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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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Dr
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N:
2088
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8
694
F
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i
g
u
r
atio
n
p
r
o
p
o
s
ed
in
th
i
s
p
ap
er
eli
m
i
n
ate
s
th
is
d
is
ad
v
an
ta
g
e
o
f
th
e
co
n
v
e
n
tio
n
al
ca
s
ca
d
ed
m
u
ltil
e
v
el
in
v
er
ter
[
1
4
]
[
2
5
–
2
9
]
.
T
h
e
co
n
f
i
g
u
r
atio
n
r
eq
u
ir
es
o
n
l
y
o
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e
D
C
s
o
u
r
ce
ir
r
esp
ec
tiv
e
o
f
le
v
el
s
,
r
esu
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g
i
n
r
ed
u
ce
d
co
s
t.
T
h
e
p
r
o
p
o
s
ed
f
iv
e
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le
v
el
ca
s
ca
d
ed
in
v
er
ter
e
m
p
lo
y
i
n
g
a
s
in
g
le
s
o
u
r
ce
o
f
D
C
s
h
o
w
n
in
Fig
u
r
e
1
(
a)
.
T
h
e
in
v
er
ter
u
s
e
s
o
n
l
y
o
n
e
DC
s
o
u
r
ce
ir
r
esp
ec
ti
v
e
o
f
th
e
n
u
m
b
er
o
f
lev
el
s
.
An
m
-
le
v
el
in
v
er
ter
o
f
th
e
p
r
o
p
o
s
ed
in
v
er
ter
u
s
es
2
1
m
tr
an
s
f
o
r
m
er
s
.
T
h
e
o
u
tp
u
t
o
f
th
e
in
v
er
ter
is
co
n
n
ec
ted
to
th
e
lo
ad
th
r
o
u
g
h
th
e
tr
an
s
f
o
r
m
er
s
.
T
h
e
p
r
i
m
ar
y
o
f
th
e
tr
an
s
f
o
r
m
er
s
ar
e
co
n
n
ec
ted
to
th
e
DC
s
o
u
r
ce
t
h
r
o
u
g
h
th
e
b
r
id
g
e
s
.
T
h
e
s
ec
o
n
d
ar
y
tr
an
s
f
o
r
m
er
w
in
d
i
n
g
s
ar
e
co
n
n
ec
ted
in
s
er
ie
s
ai
d
in
g
to
t
h
e
lo
ad
[
1
5
-
1
6
]
.
(
a)
(
b)
Fig
ur
e 1. F
i
v
e
-
l
ev
el
ca
sc
ad
ed m
ul
t
i
l
ev
el
i
nv
er
t
e
r
w
i
t
h
a s
i
ng
l
e DC
sour
ce
(
a)
C
i
r
c
ui
t
d
i
ag
r
am
(
b)
Wa
v
ef
or
m
of
v
ol
t
ag
e a
g
ai
n
st
t
he s
w
i
t
chi
ng
ang
l
es
.
Mo
d
ellin
g
o
f
f
i
v
e
le
v
el
in
v
er
te
r
is
d
o
n
e
u
s
i
n
g
t
h
e
b
in
ar
y
f
ac
t
o
r
s
o
f
ea
ch
leg
o
f
t
h
e
H
b
r
id
g
e
s
an
d
ar
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
166
–
1
7
3
168
O
F
F
S
ON
S
ON
S
O
F
F
S
H
3
1
3
1
11
,
,
1
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0
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F
F
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S
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H
4
2
4
2
21
,
,
1
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,
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F
F
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H
'
,
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1
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,
0
3
1
3
1
12
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F
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ON
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ON
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H
'
,
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1
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2
4
2
22
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h
er
e,
H
11
an
d
H
21
ar
e
th
e
b
i
n
ar
y
s
tates
o
f
th
e
f
ir
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t
an
d
s
ec
o
n
d
leg
o
f
t
h
e
f
ir
s
t
H
B
r
id
g
e
r
esp
ec
tiv
el
y
.
H
12
an
d
H
22
ar
e
th
e
b
in
ar
y
f
ac
to
r
s
o
f
th
e
f
ir
s
t
an
d
s
ec
o
n
d
leg
o
f
th
e
s
ec
o
n
d
H
B
r
id
g
e
r
esp
ec
tiv
el
y
.
P
o
s
s
ib
le
s
w
itc
h
in
g
co
n
f
i
g
u
r
at
io
n
s
o
f
th
e
C
HB
in
v
er
ter
ar
e
s
h
o
w
n
i
n
t
h
e
T
ab
le
1
.
T
ab
le
1
.
P
o
s
s
ib
le
s
w
i
tch
i
n
g
co
n
f
ig
u
r
atio
n
s
o
f
t
h
e
C
HB
i
n
v
er
t
er
H
1
1
H
2
1
H
1
2
H
2
2
Vo
0
0
0
0
0
0
0
0
1
-
V
DC
0
0
1
0
V
DC
0
0
1
1
0
0
1
0
0
-
V
DC
0
1
0
1
-
2V
DC
0
1
1
0
0
0
1
1
1
-
V
DC
1
0
0
0
V
DC
1
0
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0
1
0
1
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2V
DC
1
0
1
1
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DC
1
1
0
0
0
1
1
0
1
-
V
DC
1
1
1
0
V
DC
1
1
1
1
0
3.
SE
L
E
C
T
I
VE
H
ARM
O
NIC E
L
L
I
M
I
NAT
I
O
N
Selectiv
e
h
ar
m
o
n
ic
eli
m
i
n
atio
n
(
SHE)
tech
n
iq
u
e
ai
m
s
at
s
witch
i
n
g
O
N
an
d
OFF
t
h
e
s
e
m
i
co
n
d
u
cto
r
s
w
itc
h
es
i
n
s
u
c
h
a
w
a
y
t
h
at
th
e
d
esire
d
v
a
lu
e
o
f
v
o
lta
g
e
o
r
cu
r
r
en
t
f
u
n
d
a
m
e
n
tal
i
s
o
b
tain
ed
w
i
th
le
s
s
d
is
to
r
tio
n
.
T
h
e
an
g
les
f
o
r
s
w
i
tch
i
n
g
th
e
d
ev
ice
s
at
th
e
f
u
n
d
a
m
en
tal
f
r
eq
u
e
n
c
y
ar
e
ca
lcu
lated
b
y
s
o
l
v
i
n
g
th
e
tr
an
s
ce
n
d
en
tal
eq
u
at
io
n
s
et
t
h
at
ch
ar
ac
ter
ize
th
e
h
ar
m
o
n
i
cs
[
1
7
]
.
Fo
r
a
f
iv
e
-
le
v
el
in
v
e
r
ter
,
t
w
o
s
w
itch
in
g
an
g
le
s
ar
e
to
b
e
g
en
er
ated
b
y
s
o
lv
i
n
g
t
w
o
eq
u
atio
n
s
.
T
h
ese
eq
u
atio
n
s
ar
e
s
o
lv
ed
u
s
i
n
g
th
e
Ne
w
to
n
-
R
ap
h
s
o
n
(N
-
R
)
m
et
h
o
d
th
at
s
o
l
v
es
th
e
n
o
n
li
n
ea
r
eq
u
atio
n
s
w
i
th
in
it
ia
l
ap
p
r
o
x
i
m
ate
v
a
lu
e
s
is
t
h
e
o
n
e
a
m
o
n
g
t
h
e
f
a
s
tes
t
m
et
h
o
d
s
o
f
iter
atio
n
[
1
8
]
.
Fig
u
r
e
1
(
b
)
s
h
o
w
s
th
e
w
a
v
e
f
o
r
m
o
f
v
o
lta
g
e
f
o
r
th
e
f
iv
e
-
le
v
el
in
v
er
ter
ag
ai
n
s
t
t
h
e
s
w
i
tch
i
n
g
a
n
g
le
s
f
o
r
a
h
alf
c
y
cle.
E
x
p
r
es
s
in
g
t
h
i
s
w
a
v
e
f
o
r
m
i
n
E
q
n
.
(
1
)
w
it
h
t
h
e
h
elp
o
f
Fo
u
r
ier
s
er
ies.
)
s
i
n
(
)
co
s
(
co
s
4
)
(
2
1
5
,
3
,
1
t
n
n
V
t
v
n
DC
a
(
1
)
θ
1
an
d
θ
2
ar
e
t
h
e
s
w
itc
h
i
n
g
a
n
g
les,
w
h
er
e
0
<
θ
1
<
θ
2
<
π/2
.
F
r
o
m
E
q
u
atio
n
1
,
f
u
n
d
a
m
e
n
tal
v
o
ltag
e
is
g
iv
e
n
b
y
Eq
u
atio
n
2
[
1
9
-
2
1
]
.
)
c
o
s
(
c
o
s
4
2
1
1
DC
V
V
(
2
)
T
h
e
p
ea
k
f
u
n
d
a
m
e
n
tal
v
o
lta
g
e
is
DC
m
V
V
4
1
,
i.e
.
,
it
is
t
h
e
v
al
u
e
o
f
t
h
e
f
u
n
d
a
m
en
tal
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ltag
e
w
it
h
a
ll
th
e
s
w
i
tch
i
n
g
an
g
le
s
eq
u
ated
to
ze
r
o
.
Mo
d
u
latio
n
i
n
d
ex
(
M
I
)
is
d
e
f
i
n
ed
as
th
e
r
atio
b
et
w
ee
n
t
h
e
v
o
lta
g
e
f
u
n
d
a
m
en
ta
l
an
d
th
e
p
ea
k
v
o
l
tag
e
f
u
n
d
a
m
en
ta
l,
1
1
m
I
V
V
M
.
Fo
r
eli
m
i
n
ati
n
g
th
e
d
esire
d
h
ar
m
o
n
ic,
s
a
y
th
e
th
ir
d
h
ar
m
o
n
ic,
n
=3
is
s
u
b
s
tit
u
ted
i
n
E
q
u
at
io
n
1
a
n
d
i
s
eq
u
ated
to
ze
r
o
.
T
h
e
an
g
le
s
f
o
r
t
h
e
co
n
v
e
n
tio
n
al
SHE
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
F
P
GA
B
a
s
ed
S
elec
tive
Ha
r
mo
n
ic
E
limin
a
tio
n
Tech
n
iq
u
e
fo
r
M
u
ltil
ev
el
I
n
ve
r
ter
(
T.
P
o
r
s
elv
i
)
169
f
o
r
a
f
iv
e
-
le
v
el
i
n
v
er
ter
ar
e
ca
lcu
lated
u
s
i
n
g
t
h
e
f
u
n
d
a
m
e
n
tal
a
n
d
t
h
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t
h
ir
d
h
ar
m
o
n
ic
eq
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atio
n
s
g
i
v
e
n
b
y
Eq
u
atio
n
s
(
3
-
4
)
.
DC
V
V
4
c
o
s
c
o
s
1
2
1
(
3
)
0
)
3
c
o
s(
)
3
(
c
o
s
2
1
(
4
)
So
lv
i
n
g
(
3
)
an
d
(
4
)
b
y
Ne
w
to
n
-
R
ap
h
s
o
n
m
et
h
o
d
,
th
e
an
g
les
ar
e
ca
lcu
lated
as
θ
1
=
0
.
1
7
9
r
a
d
ian
s
an
d
θ
2
=0
.
8
7
r
a
d
ian
s
.
He
n
ce
,
th
e
t
h
ir
d
h
ar
m
o
n
ic
is
eli
m
i
n
ated
b
u
t
t
h
e
o
t
h
er
h
ar
m
o
n
ic
s
li
k
e
f
i
f
t
h
,
s
e
v
en
th
,
etc
ar
e
p
r
esen
t.
4.
NE
W
H
ARM
O
NIC E
L
L
I
M
I
NAT
I
O
N
A
n
e
w
SHE
t
ec
h
n
iq
u
e
to
m
in
i
m
ize
t
h
e
f
i
f
t
h
h
ar
m
o
n
ic,
a
lo
n
g
w
it
h
t
h
e
eli
m
i
n
atio
n
o
f
t
h
e
t
h
ir
d
o
r
d
er
h
ar
m
o
n
ic
i
s
co
n
s
id
er
ed
in
th
i
s
p
ap
er
.
T
h
is
is
ac
h
ie
v
ed
b
y
u
s
i
n
g
t
h
e
eq
u
a
tio
n
o
f
f
i
f
t
h
o
r
d
er
h
ar
m
o
n
ic
alo
n
g
w
it
h
eq
u
atio
n
o
f
t
h
e
t
h
ir
d
o
r
d
er
h
ar
m
o
n
ic
an
d
leav
in
g
t
h
e
f
u
n
d
a
m
en
tal
eq
u
a
tio
n
.
Fi
f
th
h
ar
m
o
n
ic
is
n
o
t
co
m
p
lete
l
y
el
i
m
in
ated
b
u
t
is
r
ed
u
ce
d
to
a
s
m
all
v
al
u
e
b
y
eq
u
ati
n
g
t
h
e
f
i
f
t
h
h
ar
m
o
n
ic
eq
u
a
tio
n
to
a
m
i
n
i
m
u
m
v
alu
e,
s
a
y
0
.
0
0
0
1
,
as g
iv
en
b
y
E
q
u
atio
n
5
.
0
0
0
1
.
0
)
5
(
c
o
s
)
5
c
o
s
(
2
1
(
5
)
B
y
s
o
l
v
i
n
g
E
q
u
atio
n
s
.
(
4
&
5
)
b
y
N
-
R
m
et
h
o
d
[
2
2
]
,
th
e
θ
1
a
n
d
θ
2
v
alu
es
ar
e
f
o
u
n
d
to
as
θ
1
=
0
.
2
0
9
4
r
ad
an
d
θ
2
=
0
.
8
3
7
8
r
ad
.
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h
e
n
e
w
s
elec
ti
v
e
h
ar
m
o
n
ic
eli
m
i
n
atio
n
r
ed
u
ce
s
o
n
e
m
o
r
e
ad
d
itio
n
al
h
ar
m
o
n
ic.
Fo
r
a
f
i
v
e
lev
e
l
in
v
er
ter
,
t
h
e
tech
n
iq
u
e
m
iti
g
a
tes
th
e
f
i
f
th
o
r
d
er
h
ar
m
o
n
ic
s
in
ad
d
itio
n
to
th
e
th
ir
d
o
r
d
er
h
ar
m
o
n
ic
s
.
Fo
r
a
s
ev
e
n
-
lev
el
i
n
v
er
ter
,
t
h
e
tec
h
n
iq
u
e
m
i
tig
ate
s
t
h
e
s
ev
e
n
t
h
o
r
d
er
h
ar
m
o
n
ic
s
alo
n
g
w
it
h
t
h
e
eli
m
i
n
atio
n
o
f
th
e
th
ir
d
an
d
f
i
f
t
h
o
r
d
er
h
ar
m
o
n
ic
s
an
d
s
o
o
n
.
He
n
ce
,
t
h
e
T
HD
v
alu
e
is
f
u
r
t
h
er
r
ed
u
ce
d
.
T
h
e
T
HD
is
o
n
e
a
m
o
n
g
th
e
v
ar
io
u
s
p
er
f
o
r
m
a
n
ce
p
ar
am
eter
s
o
f
i
n
v
er
ter
cir
cu
it
an
d
it
ca
n
b
e
f
o
u
n
d
u
s
i
n
g
Fo
u
r
ier
s
er
ies
[
2
3
]
.
T
HD
is
th
e
r
atio
b
et
w
ee
n
th
e
s
u
m
o
f
all
th
e
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
an
d
th
e
f
u
n
d
a
m
e
n
tal
co
m
p
o
n
e
n
t
o
f
t
h
e
v
o
lta
g
e
o
r
cu
r
r
en
t.
5.
RE
SU
L
T
S
AND
AN
AL
Y
SI
S
5
.
1
.
Si
m
ula
t
io
n r
esu
lt
s
Si
m
u
latio
n
w
o
r
k
o
f
t
h
e
f
i
v
e
-
l
ev
el
in
v
er
ter
is
d
o
n
e
u
s
i
n
g
MA
T
L
A
B
/
Si
m
u
li
n
k
w
it
h
t
h
e
co
n
v
e
n
tio
n
a
l
SHE
an
d
th
e
n
e
w
SHE
tech
n
iq
u
es.
W
av
e
f
o
r
m
s
o
f
t
h
e
s
i
m
u
lated
o
u
tp
u
t
v
o
lta
g
e
,
h
ar
m
o
n
ic
a
n
al
y
s
i
s
a
n
d
t
h
e
P
W
M
p
atter
n
f
o
r
b
o
th
th
e
tech
n
iq
u
e
s
ar
e
o
b
tain
ed
.
Fig
u
r
e
2
(
a
-
c)
r
esp
ec
ti
v
el
y
s
h
o
w
s
th
e
s
i
m
u
lated
o
u
tp
u
t
v
o
l
tag
e
o
f
t
h
e
M
L
I
,
th
e
h
ar
m
o
n
ic
an
al
y
s
i
s
a
n
d
th
e
P
W
M
p
atter
n
f
o
r
th
e
co
n
v
en
t
i
o
n
al
SHE.
Fig
u
r
e
3
(
a
-
c)
r
esp
ec
tiv
el
y
s
h
o
w
s
t
h
e
w
a
v
e
f
o
r
m
s
o
f
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
M
L
I
,
h
ar
m
o
n
ic
a
n
al
y
s
i
s
an
d
P
W
M
p
atter
n
f
o
r
th
e
n
e
w
SHE.
Fro
m
th
e
Fi
g
u
r
e
s
.
2
(
b
)
an
d
3
(
b
)
,
it
is
ev
id
en
t
t
h
a
t
th
e
T
HD
v
al
u
e
o
f
th
e
v
o
ltag
e
o
u
tp
u
t
is
1
8
.
4
6
%
w
it
h
th
e
co
n
v
e
n
tio
n
al
SHE
tech
n
iq
u
e
w
h
ile
it
is
1
7
.
4
%
w
i
th
t
h
e
n
e
w
SHE
m
et
h
o
d
.
Hen
ce
,
it
is
clea
r
t
h
at
t
h
e
p
r
o
p
o
s
ed
SHE
m
eth
o
d
r
es
u
lts
in
t
h
e
les
s
er
v
al
u
e
o
f
v
o
lta
g
e
T
HD
as c
o
m
p
ar
ed
t
o
th
at
o
f
th
e
co
n
v
e
n
tio
n
al
SH
E
m
et
h
o
d
.
T
h
e
T
a
b
le
2
co
m
p
ar
es th
e
T
HDs o
f
th
e
v
o
ltag
e
s
o
f
t
h
e
ML
I
f
o
r
th
e
t
wo
SHE
tech
n
iq
u
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
166
–
1
7
3
170
(
a)
(
b
)
(
c)
Fig
u
r
e
2
.
(
a)
Ou
tp
u
t v
o
lta
g
e
o
f
th
e
ML
I
,
(
b
)
Har
m
o
n
ic
An
al
y
s
is
,
an
d
(
c)
P
W
M
p
atter
n
f
o
r
th
e
co
n
v
e
n
tio
n
al
SHE.
(
a)
(
b
)
(
c)
Fig
u
r
e
3
.
(
a)
Ou
tp
u
t v
o
lta
g
e
wav
ef
o
r
m
o
f
M
L
I
,
(
b
)
w
a
v
e
f
o
r
m
o
f
Har
m
o
n
ic
An
al
y
s
i
s
,
(
c)
w
a
v
e
f
o
r
m
o
f
P
W
M
P
atter
n
f
o
r
n
e
w
SHE
T
ab
le
2
.
Vo
ltag
e
T
HD
co
m
p
ar
is
o
n
V
o
l
t
a
g
e
TH
D
w
i
t
h
t
h
e
c
o
n
v
e
n
t
i
o
n
a
l
S
H
E
t
e
c
h
n
i
q
u
e
V
o
l
t
a
g
e
TH
D
w
i
t
h
t
h
e
n
e
w
S
H
E
t
e
c
h
n
i
q
u
e
1
8
.
4
6
%
1
7
.
4
0
%
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
-
15
-
10
-5
0
5
10
15
T
i
m
e
(
S
e
c
on
ds
)
O
ut
put
V
ol
t
a
ge
of
M
L
I
(
V
ol
t
s
)
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
0
1
2
(
a
)
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
0
1
2
(
b)
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
0
1
2
(
c
)
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
0
1
2
(
d)
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
-
15
-
10
-5
0
5
10
15
T
i
m
e
(
S
e
c
on
ds
)
O
ut
put
V
ol
t
a
ge
of
M
L
I
(
V
ol
t
s
)
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
0
1
2
(
a)
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
0
1
2
(
b
)
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
0
1
2
(
c
)
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
0
1
2
(
d
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
F
P
GA
B
a
s
ed
S
elec
tive
Ha
r
mo
n
ic
E
limin
a
tio
n
Tech
n
iq
u
e
fo
r
M
u
ltil
ev
el
I
n
ve
r
ter
(
T.
P
o
r
s
elv
i
)
171
5
.
2
.
E
x
peri
m
ent
a
l r
esu
lt
s
T
h
e
p
r
o
p
o
s
ed
f
iv
e
-
lev
el
C
HB
in
v
er
ter
is
d
ev
elo
p
ed
in
h
ar
d
w
ar
e
an
d
is
ex
p
er
i
m
e
n
tal
l
y
v
er
if
ied
.
I
n
th
e
h
ar
d
w
ar
e,
MO
SF
E
T
s
w
itc
h
es a
r
e
u
s
ed
.
T
h
e
s
w
i
tch
e
s
ar
e
f
ir
ed
w
it
h
t
h
e
s
w
itc
h
in
g
a
n
g
le
s
o
b
tain
ed
w
it
h
t
h
e
n
e
w
SHE
tec
h
n
iq
u
e.
T
h
e
s
w
i
tch
i
n
g
a
n
g
les
ar
e
p
r
o
d
u
ce
d
w
it
h
t
h
e
FP
G
A
SP
AR
T
A
N
3
E
b
o
ar
d
.
Sp
ar
tan
-
3
FP
GAs
ar
e
p
er
f
ec
t
l
y
s
u
ited
t
o
all
t
y
p
e
o
f
elec
tr
o
n
ic
s
ap
p
li
ca
tio
n
s
d
u
e
to
its
lo
w
co
s
t.
F
P
GA
r
ea
lize
s
h
i
g
h
s
p
ee
d
s
w
itc
h
i
n
g
an
d
attai
n
s
a
h
i
g
h
o
v
er
s
a
m
p
li
n
g
r
ate
[
2
4
]
.
Fig
u
r
e
4
(
a)
an
d
4
(
b
)
s
h
o
w
th
e
s
n
ap
s
h
o
t
o
f
h
ar
d
w
ar
e
s
et
u
p
an
d
t
h
e
o
u
tp
u
t
v
o
ltag
e
r
esp
ec
ti
v
el
y
.
(
a)
(
b
)
Fig
u
r
e
4
.
(
a)
Sn
ap
s
h
o
t o
f
t
h
e
h
ar
d
w
ar
e
s
etu
p
,
(
b
)
Sn
ap
s
h
o
t o
f
th
e
o
u
tp
u
t
v
o
lta
g
e
w
av
e
f
o
r
m
(
a)
(
b
)
Fig
u
r
5
.
(
a)
Ou
tp
u
t v
o
lta
g
e,
(
b
)
Har
m
o
n
ic
an
al
y
s
is
.
I
t
is
s
ee
n
f
r
o
m
th
e
Fi
g
u
r
e
5
(
b
)
,
th
at
th
e
th
ir
d
h
ar
m
o
n
ic
is
r
em
o
v
ed
an
d
th
e
f
i
f
t
h
h
ar
m
o
n
ic
is
r
ed
u
ce
d
to
a
lo
w
v
alu
e.
I
t
is
al
s
o
s
ee
n
f
r
o
m
th
e
s
a
m
e
f
ig
u
r
e
th
at
t
h
e
v
o
lta
g
e
T
HD
f
o
r
ex
p
er
im
en
ta
l
o
u
tp
u
t
v
o
ltag
e
w
it
h
n
e
w
SHE
is
1
7
.
5
8
%
c
o
n
s
id
er
in
g
th
e
m
a
x
i
m
u
m
o
f
f
i
f
t
y
h
ar
m
o
n
ic
o
r
d
e
r
.
T
a
b
le
3
s
h
o
w
s
th
e
co
m
p
ar
i
s
o
n
o
f
v
o
lta
g
e
T
HDs
T
ab
le
3
.
C
o
m
p
ar
is
o
n
o
f
th
e
V
o
ltag
e
T
HDs o
f
th
e
s
i
m
u
lated
an
d
ex
p
er
i
m
e
n
tal
v
alu
e
s
V
o
l
t
a
g
e
T
H
D
w
i
t
h
t
h
e
n
e
w
S
H
E
t
e
c
h
n
i
q
u
e
f
o
r
si
m
u
l
a
t
e
d
v
o
l
t
a
g
e
V
o
l
t
a
g
e
T
H
D
w
i
t
h
t
h
e
n
e
w
S
H
E
t
e
c
h
n
i
q
u
e
f
o
r
e
x
p
e
r
i
me
n
t
a
l
v
o
l
t
a
g
e
1
7
.
4
0
%
1
7
.
5
8
%
6.
CO
NCLU
SI
O
N
A
n
e
w
SHE
m
e
th
o
d
is
p
r
o
p
o
s
ed
an
d
i
m
p
le
m
e
n
ted
f
o
r
th
e
f
i
v
e
-
le
v
el
i
n
v
er
ter
.
T
h
e
n
e
w
m
et
h
o
d
h
as
th
e
ad
v
an
tag
e
o
f
eli
m
i
n
ati
n
g
o
n
e
m
o
r
e
h
ar
m
o
n
ic
w
h
e
n
co
m
p
ar
ed
to
th
e
co
n
v
e
n
tio
n
al
o
n
e.
Si
m
u
lat
io
n
h
a
s
b
ee
n
ca
r
r
ied
o
u
t
f
o
r
th
e
in
v
er
ter
w
it
h
t
h
e
co
n
v
e
n
tio
n
a
l
an
d
t
h
e
n
e
w
S
HE
tec
h
n
iq
u
es.
T
h
e
s
i
m
u
lated
w
a
v
e
f
o
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E
lectr
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&
Dr
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Vo
l.
9
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.
1
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Ma
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ch
2
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8
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166
–
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3
172
th
e
co
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t
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ter
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C
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it
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tall
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h
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p
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tal
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lts
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t c
lo
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e
to
th
e
s
i
m
u
lat
ed
v
alu
e.
RE
F
E
R
E
NC
E
S
[
1
]
L
.
T
o
lb
e
rt,
F
-
Z.
P
e
n
g
,
a
n
d
T
.
Ha
b
e
tl
e
r,
“
M
u
lt
il
e
v
e
l
c
o
n
v
e
rter
s
f
o
r
larg
e
e
le
c
tri
c
d
riv
e
s
”
,
I
EE
E
T
ra
n
s.
In
d
Ap
p
li
c
a
ti
o
n
s,
v
o
l
.
3
5
,
p
p
.
36
-
4
4
,
1
9
9
9
.
[
2
]
J.Ro
d
rig
u
e
z
,
J
-
S
.
L
a
i,
F
.
Z.
P
e
n
g
,
“
M
u
l
ti
lev
e
l
in
v
e
rters
:
A
su
rv
e
y
o
f
to
p
o
l
o
g
ies
,
c
o
n
t
ro
ls,
a
n
d
a
p
p
l
ica
ti
o
n
s”
,
IE
EE
T
ra
n
sa
c
ti
o
n
o
n
In
d
u
stri
a
l
E
lec
tro
n
ics
,
v
o
l.
4
9
,
No
.
4
,
p
p
.
7
2
4
-
7
3
8
,
A
u
g
u
st 2
0
0
2
.
[
3
]
Jin
g
Nin
g
Yu
y
a
o
He
X
i’an
,
S
h
a
a
n
x
i,
“
Ph
a
se
-
S
h
if
ted
S
u
b
o
p
ti
ma
l
Pu
lse
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wid
th
mo
d
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la
t
io
n
stra
teg
y
fo
r
mu
lt
il
e
v
e
l
in
v
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r
”
,
P
r
o
c
e
e
d
in
g
s o
f
IEE
E
c
o
n
f
e
re
n
c
e
o
n
In
d
u
str
ial
El
e
c
tro
n
ics
a
n
d
A
p
p
li
c
a
ti
o
n
s,
p
p
.
-
1
-
5
,
2
0
0
6
.
[
4
]
Bu
m
-
S
e
o
k
S
u
h
,
S
i
n
h
a
G
.
,
M
a
n
jrek
a
r
M
.
D.,
L
ip
o
T
.
A
.
,
“
Po
we
r
Co
n
v
e
rs
io
n
:
A
n
Ov
e
rv
iew
o
f
T
o
p
o
lo
g
ie
a
n
d
M
o
d
u
l
a
ti
o
n
S
tr
a
teg
ies
”
,
P
ro
c
e
e
d
i
n
g
s
o
f
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th
In
tern
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ti
o
n
a
l
Co
n
f
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re
n
c
e
o
n
Op
ti
m
iza
ti
o
n
o
f
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e
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tri
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a
l
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n
d
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e
c
tro
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ic
Eq
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i
p
m
e
n
ts,
v
o
l
.
2
,
p
p
.
A
D
-
11
-
AD
-
2
4
,
1
9
9
8
.
[
5
]
T
.
M
e
y
n
a
rd
a
n
d
H.
F
o
c
h
,
“
M
u
lt
i
-
lev
e
l
c
o
n
v
e
rsio
n
:
“
Hig
h
v
o
lt
a
g
e
c
h
o
p
p
e
rs
a
n
d
v
o
lt
a
g
e
-
so
u
rc
e
i
n
v
e
rte
rs
,
”
P
ro
c
.
2
3
r
d
A
n
n
u
.
P
o
w
e
r
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e
c
tro
n
.
S
p
e
c
.
Co
n
f
.
,
J
u
n
.
1
9
9
2
,
v
o
l.
1
,
p
p
.
3
9
7
–
4
0
3
.
[
6
]
S
.
A
ll
e
b
ro
d
,
R
.
Ha
m
e
rs
k
i,
a
n
d
R.
M
a
rq
u
a
r
d
t,
“
Ne
w
tra
n
sfo
rm
e
rle
ss
,
sc
a
la
b
le
mo
d
u
l
a
r
mu
lt
il
e
v
e
l
c
o
n
v
e
rte
rs
fo
r
HVDC
-
tra
n
sm
issio
n
,
”
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ro
c
.
IEE
E
P
o
w
e
r
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e
c
tro
n
.
S
p
e
c
.
Co
n
f
.
,
Ju
n
.
2
0
0
8
,
p
p
.
1
7
4
–
1
7
9
.
[
7
]
A
.
A
n
to
n
o
p
o
u
lo
s
,
L
.
A
n
g
q
u
ist,
S
.
No
rrg
a
,
K.
Ilv
e
s,
L
.
Ha
rn
e
f
o
rs,
a
n
d
¨
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P
.
Ne
e
,
“
M
o
d
u
lar
m
u
lt
il
e
v
e
l
c
o
n
v
e
rte
r
a
c
m
o
to
r
d
riv
e
s
w
it
h
c
o
n
sta
n
t
to
r
q
u
e
f
ro
m
z
e
ro
to
n
o
m
in
a
l
sp
e
e
d
,
”
IEE
E
T
ra
n
s.
I
n
d
.
Ap
p
l
.
,
v
o
l.
5
0
,
n
o
.
3
,
p
p
.
1
9
8
2
–
1
9
9
3
,
M
a
y
2
0
1
4
.
[
8
]
S
.
De
b
n
a
th
,
J.
Qin
,
B.
Ba
h
ra
n
i,
M
.
S
a
e
e
d
if
a
rd
,
a
n
d
P
.
Ba
rb
o
sa
,
“
Op
e
ra
ti
o
n
,
c
o
n
tr
o
l,
a
n
d
a
p
p
l
ica
ti
o
n
s
o
f
th
e
m
o
d
u
lar
m
u
lt
il
e
v
e
l
c
o
n
v
e
rter:
A
re
v
ie
w
,
”
IEE
E
T
ra
n
s.
P
o
we
r E
lec
tro
n
.
,
v
o
l.
3
0
,
n
o
.
1
,
p
p
.
3
7
–
5
3
,
Ja
n
.
2
0
1
5
.
[
9
]
J.
N.
C
h
a
isso
n
,
L
.
M
.
T
o
lb
e
rt,
K.
J.
M
c
k
e
n
z
ie,
a
n
d
Z.
Du
,
“
A
Un
if
ied
A
p
p
ro
a
c
h
to
S
o
lv
i
n
g
th
e
Ha
rm
o
n
ic
El
im
in
a
ti
o
n
Eq
u
a
ti
o
n
s
in
M
u
lt
il
e
v
e
l
Co
n
v
e
rters
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
El
e
c
tro
n
ics
,
v
o
l.
1
9
,
n
o
.
2
,
M
a
rc
h
2
0
0
4
,
p
p
.
4
7
8
-
4
9
0
.
[
1
0
]
S
.
S
iri
s
u
k
p
ra
se
rt,
J.
S
.
L
a
i,
a
n
d
T
.
H.
L
iu
,
“
Op
ti
m
u
m
Ha
r
m
o
n
ic
Re
d
u
c
ti
o
n
w
it
h
a
W
id
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
E
T
ra
n
s
a
c
ti
o
n
s
o
n
In
d
u
st
ria
l
El
e
c
tro
n
ics
,
v
o
l.
4
9
,
n
o
.
4
,
A
u
g
u
st
2
0
0
2
,
p
p
.
875
-
8
8
1
.
[
1
1
]
O.
Bo
u
h
a
li
,
E.
M
.
Be
rk
o
u
k
,
C.
S
a
u
d
e
m
o
n
t,
a
n
d
B.
F
ra
n
ç
o
is,
“
A
Fi
v
e
lev
e
l
Dio
d
e
Cla
mp
e
d
In
v
e
rte
r
wit
h
se
lf
-
sta
b
il
iz
a
ti
o
n
o
f
t
h
e
DC
-
L
in
k
Vo
lt
a
g
e
fo
r
Gr
id
Co
n
n
e
c
ti
o
n
o
f
Distrib
u
ted
Ge
n
e
ra
to
rs
”
,
IEE
E
In
tern
a
ti
o
n
a
l
S
y
m
p
o
s
iu
m
o
n
In
d
u
strial
El
e
c
tro
n
ics
:
IS
IE
2
0
0
4
,
M
a
y
3
-
7
,
2
0
0
4
.
[
1
2
]
Iw
a
sz
k
i
e
w
icz
Ja
n
a
n
d
P
e
rz
Ja
c
e
k
,
“
Fo
u
rie
r
S
e
rie
s
a
n
d
W
a
v
e
let
T
ra
n
sfo
rm
A
p
p
li
e
d
to
S
tep
p
e
d
W
a
v
e
fo
rm
s
S
y
n
th
e
sis
in
M
u
lt
i
lev
e
l
Co
n
v
e
rto
rs
”
,
P
r
o
c
e
e
d
in
g
s o
f
El
e
c
tro
tec
h
n
ica
l
In
sti
tu
t
e
,
2
0
0
6
,
p
p
.
5
9
-
74.
[
1
3
]
J.W
a
n
g
,
Y.
Hu
a
n
g
,
a
n
d
F
.
Z.
P
e
n
g
,
“
A
p
ra
c
ti
c
a
l
h
a
rm
o
n
ics
e
li
m
in
a
ti
o
n
m
e
th
o
d
f
o
r
m
u
lt
il
e
v
e
l
in
v
e
r
ters
”
,
IEE
E
IA
S
An
n
u
a
l
M
e
e
ti
n
g
,
2
0
0
5
,
p
p
.
1
6
6
5
-
1
6
7
0
.
[
1
4
]
T
P
o
rse
lv
i,
R
M
u
t
h
u
,
“
S
e
v
e
n
lev
e
l
th
re
e
p
h
a
se
c
a
sc
a
d
e
d
h
b
rid
g
e
in
v
e
rter
w
it
h
a
sin
g
le
d
c
so
u
rc
e
"
,
A
RP
N
J
o
u
rn
a
l
o
f
En
g
i
n
e
e
rin
g
a
n
d
A
p
p
li
e
d
S
c
ien
c
e
s
,
v
o
l.
7
,
n
o
.
1
2
,
p
p
.
1
5
4
6
-
1
5
5
4
.
[
1
5
]
S
u
n
g
G
e
u
n
S
o
n
g
,
F
e
e
l
S
o
o
n
Ka
n
g
,
S
u
n
g
-
Ju
n
P
a
rk
,
“
Ca
sc
a
d
e
d
M
u
lt
il
e
v
e
l
In
v
e
rter
E
m
p
lo
y
i
n
g
T
h
re
e
-
P
h
a
se
T
ra
n
s
f
o
r
m
e
rs
a
n
d
S
in
g
le
DC
In
p
u
t”,
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
In
d
u
st
ria
l
El
e
c
tro
n
ics
,
V
o
l
.
5
6
,
No
.
6
,
p
p
.
2
0
0
5
-
2
0
1
4
,
2
0
0
9
.
[
1
6
]
Y.
S
u
re
sh
,
A
.
K.
P
a
n
d
a
,
“
Per
fo
rm
a
n
c
e
o
f
Ca
sc
a
d
e
M
u
lt
il
e
v
e
l
H
-
Brid
g
e
In
v
e
rte
r
wit
h
S
in
g
l
e
DC
S
o
u
rc
e
b
y
Emp
lo
y
i
n
g
L
o
w
Fre
q
u
e
n
c
y
T
h
r
e
e
Ph
a
se
T
ra
n
sfo
rm
e
rs
”
,
IECON
-
36
th
A
n
n
u
a
l
Co
n
f
e
re
n
c
e
o
f
IEE
E
In
d
u
strial
El
e
c
tro
n
ics
S
o
c
iety
,
P
h
e
o
n
ix
,
A
Z,
USA
,
p
p
.
1
9
8
1
-
1
9
8
6
,
2
0
1
0
.
[
1
7
]
F
a
n
g
Zh
e
n
g
P
e
n
g
,
Jih
-
S
h
e
n
g
L
a
i
,
J.
M
c
Ke
e
v
e
r
a
n
d
J.
V
a
n
C
o
e
v
e
rin
g
,
“
A
M
u
lt
il
e
v
e
l
V
o
lt
a
g
e
-
S
o
u
r
c
e
In
v
e
rter
w
it
h
S
e
p
a
ra
te
DC
S
o
u
rc
e
s
f
o
r
S
tatic
V
a
r
G
e
n
e
ra
ti
o
n
”
,
IEE
E
T
r
a
n
sa
c
t
io
n
s
o
n
In
d
u
stry
A
p
p
l
ica
ti
o
n
s
,
v
o
l.
3
2
,
No
.
5
,
p
p
.
1
1
3
0
-
1
1
3
8
,
S
e
p
tem
b
e
r/
Oc
to
b
e
r
1
9
9
6
.
[
1
8
]
C.
W
o
o
d
f
o
rd
a
n
d
C.
P
h
il
li
p
s,
“
Nu
m
e
ric
a
l
M
e
th
o
d
s
w
it
h
W
o
rk
e
d
Ex
a
m
p
les
”
,
Ch
a
p
m
a
n
a
n
d
Ha
ll
,
p
p
.
4
5
-
5
7
,
F
irst
e
d
it
io
n
1
9
9
7
.
[
1
9
]
Ja
g
d
ish
Ku
m
a
r
a
n
d
Biswa
ru
p
Da
s,
“
S
e
lec
ti
v
e
Ha
rm
o
n
ic
El
imi
n
a
t
i
o
n
T
e
c
h
n
i
q
u
e
f
o
r
a
M
u
lt
il
e
v
e
l
In
v
e
rte
r
”
,
F
if
te
e
n
th
Na
ti
o
n
a
l
P
o
w
e
r
S
y
ste
m
s Co
n
fe
re
n
c
e
(NPS
C),
IIT
Bo
m
b
a
y
,
p
p
.
6
0
8
-
6
1
,
2
0
0
8
.
[
2
0
]
A
li
A
ja
m
i,
M
o
h
a
m
m
a
d
Re
z
a
J
a
n
n
a
ti
Os
k
u
e
e
,
a
n
d
A
ta
Ollah
M
o
k
h
b
e
rd
o
ra
n
,
“
Im
p
lem
e
n
tatio
n
o
f
No
v
e
l
T
e
c
h
n
iq
u
e
f
o
r
S
e
lec
ti
v
e
Ha
r
m
o
n
ic
El
i
m
in
a
ti
o
n
in
M
u
lt
il
e
v
e
l
In
v
e
rters
Ba
se
d
o
n
ICA
”
,
A
d
v
a
n
c
e
s
in
P
o
w
e
r
El
e
c
tro
n
ics
,
2
0
1
3
,
p
p
1
-
1
1
.
[
2
1
]
D.
A
h
m
a
d
i,
K.
Zo
u
,
C.
L
i,
Y.
H
u
a
n
g
,
a
n
d
J.
W
a
n
g
,
“
A
u
n
iv
e
rsa
l
se
lec
ti
v
e
h
a
r
m
o
n
ic
e
li
m
in
a
ti
o
n
m
e
th
o
d
f
o
r
h
ig
h
-
p
o
w
e
r
in
v
e
rters
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
Po
we
r E
lec
tro
n
ics
,
v
o
l.
2
6
,
n
o
.
1
0
,
p
p
.
2
7
4
3
–
2
7
5
2
,
2
0
1
1
.
[
2
2
]
T
.
P
o
rse
lv
i
&
R.
M
u
t
h
u
,
“
M
o
d
e
li
n
g
a
n
d
Co
n
tro
l
o
f
th
e
P
M
S
G
f
o
r
th
e
W
in
d
En
e
rg
y
Co
n
v
e
rsio
n
S
y
ste
m
w
it
h
th
e
CHB
In
v
e
rter
w
it
h
th
e
Ne
w
S
e
lec
ti
v
e
Ha
r
m
o
n
ic
El
im
in
a
ti
o
n
T
e
c
h
n
i
q
u
e
”
,
In
ter
n
a
ti
o
n
a
l
Rev
iew
o
n
M
o
d
e
ll
in
g
a
n
d
S
imu
l
a
ti
o
n
,
v
o
l.
6
,
n
o
.
3
,
p
p
.
7
6
7
-
7
7
3
,
2
0
1
3
.
[
2
3
]
Hu
ss
a
in
Ba
ss
i,
“
A
M
o
d
u
latio
n
S
c
h
e
m
e
f
o
r
F
lo
a
ti
n
g
S
o
u
rc
e
M
u
lt
il
e
v
e
l
In
v
e
rter
T
o
p
o
lo
g
y
w
it
h
In
c
re
a
se
d
Nu
m
b
e
r
o
f
Ou
tp
u
t
L
e
v
e
ls
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
te
r
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
Vo
l.
6
,
No
.
5
,
Oc
to
b
e
r
2
0
1
6
,
p
p
.
1
9
8
5
-
1
9
9
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
F
P
GA
B
a
s
ed
S
elec
tive
Ha
r
mo
n
ic
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limin
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Tech
n
iq
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e
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r
M
u
ltil
ev
el
I
n
ve
r
ter
(
T.
P
o
r
s
elv
i
)
173
[2
4
]
Hir
o
k
i
Ku
ru
m
a
tan
i
,
“
FP
GA
-
b
a
se
d
v
o
lt
a
g
e
c
o
n
tro
l
wit
h
PD
M
in
v
e
rte
r
fo
r
wid
e
b
a
n
d
d
riv
e
sy
ste
m
u
sin
g
T
-
typ
e
n
e
u
tra
l
-
p
o
in
t
-
c
l
a
mp
e
d
to
p
o
l
o
g
y
”
,
EE
E
I
n
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
M
e
c
h
a
tro
n
ics
(ICM
),
2
0
1
7
,
p
p
.
1
-
5.
[2
5
]
A
th
ira
S
,
De
e
p
a
K
,
“
M
o
d
if
ied
Bid
irec
ti
o
n
a
l
Co
n
v
e
rter
w
it
h
Cu
rre
n
t
F
e
d
I
n
v
e
rter”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(
IJ
PE
DS
)
,
v
o
l
.
6
,
No
2
,
p
p
.
3
9
6
–
4
1
0
,
Ju
n
e
2
0
1
5
.
[2
6
]
R.
Na
ir,
M
a
h
a
lak
sh
m
i
R
a
n
d
S
in
d
h
u
T
h
a
m
p
a
tt
y
K.
C.
,
“
Per
fo
rm
a
n
c
e
o
f
th
re
e
p
h
a
se
1
1
-
lev
e
l
i
n
v
e
rte
r
wit
h
re
d
u
c
e
d
n
u
mb
e
r
o
f
switc
h
e
s
u
sin
g
d
if
fer
e
n
t
PW
M
tec
h
n
iq
u
e
s
,”
I
n
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
T
e
c
h
n
o
l
o
g
ica
l
A
d
v
a
n
c
e
m
e
n
ts
in
P
o
w
e
r
a
n
d
En
e
rg
y
(
TA
P
En
e
rg
y
)
,
Ko
ll
a
m
,
p
p
.
3
7
5
-
3
8
0
,
2
0
1
5
.
[2
7
]
K.
De
e
p
a
,
S
a
v
it
h
a
.
P
b
,
a
n
d
Vin
o
d
h
i
n
i.
Bb
,
“
Ha
rm
o
n
ic
a
n
a
lys
is
o
f
a
mo
d
if
ie
d
c
a
sc
a
d
e
d
mu
lt
il
e
v
e
l
in
v
e
rte
r
”
,
2
0
1
1
1
st
In
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
El
e
c
t
rica
l
En
e
rg
y
S
y
ste
m
s,
2
0
1
1
,
p
p
.
9
2
-
9
7
.
[2
8
]
R.
M
a
h
a
lak
sh
m
i
a
n
d
T
h
a
m
p
a
tt
y
,
K.
C.
S
in
d
h
u
,
“
Im
p
lem
e
n
tat
io
n
o
f
G
rid
Co
n
n
e
c
ted
P
V
a
rra
y
u
sin
g
Qu
a
d
ra
ti
c
DC
-
DC Co
n
v
e
rter an
d
S
in
g
le
P
h
a
se
M
u
lt
i
L
e
v
e
l
In
v
e
rter
”
,
In
d
i
a
n
J
o
u
rn
a
l
o
f
S
c
ien
c
e
a
n
d
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
8
,
2
0
1
5
.
[
2
9
]
P
a
rv
a
ti
Na
ir
,
De
e
p
a
.
K,
"
Tw
o
-
p
o
rt
DC
-
DC
c
o
n
v
e
rter
w
it
h
f
l
y
b
a
c
k
in
v
e
rter
f
o
r
ru
ra
l
li
g
h
ti
n
g
a
p
p
li
c
a
ti
o
n
s"
,
P
r
o
c
e
e
d
in
g
s
o
f
IEE
E
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
Tec
h
n
o
lo
g
ica
l
Ad
v
a
n
c
e
m
e
n
ts
in
P
o
w
e
r
a
n
d
En
e
rg
y
,
TA
P
En
e
rg
y
2
0
1
5
,
p
p
.
2
4
9
-
2
5
3
,
2
0
1
5
.
B
I
O
G
RAP
H
I
E
S O
F
AUTH
O
RS
Dr
.
T.
Po
r
se
l
v
i,
A
ss
o
c
iate
P
ro
f
e
ss
o
r
in
th
e
De
p
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l
&
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
h
a
s
1
9
y
e
a
rs
o
f
te
a
c
h
in
g
e
x
p
e
rie
n
c
e
.
S
h
e
re
c
e
iv
e
d
h
e
r
B.
E.
d
e
g
re
e
in
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
f
ro
m
M
a
d
ra
s
Un
iv
e
rsity
,
M
.
E.
d
e
g
re
e
in
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Driv
e
s
f
r
o
m
A
n
n
a
Un
iv
e
rsit
y
a
n
d
P
h
.
D
d
e
g
re
e
f
ro
m
A
n
n
a
Un
iv
e
rsit
y
.
S
h
e
is
a
li
fe
m
e
m
b
e
r
o
f
IE
T
E
a
n
d
IS
T
E.
He
r
a
re
a
s
o
f
in
tere
st
in
c
lu
d
e
P
o
w
e
r
E
lec
tro
n
ics
,
W
in
d
En
e
rg
y
S
y
st
e
m
s
,
El
e
c
tri
c
a
l
M
a
c
h
in
e
s,
Co
n
tro
l
S
y
st
e
m
s,
a
n
d
Ne
tw
o
rk
T
h
e
o
ry
.
S
h
e
h
a
s
a
u
th
o
re
d
2
tex
tb
o
o
k
s
o
n
“
El
e
c
tri
c
a
l
M
a
c
h
in
e
s”
a
n
d
“
Co
n
tro
l
S
y
ste
m
s”
.
S
h
e
h
a
s
p
u
b
l
ish
e
d
1
5
in
ter
n
a
ti
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n
a
l
jo
u
rn
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l
p
a
p
e
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9
p
a
p
e
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ter
n
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ti
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l
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f
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n
d
9
p
a
p
e
rs i
n
n
a
ti
o
n
a
l
c
o
n
f
e
re
n
c
e
Dr
.
K
.
De
e
p
a
g
ra
d
u
a
ted
f
ro
m
A
l
a
g
a
p
p
a
c
h
e
tt
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o
ll
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g
e
o
f
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g
in
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rin
g
a
n
d
T
e
c
h
n
o
il
o
g
y
,
T
.
N,
In
d
ia i
n
1
9
9
8
.
S
h
e
o
b
tain
e
d
M
.
T
e
c
h
d
e
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re
e
f
ro
m
A
n
n
a
Un
iv
e
rsit
y
,
G
u
in
d
y
c
a
m
p
u
s,
T
.
N,
In
d
ia i
n
2
0
0
5
.
S
h
e
re
c
e
iv
e
d
Do
c
to
ra
l
d
e
g
re
e
f
ro
m
Ja
wa
h
a
rlal
Ne
h
ru
T
e
c
h
n
o
l
o
g
ica
l
Un
iv
e
rsit
y
,
A
n
a
n
tap
u
r,
A
.
P
,
In
d
ia
in
2
0
1
7
.
Cu
r
re
n
tl
y
sh
e
is
w
o
rk
in
g
a
s
A
ss
ist
a
n
t
p
ro
f
e
ss
o
r
in
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
E
n
g
in
e
e
rin
g
De
p
a
rtm
e
n
t,
Am
rit
a
S
c
h
o
o
l
o
f
En
g
in
e
e
rin
g
,
Am
rit
a
V
ish
w
a
V
id
y
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