
t
i
n
ove
r
h
ea
ti
ng
an
d
fa
ult
of
t
r
a
n
sf
or
me
r.
I
n
so
me t
o
p
o
l
ogi
e
s
,
hig
h
f
r
e
q
u
e
n
c
y
po
w
e
r t
r
a
n
s
f
or
me
r i
s
a
p
pli
e
d t
o
mi
nimi
ze
t
h
e
si
ze a
n
d v
o
l
u
me
of the
e
n
t
i
r
e s
y
st
em.
Ho
weve
r, effic
i
en
cy i
s
st
i
l
l
a p
r
obl
em
in
t
h
i
s
syst
em.
Pow
e
r l
o
ss
es in
a
h
i
gh
f
r
equ
e
n
c
y pow
e
r
tr
an
sfor
mer
i
s
st
ill a
r
e
m
a
in
ed prob
le
m
[20
-
22
].
A
n
al
te
rn
a
tiv
e me
thod
t
o
i
n
t
e
g
r
a
t
e
th
e PV syst
em
w
i
t
h
p
o
w
er
g
r
i
d
is
b
y
e
lim
in
a
ting th
e pow
er
tr
an
sfor
mer
.
Th
is
tec
h
n
i
q
u
e
is
ca
lle
d
as tr
an
sf
or
mer
-
l
e
ss
pho
to
v
o
lta
ic
sy
st
e
m
. In
t
h
is
tr
an
sf
orm
e
r
-
l
e
s
s
me
th
od
,
th
e
PV
i
s
link
e
d
t
o
th
e
p
o
w
e
r
g
r
id w
i
th
ou
t u
s
ing
p
o
w
e
r
tran
sforme
r
[23
-
29
].
As
a
resu
lt
,
th
e
sy
ste
m
b
e
c
o
me
mu
ch
si
mp
le
r. It a
l
so
el
imin
a
t
e
s
t
h
e
po
w
e
r l
o
ss
es g
e
n
e
r
a
te
d
b
y
th
e
tr
an
sfo
r
m
e
r
.
H
o
w
e
v
e
r,
lea
k
ag
e
cu
rr
en
t
is a
n
o
t
h
e
r n
e
w p
r
ob
le
m
in
trod
u
c
e
d
in
th
is
syste
m
[3
0-34
].
Eli
m
in
a
t
i
n
g
le
ak
a
g
e
c
u
r
r
e
n
t
in
this
ty
p
e
sy
ste
m
w
ill
b
e
g
r
e
a
tly
g
i
v
e
a
d
v
a
n
t
ag
e.
Th
is
p
a
p
e
r
d
i
sc
u
s
ses
a d
i
f
f
e
re
n
t
t
r
a
n
sf
or
me
r
-
l
e
ss
g
r
id
con
n
e
c
t
ed
ph
ot
o
v
o
lt
a
i
c
syst
em
usi
n
g
th
r
ee-
le
vel
ne
ut
r
a
l-
p
o
i
n
t
-
s
h
ort
e
d
(
T
L
N
PS
) i
n
v
e
rt
er
ci
rc
uit
s
.
The
pe
rf
or
man
c
e
wa
s
c
o
mpa
r
e
d
wi
t
h
tr
ans
f
or
mer
l
e
s
s
sy
st
em usi
n
g
t
h
ree
-
l
e
vel
di
ode
-c
la
mpe
d
(
T
LDC)
in
ve
rt
er
[6
,
26
, 28
, 2
9
].
The
TLD
C
i
nve
rt
er
c
o
nsi
s
t
s
o
f
f
our
po
w
e
r
s
w
i
t
c
h
es
an
d t
w
o
po
we
r
di
o
d
e
s
.
I
n
case
of
t
h
e
TL
NP
S
i
n
vert
e
r
c
i
rcui
t
,
it is c
o
n
s
tru
c
ted
w
i
th fo
u
r
pow
e
r
sw
it
ch
e
s
on
ly
. Th
e
y
op
e
r
at
e in
pu
ls
e
w
i
d
t
h
mo
du
la
tion
(
P
WM
) op
e
r
a
tio
n
.
Th
e
pow
e
r
d
e
liv
e
r
e
d
in
to
t
h
e
gr
id is
r
e
gu
la
te
d
by
pr
opor
tio
n
a
l
in
t
e
gra
l
cur
r
e
n
t
co
n
t
r
o
l.
The
pe
rf
o
r
ma
n
c
e
s
wer
e
e
v
a
l
u
a
t
e
d b
y
usi
ng
com
put
e
r
si
mu
la
ti
on t
e
st
s. T
h
e
fe
at
ure
s
of
t
h
e sy
st
em we
r
e
a
l
so
c
o
mpa
r
e
d
t
o
t
h
e
syst
em
e
m
pl
oyi
ng co
n
v
e
n
ti
onal
H
-
b
r
i
d
ge i
nve
r
t
e
r
.
2.
PROP
OSE
D
GRI
D
TIE
D
PV
SYSTEM
Fi
gu
re
1 p
r
ese
n
t
s
a c
o
n
v
e
n
t
i
ona
l
of
g
r
i
d
ti
ed
ph
ot
o
v
o
lt
a
i
c
syst
em
usi
n
g H
-
bri
d
ge
v
o
l
ta
ge so
urc
e
i
nve
r
t
e
r
a
nd
p
o
we
r
tr
a
n
s
f
o
r
mer
.
The
H
-
b
r
i
dge i
n
v
e
rt
er
w
o
r
k
s
t
o
pr
o
d
u
ce
ac
out
put
vol
t
a
ge
f
r
o
m
d
c
i
n
p
u
t
vol
t
a
ge
ge
ne
ra
te
d b
y
t
h
e
ph
o
t
ov
ol
ta
i
c
syste
m
.
T
h
e t
r
a
n
sf
o
r
mer
i
n
t
h
is s
y
st
em is e
m
pl
o
y
ed
t
o
l
e
vel
-
up
t
h
e a
c
v
o
lta
g
e
of
i
n
ve
r
t
e
r
to me
e
t
th
e p
o
we
r gr
id v
o
lta
g
e
.
H
e
rea
f
t
e
r
,
Fi
gu
re 2
sho
w
s co
nf
igu
r
at
ion
o
f
a
g
r
id
tie
d
p
h
o
t
ovo
l
t
ai
c sy
s
t
em wi
thou
t
tr
a
n
sf
orm
e
r
call
e
d
a
s
t
r
ansfo
r
me
r
-
le
ss sy
s
t
em.
P
o
w
e
r tr
a
n
s
f
or
mer
i
s
el
imin
a
t
e
d
i
n
t
h
is s
y
ste
m
.
To
obta
i
n
a
hi
ghe
r
ac
out
p
u
t
vol
t
a
ge
, t
w
o al
te
rnat
i
v
e
wa
y
s
c
a
n
be a
ppl
i
e
d.
The
fi
rst
o
n
e i
s
b
y
c
o
n
n
ect
i
n
g
some
phot
o
v
o
l
t
a
i
c mo
d
u
l
e
s
i
n
ser
i
e
s
.
He
nce,
t
h
e
dc i
n
p
u
t
volt
a
ge
wi
ll
b
e
hi
ghe
r.
T
h
e
seco
n
d
man
n
e
r
i
s
b
y
u
t
il
i
z
i
ng
dc-
d
c
st
e
p
-
up pow
e
r
c
o
n
v
e
r
t
e
r.
T
h
e
l
o
w dc v
o
l
t
a
g
e of p
hot
o
v
ol
t
a
i
c
i
s
b
oost
e
d
t
o
meet
t
h
e a
c
gri
d
v
o
l
t
a
g
e.
An
othe
r
fe
at
ure s
u
c
h
a
s
ma
xim
u
m
p
o
wer p
o
i
n
t
trac
k
i
ng
(MP
P
T) sy
st
em ca
n
be
re
al
iz
ed
i
n
t
h
e
dc
-
d
c
c
o
nve
rt
er
t
o
obt
ai
n
ma
xi
m
u
m en
e
r
g
y
of
s
unli
g
h
t
.
In
f
act
, t
h
e
r
e
are
para
sit
i
c
c
a
p
ac
i
t
a
n
ces
be
twee
n
t
h
e
PV s
y
st
ems
a
n
d
gr
oun
d.
T
h
ese
pa
ra
sit
i
c
c
a
pac
i
ta
nce
va
lue
s
a
r
e
n
o
t
f
i
xe
d
.
The
y
are
g
r
ea
tl
y
af
fec
t
e
d
b
y
en
vi
r
o
n
m
ent
a
l
c
o
ndi
t
i
ons
,
an
d
P
V
mo
dul
e
co
ns
tr
u
c
ti
on
. Typ
i
c
a
l
l
y
,
t
h
e p
a
ra
sit
i
c
ca
pa
ci
ta
n
c
e
v
a
l
u
es r
a
n
g
e
fro
m 5
0
- 15
0 nF
/kW
[
3
5
]
. Th
e
p
a
r
a
s
itic
c
a
pac
i
ta
nces
c
oul
d a
d
d l
o
sse
s,
a
n
d ca
use
r
i
sk
f
o
r
h
u
m
an
as P
V
ope
rat
o
r.
The
s
e
par
a
si
ti
c c
a
pac
i
ta
nce
s
ar
e
r
e
p
r
e
s
e
n
te
d
b
y
c
a
pa
ci
ta
nce
C
pv1
and
C
pv2
as
sh
ow
n i
n
Fi
g
u
re
2.
I
n
thi
s
pape
r,
t
h
ree
sy
ste
m
s ar
e
c
o
nsi
d
er
e
d
a
n
d
t
e
st
ed.
T
h
e
fi
rst
syst
em
is
by
u
s
i
n
g c
onve
nti
ona
l
H
-
b
r
i
d
ge
i
n
ve
rt
er
a
s
i
ndi
cat
ed
i
n
F
i
g
u
r
e
3.
T
h
e
H
-
b
r
i
d
ge
i
nve
r
t
e
r
i
s
c
o
n
s
t
r
uc
te
d
by
f
o
ur
co
nt
r
o
l
l
e
d
po
we
r s
w
i
t
c
he
s.
T
h
e
se
c
o
nd
syst
em
i
s
by
a
ppl
yi
ng
t
h
e
TLD
C
i
nve
r
t
e
r
as
sh
o
w
n
i
n
F
i
g
u
r
e
4.
F
o
u
r
co
nt
r
o
l
l
e
d s
w
i
t
c
h
es
plus
t
w
o
p
o
w
e
r
di
o
d
es
a
r
e
re
qui
r
e
d
t
o
bui
l
d
t
h
i
s
i
nve
r
t
e
r
ci
rc
uit
.
The
t
h
i
r
d s
y
st
e
m
i
s
a
ne
w s
y
st
em.
T
h
i
s
syst
em ut
il
i
z
e
s
TL
NP
S i
nve
rt
e
r
a
s
de
pi
ct
ed i
n
F
i
g
u
r
e
5.
F
o
ur
co
nt
r
o
ll
e
d
swi
t
c
hes
a
r
e
u
s
e
d
t
o
c
o
n
s
t
r
uc
t
t
h
i
s
i
nve
rt
er
. T
h
e
TLN
PS
in
ve
rt
e
r
ci
r
c
uit
is simpl
e
r
t
h
an
t
h
e TLDC
i
nve
rt
er,
beca
use o
f
it
nee
d
s o
n
l
y
fo
ur
p
o
we
r
s
w
i
t
c
hes wi
t
h
o
u
t po
we
r
d
i
odes
.
T
h
e in
ve
rt
er c
i
r
c
ui
t
s
ar
e
li
nk
ed
to
t
h
e
a
c
pow
e
r
gr
id
d
i
r
e
c
tly
w
itho
u
t
po
w
e
r
tr
ansf
orm
e
r
.
F
i
gur
e
1.
C
o
nv
ent
i
onal
g
r
i
d
ti
ed P
V
s
y
ste
m
[
4
,
5
]
F
i
gu
r
e
2.
Tr
a
n
s
f
o
r
me
r
-
l
ess PV
system
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
I
n
t J
P
o
w
El
ec
&
D
r
i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
:
7
02
– 71
0
70
4
Fi
gu
re 3.
Tra
n
s
f
or
me
r-l
e
s
s
PV
s
y
st
e
m
s
u
s
i
n
g
H
-
bri
dge
i
n
ver
t
e
r
[
2
5
]
F
i
gu
r
e
4.
Tr
a
n
s
f
o
r
me
r
-
l
e
ss P
V
syst
em
s usi
ng
TLDC
i
nve
rt
er
F
i
gu
re
5.
P
r
o
p
o
se
d t
r
a
n
sf
o
r
m
e
r
-
l
e
ss PV
usi
ng TL
NP
S in
ve
r
t
e
r
To
ma
na
ge t
h
e p
o
we
r
se
nt t
o
t
h
e
p
o
w
er
g
r
i
d
,
a
p
r
op
ort
i
ona
l i
n
t
e
g
r
a
l
(
P
-I
) c
u
r
r
e
nt
c
o
ntr
o
ll
e
r
wa
s
e
m
pl
o
y
e
d
t
o
g
e
t
h
er
wi
th t
h
e
pul
se
wi
dt
h
mo
dul
at
i
o
n ci
r
c
ui
t
s
. F
i
g
u
r
e
6 sh
o
w
s t
h
e
cont
rol
l
e
r a
p
pli
e
d i
n
th
e
inv
e
rt
er
sy
ste
m
.
Th
is co
n
t
r
o
ll
er
is the sa
me
fo
r all
th
r
e
e
inv
e
rter
syst
em
s. Th
e
PWM
st
rate
g
y
i
m
ple
m
e
n
t
e
d c
a
r
r
i
e
r a
n
d si
n
u
soi
d
al
sig
n
a
l
s t
o
ge
ne
ra
te
f
i
r
i
ng si
gnal
of
i
n
ver
t
e
r
’s
po
we
r
swi
t
c
hes.
T
h
e
si
gnal
s
C
r1
and
C
r2
a
r
e t
h
e
c
a
r
r
i
er
si
g
n
al
s t
o
ge
ner
a
t
e
p
u
l
s
e
w
i
dt
h
m
o
dula
t
i
o
n
(
P
WM)
w
a
ve.
Th
e
ou
t
p
ut
s
of
t
h
e co
mpa
r
a
t
or
s
wi
l
l
be
the
i
n
put
s o
f
ga
t
e
d
r
i
v
e
c
i
r
c
ui
ts o
f
p
o
we
r swi
t
c
he
s.
.
Fi
gu
re
6.
Cu
r
r
e
n
t
c
o
ntr
o
ll
e
r
of
i
nve
rt
er
syst
e
m
3.
TEST R
E
SULTS A
N
D D
I
SCU
S
S
I
ON
Th
e
p
e
r
f
or
manc
e o
f
th
e p
r
op
ose
d
tr
a
n
sfor
mer
-
l
e
s
s
g
r
i
d
co
nn
e
c
t
e
d
PV
sy
s
t
e
m
mak
i
ng
u
s
e o
f
TLN
P
S
i
nve
r
t
e
r
wa
s
t
e
st
ed a
n
d e
v
a
l
ua
te
d
b
y
com
p
u
t
e
r
sim
u
l
a
t
i
ons
o
f
p
o
we
r P
S
I
M
sof
t
wa
re
. T
h
e
r
eu
nt
o
,
t
h
e
pe
r
f
o
r
ma
nc
e o
f
the
ne
w
s
y
st
em
was
c
o
mpa
r
ed
wi
t
h
t
w
o
ot
he
r
s
y
st
e
m
s,
i.
e.
H
-
b
r
i
d
ge a
n
d
TL
DC
i
nve
r
t
e
r
sy
ste
m
s.
Th
e
c
o
n
d
itio
ns
an
d p
a
r
a
me
ter
s
w
e
r
e
se
t
t
h
e
s
a
me
fo
r
al
l
inv
e
rter
-
P
V
sy
stems.
Th
e d
i
ffe
r
e
n
c
e
w
a
s
onl
y t
h
e
i
n
v
e
rt
er
ci
rc
uit
s
ap
pl
i
e
d as
p
o
we
r
c
o
n
v
e
r
te
r.
3.
1.
Tr
a
n
sfo
r
m
er-les
s
S
y
st
em
wit
h
H-
br
idg
e
inv
e
r
t
e
r
Th
e tr
an
sfo
r
mer
-
l
e
s
s H-b
r
i
d
g
e
sy
stem a
s
in
d
i
ca
te
d in
Fig
u
re
3
wa
s te
ste
d
.
Tab
l
e 1 lis
ts
t
h
e p
a
ramet
e
rs
in t
h
i
s
te
st.
T
h
e P
V
syst
e
m
wa
s
epi
t
o
m
i
zed
by
dc
volt
a
ge
so
ur
ce
w
i
t
h
ma
g
n
i
t
u
d
e
2
20 V
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
A Perf
orm
a
nc
e
co
mp
ari
s
on
of
t
r
a
n
sf
or
mer-l
e
ss
gri
d
t
i
ed
PV
syst
em
usi
n
g
d
i
ode
cl
am
pe
d … (S
ur
os
o)
7
05
The i
n
verte
r
ci
rc
uit
wa
s o
p
e
r
at
ed i
n
2
2
kHz
swi
t
c
hi
n
g
fre
q
uenc
y.
Pa
rasi
t
i
c
capa
c
i
t
ance
val
u
es
of
P
V
s
y
st
e
m
were set
a
s
10
0 n
F
,
a
n
d 1 n
F
whi
l
e
t
h
e fi
l
t
er i
n
d
u
ct
o
r
w
a
s 1 m
H
. T
h
e i
n
v
e
rt
er
sy
st
em
w
a
s
l
i
nked t
o
2
2
0
V 50
H
z
a
c
pow
er
gr
id
.
F
i
g
u
r
e
7
pre
s
en
t
s
th
e wa
ve
for
m
s
o
f
i
nve
rt
er’s
c
u
rre
n
t sent
i
n
t
o
the
p
o
w
e
r
gri
d
b
y
H
-
bri
dge
in
v
e
r
t
e
r
cir
c
u
it,
a
n
d
pow
er
g
r
id
vo
lta
g
e
wave
fo
rm
.
In
th
i
s
te
st,
th
e
mag
n
itu
d
e
o
f
th
e a
c
c
u
rr
en
t
w
a
s
set
as
1
5
A.
Fi
gu
re
8
prese
n
t
s
t
h
e
h
a
rm
oni
cs c
ont
e
n
t
of t
h
e
i
n
j
e
ct
ed
cu
rre
nt.
The
o
d
d
ha
rmo
n
ic
s
o
r
de
rs
were
th
e
pre
d
o
m
in
a
n
t
,
i.e
.
3
rd
, 5
th
, 7
th
wit
h
ma
g
n
it
ude
s 0
.
3
1
%
,
0.
25%
a
n
d
0.18
%, re
spec
t
i
v
el
y.
F
i
g
u
re 9 an
d
F
i
g
u
r
e
10
d
e
p
i
ct
t
h
e
le
ak
ag
e cu
rr
en
t
s
I
C
pv
1
an
d
I
C
pv2
f
l
owin
g
th
ru
th
e
p
a
r
a
siti
c
ca
p
a
ci
tan
c
e
s
. As on
e
see
in
th
e
s
e
f
i
g
u
r
e
s
, a l
a
r
g
er p
a
r
a
sitic
c
a
p
a
ci
ta
n
ce
val
u
e
w
ill
cau
se
lar
g
er
le
ak
ag
e cu
rr
en
t
s
i
n
t
h
e
PV
sy
ste
m
.
Ta
ble
1. T
e
st
p
a
ramet
e
r o
f
s
y
s
t
e
m
.
P
a
r
a
me
te
rs
Value
DC
voltage
sourc
e
220 V
Pow
e
r
gri
d
,
rm
s
220 V
Switc
hin
g
fr
eque
nc
y
22
kH
z
Filt
er
inducto
r
1
m
H
Pa
ra
sitic
ca
pac
ita
n
c
e
of PV
100 nF, 1 nF
L
o
a
d
R =
20
Ω
, L = 5
mH
F
i
gu
re
7.
H
-
b
r
i
dge
i
n
vert
e
r
i
n
j
ect
e
d
cu
rrent
(I
inv
)
,
and
gr
id
vo
lta
g
e
(
V
gr
i
d
)
Fi
gu
re
8.
Ha
rmoni
c
s
spect
ra
o
f
c
u
rrent
, I
inv
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
7
0
2
–
710
70
6
Fi
gu
re
9. Leak
a
g
e c
u
rre
n
ts
at
C
pv
=1
00
n
F
F
i
gu
re
1
0
.
Le
a
k
age
cu
rre
n
t
i
n
H
-
b
r
i
d
ge ba
se
d gri
d
c
o
n
n
ec
t
e
d
P
V
s
y
st
em
at
C
pv
1
nF
3.2.
Transformer
-
less syst
em
usi
n
g
TLD
C in
v
ert
er
The
P
V
-i
n
v
ert
e
r s
y
ste
m
e
m
plo
y
i
n
g TL
D
C
i
nve
rte
r
a
s
desc
ribe
d i
n
F
i
g
u
re
4
wa
s t
e
st
ed
wit
h
t
h
e sa
me
pa
ra
me
te
rs
a
s
i
n
T
a
bl
e
1. Fi
gu
re
11
pre
s
e
n
ts
t
h
e
wa
ve
fo
rms
of in
ve
rt
e
r
’s ac
c
u
rre
n
t
a
n
d
po
w
e
r g
r
i
d
vol
ta
ge
.
A
sin
u
soi
d
al
a
c
cu
rrent
w
a
s
se
n
t
t
o
po
we
r grid
b
y
usi
n
g
the
TL
DC
in
ve
rt
er s
y
ste
m
.
T
h
e
l
o
w
fre
que
nc
y
har
m
o
n
i
c
s
orders
o
f
i
n
ve
rt
er’
s
c
u
rre
n
t
i
s
s
h
o
w
n
i
n
Fi
g
u
r
e
12
.
As
o
n
e ca
n see
i
n
the
fi
gu
re
,
mag
n
i
t
ude
s of t
h
e
3
rd
, 5
th
, and
7
th
ha
rmo
n
i
c
s
com
pone
nts w
e
re get
t
in
g
do
wn
co
mpa
r
e
d
wi
t
h
t
h
e
ha
rmo
n
i
c
s o
f
i
nve
rt
er’s c
u
rr
ent
pro
d
u
c
e
d
in
H-b
r
i
d
ge i
nve
rte
r
c
i
rc
ui
t. Ma
gni
tu
de
s
of t
h
e
3
rd
, 5
th
, and 7
th
harm
on
ics
com
p
o
n
e
n
t
s
i
n
t
h
i
s
figu
re are
0.
03
2%
, 0.0
4
%
and
0.0
61%
,
suc
cessi
vel
y
.
Fi
gu
re
1
3
pre
s
e
n
ts t
h
e capt
u
re
d
z
e
r
o
le
a
k
ag
e c
u
rr
en
t
wa
v
e
fo
rm
s
i
n
t
h
is sy
st
e
m
.
U
s
i
n
g th
e d
i
o
d
e
c
l
a
m
pe
d
i
n
ve
rt
er,
th
e le
ak
a
g
e
c
u
rr
en
t
s
have
bee
n
el
i
m
ina
t
e
d
.
Fi
gu
re
1
1
.
In
ve
r
t
e
r’s
cu
rr
e
n
t
a
n
d
p
o
w
er
g
r
i
d
vol
t
a
ge
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
A Perf
orm
a
nc
e
co
mp
ari
s
on
of
t
r
a
n
sf
or
mer-l
e
ss
gri
d
t
i
ed
PV
syst
em
usi
n
g
d
i
ode
cl
am
pe
d … (S
ur
os
o)
7
07
Fig
u
r
e
12
.
Ha
rmon
ic
s
sp
e
c
tr
a of
inv
e
rt
e
r
’
s
cu
rr
en
t
Fi
g
u
re
13
. Leak
a
g
e
cu
rr
en
ts
of TLD
C
inv
e
rt
er
sy
ste
m
3.3.
Prop
ose
d
tr
an
sfor
m
er-le
ss
s
y
stem usi
n
g T
L
N
PS i
n
ver
t
e
r
The t
h
ir
d
s
y
st
e
m
i
s
t
h
e
P
V
s
y
ste
m
a
ppl
yi
ng
t
h
e t
h
re
e-l
e
ve
l
neut
ra
l p
o
i
n
t
s
h
o
r
t
e
d
(T
LNP
S
)
i
nve
rte
r
c
i
r
c
u
i
t a
s
th
e po
w
e
r
co
nd
iti
oner
a
n
d
i
n
te
rf
ace s
h
o
w
n
i
n
Figu
r
e
5
.
By
u
s
i
n
g
th
i
s
i
n
v
e
rt
er
c
i
r
c
u
i
t, a
t
h
r
e
e
-
le
v
e
l
v
o
l
t
a
g
e
w
a
v
e
fo
rm
a
l
so
c
a
n b
e
ob
ta
in
ed
. Th
e
TLNP
S
inve
r
t
er
ci
rc
u
it n
eed
s fo
ur pow
er
sw
it
ch
e
s
,
on
l
y
.
I
t
i
s
simpl
e
r t
h
a
n
t
h
e TL
DC
i
nve
rt
er.
It
s o
u
t
p
ut
w
a
ve
form i
s
th
e
sa
me
wi
th
t
h
e wa
ve
fo
rm
of H
-
brid
ge
a
n
d
TLD
C
i
nve
rt
ers, i.e
.
t
h
re
e
-
l
e
ve
l v
o
l
t
a
ge wa
ve
fo
rm.
T
h
e
P
V
-i
n
v
er
te
r syst
em
usin
g TL
NPS i
nve
rt
er wa
s e
x
a
m
i
n
ed as
t
h
e s
y
st
ems e
m
pl
o
y
e
d
H-
bridge
an
d
TL
D
C
inve
rt
ers
.
F
i
gu
re
1
4
a
r
e
th
e
wa
veforms
o
f
t
h
e
de
li
vere
d
c
u
rre
n
t
and
gri
d
v
o
lt
a
g
e i
n
t
h
i
s
syst
em. A si
nus
oi
da
l c
u
rre
n
t
wa
s i
n
j
ect
e
d
t
o
t
h
e ac
p
o
w
e
r
g
r
i
d
b
y
usin
g T
L
NP
S
i
nve
rt
er. T
h
e
h
a
rm
oni
c s
p
ec
tr
a of the
i
n
je
ct
ed a
c
c
u
rre
n
t
i
s
sho
w
n i
n
F
i
g
u
re
15
. T
h
e
m
a
gni
tu
de
s
of t
h
e l
o
w
harmo
n
i
c
or
de
rs e
s
peci
al
l
y
t
h
e
3
rd
, 5
th
an
d
7
th
were
0
.
28
%,
0.22%
a
n
d
0.
18%
re
spe
c
t
i
v
el
y. T
h
e
l
e
a
k
age
current
s
i
n
t
h
i
s
syste
m
di
d n
o
t
ap
pe
ar a
s
sho
w
n in Fi
gu
re
16
. He
nc
e,
t
h
i
s
TL
NP
S sy
st
em
wa
s
a
l
s
o
a
b
l
e
t
o
re
move
t
h
e
l
e
a
k
c
u
rre
nt
s in
t
h
e
P
V
s
y
st
e
m
.
Fi
g
u
re
17
s
h
o
w
s a
c
o
mpa
r
i
s
on
of l
o
w
ha
rmoni
c
s
c
o
mp
o
n
ent
s
o
f
out
put
c
u
r
r
ent
sent
t
o
t
h
e a
c
po
we
r gri
d
b
y
H-bri
dge
,
TLD
C
an
d
TL
NPS
i
n
ve
rt
ers.
As
c
a
n
be
not
i
ced
i
n
t
h
is
f
i
gu
r
e
, th
e TLDC
i
n
v
e
rt
er de
liv
e
re
d th
e low
e
s
t
ma
gn
itude
of
h
a
r
m
o
n
i
cs co
mp
on
en
ts. It
s to
ta
l
h
a
rmo
n
i
c
s
di
st
ort
i
o
n i
s
a
l
so
the
smal
le
st amo
n
g
t
h
e
t
h
re
e-syst
e
m
s.
F
i
g
u
r
e
14
.
D
e
liv
e
r
e
d
cu
rr
en
t b
y
inv
e
r
t
e
r
an
d
a
c
gr
id
vo
lta
g
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
7
0
2
–
710
70
8
Fi
gu
re
1
5
.
Har
m
o
n
i
c
s c
o
m
pone
nt
s o
f
T
L
N
P
S
i
n
vert
er
c
u
rrent
Fi
gu
re
1
6
. Lea
k
age
cu
rre
n
t
w
a
veforms of
T
L
NP
S
in
ve
rt
e
r
syst
e
m
F
i
gu
re 1
7
.
C
o
mpa
r
i
s
on
of inj
e
c
t
e
d
c
u
rrent
ha
rm
onic
orde
rs
4.
CO
NCL
U
S
I
O
N
Thi
s
pa
per
pre
s
ent
e
d pe
rfo
r
m
a
nc
es
o
f
t
r
a
n
sf
o
r
me
r-l
e
ss g
r
i
d
t
i
e
d
P
V
syste
m
s usi
n
g
H
-
bri
dge
,
T
L
D
C
and
TL
N
P
S
in
ve
rt
er
ci
rc
ui
t
s
. The
H
-
brid
ge
inv
e
rt
er
ge
ne
ra
t
e
s n
o
n
-
z
e
ro
l
e
a
k
c
u
r
r
e
n
t
d
u
r
i
n
g t
r
a
n
s
f
orme
r-l
e
s
s
g
r
i
d
tie
d
o
p
e
r
a
t
io
n
of PV
sy
stem
. Th
e
la
rg
e
r
t
h
e p
a
r
a
siti
ca
l ca
p
a
cit
a
n
c
e
s
of
PV
sy
ste
m
wi
ll
ri
se
t
h
e m
a
g
n
i
tu
d
e
of l
e
aka
g
e
c
u
rrent
.
Th
e s
u
g
g
e
st
ed
tra
n
sfo
r
mer-l
e
ss
g
r
i
d
t
i
e
d P
V
s
y
st
em
usi
ng
TL
NPS
i
nve
rte
r
w
o
r
k
ed
we
ll
w
i
t
h
ze
ro
le
ak
c
u
rre
n
t
. Th
e TLN
PS inv
e
r
t
e
r
h
a
s
mer
it r
e
la
ted
w
i
t
h
its
simp
l
e
r
c
i
r
c
u
it t
h
a
n
TLD
C
in
v
e
r
t
e
r
.
A
c
c
u
rre
n
t
d
i
st
o
r
tio
n
o
f
th
e
tr
an
sfo
r
mer-
le
ss
g
r
id
t
i
ed PV sy
stem
u
s
in
g
TLD
C
inv
e
r
t
er is sma
lle
r
th
an
t
h
e
TLN
P
S
and
H
-
bri
d
ge i
nve
rt
ers
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
A Perf
orm
a
nc
e
co
mp
ari
s
on
of
t
r
a
n
sf
or
mer-l
e
ss
gri
d
t
i
ed
PV
syst
em
usi
n
g
d
i
ode
cl
am
pe
d … (S
ur
os
o)
7
09
RE
FERE
NC
E
S
[1]
G.
N.
Ti
wa
ri, R.K. Mi
sh
ra
, a
n
d
S.
C.
Sol
a
n
k
i
,
“
P
ho
to
vo
l
t
ai
c m
odu
le
s a
nd the
i
r app
l
i
c
a
t
io
ns: A re
v
i
e
w
on the
r
ma
l
mod
e
ll
ing
”
,
A
p
p
l
ied
En
erg
y
,
vol
8
8
,
p
p
.
2
2
8
7
-2
304,
2
0
1
1
.
[2]
A.
S.
Josh
i, I.
Dinc
e
r
,
a
nd B
.
V.
Re
dd
y,
“
P
e
rfo
rm
an
c
e
an
alys
is
o
f
p
hotov
oltai
c
s
y
stems:
a
rev
i
ew
”,
Re
ne
wa
bl
e a
n
d
Su
stainab
le
Ene
r
gy
Re
views
, v
o
l
1
3
,
p
p
. 18
8
4
–
1897
,
2
0
09.
[3]
D.
Hwa
ng
,
J. Le
e
,
a
n
d
Y.
Ch
o,
“
S
i
n
gl
e
-
pha
se
si
ng
le
-sta
ge
dual
-
bu
c
k
p
h
o
t
ov
olta
ic
in
v
e
rte
r
with ac
t
i
ve
p
o
wer
deco
up
lin
g
stra
t
e
gy
”,
Re
ne
wa
ble En
e
r
gy
,
vol 1
26,
p
p
. 4
5
4
-
46
4, 201
8.
[4]
S.
B. Kjae
r
,
J.
K.
Pe
derse
n
,
a
nd
F.
Bl
aa
bje
r
g, "
A
re
vie
w
of si
ng
le
-p
ha
se g
r
id
-c
o
n
n
e
c
t
e
d
i
n
v
e
rte
r
s
fo
r p
h
o
t
o
v
o
lta
ic
mod
u
les"
,
IE
EE
Tra
n
sac
t
i
o
n
s
In
du
st
ri
al
Ap
plic
a
t
io
n
,
vo
l
4
1
, n
o
. 5, pp
.
1
2
9
2
-
13
06
,
20
05
.
[5]
J.
M
.
Carr
asco
, L.G.
F
r
an
qu
elo
,
Bialasiewic
z
,
J
.
T., and
Alfonso
,
N.
M,
“Pow
er-
e
lect
roni
c
s
sys
t
ems
for
the gr
id
in
teg
r
atio
n
of
ren
e
wab
l
e
en
ergy
so
urces
:
a
su
rve
y
”,
I
E
E
E
T
r
a
n
s
a
ct
ion
s
on
I
n
dus
t
r
ia
l
E
l
e
c
t
r
o
n
i
c
s
,
vol 5
3
,
pp
.
100
2
-
10
16
, 2
008
.
[6]
J.
Ro
dri
gue
z, S. B
e
rn
e
t
, P. K.
St
e
i
m
e
r,
a
nd I. E.
Liza
ma
, "A
s
u
rv
ey on
n
e
u
t
r
a
l-po
in
t-clamp
e
d inv
e
rters
"
,
IEEE
Tran
sac
t
io
ns on
In
dustrial
Electro
nics
,
vo
l 5
7
,
no
.
7
,
pp
. 22
19
-22
30,
20
10
.
[7]
X.
Z
h
a
ng, H. Ni,
D.
Y
a
o
,
R.x
.
Ca
o,
a
n
d
W
.
X.
Sh
e
n
,
"De
s
i
g
n
o
f
sin
g
l
e
-
p
h
a
s
e
g
r
id
-c
on
nec
t
e
d
ph
ot
ov
ol
ta
ic p
o
we
r
p
l
a
n
t b
a
se
d on
strin
g
i
nve
rte
r
s",
1
st
IEEE Co
nfer
en
ce o
n
In
du
strial
El
ect
ro
ni
cs a
n
d
Ap
pl
ica
t
io
ns
,
p
p
.
1
-
5,
20
06.
[8]
S
u
ro
so,
D.
T.
Nu
groh
o, and
T. No
guch
i
,
"A
nine-l
evel
hy
brid
curr
en
t s
o
u
r
c
e
in
v
e
rter
using
com
m
o
n
-em
i
tte
r
to
po
lo
gy and
in
d
u
ctor-c
ell"
,
In
ter
n
atio
nal Jo
urn
a
l
of Power Ele
c
tr
o
n
ics
a
nd Dr
iv
e S
y
s
t
em
s
(IJ
PED
S
)
,
vo
l 1
0
, no
.
2
,
p
p
.
85
2-8
5
9
,
2019
.
[9]
N.
C. Na
ir, and
N. Garime
lla
,
“Batte
ry
energy
storag
e
sy
stem
s
:
as
ses
s
ment f
o
r s
m
all
-
scale
ren
e
wab
l
e
energ
y
in
teg
r
atio
n
”
,
E
n
ergy and Buildings
,
v
o
l
42,
pp. 212
4
-
21
30
,
2
0
1
0
.
[10]
H. Liu
,
a
n
d
S. Wu
,
“A
n as
sess
ment
on
th
e
p
l
ann
i
n
g
an
d
co
ns
tru
c
tio
n
of an
is
lan
d
r
e
new
a
bl
e en
erg
y
s
y
stem e
A
c
a
se
stud
y o
f
Kinm
en
Island”
,
Ren
e
w
a
bl
e En
erg
y
, vo
l
35,
pp
. 2
7
2
3
-27
3
2
,
2
010
.
[11]
S.
Pa
rk, G. Cha
,
Y. Ju
ng
,
a
n
d
C.
Wo
n,
“
D
e
s
i
gn
a
n
d
a
p
pl
ic
a
t
i
on
for PV ge
ne
ra
t
i
o
n
sy
st
e
m
usin
g a so
ft-swi
tc
hi
n
g
bo
os
t co
nv
erter
with
S
A
RC”,
I
E
EE
T
r
a
n
s
a
ctio
ns
on Ind
u
strial
El
ectr
oni
cs
,
vo
l 5
7
,
no
.
2
,
pp
. 5
15-
5
2
2
,
2
010
.
[12]
L
.
L
a
i, W. Hou
,
Y.
Fe
n
g
,
a
n
d
Y.
Ch
e
n
,
"Nov
el
g
r
id
-c
o
n
n
e
c
t
e
d
phot
o
v
o
l
t
a
ic g
e
n
e
ra
ti
on
sy
st
e
m
",
Thi
r
d
Int
e
rn
ati
onal
Con
f
er
e
n
c
e
on
Elec
t
r
i
c U
tili
t
y
D
e
regu
la
tion
an
d R
e
stru
c
t
ur
in
g a
n
d
Po
wer T
e
ch
nol
og
ies
,
pp.
2
5
3
6
-
25
4
1
,
20
08.
[13]
V.
J.
F
a
rias
, an
d
L. C
.
G
.
d
e
F
r
e
i
tas
,
“D
ual
tran
sfor
merl
ess single-st
age cu
rr
ent so
urce
inve
rter with
energ
y
manag
e
men
t
co
n
t
rol
str
a
tegy
”,
IEE
E
Tran
sac
t
io
ns on
Po
we
r Ele
c
t
r
on
ic
s
,
v
o
l
28,
n
o
. 1
0
,
pp.
46
44
-4
6
5
6
,
20
12.
[14]
P.
G.
Barbosa, H
.
A.
C.
Braga, M.
C.
Barbosa,
and E.
C.
Te
ixeria
, “Boo
st
cu
rren
t
mu
lti
l
ev
e
l
in
verter an
d its
app
l
i
catio
n on
s
i
ng
le ph
ase
g
r
id
co
nnec
t
ed ph
o
t
o
v
o
l
taic
s
y
s
t
e
m
”
,
I
E
E
E
T
r
an
sa
ct
io
ns
o
n
Pow
e
r
E
l
e
c
tr
on
ics
, vo
l 21,
p
p
.
11
16
-1
12
4
,
20
0
6
.
[15]
C.
Wu,
"To
p
o
l
og
y
for c
u
rre
nt-so
u
r
c
e
grid
-c
o
nne
cte
d
in
ve
rte
r
with i
m
p
r
ove
d e
ffic
i
e
n
c
y
a
n
d
p
u
l
s
e
wi
d
t
h
m
o
dul
a
t
i
o
n
cont
rol s
t
rat
e
gy"
,
Jo
ur
na
l o
f
S
h
a
ngh
ai Un
iv
er
sity
, vol
12
,
p
p
.
55
4
-
55
9, 20
08
.
[16]
Su
roso
,
D.
T.
Nug
r
oh
o,
Am
ran
,
a
nd T.
Nog
u
c
h
i, “
P
a
r
a
lle
l
ope
ra
tio
n
of c
u
rren
t-so
urc
e
in
ve
rte
r
fo
r l
o
w-v
o
l
t
ag
e
high
-curren
t
gri
d
-con
nec
t
ed ph
o
t
ovo
lta
i
c
sy
stem
”,
In
terna
t
ion
a
l
Jo
ur
na
l of
El
ectri
cal and
Com
p
uter Engin
eer
in
g
,
vo
l
9
,
n
o
.
4,
pp.
22
20
-222
9,
20
1
9
.
[17]
R.
Gonzl
e
z,
E.
Guba,
J.
Lpez,
and
L
.
Marro
yo, "
T
ra
nsformerless si
ngl
e-phase multil
ev
el
-based photovol
t
ai
c
i
n
vert
er
",
IEEE T
r
a
n
s
a
ction
s
on
Indu
strial
Elec
t
r
onics
,
vo
l 5
5
,
no
.
7
,
pp
. 2
694
-27
0
2
,
20
08
.
[18]
Ja
ya
l
a
ksh
m
i N.
S.
,
Ank
i
t
K.
,
a
nd Ashi
sh
K.
, “
A
n
a
l
y
sis
a
n
d d
e
sig
n
of si
ng
le
-
phase
hi
gh
e
f
fi
ci
e
n
cy
t
r
a
n
sfo
r
me
r
less
PV invert
er
top
o
logy”,
I
n
ter
nat
io
na
l
Jo
ur
nal
o
f
P
o
w
e
r
El
e
c
tro
n
i
cs a
n
d
Dr
iv
e S
y
st
em
,
vol 9, n
o
.
2, pp
. 73
0-7
37,
20
18
.
[19]
Dau
t
a, M
.
Irw
antoa
,
Y.M
.
Ir
wana,
N
.
G
o
m
e
sh
a, M
.
adzri
a
, an
d M
.
F
i
tr
aa, “High
po
wer tr
ans
f
ormer
l
e
s
s
ph
otov
olta
ic
inv
e
rter
”,
En
er
gy P
r
o
cedia
,
p
p
.
46
5 –
47
2,
201
3.
[20]
V. Gerard
o
,
M
.
P
.
R
a
ymu
n
d
o
, and
S
.
J.
M
i
g
u
el,
“H
ig
h
effic
i
en
cy
single
-
ph
ase tr
ans
f
ormer-
les
s
in
ver
t
er
for
ph
otov
olta
ic
ap
p
l
ic
ation
s
”
,
Ing
e
n
i
er
ía
In
ves
tiga
ci
ón
y T
e
cno
l
o
g
í
a
, vo
l 6, n
o
.
2
,
pp.
17
3-1
8
4
,
20
15.
[21]
E.
K
out
rou
l
is,
a
n
d
F
.
B
l
aab
jerg
,
"
D
es
ig
n opt
imi
zation o
f
tra
n
sfo
r
me
rl
ess
g
r
id
-co
n
n
ected
P
V
in
verters
in
c
l
ud
in
g
rel
i
abili
ty",
IEEE Transact
ions
Power
Elect
roni
cs
,
vo
l 2
8
,
no.
1,
pp
.
3
25-3
3
5
,
2
0
1
3
.
[22]
T.
Ker
e
kes
,
R
.
Teod
orescu
, P
.
Ro
dríguez
,
G.
V
ázqu
e
z
,
a
n
d
E.
Al
da
b
a
s
,
“
A
ne
w hi
gh
-e
ffic
i
en
c
y
sin
g
l
e
-p
h
a
se
tran
sfo
r
mer
l
ess
P
V
inv
e
rter top
o
logy
”,
IEE
E
Tran
sac
t
io
ns on
Ind
u
stria
l
Elec
t
r
on
ic
s
,
v
o
l 58
,
no.
1,
p
p
. 18
4-1
91,
20
11
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[23]
T
.
Salm
i, M.
Bouz
g
u
e
n
d
a
,
A
.
Ga
st
li,
a
n
d A. Masm
ou
di
,
“
A
no
ve
l
t
r
a
n
sfo
r
me
rle
s
s in
ve
rte
r
t
o
p
o
l
ogy
wit
h
o
u
t ze
ro
-
cros
sing distorti
on
”,
Inte
rna
t
i
ona
l J
o
u
r
na
l o
f
Re
ne
wa
bl
e Re
sea
r
ch
,
vo
l 2
,
n
o
.
1
,
p
p
.
140
-14
6
,
201
2.
[24]
S
.
Vas
c
on
celos
,
Arau
jo,
P.
Zach
arias,
and
R. M
a
llw
itz
,
“High
l
y
efficient
sing
l
e
-p
ha
s
e
t
r
a
n
s
f
or
me
r
l
e
s
s i
n
ve
rt
e
r
fo
r
g
r
id
-c
on
n
e
c
t
e
d
pho
to
vo
lt
ai
c sy
stem
s”
,
I
E
E
E
T
r
an
s
a
ct
io
ns o
n
I
n
d
u
s
tr
ial
E
l
ec
tro
n
i
c
s
,
vo
l
57
, no.
9
,
p
p
.
3
1
1
8
-
31
28,
20
10
.
[25]
H. F
.
X
i
ao
,
S
.
J. X
i
e
,
C
.
Y
a
ng
,
an
d R
.
H
.
Hu
an
g,
"
A
n
op
ti
m
i
zed
tra
n
sfo
r
m
e
rl
ess
ph
oto
v
o
l
t
a
ic
grid-
c
o
nnec
t
ed
i
n
vert
er
",
IEEE T
r
a
n
s
a
ction
s
on
Indu
strial
Elec
t
r
onics
,
vo
l 5
8
,
no
.
5
,
pp
. 1
887
-18
9
5
,
20
11
.
[26]
L
.
Z
h
a
n
g
,
K. Su
n,
L.
Fe
ng,
H.
W
u
, a
nd Y.
Xing
,
"
A
fam
i
ly
of ne
u
t
ra
l poin
t
cl
a
m
pe
d full-b
r
i
d
g
e
t
o
polo
g
i
e
s for
t
r
a
n
sfor
m
e
rle
s
s ph
ot
o
v
o
l
t
a
ic
grid-t
ie
d
i
n
v
e
rte
r
s"
,
IEEE T
r
ans
actio
n
s o
n
Po
wer El
ectro
ni
cs
,
vo
l
28,
n
o
.
2,
pp.
7
3
0
-
73
8, 20
13
.
[27]
Y.
Gu,
W
.
Li,
Y. Zh
ao,
B
.
Yan
g
,
C.
Li, an
d X. He, "T
ran
s
form
erles
s
in
ver
t
er
with
virtu
a
l DC
b
u
s
con
cep
t
fo
r
cos
t
-
effec
t
ive
g
r
id
-co
n
n
ected
P
V
po
wer
sy
stems
"
,
IEE
E
T
r
an
sa
ction
s
o
n
Po
wer Electr
o
nics
, vo
l 28
,
n
o
.
2, pp
.
7
9
3
-
80
5,
20
13
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
7
0
2
–
710
71
0
[28]
F.
Fa
ra
ji
,
S.
M.
Mo
usa
v
i
G.
,
A. Ha
j
i
ra
y
a
tc
,
A.
A.
M. Bi
rjan
di
e
,
an
d K
.
A
l
-Ha
d
dad
f
,
“S
ing
l
e-stage
sing
le-ph
a
s
e
th
ree-
leve
l n
e
ut
ral-po
in
t-clamp
e
d trans
f
or
merle
s
s
grid
-c
on
ne
cted
p
h
o
t
o
v
o
ltaic
inver
t
ers:
To
po
lo
gy
r
e
view”
,
R
e
ne
wa
ble
an
d
S
u
s
t
a
i
n
a
b
l
e
En
ergy
Re
v
i
e
w
s
,
vo
l 8
0
,
p
p
.
19
7-2
1
4
,
20
17
.
[29]
P
r
em
s
a
i. T,
A
m
bic
a
so
ny
.S
, S
u
math
i.A, and
U
m
as
ank
a
r.S
,
“
T
rans
former
les
s
ful
l
br
idg
e
n
e
u
t
ral
p
o
in
t
cl
am
p
e
d
i
n
v
e
rte
r
to
pol
ogy f
o
r re
n
e
wa
ble
e
n
e
r
gy
sou
r
c
e
s
”
,
In
ter
nat
io
na
l C
o
n
f
er
enc
e
on
Ad
van
ces
in
Electr
i
cal
Eng
i
n
e
e
r
in
g
(ICA
E
E
)
,
p
p
.
1-
6
,
20
14
.
[30]
O.
Lo
´p
ez
, F
.
D
.
F
r
eijed
o
,
A.
G.
Y
e
pes
,
P
.
F
e
rn
´
a
nd
ez-Co
m
e
sa˜na
,
J.
M
a
lv
ar, R
.
T
e
od
orescu
,
an
d J
.
D
o
v
a
l-Gan
d
o
y
,
“Elimin
ating
gr
ou
nd
cu
rr
ent i
n
a
tran
sf
orm
e
rle
s
s ph
ot
ov
olt
a
ic
a
p
p
lic
ati
o
n
”
,
IEE
E
T
r
ans
ac
tio
n
s o
n
En
eg
y
Conversion
,
vol
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5
,
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40-1
4
7
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2
0
1
0
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[31]
J. Lee
,
and
K.
Lee,
“New
m
o
du
latio
n
t
echn
i
qu
es
fo
r a le
akag
e cur
r
en
t red
u
c
tion
an
d
a n
e
utr
a
l-p
o
in
t
voltag
e
bal
a
nc
e
i
n
tra
n
sform
e
rl
ess ph
ot
ov
o
l
t
a
ic s
y
ste
m
s
u
s
i
ng a
thre
e
-
le
v
e
l
in
ve
rte
r
”
,
I
E
EE
T
r
a
n
s
a
ct
io
ns on
P
o
w
e
r El
e
c
tro
n
i
c
s
, vo
l
2
9
,
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7
2
0
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17
32
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2
0
1
4
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[32]
B. Y
a
ng
,
W.
Li,
Y
.
G
u
,
W
.
Cu
i,
a
nd
X.
He,
"
I
mpr
o
ved
tr
an
sforme
rless
in
v
e
rter with com
m
on
-mod
e le
ak
ag
e cu
rren
t
elim
in
atio
n
for
a ph
o
t
ov
olt
a
ic
g
r
id
-con
ne
cted
p
o
w
e
r sy
stem"
,
I
E
EE Tr
an
sa
ctio
ns
o
n
Po
wer
E
l
ectr
o
n
i
cs
, vo
l 27,
n
o
.
2
,
pp.
75
2-762
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20
13.
[33]
M
.
C. Cav
a
lc
an
ti,
A
.
M
.
F
a
r
i
as,
K.
C. Oliv
e
i
ra
,
F
.
A. S
.
Nev
e
s,
and
J
.
L. A
f
o
n
s
o
, "
E
limin
a
t
ing
l
e
akage
curren
t
s
i
n
n
e
ut
ral
poin
t
cla
m
pe
d in
ve
rte
r
s fo
r p
h
o
t
o
vol
taic
system
"
,
IE
EE T
r
ans
actio
n
s
o
n
Ind
u
s
t
rial
Electro
ni
cs
, v
o
l 59,
n
o
.
1
,
pp.
43
5-443
,
20
12.
[34]
T. S
e
lm
i, an
d
M
.
Rezg
ui
, “A
no
vel
D
C
-AC in
v
e
rter
topo
lo
gy
to
elim
in
ate
leak
ag
e
curren
t
”,
In
ter
n
ation
a
l
Jour
na
l
of Po
w
e
r Elec
tron
ics
an
d
Driv
e
Sys
t
em
s
,
v
o
l
9, no.
4
,
pp.
1
7
3
3
-
1
7
4
4
,
20
18.
[35]
T
.
Ke
re
ke
s, R.
Te
o
d
o
r
e
s
c
u
, a
n
d
M. Li
se
rre
,
"Com
m
o
n
m
o
d
e
v
o
l
t
a
ge
i
n
ca
se
of
t
r
a
n
sfor
merle
s
s PV
in
ve
rters
con
n
ec
ted
to the
g
r
id
,"
I
EEE
Int
e
rn
atio
nal S
y
m
p
o
s
ium
on
Ind
u
s
t
ri
al Elec
t
r
o
n
i
cs
,
pp.
23
90
-2
39
5
,
200
8.
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