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4
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s
es
t
h
e
p
o
w
er
r
at
in
g
b
e
ca
u
s
e
th
e
b
lo
ck
i
n
g
v
o
lta
g
e
o
f
ea
ch
s
w
itc
h
i
s
o
n
e
-
h
al
f
o
f
t
h
e
d
c
-
b
u
s
v
o
lt
a
g
e.
Mo
r
eo
v
er
,
th
eir
o
u
tp
u
t
v
o
lta
g
e
h
ar
m
o
n
ic
co
n
te
n
t
i
s
m
u
c
h
s
m
aller
t
h
an
th
at
o
f
t
h
e
co
n
v
en
tio
n
al
i
n
v
er
ter
s
w
it
h
th
e
s
a
m
e
s
w
itc
h
i
n
g
f
r
eq
u
e
n
c
y
o
w
in
g
to
t
h
e
o
u
tp
u
t
v
o
ltag
e
w
a
v
e
f
o
r
m
i
m
p
r
o
v
e
m
e
n
t
s
[
2
2
]
.
Ma
n
y
s
w
i
tch
e
s
s
tr
ateg
ie
s
ar
e
u
s
ed
f
o
r
th
e
co
n
tr
o
l
o
f
t
h
e
NP
C
to
p
o
lo
g
y
an
d
ca
n
b
e
d
i
v
id
ed
i
n
to
t
w
o
ca
teg
o
r
ies,
s
tr
ateg
ie
s
d
ea
lin
g
w
i
th
h
i
g
h
s
w
itc
h
i
n
g
f
r
eq
u
en
cie
s
s
u
ch
as
s
i
n
u
s
o
id
al
p
u
ls
e
w
id
t
h
m
o
d
u
latio
n
(
SP
W
M)
an
d
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
(
SVM)
an
d
m
e
th
o
d
s
d
ea
lin
g
w
i
th
lo
w
er
s
w
it
ch
in
g
f
r
eq
u
e
n
cie
s
s
u
c
h
as
s
p
ac
e
v
e
cto
r
co
n
tr
o
l
(
SVC
)
an
d
o
p
ti
m
ized
h
ar
m
o
n
ic
s
tep
p
ed
w
a
v
ef
o
r
m
(
O
HSW
)
.
SP
W
M
is
a
v
er
y
p
o
p
u
lar
m
eth
o
d
in
i
n
d
u
s
tr
ial
ap
p
licatio
n
an
d
it
is
b
ased
o
n
th
e
class
ic
co
m
p
ar
is
o
n
o
f
th
e
tr
ian
g
u
lar
ca
r
r
ier
w
it
h
th
e
s
i
n
u
s
o
id
al
p
u
ls
e
w
id
t
h
m
o
d
u
latio
n
w
h
ic
h
is
u
s
ed
to
r
ed
u
c
e
th
e
T
HD
in
th
e
o
u
t
p
u
t
v
o
lta
g
e
[
2
3
]
.
Ho
w
ev
er
,
o
p
tim
izatio
n
o
f
t
h
i
s
co
n
tr
o
llin
g
m
eth
o
d
is
r
eq
u
ir
ed
to
ass
u
r
e
a
lo
w
er
h
ar
m
o
n
ic
s
t
r
ess
o
n
t
h
e
s
w
i
tch
e
s
o
p
er
atin
g
.
I
n
th
i
s
p
ap
er
,
th
e
NP
C
to
p
o
lo
g
y
o
f
th
e
M
L
I
w
a
s
s
i
m
u
lated
a
n
d
co
n
tr
o
lled
b
y
t
h
e
SP
W
M
s
tr
ate
g
y
.
T
h
e
m
o
d
u
latio
n
i
n
d
e
x
co
m
p
ar
i
n
g
t
h
e
ca
r
r
ier
w
a
v
e
f
o
r
m
w
it
h
th
e
s
in
u
s
o
id
al
f
u
n
d
a
m
en
tal
f
o
r
m
w
as
v
ar
iated
o
n
its
d
ep
en
d
en
c
y
w
it
h
T
HD
w
a
s
o
p
ti
m
ized
.
2.
SYST
E
M
DE
SCRI
P
T
I
O
N
Fif
tee
n
-
le
v
el
m
u
lt
ilev
el
NP
C
to
p
o
lo
g
y
w
a
s
r
ev
ie
w
ed
in
t
h
is
p
ap
er
.
T
h
e
NP
C
s
tr
u
ctu
r
e
h
as
t
h
e
a
d
v
an
ta
g
e
o
f
lo
w
er
i
n
g
t
h
e
el
ec
tr
o
m
a
g
n
etic
i
n
ter
f
er
e
n
ce
(
E
MI
)
ef
f
ec
t
o
n
th
e
o
u
tp
u
t
v
o
l
tag
e
o
f
t
h
e
lo
ad
s
.
C
o
m
b
i
n
in
g
t
h
i
s
to
p
o
lo
g
y
w
it
h
an
ad
eq
u
ate
co
n
tr
o
l stra
te
g
y
s
u
ch
as t
h
e
SP
W
M
it
m
a
y
b
e
w
i
ll lea
d
to
e
m
er
g
i
n
g
n
e
w
ad
v
a
n
tag
e
s
s
u
c
h
as T
HD
r
ed
u
cin
g
an
d
w
av
e
f
o
r
m
o
u
tp
u
t
i
m
p
r
o
v
e
m
en
t.
2
.
1
.
M
L
I
Circ
uit
Sche
m
a
t
ic
Fig
u
r
e
1
il
lu
s
tr
ates
th
e
cir
c
u
it
s
c
h
e
m
at
ic
o
f
t
h
e
f
i
f
tee
n
-
lev
el
NP
C
to
p
o
lo
g
y
.
T
h
is
s
t
r
u
ctu
r
e
is
p
o
w
er
ed
u
p
u
s
in
g
f
o
u
r
teen
p
o
w
er
s
o
u
r
ce
s
an
d
o
n
e
le
g
o
f
th
e
t
h
r
ee
p
h
ase
cir
c
u
it
co
n
s
is
t
o
f
2
8
p
r
in
cip
al
d
is
p
o
s
itiv
e
o
f
co
m
m
u
tatio
n
(
I
GB
T
s
)
an
d
5
4
d
io
d
es
to
ass
u
m
e
t
h
e
co
n
tr
o
l
o
f
th
e
I
GB
T
s
.
T
h
e
co
m
p
o
n
en
t
s
n
u
m
b
er
o
f
th
is
to
p
o
lo
g
y
w
a
s
c
alcu
lated
as s
h
o
w
n
i
n
T
ab
le
1
.
On
e
o
f
t
h
e
m
er
its
o
f
t
h
e
NP
C
to
p
o
lo
g
y
i
s
t
h
e
ab
s
en
ce
o
f
ca
p
ac
ito
r
s
in
t
h
e
cir
cu
i
t
w
h
ich
d
e
cr
ea
s
e
th
e
cir
cu
it
r
ea
ctio
n
ti
m
e
as
s
h
o
w
n
in
T
ab
le
1
.
T
h
e
2
8
I
GB
T
s
ar
e
d
iv
id
ed
in
to
t
w
o
g
r
o
u
p
s
(
S)
an
d
(
S’
)
in
o
n
e
leg
,
an
d
ea
ch
p
air
w
as
o
p
er
ated
in
co
m
p
le
m
en
tar
y
m
o
d
e
(
Sa1
,
S’
a1
)
to
(
Sa1
4
,
S’
a1
4
)
.
T
h
e
o
p
er
atin
g
d
etail
an
d
th
e
lo
g
ical
d
ia
g
r
a
m
o
f
th
e
SP
W
M
ar
e
d
i
s
cu
s
s
ed
in
t
h
e
n
e
x
t
s
u
b
s
ec
tio
n
.
Fig
u
r
e
1
.
T
h
r
ee
p
h
ase
f
if
tee
n
-
l
ev
el
NP
C
in
v
er
ter
s
c
h
e
m
a
tic
c
ir
cu
it
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2017
:
1
8
9
2
–
1
8
9
8
1894
T
ab
le
1
.
C
o
m
p
o
n
e
n
ts
n
u
m
b
er
o
f
th
e
NP
C
to
p
o
lo
g
y
(
N
u
m
b
er
o
f
s
w
itc
h
es,
N
u
m
b
er
o
f
Dio
d
es,
Nu
m
b
er
o
f
C
ap
ac
ito
r
s
)
T
o
p
o
l
o
g
y
N
P
C
m
l
e
v
e
l
(
3
Ø
)
S
t
u
d
i
e
d
1
5
-
l
e
v
e
l
N
P
C
(
3
Ø
)
P
o
w
e
r
S
o
u
r
c
e
m
-
1
14
P
r
i
n
c
i
p
a
l
d
i
sp
o
s
i
t
i
v
e
o
f
c
o
mm
u
t
a
t
i
o
n
6
(
m
-
1)
84
D
i
o
d
e
s
6
(
2
m
-
3)
1
6
2
C
a
p
a
c
i
t
o
r
s
0
0
T
o
t
a
l
n
u
m
b
e
r
o
f
c
o
mp
o
n
e
n
t
s
19m
-
25
2
6
0
2
.
2
.
Co
ntr
o
l
Str
a
t
eg
y
SPWM
T
h
e
s
in
u
s
o
id
al
p
u
ls
e
w
id
t
h
m
o
d
u
latio
n
i
s
b
ased
o
n
h
i
g
h
-
f
r
eq
u
en
c
y
s
w
itc
h
in
g
as
a
lr
ea
d
y
d
is
cu
s
s
ed
ab
o
v
e,
it
co
n
s
i
s
t
s
of
co
m
p
ar
in
g
th
e
f
u
n
d
a
m
e
n
tal
f
r
eq
u
e
n
c
y
s
i
n
u
s
o
id
al
s
ig
n
al
w
it
h
a
h
i
g
h
-
f
r
eq
u
e
n
c
y
ca
r
r
ier
w
a
v
e
f
o
r
m
.
T
h
e
lo
g
ical
co
n
tr
o
l
o
f
t
h
e
SP
W
M
is
b
ased
o
n
t
h
e
p
h
ase
eq
u
alit
y
o
f
all
ca
r
r
ier
s
k
n
o
w
n
as
th
e
P
D
co
n
tr
o
l a
s
s
h
o
w
n
in
Fig
u
r
e
2
.
On
e
tr
ia
n
g
u
lar
s
i
g
n
al
ca
r
r
ier
i
s
co
m
p
ar
ed
to
a
s
in
u
s
o
id
al
s
i
g
n
al
an
ea
ch
in
ter
ac
tio
n
s
g
iv
e
a
s
i
g
n
a
l,
w
h
ile
t
h
e
d
c
g
e
n
er
ato
r
is
u
s
e
d
to
s
h
if
t
t
h
e
o
u
tp
u
t
s
i
g
n
al
f
r
o
m
th
e
co
m
p
ar
i
s
o
n
d
ep
en
d
in
g
o
n
t
h
e
n
u
m
b
er
o
f
i
m
p
u
l
s
io
n
r
eq
u
ir
ed
to
co
n
tr
o
l o
n
e
h
an
d
o
f
t
h
e
i
n
v
er
ter
.
Fig
u
r
e
2
.
SP
W
M
L
o
g
ical
C
o
n
tr
o
llin
g
D
iag
r
a
m
f
o
r
On
e
L
e
g
1
5
-
lev
el
i
n
v
er
ter
E
ac
h
i
n
ter
s
ec
tio
n
b
et
w
ee
n
t
h
e
s
i
n
u
s
o
id
al
an
d
th
e
ca
r
r
ier
s
s
i
g
n
al
s
r
es
u
lt
s
i
n
a
co
m
m
a
n
d
o
r
d
er
.
I
n
th
i
s
ca
s
e
s
t
u
d
y
,
th
e
s
i
n
u
s
o
id
al
s
i
g
n
al
i
s
co
m
p
ar
ed
to
9
ca
r
r
ier
’
s
s
i
g
n
al
s
i
n
p
h
a
s
e
a
s
s
h
o
w
n
in
Fig
u
r
e
3
.
T
h
e
P
D
co
n
tr
o
l
h
as
th
e
ad
v
a
n
tag
e
o
f
d
ec
r
ea
s
in
g
th
e
T
HD
f
ac
to
r
b
y
r
ed
u
cin
g
th
e
h
ar
m
o
n
ic
s
tr
e
s
s
o
n
th
e
s
w
itc
h
e
s
.
T
h
e
co
n
tr
o
l
s
i
g
n
al
G1
to
G1
4
ar
e
g
en
er
ated
b
y
t
h
e
i
n
ter
s
ec
tio
n
o
f
th
e
tr
ia
n
g
u
lar
ca
r
r
ier
s
s
i
g
n
a
l
C
1
to
C
1
4
w
it
h
t
h
e
f
u
n
d
a
m
en
ta
l f
r
eq
u
e
n
c
y
s
i
n
u
s
o
id
al
s
ig
n
al.
T
h
e
s
w
itch
e
s
o
p
er
atin
g
is
d
o
n
e
b
y
e
x
ec
u
tio
n
o
f
f
e
w
lo
g
ic
al
p
r
o
ce
s
s
,
an
d
t
h
e
co
n
tr
o
l
r
e
s
u
lt
o
f
t
h
e
s
w
itc
h
es
i
s
s
h
o
w
n
in
T
ab
le
2
.
T
h
e
co
n
tr
o
l
is
d
o
n
e
in
c
o
m
p
le
m
e
n
tar
y
m
o
d
e
w
h
ich
m
ea
n
s
ea
c
h
p
air
o
f
in
ter
r
u
p
ter
s
co
u
ld
h
av
e
t
w
o
s
p
ec
if
ic
v
alu
e
s
u
c
h
as 1
(
On
)
f
o
r
th
e
f
ir
s
t
s
u
ch
a
s
Sa1
an
d
0
(
Of
f
)
f
o
r
S’
a1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mo
d
u
la
tio
n
I
n
d
ex
V
a
r
ia
tio
n
E
ffect
o
n
Ha
r
mo
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ic
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eh
a
vio
r
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f
F
ifteen
Mu
ltil
ev
el
I
n
ve
r
ter …
.
(
R
a
b
ie
B
en
io
u
b
)
1895
Fig
u
r
e
3
.
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w
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tch
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o
n
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n
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SP
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lev
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T
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e
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lit
u
d
e
m
o
d
u
latio
n
i
n
d
ex
also
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s
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n
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w
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ip
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e
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ier
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a
m
p
lit
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c)
w
it
h
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in
u
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p
lit
u
d
e
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i
s
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v
en
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y
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q
.
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1
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w
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er
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m
i
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e
n
u
m
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er
o
f
le
v
e
l o
f
th
e
i
n
v
er
ter
,
an
d
it
s
v
ar
iati
o
n
is
s
h
o
w
n
i
n
T
ab
le
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2017
:
1
8
9
2
–
1
8
9
8
1896
(
1
)
T
a
b
le 3
.
M
o
d
u
lati
o
n
In
d
e
x
V
a
riat
io
n
C
a
r
r
i
e
r
A
mp
l
i
t
u
d
e
S
i
n
u
so
i
d
a
l
A
mp
l
i
t
u
d
e
M
o
d
u
l
a
t
i
o
n
f
a
c
t
o
r
0
.
1
4
3
1
.
7
6
0
.
8
8
1
.
7
8
0
.
8
9
1
.
8
0
.
9
1
.
8
2
0
.
9
1
1
.
8
4
0
.
9
2
1
.
8
6
0
.
9
3
1
.
8
8
0
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9
4
1
.
9
0
0
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9
5
1
.
9
2
0
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9
6
1
.
9
4
0
.
9
7
1
.
9
6
0
.
9
8
1
.
9
8
0
.
9
9
2
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2
.
0
2
1
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0
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2
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0
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1
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2
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1
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6
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2
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2
1
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2
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2
4
1
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1
2
3.
SI
M
UL
AT
I
O
N
A
ND
RE
SU
L
T
S DIS
CUSS
I
O
N
Fig
u
r
e
4
s
h
o
w
s
th
e
p
h
a
s
e
o
u
t
p
u
t
v
o
ltag
e
s
an
d
lin
e
-
to
-
li
n
e
v
o
ltag
e
s
V
AB
,
V
BC
an
d
V
CA
.
Mo
r
eo
v
er
,
th
e
y
ar
e
d
ed
u
cted
f
r
o
m
th
e
p
o
l
e
o
u
tp
u
t
v
o
lta
g
es a
s
ill
u
s
tr
ated
in
E
q
u
atio
n
(
2
)
.
(
2)
T
h
e
lin
e
-
to
-
l
in
e
v
o
lta
g
es
ar
e
s
h
i
f
ted
b
y
1
2
0
°
b
et
w
ee
n
ea
c
h
o
th
er
’
s
,
th
e
1
5
lev
e
l
li
n
e
-
to
-
l
i
n
e
v
o
ltag
e
s
(
7
E
,
6
E
,
5
E
,
4
E
,
3
E
,
2
E
,
E
,
0
,
-
E,
-
2
E
,
-
3
E
,
-
4
E
,
-
5
E
,
-
6
E
,
-
7
E
)
ar
e
p
r
o
d
u
ce
d
f
r
o
m
1
3
lev
el
p
o
le
f
ig
u
r
e
r
elate
d
b
y
th
e
p
o
le
v
o
lta
g
e
n
u
m
b
er
[
m
-
2
]
(
w
h
er
e
m
i
s
t
h
e
n
u
m
b
er
o
f
M
L
I
le
v
els)
i
s
u
s
ed
to
g
et
[
m
]
li
n
e
-
to
-
li
n
e
o
u
tp
u
t
v
o
ltag
e
s
.
Fi
g
u
r
e
5
ill
u
s
tr
ates
t
h
e
s
i
m
u
lat
io
n
r
es
u
lt
s
o
f
th
e
p
h
ase
s
c
u
r
r
en
ts
s
h
if
ted
b
y
1
2
0
°
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d
in
th
e
ca
s
e
o
f
p
u
r
e
i
n
d
u
cti
v
e
lo
ad
,
th
e
cu
r
r
en
t
s
h
ap
e
w
a
s
s
tab
le
a
n
d
h
ad
a
s
m
o
o
t
h
er
w
a
v
ef
o
r
m
,
an
d
it
is
d
u
e
to
th
e
in
d
u
ctio
n
f
ilter
in
g
co
m
p
ar
ab
l
e
to
th
e
p
u
r
e
ca
p
ac
itiv
e
lo
a
d
(
b
)
.
S
m
o
o
th
er
w
a
v
e
f
o
r
m
an
d
its
d
u
e
to
t
h
e
in
d
u
ctio
n
f
ilter
in
g
o
f
t
h
e
h
ar
m
o
n
ic
co
m
p
o
n
en
t.
Fu
r
t
h
er
m
o
r
e,
th
e
v
ar
iat
io
n
e
f
f
ec
t
o
f
t
h
e
m
o
d
u
latio
n
f
ac
to
r
o
n
t
h
e
T
HD
is
i
llu
s
tr
ated
i
n
Fi
g
u
r
e
6
.
T
h
e
ch
an
g
e
o
f
t
h
e
m
o
d
u
latio
n
i
n
d
e
x
h
a
s
an
i
m
p
ac
t
o
n
t
h
e
T
HD
v
alu
e,
an
d
th
e
s
e
r
es
u
lts
p
r
o
v
e
t
h
at
a
s
p
ec
if
ic
v
al
u
e
o
f
th
e
m
o
d
u
latio
n
f
ac
to
r
co
r
r
esp
o
n
d
s
to
t
h
e
lo
w
er
v
al
u
e
o
f
T
HD.
I
n
t
h
is
ca
s
e,
t
h
e
o
p
tim
u
m
co
n
d
itio
n
f
o
r
lo
w
er
i
n
g
T
HD
r
eq
u
ir
ed
th
at
t
h
e
a
m
p
li
tu
d
e
o
f
t
h
e
s
i
n
u
s
o
id
al
s
ig
n
al
b
e
in
[
1
.
0
5
-
1
.
0
7
]
tim
e
s
th
e
ca
r
r
ier
s
s
i
g
n
al
a
m
p
lit
u
d
e.
T
h
e
s
e
r
esu
lts
ca
n
b
e
ex
p
lain
ed
as
th
e
lar
g
er
a
m
p
litu
d
e
o
f
th
e
s
in
u
s
o
id
al
w
a
v
ef
o
r
m
w
ill
i
n
ter
ac
t
m
o
r
e
a
n
d
in
a
n
ef
f
icie
n
t
w
a
y
l
ea
d
in
g
to
r
ed
u
ce
th
e
h
ar
m
o
n
ic
s
tr
ess
o
n
t
h
e
co
n
tr
o
lli
n
g
s
w
itc
h
es (
I
GB
T
s
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mo
d
u
la
tio
n
I
n
d
ex
V
a
r
ia
tio
n
E
ffect
o
n
Ha
r
mo
n
ic
B
eh
a
vio
r
o
f
F
ifteen
Mu
ltil
ev
el
I
n
ve
r
ter …
.
(
R
a
b
ie
B
en
io
u
b
)
1897
Fig
u
r
e
4
.
I
n
v
er
ter
Ou
tp
u
t (
a)
Po
le
v
o
ltag
es,
(
b
)
L
i
n
e
-
to
-
li
n
e
v
o
ltag
e
s
F
ig
u
r
e
5
.
I
n
v
er
ter
Ou
tp
u
t p
h
as
e
cu
r
r
en
t (
a)
P
u
r
e
I
n
d
u
ctiv
e
c
h
ar
g
e
(
R
=2
0
Ω
,
XL
=6
3
Ω
)
(
b
)
P
u
r
e
C
ap
ac
itiv
e
c
h
ar
g
e
(
R
=2
0
Ω
,
X
C
=6
3
Ω
)
F
ig
u
r
e
6
.
T
o
tal
Har
m
o
n
ic
Dis
t
o
r
tio
n
(
T
HD)
d
ep
en
d
ec
y
o
n
t
h
e
v
ar
iatio
n
o
f
t
h
e
m
o
d
u
altio
n
i
n
d
ex
(
a)
(
b
)
(
a)
(
b
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2017
:
1
8
9
2
–
1
8
9
8
1898
4.
CO
NCLU
SI
O
N
I
n
t
h
is
p
ap
er
,
th
e
s
i
m
u
lat
io
n
o
f
t
h
e
M
L
I
NP
C
to
p
o
lo
g
y
w
a
s
d
is
c
u
s
s
ed
w
it
h
t
h
e
f
i
f
tee
n
-
le
v
el
o
u
tp
u
t
v
o
ltag
e.
T
h
e
i
m
p
r
o
v
e
m
en
t
o
f
th
e
SP
W
M
co
n
tr
o
l
s
tr
ateg
y
w
a
s
d
is
cu
s
s
ed
in
ter
m
o
f
w
av
e
f
o
r
m
a
m
p
lit
u
d
es.
T
h
e
m
o
d
u
latio
n
i
n
d
ex
d
escr
ib
in
g
th
e
a
m
p
l
itu
d
e
r
ela
tio
n
s
h
ip
b
et
w
ee
n
th
e
s
i
n
u
s
o
id
al
s
ig
n
al
a
m
p
lit
u
d
e
a
n
d
t
h
e
tr
ian
g
u
lar
w
av
e
f
o
r
m
a
m
p
lit
u
d
e
w
as
o
p
ti
m
ized
b
ased
o
n
its
d
ep
en
d
en
c
y
to
th
e
T
HD
ch
an
g
i
n
g
.
L
o
w
er
T
HD
v
alu
e
s
w
er
e
o
b
s
er
v
ed
f
o
r
s
m
a
l
l v
ar
iatio
n
r
an
g
e
o
f
t
h
e
a
m
p
l
it
u
d
e
m
o
d
u
latio
n
in
d
e
x
.
RE
F
E
R
E
NC
E
S
[1
]
C
io
b
o
taru
.
R,
e
t
al
,
“
C
o
n
tr
o
l
o
f
sin
g
le
-
sta
g
e
sin
g
le
-
p
h
a
se
P
V I
n
v
e
rt
e
r”
,
P
r
o
c
.
P
EL
INCEC
,
2
0
0
5
.
[2
]
O
.
A
.
El
Ba
ss
io
u
n
y
,
e
t
al
,
“
En
e
rg
y
E
ff
icie
n
t
Co
st
-
e
ff
e
c
ti
v
e
In
v
e
rter
Co
n
f
ig
u
ra
ti
o
n
f
o
r
Re
sid
e
n
ti
a
l
P
h
o
t
o
v
o
lt
a
ic
S
y
st
e
m
s”
,
J
o
u
rn
a
l
o
f
P
o
we
r E
lec
tro
n
ics
,
2
0
1
0
;
1
0
:
6
5
-
7
1
.
[3
]
M.
Ora
b
i
,
e
t
al
,
“
S
t
u
d
y
a
n
d
A
n
a
ly
sis
o
f
N
e
w
T
h
re
e
-
p
h
a
se
M
o
d
u
l
a
r
M
u
lt
i
-
L
e
v
e
l
In
v
e
rter”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stria
l
El
e
c
tro
n
ics
,
2
0
1
6
;
9
9
.
[4
]
M
.
T
h
iru
m
a
lai,
e
t
al
,
“
De
sig
n
a
n
d
I
m
p
le
m
e
n
tatio
n
o
f
H
y
b
rid
M
u
lt
il
e
v
e
l
In
v
e
rter
f
o
r
h
ig
h
Ou
t
p
u
t
E
f
f
i
c
ien
c
y
”
,
S
m
a
rt
S
tru
c
tu
re
s an
d
S
y
ste
m
s (ICS
S
S
),
IEE
E
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
,
2
0
1
3
;
4
1
-
4
5
.
[5
]
P
.
M
.
Bh
a
g
w
a
t
e
t
al
,
“
Ge
n
e
ra
li
z
e
d
S
tr
u
c
tu
re
o
f
a
M
u
lt
il
e
v
e
l
P
W
M
I
n
v
e
rter
”,
IEE
E
T
ra
n
s
.
In
d
.
A
p
p
li
c
a
t
,
1
9
8
3
;
1
9
(
6
):
1
0
5
7
-
1
0
6
9
.
[6
]
V
.
G
.
Ag
e
li
d
is,
e
t
al
,
“
A
M
u
lt
il
e
v
e
l
P
W
M
In
v
e
rter
T
o
p
o
lo
g
y
f
o
r
P
h
o
t
o
v
o
lt
a
ic
A
p
p
li
c
a
ti
o
n
s”
,
P
r
o
c
.
IEE
E
IS
IE
.
1
9
9
7
;
5
8
9
-
5
9
4
.
[7
]
J.
Ro
d
rig
u
e
z
,
e
t
al
,
“
M
u
lt
il
e
v
e
l
I
n
v
e
rter:
A
S
u
rv
e
y
o
f
T
o
p
o
lo
g
ies
,
Co
n
tro
ls,
a
n
d
A
p
p
li
c
a
ti
o
n
s
“
,
I
EE
E
T
ra
n
s
I
n
d
El
e
c
tro
n
,
2
0
0
2
;
4
9
(4
):
7
2
4
–
3
8
.
[8
]
Bh
a
g
wa
t
P
.
M
.
,
e
t
a
l.
,
“
G
e
n
e
ra
li
se
d
S
tru
c
t
u
re
o
f
a
M
u
lt
il
e
v
e
l
P
W
M
In
v
e
rter
”
,
IEE
E
T
ra
n
s.
o
n
I
n
d
u
str
y
Ap
p
li
c
a
ti
o
n
s
,
1
9
8
3
;
1
9
(6
):
1
0
5
7
-
1
0
6
9
.
[9
]
Ku
m
a
r.
R.
N,
Ba
s
k
a
ra
n
.
J,
“
En
e
rg
y
M
a
n
a
g
e
m
e
n
t
S
y
ste
m
f
o
r
H
y
b
rid
RES
w
it
h
H
y
b
rid
Ca
sc
a
d
e
d
M
u
lt
iv
e
l
In
v
e
rter”
,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
.
2
0
1
4
;
4
(1
):
2
4
-
3
0
.
[1
0
]
Ro
sli.
M
.
A
,
Ya
h
a
y
a
.
N.
Z,
Ba
h
a
ru
d
i
n
.
Z,
“
M
u
lt
i
-
i
n
p
u
t
DC
-
A
C
In
v
e
rter
f
o
r
H
y
b
rid
Re
n
e
w
a
b
le
En
e
rg
y
P
o
w
e
r
S
y
st
e
m
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
.
2
0
1
5
;
6
(
1
):
4
0
-
5
2
.
[1
1
]
Ba
ss
i.
H.
M
,
“
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
i
lv
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
t
e
rn
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
.
2
0
1
6
;
6
(5
).
[1
2
]
Ch
o
i
N.
S
.
,
e
t
a
l
,
“
A
G
e
n
e
ra
l
Circ
u
it
T
o
p
o
lo
g
y
o
f
M
u
lt
il
e
v
e
l
In
v
e
rter”
,
IEE
E
T
ra
n
s.
On
Po
we
r
El
e
c
t
ro
n
ics
.
1
9
9
1
;
6
:
96
-
1
0
3
.
[1
3
]
M
e
y
n
a
rd
T
.
A
.
,
e
t
a
l,
“
M
u
lt
i
-
L
e
v
e
l
Co
n
v
e
rsio
n
:
Hig
h
V
o
l
t
a
g
e
Ch
o
p
p
e
rs an
d
V
o
l
tag
e
S
o
u
rc
e
In
v
e
rters
”
,
IEE
E
T
ra
n
s.
o
n
P
o
we
r E
lec
tro
n
ics
,
1
9
9
2
;3
:
3
9
7
-
4
0
3
.
[1
4
]
Na
b
a
e
A
.
,
e
t
a
l,
“
A
Ne
w
Ne
u
tra
l
-
P
o
i
n
t
-
Clam
p
e
d
P
W
M
In
v
e
rter
”
,
IEE
E
T
ra
n
s.
On
In
d
u
stry
Ap
p
li
c
a
ti
o
n
s
,
1
9
8
1
;
1
7
(
5
):
5
1
8
-
5
2
3
.
[1
5
]
L
iu
H.L
.
,
e
t
al
,
“
Op
ti
m
a
l
P
W
M
De
sig
n
f
o
r
Hig
h
P
o
w
e
r
T
h
re
e
-
L
e
v
e
l
In
v
e
r
ter
th
ro
u
g
h
Co
m
p
a
ra
ti
v
e
S
tu
d
ies
”
,
IEE
E
T
ra
n
s.
o
n
Po
we
r E
lec
tro
n
ics
.
1
9
9
5
;
1
0
(1
)
:
3
8
-
4
4
.
[1
6
]
S
I
M
a
ru
y
a
m
a
T
.
,
e
t
al
,
“
A
N
e
w
A
s
y
n
c
h
ro
n
o
u
s
P
W
M
M
e
t
h
o
d
f
o
r
a
T
h
re
e
-
L
e
v
e
l
In
v
e
rter”
,
Co
n
f.
R
e
c
.
IEE
E
PE
S
C
,
1
9
9
1
;
3
6
6
-
3
7
1
.
[1
7
]
L
a
i
R.
,
e
t
al
,
“
A
P
W
M
M
e
th
o
d
fo
r
Re
d
u
c
ti
o
n
o
f
S
w
it
c
h
in
g
L
o
ss
i
n
a
F
u
ll
-
Brid
g
e
In
v
e
rter”
,
IEE
E
T
ra
n
s.
o
n
P
o
we
r
El
e
c
tro
n
ics
,
1
9
9
5
;
1
0
(
3
):
3
2
6
-
3
3
2
.
[1
8
]
Oh
sa
to
M
.
H.
,
e
t
al
,
“
Ch
a
ra
c
teristics
o
f
Re
so
n
a
n
t
Ty
p
e
F
iv
e
-
L
e
v
e
l
P
W
M
In
v
e
rter
Us
e
d
in
S
m
a
ll
-
S
c
a
led
P
h
o
t
o
v
o
lt
a
ic S
y
ste
m
s”
,
Co
n
f.
R
e
c
.
IEE
E
PE
S
C
,
1
9
9
2
;
7
2
6
-
7
3
1
.
[1
9
]
Hin
g
a
P
.
K.,
e
t
al
,
“
A
Ne
w
P
WM
In
v
e
rter
f
o
r
P
h
o
t
o
v
o
lt
a
ic
P
o
w
e
r
G
e
n
e
ra
ti
o
n
S
y
ste
m
”
,
Co
n
f.
Rec
.
IEE
E
PE
S
C
,
1
9
9
4
;
3
9
1
-
3
9
5
.
[2
0
]
F
ra
n
q
u
e
lo
.
L
.
G
,
e
t
al
,
“
A
F
lex
i
b
le
S
e
lec
ti
v
e
Ha
r
m
o
n
ic
M
it
ig
a
ti
o
n
T
e
c
h
n
iq
u
e
to
M
e
e
t
g
rid
C
o
d
e
s
in
th
re
e
-
L
e
v
e
l
P
W
M
C
o
n
v
e
rters
”
,
IEE
E
T
r
a
n
s I
n
d
E
lec
tro
n
,
2
0
0
7
;
5
4
(6
)
:
3
0
2
2
–
3
0
2
9.
[2
1
]
A
.
N
a
b
a
e
,
I.
e
t
al
,
“
A
Ne
w
Ne
u
tral
-
P
o
in
t
-
Clam
p
e
d
P
W
M
In
v
e
rter,”
In
d
u
stry
Ap
p
l
ica
ti
o
n
s,
IEE
E
T
ra
n
sa
c
ti
o
n
s
,
1
9
8
1
;
1
7
(
5
):
5
1
8
-
5
2
3
.
[2
2
]
M
a
li
n
o
w
sk
i.
M
,
e
t
al
,
“
A
S
u
rv
e
y
o
n
Ca
sc
a
d
e
d
M
u
lt
i
lev
e
l
In
v
e
rters
”
,
In
d
u
stri
a
l
El
e
c
tro
n
ics
,
I
EE
E
T
ra
n
sa
c
ti
o
n
s
.
2
0
1
0
;
5
7
(
7
):
2
1
9
7
-
2
2
0
6
.
[2
3
]
El
-
Na
g
g
a
r.
K,
e
t
al
,
“
S
e
lec
ti
v
e
Ha
r
m
o
n
ic
E
li
m
in
a
ti
o
n
o
f
n
e
w
f
a
m
il
y
o
f
M
u
lt
il
e
v
e
l
In
v
e
rters
u
sin
g
G
e
n
e
ti
c
A
l
g
o
rit
h
m
s”
,
En
e
rg
y
Co
n
v
e
rs
M
a
n
a
g
e,
2
0
0
8
;
4
9
(
1
):8
9
–
9
5
.
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