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,
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.
14
~
24
I
SS
N:
2252
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8
7
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h
ttp
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a
p
e
.
ia
esco
r
e.
co
m
Ana
ly
sis
of
switch
ed impeda
nc
e so
u
rce/qua
si
-
impe
da
nce so
urce
DC
-
D
C
co
nv
ert
er
s for pho
tov
o
ltaic
sy
stem
Sa
pa
v
a
t
h Sre
enu,
J
a
lla
Upenda
r,
B
o
g
im
i Siris
ha
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
En
g
i
n
e
e
r
i
n
g
,
U
n
i
v
e
r
s
i
t
y
C
o
l
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e
g
e
o
f
E
n
g
i
n
e
e
r
i
n
g
(
A
)
,
O
sman
i
a
u
n
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v
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r
si
t
y
,
H
y
d
e
r
a
b
a
d
,
I
n
d
i
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
1
6
,
2
0
2
1
R
ev
is
ed
J
an
2
8
,
2
0
2
2
Acc
ep
ted
Feb
8
,
2
0
2
2
Th
is
p
a
p
e
r
p
ro
p
o
se
s
th
e
s
witch
e
d
imp
e
d
a
n
c
e
so
u
rc
e
c
o
n
v
e
rter
(
S
ZS
C)
o
r
sw
it
c
h
e
d
q
u
a
si
imp
e
d
a
n
c
e
so
u
rc
e
DC
-
DC
c
o
n
v
e
rter
(S
-
q
ZS
C)
b
a
se
d
p
h
o
to
v
o
lt
a
ic
(
PV
)
g
r
id
-
c
o
n
n
e
c
ted
sy
ste
m
s.
To
in
c
re
a
se
th
e
v
o
lt
a
g
e
fro
m
lo
w
lev
e
l
to
h
i
g
h
le
v
e
l,
a
ll
P
V
g
ri
d
-
c
o
n
n
e
c
ted
sy
ste
m
s
n
e
e
d
ste
p
-
u
p
DC
-
DC
c
o
n
v
e
rters
.
Th
is
ste
p
-
u
p
fa
c
to
r
c
a
n
b
e
i
n
c
re
a
se
d
b
y
c
o
n
n
e
c
ti
n
g
th
e
term
in
a
ls
o
f
a
trad
it
i
o
n
a
l
q
u
a
si
im
p
e
d
a
n
c
e
s
o
u
rc
e
DC
-
DC
c
o
n
v
e
rter
wit
h
a
n
a
d
d
it
i
o
n
a
l
d
io
d
e
a
n
d
a
sw
it
c
h
.
I
n
t
h
is
p
r
o
p
o
se
d
c
o
n
v
e
rter,
t
h
e
c
a
p
a
c
it
o
r
n
o
t
o
n
ly
se
rv
e
s
a
s
a
fil
ter.
It
is,
h
o
we
v
e
r,
b
o
u
n
d
i
n
se
ries
to
th
e
c
h
a
rg
i
n
g
l
o
o
p
s
o
f
t
h
e
in
d
u
c
to
rs
.
O
n
t
h
e
o
n
e
h
a
n
d
,
sa
tu
r
a
ted
in
d
u
c
to
rs
c
a
n
tri
g
g
e
r
i
n
sta
b
il
it
y
,
w
h
ich
c
a
n
b
e
a
v
o
id
e
d
.
Wh
e
n
u
se
d
fo
r
d
c
-
a
c
c
o
n
v
e
rsio
n
,
h
o
we
v
e
r,
th
e
m
o
d
u
lati
o
n
in
d
e
x
o
f
th
e
b
a
c
k
e
n
d
H
-
b
rid
g
e
c
a
n
b
e
se
t
t
o
a
wid
e
r
ra
n
g
e
.
As
c
o
m
p
a
re
d
to
e
x
isti
n
g
Z
-
so
u
rc
e
-
b
a
se
d
sy
ste
m
s,
a
sh
o
rt
e
r
d
u
t
y
p
e
rio
d
re
su
lt
s
in
a
h
i
g
h
e
r
b
o
o
st
fa
c
to
r.
K
ey
w
o
r
d
s
:
DC
-
DC
co
n
v
er
ter
I
m
p
ed
an
ce
-
s
o
u
r
ce
c
o
n
v
e
r
ter
PV a
r
r
ay
Qu
asi im
p
ed
an
ce
s
o
u
r
ce
co
n
v
er
ter
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
B
o
g
im
i Sir
is
h
a
Dep
ar
tm
en
t
o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
U
n
iv
er
s
ity
C
o
lleg
e
o
f
E
n
g
in
ee
r
i
n
g
(
A)
Osma
n
ia
Un
iv
er
s
ity
,
Hy
d
er
ab
ad
,
T
elan
g
a
n
a
-
5
0
0
0
0
7
,
I
n
d
ia
E
m
ail: sirish
ab
@
o
s
m
an
ia.
ac
.
i
n
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
in
cr
ea
s
ed
u
s
e
o
f
r
en
ewa
b
le
en
er
g
y
h
as
b
ee
n
f
u
ele
d
b
y
th
e
g
lo
b
al
en
e
r
g
y
cr
is
is
[
1
]
.
On
e
o
f
th
e
m
o
s
t
im
p
o
r
ta
n
t
p
lay
e
r
s
in
t
h
e
b
attle
a
g
ain
s
t
th
e
e
n
er
g
y
cr
is
is
is
s
o
lar
en
er
g
y
.
As
s
h
o
wn
in
Fig
u
r
e
1
,
p
h
o
to
v
o
ltaic
(
PV
)
ar
r
ay
s
ar
e
a
lo
w
d
c
s
o
u
r
ce
v
o
ltag
e
th
a
t
r
eq
u
ir
es
a
h
ig
h
s
tep
-
up
DC
-
DC
co
n
v
er
ter
to
tr
an
s
f
o
r
m
to
a
h
ig
h
er
v
o
ltag
e
l
ev
el
b
ef
o
r
e
co
n
n
ec
tin
g
t
o
a
g
r
id
-
co
n
n
ec
t
e
d
in
v
e
r
ter
[
2
]
,
[
3
]
.
Ho
wev
er
,
a
h
i
g
h
er
s
witch
in
g
d
u
ty
cy
cles
is
n
ee
d
ed
to
ac
h
iev
e
th
e
h
ig
h
v
o
ltag
e
g
ain
,
wh
ich
d
ec
r
ea
s
es
ef
f
icien
cy
an
d
ca
u
s
es
in
d
u
cto
r
s
atu
r
atio
n
.
T
r
a
d
itio
n
al
im
p
ed
an
ce
s
o
u
r
ce
in
v
e
r
ter
(
Z
SI)
h
as
m
an
y
f
laws,
in
clu
d
in
g
a
h
i
g
h
in
r
u
s
h
cu
r
r
en
t,
d
is
co
n
tin
u
o
u
s
in
p
u
t
cu
r
r
en
t,
an
d
h
ig
h
er
v
o
ltag
e
s
tr
ess
o
n
co
n
d
e
n
s
er
s
[
4
]
–
[
1
1
]
s
u
g
g
ests
q
u
asi
im
p
ed
an
ce
s
o
u
r
ce
in
v
e
r
ter
s
to
o
v
er
c
o
m
e
lim
itatio
n
s
.
T
h
e
b
o
o
s
t
f
ac
to
r
o
f
th
e
Z
SI
c
an
b
e
in
cr
ea
s
ed
u
s
in
g
a
v
ar
iety
o
f
m
eth
o
d
s
.
W
h
en
d
io
d
es,
in
d
u
cto
r
s
an
d
ca
p
ac
it
o
r
s
ar
e
co
n
n
ec
ted
to
th
e
Z
-
s
o
u
r
ce
n
etwo
r
k
,
f
o
r
ex
am
p
le,
a
h
i
g
h
er
d
c
-
lin
k
v
o
lt
ag
e
is
g
en
er
ated
[
1
2
]
,
[
1
3
]
.
A
ca
s
ca
d
ed
q
u
asi
-
Z
-
s
o
u
r
ce
n
etw
o
r
k
[
1
4
]
is
u
s
ed
in
th
e
to
p
o
lo
g
y
to
ac
h
iev
e
h
ig
h
er
v
o
ltag
e
g
ai
n
.
C
u
r
r
en
tly
,
r
esear
c
h
o
n
th
e
Z
-
s
o
u
r
ce
n
etwo
r
k
f
o
cu
s
es
p
r
im
a
r
ily
o
n
th
e
co
n
v
er
s
io
n
o
f
DC
-
AC
p
o
wer
,
d
esp
ite
th
e
f
ac
t
th
at
th
e
Z
-
s
o
u
r
ce
n
etwo
r
k
,
with
its
u
n
iq
u
e
ad
v
an
tag
es,
ca
n
also
b
e
u
s
ed
in
th
e
co
n
v
er
s
io
n
o
f
DC
-
DC
[
1
5
]
,
[
1
6
]
.
Fig
u
r
e
2
d
ep
icts
th
e
in
itial
im
p
e
d
an
ce
s
o
u
r
ce
DC
-
DC
co
n
v
er
ter
s
with
a
1
/(
1
-
2
*
D)
b
o
o
s
t
f
ac
to
r
(
s
witch
S
d
u
ty
cy
cle
is
D)
.
Yu
et
a
l.
[
1
7
]
d
ef
in
ed
a
h
y
b
r
id
t
h
r
ee
Z
-
to
p
o
l
o
g
y
b
o
o
s
t
co
n
v
er
ter
th
at
Un
it
e
tr
ad
itio
n
al
Z
-
s
o
u
r
ce
to
p
o
l
o
g
y
in
a
n
u
m
b
e
r
o
f
d
if
f
er
e
n
t
wa
y
s
.
T
h
e
b
o
o
s
t
f
ac
to
r
,
w
h
ich
i
s
b
est
s
u
ited
to
PV
ap
p
licatio
n
s
,
ca
n
b
e
g
r
ea
ter
t
h
an
1
/(
1
-
4
D)
.
T
h
e
m
ain
d
is
ad
v
an
tag
e
is
th
at
it
n
ec
ess
itates
a
lar
g
e
n
u
m
b
er
o
f
p
ass
iv
e
m
ater
ials
,
m
ak
in
g
it m
o
r
e
ex
p
e
n
s
iv
e
an
d
lar
g
er
i
n
v
o
lu
m
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
a
lysi
s
o
f sw
itch
ed
imp
ed
a
n
ce
s
o
u
r
ce
/q
u
a
s
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-
imp
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a
n
c
e
s
o
u
r
ce
DC
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DC
co
n
ve
r
ter
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… (
S
a
p
a
va
t
h
S
r
ee
n
u
)
15
Fig
u
r
e
1
.
T
h
e
g
r
i
d
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
tem
T
h
is
wo
r
k
in
tr
o
d
u
ce
s
a
n
o
v
el
class
o
f
DC
-
DC
co
n
v
er
ter
d
es
ig
n
ed
f
o
r
PV
s
y
s
tem
s
with
lo
w
p
ass
iv
e
co
m
p
o
n
en
ts
.
B
y
co
n
n
ec
tin
g
th
e
s
tan
d
ar
d
o
u
t
p
u
t
p
o
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ts
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m
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ed
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ce
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r
ce
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u
asi
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im
p
ed
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ce
s
o
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r
ce
to
p
o
lo
g
y
with
o
n
e
m
o
r
e
s
witch
an
d
d
io
d
e
as
s
h
o
wn
in
Fi
g
u
r
e
1
.
W
h
en
th
e
s
witch
es
ar
e
s
witch
ed
o
n
,
th
e
o
u
tp
u
t
ca
p
ac
ito
r
n
o
t
o
n
ly
ac
ts
as
th
e
DC
co
n
n
ec
tio
n
.
H
o
we
v
er
,
i
t
is
b
o
u
n
d
in
ca
s
ca
d
ed
to
th
e
ch
ar
g
in
g
l
o
o
p
s
o
f
th
e
in
d
u
ct
o
r
s
.
T
h
e
p
r
o
p
o
s
ed
b
o
o
s
t
co
n
v
er
ter
,
W
ill
ac
h
i
ev
e
th
e
id
e
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tical
v
o
ltag
e
g
ai
n
o
f
1
/(
1
-
4
D)
with
f
ewe
r
m
o
d
u
les
th
an
th
e
h
y
b
r
id
th
r
ee
Z
-
to
p
o
lo
g
y
b
o
o
s
t
co
n
v
er
ter
s
in
less
er
u
n
it
co
s
t
an
d
h
ig
h
p
o
wer
d
en
s
ity
[
1
7
]
.
I
n
a
n
o
th
e
r
way
,
f
o
r
th
e
s
am
e
b
o
o
s
tin
g
v
o
lta
g
e,
th
e
latest
to
p
o
lo
g
ies
n
ee
d
a
lo
w
d
u
ty
r
atio
,
r
esu
ltin
g
in
s
m
aller
in
d
u
cto
r
s
an
d
a
lo
wer
r
is
k
o
f
in
d
u
ctiv
e
s
atu
r
a
tio
n
[
1
8
]
.
Fig
u
r
e
2
(
a)
d
ep
icts
th
e
s
tan
d
ar
d
im
p
ed
an
ce
s
o
u
r
ce
co
n
v
er
ter
c
ir
cu
it,
wh
ich
in
clu
d
es
th
e
two
in
d
u
ct
o
r
s
(
L
1
a
n
d
L
2
)
an
d
two
ca
p
ac
ito
r
s
(
C
1
an
d
C
2
)
in
an
X
-
s
h
ap
e.
Fig
u
r
e
2
(
b
)
in
d
icate
s
o
n
e
s
witch
in
g
cy
cle.
T
h
e
q
u
asi
-
Z
-
s
o
u
r
ce
in
v
er
ter
s
(
q
Z
SIs)
co
n
tin
u
o
u
s
cu
r
r
en
t
m
o
d
e
s
tat
e
co
n
s
is
ts
o
f
two
s
tates:
s
h
o
o
t
-
th
r
o
u
g
h
an
d
n
o
n
-
s
h
o
o
t
-
th
r
o
u
g
h
.
Fig
u
r
e
2
(
c
)
r
ep
r
esen
ts
ch
an
g
ea
b
le
in
p
u
t
c
u
r
r
en
t
t
h
at
ca
n
a
r
is
e
wh
en
th
e
cir
cu
it
s
tar
ts
to
in
cr
ea
s
e
th
e
c
u
r
r
en
t
b
y
t
u
r
n
in
g
a
p
o
r
tio
n
o
f
th
e
s
h
o
r
t z
er
o
s
tates in
to
o
p
e
n
ze
r
o
s
tates d
ep
en
d
i
n
g
o
n
th
e
lo
a
d
co
n
d
itio
n
an
d
c
ap
ac
itan
ce
v
alu
e.
(
a)
(
b
)
(
c)
Fig
u
r
e
2
.
T
h
e
o
r
i
g
in
al
Z
-
s
o
u
r
c
e
co
n
v
er
te
r
of
(
a)
th
e
s
tan
d
ar
d
Z
-
s
o
u
r
ce
DC
-
DC
co
n
v
er
ter
,
(
b
)
a
DC
-
DC
co
n
v
er
ter
with
a
co
n
s
tan
t in
p
u
t c
u
r
r
en
t th
at
u
s
es a
q
u
asi
-
im
p
ed
an
ce
s
o
u
r
ce
,
an
d
(
c)
A
DC
-
DC
co
n
v
er
ter
with
a
ch
an
g
ea
b
le
in
p
u
t c
u
r
r
e
n
t th
a
t u
s
es a
s
tan
d
ar
d
q
u
asi
-
im
p
e
d
a
n
ce
s
o
u
r
ce
Fig
u
r
e
3
s
h
o
ws
th
e
p
r
o
p
o
s
ed
s
witch
ed
-
Z
-
s
o
u
r
ce
d
c
-
ac
in
v
e
r
ter
as
an
ex
a
m
p
le.
T
h
e
b
o
o
s
t
f
ac
to
r
o
f
th
e
f
r
o
n
ten
d
s
witch
ed
-
Z
-
s
o
u
r
c
e
n
etwo
r
k
is
1
/(
1
-
4
D)
,
wh
ich
allo
ws
f
o
r
a
s
u
b
s
tan
tial
v
o
ltag
e
g
ain
with
a
lo
w
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
11
,
No
.
1
,
Ma
r
ch
2
0
2
2
:
1
4
-
24
16
d
u
ty
c
y
cle.
As
a
r
esu
lt,
th
e
b
a
ck
en
d
H
-
m
o
d
u
latio
n
B
r
id
g
e’
s
in
d
ex
ca
n
b
e
tu
n
e
d
to
a
wid
e
r
r
an
g
e.
As
in
d
icate
d
in
Fig
u
r
e
3
,
th
er
e
ar
e
s
ev
er
al
d
if
f
er
en
t ty
p
es
o
f
f
u
n
ctio
n
in
g
a
s
:
-
Mo
d
e
1
:
d
u
r
in
g
th
e
Sh
o
o
t
-
t
h
r
o
u
g
h
s
itu
atio
n
,
th
e
o
u
tp
u
t
s
id
e
o
f
th
e
im
p
ed
an
ce
n
etwo
r
k
,
i.e
.
th
e
in
v
er
ter
b
r
id
g
e
ter
m
i
n
als,
is
s
h
o
r
t
-
cir
cu
ited
b
y
a
co
m
b
in
atio
n
o
f
s
e
m
ico
n
d
u
ct
o
r
s
witch
es
(
S
21
,
S
22
,
S
23
an
d
S
24
)
.
T
h
e
in
p
u
t
d
io
d
e
D
1
tu
r
n
s
o
f
f
d
u
r
i
n
g
th
is
tim
e
i
n
ter
v
al,
a
n
d
en
e
r
g
y
is
tr
an
s
m
itted
f
r
o
m
ca
p
ac
ito
r
s
to
in
d
u
cto
r
s
[
1
9
]
–
[
2
2
]
.
T
h
e
s
to
r
e
d
en
er
g
y
is
s
en
t
t
o
th
e
l
o
ad
i
n
th
e
in
v
er
ter
'
s
n
ex
t
ac
tiv
e
s
witch
in
g
s
tates,
an
d
th
e
in
p
u
t
d
io
d
e
c
o
n
d
u
cts.
-
Mo
d
e
2
:
th
e
p
r
im
a
r
y
cir
cu
it
alter
n
ates
b
etwe
en
two
ac
tiv
e
an
d
two
ze
r
o
s
tates
d
u
r
in
g
th
e
n
o
n
-
s
h
o
o
t
-
th
r
o
u
g
h
co
n
d
itio
n
.
Du
r
in
g
th
is
m
o
d
e
th
e
d
io
d
es D
1
, D
2
,
an
d
D
3
ar
e
r
ev
er
s
e
b
iased
an
d
s
witch
es S
21
an
d
S
24
ca
n
b
e
t
u
r
n
ed
o
n
at
s
am
e
tim
e.
T
h
e
in
d
u
cto
r
s
L
1
an
d
L
2
s
t
o
r
e
en
e
r
g
y
wh
ile
th
e
ca
p
ac
ito
r
s
C
1
,
C
2
,
an
d
C
3
ar
e
d
is
ch
ar
g
ed
,
an
d
th
e
en
e
r
g
y
s
to
r
ed
in
ca
p
ac
ito
r
C
3
is
s
u
p
p
lied
to
th
e
lo
a
d
.
Fig
u
r
e
3
.
T
h
e
p
r
o
p
o
s
ed
d
c/ac
i
n
v
er
ter
s
witch
ed
im
p
e
d
an
ce
s
o
u
r
ce
cir
c
u
it to
p
o
lo
g
y
2.
M
O
DE
L
I
NG
T
H
E
P
V
C
E
L
L
A
p
h
o
to
v
o
ltaic
(
PV)
m
ater
ial
is
o
n
e
th
at
ca
n
co
n
v
e
r
t
p
h
o
t
o
n
in
to
elec
tr
ical
en
er
g
y
.
E
lectr
o
n
s
ca
n
b
e
r
elea
s
ed
f
r
o
m
an
at
o
m
b
y
p
h
o
to
n
s
with
s
h
o
r
t
wav
elen
g
th
s
.
On
a
co
n
d
u
ct
o
r
,
elec
tr
o
n
s
ca
n
f
lo
w
an
d
f
o
r
m
a
n
elec
tr
ic
cu
r
r
en
t.
T
h
e
s
u
n
p
r
o
v
id
es
th
e
en
er
g
y
r
eq
u
ir
e
d
to
b
r
ea
k
th
e
b
o
n
d
s
.
T
h
is
is
a
s
ig
n
i
f
ican
t
o
p
p
o
r
tu
n
ity
b
ec
au
s
e
th
e
ea
r
th
'
s
s
u
r
f
ac
e
r
ec
eiv
es
6
0
0
0
tim
es
th
e
to
tal
d
aily
en
er
g
y
co
n
s
u
m
p
tio
n
.
A
PV
m
o
d
u
le
ca
n
b
e
d
escr
ib
ed
u
s
in
g
an
eq
u
iv
alen
t
cir
cu
it
th
at
in
clu
d
es
a
cu
r
r
en
t
s
o
u
r
ce
,
a
d
io
d
e
,
an
d
a
r
esis
to
r
to
r
ep
r
esen
t
in
ter
n
al
r
esis
tan
ce
.
W
h
en
th
e
s
u
n
'
s
r
ay
s
s
tr
ik
e
th
e
s
o
lar
ce
ll,
cu
r
r
en
t is g
en
e
r
ated
as:
ℎ
=
(
+
(
−
2
98
)
∗
100
)
(
1
)
W
h
e
r
e
=
s
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
,
=
t
e
m
p
e
r
a
t
u
r
e
c
o
n
s
t
a
n
t
,
=
i
r
r
a
d
i
a
n
c
e
,
a
n
d
=
t
e
m
p
e
r
a
t
u
r
e
i
n
K
el
v
i
n
.
C
u
r
r
en
t
f
lo
win
g
th
r
o
u
g
h
th
e
d
io
d
e
I
D
d
eter
m
in
es
th
e
o
u
tp
u
t
cu
r
r
en
t
f
r
o
m
th
e
s
o
lar
ce
ll,
an
d
cu
r
r
en
t
f
lo
ws to
th
e
in
ter
n
al
r
esis
tan
ce
ℎ
[
2
]
.
T
h
e
eq
u
atio
n
th
e
n
b
ec
o
m
es:
=
ℎ
−
–
ℎ
(
2)
In
(
3
)
,
m
u
s
t b
e
u
s
ed
to
c
o
m
p
u
t
e
cu
r
r
en
t
f
lo
ws in
a
d
io
d
e.
=
[
^
(
(
+
∗
)
)
−
1
]
(
3
)
W
h
er
e
0
(
)
=
s
atu
r
atio
n
cu
r
r
en
t
,
=
v
o
l
tag
e
ac
r
o
s
s
s
o
lar
ce
ll
,
=
s
er
ies
b
r
an
ch
r
esis
tan
ce
,
=
B
o
ltzm
an
n
co
n
s
tan
t
,
=
ch
ar
g
e
o
f
an
elec
tr
o
n
(
1
̅
=
1
.
6
0
2
×
10
−
19
c
)
,
an
d
=
id
ea
lity
f
ac
to
r
(
I
d
ea
lly
1
)
.
Fro
m
Fig
u
r
e
4
,
PV
m
o
d
u
le
o
u
tp
u
t c
u
r
r
e
n
t a
n
d
v
o
ltag
e
r
elatio
n
s
h
ip
is
g
iv
en
b
y
(
4
)
.
=
ℎ
–
[
^
(
(
+
∗
)
)
−
1
]
−
(
+
∗
ℎ
)
(
4
)
Fro
m
(
4
)
,
t
h
e
I
-
V
ch
a
r
ac
ter
is
tic
cu
r
v
e
ca
n
b
e
o
b
tain
ed
wh
ich
g
iv
es
o
p
er
atio
n
o
f
th
e
s
o
l
ar
p
an
el.
At
f
i
x
ed
tem
p
er
atu
r
e
an
d
ir
r
a
d
ian
ce
,
th
e
m
ee
tin
g
o
f
th
e
I
-
V
ch
ar
ac
te
r
is
tic
cu
r
v
e
a
n
d
th
e
l
o
ad
ch
ar
ac
ter
is
tics
is
th
e
s
o
lar
p
an
el'
s
o
p
er
atio
n
al
p
o
in
t.
T
h
e
o
p
er
ativ
e
p
o
s
itio
n
o
f
t
h
e
p
an
e
l
g
o
es
f
r
o
m
ze
r
o
r
esis
tan
ce
to
in
f
in
ite
r
esis
tan
ce
,
r
esu
ltin
g
in
th
e
a
p
p
ea
r
an
c
e
o
f
o
p
en
cir
c
u
it v
o
ltag
e
(
)
[
2
3
]
–
[
3
0
]
.
T
h
e
m
u
ltip
licatio
n
o
f
h
ig
h
est
v
alu
e
o
f
th
e
v
o
ltag
e
an
d
cu
r
r
e
n
t
g
iv
es
m
a
x
im
u
m
p
o
wer
.
As
s
h
o
wn
in
Fig
u
r
e
5
,
wh
en
t
h
e
p
a
n
el
v
o
l
tag
e
r
ea
ch
es
v
o
ltag
e
at
m
a
x
i
m
u
m
p
o
wer
(
)
,
a
PV
m
o
d
u
le
o
p
er
ates
at
its
m
ax
im
u
m
p
o
wer
.
B
y
m
o
d
if
y
i
n
g
th
e
lo
ad
,
th
e
m
a
x
im
u
m
p
o
wer
ca
n
b
e
o
b
tain
ed
,
w
h
ich
w
ill
ca
u
s
e
th
e
cu
r
r
en
t
f
lo
win
g
in
th
e
cir
cu
it is
lim
ited
an
d
i
n
ad
d
itio
n
to
th
e
p
an
el
v
o
ltag
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
a
lysi
s
o
f sw
itch
ed
imp
ed
a
n
ce
s
o
u
r
ce
/q
u
a
s
i
-
imp
ed
a
n
c
e
s
o
u
r
ce
DC
-
DC
co
n
ve
r
ter
s
… (
S
a
p
a
va
t
h
S
r
ee
n
u
)
17
Fig
u
r
e
4
.
PV c
ell
eq
u
i
v
alen
t c
i
r
cu
it
Fig
u
r
e
5
.
PV m
o
d
u
le
ch
a
r
ac
te
r
is
tic
cu
r
v
e
3.
WO
RK
I
NG
PR
I
N
C
I
P
L
E
A
N
D
C
I
R
C
U
I
T
TO
PO
LO
G
I
E
S
OF
T
H
E
PR
OP
O
S
E
D
C
ON
V
ER
T
ER
S
T
h
e
f
o
llo
win
g
s
im
u
latio
n
is
m
ain
ly
f
o
c
u
s
ed
o
n
f
ir
s
t
n
etw
o
r
k
i.e
.
,
s
witch
ed
-
Z
SC
,
s
in
ce
th
e
cir
cu
it
co
n
f
ig
u
r
atio
n
s
o
f
th
e
p
r
o
p
o
s
e
d
th
r
ee
cir
cu
its
ar
e
id
en
tical.
T
h
e
f
o
llo
win
g
o
th
e
r
two
SQZSC
s
ca
n
also
b
e
an
aly
ze
d
with
s
im
ilar
tech
n
iq
u
e.
T
h
e
c
r
itical
cu
r
r
en
t
m
o
d
e
(
C
R
M)
is
a
s
u
b
s
et
o
f
eit
h
er
th
e
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
(
C
C
M)
o
r
th
e
d
is
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
(
DC
M)
.
T
wo
ca
s
es
(
C
ases
1
an
d
2
)
m
ay
ap
p
ea
r
in
C
C
M
u
n
d
er
d
if
f
er
in
g
co
m
b
in
atio
n
s
o
f
in
d
u
ctan
ce
,
d
u
ty
cy
cle,
an
d
lo
a
d
r
esis
tan
ce
,
b
u
t
o
n
ly
in
ca
s
e
3
m
a
y
ap
p
ea
r
in
Dis
co
n
tin
u
o
u
s
C
o
n
d
u
ctio
n
Mo
d
e
.
T
h
r
o
u
g
h
o
u
t
a
lo
o
p
,
ea
ch
an
d
ev
er
y
cir
cu
it
h
as
d
if
f
er
en
t
s
tate
[
2
0
]
,
[
2
1
]
.
All o
f
th
e
cir
c
u
it
s
tates a
r
e
f
o
u
n
d
in
t
h
e
two
m
o
d
es wh
ich
ar
e
d
ep
icted
in
F
ig
u
r
es
6
(
a)
-
(
e)
(
s
ee
Ap
p
en
d
ix
)
.
I
n
Fig
u
r
e
6
(
a)
th
e
r
ef
er
en
ce
d
ir
ec
tio
n
s
f
o
r
ea
ch
v
ar
iab
le
ar
e
s
h
o
wn
i)
C
ase
1
-
State1
→
State2
,
ii)
C
ase
2
-
State1
→
State2
→
State3
,
an
d
iii)
C
ase
3
-
State1
→
State2
→
State
3
.
I
n
t
h
is
s
tate,
th
e
v
o
ltag
es
ac
r
o
s
s
th
e
th
r
ee
ca
p
ac
ito
r
s
ca
n
b
e
ca
lc
u
lated
u
s
in
g
KVL
.
Sta
te1
→
State2
→
State3
→
State4
.
Fo
r
th
e
s
ak
e
o
f
s
im
p
licity
,
ass
u
m
in
g
:
i
)
all
id
ea
l
p
o
wer
co
m
p
o
n
e
n
ts
;
ii
)
L
1
=
L
2
an
d
C
1
=
C
2
ar
e
ig
n
o
r
e
d
;
an
d
iii
)
L
1
=
L
2
a
nd
C
1
=
C
2
.
Fig
u
r
e
6
(
b
)
r
ep
r
esen
ts
th
e
cu
r
r
en
t
lo
o
p
co
r
r
esp
o
n
d
in
g
to
s
tate1
,
wh
ich
in
d
icat
es
cu
r
r
en
t
th
r
o
u
g
h
L
1
&
C
1
ar
e
eq
u
al.
Fig
u
r
e
6
(
c)
in
d
icate
s
p
ath
o
f
th
e
cu
r
r
e
n
ts
f
o
r
State2
.
Fig
u
r
e
6
(
d
)
i
n
d
icate
s
th
e
cu
r
r
en
ts
p
ath
in
s
tate3
,
f
u
r
th
e
r
Fig
u
r
e
6
(
e)
r
ep
r
es
en
ts
p
ath
o
f
cu
r
r
e
n
ts
co
r
r
esp
o
n
d
in
g
to
State4
.
4.
I
M
P
E
DANC
E
N
E
T
WO
RK
M
AT
H
E
M
AT
I
CA
L
ANA
L
YSI
S
L
et
u
s
as
s
u
m
in
g
th
at
th
e
ca
p
ac
ito
r
s
(
C
1
&C
2
)
an
d
in
d
u
cto
r
s
(
L
1
&L
2
)
h
av
e
id
en
tical
v
alu
es
.
th
e
in
p
u
t
v
o
ltag
e
is
Vd
; th
e
o
u
tp
u
t v
o
ltag
e
Vi; ser
ies ar
m
in
d
u
cto
r
s
L
1
an
d
L
2
; p
ar
allel
ar
m
ca
p
ac
ito
r
s
C
1
an
d
C
2
.
An
im
p
ed
an
ce
s
o
u
r
ce
in
v
er
ter
eq
u
iv
alen
t c
ir
cu
it
m
o
d
el
is
d
er
iv
ed
f
r
o
m
Fig
u
r
e
7
in
(
5
)
-
(
1
5
)
;
1
=
2
=
(
5
)
1
=
1
=
(
6
)
=
,
=
2
=
0
At
s
witch
in
g
cy
cle
T
=
0
–
(
7
)
=
0
=
–
=
2
–
0
(
8
)
W
h
er
e
=
0
+
1
an
d
th
e
d
c
s
o
u
r
ce
v
o
l
tag
e
is
.
T
h
e
a
v
er
ag
e
v
o
ltag
e
o
f
th
e
in
d
u
ct
o
r
s
s
h
o
u
ld
b
e
ze
r
o
in
s
tead
y
s
tate
af
ter
o
n
e
s
witch
in
g
cy
cle
(
T
)
.
=
(
0
.
+
1
(
0
−
)
)
/
=
0
/
0
=
1
/
(
1
−
0
)
(
9
)
Similar
ly
,
th
e
Av
g
DC
v
o
ltag
e
ac
r
o
s
s
th
e
in
v
er
ter
b
r
id
g
e
ca
n
b
e
d
eter
m
in
e
d
u
s
in
g
(
8
)
.
=
(
0
∗
0
+
1
)
∗
(
2
–
0
)
/
(
1
0
)
=
(
2
.
1
/
)
−
(
1
0
/
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
11
,
No
.
1
,
Ma
r
ch
2
0
2
2
:
1
4
-
24
18
2
=
0
Fro
m
(
1
0
)
1
∗
0
/
(
1
−
0
)
=
2
.
1
/
(
1
−
0
)
=
0
∗
1
/
(
1
−
0
)
T
h
e
m
ax
im
u
m
d
c
-
lin
k
v
o
ltag
e
o
f
th
e
in
v
er
ter
b
r
id
g
e
is
,
=
−
=
2
–
0
=
/
(
1
−
0
)
∗
0
=
∗
0
h
er
e
=
/
(
1
−
0
)
i.e
.
(
1
1
)
B
o
o
s
t f
ac
to
r
is
B
,
Ou
tp
u
t p
ea
k
p
h
ase
v
o
ltag
e
o
f
th
e
in
v
er
ter
is
,
=
∗
/
2
(
1
2
)
Her
e
m
o
d
u
latio
n
in
d
e
x
is
M
an
d
s
o
u
r
ce
v
o
ltag
e
=
∗
∗
0
/
2
(
1
3
)
B
ef
o
r
e
s
elec
tin
g
an
ac
ce
p
tab
le
b
u
ck
-
B
o
o
s
t f
ac
t
o
r
,
th
e
V
0
ca
n
b
e
s
tep
p
ed
d
o
wn
a
n
d
u
p
(
B
B
)
.
=
∗
(
r
an
g
e
f
r
o
m
0
to
1
)
(
1
4
)
T
h
e
ca
p
ac
ito
r
v
o
ltag
e
is
1
=
2
=
=
(
1
–
0
/
)
∗
0
/
(
1
−
2
0
/
)
(
1
5
)
Fig
u
r
e
7
.
I
m
p
ed
a
n
ce
s
o
u
r
ce
in
v
er
ter
eq
u
iv
alen
t c
ir
cu
it
5.
E
F
F
E
C
T
O
F
T
H
E
P
ARA
SI
T
I
C
P
AR
AM
E
T
E
RS O
F
T
H
E
E
F
F
I
C
I
E
N
CY
5
.
1
.
P
o
wer
s
wit
ching
lo
s
s
C
o
n
d
u
ctio
n
lo
s
s
an
d
s
witch
in
g
lo
s
s
ar
e
two
ty
p
es
o
f
lo
s
s
es
in
p
o
wer
s
witch
es.
T
h
e
co
n
d
u
ctin
g
lo
s
s
ca
n
b
e
m
ea
s
u
r
e
d
u
s
in
g
Fig
u
r
e
7.
=
8
2
(
1
6
)
T
h
e
p
o
we
r
s
witch
l
o
s
s
ca
n
b
e
d
eter
m
in
ed
b
y
lin
ea
r
izin
g
th
e
v
o
ltag
es
an
d
cu
r
r
e
n
ts
o
f
th
e
c
o
m
m
u
n
icate
s
witch
es
[
2
0
]
,
[
2
1
]
as c
h
an
g
e
t
h
eir
s
tates,
P
s
=
2
f
s
.
V
0
.
I
L
(
t
on
+
t
o
f
f
)
3
(
1
7
)
T
h
e
in
p
u
t
p
o
wer
ca
n
b
e
ca
lcu
lated
u
s
in
g
(
1
1
)
as
wh
e
r
e
th
e
s
witch
in
g
f
r
eq
u
e
n
cy
is
f
s
an
d
t
o
f
f
an
d
t
on
ar
e
th
e
s
witch
tu
r
n
-
o
f
f
an
d
t
u
r
n
-
o
n
d
e
lay
s
.
5
.
2
.
Dio
de
po
wer
lo
s
s
R
ev
er
s
e
r
ec
o
v
er
y
l
o
s
s
an
d
co
n
d
u
ctio
n
lo
s
s
ar
e
th
e
two
f
o
r
m
s
o
f
d
io
d
e
p
o
wer
lo
s
s
es.
C
o
n
d
u
ctio
n
lo
s
s
is
d
en
o
ted
b
y
_
=
3
(
1
–
)
(
1
8
)
Dio
d
es r
ev
er
s
e
r
ec
o
v
er
y
l
o
s
s
is
g
iv
en
b
y
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
a
lysi
s
o
f sw
itch
ed
imp
ed
a
n
ce
s
o
u
r
ce
/q
u
a
s
i
-
imp
ed
a
n
c
e
s
o
u
r
ce
DC
-
DC
co
n
ve
r
ter
s
… (
S
a
p
a
va
t
h
S
r
ee
n
u
)
19
=
1
1
+
2
2
+
3
3
(
1
9
)
W
h
er
e
D
1
, D
2
an
d
D
3
d
io
d
es a
n
d
Q
RR1
, Q
RR2
an
d
Q
RR3
r
ev
e
r
s
e
r
ec
o
v
er
y
ch
ar
g
e
o
f
d
io
d
es r
e
s
p
ec
tiv
ely
.
5
.
3
.
I
nd
uct
o
r
lo
s
s
An
id
ea
l
in
d
u
cto
r
h
as
ze
r
o
p
o
wer
lo
s
s
b
ec
au
s
e
i
t
h
as
n
o
r
es
is
tan
ce
an
d
ju
s
t
in
d
u
ctan
ce
,
=
0
,
an
d
n
o
p
o
wer
is
d
is
s
ip
ated
with
in
th
e
co
il.
A
d
ev
ice
th
at
s
to
r
es
en
er
g
y
as
an
elec
t
r
o
m
ag
n
etic
f
ield
an
d
m
ea
s
u
r
es
in
h
en
r
y
s
is
k
n
o
wn
as
an
i
n
d
u
cto
r
(
H)
,
C
o
n
d
u
ctio
n
lo
s
s
es
will
o
cc
u
r
in
a
p
r
ac
tical
in
d
u
cto
r
with
in
ter
n
al
r
esis
tan
ce
.
So
,
th
e
co
n
d
u
ctio
n
lo
s
s
ca
n
b
e
m
ea
s
u
r
ed
,
d
ec
id
es
th
e
k
ey
p
o
wer
lo
s
s
.
=
2
2
(
2
0
)
5
.
4
.
Ca
pa
ci
t
o
r
lo
s
s
T
h
e
ca
p
ac
ito
r
s
to
tal
p
o
wer
lo
s
s
es a
r
e
ca
lcu
lated
as,
=
2
(
1
−
5
)
(
2
1
)
T
h
en
,
th
e
d
er
iv
e
d
to
tal
co
n
d
u
c
tio
n
lo
s
s
es a
r
e
=
+
+
+
(
2
2
)
T
h
e
in
p
u
t
p
o
wer
ca
l
c
u
lated
as,
=
=
(
2
3
)
Fo
llo
win
g
th
at,
th
e
p
r
o
p
o
s
ed
SZSC
ef
f
icien
cy
ca
n
b
e
d
eter
m
in
ed
b
y
u
s
in
g
=
/
=
Pi
−
P
co
n
d
−
(
Ps
+
PR
RD
)
Pi
(
2
4
)
6.
CO
NT
RA
ST
S
WI
T
H
P
RE
V
I
O
US Z
-
SO
U
RCE
T
O
P
O
L
O
G
I
E
S
Fu
r
th
er
m
o
r
e
,
as
s
h
o
wn
in
T
a
b
le
1
,
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
o
u
tp
u
t
is
d
if
f
e
r
en
tiated
to
t
h
at
o
f
th
e
co
n
v
er
ter
s
in
[
1
7
]
,
[
2
2
]
–
[
3
0
]
.
T
h
e
ca
p
ac
ity
t
o
b
o
o
s
t
is
a
cr
itical
m
etr
ic
f
o
r
ass
ess
in
g
th
e
ef
f
icien
cy
o
f
a
d
c
-
d
c
co
n
v
er
ter
.
W
h
en
th
e
v
o
ltag
e
g
ain
G
is
g
r
ea
ter
t
h
an
5
,
with
t
h
e
s
am
e
d
u
ty
r
atio
t
h
e
p
r
o
p
o
s
ed
wo
r
k
p
r
o
d
u
ce
s
a
h
ig
h
er
b
o
o
s
t
f
ac
to
r
th
an
th
e
o
th
er
c
o
n
v
e
r
ter
s
.
Alth
o
u
g
h
th
e
b
o
o
s
t
f
ac
to
r
is
th
e
s
am
e
as
in
[
1
7
]
,
wh
ich
is
a
co
m
p
licated
h
y
b
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d
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r
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eq
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.
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h
e
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im
u
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o
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b
ased
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r
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s
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al
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es
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)
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is
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8
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s
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s
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5
k
Hz;
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d
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s
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2
;
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e
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alu
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t
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5
w
as
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=
3
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,
with
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ic
r
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f
2
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m
Ω
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v
)
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1
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2
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with
a
1
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S
2
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e
an
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v
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2
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d
D
3
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u
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9
s
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r
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5
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.
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u
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1
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ar
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A
with
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8
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8
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pv
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in
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s
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as sh
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in
Fig
u
r
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1
1
.
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I
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8
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Fig
u
r
e
1
2
(
c
)
s
h
o
ws v
o
ltag
e
ac
r
o
s
s
in
d
u
cto
r
5
2
V
with
r
esp
ec
t
to
tim
e
in
s
ec
o
n
d
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
11
,
No
.
1
,
Ma
r
ch
2
0
2
2
:
1
4
-
24
22
Fig
u
r
e
1
2
.
Stead
y
s
tate
wav
ef
o
r
m
s
o
f
(
a
)
b
atter
y
SOC
(
%),
(
b
)
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atter
y
cu
r
r
e
n
t
,
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d
(
c)
b
atter
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v
o
ltag
e
8.
CO
NCLU
SI
O
N
I
t
is
s
u
g
g
ested
t
h
at
a
s
er
ies
o
f
s
witch
ed
im
p
e
d
an
ce
s
o
u
r
ce
/s
witch
ed
q
u
asi
-
Z
SC
s
with
m
o
d
if
ied
to
p
o
lo
g
y
b
e
d
ev
elo
p
e
d
f
o
r
Ph
o
to
v
o
ltaic
s
y
s
tem
s
.
B
y
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u
ttin
g
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tr
a
s
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d
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io
d
e
t
o
o
r
d
i
n
ar
y
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S/q
Z
S
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-
DC
co
n
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ter
s
,
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e
in
cr
ea
s
ed
b
o
o
s
t
f
ac
to
r
u
p
to
1
/(
1
-
4
D)
.
T
o
ac
h
iev
e
h
ig
h
er
v
o
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e
g
ain
wh
ile
av
o
id
in
g
th
e
in
s
tab
ilit
y
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d
u
ce
d
b
y
in
d
u
cto
r
s
atu
r
atio
n
,
a
s
h
o
r
t
d
u
t
y
cy
cle
is
u
s
ed
.
T
h
e
b
o
o
s
t
r
ati
o
o
f
th
e
p
r
o
p
o
s
ed
co
n
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er
ter
s
is
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e
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e
as
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e
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y
b
r
id
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r
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Z
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n
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b
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o
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t
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ter
s
.
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h
at
wer
e
r
ec
e
n
tly
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r
o
p
o
s
ed
,
b
u
t
with
f
ewe
r
p
ass
iv
e
co
m
p
o
n
en
ts
,
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o
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g
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o
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h
i
g
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er
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en
s
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ty
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d
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n
it
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s
ts
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h
e
o
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er
atin
g
p
r
i
n
cip
les
o
f
th
ese
d
ev
ices
ar
e
d
etailed
i
n
th
is
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ap
er
,
as
ar
e
th
e
p
ar
am
eter
s
o
f
cu
r
r
e
n
t
an
d
v
o
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e,
a
s
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n
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er
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n
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icien
cy
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f
th
e
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ar
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ic
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ar
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m
eter
s
th
e
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f
ec
ts
.
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v
en
tu
ally
,
r
esu
lts
o
f
th
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s
im
u
latio
n
p
r
o
v
id
ed
to
s
u
p
p
o
r
t
th
e
p
r
o
p
er
ties
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d
th
eo
r
etica
l a
n
aly
s
is
p
r
ev
io
u
s
ly
m
en
tio
n
ed
.
APPENDI
X
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
6
.
Op
e
r
atin
g
s
tates o
f
S
Z
SC
; (
a)
s
p
ec
if
icatio
n
s
o
f
r
ef
e
r
en
ce
d
ir
ec
tio
n
s
,
(
b
)
c
u
r
r
e
n
t lo
o
p
o
f
th
e
p
r
o
p
o
s
ed
SZSC
in
State1
: S
1
an
d
S
2
o
n
;
D
1
, D
2
an
d
D
3
o
f
f
,
(
c)
cu
r
r
en
t l
o
o
p
o
f
th
e
p
r
o
p
o
s
ed
SZSC
in
State2
: D
1
, D
2
an
d
D
3
o
n
; S
1
an
d
S
2
o
f
f
,
an
d
(
d
)
c
u
r
r
en
t lo
o
p
o
f
th
e
p
r
o
p
o
s
ed
S
Z
SC
in
State3
: D
1
, D
2
an
d
D
3
o
n
; S
1
an
d
S
2
o
f
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
a
lysi
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ce
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ce
/q
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a
s
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n
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ce
DC
-
DC
co
n
ve
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ter
s
… (
S
a
p
a
va
t
h
S
r
ee
n
u
)
23
(e
)
Fig
u
r
e
6
.
Op
e
r
atin
g
s
tates o
f
S
Z
SC
; (
e)
th
e
p
r
o
p
o
s
ed
SZSC
's
cu
r
r
en
t l
o
o
p
i
n
State
4
is
as: S
1
, S
2
, D
1
, D
2
,
an
d
D
3
ar
e
all
tu
r
n
ed
o
f
f
(
co
n
tin
u
e
)
RE
F
E
R
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NC
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S
[
1
]
N
.
Jav
a
i
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2
]
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.
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y
o
a
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,
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2
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0
.
[
3
]
S
.
B
o
g
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m
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A
g
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rn
a
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a
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o
u
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a
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o
f
Ap
p
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(
I
J
AP
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,
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3
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v
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[
4
]
W
.
T
u
sh
a
r
,
J
.
A
.
Zh
a
n
g
,
C
.
Y
u
e
n
,
D
.
B
.
S
mi
t
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,
a
n
d
N
.
U
l
H
a
ssa
n
,
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M
a
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me
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o
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R
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w
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En
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a
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d
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a
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o
l
l
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S
mar
t
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r
i
d
,
”
I
EEE
Ac
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,
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4
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C
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2
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6
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5
9
2
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0
9
.
[
5
]
G
.
Z
h
a
n
g
,
B
.
Zh
a
n
g
,
Z.
L
i
,
D
.
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u
,
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a
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,
a
n
d
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.
A
.
H
a
l
a
n
g
,
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3
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v
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,
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T
ra
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s
a
c
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d
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st
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a
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El
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,
v
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.
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2
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1
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p
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7
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–
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,
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a
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2
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/
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2
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4
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2
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6
9
9
0
.
[
6
]
B
.
A
x
e
l
r
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,
Y
.
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k
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v
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Tr
a
n
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o
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merl
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y
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M
C
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,
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I
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T
ra
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:
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.
[
7
]
R.
-
J.
W
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i
,
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.
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.
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,
R
.
-
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[
8
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.
[
9
]
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,
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