I
nte
rna
t
io
na
l J
o
urna
l o
f
Appl
ied P
o
w
er
E
ng
ineering
(
I
J
AP
E
)
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
,
p
p
.
7
1
2
~
7
2
1
I
SS
N:
2252
-
8792
,
DOI
:
1
0
.
1
1
5
9
1
/
i
j
ap
e
.
v
1
4
.
i
3
.
pp
712
-
721
712
J
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th
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in
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rter
(V
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h
a
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th
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s.
In
th
is
p
a
p
e
r,
a
n
e
w
c
o
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f
ig
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ra
ti
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o
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m
u
lt
il
e
v
e
l
V
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I
is
in
tr
o
d
u
c
e
d
.
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is
c
o
n
stru
c
ted
o
f
a
u
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d
irec
ti
o
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a
l
v
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lt
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g
e
su
p
p
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y
h
a
v
in
g
15
-
n
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z
e
ro
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a
n
d
f
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in
g
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sin
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-
p
h
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se
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e
q
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w
it
h
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n
e
x
tra
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w
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ircu
it
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e
o
u
t
p
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t
v
o
lt
a
g
e
o
f
th
is
c
o
n
f
ig
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ra
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h
a
s
3
1
d
if
f
e
r
e
n
t
v
o
lt
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g
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lev
e
ls
f
o
ll
o
w
in
g
a
sin
u
so
i
d
a
l
p
a
th
.
T
h
e
u
n
id
irec
ti
o
n
a
l
v
o
lt
a
g
e
su
p
p
ly
is
b
u
il
t
o
f
e
ig
h
t
so
li
d
-
sta
te
sw
it
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h
in
g
d
e
v
ice
s
a
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d
f
o
u
r
b
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a
ry
we
ig
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ted
DC
v
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lt
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g
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so
u
rc
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s,
w
h
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a
re
re
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e
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b
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sin
g
a
p
p
ro
p
riate
so
lar
p
a
n
e
ls.
T
h
e
sim
u
latio
n
re
su
lt
s
o
f
th
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in
tro
d
u
c
e
d
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o
n
f
ig
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ra
ti
o
n
h
a
v
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v
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led
a
l
m
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st
sin
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id
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tp
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v
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a
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in
d
u
c
ti
v
e
a
n
d
re
sistiv
e
a
p
p
li
a
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s.
T
h
e
n
u
m
b
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r
o
f
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m
p
lo
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d
sw
it
c
h
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g
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e
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s
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l
y
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d
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d
c
o
m
p
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d
to
a
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ti
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a
l
m
u
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v
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l
V
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I.
No
h
a
rm
o
n
ic
re
d
u
c
ti
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c
ir
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trad
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p
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lse
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th
m
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u
latio
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tec
h
n
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e
is
e
m
p
lo
y
e
d
in
t
h
e
c
u
rre
n
t
d
e
sig
n
.
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h
is
sy
ste
m
is
d
e
sig
n
e
d
a
n
d
tes
ted
o
n
P
S
p
ice
.
K
ey
w
o
r
d
s
:
Har
m
o
n
ic
r
ed
u
ctio
n
Mu
ltil
e
v
el
i
n
v
er
ter
P
o
w
er
co
n
v
er
s
io
n
R
en
e
w
ab
le
e
n
er
g
y
Vo
ltag
e
s
o
u
r
ce
i
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
:
A
b
d
u
l
k
ar
ee
m
Mo
k
i
f
Ob
ais
Dep
ar
t
m
en
t o
f
B
io
m
ed
ical
E
n
g
in
ee
r
i
n
g
,
Un
i
v
er
s
i
t
y
o
f
B
ab
y
l
o
n
Al
-
Hi
lla,
B
ab
y
lo
n
,
I
r
aq
E
m
ail:
e
n
g
.
ab
d
u
l.
k
ar
ee
m
@
u
o
b
ab
y
lo
n
.
ed
u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
Ov
er
t
h
e
y
ea
r
s
,
in
v
er
ter
tec
h
n
o
lo
g
ies
h
av
e
ad
v
a
n
ce
d
s
ig
n
i
f
i
ca
n
tl
y
.
M
u
ltil
e
v
el
ap
p
r
o
ac
h
es
h
av
e
s
ee
n
n
o
tab
le
atte
m
p
ts
to
ap
p
r
o
ac
h
s
i
n
u
s
o
id
al
w
a
v
ef
o
r
m
s
f
o
r
o
u
tp
u
t
v
o
lta
g
es
o
r
cu
r
r
e
n
ts
.
A
th
r
ee
-
le
v
el
v
o
ltag
e
s
o
u
r
ce
i
n
v
er
ter
(
V
SI)
an
d
s
tar
-
co
n
n
ec
ted
m
u
ltip
h
ase
s
tato
r
win
d
in
g
s
w
it
h
s
e
g
r
eg
ated
n
e
u
tr
al
p
o
in
ts
w
er
e
u
s
ed
in
[
1
]
to
p
r
o
v
id
e
t
w
o
d
is
tin
c
t
m
u
ltip
h
ase
s
u
p
p
lies
.
Ne
v
er
t
h
eles
s
,
a
m
u
ltil
a
y
er
V
SI
w
as
co
n
tr
o
lled
u
s
i
n
g
a
m
et
h
o
d
ca
lled
p
h
ase
d
is
p
o
s
iti
o
n
s
w
itc
h
i
n
g
f
r
eq
u
e
n
c
y
o
p
ti
m
u
m
p
u
ls
e
w
id
t
h
m
o
d
u
latio
n
(
P
D
-
SF
O
P
W
M)
to
g
en
er
ate
t
h
r
ee
-
p
h
ase,
f
iv
e
-
le
v
el
AC
v
o
lta
g
es
[
2
]
.
T
o
p
r
o
v
id
e
a
m
u
ltil
a
y
er
o
u
tp
u
t
cu
r
r
en
t
[
3
]
u
s
in
g
f
e
w
er
s
w
itc
h
in
g
d
ev
ice
s
,
a
m
u
ltil
e
v
el
cu
r
r
en
t
s
o
u
r
ce
i
n
v
er
ter
(
C
SI)
w
a
s
co
n
tr
o
lled
v
ia
a
m
u
lticar
r
ier
P
W
M
s
w
itc
h
in
g
ap
p
r
o
ac
h
.
Dep
en
d
i
n
g
o
n
h
o
w
t
h
e
p
o
w
er
ce
lls
(
m
o
d
u
les)
i
n
a
ca
s
ca
d
ed
s
tr
u
ct
u
r
e
ar
e
co
n
n
ec
ted
i
n
s
er
ies,
m
u
ltil
e
v
el
co
n
v
er
ter
s
u
s
i
n
g
in
d
i
v
id
u
al
lo
w
-
v
o
lta
g
e
co
m
p
o
n
e
n
t
s
ca
n
w
o
r
k
at
m
e
d
iu
m
o
r
ev
e
n
h
i
g
h
v
o
ltag
e
s
[
4
]
.
Fo
r
n
-
lev
el
v
o
lt
ag
e
s
o
u
r
ce
in
v
er
ter
s
,
a
ti
m
e
d
o
m
ai
n
s
t
u
d
y
w
a
s
u
ti
lized
to
d
eter
m
i
n
e
a
d
ir
ec
t
co
r
r
elatio
n
b
et
w
ee
n
s
a
m
p
l
in
g
,
ca
r
r
ier
,
an
d
f
u
n
d
a
m
en
ta
l
f
r
eq
u
en
cie
s
at
d
if
f
er
en
t
m
o
d
u
l
atio
n
in
d
ice
s
u
s
in
g
s
in
u
s
o
id
al
p
u
l
s
e
w
id
th
m
o
d
u
l
ated
(
SP
W
M)
[
5
]
.
W
h
ile
th
e
in
v
er
ter
's
r
atin
g
n
ee
d
s
to
b
e
th
r
ee
ti
m
e
s
o
r
m
o
r
e
th
an
th
e
ca
p
ac
it
y
o
f
lo
ad
s
w
it
h
h
i
g
h
s
tar
ti
n
g
cu
r
r
en
t
s
,
it
s
h
o
u
ld
b
e
2
5
–
3
0
%
g
r
ea
ter
th
an
th
e
ap
p
lian
ce
s
w
i
th
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
er
E
n
g
I
SS
N:
2252
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8792
Desig
n
o
f a
b
in
a
r
y
w
eig
h
ted
mu
ltil
ev
el
vo
lta
g
e
s
o
u
r
ce
in
ve
r
ter
…
(
A
b
d
u
lka
r
ee
m
Mo
kif
Ob
a
is
)
713
lo
w
s
tar
ti
n
g
c
u
r
r
en
ts
[
6
]
.
Du
e
to
th
eir
in
cr
ea
s
in
g
v
iab
ili
t
y
as
a
tec
h
n
o
lo
g
y
f
o
r
n
u
m
er
o
u
s
a
p
p
licatio
n
s
,
s
u
c
h
a
s
d
r
iv
e
s
y
s
te
m
s
a
n
d
co
n
v
er
s
io
n
in
r
en
e
w
ab
le
e
n
er
g
y
,
m
u
ltil
e
v
el
i
n
v
er
ter
s
h
av
e
attr
ac
ted
a
lo
t
o
f
i
n
ter
est
f
r
o
m
b
o
th
ac
ad
e
m
ia
a
n
d
in
d
u
s
tr
y
[
7
]
,
[
8
]
.
Ma
n
y
s
t
u
d
ies
w
er
e
co
n
d
u
cted
to
d
ev
elo
p
n
e
w
m
u
ltil
e
v
el
i
n
v
er
te
r
to
p
o
lo
g
ies
th
at
w
o
u
ld
ta
k
e
in
t
o
ac
co
u
n
t
t
h
e
ad
v
a
n
ce
m
en
t
s
i
n
s
w
i
tch
i
n
g
d
ev
ice
s
,
w
h
ich
ar
e
t
y
p
icall
y
u
s
ed
in
th
e
co
n
s
tr
u
ctio
n
o
f
i
n
v
er
ter
s
,
t
h
e
s
w
itc
h
i
n
g
f
r
eq
u
en
cie
s
u
s
ed
in
th
e
in
v
er
ter
co
n
tr
o
llin
g
cir
cu
its
,
w
h
ich
ca
u
s
e
elec
tr
o
m
ag
n
etic
in
ter
f
er
en
ce
,
an
d
m
in
i
m
ized
s
w
itc
h
i
n
g
lo
s
s
es
t
h
at
i
n
cr
ea
s
e
o
v
er
all
e
f
f
icie
n
c
y
to
i
m
p
r
o
v
e
t
h
e
in
v
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ter
v
o
ltag
e
p
r
o
f
ile
a
n
d
ef
f
icien
c
y
[
9
]
–
[
13
]
.
T
h
e
d
esig
n
o
f
s
tat
ic
s
y
n
c
h
r
o
n
o
u
s
co
m
p
e
n
s
a
to
r
s
,
o
r
S
T
A
T
C
OM
s
,
is
o
f
ten
b
ased
o
n
t
h
e
d
esig
n
p
r
in
cip
les
o
f
th
e
i
n
v
er
ter
.
I
n
o
r
d
er
t
o
ex
ch
an
g
e
r
ea
l
p
o
w
er
o
r
r
ea
ctiv
e
p
o
w
er
f
o
r
lo
ad
cu
r
r
en
t
an
d
v
o
ltag
e
b
alan
cin
g
w
it
h
litt
le
h
ar
m
o
n
ic
ass
o
ciatio
n
,
a
ST
A
T
C
OM
ca
n
b
e
co
n
s
tr
u
cted
w
it
h
a
s
in
g
l
e
H
-
b
r
id
g
e
o
r
w
ith
ca
s
ca
d
ed
H
-
b
r
id
g
es
an
d
m
a
n
ag
ed
u
s
i
n
g
a
v
ar
iet
y
o
f
te
ch
n
iq
u
es
[
14
]
–
[
16
]
.
T
o
m
ee
t
th
e
v
o
lta
g
e
le
v
el
r
eq
u
ir
e
m
en
ts
i
n
p
o
w
er
tr
an
s
m
is
s
io
n
s
y
s
te
m
s
,
t
h
e
p
er
f
o
r
m
an
ce
o
f
h
ig
h
-
v
o
lta
g
e
D
C
v
o
lta
g
e
s
o
u
r
ce
co
n
v
er
ter
s
w
a
s
ex
a
m
i
n
ed
in
[
17
]
.
C
o
n
v
en
tio
n
al
2
-
lev
el
i
n
v
er
ter
s
h
a
v
e
li
m
itatio
n
s
w
h
e
n
o
p
er
atin
g
at
h
i
g
h
s
a
m
p
li
n
g
f
r
eq
u
en
c
ies
d
u
e
to
h
i
g
h
s
w
it
ch
in
g
lo
s
s
e
s
.
T
o
ad
d
r
ess
th
i
s
is
s
u
e,
m
u
ltil
e
v
el
in
v
er
ter
s
w
it
h
lo
w
s
w
itc
h
in
g
f
r
eq
u
en
c
ies
a
n
d
r
ed
u
ce
d
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
ar
e
u
s
ed
,
w
h
ic
h
r
e
m
o
v
es
t
h
e
n
ee
d
f
o
r
a
d
d
itio
n
al
f
il
ter
s
an
d
ev
en
lar
g
e
tr
a
n
s
f
o
r
m
er
s
[
18
]
–
[
23
]
.
A
s
tu
d
y
co
m
p
ar
ed
I
co
s
θ
an
d
en
h
a
n
ce
d
s
y
n
ch
r
o
n
o
u
s
r
ef
er
e
n
ce
f
r
a
m
e
s
ec
o
n
d
-
o
r
d
er
g
en
er
alize
d
in
te
g
r
ato
r
f
r
eq
u
en
c
y
-
lo
ck
ed
lo
o
p
(
SR
F
SO
GI
-
F
L
L
)
co
n
tr
o
ller
s
,
f
o
cu
s
i
n
g
o
n
p
o
w
er
q
u
alit
y
,
DC
-
li
n
k
v
o
ltag
e
r
eg
u
l
atio
n
,
an
d
h
ar
m
o
n
ic
r
ed
u
c
tio
n
ca
p
ab
ilit
ies
i
n
a
d
i
s
tr
ib
u
tio
n
S
T
A
T
C
OM
[
24
]
.
I
n
co
n
tr
ast,
ca
s
ca
d
ed
H
-
b
r
id
g
es
m
u
ltil
e
v
el
i
n
v
er
ter
s
b
ased
o
n
s
tack
ed
T
-
s
h
ap
e
v
o
ltag
e
g
en
er
atio
n
m
o
d
u
les
w
er
e
in
tr
o
d
u
ce
d
in
[
25
]
to
ac
h
iev
e
r
ed
u
ce
d
cu
r
r
en
t
co
n
d
u
cti
n
g
s
w
itc
h
e
s
d
ev
ice
s
i
n
t
h
e
lo
ad
p
ath
s
.
Fo
u
r
H
-
b
r
id
g
e
s
b
u
ilt
o
n
th
e
b
asi
s
o
f
a
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
w
er
e
ca
s
ca
d
ed
in
[
26
]
to
cr
ea
te
a
h
ig
h
v
o
ltag
e
s
i
n
g
le
-
p
h
a
s
e
ST
A
T
C
OM
eq
u
ip
p
ed
w
it
h
a
n
ad
ap
tiv
e
cu
r
r
en
t
co
n
tr
o
ller
a
n
d
a
b
alan
ci
n
g
m
et
h
o
d
f
o
r
t
h
e
v
o
ltag
e
s
o
f
its
D
C
ca
p
ac
ito
r
to
m
ee
t
t
h
e
r
eq
u
ir
e
m
en
ts
o
f
lo
ad
cu
r
r
en
t
b
alan
cin
g
i
n
h
i
g
h
v
o
ltag
e
A
C
n
et
w
o
r
k
s
.
T
w
o
-
s
ta
g
e
DC
-
DC
co
n
v
er
ter
s
w
er
e
d
is
c
u
s
s
ed
i
n
[
27
]
as
w
o
r
k
ab
le
s
o
l
u
t
io
n
s
to
t
h
ese
p
r
o
b
lem
s
b
ec
au
s
e
th
e
i
n
te
g
r
atio
n
o
f
m
u
lti
-
ter
m
in
al
s
h
y
b
r
id
h
ig
h
v
o
ltag
e
D
C
g
r
id
s
co
n
n
ec
ti
n
g
li
n
e
-
co
m
m
u
tated
co
n
v
er
ter
s
V
SC
-
b
ased
n
et
w
o
r
k
s
co
u
n
ter
s
s
e
v
er
al
c
h
alle
n
g
es
li
k
e
D
C
f
a
u
lt
is
o
latio
n
s
a
n
d
ac
h
iev
in
g
h
i
g
h
-
s
p
ee
d
p
o
w
er
r
e
v
er
s
al
w
it
h
o
u
t
an
y
in
ter
r
u
p
tio
n
.
T
h
e
is
s
u
e
o
f
p
o
w
er
p
o
in
t
o
f
m
a
x
i
m
u
m
tr
ac
k
i
n
g
in
s
o
lar
s
y
s
te
m
s
i
n
p
o
w
er
-
p
r
o
d
u
cin
g
s
tatio
n
s
w
a
s
ad
d
r
ess
ed
b
y
t
h
e
p
r
o
p
o
s
al
o
f
a
d
ep
en
d
ab
le
v
o
ltag
e
s
o
u
r
c
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in
v
er
ter
p
o
w
er
ed
b
y
a
s
p
ec
i
f
ic
P
W
M
ap
p
r
o
ac
h
[
28
]
.
Deta
iled
r
ev
ie
w
s
w
er
e
i
n
tr
o
d
u
ce
d
in
[
2
9
]
,
[
3
0
]
c
o
n
ce
r
n
in
g
t
h
e
d
ev
elo
p
m
e
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t
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o
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ter
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n
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ies.
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ap
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in
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w
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I
SS
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2
2
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8792
I
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A
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p
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14
,
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20
25
:
7
1
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721
716
Fig
u
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5
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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14
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3
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Sep
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1
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721
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DATA AV
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