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m
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ter
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n
d
c
o
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tro
l
with
les
se
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c
o
m
p
o
n
e
n
ts.
T
h
is
p
a
p
e
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re
v
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s
d
iffere
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t
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u
l
ti
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l
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t
o
p
o
l
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ies
t
h
a
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h
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led
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m
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d
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WM
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q
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s
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to
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o
g
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h
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se
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a
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t
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e
c
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sc
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e
d
H
-
b
rid
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m
u
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v
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l
in
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M
LI
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to
p
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g
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r
5
-
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7
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lev
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a
n
d
9
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rm
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ic
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tai
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d
f
o
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t
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t
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o
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n
LC
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ter
in
t
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t.
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se
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e
th
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re
a
p
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n
th
e
c
a
sc
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d
e
d
m
u
lt
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l
in
v
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rter
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n
d
re
su
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a
re
c
o
m
p
a
re
d
fo
r
h
a
rm
o
n
ic red
u
c
t
io
n
in
t
h
e
i
n
v
e
rter o
u
t
p
u
t
.
K
ey
w
o
r
d
s
:
C
ascad
ed
H
-
b
r
id
g
e
in
v
er
ter
Mu
ltil
ev
el
in
v
er
ter
s
Ph
ase
d
is
p
o
s
itio
n
Ph
ase
o
p
p
o
s
itio
n
Var
iab
le
f
r
eq
u
e
n
cy
PW
M
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
:
Nay
an
a
Gan
g
ad
h
ar
a
Dep
ar
tm
en
t o
f
E
lectr
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an
d
E
lectr
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ics E
n
g
in
ee
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n
g
,
Sri
S
id
d
h
ar
th
a
I
n
s
titu
te
o
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T
ec
h
n
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l
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g
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T
u
m
k
u
r
,
Kar
n
atak
a
,
I
n
d
ia
E
m
ail:
n
ay
an
ass
ittu
m
k
u
r
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
R
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
(
R
E
S)
ap
p
licatio
n
s
,
h
ig
h
v
o
ltag
e
D
C
tr
an
s
m
is
s
io
n
(
HVDC),
u
n
in
ter
r
u
p
tib
le
p
o
wer
s
u
p
p
ly
(
UPS),
elec
tr
ic
v
eh
icles
(
E
V)
an
d
m
icr
o
g
r
id
a
p
p
licatio
n
s
with
b
atter
y
s
to
r
ag
e
ap
p
licatio
n
s
u
s
es
in
v
er
ter
s
as
its
im
p
o
r
tan
t
p
o
we
r
p
r
o
ce
s
s
in
g
u
n
it
[
1
]
,
[
2
]
.
Per
f
o
r
m
an
ce
o
f
th
e
s
q
u
ar
e
wav
e
i
n
v
er
ter
s
ar
e
im
p
r
o
v
e
d
u
s
in
g
ad
v
a
n
ce
d
to
p
o
l
o
g
ies
an
d
d
if
f
e
r
en
t
PW
M
tech
n
iq
u
es.
Mu
ltil
ev
el
in
v
er
ter
t
o
p
o
lo
g
ies
an
d
s
in
u
s
o
id
al
two
-
lev
el
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
tech
n
iq
u
es
ar
e
f
ew
o
f
th
em
[
3
]
,
[
4
]
.
Hig
h
er
p
en
etr
a
tio
n
o
f
R
E
S
in
t
h
e
d
is
tr
ib
u
tio
n
s
y
s
tem
s
h
av
e
m
a
d
e
th
e
h
ig
h
e
r
s
u
r
g
e
in
th
e
u
s
e
o
f
DC
-
DC
co
n
v
er
ter
s
,
in
v
er
te
r
s
an
d
o
th
e
r
r
elate
d
p
o
wer
elec
tr
o
n
ics
d
ev
ices.
S
i
n
ce
th
e
R
E
S
p
o
wer
g
en
er
atio
n
is
a
c
o
s
tly
p
h
e
n
o
m
en
o
n
,
th
e
co
n
v
er
ter
s
u
s
ed
in
th
ese
ap
p
licatio
n
s
a
r
e
ex
p
ec
te
d
to
h
av
e
ex
ce
llen
t
p
er
f
o
r
m
a
n
ce
an
d
d
e
p
en
d
a
b
le
[
5
]
.
I
n
v
er
t
er
s
ar
e
e
x
p
ec
ted
to
g
en
er
ate
v
o
ltag
e
th
at
ca
n
g
e
n
er
ate
n
ea
r
s
in
u
s
o
id
al
v
o
ltag
e
wav
ef
o
r
m
s
o
th
at
it
ca
n
b
e
co
n
n
ec
ted
an
d
s
y
n
ch
r
o
n
ize
d
[
6
]
t
o
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
.
T
h
e
b
asic
in
v
er
t
er
th
at
g
en
er
ates
wav
e
th
at
p
r
o
d
u
ce
s
p
o
s
itiv
e
h
alf
with
0
=+
(
/
2
)
,
an
d
th
e
n
e
g
ativ
e
h
alf
with
0
=
−(
/
2
)
[
7
]
,
[
8
]
th
u
s
p
r
o
d
u
cin
g
th
e
s
q
u
ar
e
wav
e.
Switch
i
n
g
lo
s
s
es
an
d
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
ar
e
h
i
g
h
f
o
r
th
ese
in
v
er
ter
s
an
d
th
ey
ar
e
n
o
t f
it
f
o
r
s
y
n
ch
r
o
n
izatio
n
with
o
u
t
a
d
o
p
tin
g
s
o
p
h
is
ticated
PW
M
t
ec
h
n
iq
u
es
[
9
]
.
B
o
th
s
tr
ess
o
n
th
e
s
witch
an
d
th
e
h
ar
m
o
n
ic
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is
to
r
tio
n
is
ev
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in
th
ese
tr
ad
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in
v
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ter
s
,
an
d
th
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it
lo
s
es
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f
ea
s
ib
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to
co
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to
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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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s
t
I
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N:
2088
-
8
6
9
4
Ha
r
mo
n
ic
r
ed
u
ctio
n
tech
n
i
q
u
e
s
in
r
en
ewa
b
le
en
erg
y
d
is
tr
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tio
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s
ystems
…
(
N
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Ga
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a
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r
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77
d
is
tr
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u
tio
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etwo
r
k
[
1
0
]
,
[
1
1
]
.
R
ed
u
ctio
n
o
f
h
ar
m
o
n
ic
d
is
to
r
tio
n
an
d
g
en
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r
atin
g
n
ea
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s
in
u
s
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id
al
wav
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r
m
f
r
o
m
th
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in
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ter
s
ar
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all
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ess
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to
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ak
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in
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id
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v
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s
m
u
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ev
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in
v
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ter
(
ML
I
)
to
p
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lo
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wh
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d
eliv
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p
r
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v
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p
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f
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m
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d
[
1
2
]
.
R
ed
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d
h
ar
m
o
n
ics
in
h
ig
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s
witch
in
g
f
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m
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th
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ch
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ac
ter
is
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f
th
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ML
I
s
.
Hig
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n
u
m
b
er
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f
s
witch
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in
clu
d
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in
t
h
e
ML
I
to
p
o
lo
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in
cr
ea
s
es
th
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s
y
s
tem
co
m
p
lex
ity
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u
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f
d
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cir
cu
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f
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ate
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r
im
p
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ML
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wh
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a
d
d
s
to
th
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s
y
s
tem
'
s
co
m
p
lex
ity
.
T
h
u
s
,
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c
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o
f
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attem
p
ted
b
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ch
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g
in
g
th
e
t
o
p
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lo
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y
o
f
ML
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th
at
co
u
ld
wo
r
k
i
n
th
e
s
am
e
m
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er
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with
r
e
d
u
ce
d
s
witch
es [
1
3
]
,
[
1
4
]
.
T
h
e
to
p
o
lo
g
ical
im
p
r
o
v
em
en
t
o
f
th
e
ML
I
s
led
to
its
u
s
ag
e
in
in
d
u
s
tr
ial
ap
p
licatio
n
s
th
at
r
ec
k
o
n
s
h
i
g
h
p
o
wer
[
1
5
]
,
[
1
6
]
.
T
h
e
tr
a
n
s
itio
n
o
f
th
e
to
p
o
lo
g
ical
v
ar
iatio
n
o
f
th
e
ML
I
s
in
v
o
lv
es
th
e
Dio
d
e
-
clam
p
ed
to
p
o
lo
g
y
,
f
ly
in
g
ca
p
ac
ito
r
(
ca
p
ac
ito
r
-
cla
m
p
ed
)
,
to
th
e
c
ascad
ed
H
-
b
r
id
g
e
m
u
ltil
ev
el
t
o
p
o
l
o
g
ies
[
1
7
]
.
I
n
th
e
d
io
d
e
clam
p
e
d
ML
I
to
p
o
lo
g
y
to
o
b
tain
n
-
lev
e
l
o
u
tp
u
t
n
-
1
ca
p
ac
ito
r
s
,
2
(
n
-
1
)
s
witch
es,
(
n
-
1
)
(
n
-
2
)
clam
p
i
n
g
d
io
d
es
ar
e
r
eq
u
ir
ed
[
1
8
]
-
[
2
2
]
.
T
h
e
c
o
n
tr
o
l
o
f
b
o
th
r
ea
l a
n
d
r
ea
ctiv
e
p
o
wer
d
u
e
to
to
p
o
l
o
g
ical
a
d
v
an
tag
e,
n
o
f
u
r
t
h
er
u
s
e
o
f
f
ilter
s
to
r
ed
u
ce
h
ar
m
o
n
ics,
less
er
s
tr
ess
o
n
th
e
s
witch
es
d
u
e
to
s
p
lit
v
o
ltag
e
ac
r
o
s
s
s
witch
es
ar
e
f
e
w
o
f
t
h
e
im
p
o
r
tan
t
ad
v
an
tag
es
o
f
th
e
d
io
d
e
clam
p
ed
to
p
o
lo
g
y
[
2
3
]
-
[
2
5
]
.
T
h
er
e
is
an
o
th
er
s
im
ilar
to
p
o
lo
g
y
as
th
at
o
f
th
e
d
io
d
e
clam
p
ed
ML
I
ca
lled
t
h
e
ca
p
ac
ito
r
clam
p
ed
to
p
o
lo
g
y
wh
ich
u
s
es
ca
p
ac
ito
r
to
r
estrict
th
e
v
o
ltag
e
u
n
lik
e
d
i
o
d
e
clam
p
ed
ML
I
wh
er
e
d
i
o
d
e
is
u
s
ed
f
o
r
th
e
p
u
r
p
o
s
e
[
2
6
]
,
[
2
7
]
.
E
v
en
th
e
v
o
ltag
e
le
v
els ar
e
o
n
e
an
d
th
e
s
am
e
f
o
r
b
o
th
th
ese
to
p
o
lo
g
ies [
2
8
]
,
[
2
9
]
.
C
ap
ac
ito
r
clam
p
ed
ML
I
s
a
r
e
p
o
p
u
lar
l
y
k
n
o
wn
as
f
ly
i
n
g
ca
p
ac
ito
r
ML
I
s
.
T
o
o
b
t
ain
n
-
lev
el
o
u
tp
u
t
i
n
th
is
to
p
o
lo
g
y
n
-
1
ca
p
ac
ito
r
s
,
(
n
-
1
)
(
n
-
2
)
n
u
m
b
e
r
o
f
f
ly
in
g
ca
p
ac
ito
r
s
,
an
d
t
o
tal
2
(
n
-
1
)
s
witch
es
ar
e
r
eq
u
ir
ed
[
3
0
]
,
[
3
1
]
.
Alth
o
u
g
h
th
e
f
ly
i
n
g
ca
p
ac
ito
r
to
p
o
lo
g
y
g
ets
r
id
o
f
th
e
clam
p
in
g
d
io
d
e
p
r
o
b
le
m
s
in
clu
d
in
g
h
ig
h
e
r
s
tr
ess
o
n
th
e
d
i
o
d
es,
r
ev
er
s
e
r
ec
o
v
er
y
o
f
d
io
d
es
h
av
e
th
e
d
i
s
ad
v
an
tag
e
o
f
h
ig
h
er
co
s
t
d
u
e
to
u
s
ag
e
o
f
m
o
r
e
ca
p
ac
ito
r
s
[
3
2
]
-
[
3
4
]
.
T
h
u
s
,
i
n
o
r
d
er
to
s
o
lv
e
th
ese
p
r
o
b
lem
s
in
th
e
f
ly
i
n
g
ca
p
ac
ito
r
to
p
o
lo
g
y
f
u
r
th
e
r
im
p
r
o
v
em
e
n
t in
th
e
t
o
p
o
lo
g
y
i
s
ca
r
r
ied
o
u
t w
ith
th
e
i
n
tr
o
d
u
c
tio
n
o
f
ca
s
ca
d
ed
H
-
b
r
id
g
e
to
p
o
lo
g
y
[
3
5
]
-
[
3
7
]
.
B
y
co
n
n
ec
tin
g
th
e
s
er
ies
o
f
H
-
b
r
id
g
es
th
e
ca
s
ca
d
ed
H
-
b
r
id
g
e
ML
I
s
ar
e
ar
ticu
lated
f
o
r
d
if
f
e
r
en
t
v
o
ltag
e
lev
els
[
3
8
]
-
[
4
0
]
.
C
ascad
ed
ML
I
d
esig
n
d
o
es
n
o
t
h
av
e
th
e
p
r
o
b
lem
s
en
co
u
n
ter
ed
in
b
o
th
th
e
d
io
d
e
clam
p
e
d
a
n
d
th
e
f
ly
in
g
ca
p
ac
ito
r
to
p
o
l
o
g
ies
s
in
ce
it
d
o
es
n
o
t
h
av
e
th
e
d
io
d
es
a
n
d
ca
p
ac
ito
r
s
f
o
r
clam
p
in
g
.
T
h
e
n
u
m
b
er
o
f
v
o
ltag
e
lev
els
is
th
e
s
u
m
o
f
all
th
e
v
o
l
tag
e
lev
els
g
en
e
r
ated
b
y
ea
c
h
o
f
th
e
H
-
b
r
id
g
es
[
4
1
]
.
Alth
o
u
g
h
th
is
to
p
o
lo
g
y
h
as
th
e
ad
v
an
tag
e
o
f
im
p
lem
e
n
tin
g
s
o
f
t
s
witch
in
g
m
eth
o
d
f
o
r
r
e
d
u
cin
g
th
e
s
witch
s
tr
ess
an
d
all
th
e
ad
v
an
tag
es
o
f
th
e
p
r
ev
io
u
s
to
p
o
lo
g
ies,
it
r
eq
u
ir
es
in
d
ep
en
d
en
t
d
c
s
o
u
r
ce
s
f
o
r
p
o
wer
co
n
v
er
s
io
n
s
in
ea
ch
H
-
b
r
id
g
e
[
4
2
]
-
[
4
4
]
.
T
o
p
o
lo
g
ical
v
ar
iatio
n
s
a
r
e
co
u
p
led
with
t
h
e
v
ar
iatio
n
s
in
th
e
PW
M
tech
n
iq
u
es
to
o
b
tain
t
h
e
b
etter
h
ar
m
o
n
ic
r
ed
u
ctio
n
in
th
e
ML
I
to
p
o
lo
g
i
es.
T
h
u
s
,
to
f
ac
ilit
ate
th
is
im
p
r
o
v
em
en
t
m
u
lti
-
ca
r
r
ier
m
o
d
u
la
tio
n
tech
n
iq
u
es
g
o
t
in
tr
o
d
u
ce
d
.
Mu
lti
-
ca
r
r
ier
PW
M
m
eth
o
d
s
in
clu
d
in
g
p
h
ase
d
is
p
o
s
itio
n
,
p
h
ase
o
p
p
o
s
itio
n
an
d
alter
n
ate
p
h
ase
o
p
p
o
s
itio
n
a
r
e
m
eth
o
d
s
u
s
ed
f
o
r
th
e
p
u
r
p
o
s
e
[
4
5
]
.
T
h
is
p
ap
er
p
r
esen
ts
th
e
im
p
le
m
en
tatio
n
o
f
th
e
p
h
ase
d
is
p
o
s
itio
n
m
eth
o
d
o
n
a
ca
s
ca
d
ed
m
u
ltil
ev
el
in
v
er
ter
(
ML
I
)
ac
r
o
s
s
th
r
ee
d
if
f
er
en
t
lev
els
o
f
th
e
to
p
o
lo
g
y
:
f
iv
e
-
lev
el,
s
ev
en
-
lev
el,
an
d
n
in
e
-
lev
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
in
v
er
ter
s
.
T
h
e
o
b
jectiv
e
is
to
co
m
p
ar
e
t
h
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
o
b
tain
e
d
f
r
o
m
ea
ch
in
v
e
r
ter
lev
el
wh
en
a
p
p
ly
in
g
th
e
p
h
as
e
d
is
p
o
s
itio
n
tech
n
i
q
u
e.
A
d
d
i
tio
n
ally
,
a
c
o
m
p
ar
ativ
e
an
aly
s
is
is
p
er
f
o
r
m
ed
to
ev
alu
ate
th
e
in
v
er
ter
o
u
tp
u
t
T
HD
with
an
d
with
o
u
t
th
e
u
s
e
o
f
an
L
C
f
ilter
f
o
r
ea
ch
ML
I
lev
e
l.
Sectio
n
2
p
r
o
v
id
es
a
d
etailed
d
is
cu
s
s
io
n
o
f
th
e
p
h
ase
d
is
p
o
s
itio
n
m
eth
o
d
,
elab
o
r
atin
g
o
n
its
o
p
er
atio
n
al
p
r
in
cip
les
an
d
th
e
r
o
le
o
f
v
ar
io
u
s
f
ilter
s
i
n
im
p
r
o
v
i
n
g
t
h
e
ML
I
o
u
t
p
u
t.
T
h
is
s
ec
tio
n
also
co
v
er
s
t
h
e
th
e
o
r
etica
l
b
a
ck
g
r
o
u
n
d
an
d
th
e
im
p
lem
en
tatio
n
s
p
ec
if
ics o
f
th
e
L
C
f
ilter
in
th
e
in
v
er
ter
cir
cu
it.
Sectio
n
3
d
is
cu
s
s
es th
e
r
es
u
lts
an
d
d
is
cu
s
s
io
n
,
o
f
f
er
in
g
a
th
o
r
o
u
g
h
q
u
an
titati
v
e
an
aly
s
is
o
f
th
e
T
HD
m
ea
s
u
r
ed
at
ea
ch
lev
el
o
f
th
e
ca
s
ca
d
ed
to
p
o
lo
g
y
.
T
h
e
an
aly
s
is
in
clu
d
es
a
c
o
m
p
ar
is
o
n
o
f
T
HD
v
alu
es
with
an
d
with
o
u
t
th
e
i
n
co
r
p
o
r
atio
n
o
f
th
e
L
C
f
ilter
in
th
e
in
v
er
te
r
o
u
tp
u
t.
T
h
e
r
esu
lts
ar
e
s
y
s
tem
atica
lly
tab
u
lated
,
h
ig
h
lig
h
tin
g
th
e
ex
te
n
t o
f
im
p
r
o
v
em
e
n
t a
c
h
iev
ed
at
ea
ch
ML
I
lev
el
an
d
th
e
ad
d
itio
n
al
b
en
e
f
i
ts
r
ea
lized
th
r
o
u
g
h
th
e
u
s
e
o
f
th
e
L
C
f
ilter
.
Fin
ally
,
th
e
p
a
p
er
co
n
cl
u
d
es
with
a
s
u
m
m
ar
y
o
f
th
e
f
in
d
in
g
s
,
em
p
h
asizin
g
th
e
ef
f
ec
tiv
en
ess
o
f
t
h
e
p
h
ase
d
is
p
o
s
itio
n
m
eth
o
d
i
n
r
ed
u
cin
g
T
HD
in
ca
s
ca
d
ed
ML
I
s
a
n
d
th
e
s
ig
n
if
ican
t
im
p
ac
t
o
f
u
s
in
g
L
C
f
ilter
s
.
T
h
e
co
n
clu
s
io
n
is
f
o
llo
w
ed
b
y
r
e
f
er
en
ce
s
t
o
r
elev
an
t liter
atu
r
e
a
n
d
s
tu
d
ies
th
at
s
u
p
p
o
r
t t
h
e
r
esear
ch
.
2.
P
RO
P
O
SE
D
I
M
P
L
E
M
E
N
T
AT
I
O
N
T
h
e
p
r
o
p
o
s
ed
im
p
lem
en
tatio
n
co
m
p
ar
es
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
h
ase
d
is
p
o
s
itio
n
PW
M
m
eth
o
d
o
n
f
iv
e,
s
ev
en
a
n
d
n
in
e
lev
el
in
v
e
r
ter
s
.
Ph
ase
d
is
p
o
s
itio
n
PW
M
m
eth
o
d
is
a
s
in
u
s
o
id
al
PW
M
m
eth
o
d
wh
ic
h
u
s
es
d
if
f
er
en
t
lev
els
o
f
tr
ian
g
u
lar
c
ar
r
ier
wav
es
to
g
en
er
ate
th
e
p
u
ls
es
f
o
r
th
e
3
-
p
h
ase
in
v
e
r
ter
.
Ph
ase
d
is
p
o
s
itio
n
m
eth
o
d
is
a
lev
el
-
s
h
if
tin
g
ty
p
e
o
f
PW
M
tech
n
iq
u
e
a
p
p
lied
o
n
ML
I
to
r
ed
u
ce
th
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
in
th
e
ca
s
ca
d
ed
m
u
ltil
ev
el
in
v
er
ter
(
C
ML
I
)
to
p
o
l
o
g
y
.
C
o
m
p
ar
is
o
n
o
f
C
ML
I
with
th
r
ee
d
if
f
er
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d
tab
u
lated
in
th
e
im
p
lem
en
tatio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
76
-
85
78
T
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ter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Ha
r
mo
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
76
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80
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sa
v
it
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d
to
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c
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m
.
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