Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
6, N
o
. 1
,
Mar
c
h
20
15
,
pp
. 14
8
~
15
9
I
S
SN
: 208
8-8
6
9
4
1
48
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Leakage Current Paths in PV
Transform
e
r-Less Single-Ph
a
se
Inverter Topology and Its
Mitigation throu
g
h PWM for
Switching
M
.
N
.
H. Khan*
,
K. J.
A
h
ma
d*
*, S. Khan*
*
,
M
.
Hasanuzza
m
a
n
*
*UM Power Energ
y
Dedicated A
dvanced
Ce
ntre (UMPEDAC),
Le
vel 4, Wisma R&D,
University
of
Malay
a
, 59990 Ku
ala Lumpur, M
a
lay
s
ia
**Ele
ctri
cal
and
Com
puter Engin
eering
,
In
tern
ati
onal Is
l
a
m
i
c Uni
v
ers
i
t
y
M
a
la
ys
ia
,
P.O. Box 10
, 50
728 Kuala Lump
ur, Malay
s
ia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 20, 2014
Rev
i
sed
D
ec 14
, 20
14
Accepte
d Ja
n
6, 2014
The Photovoltaic (PV) is a par
t
and
par
cel and
well known for
cost-effectiv
e
and e
a
s
y
to op
e
r
atef
eatu
r
es
whe
n
it
is
us
ed wit
h
trans
f
orm
e
r-le
s
s
inverter-
based grid-tied d
i
stribution g
e
ner
a
tion s
y
s
t
em
s
.
It reduces
th
e le
ak
age curr
ent
is
s
u
e that
a
c
tua
l
l
y
occu
rs
m
a
kin
g
pa
ths from PV penal
to grou
nd. In th
is
paper h
a
s been
addressed th
is issue
as main pr
oblem for redu
cing leakag
e
current. Moreov
er, her
e
iscomp
ared th
e proposed topolog
y
’
s results to AC
and DC-based tr
ansform
e
r-less topologies.
The p
o
ssibiliti
es of lar
g
er num
ber
of leak
age
curre
nt paths ind
i
c
a
t
e
power loss, wh
ich is th
e foc
u
s of work in
this paper fo
r different switchin
g c
onditions. Th
e results on leak
age curr
en
t
paths using PSpice with diff
eren
t paras
itic capacitance valu
es from inverters
of differen
t
top
o
logies ar
e co
m
p
ared with th
e sim
u
lation r
e
sults of the
topolog
y
propos
ed in
this
paper
.
Keyword:
C
o
m
m
on M
o
d
e
V
o
l
t
a
ge
EMF filter
In
verte
r
L
e
a
k
ag
e
cu
rr
en
t
Pho
t
ov
o
ltaic Pan
e
l
PW
M
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
M
.
N.
H
.
Kha
n
,
UM
P
o
we
r E
n
ergy
De
di
cat
ed
A
dva
nce
d
C
e
nt
re
(UM
P
ED
AC
)
Lev
e
l 4
,
Wisma
R&D, Un
i
v
ersity
o
f
Malaya
5
999
0 Ku
ala Lu
m
p
u
r
, Malaysia.
Em
ail: nom
anxp76@siswa
.
um
.e
du.m
y
, nom
a
nxp76@gm
a
il.com
1.
INTRODUCTION
El
ect
ri
cal
gene
rat
i
on
usi
ng c
o
al
, oi
l
an
d nat
u
ral
gas a
r
e c
o
m
m
onl
y
used,
ho
we
ver
,
m
o
st
al
l
of t
h
ese
sou
r
ces ha
ve
re
sul
t
e
di
nt
op
ol
l
u
t
i
ng o
u
r en
vi
r
o
nm
ent
.
B
e
si
des havi
n
g
bee
n
t
h
e m
a
i
n
reaso
n
for m
a
ny
of u
s
wi
t
h
envi
ro
nm
ent
a
l co
ncer
ns, s
u
c
h
ki
n
d
s o
f
pr
o
duct
i
o
n a
r
e
no
t
onl
y
de
spi
c
a
b
l
e
rat
h
e
r
t
h
ey
arel
eadi
n
g t
o
havi
n
g
ou
rre
so
urce
s
g
e
t
t
i
ng cl
ose
r
t
o
de
pl
et
i
on.
I
n
t
h
e case
o
f
havi
ng
ene
r
gy
ge
n
e
rat
e
d
fr
om
renewa
bl
e m
eans, s
u
ch
as sola
r,
wind, biom
ass,
hydroge
n,
ge
ot
hermal, ocean energies
are m
o
s
t
reliable, t
h
e
sources
do
not suffe
r
fro
m
th
e d
ile
mma o
f
ex
tin
ction
.
Fu
rth
e
rm
o
r
e, it is
actu
a
l
l
y
envi
ro
nm
ent
a
l
l
y
benefi
ci
al
and energy effici
ent as
wel
l
.
In
bet
w
e
e
n al
l
of t
h
ose
rene
wa
bl
e so
ur
ces of e
n
er
gy
,
sol
a
r a
nd
wi
n
d
are
m
o
re co
nv
eni
e
nt
an
d ef
fi
ci
ent
i
n
t
h
e case
of
el
ect
ri
cal
po
we
r ge
ner
a
t
i
on
[
1
]
and c
o
u
n
t
r
i
e
s
have
bee
n
get
t
i
ng si
g
n
i
f
i
c
a
n
t
bene
fi
t
s
f
r
om
t
h
ese
t
w
o t
y
pe
s
of
r
e
newa
bl
e,
i
n
cl
ude
Ja
panese
,
C
y
pri
o
t
s
,
C
h
i
n
ese [
2
]
-
[
4
]
.
Ig
no
ri
n
g
t
h
e l
i
m
it
at
i
ons
of
usi
n
g s
o
l
a
r
(h
i
g
h
fran
k
cost, larg
e area
req
u
i
red, sunn
y area req
u
i
re
d
,
n
o
n
i
gh
t ti
m
e
fun
c
tion
a
lity
an
d
so
o
n
) and
wi
nd
en
erg
y
n
e
ed
ing
av
ailab
ility
o
f
wind
,
k
illing
b
i
rds, with
l
o
w en
erg
y
d
e
n
s
ity,
with
t
u
rb
in
e p
r
od
u
c
i
n
g
n
o
i
se
besi
des
ha
vi
n
g
t
o
us
e l
a
r
g
e ar
ea of
l
a
n
d
, a
n
d
so
on
), t
h
e
be
nefi
t
s
are
t
o
o h
i
gh a
n
d p
r
ofi
t
a
bl
e as
wel
l
as u
s
eabl
e
fo
r di
ffe
re
nt
se
ct
ors
i
n
bot
h d
e
vel
o
ped
an
d u
nde
vel
o
pe
d
c
o
unt
i
e
s [5]
.
Here, th
e Fi
gure 1
is act
u
a
lly sh
owing
th
at
h
o
w so
lar cel
l g
e
ts en
erg
y
fro
m
th
e sun
ligh
t
, wh
ich
is
pure and cost free. As a
result
, it can be take
n as m
u
ch
as energy from
the solar ce
lls th
at actu
a
lly h
a
v
e
b
een
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Leak
age
C
u
r
r
e
n
t
P
a
t
h
s i
n
P
V
Tra
n
sf
or
mer
-
L
e
ss Si
ngl
e
-
Ph
a
s
e I
n
vert
e
r T
o
p
o
l
o
gy
an
d
It
s…
(
M
. N
.
H. K
h
a
n
)
14
9
g
e
ttin
g th
rou
g
h
the ray
of ligh
t
.
On th
e o
t
h
e
r
h
a
nd
, in
si
d
e
o
f
th
e
so
lar cel
l h
a
s
ph
o
t
o
n
that h
a
s
p and
n
ch
ann
e
l
wh
ere it can
p
o
ssib
l
e to
g
e
t el
ectricity. After
th
at, it can
be
c
ont
rolled and t
r
ans
f
ere
d
t
o
ba
ttery as loaded.
Fig
u
re
1
.
So
lar cells are
g
e
tting
en
erg
y
fro
m
th
e su
n
The P
V
pa
nel
s
are use
d
st
and al
o
n
e a
nd
or e
v
en
co
nn
ected
to
g
r
i
d
; in
bo
th
of th
e
cases, po
wer
con
d
i
t
i
oni
n
g
and
reg
u
l
a
t
i
on
m
a
ke up t
h
e c
o
re c
o
m
pone
nt
s. M
o
re
o
v
er,
d
a
y
-
by
-
d
ay
, PV
panel
i
s
bec
o
m
i
ng a
part
a
n
d
pa
rcel
fo
r
di
st
ri
b
u
t
i
o
n
po
wer
ge
ner
a
t
i
on [
6
]
-
[
8]
.
I
n
t
h
e ca
se o
f
g
r
i
d
t
i
e
d s
o
l
a
r
g
e
nerat
i
o
n, i
n
ve
rt
ers
becom
e
t
h
e se
con
d
c
o
re c
o
m
ponent
s t
o
b
e
use
d
;
i
n
ve
rt
er m
a
y
be t
r
a
n
sf
orm
e
r-
base
d
or
t
r
a
n
sf
orm
e
r-l
ess.
H
o
w
e
v
e
r, in
bo
th
cases, it do
es
v
e
r
y
g
ood
p
e
rf
or
m
a
n
ce and e
x
pected
outcom
e. PV
p
a
n
e
l actu
a
lly wo
rk
s to
m
a
nage DC
c
u
rre
nt
t
h
at
act
ua
l
l
y
convert
e
d
t
o
AC
t
h
ro
u
gh
i
nve
rt
er, al
t
h
o
u
g
h
t
h
e m
a
i
n
conce
n
t
r
at
i
o
n i
s
cl
ean
the environm
ent as m
u
ch as
pos
sible [9
], [1
0
]
. To
do
so, tran
sform
e
r is h
i
gh
ly n
e
ed
ed to
m
a
k
e
th
e syste
m
pr
o
p
er h
a
n
d
e
d
.
W
h
ere t
h
e P
V
pa
nel
i
s
us
ed as f
o
r
DC
si
gnal
achi
e
vi
ng
, b
u
t
ot
he
r
si
de of t
h
e sy
st
em
is
co
nn
ected to grid
t
h
at isu
s
ed
for
AC sign
al.
In add
itio
n,
Grid
conn
ected in
v
e
rter is nowad
ays
h
i
gh
ly po
pu
lar
t
o
get
hi
gh
ra
n
g
e o
f
po
wer
p
o
i
n
t
o
v
e
r
t
h
e s
y
st
em
where t
h
e m
a
xim
u
m
poi
nt
s are
dev
e
l
ope
d t
h
ro
u
g
h
anal
o
g
m
a
xim
u
m
or n
o
rm
al
poi
nt
t
r
a
c
ki
n
g
m
e
t
hods
[1
1]
. Pre
v
i
o
usl
y
i
s
ol
at
i
on t
r
an
sfo
r
m
e
r-base
d
t
o
p
o
l
o
gy
ha
d h
i
ghl
y
p
opu
lated
,
altho
ugh
th
e m
a
in
p
r
ed
icam
en
t is
size, co
st
and efficiency.
In
c
ont
rast,
to
recov
e
r th
ese
p
r
ob
le
m
s
,
t
h
e be
st
s
o
l
u
t
i
o
n
w
o
ul
d
be
u
s
ed
n
o
t
r
a
n
sf
o
r
m
e
r-base
d t
o
p
o
l
o
gy
f
o
r
b
o
t
h
cases si
ngl
e
p
h
ase a
n
d t
h
ree
p
h
ase
[8]
.
As f
o
r
get
t
i
ng sm
al
l
e
r wei
ght
, l
o
w c
o
st
and
hi
g
h
ef
fi
ci
ency
sy
st
em
no t
r
an
sf
orm
e
r t
o
p
o
l
o
gy
i
s
t
h
e
best
so
lu
tion
wh
ere th
e g
a
lv
an
ic iso
l
atio
n
is no
t
in
clu
d
e
d
,
t
h
e main
p
r
ob
lem
can
b
e
seen
that is co
mm
o
n
m
o
d
e
leak
ag
e issu
e
w
h
ich
is actu
a
lly th
e r
easo
n
of
r
e
du
cing
th
e
ef
f
i
cien
cy and
in
cr
easing
th
e lo
ss
[
8
], [1
2
]-[13
]
.
Fi
gu
re 2.
The
ove
ral
l
sy
st
em
ei
t
h
er
tra
n
sform
e
r-base
d
or
transform
e
r-less
On
a comm
ercial scale gene
ration, large
num
ber of
so
lar
p
h
o
t
ovo
ltaic (SPV) cells is co
nn
ected fo
r
m
a
ki
ng a sol
a
r
panel
m
odul
e,
and al
l
such
m
odul
es are con
n
ect
ed i
n
pa
ral
l
e
l
as a si
ng
l
e
generat
i
o
n s
t
ruct
u
r
e
b
e
fo
re tied
t
o
utili
ty g
r
id
u
s
i
n
g
p
o
wer co
nd
itio
n
e
r circu
its as shown in
Figu
re 2.
The comm
on m
ode leakage
issue is
th
e seriou
s pro
b
l
ematic
issu
e to
d
a
y’s situ
ation. It actu
a
lly
o
ccurs in
b
e
tween
th
e PV p
a
n
e
l to
g
r
ou
nd
t
h
rou
g
h
p
a
rasitic cap
acito
r.
Howev
e
r, it h
a
s differen
t
curren
t
p
a
th
s
su
ch
as inv
e
rter to
gro
und
, PV p
a
n
e
l to
grou
nd
,
filters
to
groun
d
an
d
so
on
.
As fo
r
redu
cin
g
th
e leak
ag
e issu
e,
m
o
st
im
port
a
n
t
and ef
fect
i
v
e way
i
s
swi
t
c
hi
ng c
o
nfi
g
u
r
at
i
on t
h
at
ca
n be d
o
n
e t
h
ro
u
gh P
u
l
s
e W
i
dt
h
Mo
du
latio
n
(PWM).
In
add
itio
n
,
t
h
is p
a
p
e
r is ab
ou
t to
find
ing
th
e
p
a
th
s
o
f
leakag
e issue an
d
t
o
red
u
c
e th
e
co
mm
o
n
m
o
d
e
leak
ag
e issu
e fo
r transfo
r
m
e
r-less to
po
log
y
by u
s
ing
PW
M
co
nd
itio
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6
,
No
. 1
,
Mar
c
h
2
015
:
14
8
–
15
9
15
0
2.
PROTO
P
OL
OGY WITH
LEAKAGE P
A
THS
In
th
is ap
pro
a
ch
is a tran
sformer-less to
po
l
o
g
y
,
wh
ich
is actu
a
lly
m
a
d
e
b
y
AC and
DC d
ecou
p
ling
with
n
i
n
e
swit
ch
es. AC
d
e
cou
p
ling
h
a
s two switch
e
s th
at
co
nn
ect w
ith
ou
tpu
t
of
i
n
v
e
r
t
er
an
d
D
C
d
e
co
up
ling
has t
w
o
swi
t
c
hes a
f
t
e
r
DC
s
i
gnal
t
h
at
co
nt
rol
t
h
e
DC
signal. M
o
re
over last switch is
conne
cted a
f
t
e
r
AC
d
ecoup
lin
g which
is h
e
l
p
ing
to
get sign
al fo
r EMC filter.
Here used
a fu
ll b
r
i
d
g
e
i
n
v
e
rter with
fou
r
swit
ch
es.
Fig
u
re
3
sho
w
s th
e ap
pro
ach to
po
log
y
with
EMC f
ilter wit
h
tran
sfer
fu
n
c
t
i
o
n
and
related figu
res.
Fi
gu
re
3.
A
p
pr
oach
t
o
pol
ogy
Mo
reo
v
e
r, Electro
m
a
g
n
e
tic co
m
p
atib
ilit
y (EMC) filter [1
4
]
is
u
s
ed
fo
r filtering
p
u
rpo
s
es.
However,
the transfe
r
function of EM
C filter
indicat
es one low fre
que
ncy c
o
m
pone
nt s
h
ownbelow
with a
p
propriate
t
r
ans
f
er
f
unct
i
o
n, e
q
ui
val
e
nt
i
m
peda
nce a
n
d
theoretical curve as
well.
Fig
u
re
4
.
EMC Filter with 10V,
50
Hz inp
u
t
[15
]
In
Figu
re
4
is
sh
own
th
e
d
i
agram
o
f
EMC filter, for th
e
assu
m
e
d
in
d
u
ctance an
d cap
acit
a
n
ce valu
es
o
f
a
1
m
H an
d
1
m
F resp
ectiv
ely, th
e tran
sfer
fun
c
tion
,
H (s) =VO(s)
/Vi(s),
is
de
ri
ve
d as
a
ccor
d
i
n
gl
y
.
At afre
quency
is
ω
,and ca
pac
itance and i
n
ductance a
r
e L
and C res
p
ec
tively, the the fre
que
ncy
respon
se
for t
h
e abo
v
e
filter i
s
as sh
own
:
Z
ω
.
ω
Z
ω
ω
ω
.
ω
Z
ω
ω
ω
ω
ω
.
ω
Fig
u
re
5
sh
ows th
e
curren
t
d
i
rection
s
o
f
EMF f
ilter,
wh
ich
is
n
eeded
for fi
n
d
out th
e tran
sfer
fun
c
tion
.
Th
e ov
erall cu
rren
t
by Oh
m
’
s law is g
i
v
e
n
:
I
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Leak
age
C
u
r
r
e
n
t
P
a
t
h
s i
n
P
V
Tra
n
sf
or
mer
-
L
e
ss Si
ngl
e
-
Ph
a
s
e I
n
vert
e
r T
o
p
o
l
o
gy
an
d
It
s…
(
M
. N
.
H. K
h
a
n
)
15
1
Fi
gu
re
5.
C
u
rre
nt
di
rect
i
o
n
s
f
o
r fi
ndi
ng
t
r
a
n
sf
er f
u
nct
i
o
n
No
w
usi
n
g
t
h
e Ki
rc
h
h
o
ff'
s
ci
rcui
t
l
a
ws
b
e
l
o
w
sh
o
w
s t
h
e
di
vi
ded
t
w
o c
u
r
r
ent
val
u
es
w
h
ere
im
pedances
va
l
u
es are
s
h
o
w
n
ab
ove
.
Cu
rren
t,
I
=
ω
∗
ω
=
ω
ω
C
u
rr
ent,
I
=
ω
No
w t
h
e
out
pu
t
Vol
t
a
ge
i
s
V
=
ω
∗C
Now t
h
e T
r
ans
f
er
Function
(T
F):
H (
j
ω
) =
V
OUT
/V
IN
=
ω
Now in th
e case o
f
im
p
e
d
a
nce o
f
u
s
i
n
g
EMC filter is in
b
e
low Fi
g
u
re 6
wh
ere
X
is th
e in
du
ctor
im
pedance
w
h
i
l
e
X
i
s
t
h
e ca
pac
i
t
a
nce i
m
pedan
ce an
d t
h
e
e
qui
val
e
nt
i
m
pedan
ce i
s
Z
.
Fig
u
re
6
.
Equ
i
v
a
len
t
im
p
e
d
a
nce of EMC Filter
No
w,
Z
3.1416
3
.1416
|
3.1416
0
.
31416
0
.3141
6
|
|
3.1416
3
.1416
|
3.1416
0.
31416
0
.31416
|
|
0.3141
6
0
.26774
o
h
m
On
t
h
e
o
t
h
e
r han
d
, th
e t
h
eo
retical wav
e
fo
rm
p
l
o
t
o
f
t
h
e EM
C filter is as sho
w
n
i
n
Figure
7
wh
ere th
e
i
n
p
u
t
vol
t
a
ge
of 5
V
at
50
Hz
i
s
used. The i
n
p
u
t
swi
t
c
hi
ng
at
50Hz i
s
m
a
ki
n
g
t
h
e cur
r
e
n
t
t
o
m
a
ke and bre
a
k
t
h
r
o
u
g
h
t
h
e ser
i
es i
nduct
a
nces
, pr
o
duci
ng a k
i
nd o
f
v
o
l
t
a
ge
bo
ost
i
n
g p
h
e
n
om
enon,
whi
c
h i
s
sup
p
o
rt
e
d
by
t
h
e
p
a
rallel cap
acitan
ces. As for u
s
in
g
th
is typ
e
o
f
indu
ctan
ces and
cap
acitan
ces b
a
sed EMC filter
t
h
e
5V
a
m
p
litu
d
e
is increased to
a valu
e
at
arou
nd
23
.9
32V
p
eak
valu
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6
,
No
. 1
,
Mar
c
h
2
015
:
14
8
–
15
9
15
2
Fig
u
re
7
.
Plo
t
o
f
EMC Filter
for
5
V
inp
u
t
with
50
Hz frequen
c
y
Leaka
g
e c
u
r
r
e
n
t
s
occu
rri
ng
a
t
di
f
f
ere
n
t
poi
n
t
s al
on
g t
h
e
pa
t
h
f
r
om
PV
Pa
nel
t
o
g
r
i
d
are
a
s sh
o
w
n
i
n
Fig
u
re
8
,
i
n
clud
ing
PV
p
a
n
e
l, switch
e
s, and filter and
l
o
ad as well.
Actually leak
ag
e cu
rren
t
flows i
n
fro
m
b
o
t
h
sid
e
s of PV
p
a
n
e
l th
rough
Parasitic Cap
acitan
ce (PC
)
[1
6
]
. H
e
re th
e u
s
in
g
inv
e
rter is fu
ll b
r
id
g
e
w
h
ere
fo
ur
swi
t
c
hes
are c
o
n
n
ect
ed
wi
t
h
i
n
ve
rt
i
n
g
m
a
nner
an
d l
e
akage
cu
rre
nt
f
l
ows i
n
bet
w
ee
n t
w
o
swi
t
c
hes
.
O
n
e
pat
h
i
s
i
n
bet
w
een
M
1
a
n
d
M
2
w
h
i
l
e
an
ot
her
pat
h
i
s
i
n
bet
w
ee
n M
3
a
nd M
4
.
He
re i
s
dra
w
n t
h
e
di
agram
whe
r
e s
h
ows
the diffe
r
ent
paths and c
u
rre
nt flowin
g
direction. M
o
re
over, itshows
the
place where the
com
m
on
m
ode
val
o
t
a
ge
(C
M
V
) i
s
de
vel
o
pe
d i
n
t
h
e t
r
ans
f
o
r
m
e
r-l
ess i
nve
r
t
er base
d t
o
p
o
l
ogy
i
n
P
V
-
g
ri
d
t
r
i
e
d
syste
m
.
Fi
gu
re
8.
Di
f
f
e
r
ent
l
e
a
k
age
cu
rre
nt
pat
h
s
3.
LEAKAGE CURRETNT MI
TIGATION SIMULA
TION DETAILS
In
Fi
g
u
re
9
be
l
o
w i
s
a
DC
-d
ecou
p
l
i
n
g
base
d t
r
a
n
sf
o
r
m
e
r-l
ess i
n
vert
er
t
o
pol
ogy
w
h
i
c
h
i
s
hel
p
e
d
t
o
switch
th
e
DC
v
a
lu
e an
d
b
e
l
o
w
u
s
e th
e
Duty Ratio
to
see th
e effect
o
f
switch
e
s in
the syste
m
wh
ich
can
b
e
veri
fi
e
d
by
o
u
t
put
v
o
l
t
a
ge an
d al
so cha
nge
s
of Leaka
g
e cu
rre
nt
whe
r
e o
n
l
y
one pat
h
(P
V pa
nel
t
o
gr
o
u
n
d
)i
s
consider.In the
case of 50% du
t
y
cy
cl
e
i
n
Tabl
e 1 w
h
en s
w
i
t
c
h S1 an
d S3
i
s
i
n
on S2 an
d S4 i
s
i
n
o
ff
m
ode
th
at wo
rk
s is in
o
ppo
site d
i
rectio
n
and
S5
an
d S6
is
t
h
e
D
C
dec
o
u
p
l
i
n
g s
w
i
t
c
hes.
A
f
t
e
r
usi
n
g t
h
e si
x s
w
i
t
c
he
s
i
n
50%
dut
y
ra
t
i
o
,
out
put
v
o
l
t
a
ge ca
n
be
g
o
t
m
o
re t
h
a
n
10
.
5
V
,
but
t
h
e
l
eakage
c
u
r
r
ent
i
s
occ
u
r
r
e
d
m
o
r
e
t
h
at
vari
es
fr
om
11
0.
30
9
u
A
t
o
1.
1
5
2
3
m
A
. He
re s
e
lected only one leakage
path.
Fi
gu
re
9.
DC
-d
ecou
p
l
i
n
g
base
d t
r
a
n
s
f
o
r
m
e
rs-l
ess i
nve
rt
er t
o
pol
ogy
[
17]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Leak
age
C
u
r
r
e
n
t
P
a
t
h
s i
n
P
V
Tra
n
sf
or
mer
-
L
e
ss Si
ngl
e
-
Ph
a
s
e I
n
vert
e
r T
o
p
o
l
o
gy
an
d
It
s…
(
M
. N
.
H. K
h
a
n
)
15
3
Tab
l
e
1
.
50
%
du
ty cycle o
f
inv
e
rter switch
i
ng
co
nd
itio
n uses fo
r
DC
d
e
co
up
lin
g top
o
l
o
g
y
S1
S2
S3 S4 S5 S6 Vout
LC
(A
)
ON
OFF
ON OFF
ON OFF
10.
546V
1.
0789m
OFF
ON
OFF ON
OFF ON
10.
546V
1.
0727m
ON
OFF
ON
OFF OFF ON
10.
538V
110.
30
9u
OFF
ON
OFF
ON ON OFF
10.
538V
1.
1523m
In the case
of 75%
duty cycle whe
n
leakage cu
rre
nt
ha
s occu
rre
d t
h
r
o
u
g
h
o
n
e
p
at
h t
h
at
has
been
sho
w
n i
n
Tabl
e 2 for
DC
dec
o
u
p
l
i
n
g, w
h
e
n
swi
t
c
h S1 a
nd
S3 i
s
i
n
on m
ode t
h
an t
h
e s
w
i
t
c
hes S2 an
d S
4
i
s
i
n
o
f
f m
o
d
e
th
at works is in
opp
o
s
ite d
i
rection
and
S5
and
S6
is th
e
DC deco
up
ling
swit
ch
es th
at fi
x
e
d in
50
%
dut
y
rat
i
o
n
an
d a
f
t
e
r
usi
n
g t
h
e i
n
ve
rt
er s
w
i
t
ches i
n
7
5
%
dut
y
rat
i
o
n
an
d
rest
o
f
t
h
e t
w
o
swi
t
c
hes
w
h
i
c
h a
r
e
DC
dec
o
u
p
l
i
n
g swi
t
c
he
s are
fi
xed i
n
5
0
%
dut
y
cy
cl
e, o
u
t
put
vol
t
a
ge ca
n be
got
m
o
re
t
h
an 1
0
.
5
V w
h
i
c
h i
s
ap
pro
x
i
m
a
tel
y
si
m
ilar with
5
0
%
du
ty ration
bu
t th
e l
eakage curre
nt is occurre
d
whic
h is reduce
d from
the
50
%
dut
y
rat
i
o
n t
h
at
va
ri
es f
r
o
m
129
.0
9
u
t
o
1.
18
6
9
m
A
m
p.
Tab
l
e
2
.
75
%
du
ty cycle o
f
inv
e
rter switch
i
ng
co
nd
itio
n uses fo
r
DC
d
e
co
up
lin
g top
o
l
o
g
y
S1
S2
S3
S4
S5 S6 Vout
Lekage
Cu
rren
t
ON OFF
ON
OFF
ON
OFF
10.
526V
129.
09
uA
ON OFF
ON
OFF
OFF
ON
10.
531V
12.
922
uA
ON OFF
ON
OFF
OFF
ON
10.
521V
2.
2429
uA
OFF ON
OFF
ON
ON
OFF
10.
538V
1.
1869m
A
In
b
e
low
Figu
re 10
is an AC
-d
ecoup
lin
g b
a
sed
tran
sform
e
r
-
less inv
e
rter to
po
log
y
wh
ich is h
e
lp
ed
t
o
switch
th
e
AC
v
a
lu
e an
d
b
e
l
o
w
u
s
e th
e
Duty Ratio
to
see th
e effect
o
f
switch
e
s in
the syste
m
wh
ich
can
b
e
veri
fi
e
d
by
o
u
t
put
v
o
l
t
a
ge an
d al
so cha
nge
s
of Leaka
g
e cu
rre
nt
whe
r
e o
n
l
y
one pat
h
(P
V pa
nel
t
o
gr
o
u
n
d
)
i
s
consider.
In t
h
e case of
50% duty cycle in
Tabl
e
3 w
h
en s
w
i
t
c
h
S1
and
S3 i
s
i
n
o
n
an
d S
2
a
nd
S4 i
s
i
n
of
f
m
ode t
h
at
wor
k
s i
s
i
n
op
p
o
si
t
e
di
rect
i
on an
d S5 a
nd
S6
is th
e AC d
ecoup
lin
g
switch
e
s. After using
the six
swi
t
c
hes i
n
5
0
%
d
u
t
y
rat
i
on,
out
put
vol
t
a
ge
can be
va
ri
ed
f
r
om
9.3
5
V
t
o
10
.2
8
3
V
,
b
u
t
t
h
e occ
u
rri
n
g
l
e
akage
cur
r
ent
i
s
occ
u
rre
d m
o
re c
o
m
p
are
d
t
o
usi
n
g
DC
-
d
eco
u
p
l
i
n
g sy
st
em
t
h
at
vari
es f
r
om
1.
47
m
t
o
7
5
.
8
4
3
m
Am
p.
Fig
u
r
e
10
.
A
C
-d
ecoup
lin
g based
tr
an
sf
or
m
e
r
s
-
l
ess inv
e
r
t
er
t
o
po
log
y
[
1
8
]
Tabl
e 3. D
u
t
y
C
y
cl
e
of 50
% of
i
n
vert
er
an
d di
ffe
re
nt
swi
t
c
hi
n
g
c
o
n
d
i
t
i
o
n
s
are use
d
fo
r AC
d
eco
u
p
l
i
n
g
to
po
log
y
S1 S2 S3 S4 S5
S6 Vout
Leakage
Cu
rren
t
ON
OFF ON
OFF ON
OFF 9.
3485V
1.
5209m
A
OFF
ON OFF
ON OFF
ON 10.
283V
1.
9483m
A
ON OFF
ON OFF
OFF
ON 9.
750V
1.
4732m
A
OFF ON
OFF ON
ON
OFF 9.
982V
75.
843m
A
The case
of
7
5
%
d
u
t
y
cy
cl
e in Ta
bl
e 4
fo
r
AC
dec
o
upl
i
n
g,
whe
n
s
w
i
t
c
h S
1
a
nd
S3 i
s
i
n
o
n
m
o
d
e
th
an
t
h
e switch
e
s S2
and
S4 is in
off m
o
d
e
th
at wo
rk
s i
s
i
n
op
p
o
si
t
e
di
rect
i
o
n a
nd
S5 a
n
d S
6
i
s
t
h
e
AC
deco
u
p
l
i
ng s
w
i
t
c
hes t
h
at
fi
xe
d i
n
5
0
% d
u
t
y
rat
i
on an
d aft
e
r usi
n
g t
h
e i
n
vert
er s
w
i
t
c
hes
i
n
75%
dut
y
r
a
t
i
o
n
an
d rest
o
f
th
e two
switch
e
s
wh
ich
are AC
d
ecoup
lin
g
switches are
fixe
d in 50%
duty cycle, out
put
voltage
can
be
got
m
o
re t
h
a
n
9.
5
V
whi
c
h i
s
a
p
pr
o
x
i
m
at
el
y
sim
i
lar wi
t
h
50%
d
u
t
y
rat
i
o
n
of
AC
-
d
eco
u
p
l
i
n
g
base
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
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94
I
J
PED
S
Vo
l. 6
,
No
. 1
,
Mar
c
h
2
015
:
14
8
–
15
9
15
4
syste
m
but in t
h
e case
of lea
k
age c
u
rr
en
t t
h
at sho
w
s m
o
re th
an 39
m
Am
p
.
Tab
l
e
4
.
75
%
du
ty cycle for i
n
v
e
rter and
d
i
fferen
t
switch
i
n
g
con
d
ition
s
are
u
s
ed
for AC
d
e
co
up
ling
topo
l
o
g
y
.
S1
S2
S3 S4
S5 S6 V
out
Leakage
Cu
rren
t
ON
OFF
ON OFF
ON OFF
9.
3486V
1.
5209m
A
ON
OFF
ON OFF
OFF
ON 9.
745V
39.
604m
A
ON
OFF
ON OFF
OFF
ON 9.
745V
39.
532m
A
OFF
ON
OFF ON
ON
OFF 9.
986V
73.
782m
A
In b
e
l
o
w i
n
Fi
gu
re 1
1
, s
h
o
w
s
t
h
e l
eakage pa
t
h
s of
ou
r p
r
o
p
o
si
n
g
t
o
pol
ogy
wher
e has bee
n
sh
ow
n t
h
e
d
i
fferen
t
p
a
th
s th
at actu
a
lly f
l
o
w
s fro
m
in
verter, PV p
a
n
e
l
in
b
o
t
h
sid
e
s,
EMF filter, lo
ad
and
all are flo
w
ed
th
ro
ugh
g
r
o
und
.
F
i
g
u
r
e
11
.
Ap
pr
o
a
ch
to
po
log
y
wh
e
r
e le
a
k
ag
e p
a
ths
a
r
e sh
ow
n
No
w i
n
bel
o
w
,
sh
ows t
h
e s
w
i
t
c
hi
ng
co
n
d
i
t
i
ons
of a
p
pr
oach
i
ng t
o
p
o
l
o
gy
i
n
t
a
b
u
l
a
r
fo
rm
i
n
Tabl
e
5
an
d 3.6 fo
r 50% and
75
%
d
u
t
y r
a
tio
r
e
sp
ecti
v
ely.
Tab
l
e
5
.
50
%
du
ty cycle o
f
inv
e
rter and
d
i
fferen
t
switch
i
n
g
con
d
ition
s
are
u
s
ed
for App
r
oach
topo
log
y
.S1 S2
S3
S4
S5
S6
S7
S8 S9 Vout Leakage
Cu
rren
t
ON
OFF ON
OFF
ON
OFF
ON
OFF ON
8.
32V
-
646.
21nA
OFF ON
OFF
ON
OFF
ON
OF
F ON
OFF
8.
32V
373.
99
7pA
ON
OFF ON
OFF
OFF
ON
ON
OFF ON
8.
81V
-
153.
45nA
OFF ON
OFF
ON
ON
OFF
OF
F ON
OFF
8.
81V
-
541.
75
fA
Here i
n
Tab
l
e 5
and
6
are
sho
w
n
so
m
e
swit
ch
ing
cond
ition
s
wh
ere inv
e
rter switch
e
s are fix
e
d
50%
an
d 75
%
du
ty ratio
resp
ectively wh
ile th
e
oth
e
r switch
e
s are cond
ucted
i
n
5
0
%
du
ty rat
i
o
n
,
h
e
n
ce it is clear
t
o
obse
r
ve t
h
at
i
n
m
y
appr
oac
h
i
n
g ci
rcui
t
o
u
t
put
v
o
l
t
a
ge i
s
aro
u
nd
8.
5V a
nd t
h
e
occu
rri
ng l
eaka
g
e cu
r
r
ent
i
s
very
sm
al
l
am
ou
nt
i
n
pi
co
a
n
d
ni
no
ra
nge
and
7
5
%
d
u
ty cycle shows
re
duci
n
g leak
a
g
e
curre
n
t com
p
ared t
o
50
%
dut
y
rat
i
o
n.
I
ndee
d
,
i
n
b
o
t
h
ca
ses l
eak
a
g
e c
u
r
r
ent
sh
o
w
s
very
sm
al
l
range
.
Tab
l
e
6
.
75
%
du
ty cycle o
f
inv
e
rter and
d
i
fferen
t
switch
i
n
g
con
d
ition
s
are
u
s
ed
for App
r
oach
topo
log
y
S1 S2
S3
S4
S5
S6 S7
S8 S9
V
out
LC
(A
)
ON
OFF
ON
OFF
ON OFF
ON OFF
ON
8.
3152V
99.
474
n
ON OFF
ON
OFF
OFF
ON OFF
ON
OFF
8.
3188V
373.
99
7p
ON OFF
ON
OFF
OFF
ON ON
OFF
ON
8.
319V
-
692.
7n
OFF ON
OFF
ON
ON
OFF OFF
ON
OFF
8.
8010V
-
41.
75f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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PED
S
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SN
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8-8
6
9
4
Leak
age
C
u
r
r
e
n
t
P
a
t
h
s i
n
P
V
Tra
n
sf
or
mer
-
L
e
ss Si
ngl
e
-
Ph
a
s
e I
n
vert
e
r T
o
p
o
l
o
gy
an
d
It
s…
(
M
. N
.
H. K
h
a
n
)
15
5
4.
RESULT AND DIS
C
USSI
ON
Leaka
g
e c
u
rre
n
t ha
s
occurre
d in
diffe
rent
places a
n
d when it issim
u
lated a
f
ter c
o
nstri
c
ting t
oget
h
er
t
h
e val
u
e o
f
l
eakage c
u
r
r
ent
f
o
r P
V
pa
nel
t
o
gro
u
nd i
s
cha
nge
d f
r
om
when we co
nsi
d
e
r
i
n
one pat
h
t
h
at
has
b
een
sho
w
n
in ab
ov
e in
a tab
u
l
ar form
. B
e
lo
w is sh
ow
n
fi
ve co
nsi
d
e
r
i
ng
pat
h
s
whe
r
e leakage current is
occurre
d. Mea
n
while, the
s
e leakage
curre
nt
wa
ve s
h
ap
e
s
are s
h
own for both
50% a
n
d
75%
duty c
y
cle as
wel
l
.
In Fi
g
u
r
e 2-6 i
s
sh
ow
n t
h
e di
f
f
ere
n
t
pat
h
s of
o
ccurring leaka
g
e current in
a transform
e
r-less syste
m
wh
ere lo
ad
and
filter is
g
r
oun
d
e
d
and
inv
e
rter leak
ag
e curr
en
t is fl
o
w
ed
fro
m
two
sid
e
o
n
e
sid
e
is co
nsid
ered
as be
fore tiny
resistance whe
n
R=10
Ω
an
d anoth
e
r
on
e is after
u
s
ing
th
is resi
stan
ce as
well.
B
e
l
o
w has bee
n
s
h
o
w
n
t
h
e
si
m
u
l
a
t
i
ons of u
s
i
n
g
t
w
o dut
y
c
y
cl
es
(5
0%
a
n
d 75
%) f
o
r p
r
o
pos
ed
t
r
ans
f
o
r
m
e
r-l
ess t
o
pol
ogy
.
4.
1.
5
0
%
Duty
C
y
cl
e
a) PV P
a
nel to Ground
:
The l
e
a
k
age
cu
rre
nt
s
h
o
w
s i
n
Fi
gu
re
1
2
(a
)
w
h
ere
i
t
occ
u
rs
i
n
bet
w
ee
n P
V
panel
t
o
gr
o
u
n
d
whe
n
al
l
leakage curre
nt is flowed by
differe
nt path
s whe
r
e leaka
g
e curre
n
t f
l
ow
s aro
und
-
3
.4
048
η
A
to
291
.8
56
µA
an
d it shows
flu
c
tu
ation
i
n
n
e
g
a
tiv
e
d
i
rection
as well.
Figure
12(a
). L
eakage
current
i
n
bet
w
een
P
V
panel
t
o
gr
o
u
n
d
b) I
n
ver
t
er
Side Before
and After
Using T
i
ny
Resistance
:
Leaka
g
e cur
r
e
n
t
has bee
n
sh
ow
n o
n
t
h
e i
n
vert
er si
d
e
an
d i
t
shows
ver
y
hi
gh be
fo
re usi
n
g a t
i
n
y
resi
st
ance.
He
r
e
we ha
ve
use
d
10
0
Ω
ohm
resistance to see t
h
e effect of le
a
k
age c
u
rre
nt in the inverter, hence
in Figure 12(b) shows the le
akage c
u
rr
ent in inve
rter without any effect
of resi
st
a
n
ce t
h
at
got
-
5
78
.8
p A t
o
8.
63
3
n
A,
h
o
w
e
ver
,
t
h
i
s
val
u
e
can be re
d
u
ce
d aft
e
r
usi
n
g a 10
0 o
h
m
resi
stance t
h
at
sh
o
w
s i
n
Fi
gu
re 1
2
(
c) an
d
th
e r
a
ng
e is ar
ou
nd
-7
6.977
fA
to
4.667
7nA
.
Figure
12(b). L
eakage
current
of
an inverter
Figure
12(c
). L
eakag
e
current
of an inverter a
f
ter
u
s
ing
tin
y
resistan
ce
c) In Between
Switches S1
and S2:
I
n
b
e
tw
een
Sw
itch
S1
an
d S2
, th
e leak
ag
e cu
rr
en
t
f
l
ow
s in
-1
93
.42n
A to
2
1
5
.
61
9uA
r
a
ng
e,
ho
we
ver
,
i
n
t
h
e swi
t
c
hi
n
g
o
n
/
off
t
i
m
e
l
eakage c
u
r
r
ent
occ
u
r
r
ed
hi
ghl
y
.
I
n
Fi
gu
re
12
(d
)
sh
ows
t
h
e l
e
a
k
age
cu
rren
t
of th
is
p
o
i
n
t
th
at show for two
fu
ll cycles.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6
,
No
. 1
,
Mar
c
h
2
015
:
14
8
–
15
9
15
6
Figure
12(d). L
eakage
current
in
b
e
t
w
een switch
S1
an
d S2
d) I
n
Between
Switches
S7 and S
8
:
The leaka
g
e
current is als
o
occ
u
rre
d in be
t
w
ee
n AC
deco
u
p
l
i
ng s
w
i
t
c
hes M
7
a
nd M
8
, i
n
ad
d
ition
a
lly, th
is flo
w
i
n
g
cu
rren
t
is flu
c
tu
ated
and
v
a
rying
fro
m
-2
4
8
.224p
A
to
78
.7
39u
A
an
d
i
n
sw
i
t
ch
es
o
n
and
of
f
bo
th ti
m
e
it f
l
o
w
s ar
oun
d 0.5
m
A
t
h
at sh
ow
s i
n
Fi
g
u
r
e
12
(
e
)
.
Figure
12(e
). L
eakage
current
in
bet
w
een
AC
dec
o
u
p
l
i
n
g s
w
i
t
c
hes
4.
2.
7
5
%
Duty
C
y
cl
e
a) PV P
a
nel to Ground
:
The
P
V
panel
t
o
g
r
o
u
nd has been fl
o
w
e
d
t
h
e
l
eak
age c
u
rrent which is
di
ffe
rent from
th
e 50% duty
cy
cl
e. Here t
h
e
l
eakage cur
r
e
n
t
i
s
vary
i
ng f
r
o
m
-773.
2
1
η
A
t
o
23
5.
63µ
A whe
r
eas i
t
had
aro
u
nd -
3
.
4
04
8
η
A to
29
1.
8
56µ
A ra
n
g
e.
Here t
h
e l
eakage c
u
rre
nt
f
l
uct
u
at
es b
u
t
o
n
e fe
w sec
o
n
d
s
i
t
i
s
show
n i
n
m
i
ll
i
range c
u
rre
nt
,
on
t
h
e
ot
he
r
ha
nd
, t
h
e
m
a
xim
u
m
curre
nt
fl
o
w
s i
n
n
e
gat
i
v
e
si
de
whi
c
h i
s
s
h
o
w
n
by
Fi
g
u
r
e 1
3
(a
).
Figure
13(a
). L
eakage
current
i
n
bet
w
een
P
V
panel
t
o
Gr
o
u
n
d
b) I
n
ver
t
er
Side Before
and After
Using T
i
ny
Resistance
:
Inverte
r
actual
l
y used t
o
inverter the
DC
signal
to AC
sig
n
a
l, t
o
d
o
so
th
e leak
ag
e cu
rren
t is
occu
rri
ng i
n
t
h
e i
n
vert
er
si
d
e
and t
h
i
s
cu
r
r
ent
i
s
-
1
10
.4
4n
A t
o
6
0
6
.
7
0
1
p
A,
ho
we
v
e
r, t
h
i
s
val
u
e
can b
e
m
i
nim
i
zed t
h
r
o
u
g
h
usi
n
g a
resistance, he
nc
e this va
lu
es
go
es dow
n
t
o
1.16
18
η
A
t
o
15
.5
47p
A. In
Fig
u
re
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
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:
208
8-8
6
9
4
Leak
age
C
u
r
r
e
n
t
P
a
t
h
s i
n
P
V
Tra
n
sf
or
mer
-
L
e
ss Si
ngl
e
-
Ph
a
s
e I
n
vert
e
r T
o
p
o
l
o
gy
an
d
It
s…
(
M
. N
.
H. K
h
a
n
)
15
7
13
(
b
) a
n
d Fi
g
u
r
e 1
3
(
c
) a
r
e s
h
ow
n t
h
e wa
vef
o
rm
of t
h
e l
e
a
k
age
curre
nt that actually
occurred i
n
the
inverte
r
an
d af
ter using tin
y r
e
si
stance
res
p
ectively.
Figure
13(b). L
eakage
curr
ent
sho
e
s in
the i
n
verter
Figu
re
1
3
(c
).
L
eakage
current
of
an inverter a
f
ter
u
s
ing
10
0 oh
m r
e
sistan
ce
c) In betwee
n
switches S1
and S2:
Swi
t
c
hes S
1
a
nd S
2
are a
d
de
d o
n
o
n
e si
de
of t
h
e
i
nve
rter whe
r
e
the
leakag
e curre
nt is occurre
d in
b
e
tween
these
two
switch
e
s
an
d th
is
v
a
lu
e is 99
4.2
η
A t
o
19.375µ
A
,
he
nc
e the lea
k
age
c
u
rrent is
ve
ry
sm
a
ll
am
ount
c
o
m
p
ared
t
o
5
0
%
dut
y
cy
cl
e as wel
l
.
I
n
Fi
g
u
re
1
3
(
d
)
sh
o
w
s t
h
at
l
eakage
cu
rr
ent
by
wa
ve
f
o
rm
.
Figure
13(d). L
eakage
current
in
b
e
t
w
een switch
S1
an
d S2
d) I
n
Between
Switches
S7 and S
8
:
In
AC
deco
u
p
l
i
ng
of m
y
appr
oac
h
i
n
g sy
st
em
can be
see
n
that the lea
k
age c
u
rrent is
very sm
all
am
ount
a
nd t
h
at
al
so sm
al
l com
p
ared t
o
5
0
%
dut
y
cy
cl
e. M
o
re
ove
r t
h
i
s
ran
g
e i
s
vary
i
n
g fr
om
-32
1
.
1
6
2p
A t
o
7
9
6
.
07
7u
A
t
h
at sho
w
s in
Figu
r
e
13
(
e
)
.
Fig
u
re
13
(e). Leak
ag
e curren
t
in
b
e
t
w
een AC
d
e
co
up
ling
switch
e
s in
75
%
d
u
t
y
ratio
n
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