I
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Adv
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p
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lt
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ste
m
s.
A
m
o
d
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e
d
sin
u
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l
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m
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iq
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se
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it
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h
e
si
m
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latio
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re
su
lt
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tain
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d
in
term
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d
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ly
sis
c
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firms
imp
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m
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t
in
v
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th
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su
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d
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to
p
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.
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e
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x
p
e
rime
n
tal
re
su
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ts
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sim
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latio
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w
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s
:
Sev
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lev
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Sin
g
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p
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ase
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lar
p
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to
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ltaic
s
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Z
SI
T
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s
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d
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CC B
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C
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Sar
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Dep
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Ar
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c
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i
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1.
I
NT
RO
D
UCT
I
O
N
Dis
tr
ib
u
ted
en
er
g
y
s
y
s
tem
s
e
m
p
lo
y
in
g
f
u
el
ce
ll
an
d
PV
ar
r
ay
ca
n
ea
s
ily
co
n
f
ig
u
r
e
with
d
if
f
er
e
n
t
to
p
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lo
g
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o
f
p
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c
o
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v
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s
i
o
n
u
n
its
f
o
r
ex
am
p
le
m
u
ltil
ev
el
in
v
er
ter
s
a
r
e
im
p
lem
e
n
te
d
f
o
r
elec
tr
if
icatio
n
o
v
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th
e
y
ea
r
s
.
R
ec
en
t a
d
v
an
c
em
en
ts
o
f
m
u
ltil
ev
el
in
v
er
ter
s
eith
er
in
th
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o
p
er
atin
g
p
r
i
n
cip
le
an
d
m
o
d
u
latio
n
s
tr
ateg
y
f
o
cu
s
ed
f
o
r
in
d
u
s
tr
ial
ap
p
licatio
n
s
an
d
u
tili
ty
s
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tem
s
ar
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d
t
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b
e
in
ter
esti
n
g
a
n
d
g
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win
g
f
o
r
th
e
ap
p
licato
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s
o
f
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ea
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p
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co
m
p
en
s
atio
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,
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en
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b
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n
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r
g
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s
y
s
tem
p
o
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s
io
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,
r
eso
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cir
c
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it,
UPS p
o
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co
n
v
er
s
io
n
u
n
it a
n
d
elec
tr
ic
-
d
r
iv
e
v
eh
icles [
1
]
-
[
6
]
.
Mu
lti
-
lev
el
in
v
er
ter
s
ar
e
d
esig
n
ed
with
p
h
o
to
v
o
ltaic
v
o
lta
g
e
s
o
u
r
ce
,
s
em
ico
n
d
u
cto
r
s
witch
in
g
d
e
v
ice
an
d
ca
p
ac
ito
r
,
an
d
th
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p
e
r
f
o
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m
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ce
an
d
o
u
t
p
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t
ar
e
e
v
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a
te
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b
y
th
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s
tep
.
T
h
e
s
em
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n
d
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s
witch
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ev
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m
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s
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ab
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to
with
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t
an
d
th
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o
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s
u
r
g
e
th
at
o
cc
u
r
s
wh
en
s
witch
in
g
s
witch
es.
T
h
e
m
ain
f
u
n
ctio
n
o
f
m
u
ltil
ev
el
i
n
v
er
ter
s
is
to
c
o
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v
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t
th
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p
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t
o
th
e
d
esire
d
am
o
u
n
t
o
f
ac
p
o
wer
[7
]
,
[
8
]
.
T
h
e
to
p
ic
u
n
d
er
s
tu
d
y
is
ca
s
ca
d
ed
m
u
ltil
ev
el
in
v
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ter
,
wh
ich
is
m
o
d
u
lar
in
n
atu
r
e
an
d
it
ca
n
b
e
co
n
f
ig
u
r
ed
with
m
u
ltip
le
m
o
d
u
les
[
9
]
-
[
1
3
]
.
No
n
-
tr
an
s
f
o
r
m
er
p
o
wer
co
n
v
er
ter
s
ar
e
u
s
ed
f
o
r
th
e
p
u
r
p
o
s
e
o
f
m
ak
i
n
g
s
u
ch
a
s
y
s
tem
l
o
w
co
s
t,
wh
ich
is
th
e
u
n
iq
u
e
f
u
n
ct
io
n
o
f
m
u
l
tilev
el
in
v
er
ter
s
a
r
e
as
d
escr
ib
ed
in
[
1
4
]
-
[
2
0
]
.
Me
r
its
an
d
d
em
e
r
its
o
f
ca
s
ca
d
ed
m
u
lti
-
lev
el
in
v
er
te
r
s
ar
e
d
is
cu
s
s
ed
th
r
o
u
g
h
m
an
y
ap
p
licatio
n
s
in
[
2
1
]
-
[
2
4
]
.
I
n
f
u
s
io
n
o
f
Z
-
s
o
u
r
ce
n
etwo
r
k
in
t
o
th
e
ex
is
tin
g
m
u
l
tilev
el
an
d
o
th
er
i
n
v
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ter
to
p
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lo
g
ies
im
p
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v
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th
e
v
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ltag
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b
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s
tin
g
ca
p
ab
ilit
y
wh
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ca
n
b
e
p
r
ef
er
a
b
ly
u
s
ed
f
o
r
p
h
o
to
v
o
ltaic
s
y
s
tem
s
[
2
5
]
,
[
2
6
]
.
I
n
th
is
p
ap
e
r
,
Z
-
s
o
u
r
ce
C
ascad
ed
H
-
b
r
id
g
e
m
u
lti
-
lev
el
in
v
e
r
ter
with
s
y
m
m
etr
ic
co
n
f
ig
u
r
atio
n
its
s
tead
y
-
s
tate
o
p
er
atio
n
is
d
is
cu
s
s
ed
in
s
ec
tio
n
2
,
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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Ap
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latio
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tech
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3
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Simu
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2.
T
O
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SCRI
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N:
Z
-
SO
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D
M
L
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O
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P
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Fig
u
r
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Fig
u
r
e
2
.
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ic
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[
2
7
]
,
[
2
8
]
.
Fig
u
r
e
1
.
Po
wer
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r
cu
it o
f
a
s
in
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p
h
ase
s
ev
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e
r
ter
Fig
u
r
e
2
.
Ou
t
p
u
t
v
o
ltag
e
wav
e
f
o
r
m
o
f
s
in
g
le
p
h
ase
s
ev
en
lev
el
Z
-
s
o
u
r
ce
ca
s
ca
d
ed
H
-
b
r
id
g
e
in
v
er
ter
T
h
e
p
r
o
p
o
s
ed
s
in
g
le
p
h
ase
s
ev
en
lev
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
Z
-
s
o
u
r
ce
in
v
er
te
r
to
p
o
lo
g
y
is
f
o
r
m
ed
b
y
h
av
in
g
p
h
o
to
v
o
ltaic
ar
r
ay
co
n
n
ec
ted
s
er
ies
in
ter
lin
k
ed
s
in
g
le
p
h
ase
two
lev
el
in
v
er
ter
an
d
its
o
u
tp
u
t
v
o
ltag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
10
,
No
.
1
,
Ma
r
c
h
2
0
2
1
:
60
–
69
62
is
d
ep
en
d
s
o
n
t
h
e
n
u
m
b
e
r
o
f
s
in
g
le
p
h
ase
in
v
er
ter
co
n
n
ec
te
d
in
cir
cu
it.
T
h
e
n
u
m
b
e
r
o
f
o
u
tp
u
t
v
o
ltag
e
le
v
els
(
m
)
in
th
e
p
h
ase
v
o
ltag
e
o
f
s
y
m
m
etr
ical
ca
s
ca
d
ed
ML
I
is
g
i
v
en
b
y
(
1
)
.
=
2
+
1
(
1
)
W
h
er
e,
N
-
n
u
m
b
er
o
f
s
in
g
le
p
h
ase
in
v
er
ter
.
I
n
o
th
er
w
o
r
d
s
,
a
ty
p
ical
ca
s
ca
d
e
ML
I
r
eq
u
i
r
es
a
p
h
o
t
o
v
o
ltaic
ar
r
ay
s
f
o
r
2
+
1
.
I
f
t
h
e
in
v
er
ter
p
h
ase
v
o
ltag
e
s
tep
s
ar
e
ca
lcu
l
ated
as
a
v
alu
e
o
f
q
,
th
e
n
th
e
lin
e
v
o
ltag
e
o
f
th
e
in
v
e
r
ter
is
ca
lcu
lated
as
(
2
)
,
=
2
+
1
(
2
)
an
d
also
,
th
e
s
tep
s
lev
el
f
o
r
th
r
ee
p
h
ase
d
if
f
e
r
en
t ty
p
es o
f
lo
a
d
co
n
n
ec
tio
n
ca
n
b
e
ca
lcu
lted
as
(
3
)
.
=
2
−
1
(
3
)
T
h
e
ac
o
u
tp
u
t
v
o
ltag
e
o
f
each
s
in
g
le
-
p
h
ase
H
-
b
r
id
g
e
in
v
er
t
er
an
d
th
e
to
tal
s
u
m
o
f
o
u
tp
u
t
v
o
ltag
e
(
V
o
)
v
al
u
e
o
f
th
e
m
u
ltil
ev
el
in
v
er
ter
as d
e
ter
m
in
ed
b
y
u
s
in
g
(
4
)
.
=
1
+
2
+
3
(
4
)
T
h
e
ca
s
ca
d
ed
H
-
b
r
id
g
e
m
u
lti
-
lev
el
in
v
er
ter
d
esire
d
s
in
u
s
o
id
a
l o
u
tp
u
t
v
o
ltag
e
ca
n
ca
lcu
late
b
y
u
s
in
g
u
s
in
g
(
5
)
.
=
s
in
(
ω
t
)
(
5
)
T
o
d
esig
n
ca
s
ca
d
ed
m
u
ltil
ev
e
l
in
v
er
ter
r
eq
u
ir
ed
n
u
m
b
er
o
f
s
witch
es
f
o
r
ea
c
h
p
h
ase
o
r
ea
ch
H
-
b
r
id
g
e
ca
n
esti
m
ate
as p
er
(
6
)
.
=
4
(
6
)
T
h
e
o
p
e
r
atin
g
p
r
in
cip
le
o
f
Z
SI
Mo
d
u
le
ca
n
b
e
ex
p
lain
ed
as
f
o
llo
ws.
T
h
e
Z
-
s
o
u
r
ce
i
n
v
er
ter
is
o
p
er
atin
g
at
two
s
tate
o
f
o
p
er
atio
n
s
u
ch
as
s
h
o
o
t
-
th
r
o
u
g
h
a
n
d
n
o
n
-
s
h
o
o
t
-
th
r
o
u
g
h
s
tates.
W
h
en
th
e
in
v
er
ter
is
o
p
er
atin
g
at
s
h
o
o
t
-
th
r
o
u
g
h
s
tate,
th
e
p
h
o
to
v
o
itaic
d
c
o
u
tp
u
t
p
o
wer
is
co
v
er
tin
g
in
to
ac
p
o
wer
an
d
n
o
n
-
s
h
o
o
t
-
th
r
o
u
g
h
s
tates c
o
n
d
itio
n
th
e
p
o
wer
co
n
v
er
s
io
n
is
ze
r
o
b
ec
au
s
e
o
f
d
c
-
lin
k
v
o
ltag
e
is
ze
r
o
.
T
h
e
p
o
wer
b
alan
ce
e
q
u
atio
n
o
f
each
Z
-
s
o
u
r
ce
in
v
e
r
ter
as
(
7
)
.
PN
x
PN
x
(
1
−
)
+
0
x
=
x
a
(
7
)
W
h
er
e,
ν
PN
a
n
d
i
PN
a
r
e
ea
ch
H
-
b
r
id
g
e
in
v
er
ter
in
p
u
t
v
o
ltag
e
an
d
cu
r
r
e
n
t
v
alu
es,
V
a
an
d
i
a
ar
e
each
H
-
b
r
i
d
g
e
in
v
er
ter
o
u
tp
u
t
v
o
ltag
e
an
d
c
u
r
r
en
t
v
al
u
es
an
d
D
is
a
d
u
t
y
r
atio
o
f
t
h
e
Z
-
s
o
u
r
ce
i
n
v
er
ter
.
T
h
e
Z
-
s
o
u
r
ce
in
v
er
ter
o
u
tp
u
t
v
o
ltag
e
is
d
eter
m
in
ed
as
(
8
)
.
ν
=
ν
PN
(
8
)
W
h
er
e
m
d
ef
in
e
d
as M
s
in
ω
t,
M
-
m
o
d
u
latio
n
in
d
ex
.
Fro
m
(
7
)
an
d
(
8
)
,
PN
is
d
ed
u
ce
d
as
(
9
)
.
=
2
(
1
−
)
(
−
(
2
−
)
)
=
+
̃
(
9
)
B
o
th
an
d
̃
af
f
ec
t th
e
m
o
d
u
le
v
ar
iab
les
1
,
2
,
1
an
d
2
.
1
=
1
+
̃
1
2
=
2
+
̃
2
1
=
1
+
̃
1
2
=
2
+
̃
2
(
1
0
)
T
h
e
im
p
ed
a
n
ce
d
esig
n
o
f
Z
SI
n
etwo
r
k
[
2
9
]
is
g
iv
e
n
b
y
(
1
1
)
.
=
2
PV
(
1
−
)
3
&
=
3
8
PV
(
1
−
)
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2
2
5
2
-
8
8
1
4
S
in
g
le
p
h
a
s
e
s
ev
en
leve
l Z
s
o
u
r
ce
ca
s
ca
d
ed
H
b
r
id
g
e
i
n
ve
r
ter fo
r
p
h
o
to
vo
lta
ic
…
(
K
.
M
.
V
en
ka
ta
ch
a
la
m
)
63
T
s
,
I
m
,
an
d
ar
e
th
e
Switcin
g
ti
m
e
p
er
io
d
,
m
a
x
im
u
m
p
h
ae
cu
r
r
en
t
an
d
an
g
le
b
etwe
en
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
o
n
in
v
e
r
ter
o
u
tp
u
t.
an
d
ar
e
v
o
ltag
e
an
d
c
u
r
r
e
n
t r
ip
p
le
f
ac
to
r
s
.
3.
M
O
DUL
AT
I
O
N
T
E
CH
NIQ
UE
Ph
ase
s
h
if
ted
s
in
u
s
o
id
al
PW
M
s
witch
in
g
s
tr
ateg
y
ca
n
b
e
wid
ely
ad
o
p
ted
f
o
r
ca
s
ca
d
ed
Z
SI
wh
ich
is
b
ased
o
n
class
ical
s
in
u
s
o
id
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
.
Her
e
t
h
e
tr
ian
g
u
lar
s
ig
n
al
is
tak
en
as
th
e
ca
r
r
ier
an
d
th
e
s
ig
n
al
is
co
m
p
ar
ed
to
th
e
s
in
u
s
o
id
al
m
o
d
u
latin
g
s
ig
n
al.
T
h
e
f
r
eq
u
e
n
cy
v
alu
e
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
in
v
er
ter
d
ep
en
d
s
o
n
t
h
ese
two
s
ig
n
als.
T
h
e
o
u
tp
u
t
f
r
e
q
u
e
n
cy
v
al
u
e
o
f
th
e
in
v
er
ter
ca
n
b
e
ch
a
n
g
ed
to
th
e
d
esire
d
lev
el
b
y
ch
an
g
i
n
g
t
h
e
s
ig
n
al
f
r
eq
u
en
c
y
o
f
th
e
tr
ian
g
u
lar
ca
r
r
ier
.
T
h
e
tr
ian
g
u
lar
ca
r
r
ier
s
ig
n
al
f
r
eq
u
e
n
cy
is
tak
en
as a
n
o
d
d
m
u
ltip
lier
f
o
r
t
h
e
elim
in
atio
n
o
f
ev
en
h
ar
m
o
n
ics at
th
e
o
u
tp
u
t o
f
th
e
i
n
v
er
ter
.
T
h
e
tr
ian
g
u
lar
ca
r
r
ier
s
ig
n
al
is
(
N
c)
r
esp
o
n
s
ib
le
f
o
r
th
e
s
witch
in
g
lo
s
s
es
o
f
each
in
v
er
ter
.
So
,
b
y
s
elec
tin
g
th
e
r
ig
h
t
tr
ian
g
u
lar
c
ar
r
ier
it
is
p
o
s
s
ib
le
to
g
et
ef
f
e
ctiv
e
in
v
er
ter
o
u
tp
u
t
v
o
ltag
e
with
lo
w
co
n
v
er
s
io
n
lo
s
s
es.
T
h
e
n
u
m
b
er
o
f
ca
r
r
ier
s
,
n
c
ess
en
tial to
g
en
er
ate
m
-
lev
el
in
v
er
ter
o
u
tp
u
t is g
iv
e
n
b
y
n
c
=
m
–
1
(
1
2
)
All
th
e
tr
ian
g
u
lar
ca
r
r
ier
s
ig
n
als
h
av
e
th
e
s
am
e
p
ea
k
-
p
e
ak
am
p
litu
d
e
an
d
f
r
e
q
u
en
c
y
wh
ich
ar
e
d
esig
n
ated
as
A
c
an
d
f
c
r
esp
e
ctiv
ely
,
wh
er
ea
s
th
e
s
in
g
le
s
in
u
s
o
id
al
r
ef
er
en
ce
o
r
m
o
d
u
lati
n
g
s
ig
n
al
h
as
p
ea
k
-
p
ea
k
am
p
litu
d
e
o
f
A
m
a
n
d
ca
r
r
ier
f
r
eq
u
e
n
cy
f
m
.
Sin
u
s
o
id
al
s
ig
n
al
as c
o
n
s
id
er
ed
as a
r
ef
er
e
n
ce
s
ig
n
al
is
alwa
y
s
m
atch
ed
with
th
e
ca
r
r
ier
s
ig
a
n
o
f
tr
ian
g
u
lar
s
ig
n
al.
W
h
en
th
e
s
in
u
s
o
id
al
s
ig
n
al
am
p
litu
d
e
is
m
o
r
e
th
an
th
e
tr
ian
g
u
lar
s
ig
n
al
am
p
litu
d
e,
t
h
e
s
with
ch
in
g
p
u
ls
e
is
p
r
o
d
u
ce
d
an
d
it’s g
i
v
en
to
t
h
e
in
v
er
te
r
g
ate
s
ig
n
al.
T
h
e
im
p
o
r
tan
t
f
ac
t
o
r
s
o
f
th
e
m
o
d
u
latio
n
p
r
o
ce
d
u
r
e
[
3
0
]
-
[
3
6
]
ar
e
t
h
e
r
atio
o
f
th
e
ca
r
r
ier
a
n
d
r
ef
er
en
ce
f
r
eq
u
e
n
cy
k
=f
c
/f
m
,
w
h
er
e,
f
c
a
n
d
f
m
ar
e
f
r
eq
u
en
cy
o
f
th
e
tr
ia
n
g
u
lar
an
d
th
e
s
in
u
s
o
id
al
s
ig
n
al,
r
esp
ec
tiv
ely
.
T
h
e
m
o
d
u
latio
n
in
d
e
x
M
=
A
m
/
(
m
'
*
A
c
)
,
m
'
=
(
m
-
1
)
/2
.
W
h
er
e
A
m,
A
c
a
n
d
m
a
r
e
th
e
m
o
d
u
lati
n
g
s
ig
n
al
am
p
litu
ted
,
p
ea
k
-
p
ea
k
tr
ian
g
u
lar
s
ig
n
al
am
p
litu
d
e
an
d
in
v
er
ter
o
u
tp
u
t
lev
el,
r
esp
ec
tiv
ely
.
T
r
ad
it
io
n
ally
,
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
in
v
e
r
ter
ca
n
b
e
ex
p
r
ess
in
Fo
u
r
ier
s
er
ies ex
p
a
n
s
io
n
as
(
1
3
)
.
V
pn
(
ω
t)
=
∑
(
+
)
∞
=
1
(
1
3
)
W
h
en
th
e
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M
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AND
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h
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m
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
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1
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I
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Ap
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
10
,
No
.
1
,
Ma
r
c
h
2
0
2
1
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–
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66
5.
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r
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.
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es
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tiv
ely
.
RE
F
E
R
E
NC
E
S
[1
]
S
a
m
ir
Ko
u
ro
,
M
a
ri
u
sz
M
a
li
n
o
ws
k
i,
K.
G
o
p
a
k
u
m
a
r,
Jo
se
p
P
o
u
,
Le
o
p
o
ld
o
G
.
F
ra
n
q
u
e
lo
,
Bin
Wu
,
Jo
se
Ro
d
rig
u
e
z
,
M
a
rc
e
lo
A.
P
é
re
z
,
a
n
d
Jo
se
I.
Le
o
n
,
“
Re
c
e
n
t
Ad
v
a
n
c
e
s a
n
d
I
n
d
u
stri
a
l
Ap
p
li
c
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ti
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M
u
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Co
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v
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rters
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IEE
E
T
ra
n
sa
c
ti
o
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s
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In
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stri
a
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El
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tr
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ics
,
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5
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p
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2
5
5
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5
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0
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0
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0
.
[2
]
F
.
Z.
P
e
n
g
a
n
d
J.
S
.
Lai,
M
u
lt
il
e
v
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sc
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d
e
v
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g
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in
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C
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rc
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3
7
1
2
6
(5
6
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5
),
Ap
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2
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1
.
[3
]
Ha
n
k
e
u
n
Ja
n
g
,
M
u
lt
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e
v
e
l
in
v
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rt
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sin
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c
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sc
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g
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ra
ti
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me
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tate
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ten
t
8
0
1
8
3
3
1
,
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p
2
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1
.
[4
]
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v
in
P
.
Ke
p
ley
,
Ca
sc
a
d
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d
mu
lt
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e
v
e
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in
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me
th
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to
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2
0
1
3
0
2
8
5
4
5
7
,
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t
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3
.
[5
]
Jin
g
b
o
Li
u
,
Th
o
m
a
s
No
n
d
a
h
l,
Z
h
o
n
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a
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Na
v
id
Zarg
a
ri,
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a
sc
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(CHB)
i
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sh
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wit
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0
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A
1
,
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.
[6
]
G
n
a
n
a
P
ra
k
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sh
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,
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lam
u
ru
g
a
n
M
,
Um
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k
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,
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Ne
w
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w
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th
Re
d
u
c
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d
Nu
m
b
e
r
o
f
S
witch
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s,”
In
ter
n
a
ti
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n
a
l
J
o
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n
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l
o
f
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we
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Dr
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5
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o
.
4
,
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p
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3
-
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0
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[7
]
Jo
sé
Ro
d
rí
g
u
e
z
,
Jih
-
S
h
e
n
g
La
a
n
d
F
a
n
g
Zh
e
n
g
P
e
n
g
,
“
M
u
lt
il
e
v
e
l
In
v
e
rters
:
A
S
u
r
v
e
y
o
f
To
p
o
l
o
g
i
e
s,
Co
n
tro
ls,
a
n
d
Ap
p
li
c
a
ti
o
n
s,”
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
v
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l.
4
9
,
n
o
.
4
,
p
p
.
7
2
4
-
7
3
8
,
2
0
0
2
.
[8
]
Jih
-
S
h
e
n
g
Lai
a
n
d
F
a
n
g
Zh
e
n
g
P
e
n
g
,
“
M
u
lt
il
e
v
e
l
Co
n
v
e
rters
-
A
Ne
w
Bre
e
d
o
f
P
o
we
r
Co
n
v
e
rters
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stry
A
p
p
li
c
a
ti
o
n
s
,
v
o
l.
3
2
,
n
o
.
3
,
p
p
.
5
0
9
-
5
1
7
,
1
9
9
6
.
[9
]
Ke
it
h
Co
rz
in
e
a
n
d
Ya
k
o
v
F
a
m
il
i
a
n
t,
“
A
Ne
w
Ca
sc
a
d
e
d
M
u
lt
il
e
v
e
l
H
Brid
g
e
Driv
e
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l.
1
7
,
n
o
.
1
,
p
p
.
1
2
5
-
1
3
1
,
2
0
0
2
.
[1
0
]
Ke
it
h
A.
Co
rz
i
n
e
,
M
i
k
e
W.
W
iele
b
sk
i,
F
a
n
g
Z
.
P
e
n
g
,
a
n
d
Ji
n
Wa
n
g
,
“
C
o
n
tr
o
l
o
f
Ca
sc
a
d
e
d
M
u
l
ti
l
e
v
e
l
In
v
e
rters
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
le
c
tro
n
ics
,
v
o
l.
1
9
,
n
o
.
3
,
p
p
.
7
3
2
-
7
3
8
,
2
0
0
4
.
[1
1
]
M
a
riu
sz
M
a
li
n
o
ws
k
i
,
K.
G
o
p
a
k
u
m
a
r,
Jo
se
Ro
d
rig
u
e
z
a
n
d
M
a
rc
e
lo
A.
P
é
re
z
,
“
A
S
u
r
v
e
y
o
n
Ca
sc
a
d
e
d
M
u
lt
il
e
v
e
l
In
v
e
rters
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
In
d
u
stria
l
El
e
c
tro
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2
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b
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a
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li
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v
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[1
3
]
S
u
re
sh
Na
tara
jan
,
R.
S
a
m
u
e
l
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j
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sh
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b
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[1
4
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S
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id
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.
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ies
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m
s,”
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n
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ti
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Evaluation Warning : The document was created with Spire.PDF for Python.
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2
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I
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t J Ad
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Ap
p
l Sci
,
Vo
l.
10
,
No
.
1
,
Ma
r
c
h
2
0
2
1
:
60
–
69
68
[1
5
]
Re
m
u
s
Teo
d
o
re
sc
u
,
F
re
d
e
Blaa
b
jerg
,
Jo
h
n
.
K.
P
e
d
e
rse
n
,
Ek
re
m
Ce
n
g
e
lci,
a
n
d
P
ra
sa
d
N.
En
j
e
ti
,
“
M
u
lt
il
e
v
e
l
In
v
e
rt
e
r
b
y
Ca
sc
a
d
in
g
In
d
u
strial
VSI,
”
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ti
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4
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.
8
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8
,
2
0
0
2
.
[1
6
]
Leo
n
M
.
T
o
l
b
e
rt,
F
a
n
g
Zh
e
n
g
P
e
n
g
,
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m
Cu
n
n
y
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g
h
a
m
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n
d
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h
n
N.
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ias
so
n
,
“
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a
r
g
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lan
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tr
o
l
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c
h
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m
e
s
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e
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u
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l
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n
v
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n
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b
ri
d
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e
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tri
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h
icle
s
,
”
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ti
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d
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stri
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l
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ics
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l
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4
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o
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p
p
.
1
0
5
8
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0
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4
,
2
0
0
2
.
[1
7
]
P
o
h
C
h
ian
g
Lo
h
,
Do
n
a
ld
G
ra
h
a
m
e
Ho
lme
s,
a
n
d
Th
o
m
a
s
A.
Li
p
o
,
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Im
p
lem
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tatio
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a
n
d
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n
tro
l
o
f
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u
te
d
P
WM
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sc
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v
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with
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ima
l
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rm
o
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ic
D
isto
rti
o
n
a
n
d
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o
m
m
o
n
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o
d
e
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lt
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g
e
,
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1
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p
.
9
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9
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[1
8
]
Jo
sé
Ro
d
r
íg
u
e
z
,
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teffe
n
Be
rn
e
t,
Bin
Wu
,
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g
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o
n
tt
a
n
d
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a
m
ir
Ko
u
ro
,
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u
lt
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v
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l
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lt
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e
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m
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lt
a
g
e
Dri
v
e
s
,”
IEE
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T
ra
n
s
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ti
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n
I
n
d
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stria
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l.
54
,
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p
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5
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2
0
0
7
.
[1
9
]
E.
Vill
a
n
u
e
v
a
,
P
.
C
o
rre
a
,
J.
Ro
d
rig
u
e
z
,
a
n
d
M
.
P
a
c
a
s,
“
Co
n
tr
o
l
o
f
a
sin
g
le
p
h
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se
c
a
sc
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d
e
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lt
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d
c
o
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n
e
c
ted
p
h
o
to
v
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lt
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ic
sy
ste
m
s,”
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T
ra
n
sa
c
ti
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,
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l.
5
6
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o
.
1
1
,
pp.
4
3
9
9
-
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4
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6
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9
.
[2
0
]
Ha
it
h
a
m
Ab
u
Ru
b
,
Jo
a
c
h
im
Ho
lt
z
,
Jo
se
Ro
d
rig
u
e
z
,
a
n
d
G
e
Ba
o
m
in
g
,
“
M
e
d
iu
m
-
Vo
lt
a
g
e
M
u
lt
il
e
v
e
l
Co
n
v
e
rters
—
S
tate
o
f
t
h
e
Art,
Ch
a
ll
e
n
g
e
s,
a
n
d
Re
q
u
irem
e
n
ts
in
In
d
u
strial
Ap
p
li
c
a
ti
o
n
s
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
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stri
a
l
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e
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ics
,
v
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l.
5
7
,
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o
.
8
,
p
p
.
2
5
8
1
-
2
5
9
6
,
2
0
1
0
.
[2
1
]
Y.M
.
P
a
rk
,
J.Y.
Y
o
o
,
a
n
d
S
.
B
.
Le
e
,
“
P
ra
c
ti
c
a
l
imp
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e
n
tatio
n
o
f
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WM
sy
n
c
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ro
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iza
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n
d
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h
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se
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se
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n
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sta
n
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rd
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o
m
m
u
n
ica
ti
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n
p
r
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to
c
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l
,
”
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ra
n
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ti
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n
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d
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ti
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n
s
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l.
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2
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p
p
.
6
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4
3
,
2
0
0
8
.
[2
2
]
S
.
Va
z
q
u
e
z
,
J.
I
.
Leo
n
,
L.
G
.
F
r
a
n
q
u
e
l
o
,
J.
J
.
P
a
d
il
la
a
n
d
J.
M
.
Ca
rra
sc
o
,
“
DC
v
o
lt
a
g
e
ra
ti
o
c
o
n
t
ro
l
stra
teg
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fo
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m
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lt
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l
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sc
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o
n
v
e
rte
rs
fe
d
with
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si
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g
le
d
c
so
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rc
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,
”
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ra
n
s
a
c
ti
o
n
s
o
n
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d
u
stri
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l
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t
ro
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ics
,
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l.
5
6
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o
.
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,
p
p
.
2
5
1
3
-
2
5
2
1
,
2
0
0
9
.
[2
3
]
F
a
rid
Kh
o
u
c
h
a
,
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o
u
m
ia
M
o
u
n
a
Lag
o
u
n
,
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h
o
u
d
ir
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a
ro
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a
n
i,
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d
e
laz
iz
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e
lo
u
i
a
n
d
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o
h
a
m
e
d
El
Ha
c
h
e
m
i
Be
n
b
o
u
z
id
,
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b
rid
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sc
a
d
e
d
H
Brid
g
e
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u
lt
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lev
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l
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n
v
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d
u
c
ti
o
n
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o
to
r
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e
Dire
c
t
T
o
r
q
u
e
C
o
n
tr
o
l
fo
r
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to
m
o
ti
v
e
Ap
p
li
c
a
ti
o
n
s,”
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E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stri
a
l
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e
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tr
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n
ics
,
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l
.
5
7
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o
.
3
,
p
p
.
8
9
2
-
8
9
9
,
2
0
1
0
.
[2
4
]
B.
Dio
n
g
,
H.
S
e
p
a
h
v
a
n
d
,
a
n
d
K
.
A.
C
o
rz
in
e
,
“
Ha
rm
o
n
ic
d
isto
r
ti
o
n
o
p
ti
m
iza
ti
o
n
o
f
c
a
sc
a
d
e
d
H
-
b
rid
g
e
in
v
e
rters
c
o
n
sid
e
ri
n
g
d
e
v
ice
v
o
lt
a
g
e
d
r
o
p
s
a
n
d
n
o
n
-
in
teg
e
r
d
c
v
o
lt
a
g
e
ra
ti
o
s,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
str
ia
l
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e
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tro
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ics
,
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l.
6
0
,
n
o
.
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,
p
p
.
3
1
0
6
-
3
1
1
4
,
2
0
1
3
.
[2
5
]
M
o
h
a
m
a
d
Re
z
a
Ba
n
a
e
i,
Ali
Re
z
a
De
h
g
h
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n
z
a
d
e
h
,
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F
a
z
e
l
a
n
d
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d
a
Ba
g
h
b
a
n
y
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k
o
u
e
i,
“
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witch
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n
g
a
lg
o
rit
h
m
f
o
r
sin
g
le
Z
so
u
rc
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b
o
o
st
m
u
lt
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lev
e
l
in
v
e
rter
with
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b
il
it
y
o
f
v
o
lt
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g
e
c
o
n
tr
o
l”,
IET
P
o
we
r
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e
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tro
n
ics
,
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o
l.
6
,
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o
.
7
,
p
p
.
1
3
5
0
-
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3
5
9
,
2
0
1
3
.
[2
6
]
V.
S
a
ra
v
a
n
a
n
,
M
.
Ara
v
i
n
d
a
n
,
V.
Ba
a
laji,
M
.
Aru
m
u
g
a
m
,
“
Ex
p
e
r
ime
n
tal
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rifi
c
a
ti
o
n
o
f
S
i
n
g
le
P
h
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se
Z
S
o
u
rc
e
In
v
e
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f
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r
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h
o
t
o
v
o
lt
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ic
A
p
p
li
c
a
t
io
n
s,”
In
ter
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
P
o
we
r
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e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
,
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l.
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,
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o
.
2
,
p
p
.
6
9
8
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7
0
3
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2
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.
[2
7
]
Y.
Li
u
,
B
.
G
e
,
H.
Ab
u
Ru
b
a
n
d
F
.
Z.
P
e
n
g
,
“
An
e
ffe
c
ti
v
e
c
o
n
tr
o
l
m
e
th
o
d
f
o
r
q
u
a
si
Z
so
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rc
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a
sc
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d
e
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m
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lt
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l
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a
se
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g
rid
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g
le
p
h
a
se
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h
o
t
o
v
o
lt
a
ic
p
o
we
r
sy
ste
m
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stri
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l
I
n
fo
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t
ics
,
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o
l.
10,
n
o
.
1
,
p
p
.
3
9
9
-
4
0
7
,
2
0
1
4
.
[2
8
]
R.
P
a
lan
isa
m
y
,
K.
Vijay
a
k
u
m
a
r,
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a
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imu
m
Bo
o
st
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o
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tro
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lev
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o
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sc
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g
e
In
v
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rter,”
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ter
n
a
t
io
n
a
l
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o
u
rn
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o
f
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o
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r E
lec
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n
ics
a
n
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Dr
ive
S
y
ste
m
,
v
o
l.
8
,
n
o
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2
,
p
p
.
7
3
9
-
7
4
6
,
2
0
1
7
.
[2
9
]
Do
n
g
se
n
S
u
n
,
Ba
o
m
in
g
G
e
,
Xin
g
y
u
Ya
n
,
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q
ian
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o
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h
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n
g
,
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u
sh
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n
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u
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it
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m
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u
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b
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h
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r
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n
Bra
h
im
a
n
d
F
a
n
g
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h
e
n
g
P
e
n
g
,
“
M
o
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li
n
g
,
Im
p
e
d
a
n
c
e
De
sig
n
,
a
n
d
Eff
icie
n
c
y
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n
a
ly
sis
o
f
Q
u
a
si
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o
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rc
e
M
o
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le
in
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sc
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v
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h
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to
v
o
l
t
a
ic
P
o
we
r
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y
ste
m
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stri
a
l
El
e
c
tro
n
ics
,
v
o
l.
6
1
,
n
o
.
1
1
,
pp.
6
1
0
8
-
6
1
1
7
,
2
0
1
4
.
[3
0
]
Ja
v
ier
Ch
a
v
a
rría,
Do
m
i
n
g
o
Biel,
F
ra
n
c
e
sc
G
u
in
jo
a
n
,
Ca
rl
o
s
M
e
z
a
a
n
d
Ju
a
n
J.
Ne
g
r
o
n
i
,
“
En
e
r
g
y
Ba
l
a
n
c
e
Co
n
tr
o
l
o
f
P
V
Ca
sc
a
d
e
d
M
u
lt
il
e
v
e
l
G
r
id
Co
n
n
e
c
ted
In
v
e
rters
Un
d
e
r
Lev
e
l
S
h
ift
e
d
a
n
d
P
h
a
se
S
h
ift
e
d
P
WM
s,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stri
a
l
El
e
c
tr
o
n
ics
,
v
o
l
.
6
0
,
n
o
.
1
,
p
p
.
9
8
-
1
1
1
,
2
0
1
3
.
[3
1
]
Leo
n
M
.
T
o
l
b
e
rt,
F
a
n
g
Zh
e
n
g
P
e
n
g
,
Th
o
m
a
s
G
.
Ha
b
e
tl
e
r,
“
M
u
lt
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e
v
e
l
P
WM
M
e
th
o
d
s
a
t
Lo
w
M
o
d
u
latio
n
I
n
d
ice
s”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
le
c
tro
n
ics
,
v
o
l.
1
5
,
n
o
.
4
,
p
p
.
7
1
9
-
7
2
5
,
2
0
0
0
.
[3
2
]
S
iri
ro
j
S
ir
isu
k
p
ra
se
rt,
Ji
h
-
S
h
e
n
g
Lai,
Ti
a
n
-
Hu
a
Li
u
,
“
Op
ti
m
u
m
Ha
rm
o
n
ic
Re
d
u
c
ti
o
n
Wi
t
h
a
Wi
d
e
Ra
n
g
e
o
f
M
o
d
u
latio
n
In
d
e
x
e
s
f
o
r
M
u
lt
il
e
v
e
l
Co
n
v
e
rters
,
”
IEE
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T
ra
n
s
a
c
ti
o
n
s
o
n
In
d
u
stri
a
l
El
e
c
tro
n
ics
,
v
o
l.
4
9
,
n
o
.
4
,
pp
.
875
-
8
8
1
,
2
0
0
2
.
[3
3
]
Zh
o
n
g
Du
,
Leo
n
M
.
To
l
b
e
rt,
Bu
r
a
k
Oz
p
in
e
c
i,
a
n
d
Jo
h
n
N.
C
h
ias
so
n
,
“
F
u
n
d
a
m
e
n
tal
F
re
q
u
e
n
c
y
S
wit
c
h
in
g
S
trate
g
ies
o
f
a
S
e
v
e
n
Lev
e
l
H
y
b
ri
d
Ca
sc
a
d
e
d
H
Brid
g
e
M
u
lt
il
e
v
e
l
In
v
e
rter,”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
Po
we
r
El
e
c
tro
n
ics
,
v
o
l
.
2
4
,
n
o
.
1
,
p
p
.
25
-
3
3
,
2
0
0
9
.
[3
4
]
Ho
ss
e
in
S
e
p
a
h
v
a
n
d
,
Ji
n
g
s
h
e
n
g
L
i
a
o
,
M
e
h
d
i
F
e
rd
o
ws
i
,
“
In
v
e
stig
a
t
i
o
n
o
n
Ca
p
a
c
it
o
r
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lt
a
g
e
Re
g
u
lati
o
n
i
n
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sc
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d
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d
H
Brid
g
e
M
u
lt
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v
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l
Co
n
v
e
rters
Wi
t
h
F
u
n
d
a
m
e
n
tal
F
re
q
u
e
n
c
y
S
witch
in
g
,
”
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
I
n
d
u
stria
l
El
e
c
tro
n
ic
s
,
v
o
l.
5
8
,
n
o
.
1
1
,
pp.
5
1
0
2
-
5
1
1
1
,
2
0
1
1
.
[3
5
]
Vin
c
e
n
t
Ro
b
e
rg
e
,
M
o
h
a
m
m
e
d
T
a
rb
o
u
c
h
i,
a
n
d
F
ra
n
c
is
Ok
o
u
,
“
S
tr
a
teg
ies
to
Ac
c
e
lera
te
Ha
rm
o
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ic
M
in
imiz
a
ti
o
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i
n
M
u
lt
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I
n
v
e
rters
Us
i
n
g
a
P
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r
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ll
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l
G
e
n
e
ti
c
Alg
o
rit
h
m
o
n
G
ra
p
h
ica
l
P
ro
c
e
ss
in
g
Un
i
t
,”
IE
EE
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r E
lec
tro
n
ics
,
v
o
l
.
2
9
,
n
o
.
1
0
,
pp
.
5
0
8
7
-
5
0
9
0
,
2
0
1
4
.
[3
6
]
Ra
jas
e
k
a
r
S
e
lv
a
m
u
th
u
k
u
m
a
ra
n
,
Ab
h
ish
e
k
G
a
rg
,
a
n
d
Ra
jes
h
G
u
p
ta,
“
Hy
b
ri
d
M
u
lt
ica
rrier
M
o
d
u
la
ti
o
n
to
Re
d
u
c
e
Lea
k
a
g
e
Cu
rre
n
t
in
a
Tran
sfo
rm
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rles
s
Ca
sc
a
d
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d
M
u
lt
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e
l
I
n
v
e
rte
r
fo
r
P
h
o
to
v
o
l
taic
S
y
ste
m
s
,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r E
lec
tro
n
ics
,
v
o
l.
3
0
,
n
o
.
4
,
pp
.
1
7
7
9
-
1
7
8
3
,
2
0
1
5
.
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69
B
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RAP
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AUTH
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r.
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tac
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Un
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