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m
each
H
-
br
i
dge
c
e
l
l
(
W
he
r
e
N
i
s
num
be
r
of
l
e
ve
l
)
.
S
i
n
gl
e
l
e
g
N
-
l
e
v
e
l
i
n
v
e
r
t
e
r
C
H
B
i
n
v
e
r
t
e
r
i
s
s
ho
wn i
n F
i
gu
r
e
1.
E
a
c
h
c
e
l
l
c
ont
a
i
ns
f
o
ur
a
c
t
i
ve
s
w
i
t
c
he
s
S
1 t
o S
4 w
i
t
h a
nt
i
-
p
a
r
a
l
l
e
l
d
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o
d
e
s
D
1
t
o
D
4
.
E
ac
h
cel
l
c
o
n
t
ai
n
s
s
e
p
ar
at
ed
D
C
s
o
u
r
ce.
A
n
d
each
cel
l
p
r
o
d
u
ced
t
h
r
e
e d
i
f
f
er
e
n
t
v
o
l
t
ag
e l
ev
el
(
+E
,
0
,
-
E
).
T
he
pha
s
e
v
ol
t
a
ge
c
ons
i
s
t
s
of
N
-
l
e
v
el
i
n
v
er
t
er
.
t
h
e
l
ev
el
s
i
n
p
h
as
e
v
o
l
t
ag
e ar
e
2
N
+
1
,
h
e
r
e N
i
s
1
-
ϕ
i
n
v
er
t
er
cel
l
s
p
r
es
en
t
i
n
a p
h
as
e a
n
d
t
h
e n
u
m
b
er
o
f
l
ev
el
s
i
n
l
i
n
e v
o
l
t
ag
e ar
e 2
M
-
1
,
whe
r
e
M
i
s
t
he
num
be
r
o
f
l
e
ve
l
i
n
pha
s
e
vol
t
a
g
e
[8
],
[9
].
F
i
gu
r
e
1.
S
i
n
g
l
e
l
e
g
N
-
l
e
v
el
c
as
cad
e
d
H
-
b
r
i
d
g
e
m
u
l
t
i
l
e
v
e
l
i
n
v
e
r
t
e
r
3.
G
E
N
E
R
AL
I
Z
E
D U
NI
P
O
L
AR
P
W
M
T
E
CH
N
I
Q
UE
F
O
R
C
A
S
C
AD
E
D
H
-
B
R
I
D
G
E M
U
LTI
-
LEV
EL
I
N
V
E
R
TER
F
i
g
u
r
e
2
.
I
l
l
u
s
t
r
a
t
e
s
t
h
e
u
n
i
p
o
l
a
r
m
u
l
t
i
l
e
v
e
l
m
o
d
u
l
a
t
i
o
n
s
t
r
a
t
e
g
y
.
t
h
e
m
o
d
u
l
a
t
i
o
n
s
i
gna
l
s
ha
ve
t
he
s
a
m
e
f
r
e
qu
e
nc
y
(
f
o)
a
nd a
m
pl
i
t
ude
(
A
m
)
.
T
he
s
i
n
us
oi
da
l
s
i
gna
l
s
a
r
e
s
a
m
pl
e
d by
a
t
r
ia
ng
ul
a
r
c
a
r
r
i
e
r
s
i
gna
l
w
i
t
h
f
r
e
q
u
en
c
y
(
f
c)
an
d
am
p
l
i
t
u
d
e (
A
c
)
o
n
ce ev
e
r
y
cy
cl
e,
i
n
t
er
s
ect
i
o
n
b
et
w
een
t
h
e s
am
p
l
ed
m
o
d
u
l
at
i
o
n
s
i
g
n
al
s
an
d
t
h
e car
r
i
er
s
i
g
n
a
l
d
e
f
i
ne
s
t
he
s
wi
t
c
hi
n
g i
ns
t
a
nt
of
t
he
P
W
M
p
ul
s
e
s
.
I
n
o
r
de
r
t
o e
ns
ur
e
qua
r
t
e
r
w
a
ve
s
y
m
m
e
t
r
i
c
pr
o
pe
r
t
i
e
s
o
f
t
he
P
W
M
o
ut
p
ut
w
a
ve
f
or
m
,
t
he
s
t
a
r
t
i
ng
poi
nt
of
t
he
m
odul
a
t
i
on s
i
gna
l
s
i
s
pha
s
e
s
hi
f
t
e
d b
y
one
pe
r
i
o
d
o
f
t
he
c
a
r
r
i
e
r
w
a
ve
,
i
n a
d
di
t
i
on t
he
f
r
e
que
nc
y
m
odul
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t
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n
r
a
t
i
o
(
m
f
)
m
u
s
t
a
l
s
o
b
e
e
ve
n
n
um
be
r
[
10]
,
[
11]
.
T
h
e
un
ipo
la
r
P
W
M m
e
th
o
d of
f
e
r
s
a
goo
d opp
or
tun
ity f
o
r
th
e
r
e
a
liz
a
tio
n
o
f
th
e
T
hr
e
e
-
p
ha
s
e
i
nve
r
t
e
r
c
ont
r
ol
.
I
n c
a
s
e
of
t
he
f
i
ve
-
l
ev
el
,
s
e
v
en
-
l
e
v
e
l
,
n
i
n
e
-
l
e
v
el
an
d
el
ev
e
n
-
l
e
v
e
l
i
n
v
e
r
t
e
r
s
i
t
i
s
b
e
t
t
e
r
t
o
u
s
e t
h
e
uni
pol
a
r
P
W
M
m
e
t
hod
w
i
t
h
t
hr
e
e
c
a
r
r
i
e
r
w
a
ve
s
.
I
n
s
uc
h
c
a
s
e
t
he
m
ot
or
h
a
r
m
oni
c
l
os
s
e
s
w
i
l
l
be
c
o
ns
i
d
e
r
a
bl
y
l
owe
r
.
T
he
u
ni
pol
a
r
s
p
wm
vo
l
t
a
ge
s
wi
t
c
hi
n
g s
c
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m
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pe
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y
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t
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Vd
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
A
S
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:
225
2
-
88
14
A
n
al
y
s
i
s
a
n
d
I
m
pl
e
m
e
nt
at
i
on
of
U
ni
pol
ar
P
W
M
St
r
at
e
gi
e
s
f
or
T
h
re
e
P
h
a
se
C
a
s
ca
d
e
…
(
R
a
vi
ku
m
a
r
B
h
u
kya
)
2
47
T
ha
t
m
e
a
ns
,
s
e
l
e
c
t
i
ng u
ni
p
ol
a
r
P
W
M
a
s
s
w
i
t
c
hi
n
g s
c
he
m
e
in t
he
pr
o
pos
e
d
i
nve
r
t
e
r
i
s
a
p
pr
o
p
r
i
at
e as
t
h
er
e i
s
no
f
i
l
t
e
r
a
t
t
he
i
nve
r
t
e
r
out
p
ut
c
om
pa
r
e
d
t
o
o
t
he
r
s
p
w
m
t
e
c
hni
q
ue
s
.
I
n
t
h
i
s
s
ch
em
e,
t
h
e t
r
i
an
g
u
l
ar
car
r
i
er
w
a
v
ef
o
r
m
i
s
co
m
p
ar
ed
w
i
t
h
t
w
o
r
e
f
er
e
n
ce s
i
g
n
al
s
w
h
i
ch
ar
e
pos
i
t
i
ve
a
n
d n
e
ga
t
i
ve
s
i
g
na
l
.
T
he
ba
s
i
c
i
de
a
t
o p
r
o
d
uc
e
S
P
W
M
w
i
t
h u
ni
pol
a
r
v
o
l
t
a
g
e
s
w
i
t
c
h
i
n
g
i
s
s
h
o
w
n
i
n
F
i
gu
r
e
2.
T
he
di
f
f
e
r
e
nt
be
t
w
e
e
n t
he
B
i
pol
a
r
S
P
W
M
ge
ne
r
a
t
or
s
i
s
t
ha
t
t
he
ge
ne
r
a
t
o
r
us
e
s
a
not
he
r
c
om
pa
r
a
t
o
r
t
o
co
m
p
ar
e b
e
t
w
een
t
he
i
nve
r
s
e
r
e
f
er
e
n
ce w
av
e
f
o
r
m
−
V
r
.
T
he
pr
oc
e
s
s
of
c
om
pa
r
i
ng
t
he
s
e
t
wo
s
i
gn
a
l
s
t
o
pr
o
duc
e
t
h
e
u
ni
p
o
l
a
r
v
o
l
t
a
g
e
s
w
i
t
c
h
i
n
g
s
i
g
n
a
l
i
s
g
r
a
p
h
i
c
a
l
l
y
i
l
l
u
s
t
r
a
t
e
d
i
n
F
i
g
u
r
e
2
.
I
n
U
n
i
p
o
l
a
r
v
o
l
t
a
g
e
s
wi
t
c
hi
n
g
t
he
out
put
vol
t
a
ge
s
wi
t
c
he
s
be
t
w
e
e
n
0
a
nd
V
dc
,
or
be
t
w
e
e
n
0
a
nd
−
V
d
c
.
T
hi
s
i
s
i
n
c
ont
r
a
s
t
t
o
t
he
B
i
pol
a
r
s
w
i
t
c
h
i
ng
s
t
r
a
t
e
gy
i
n
whi
c
h
t
he
o
ut
p
ut
s
w
i
ngs
be
t
w
een
V
d
c
a
n
d
−
V
dc
.
O
ve
r
m
odul
a
t
i
o
n
oc
c
u
r
s
w
he
n
a
m
pl
i
t
ude
m
odul
a
t
i
on i
n
de
x
m
a
i
s
gr
e
a
t
e
r
t
ha
n
u
ni
t
y
.
I
t
c
a
us
e
s
a
r
e
d
uc
t
i
o
n i
n
num
be
r
of
pul
s
e
s
i
n t
he
l
i
ne
t
o
l
i
ne
vol
t
a
ge
w
a
ve
f
or
m
l
e
a
di
ng t
o e
m
e
r
ge
nc
e
of
l
o
w
e
r
o
r
d
e
r
ha
r
m
oni
c
s
.
M
or
e
ove
r
t
he
not
c
h a
n
d
pul
s
e
w
i
d
t
h
s
n
e
a
r
t
h
e
c
e
n
t
e
r
o
f
p
o
s
i
t
i
v
e
a
n
d
n
e
g
a
t
i
v
e
h
a
l
f
c
y
c
l
e
t
e
n
d
t
o
v
a
n
i
s
h
.
T
o
c
o
m
p
l
e
t
e
t
h
e
s
w
i
t
c
h
i
n
g
o
p
e
r
a
t
i
o
n
s
o
f
t
h
e
de
vi
c
e
,
m
i
nim
um
not
c
h
a
n
d pul
s
e
w
i
dt
hs
m
us
t
be
m
a
i
nta
i
ne
d.
W
he
n m
i
nim
u
m
w
i
dt
h not
c
he
s
a
nd
pul
s
e
s
a
r
e
dr
o
ppe
d,
t
he
r
e
w
i
l
l
be
s
om
e
t
r
a
ns
i
e
nt
j
um
p o
f
l
oa
d c
u
r
r
e
n
t
.
T
he
ge
ne
r
a
t
e
d s
i
g
n
a
ls
a
r
e
a
s
s
how
n in F
igu
r
e
2
a
nd t
he
s
wi
t
c
h
i
ng
pul
s
e
s
ge
n
e
r
a
t
e
d s
h
ow
n i
n F
i
g
u
r
e
3
.
a
n
d
t
he
o
ut
p
ut
c
u
r
r
e
nt
s
a
t
t
he
l
oa
d s
ho
w
n i
n F
i
g
ur
e
4.
T
he
m
od
ul
a
t
i
on
i
n
de
x
i
s
t
he
r
a
t
i
o
o
f
pe
a
k
m
a
gni
t
u
de
s
o
f
t
h
e
m
odul
a
t
i
ng
s
i
gna
l
V
m
an
d
t
h
e
ca
r
r
i
er
s
i
g
n
al
:
V
m
m
V
c
=
(
2)
T
he
m
od
ul
a
t
i
on
i
n
de
x
i
n
S
P
W
M
t
e
c
h
ni
q
ue
f
or
c
a
s
c
a
de
d
m
ult
i
l
e
ve
l
i
nve
r
t
e
r
c
o
nf
i
gu
r
a
t
i
on
i
s
gi
ve
n
b
y
:
(
1)
V
m
m
N
V
c
=
−
(
3)
w
h
e
r
e
N
is
num
b
e
r
of
le
v
e
l
s
.
F
o
r
und
e
r
m
o
du
la
tio
n
0
<
m
<
1.
F
o
r
o
ve
r
m
odul
a
t
i
o
n
m
>
1.
G
e
ne
r
a
l
l
y
,
ov
e
r
m
odul
a
t
i
on
i
s
not
de
s
i
r
e
d
be
c
a
us
e
of
t
he
pr
e
s
e
nc
e
of
t
he
l
o
w
e
r
f
r
e
que
nc
y
ha
r
m
oni
c
s
i
n t
he
o
ut
p
ut
v
ol
t
a
ge
a
n
d s
ubs
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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88
14
IJ
A
A
S
V
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l
.
7
,
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3
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2
48
F
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m
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3.
1.
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ni
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l
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41
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in
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one
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6
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h
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put
s
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of
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1
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.
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8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
A
S
I
S
S
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:
225
2
-
88
14
A
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2
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F
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ig
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r)
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ig
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r
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ig
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.
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a
r
t
e
c
hni
que
m
a
=
1
.
5
,
m
f
=
31
.
84
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-
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14
IJ
A
A
S
V
o
l
.
7
,
N
o
.
3
,
S
e
p
t
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b
er
201
8
:
245
–
2
54
2
50
3.
2.
U
n
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p
o
l
a
r
P
W
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t
ech
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p
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out
put
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o
f
t
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e
r
t
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r
f
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41
0
V.
H
e
r
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i
n F
i
gu
r
e
9.
One
c
a
n obs
e
r
ve
t
he
l
i
ne
v
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t
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g
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s
of
s
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n
l
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r
us
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ni
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r
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W
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t
e
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hni
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ue
.
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i
n
F
i
g
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10
.
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ndi
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s
t
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t
h
r
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e
pha
s
e
o
ut
p
ut
s
t
a
t
or
c
u
r
r
e
nt
s
o
f
t
he
l
oa
d a
nd
we
c
a
n o
bs
e
r
v
e
t
he
s
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t
e
m
i
s
uns
t
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bl
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f
r
om
o t
o 0.
2 s
ec.
D
u
e
t
o
t
r
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ns
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v
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or
of
t
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s
y
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t
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m
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t
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t
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0.
2
s
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.
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gu
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1I
.
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n
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t
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s
t
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or
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u
e
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pe
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d
of
t
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l
oa
d
of
s
e
ve
n l
e
ve
l
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f
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n t
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s
t
a
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pe
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a
t
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of
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m
ha
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at
0
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1
5
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.
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i
g
u
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1
2.
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ndi
c
a
t
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t
he
t
ot
a
l
ha
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m
oni
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di
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or
t
i
on o
f
t
he
out
put
vol
t
a
ge
i
s
a
bo
ut
1
5.
3
3%
,
a
t
m
a
=
1.
3
,
m
f
=
31.
8
4
w
he
n
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U
ni
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m
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l
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v
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r
t
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r
.
F
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gu
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9.
P
r
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d
s
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n
-
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v
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l
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p
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l
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c
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(
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g
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F
i
gu
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1
0.
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put
s
t
a
t
or
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u
r
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s
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l
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d
(
S
e
ve
n
-
l
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el
i
n
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er
t
er
)
F
i
gu
r
e
1
1.
O
ut
p
u
t
t
or
que
a
n
d
s
p
e
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d
of
t
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l
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d
(
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e
ve
ni
ve
-
l
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v
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r
t
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r
)
F
i
gu
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e
1
2.
T
H
D
F
or
U
ni
p
ol
a
r
t
e
c
h
ni
q
ue
m
a
=
1.
3,
m
f
=
31
.
8
4
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
A
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S
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:
225
2
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88
14
A
n
al
y
s
i
s
a
n
d
I
m
pl
e
m
e
nt
at
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on
of
U
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St
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s
f
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a
s
ca
d
e
…
(
R
a
vi
ku
m
a
r
B
h
u
kya
)
2
51
3.
3
.
U
n
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p
o
l
a
r
P
W
M
t
e
c
h
ni
q
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a
ppl
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e
d t
o
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l
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p
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vol
t
a
ge
of
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r
t
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f
o
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n
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t
o
l
i
ne
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s
a
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out
4
10
V.
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r
e
i
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F
i
gu
r
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13
.
O
ne
c
a
n
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bs
e
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ve
t
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l
i
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t
a
g
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of
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ne
l
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l
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nve
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r
us
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ng
uni
p
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a
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P
W
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c
hni
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e
.
He
r
e
i
n F
i
g
ur
e
14.
I
n
di
c
a
t
e
s
the
t
hr
e
e
pha
s
e
o
ut
p
ut
s
t
a
t
or
c
u
r
r
e
nt
s
o
f
t
he
l
oa
d a
nd
we
c
a
n o
bs
e
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v
e
t
he
s
y
s
t
e
m
i
s
uns
t
a
bl
e
f
r
om
o t
o 0.
3 s
e
c
.
Due
t
o
t
r
a
ns
i
e
nt
be
ha
v
i
or
o
f
t
he
s
y
s
t
e
m
a
t t
he
s
t
a
r
t
i
ng f
r
om
0.
3 s
e
c
.
a
nd F
i
gu
r
e
1
5.
I
ndi
c
a
t
e
s
t
he
t
or
q
ue
,
s
pe
e
d o
f
t
he
l
oa
d
of
ni
ne
l
e
ve
l
i
nve
r
t
e
r
f
r
om
t
he
f
i
g
u
r
e
i
t
can
b
e s
een
t
h
at
t
h
e s
t
ead
y
s
t
at
e o
p
er
at
i
o
n
o
f
t
h
e s
y
s
t
em
h
as
ach
i
ev
e
d
at
0
.
3
5
s
ec
.
F
i
gu
r
e
1
6.
I
ndi
c
a
t
e
t
he
t
ot
a
l
ha
r
m
oni
c
di
s
t
or
t
i
on o
f
t
he
out
put
vol
t
a
ge
i
s
a
bo
ut
1
0.
7
8%
,
a
t
m
a
=
1.
2
,
m
f
=
31.
8
4
w
he
n
us
i
n
g
u
ni
p
ol
a
r
P
W
M
t
e
c
h
ni
que
o
n
ni
ne
-
l
e
v
el
cas
ca
d
ed
m
u
l
t
i
-
l
e
v
e
l
i
n
v
e
r
t
e
r
.
F
i
gu
r
e
1
3.
P
r
o
pos
e
d
ni
ne
-
l
e
v
e
l
U
n
i
p
o
l
a
r
P
W
M
t
e
c
h
n
i
q
u
e
(
L
i
n
e
v
o
l
t
a
g
e
)
F
i
g
u
r
e
1
4
.
O
u
t
p
u
t
s
t
a
t
o
r
o
f
t
h
e
l
o
a
d
(
N
i
n
e
-
l
e
v
e
l
i
n
v
e
r
t
e
r
)
F
i
gu
r
e
1
5.
O
ut
put
t
or
q
ue
a
nd
s
pe
e
d
of
t
he
l
o
a
d(
N
i
ne
-
l
e
v
e
l
i
n
v
e
r
t
e
r
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-
88
14
IJ
A
A
S
V
o
l
.
7
,
N
o
.
3
,
S
e
p
t
em
b
er
201
8
:
245
–
2
54
2
52
F
ig
ur
e
16
.
T
H
D
F
or
U
ni
p
ol
a
r
t
e
c
h
ni
q
ue
m
a
=
1.
2,
m
f
=
31
.
8
4
3.
3
.
U
n
i
p
o
l
a
r
P
W
M
t
ech
n
i
q
u
e
a
p
p
l
i
ed
t
o
el
ev
en
-
l
e
v
e
l
C
H
BM
LI
T
he
out
put
vol
t
a
ge
o
f
t
he
i
n
v
e
r
t
e
r
f
or
l
i
ne
t
o
l
i
ne
i
s
a
bo
ut
4
10
V.
H
e
r
e
i
n F
i
gu
r
e
17
.
O
ne
c
a
n o
bs
e
r
v
e
t
he
l
i
ne
vol
t
a
g
e
of
e
l
e
ve
n l
e
ve
l
i
nve
r
t
e
r
us
i
ng
u
ni
pol
a
r
P
W
M
t
e
c
h
ni
q
ue
.
He
r
e
i
n F
i
gu
r
e
1
8.
I
n
di
c
a
t
e
s
t
he
t
hr
e
e
p
ha
s
e
o
u
t
put
s
t
a
t
o
r
c
u
r
r
e
nt
s
of
t
he
l
oa
d a
nd
we
c
a
n
obs
e
r
ve
t
he
s
y
s
t
e
m
i
s
uns
t
a
bl
e
f
r
om
o t
o
0.
4 s
e
c
.
D
ue
t
o t
r
a
ns
i
e
nt
be
ha
vi
or
o
f
t
he
s
y
s
t
e
m
a
t
the
s
t
a
r
t
i
n
g
f
r
o
m
0.
4 s
e
c
.
F
i
g
ur
e
1
9.
I
n
di
c
a
t
e
s
th
e
tor
qu
e
,
s
p
e
e
d of
t
h
e
l
o
a
d
o
f
e
l
e
v
e
n
l
e
v
e
l
i
n
v
e
r
t
e
r
f
r
o
m
t
h
e
f
i
g
u
r
e
i
t
c
a
n
b
e
s
e
e
n
t
h
a
t
t
h
e
s
t
e
a
d
y
s
t
a
t
e
o
p
e
r
a
t
i
o
n
o
f
t
h
e
s
y
s
t
e
m
ha
s
a
c
hi
e
ve
d
a
t
0.
4
5
s
e
c
.
F
i
gu
r
e
2
0.
I
ndi
c
a
t
e
t
he
t
ot
a
l
ha
r
m
oni
c
di
s
t
or
t
i
on o
f
t
he
out
put
vol
t
a
ge
i
s
a
bo
ut
1
0.
1
3%
,
a
t
m
a
=
1.
0
,
m
f
=
31.
8
4
w
he
n
us
i
n
g
u
ni
p
ol
a
r
P
W
M
t
e
c
h
ni
que
o
n
e
l
e
ve
n
-
l
ev
el
cas
cad
e
d
m
u
l
t
i
-
l
e
v
e
l
i
n
v
e
r
t
e
r
.
F
i
gu
r
e
1
7.
P
r
o
pos
e
d
e
l
e
ve
n
-
l
e
ve
l
U
ni
p
ol
a
r
P
W
M
t
e
c
hni
qu
e
(
L
i
ne
v
ol
t
a
ge
)
F
i
gu
r
e
1
8.
O
ut
put
s
t
a
t
or
c
u
r
r
e
nt
o
f
t
he
l
oa
d
(
E
l
e
ve
n
-
l
ev
el
i
n
v
er
t
er
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
A
S
I
S
S
N
:
225
2
-
88
14
A
n
al
y
s
i
s
a
n
d
I
m
pl
e
m
e
nt
at
i
on
of
U
ni
pol
ar
P
W
M
St
r
at
e
gi
e
s
f
or
T
h
re
e
P
h
a
se
C
a
s
ca
d
e
…
(
R
a
vi
ku
m
a
r
B
h
u
kya
)
2
53
F
ig
ur
e
1
9.
O
ut
put
t
or
q
ue
a
nd
s
pe
e
d
of
t
he
l
o
a
d
(
E
l
e
ve
n
-
l
e
v
e
l
i
n
v
e
r
t
e
r
)
F
i
gu
r
e
2
0.
T
H
D
f
o
r
U
ni
pol
a
r
t
e
c
hni
que
m
a
=
1.
0,
m
f
=
31
.
8
4
T
he
t
ot
a
l
ha
r
m
oni
c
di
s
t
r
a
c
t
i
on wa
ve
f
o
r
m
s
obt
a
i
ne
d
f
r
om
t
he
s
im
ul
a
t
i
on r
e
s
ul
t
s
us
i
n
g
M
A
T
L
A
B/
S
I
M
U
L
I
N
K
a
n
d
c
o
m
p
a
r
e
d
t
h
e
a
l
l
l
e
v
e
l
s
(
f
i
v
e,
s
ev
en
,
n
i
n
e an
d
el
ev
e
n
)
o
f
t
h
e
cas
cad
e
d
m
u
l
t
i
l
ev
el
i
nve
r
t
e
r
.
T
he
c
om
pa
r
i
s
on a
r
e
m
a
de
f
or
t
h
e
t
ot
a
l
ha
r
m
oni
c
di
s
t
r
a
c
t
i
on
wa
ve
f
o
r
m
s
ba
s
e
d o
n
va
r
i
a
t
i
ons
of
pa
r
a
m
e
t
e
r
s
a
m
pl
i
t
ude
m
odul
a
t
i
on (
m
a
)
a
nd f
r
e
que
nc
y
m
odul
a
t
i
on (
m
f
)
.
a
n
d w
e
c
a
n o
bs
e
r
ve
t
he
t
hr
e
e
p
h
as
e
s
t
a
t
or
c
ur
r
e
nt
s
,
t
or
q
ue
a
nd
s
pe
e
d
o
f
t
he
i
n
duc
t
i
o
n
m
ot
or
f
or
a
l
l
l
e
ve
l
s
o
f
t
he
i
n
ve
r
t
e
r
.
t
he
t
ot
a
l
ha
r
m
oni
c
di
s
t
or
t
i
o
n o
f
t
he
out
put
v
ol
t
a
ge
i
s
a
bo
ut
1
0.
13
%
,
a
t
m
a
=
1.
0,
m
f
=
31
.
8
4 on
e
l
e
ve
n
-
l
e
v
e
l
c
a
s
c
a
d
e
d
m
u
l
t
i
-
l
ev
el
i
nve
r
t
e
r
.
T
he
C
om
pa
r
i
s
on
of
T
H
D
a
na
l
y
s
i
s
o
f
a
t
h
r
e
e
-
pha
s
e
c
a
s
c
a
de
d
i
n
v
e
r
t
e
r
f
e
d
t
o
i
nd
uc
t
i
on
m
ot
or
s
ho
w
n
i
n
T
ab
l
e
2
.
T
ab
l
e
2
.
T
he
C
om
pa
r
i
s
i
on
o
f
T
H
D
O
f
F
i
ve
,
S
e
ve
n,
N
i
n
e
a
n
d
E
l
e
ve
n
-
l
ev
el
C
as
cad
ed
I
n
v
e
r
t
er
O
ut
put
V
o
ltag
e
L
e
v
el
T
ech
n
iq
u
es
%
T
HD(
V)
Fiv
e
-
lev
el
Un
ip
o
lar
PW
M
23.
13
Sev
en
-
lev
el
Un
ip
o
lar
PW
M
15.
33
Nin
e
-
lev
el
Un
ip
o
lar
PW
M
10.
78
E
lev
en
-
lev
el
Un
ip
o
lar
PW
M
10.
13
5.
C
O
N
CL
U
S
I
O
N
I
n t
hi
s
pa
pe
r
t
he
U
ni
p
ol
a
r
P
W
M
t
e
c
h
ni
q
u
e
of
m
os
t
pr
o
f
f
e
r
e
d c
o
nt
r
ol
s
t
r
a
t
e
gi
e
s
a
p
pl
i
e
d t
o t
h
r
e
e
p
h
a
s
e cas
ca
d
e
d
i
n
v
er
t
e
r
ar
e
p
r
es
e
n
t
ed
.
T
h
e
w
av
e
f
o
r
m
s
cl
e
ar
l
y
d
e
p
i
c
t
i
n
g
t
h
a
t
a
l
m
o
s
t
a
l
l
t
h
e
f
i
v
e
-
l
ev
el
,
s
ev
e
n
-
l
e
ve
l
,
ni
ne
-
l
ev
e
l
a
n
d
e
l
ev
en
-
l
e
ve
l
c
o
nt
r
ol
s
t
r
a
t
e
gi
e
s
a
r
e
f
unc
t
i
o
ni
n
g
w
e
l
l
i
n c
ont
r
ol
l
i
ng
t
he
s
pe
e
d
of
t
he
i
nd
uc
t
i
on m
ot
or
,
o
ut
p
ut
l
i
ne
vol
t
a
ge
,
s
t
a
t
o
r
c
ur
r
e
nt
,
s
pe
e
d a
n
d t
o
r
q
ue
.
B
ut
T
HD
of
t
he
U
ni
p
ol
a
r
P
W
M
s
t
r
a
t
e
gi
e
s
whe
n
c
om
pa
r
e
d,
i
t
i
s
o
bvi
ous
t
ha
t
e
l
e
ve
n
-
l
e
ve
l
c
a
s
c
a
de
d
i
n
ve
r
t
e
r
i
s
t
he
l
ow
T
H
D
of
a
b
o
ut
1
0.
13
%
.
A
C
K
N
O
W
L
E
D
G
E
ME
NT
S
W
e
t
ha
nk
t
he
U
ni
ve
r
s
i
t
y
G
r
a
nt
s
C
om
m
i
s
s
i
on
(
U
GC
)
,
G
o
vt
.
of
I
n
di
a
,
Ne
w
De
l
hi
f
or
pr
ov
i
di
ng
M
a
j
o
r
R
es
ear
ch
P
r
o
j
e
ct
t
o
car
r
y
o
u
t
t
h
e
R
e
s
e
a
r
c
h
w
or
k
on
M
ul
t
i
-
L
e
ve
l
I
nve
r
t
e
r
s
.
I
a
l
s
o
t
ha
n
k
U
GC
f
or
a
w
a
r
di
ng
m
e
w
i
t
h
R
G
NF
F
E
L
L
O
WS
H
I
P
t
o
c
a
rry
o
u
t
m
y
re
s
e
a
rc
h
w
o
r
k
(P
h
.
D
).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-
88
14
IJ
A
A
S
V
o
l
.
7
,
N
o
.
3
,
S
e
p
t
em
b
er
201
8
:
245
–
2
54
2
54
R
EF
ER
E
N
C
ES
[1]
S
.Z
ai
n
al
,J
.A
zi
z
,
S
.S
.A
h
m
ed
, “
S
i
n
g
l
e c
ar
r
i
er
P
W
M
s
ch
em
e f
o
r
c
as
cad
ed
m
u
l
t
i
l
e
v
el
v
o
l
t
ag
e
s
o
u
r
ce i
n
v
er
t
er
,
”P
o
w
er
E
l
e
c
t
roni
c
s
a
nd
D
ri
ve
s
y
s
t
e
m
s
,
I
E
E
E
Confe
r
e
nc
e
(P
E
D
C),
2003
,
V
ol
.
1
,
pp
.
406
-
410.
[2]
A
k
i
ra
N
a
b
a
e
,
Is
a
o
T
a
k
a
h
a
s
h
i
a
n
d
Hi
r
o
f
u
m
i
A
k
a
g
i
,
”
A
Ne
w
Ne
u
t
ra
l
-
P
oi
nt
-
C
l
a
m
p
ed
P
w
m
I
n
v
er
t
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[3]
Irfa
n A
hm
e
d,
V
i
j
a
y
B
.
Borgha
t
e
,
”
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i
m
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fi
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IE
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l
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r
on
.
2
014
,
V
ol
.
7
,
Is
s
.
3,
pp
.
604
–
613
.
[4]
C
ar
r
ar
a
G
.e
t
al
., “
A
n
ew
m
u
l
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ev
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W
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;
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t
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al
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s
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l
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t
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o
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i
cs
S
p
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al
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s
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s
Confe
re
nc
e
,
199
0,
P
E
S
C’90 re
c
o
r
d,
21
st
a
nnua
l
IE
E
E
,
pp.
363
-
371.
[5]
M
.
Ca
l
a
i
s
,
L
.
J
.
Borl
e
,
V
.
G
.
A
ge
l
i
di
s
,
“
A
na
l
y
s
i
s
of m
ul
t
i
c
a
rri
e
r P
W
M
m
e
t
hods
for a
s
i
ngl
e
-
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as
e f
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v
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nve
rt
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r E
l
e
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c
s
S
pe
c
i
a
l
i
s
t
s
Co
nfe
re
nc
e
(P
E
S
C)
,
2001
,
V
ol
.
3
,
p
p.
1351
-
1356
.
[6]
R
a
vi
k
um
a
r
B
hu
ky
a
,
P
.
S
a
t
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s
h
kum
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r
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er
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ce
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n
al
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s
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u
l
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-
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ve
l
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nv
e
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te
r
f
e
d I
ndu
c
tio
n
Mo
t
o
r
Dr
iv
e
”
,
in
t
e
r
n
a
tion
a
l j
our
n
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l o
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d
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r
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y
s
t
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m
s
,
V
ol
.
8,
N
o.
2,
pp
.
83
5
-
843
,
Ma
y.
2
017
.
[7]
J
.
R
o
dr
i
gue
z
,
J
.
S
.
L
a
i
,
a
n
d F
.
Z
.
P
e
n
g,
“
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ul
t
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:
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ur
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nt
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s
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s
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.
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l.
4
9,
n
o.
4,
p
p.
724
-
73
8,
Aug
.
200
2.
[8]
M
.
M
a
l
i
now
s
ki
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G
opa
k
um
a
r
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.
R
o
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T
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a
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.
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n
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E
l
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r
on
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v
ol
.
5
7,
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o.
7,
p
p.
2
19
7
-
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5,
J
u
ly
20
10
.
[9]
F
.
S
al
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m
an
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.
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zl
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"
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[10]
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l
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ni
ve
l
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.
S
.
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a
s
h
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l
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s
of T
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put
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nc
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ul
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l
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odul
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on t
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E
T
P
o
w
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E
l
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r
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n
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cs
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o
l
. 4
, n
o
. 8
, p
p
.
9
5
1
-
958,
2010
.
[11]
M
.
S
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t
y
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na
r
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y
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na
,
P
.
S
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t
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s
h K
um
a
r,
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A
na
l
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s
i
s
a
nd D
e
s
i
gn of S
ol
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r P
hot
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ol
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ri
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d Inve
rt
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,
Indone
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our
nal
of
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l
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ngi
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Inf
or
m
at
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c
s
(
IJ
E
E
I),
IA
E
S
,
D
e
c
e
m
be
r 2015,
V
ol
.
3,
pp
199
-
208
.
[12]
Ra
vi
kum
a
r Bhuk
y
a
,
P
.
S
a
t
i
s
h kum
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r,
M
ode
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na
l
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s
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nd Co
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ra
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of D
o
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pl
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s
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a
m
pi
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V
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for Ca
s
c
a
de
d a
nd D
i
ode
Cl
a
m
pe
d M
ul
t
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l
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ve
l
Inve
r
t
e
r fe
d Induc
t
i
on M
ot
or D
ri
ve
.
Indone
s
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a
n J
ourna
l
of
E
l
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c
t
ri
c
a
l
E
ngi
ne
e
ri
ng
a
nd C
om
pu
t
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r S
c
i
e
nc
e
V
ol
.
7
,
N
o.
3,
S
e
pt
e
m
be
r
2017,
pp.
69
8 ~
707 D
O
I:
10.
11591/
i
j
e
e
c
s
.
v7.
i
3.
pp698
-
707
.
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