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[
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an
d
its
as
s
o
ciate
d
w
a
v
e
f
o
r
m
T
h
e
s
w
itch
in
g
a
n
g
les
f
o
r
t
h
e
s
u
cc
es
s
f
u
l
o
p
er
atio
n
o
f
t
h
e
m
u
l
tilev
el
in
v
er
ter
is
d
esi
g
n
ed
to
m
i
n
i
m
ize
h
ar
m
o
n
ics.
T
h
is
ca
n
b
e
ac
h
ie
v
ed
b
y
o
p
ti
m
izatio
n
al
g
o
r
ith
m
.
Ma
n
y
m
et
h
o
d
s
w
er
e
p
r
o
p
o
s
ed
in
t
h
e
liter
at
u
r
e
to
esti
m
ate
s
w
i
tch
in
g
a
n
g
le
s
f
o
r
m
u
ltil
e
v
el
i
n
v
er
ter
.
Vec
to
r
-
o
p
ti
m
ized
h
ar
m
o
n
ic
eli
m
in
a
tio
n
f
o
r
s
in
g
le
p
h
as
e
P
u
ls
e
-
W
it
h
Mo
d
u
lated
in
v
er
t
er
[
7
]
,
co
n
s
id
er
s
d
c
-
li
n
k
r
ip
p
le
d
u
e
to
f
i
n
ite
d
c
-
li
n
k
ca
p
ac
itan
ce
i
n
o
p
ti
m
ized
s
w
itc
h
in
g
a
n
g
le
ca
lcu
la
tio
n
.
I
n
ap
p
licatio
n
r
eq
u
ir
i
n
g
ca
p
ac
i
to
r
s
ize
o
p
ti
m
izatio
n
,
r
ip
p
le
ca
p
ac
ito
r
f
ilter
ca
n
in
tr
o
d
u
ce
lo
w
er
o
r
d
er
h
ar
m
o
n
ics
to
f
lo
w
i
n
th
e
a
c
lo
ad
.
Hal
f
-
w
av
e
s
y
m
m
e
tr
y
s
elec
ti
v
e
h
a
r
m
o
n
ic
e
li
m
in
a
tio
n
m
et
h
o
d
w
as
i
m
p
le
m
en
ted
f
o
r
f
i
v
e
lev
el
i
n
v
er
ter
[
8
]
w
it
h
v
ar
y
in
g
m
o
d
u
latio
n
in
d
ex
r
a
n
g
e
0
to
1
.
1
5
SHEPW
M
ca
n
g
en
er
ate
m
o
r
e
s
o
lu
tio
n
s
t
h
an
q
u
ar
ter
w
a
v
e
s
y
m
m
etr
ical
m
et
h
o
d
a
n
d
as
y
m
m
e
tr
y
m
et
h
o
d
.
B
u
t
co
m
p
lex
it
y
in
cr
ea
s
es
d
u
e
to
m
o
r
e
n
u
m
b
e
r
o
f
eq
u
atio
n
s
.
S
h
u
f
f
led
Fro
g
L
ea
p
in
g
A
l
g
o
r
ith
m
h
as
b
ee
n
u
tili
ze
d
i
n
[
9
]
to
ca
lcu
late
s
w
i
tch
i
n
g
an
g
les
f
o
r
elev
en
lev
el
i
n
v
er
ter
.
I
n
O
p
ti
m
al
P
u
ls
e
W
id
th
Mo
d
u
lati
o
n
[
1
0
]
b
ased
o
n
h
ar
¬
m
o
n
ic
i
n
j
ec
tio
n
an
d
eq
u
al
ar
ea
cr
iter
ia
h
a
s
b
ee
n
a
p
p
lied
f
o
r
Selectiv
e
Har
m
o
n
ic
E
li
m
i
n
atio
n
in
m
u
ltil
e
v
el
co
n
¬v
er
ter
s
w
i
th
u
n
b
ala
n
ce
d
d
c
v
o
ltag
e
s
o
u
r
c
e.
Har
m
o
n
ic
eli
m
i
n
atio
n
an
d
o
p
tim
izatio
n
o
f
th
e
s
tep
p
ed
v
o
ltag
e
o
f
a
1
3
-
le
v
e
l
i
n
v
er
ter
w
a
s
m
ad
e
b
y
B
ac
ter
ial
Fo
r
ag
in
g
Alg
o
r
it
h
m
[
1
1
]
B
ased
o
n
th
e
f
o
r
ag
i
n
g
b
eh
av
io
r
o
f
a
co
lo
n
y
o
f
a
n
ts
,
a
n
o
v
el
al
g
o
r
ith
m
f
o
r
s
elec
t
iv
e
h
ar
m
o
n
ic
e
li
m
in
at
io
n
i
n
p
u
l
s
e
w
id
t
h
m
o
d
u
latio
n
w
a
s
d
ev
elo
p
ed
[
1
2
]
.
B
ee
alg
o
r
ith
m
h
as b
ee
n
ap
p
lied
to
7
-
le
v
el
in
v
er
ter
to
eli
m
i
n
ate
lo
w
er
o
r
d
er
h
ar
m
o
n
i
cs b
y
s
elec
ti
v
e
h
ar
m
o
n
ic
eli
m
i
n
atio
n
p
u
ls
e
w
id
th
m
o
d
u
latio
n
in
[
1
3
]
.
T
h
e
b
ac
k
lo
g
o
f
B
ee
alg
o
r
ith
m
is
t
h
at
t
h
e
co
d
e
is
co
m
p
le
x
an
d
t
h
e
r
u
n
t
i
m
e
i
s
m
o
r
e
co
m
p
ar
ed
to
g
e
n
etic
a
lg
o
r
ith
m
.
Ge
n
etic
al
g
o
r
ith
m
h
as
b
ee
n
u
tili
ze
d
to
r
ed
u
ce
h
ar
m
o
n
ic
s
in
9
-
le
v
el
in
v
er
ter
[
1
4
]
.
Selectiv
e
Har
m
o
n
ic
E
li
m
i
n
atio
n
T
ec
h
n
iq
u
e
u
s
ed
in
m
u
ltil
e
v
el
in
v
er
ter
b
y
n
eu
r
al
n
et
w
o
r
k
[
1
5
]
.
Mitig
atio
n
o
f
h
ar
m
o
n
ic
s
in
i
n
d
u
s
tr
ial
m
o
to
r
d
r
iv
e
h
a
v
e
r
ep
o
r
ted
in
[
1
6
]
.
Fil
ter
s
h
a
v
e
b
ee
n
u
s
ed
to
r
ed
u
ce
h
ar
m
o
n
ics
in
d
is
tr
ib
u
t
io
n
s
y
s
te
m
[
1
7
]
.
Mo
s
t o
f
th
e
m
et
h
o
d
s
ad
o
p
ted
in
t
h
e
liter
at
u
r
e,
d
id
n
o
t
co
n
s
i
d
er
b
o
th
th
e
cu
r
r
en
t
h
ar
m
o
n
ic
s
an
d
v
o
lta
g
e
h
ar
m
o
n
ics.
T
h
e
n
u
m
b
er
o
f
le
v
els
u
s
ed
is
le
s
s
t
h
an
1
3
an
d
th
e
y
f
ailed
to
d
escr
ib
e
ab
o
u
t
th
e
h
ar
m
o
n
ics
c
h
ar
ac
ter
is
tic
s
f
o
r
R
L
lo
ad
an
d
Mo
to
r
lo
ad
.
I
n
th
e
p
r
o
p
o
s
ed
m
e
th
o
d
,
co
m
p
ar
is
o
n
is
m
ad
e
w
it
h
1
3
lev
el,
1
5
lev
el
an
d
1
7
lev
el
in
v
er
ter
s
.
C
u
r
r
en
t
a
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
201
7
:
10
–
19
12
v
o
ltag
e
h
ar
m
o
n
ic
s
w
er
e
s
i
m
u
lated
f
o
r
R
lo
ad
,
R
L
lo
ad
an
d
s
i
n
g
le
p
h
ase
in
d
u
ctio
n
m
o
to
r
lo
ad
u
tili
zi
n
g
g
en
et
ic
alg
o
r
it
h
m
to
es
ti
m
ate
s
w
itc
h
i
n
g
an
g
les.
2.
G
E
NE
T
I
C
A
L
G
O
RI
T
H
M
Ge
n
etic
al
g
o
r
ith
m
i
s
a
co
m
p
u
tatio
n
al
m
o
d
el
t
h
at
s
o
lv
es
o
p
t
i
m
izatio
n
p
r
o
b
lem
s
b
y
i
m
ita
ti
n
g
g
e
n
etic
p
r
o
ce
s
s
es
an
d
th
e
th
eo
r
y
o
f
e
v
o
lu
tio
n
b
y
u
s
i
n
g
g
e
n
etic
o
p
er
ato
r
s
lik
e
r
ep
r
o
d
u
ctio
n
,
cr
o
s
s
o
v
er
,
m
u
tatio
n
etc.
Am
o
u
n
t
s
o
f
ap
p
licatio
n
s
h
a
v
e
b
en
ef
ited
f
r
o
m
t
h
e
u
ti
lizatio
n
o
f
g
e
n
etic
al
g
o
r
ith
m
.
Ge
n
etic
alg
o
r
ith
m
i
s
s
til
l
a
n
o
v
el
tec
h
n
iq
u
e
f
o
r
P
W
M
-
SHE
tech
n
iq
u
e.
T
h
is
alg
o
r
it
h
m
is
u
s
u
all
y
u
s
ed
to
ac
co
m
p
lis
h
a
n
ea
r
g
lo
b
al
o
p
tim
u
m
s
o
lu
tio
n
.
E
ac
h
i
ter
atio
n
o
f
t
h
e
G
A
is
a
n
e
w
s
et
o
f
s
tr
i
n
g
s
,
w
h
ich
ar
e
ca
lled
ch
r
o
m
o
s
o
m
es,
w
it
h
i
m
p
r
o
v
ed
f
it
n
es
s
is
p
r
o
d
u
ce
d
u
s
i
n
g
g
e
n
etic
o
p
er
ato
r
s
.
2
.
1
.
Chro
m
o
s
o
m
e
re
prese
nta
t
io
n
I
n
G
A
,
ea
ch
ch
r
o
m
o
s
o
m
e
i
s
u
s
ed
as
a
f
ea
s
ib
le
s
o
lu
tio
n
f
o
r
th
e
p
r
o
b
le
m
,
w
h
er
e
ea
c
h
c
h
r
o
m
o
s
o
m
e
is
d
ev
elo
p
ed
b
ased
o
n
s
in
g
le
d
i
m
en
s
io
n
a
l a
r
r
a
y
s
w
it
h
a
len
g
t
h
o
f
S,
w
h
er
e
S
is
t
h
e
n
u
m
b
er
o
f
an
g
les.
2
.
2
.
I
nitia
lize
po
pu
la
t
io
n
Set
a
p
o
p
u
latio
n
s
ize,
N,
i.e
.
th
e
n
u
m
b
er
o
f
ch
r
o
m
o
s
o
m
es
in
a
p
o
p
u
latio
n
.
T
h
en
in
i
tialize
th
e
ch
r
o
m
o
s
o
m
e
v
al
u
es
r
an
d
o
m
l
y
.
I
f
k
n
o
w
n
,
th
e
r
an
g
e
o
f
th
e
g
en
es
s
h
o
u
ld
b
e
co
n
s
id
er
ed
f
o
r
in
itializatio
n
.
P
o
p
u
latio
n
s
ize
d
ep
en
d
s
o
n
l
y
o
n
th
e
n
at
u
r
e
o
f
t
h
e
p
r
o
b
le
m
an
d
it
m
u
s
t
ac
h
iev
e
a
b
alan
c
e
b
et
w
ee
n
t
h
e
ti
m
e
co
m
p
le
x
it
y
a
n
d
t
h
e
s
ea
r
c
h
s
p
ac
e
m
ea
s
u
r
e.
T
h
e
n
ar
r
o
w
er
t
h
e
r
an
g
e,
th
e
f
a
s
ter
G
A
co
n
v
er
g
es.
I
n
t
h
is
p
ap
er
,
p
o
p
u
latio
n
s
ize
is
co
n
s
id
er
ed
as 1
0
0
.
2
.
3
.
Repro
du
ct
io
n
T
h
e
r
ep
r
o
d
u
ctio
n
o
p
er
ato
r
d
eter
m
i
n
es
h
o
w
t
h
e
p
ar
en
ts
a
r
e
ch
o
s
en
to
cr
ea
te
th
e
o
f
f
s
p
r
in
g
.
T
h
is
o
p
er
ato
r
is
a
p
r
o
ce
s
s
in
w
h
ic
h
ch
r
o
m
o
s
o
m
es
ar
e
co
p
ied
ac
co
r
d
in
g
to
th
eir
o
b
j
ec
tiv
e
f
u
n
ctio
n
v
al
u
es
i.e
.
th
e
d
eg
r
ee
o
f
co
n
f
o
r
m
it
y
o
f
ea
ch
o
b
j
ec
t is ca
lc
u
lated
a
n
d
a
n
i
n
d
iv
id
u
al
is
r
ef
o
r
m
ed
u
n
d
er
a
f
la
t r
u
le
d
ep
en
d
in
g
o
n
th
e
d
eg
r
ee
o
f
co
n
f
o
r
m
it
y
.
2
.
4
.
Cro
s
s
o
v
er
C
r
o
s
s
o
v
er
is
t
h
e
m
o
s
t
s
i
g
n
i
f
ic
an
t
o
p
er
atio
n
in
G
A
.
I
t
cr
ea
tes
a
g
r
o
u
p
o
f
ch
ild
r
en
f
r
o
m
t
h
e
p
ar
en
ts
b
y
ex
ch
a
n
g
in
g
g
e
n
es
a
m
o
n
g
t
h
e
m
.
T
h
e
n
e
w
o
f
f
s
p
r
in
g
co
n
tai
n
m
i
x
ed
g
e
n
es
f
r
o
m
b
o
th
p
ar
en
t
s
.
B
y
d
o
in
g
t
h
is
,
t
h
e
cr
o
s
s
o
v
er
o
p
er
ato
r
n
o
t
o
n
ly
p
r
o
v
id
es
n
e
w
p
o
in
ts
f
o
r
f
u
r
t
h
er
test
i
n
g
w
it
h
in
t
h
e
c
h
r
o
m
o
s
o
m
es,
w
h
ich
ar
e
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I
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PEDS
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SS
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2088
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8
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erin
g
....
(
S
u
r
esh
N
a
ta
r
a
ja
n
)
15
(
a)
(
b
)
Fig
u
r
e
4
.
15
-
lev
el
in
v
er
ter
R
l
o
ad
(
a)
Vo
ltag
e
T
HD%
(
b
)
C
u
r
r
en
t T
HD
Gen
etic
a
lg
o
r
it
h
m
h
a
s
b
ee
n
u
s
ed
to
ca
lcu
late
t
h
e
s
w
itc
h
i
n
g
a
n
g
le
s
f
o
r
th
e
m
u
lt
ilev
e
l i
n
v
er
t
er
.
B
u
t th
e
s
w
itc
h
in
g
a
n
g
les
d
eter
m
in
ed
b
y
t
h
e
alg
o
r
it
h
m
v
ar
ie
s
f
o
r
d
i
f
f
er
en
t
r
u
n
lead
in
g
to
v
ar
iatio
n
i
n
t
h
e
T
HD.
So
th
e
alg
o
r
ith
m
h
as
b
ee
n
r
u
n
f
o
r
5
ti
m
es
an
d
i
ts
r
es
u
lt
s
w
er
e
p
lo
tte
d
in
g
r
ap
h
.
F
ig
u
r
e
6
s
h
o
w
s
th
e
T
HD
co
m
p
ar
is
o
n
f
o
r
5
ti
m
es
r
u
n
o
f
1
3
,
1
5
an
d
1
7
lev
el
i
n
v
er
ter
o
f
R
lo
ad
.
Si
m
i
lar
l
y
Fi
g
u
r
e
1
0
a
n
d
1
4
s
h
o
w
s
t
h
e
T
HD
co
m
p
ar
is
o
n
f
o
r
5
ti
m
es
r
u
n
o
f
1
3
,
1
5
an
d
1
7
lev
el
in
v
er
t
er
o
f
R
L
lo
ad
an
d
m
o
to
r
lo
ad
r
esp
ec
tiv
el
y
.
T
h
e
r
esu
lt
s
in
d
icate
th
at
as
t
h
e
le
v
el
o
f
t
h
e
in
v
er
ter
i
n
c
r
ea
s
es
t
h
e
T
HD
d
ec
r
ea
s
es.
Fro
m
F
ig
u
r
e
9
(
b
)
it
is
also
clea
r
th
at
f
o
r
ce
r
tain
r
u
n
,
T
HD
o
f
1
5
lev
el
in
v
er
ter
is
less
t
h
an
1
7
-
le
v
el
in
v
er
ter
.
I
t
is
d
u
e
to
th
e
f
ac
t
th
at
t
h
e
g
e
n
etic
alg
o
r
ith
m
h
as
b
ee
n
u
s
ed
to
ca
l
cu
late
s
w
itc
h
i
n
g
an
g
les,
co
n
s
i
d
er
in
g
t
h
e
r
ed
u
ct
io
n
o
f
3
r
d
,
5
th
,
7
th
,
9
t
h
a
n
d
1
1
th
o
r
d
er
h
ar
m
o
n
ics.
B
u
t
o
t
h
er
h
i
g
h
er
o
r
d
er
h
ar
m
o
n
ic
s
w
er
e
n
o
t
tak
e
n
i
n
to
ac
co
u
n
t.
Su
c
h
h
i
g
h
o
r
d
er
h
ar
m
o
n
ic
s
m
i
g
h
t
h
a
v
e
co
n
tr
ib
u
ted
to
th
e
in
cr
ea
s
e
i
n
T
HD.
T
h
e
r
es
u
lts
s
h
o
w
t
h
at
f
o
r
s
ev
e
n
tee
n
le
v
el
ca
s
ca
d
ed
-
H
b
r
id
g
e
in
v
er
ter
t
h
e
T
HD
w
as
w
e
ll
w
it
h
in
t
h
e
I
E
E
E
5
1
9
s
tan
d
ar
d
.
(
a)
(
b
)
Fig
u
r
e
5
.
17
-
lev
el
in
v
er
ter
R
l
o
ad
(
a)
Vo
ltag
e
T
HD%
(
b
)
C
u
r
r
en
t T
HD%
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
8
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8
694
IJ
PEDS
Vo
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8
,
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1
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Ma
r
ch
201
7
:
10
–
19
16
(
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(
b
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Fig
u
r
e
6
.
13,
15,
1
7
L
ev
el
in
v
er
ter
R
l
o
ad
(
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V
o
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e
T
HD
%
co
m
p
ar
is
o
n
(
b
)
C
u
r
r
en
t T
H
D% c
o
m
p
ar
is
o
n
(
a)
(
b
)
Fig
u
r
e
7
.
13
-
lev
el
in
v
er
ter
R
L
lo
ad
(
a)
Vo
ltag
e
T
HD%
(
b
)
C
u
r
r
en
t T
HD%
(
a)
(
b
)
Fig
u
r
e
8
.
15
-
lev
el
in
v
er
ter
R
L
lo
ad
(
a)
Vo
ltag
e
T
HD%
(
b
)
C
u
r
r
en
t T
HD%
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2088
-
8
694
C
o
mp
a
r
is
o
n
o
f Ca
s
ca
d
ed
H
-
b
r
id
g
e
I
n
ve
r
ters
fo
r
Ha
r
mo
n
ic
Mit
i
g
a
tio
n
C
o
n
s
id
erin
g
....
(
S
u
r
esh
N
a
ta
r
a
ja
n
)
17
(
a)
(
b
)
Fig
u
r
e
9
.
17
-
lev
el
in
v
er
ter
R
L
lo
ad
(
a)
Vo
ltag
e
T
HD
% (
b
)
C
u
r
r
en
t T
HD%
(
a)
(
b
)
Fi
g
u
r
e
10
.
13,
15,
1
7
L
ev
el
in
v
er
ter
R
L
lo
ad
(
a)
Vo
ltag
e
T
H
D% c
o
m
p
ar
is
o
n
(
b
)
C
u
r
r
e
n
t T
HD%
co
m
p
ar
is
o
n
(
a)
(
b
)
Fig
u
r
e
11
.
13
-
lev
el
in
v
er
ter
M
lo
ad
(
a)
Vo
ltag
e
T
HD%
(
b
)
C
u
r
r
en
t T
HD%
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
694
IJ
PEDS
Vo
l.
8
,
No
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1
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Ma
r
ch
201
7
:
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18
(
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(
b
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Fig
u
r
e
12
.
15
-
lev
el
in
v
er
ter
M
lo
ad
(
a)
Vo
ltag
e
T
HD%
(
b
)
C
u
r
r
en
t T
HD%
(
a)
(
b
)
Fig
u
r
e
13
.
17
-
lev
el
in
v
er
ter
M
lo
ad
(
a)
Vo
ltag
e
T
HD%
(
b
)
C
u
r
r
en
t T
HD%
(
a)
(
b
)
Fig
u
r
e
14
.
13,
15,
1
7
L
ev
el
in
v
er
ter
M
lo
ad
(
a)
Vo
ltag
e
T
H
D% c
o
m
p
ar
is
o
n
(
b
)
C
u
r
r
e
n
t T
HD%
co
m
p
ar
is
o
n
4.
CO
NCLU
SI
O
N
T
h
e
co
m
p
ar
is
o
n
b
et
w
ee
n
t
h
ir
teen
,
f
if
teen
a
n
d
s
e
v
en
teen
l
ev
el
o
f
ca
s
ca
d
ed
H
-
b
r
id
g
e
i
n
v
er
ter
h
a
s
b
ee
n
d
o
n
e
u
s
in
g
Ma
tlab
.
T
h
e
r
esu
lt
s
i
n
d
icate
w
h
en
t
h
e
n
u
m
b
er
o
f
lev
el
i
n
cr
ea
s
e
s
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
d
ec
r
ea
s
es.
Fo
r
R
L
lo
ad
th
e
cu
r
r
en
t
h
ar
m
o
n
ics
ar
e
m
i
n
i
m
ize
d
to
a
g
r
ea
ter
ex
ten
t.
B
u
t
as
th
e
n
u
m
b
er
o
f
lev
el
in
cr
ea
s
es,
m
o
r
e
s
w
itc
h
i
n
g
d
ev
ices
h
as
to
b
e
in
co
r
p
o
r
ated
w
h
ich
r
es
u
lts
i
n
m
o
r
e
s
w
itc
h
i
n
g
lo
s
s
es
an
d
r
ed
u
ce
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2088
-
8
694
C
o
mp
a
r
is
o
n
o
f Ca
s
ca
d
ed
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-
b
r
id
g
e
I
n
ve
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ters
fo
r
Ha
r
mo
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ic
Mit
i
g
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tio
n
C
o
n
s
id
erin
g
....
(
S
u
r
esh
N
a
ta
r
a
ja
n
)
19
ef
f
icien
c
y
.
Dep
en
d
in
g
u
p
o
n
t
h
e
ap
p
licatio
n
o
f
lo
ad
,
ca
s
ca
d
ed
H
-
b
r
id
g
e
i
n
v
er
ter
ca
n
b
e
s
u
itab
l
y
d
esi
g
n
ed
,
u
tili
zi
n
g
g
e
n
etic
al
g
o
r
ith
m
f
o
r
s
w
itc
h
in
g
a
n
g
le
e
s
ti
m
atio
n
,
w
i
th
m
in
i
m
u
m
to
tal
h
ar
m
o
n
ic
d
i
s
to
r
tio
n
.
RE
F
E
R
E
NC
E
S
[1
]
R.
S
.
R
.
Ba
b
u
a
n
d
J
.
He
n
ry
,
“
A
Co
m
p
a
riso
n
o
f
Ha
lf
Brid
g
e
&
F
u
ll
Brid
g
e
Iso
late
d
DC
-
DC
Co
n
v
e
rters
f
o
r
El
e
c
tro
ly
sis
A
p
p
li
c
a
ti
o
n
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
S
o
ft
Co
mp
u
ti
n
g
a
n
d
En
g
i
n
e
e
rin
g
,
v
o
l.
1
,
p
p
.
3
7
-
4
2
,
2
0
1
1
.
[2
]
R.
D
He
n
d
e
rso
n
a
n
d
P
.
J.
Ro
se
,
“
Ha
r
m
o
n
ics
:
T
h
e
e
ffe
c
ts
o
n
p
o
we
r
q
u
a
li
ty
a
n
d
tran
sf
o
r
m
e
r
s,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
I
n
d
u
stry
Ap
p
li
c
a
t
io
n
s
,
v
o
l.
3
0
,
p
p
.
5
2
8
–
3
2
,
1
9
9
4
.
[3
]
N.
S
u
re
sh
a
n
d
R.
S
.
R
.
Ba
b
u
,
“
Re
v
ie
w
o
n
Ha
r
m
o
n
ics
a
n
d
it
s
E
li
m
in
a
ti
n
g
S
trate
g
ies
in
P
o
w
e
r
S
y
ste
m
,
”
In
d
ia
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
,
p
p
.
1
-
9
,
2
0
1
5
.
[4
]
S.
T
h
o
m
a
s,
e
t
a
l
.,
“
Co
sts
a
n
d
b
e
n
e
f
it
s
o
f
h
a
rm
o
n
ic
c
u
r¬
re
n
t
r
e
d
u
c
ti
o
n
f
o
r
sw
it
c
h
-
m
o
d
e
p
o
w
e
r
su
p
p
li
e
s
i
n
a
c
o
m
m
e
rc
ial
o
ff
ic
e
b
u
il
d
in
g
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
I
n
d
u
stry
Ap
p
li
c
a
ti
o
n
s
,
v
o
l.
3
2
,
p
p
.
1
0
1
7
–
2
5
,
1
9
9
6
.
[5
]
J
.
Ro
d
ríg
u
e
z
,
e
t
a
l
.,
“
M
u
l
ti
lev
e
l
In
v
e
rters
:
A
S
u
rv
e
y
o
f
T
o
p
o
l
o
g
ies
,
Co
n
tro
ls,
a
n
d
A
p
p
li
c
a
ti
o
n
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
.
4
9
,
p
p
.
7
2
4
-
7
3
8
,
2
0
0
2
.
[6
]
M.
G
.
V
.
K
u
m
a
r,
e
t
a
l
.,
“
Co
m
p
a
riso
n
o
f
m
u
lt
il
e
v
e
l
in
v
e
rters
w
it
h
P
W
M
Co
n
tr
o
l
M
e
t
h
o
d
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
IT
,
En
g
i
n
e
e
rin
g
a
n
d
A
p
p
l
ied
S
c
ie
n
c
e
s R
e
se
a
rc
h
,
v
o
l.
1
,
p
p
.
25
-
2
9
,
2
0
1
2
.
[7
]
S.
Ha
d
ji
,
e
t
a
l
.,
“
V
e
c
to
r
-
o
p
ti
m
ize
d
h
a
r
m
o
n
ic
e
li
m
in
a
ti
o
n
f
o
r
sin
g
le
-
p
h
a
se
p
u
lse
-
w
id
th
m
o
d
u
latio
n
in
v
e
rters
/co
n
v
e
rters
,
”
IET
El
e
c
tric P
o
we
r A
p
p
li
c
a
ti
o
n
s
,
v
o
l.
1
,
p
p
.
423
–
3
2
,
2
0
0
7
.
[8
]
W
.
F
e
i,
e
t
a
l
.,
“
Ha
lf
-
w
a
v
e
s
y
m
m
e
tr
y
s
e
lec
ti
v
e
h
a
rm
o
n
ic
e
li
m
i¬n
a
ti
o
n
m
e
th
o
d
f
o
r
m
u
lt
il
e
v
e
l
v
o
lt
a
g
e
so
u
rc
e
in
v
e
rters
,
”
IET
P
o
we
r E
lec
tro
n
,
v
o
l.
4
,
p
p
.
3
4
2
–
5
1
,
2
0
1
0
.
[9
]
H
.
L
o
u
,
e
t
a
l
.,
“
F
u
n
d
a
m
e
n
tal
m
o
d
u
latio
n
stra
teg
y
w
it
h
se
lec
ti
v
e
h
a
r
m
o
n
ic
e
li
m
in
a
ti
o
n
f
o
r
m
u
lt
il
e
v
e
l
in
v
e
rters
,
”
IET
Po
we
r E
lec
tro
n
,
v
o
l.
7
,
p
p
.
2
1
7
3
–
8
1
,
2
0
1
4
.
[1
0
]
D.
A
h
m
a
d
i,
e
t
a
l
.,
“
A
u
n
iv
e
rsa
l
se
le
c
ti
v
e
h
a
r
m
o
n
ic
e
li
m
i
n
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
s
o
n
Po
we
r E
lec
tro
n
i
c
s
,
v
o
l.
2
6
,
p
p
.
2
7
4
3
–
5
2
,
2
0
1
1
.
[1
1
]
R
.
S
a
leh
i,
e
t
a
l
.,
“
Ha
r
m
o
n
ic
e
li
m
in
a
ti
o
n
a
n
d
o
p
ti
m
iza
ti
o
n
o
f
ste
p
p
e
d
v
o
lt
a
g
e
o
f
m
u
lt
il
e
v
e
l
in
v
e
r
ter
b
y
b
a
c
t
e
rial
f
o
ra
g
in
g
a
lg
o
rit
h
m
,
”
J
o
u
rn
a
l
o
f
E
lec
trica
l
En
g
in
e
e
rin
g
a
n
d
T
e
c
h
n
o
lo
g
y
,
v
o
l.
5
,
p
p
.
5
4
5
–
5
1
,
2
0
1
0
.
[1
2
]
S.
Kin
a
tt
i
n
g
a
l,
e
t
a
l
.,
“
In
v
e
rter
h
a
rm
o
n
ic
e
li
m
in
a
ti
o
n
th
r
o
u
g
h
a
c
o
lo
n
y
o
f
c
o
n
ti
n
u
o
u
sly
e
x
p
lo
ri
n
g
a
n
ts,
”
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
.
5
4
,
p
p
.
2
5
5
8
–
6
5
,
2
0
0
7
.
[1
3
]
Ka
v
o
u
si
A
.
,
e
t
a
l
.,
“
A
p
p
li
c
a
ti
o
n
o
f
th
e
b
e
e
a
lg
o
rit
h
m
f
o
r
se
le
c
ti
v
e
h
a
r
m
o
n
ic
e
li
m
in
a
ti
o
n
stra
teg
y
in
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
Po
we
r E
lec
tro
n
ics
,
v
o
l
.
2
7
,
p
p
.
1
6
8
9
–
9
6
,
2
0
1
2
.
[1
4
]
G
.
Ge
ra
,
e
t
a
l
.,
“
Re
d
u
c
ti
o
n
o
f
T
o
tal
Ha
r
m
o
n
ic
Disto
rti
o
n
in
P
o
w
e
r
In
v
e
rto
rs
Us
in
g
Ge
n
e
ti
c
A
l
g
o
rit
h
m
,
”
In
t.
J
o
u
rn
a
l
o
f
E
n
g
i
n
e
e
rin
g
Res
e
a
rc
h
a
n
d
Ap
p
li
c
a
ti
o
n
s,
v
o
l.
3
,
p
p
.
7
6
1
-
7
6
6
,
2
0
1
3
.
[1
5
]
O.
Bo
u
h
a
l
i,
e
t
a
l
.
,
“
S
o
lv
in
g
Ha
rm
o
n
ic
El
im
in
a
ti
o
n
Eq
u
a
ti
o
n
s
i
n
M
u
lt
i
-
lev
e
l
In
v
e
rters
b
y
u
sin
g
N
e
u
ra
l
Ne
tw
o
rk
s
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
I
n
fo
rm
a
t
io
n
a
n
d
El
e
c
tro
n
ics
En
g
i
n
e
e
rin
g
,
v
o
l.
3
,
p
p
.
1
9
1
-
1
9
5
,
2
0
1
3
.
[1
6
]
Y.
K
.
L
a
th
a
,
e
t
a
l
.
,
“
Ha
r
m
o
n
ics
M
it
ig
a
ti
o
n
o
f
In
d
u
strial
M
o
t
o
r
Driv
e
s
w
it
h
Ac
ti
v
e
P
o
w
e
r
F
il
ters
in
Ce
m
e
n
t
P
lan
t
-
A
Ca
se
S
tu
d
y
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
,
v
o
l.
2
,
p
p
.
1
-
8
,
2
0
1
4
.
[1
7
]
A.
A
ri
v
a
ra
su
a
n
d
R.
Ba
las
u
b
ra
m
a
n
iu
m
,
“
Clo
se
d
L
o
o
p
No
n
L
in
e
a
r
Co
n
tro
l
o
f
S
h
u
n
t
Hy
b
rid
P
o
w
e
r
F
il
ter
f
o
r
Ha
r
m
o
n
ics
M
it
ig
a
ti
o
n
i
n
In
d
u
str
ial
Distrib
u
ti
o
n
S
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
,
v
o
l.
5
,
p
p
.
1
8
5
-
1
9
4
,
2
0
1
4
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
M
r.
N.S
u
re
sh
h
a
s
c
o
m
p
lete
d
B.
E
f
ro
m
A
n
n
a
u
n
iv
e
rsity
in
2
0
0
7
.
H
e
o
b
tain
e
d
M
.
E
d
e
g
re
e
in
t
h
e
f
ield
o
f
c
o
n
tro
l
a
n
d
i
n
stru
m
e
n
tatio
n
f
ro
m
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
,
G
u
in
d
y
A
n
n
a
Un
iv
e
rsity
in
2
0
0
9
.
P
re
se
n
tl
y
,
h
e
is
w
o
rk
in
g
a
s
A
ss
istan
t
P
ro
f
e
ss
o
r
in
S
a
th
y
a
b
a
m
a
Un
iv
e
rsit
y
,
Ch
e
n
n
a
i
a
n
d
d
o
i
n
g
re
se
a
rc
h
in
p
o
w
e
r
e
lec
tr
o
n
ics
.
His
a
re
a
s
o
f
in
tere
st
a
r
e
p
o
w
e
r
e
lec
tro
n
ics
,
c
o
n
tr
o
l
e
n
g
in
e
e
rin
g
a
n
d
a
rti
f
icia
l
in
telli
g
e
n
c
e
.
Dr.
R.
S
a
m
u
e
l
Ra
jes
h
Ba
b
u
h
a
s
o
b
tai
n
e
d
h
is
B
.
E
De
g
re
e
f
ro
m
M
a
d
ra
s
Un
iv
e
rsit
y
in
2
0
0
3
.
He
o
b
tai
n
e
d
h
is
M
.
E
d
e
g
re
e
f
ro
m
A
n
n
a
Un
iv
e
rsit
y
in
2
0
0
5
.
He
o
b
tain
e
d
h
is
P
h
.
D
d
e
g
re
e
f
ro
m
S
a
th
y
a
b
a
m
a
Un
iv
e
rsit
y
in
2
0
1
3
.
P
re
se
n
tl
y
h
e
is
a
A
ss
o
c
iate
P
ro
f
e
ss
o
r
in
S
a
th
y
a
b
a
m
a
Un
iv
e
rsit
y
.
His a
re
a
s o
f
in
tere
st are
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Dig
it
a
l
P
ro
tec
ti
o
n
.
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