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n
ap
p
l
icatio
n
n
ee
d
s
an
d
tech
n
o
lo
g
y
.
T
h
is
b
r
ea
k
t
h
r
o
u
g
h
h
as
m
ad
e
in
v
er
ter
s
m
o
r
e
r
eliab
le
an
d
ef
f
icien
t,
m
ak
i
n
g
th
em
ess
en
tial to
m
an
y
p
o
wer
s
y
s
tem
s
an
d
elec
tr
ical
eq
u
ip
m
en
t [
6
].
2
.
1
.
1
.
T
wo
-
lev
el
inv
er
t
er
s
A
two
-
lev
el
in
v
er
ter
g
en
e
r
ates
two
v
o
ltag
e
lev
els
f
o
r
a
l
o
ad
,
p
r
o
d
u
cin
g
+V
DC
a
n
d
-
V
DC
o
u
tp
u
t
v
o
ltag
es.
T
h
e
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M
)
tech
n
iq
u
e
is
u
s
ed
to
s
witch
b
etwe
en
th
ese
v
o
ltag
e
le
v
els,
g
en
er
atin
g
AC
v
o
lta
g
e.
H
o
wev
er
,
t
h
is
m
eth
o
d
h
as
d
r
aw
b
ac
k
s
,
s
u
ch
as
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
an
d
h
ig
h
v
o
ltag
e
ch
an
g
e
r
ate
(
d
v
/d
t)
co
m
p
ar
ed
to
m
u
lti
-
lev
el
in
v
er
ter
s
[
7
]
.
Desp
ite
th
e
lim
itatio
n
s
,
th
e
two
-
lev
el
in
v
e
r
ter
is
wid
ely
u
s
ed
in
ap
p
licatio
n
s
wh
er
e
o
u
t
p
u
t v
o
ltag
e
d
is
to
r
tio
n
an
d
d
v
/
d
t a
r
e
n
o
t c
r
itical
f
ac
to
r
s
[
8
]
.
2
.
2
.
M
ulti
-
lev
el
inv
er
t
er
s
Hig
h
-
p
er
f
o
r
m
an
ce
,
m
ed
iu
m
-
v
o
ltag
e
in
d
u
s
tr
ial
ap
p
licatio
n
s
f
av
o
r
m
u
lti
-
lev
el
in
v
er
ter
s
.
T
h
ey
co
n
v
er
t
DC
elec
tr
ici
ty
f
r
o
m
b
atter
ies,
s
u
p
er
ca
p
ac
ito
r
s
,
or
s
o
lar
p
an
els
in
to
AC
p
o
wer
at
d
if
f
er
en
t
v
o
ltag
es.
Mu
lti
-
lev
el
in
v
er
ter
s
co
n
v
er
t
a
n
d
u
s
e
m
ed
iu
m
-
v
o
ltag
e
p
o
wer
e
f
f
ic
ien
tly
by
p
r
o
d
u
cin
g
h
ig
h
-
o
u
tp
u
t
p
o
wer
[
9
]
,
[
1
0
]
.
T
h
er
e
a
r
e
th
r
ee
t
y
p
es
o
f
m
u
lti
-
lev
el
i
n
v
e
r
ter
s
as
g
iv
en
:
d
io
d
e
clam
p
ed
m
u
lti
-
lev
el
in
v
e
r
ter
,
f
ly
in
g
ca
p
ac
ito
r
s
m
u
lti
-
lev
el
in
v
er
ter
,
an
d
c
ascad
ed
ty
p
e
m
u
lti
-
lev
el
in
v
er
ter
.
2
.
3
.
C
a
s
ca
ded
H
-
b
ridg
e
m
ulti
-
lev
el
i
nv
er
t
er
I
n
itially
,
th
e
C
H
B
ML
I
to
p
o
lo
g
y
was
in
tr
o
d
u
ce
d
f
o
r
m
o
t
o
r
d
r
iv
e
ap
p
licatio
n
s
.
D
u
e
t
o
e
l
e
ct
r
o
n
i
c
s
w
it
c
h
p
o
w
e
r
r
a
t
i
n
g
s
,
c
o
n
v
e
n
t
i
o
n
a
l
c
o
n
v
e
r
t
e
r
s
l
o
s
t
p
o
w
e
r
a
n
d
w
e
r
e
i
n
e
f
f
i
c
i
e
n
t
i
n
h
i
g
h
-
v
o
l
t
a
g
e
s
i
t
u
a
ti
o
n
s
.
C
HB
M
L
I
o
f
f
e
r
s
l
o
w
e
r
c
o
s
ts
a
n
d
r
e
d
u
c
e
d
e
l
e
ct
r
o
m
a
g
n
e
t
i
c
in
t
e
r
f
e
r
e
n
c
e
c
o
m
p
a
r
e
d
t
o
c
o
n
v
e
n
t
i
o
n
a
l
c
o
n
v
e
r
t
e
r
s
[
1
1
]
.
Hig
h
er
p
e
r
f
o
r
m
an
ce
with
lo
w
T
HD
an
d
in
cr
ea
s
ed
ef
f
i
cien
cy
ar
e
o
b
tain
e
d
.
T
h
e
r
eq
u
ir
em
en
t
o
f
s
ep
ar
ate
,
eq
u
al
-
v
alu
e
DC
s
o
u
r
ce
s
f
o
r
e
ac
h
H
-
b
r
id
g
e
in
th
e
s
y
m
m
etr
i
ca
l
C
HB
ML
I
f
r
am
ewo
r
k
r
ed
u
ce
s
th
e
co
m
p
lex
ity
o
f
in
teg
r
atin
g
v
ar
io
u
s
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
[
1
2
]
.
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
n
u
m
b
er
o
f
H
-
b
r
i
d
g
es
(
n
)
an
d
th
e
lev
eled
o
u
t
p
u
t
p
er
p
h
a
s
e
(
m
)
is
g
iv
en
b
y
th
e
e
q
u
atio
n
m
=
2
n
+
1
.
Sy
s
tem
r
eq
u
ir
e
m
en
ts
,
ap
p
licatio
n
s
,
s
witch
lim
its
,
an
d
s
y
s
tem
lo
s
s
es sh
o
u
ld
b
e
co
n
s
id
er
ed
wh
ile
ch
o
o
s
in
g
th
e
o
p
tim
u
m
n
u
m
b
er
o
f
lev
els [
1
3
].
2
.
4
.
P
uls
e
width
m
o
du
la
t
io
n
(
P
WM
)
t
ec
hn
iqu
e
s
PW
M
tr
an
s
m
it
s
in
f
o
r
m
atio
n
t
h
r
o
u
g
h
p
u
ls
es,
with
d
ata
en
co
d
ed
in
th
e
p
u
ls
e
wid
th
s
.
To
p
r
o
d
u
ce
th
e
d
esire
d
r
esu
lt,
PW
M
tech
n
iq
u
es
ar
e
ess
en
tial.
T
h
er
e
h
a
v
e
b
ee
n
s
ev
er
al
m
o
d
u
latio
n
tec
h
n
i
q
u
es
p
r
o
p
o
s
ed
an
d
d
is
cu
s
s
ed
in
th
e
liter
atu
r
e
to
ac
co
m
p
lis
h
th
is
,
in
clu
d
i
n
g
s
p
ac
e
v
ec
to
r
PW
M
(
S
VP
W
M)
,
s
elec
tiv
e
h
ar
m
o
n
ic
elim
in
atio
n
PW
M
(
SHE
-
PW
M)
,
an
d
m
u
lti
-
ca
r
r
ier
PW
M
(
MCP
W
M)
[
14
].
2
.
4
.
1
.
M
ulti
-
ca
r
rier
P
WM
s
c
h
em
e
Am
o
n
g
t
h
e
v
a
r
io
u
s
m
o
d
u
latio
n
tech
n
iq
u
es,
MCP
W
M
is
co
m
m
o
n
ly
u
s
ed
f
o
r
c
o
n
tr
o
llin
g
ML
I
s
d
u
e
to
its
s
im
p
licity
.
T
ec
h
n
iq
u
es
s
u
ch
as
SP
W
M
an
d
SVP
W
M
g
e
n
er
ate
p
u
ls
es
th
at
co
n
tr
o
l
th
e
s
witch
es
in
ML
I
s
,
with
th
e
g
o
al
o
f
p
r
o
d
u
cin
g
a
n
ea
r
-
s
in
u
s
o
id
al
o
u
tp
u
t
v
o
ltag
e
wh
ile
m
in
im
izin
g
h
a
r
m
o
n
ic
d
is
to
r
tio
n
[
1
5
]
.
MCP
W
M,
th
e
m
o
s
t
c
o
m
m
o
n
ly
u
s
ed
,
s
im
p
lifie
s
p
u
ls
e
g
en
er
atio
n
b
y
co
m
p
ar
in
g
r
e
f
e
r
en
ce
s
ig
n
als
with
tr
ian
g
u
lar
s
ig
n
als
to
co
n
tr
o
l
in
d
iv
id
u
al
p
o
wer
s
witch
es.
MCP
W
M
r
eq
u
ir
es
(
n
-
1
)
ca
r
r
ier
w
av
es
f
o
r
an
n
-
lev
el
in
v
er
ter
[
1
6
]
.
I
t
ca
n
b
e
ca
te
g
o
r
ized
in
to
two
ty
p
es:
lev
el
-
s
h
if
ted
p
u
ls
e
wid
th
m
o
d
u
lat
io
n
(
L
SP
W
M)
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
a
lysi
s
a
n
d
s
imu
la
tio
n
o
f
7
-
l
ev
el
a
n
d
9
-
leve
l c
a
s
ca
d
e
d
H
-
b
r
id
g
e
mu
lti
-
leve
l in
ve
r
ters
(
S
u
ja
th
a
B
a
n
ka
)
13
p
h
ase
-
s
h
if
ted
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PS
PW
M)
.
L
SP
W
M
en
co
m
p
ass
es
v
ar
io
u
s
v
a
r
ian
t
s
,
in
clu
d
in
g
p
h
ase
d
is
p
o
s
itio
n
-
p
u
ls
e
wid
th
m
o
d
u
l
atio
n
(
PD
-
PW
M)
,
p
h
ase
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
-
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
POD
-
PW
M)
,
alter
n
ate
p
h
as
e
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
-
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
APOD
-
PW
M)
,
an
d
ca
r
r
ier
-
o
v
er
lap
p
i
n
g
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
C
O
-
PW
M)
[
1
7
]
-
[
2
0
]
.
2
.
4
.
2
.
Sin
us
o
ida
l P
WM
I
n
SP
W
M,
th
e
co
m
p
a
r
is
o
n
is
p
er
f
o
r
m
ed
b
etwe
en
a
s
in
u
s
o
id
al
m
o
d
u
latin
g
wav
ef
o
r
m
a
n
d
a
tr
ian
g
u
lar
ca
r
r
ier
wav
ef
o
r
m
to
d
ete
r
m
in
e
th
e
ON/OFF
s
tates
o
f
th
e
s
witch
es
.
I
f
th
e
m
o
d
u
latin
g
wa
v
e
is
g
r
ea
ter
th
an
th
e
ca
r
r
ier
wav
e,
th
e
s
witch
is
O
N
an
d
th
e
s
tate
is
h
ig
h
.
L
o
we
r
am
p
litu
d
es
in
d
icate
lo
w
s
t
at
es
an
d
tu
r
n
OFF
th
e
s
witch
[
2
1
].
T
h
e
T
HD
in
th
e
o
u
tp
u
t
v
o
ltag
e
ca
n
b
e
r
e
d
u
c
ed
b
y
co
n
tr
o
llin
g
th
e
i
n
v
er
ter
'
s
s
witch
in
g
p
atter
n
with
SP
W
M.
I
t
ca
n
ea
s
ily
elim
in
ate
lo
wer
h
ar
m
o
n
ics.
I
n
th
e
ca
s
e
o
f
th
e
m
u
lti
-
ca
r
r
ier
SP
W
M
tech
n
iq
u
e,
(m
-
1
)
ca
r
r
ier
wa
v
es
ar
e
n
ee
d
e
d
f
o
r
an
m
-
lev
el
C
HB
ML
I
.
Ma
in
tain
in
g
u
n
if
o
r
m
am
p
litu
d
e
an
d
f
r
eq
u
en
cy
f
o
r
all
ca
r
r
ier
wav
es o
r
tr
ia
n
g
u
lar
wav
es is
cr
u
cial.
2
.
4
.
3
.
L
ev
el
s
hift
P
WM
T
h
is
ap
p
r
o
ac
h
u
s
es
tr
ian
g
u
lar
wav
ef
o
r
m
s
f
o
r
all
ca
r
r
ie
r
s
ig
n
als
o
v
er
th
e
co
n
v
er
ter
'
s
v
o
ltag
e
r
an
g
e.
T
h
ese
s
ig
n
als h
av
e
th
e
s
am
e
f
r
eq
u
en
cy
a
n
d
am
p
litu
d
e
[
2
2
]
.
T
h
ey
ar
e
c
ateg
o
r
ized
b
ased
o
n
th
e
o
r
g
an
izatio
n
o
f
ca
r
r
ier
s
ig
n
als.
Pr
o
d
u
cin
g
n
l
ev
els
r
eq
u
ir
es
(
n
-
1
)
ca
r
r
ier
s
ig
n
als.
I
t
is
e
m
p
lo
y
e
d
f
o
r
in
v
e
r
ter
co
n
tr
o
l
with
o
u
t
in
co
r
p
o
r
atin
g
p
o
wer
b
ala
n
cin
g
.
3.
M
E
T
H
O
D
3
.
1
.
S
im
ula
t
i
o
n
o
f
c
a
s
ca
ded
H
-
b
ridg
e
7
-
l
ev
el
MLI
T
h
e
cir
cu
it
to
p
o
lo
g
y
o
f
th
e
7
-
l
ev
el
C
HB
ML
I
an
d
th
e
ass
o
ciate
d
o
u
tp
u
t
v
o
l
ta
g
e
wav
ef
o
r
m
ar
e
p
r
esen
ted
in
F
ig
u
r
es
2
a
n
d
3
.
I
t
c
o
n
s
is
ts
o
f
th
r
ee
H
-
b
r
id
g
e
s
,
with
ea
ch
in
d
iv
id
u
al
b
r
id
g
e
co
n
s
is
tin
g
o
f
f
o
u
r
s
witch
es
p
o
wer
ed
b
y
a
DC
s
o
u
r
ce
.
E
ac
h
H
-
b
r
i
d
g
e
is
ca
p
a
b
le
o
f
g
e
n
er
atin
g
a
p
o
s
itiv
e,
n
eg
ativ
e,
an
d
ze
r
o
v
o
ltag
e.
I
n
th
is
to
p
o
lo
g
y
,
all
th
r
ee
b
r
id
g
es
ar
e
i
n
ter
co
n
n
ec
te
d
in
s
er
ies
with
ea
ch
o
t
h
er
[
2
3
]
,
[
2
4
]
.
T
h
e
v
o
ltag
e
p
r
o
d
u
ce
d
b
y
ea
ch
b
r
id
g
e
is
ad
d
ed
to
g
eth
e
r
to
g
et
th
e
r
eq
u
i
r
ed
v
o
ltag
e.
T
h
e
v
o
ltag
e
lev
els
p
r
o
d
u
ce
d
in
th
is
ML
I
ar
e
+3
V
DC
,
+2
V
DC
,
+V
DC
,
0,
-
V
DC
,
-
2
V
DC
,
a
n
d
-
3
V
DC
.
T
h
e
ch
ar
ac
te
r
is
tics
o
f
7
-
lev
el
C
HB
ML
I
m
ak
e
it
s
u
itab
le
f
o
r
h
ig
h
ap
p
licatio
n
s
th
at
r
eq
u
ir
e
lo
w
h
ar
m
o
n
ic,
d
is
to
r
tio
n
,
a
n
d
b
etter
v
o
ltag
e
c
o
n
t
r
o
l [
25
].
S
witch
in
g
o
p
er
atio
n
s
th
at
a
r
e
u
s
ed
to
g
en
er
ate
th
e
d
if
f
er
e
n
t
v
o
ltag
es
ar
e
g
iv
en
in
F
ig
u
r
e
4
.
I
n
ML
I
s
,
co
r
r
esp
o
n
d
in
g
v
o
ltag
es
ar
e
g
en
er
ated
wh
en
s
witch
es
ar
e
t
o
g
g
led
ON
an
d
OFF
ac
co
r
d
i
n
g
to
a
s
et
p
atter
n
,
wh
er
e
1
in
d
icate
s
th
e
s
witch
is
O
N
an
d
0
in
d
icate
s
it
is
OFF
[
26
].
F
ig
u
r
es
5
(a
)
-
5(
h
)
r
ep
r
esen
t
v
ar
io
u
s
wo
r
k
in
g
m
o
d
es
o
f
t
h
e
7
-
le
v
e
l
m
u
lti
-
lev
el
in
v
e
r
ter
th
r
o
u
g
h
wh
ich
v
a
r
io
u
s
lev
els
o
f
v
o
ltag
es
ar
e
p
r
o
d
u
ce
d
.
Fig
u
r
e
6
illu
s
tr
ates th
e
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
o
f
a
7
-
lev
el
C
HB
ML
I
.
Fig
u
r
e
2
.
7
-
lev
el
C
HB
ML
I
cir
cu
it to
p
o
lo
g
y
Fig
u
r
e
3
.
7
-
lev
el
C
HB
ML
I
o
u
tp
u
t v
o
ltag
e
wa
v
ef
o
r
m
Fig
u
r
e
4
.
Switch
in
g
f
r
eq
u
en
cy
o
f
7
-
le
v
el
C
HB
ML
I
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
1
1
-
22
14
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
(
g
)
(
h
)
Fig
u
r
e
5
. W
o
r
k
i
n
g
m
o
d
es o
f
t
h
e
7
-
lev
el
m
u
lti
-
lev
el
in
v
e
r
ter
:
(
a)
V
dc
,
(
b
)
2
V
dc
,
(
c)
3
V
dc
,
(
d
)
0
V
dc
,
(
e)
-
V
dc
,
(f)
-
2
V
dc
,
(
g
)
-
3
V
dc
,
a
n
d
(
h
)
0
V
dc
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
a
lysi
s
a
n
d
s
imu
la
tio
n
o
f
7
-
l
ev
el
a
n
d
9
-
leve
l c
a
s
ca
d
e
d
H
-
b
r
id
g
e
mu
lti
-
leve
l in
ve
r
ters
(
S
u
ja
th
a
B
a
n
ka
)
15
Fig
u
r
e
6
.
7
-
l
ev
el
C
HB
ML
I
o
u
tp
u
t v
o
ltag
e
wa
v
ef
o
r
m
3
.
2
.
Sim
ula
t
i
o
n o
f
c
a
s
ca
ded
H
-
bridg
e
9
-
lev
el
M
L
I
T
h
e
9
-
le
v
el
C
HB
ML
I
is
a
s
p
ec
if
ic
co
n
f
ig
u
r
atio
n
th
at
o
f
f
er
s
ad
v
a
n
tag
es
in
p
o
wer
c
o
n
v
er
s
io
n
ap
p
licatio
n
s
.
I
t
co
n
s
is
ts
o
f
f
o
u
r
H
-
b
r
id
g
es,
ea
ch
c
o
m
p
o
s
ed
o
f
f
o
u
r
s
witch
es,
g
en
e
r
atin
g
m
u
ltip
le
v
o
ltag
e
lev
els,
in
clu
d
in
g
p
o
s
itiv
e,
n
eg
ativ
e,
an
d
ze
r
o
v
o
ltag
es.
B
y
c
o
m
b
in
in
g
th
ese
v
o
ltag
e
lev
els
,
it
ac
h
iev
es
h
ig
h
er
r
eso
lu
tio
n
an
d
f
lex
ib
ilit
y
in
g
en
er
atin
g
th
e
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
[
2
7
]
.
T
h
is
co
n
f
ig
u
r
atio
n
en
h
a
n
ce
s
th
e
q
u
ality
o
f
th
e
o
u
tp
u
t
wav
ef
o
r
m
b
y
d
ec
r
ea
s
in
g
h
a
r
m
o
n
ic
co
n
ten
t,
h
en
ce
m
in
im
izin
g
n
o
is
e
an
d
d
is
to
r
tio
n
.
I
t
also
p
r
o
v
i
d
es
r
ed
u
ce
d
s
witc
h
in
g
l
o
s
s
es
an
d
im
p
r
o
v
ed
e
f
f
icien
cy
.
T
h
e
9
-
lev
el
C
HB
ML
I
'
s
h
ig
h
v
o
ltag
e
r
eso
lu
tio
n
is
ad
v
an
tag
e
o
u
s
f
o
r
ap
p
licatio
n
s
th
at
d
em
an
d
p
r
ec
is
e
v
o
ltag
e
co
n
tr
o
l,
en
ab
lin
g
m
o
r
e
e
x
ac
t
ad
ju
s
tm
en
ts
in
o
u
tp
u
t v
o
ltag
e
an
d
en
h
an
cin
g
co
n
tr
o
l
an
d
ac
c
u
r
ac
y
in
d
if
f
er
e
n
t in
d
u
s
tr
ial
p
r
o
ce
s
s
es
[
28
].
T
h
e
g
en
er
al
s
tr
u
ctu
r
e
o
f
th
e
9
-
l
ev
el
C
HB
ML
I
an
d
its
co
r
r
esp
o
n
d
in
g
wav
e
f
o
r
m
a
r
e
s
h
o
wn
in
Fig
u
r
es
7
an
d
8
.
It
p
r
o
d
u
ce
s
an
o
u
tp
u
t
wav
ef
o
r
m
of
f
o
u
r
p
o
s
itiv
e
lev
els,
f
o
u
r
n
eg
ativ
e
lev
els,
an
d
a
ze
r
o
l
ev
el.
T
h
er
e
ar
e
9
s
witch
in
g
m
o
d
es
an
d
i
t
g
en
er
ates
th
e
r
eq
u
ir
ed
le
v
els
of
o
u
tp
u
t
of
v
o
ltag
es
wh
ich
ar
e
+4
V
DC
,
+3
V
DC
,
+2
V
DC
,
+V
DC
,
0,
-
V
DC
,
-
2
V
DC
,
-
3
V
DC
,
a
n
d
-
4
V
DC
.
Fig
u
r
e
9
in
d
icate
s
th
e
co
r
r
esp
o
n
d
i
n
g
v
o
ltag
es
ac
co
r
d
in
g
to
th
e
s
witch
in
g
p
atter
n
.
F
ig
u
r
es
1
0
(a
)
-
10(
i)
r
ep
r
esen
t
v
ar
io
u
s
wo
r
k
i
n
g
m
o
d
es
o
f
th
e
9
-
lev
el
C
HB
ML
I
th
r
o
u
g
h
w
h
ich
v
ar
io
u
s
lev
els
o
f
v
o
ltag
es
a
r
e
p
r
o
d
u
ce
d
[
2
9
]
.
Fig
u
r
e
11
r
ep
r
esen
ts
th
e
o
u
tp
u
t
vol
tag
e
wav
ef
o
r
m
o
f
a
9
-
lev
el
C
HB
ML
I
.
Fig
u
r
e
7
.
9
-
lev
el
C
HB
ML
I
cir
cu
it to
p
o
lo
g
y
Fig
u
r
e
8
.
9
-
lev
el
C
HB
ML
I
o
u
tp
u
t v
o
ltag
e
wa
v
ef
o
r
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
1
1
-
22
16
Fig
u
r
e
9
.
Switch
in
g
f
r
eq
u
en
cy
o
f
9
-
le
v
el
C
HB
ML
I
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
(
g
)
(
h
)
(
i)
Fig
u
r
e
1
0
.
W
o
r
k
in
g
m
o
d
es o
f
th
e
9
-
lev
el
C
HB
ML
I
:
(
a)
4
V
dc
,
(
b
)
3
V
dc
,
(
c)
2
V
dc
,
(
d
)
V
dc
,
(
e)
0
V
dc
,
(
f
)
-
V
dc
,
(
g
)
-
2
V
dc
,
(
h
)
-
3
V
dc
,
an
d
(
i)
-
4
V
dc
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
a
lysi
s
a
n
d
s
imu
la
tio
n
o
f
7
-
l
ev
el
a
n
d
9
-
leve
l c
a
s
ca
d
e
d
H
-
b
r
id
g
e
mu
lti
-
leve
l in
ve
r
ters
(
S
u
ja
th
a
B
a
n
ka
)
17
Fig
u
r
e
1
1
.
9
-
lev
el
C
HB
ML
I
o
u
tp
u
t v
o
ltag
e
wav
ef
o
r
m
3
.
3
.
T
H
D
a
na
ly
s
is
T
h
e
q
u
ality
o
f
a
wav
ef
o
r
m
is
m
ea
s
u
r
ed
b
y
to
tal
h
a
r
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
,
wh
ich
is
d
ef
i
n
ed
b
y
th
e
h
ar
m
o
n
ic
n
u
m
b
e
r
(
n
)
.
Har
m
o
n
ics in
th
e
s
y
s
tem
ca
n
ca
u
s
e
eq
u
ip
m
en
t d
e
g
r
ad
atio
n
a
n
d
it is
cr
u
cial
to
m
in
im
ize
th
em
.
I
n
th
e
co
n
tex
t
o
f
th
e
M
L
I
,
co
n
tr
o
lled
s
witch
in
g
p
u
ls
e
s
in
th
e
o
u
tp
u
t
v
o
ltag
e
(
V
out
)
ar
e
u
s
ed
to
r
ed
u
ce
th
e
T
HD.
L
o
wer
in
g
T
HD
h
e
lp
s
elim
in
ate
th
e
p
r
esen
ce
o
f
h
ar
m
o
n
ics
an
d
im
p
r
o
v
es
th
e
q
u
ality
o
f
p
o
wer
d
eliv
er
ed
[
3
0
]
.
Har
m
o
n
ic
d
is
to
r
tio
n
s
p
r
im
ar
ily
s
tem
f
r
o
m
th
e
u
s
ag
e
o
f
n
o
n
-
lin
ea
r
lo
a
d
s
,
p
ar
ticu
lar
ly
th
o
s
e
in
co
r
p
o
r
atin
g
p
o
wer
elec
tr
o
n
i
cs,
as
th
ese
lo
ad
s
d
o
n
o
t
d
r
aw
cu
r
r
en
t
in
a
s
in
u
s
o
id
al
m
an
n
er
.
IEEE
Stan
d
ar
d
s
ty
p
ically
d
ef
in
e
lim
it
v
alu
es
f
o
r
v
o
ltag
e
h
a
r
m
o
n
ics,
with
a
T
HD
lim
it
o
f
5
%
an
d
a
li
m
it
o
f
3
%
f
o
r
ea
ch
in
d
iv
id
u
al
h
ar
m
o
n
ic.
DC
v
o
lt
ag
es
an
d
in
v
er
t
er
co
m
m
u
tatio
n
an
g
les
af
f
ec
t
o
u
tp
u
t
v
o
ltag
e
T
HD.
I
n
an
id
ea
l
s
ce
n
ar
io
with
ca
s
ca
d
ed
s
y
m
m
etr
ical
in
v
er
ter
s
,
all
DC
s
o
u
r
c
es
r
em
ain
co
n
s
tan
t
an
d
eq
u
al
,
as
in
(
1
)
.
T
h
e
T
HD
an
aly
s
is
o
f
th
e
7
-
le
v
el
an
d
9
-
l
ev
el
C
HB
ML
I
m
o
d
el
is
s
h
o
wn
in
Fig
u
r
es 1
2
an
d
1
3
,
r
esp
ec
tiv
ely
.
ℎ
=
√
∑
(
,
)
2
∞
=
2
1
,
=
√
∑
(
)
2
−
(
1
,
)
2
∞
=
2
1
,
(
1
)
3
.
4
.
D
esig
n a
nd
im
plem
ent
a
t
io
n o
f
a
p
a
s
s
iv
e
f
ilte
r
Du
e
to
th
e
s
witch
in
g
n
at
u
r
e
o
f
ML
I
s
,
it
in
tr
o
d
u
ce
s
u
n
d
esire
d
h
ar
m
o
n
ics
an
d
d
is
to
r
ts
th
e
AC
o
u
tp
u
t
wav
ef
o
r
m
.
F
ilter
s
ar
e
u
tili
ze
d
to
m
itig
ate
th
e
h
ar
m
o
n
ics
a
n
d
en
h
an
ce
f
u
n
d
am
en
tal
co
m
p
o
n
en
ts
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
.
Fil
ter
s
allo
w
f
o
r
a
s
m
o
o
th
er
a
n
d
m
o
r
e
s
in
u
s
o
id
al
wav
ef
o
r
m
,
th
u
s
r
ed
u
cin
g
h
a
r
m
o
n
ic
d
is
to
r
tio
n
.
T
h
er
e
ar
e
th
r
ee
m
ain
ty
p
es
o
f
f
ilter
s
co
m
m
o
n
l
y
u
s
ed
,
t
h
ey
ar
e
in
d
u
ct
o
r
f
ilter
(
L
)
,
in
d
u
c
to
r
-
ca
p
ac
ito
r
f
ilter
(
L
C
)
,
an
d
in
d
u
cto
r
-
ca
p
ac
ito
r
-
in
d
u
cto
r
f
ilter
(
L
C
L
)
.
T
h
e
L
C
f
ilter
,
also
k
n
o
wn
as
a
p
a
s
s
iv
e
L
C
f
ilter
o
r
s
ec
o
n
d
-
o
r
d
er
f
ilter
,
is
an
elec
tr
o
n
ic
cir
cu
it
th
at
u
tili
ze
s
in
d
u
cto
r
s
(
L
)
an
d
ca
p
ac
ito
r
s
(
C
)
to
s
h
ap
e
o
r
f
ilter
th
e
f
r
eq
u
e
n
cy
r
esp
o
n
s
e
o
f
a
s
ig
n
a
l.
I
t
is
d
esig
n
ed
to
m
ee
t
I
E
E
E
s
tan
d
ar
d
s
b
y
ac
h
ie
v
in
g
less
th
an
a
5
%
d
ev
iatio
n
.
Th
e
L
C
f
ilter
in
co
r
p
o
r
ates
b
o
t
h
an
in
d
u
cto
r
a
n
d
a
ca
p
ac
ito
r
,
m
ak
in
g
it
a
s
ec
o
n
d
-
o
r
d
er
f
ilter
.
I
n
th
e
L
C
f
ilter
,
a
ca
p
ac
ito
r
is
c
o
n
n
ec
te
d
to
th
e
g
r
id
i
n
p
ar
allel.
Ap
p
lied
with
a
s
witch
in
g
m
eth
o
d
,
th
e
L
C
f
ilter
is
ca
p
ab
le
o
f
r
em
o
v
in
g
lo
wer
-
o
r
d
er
o
d
d
h
ar
m
o
n
ics f
r
o
m
t
h
e
o
u
t
p
u
t.
Fo
r
s
i
n
g
le
-
p
h
ase
f
u
ll b
r
id
g
e
in
v
er
ter
s
,
V
out
(
r
m
s
)
=
V
DC
,
V
=
1
0
0
√
2
s
in
wt,
I
=
2
0
% o
f
t
h
e
r
ated
cu
r
r
en
t,
a
n
d
I
=
4
×
×
.
=
4
×
I
×
(
2
)
=
(
10
2
×
×
)
2
×
1
(
3
)
W
h
er
e
is
in
d
u
ctan
ce
in
m
H,
is
s
witch
in
g
f
r
eq
u
e
n
cy
in
Hz
,
an
d
is
th
e
ca
p
ac
itan
ce
in
m
F.
Fig
u
r
es
1
4
an
d
1
5
r
ep
r
esen
t
th
e
o
u
tp
u
t
v
o
lta
g
e
wav
ef
o
r
m
s
o
f
a
7
-
lev
e
l
an
d
9
-
lev
el
C
HB
ML
I
with
a
p
ass
iv
e
L
C
f
ilter
.
F
ig
u
r
e
s
1
6
an
d
1
7
r
ep
r
esen
t
t
h
e
T
HD
an
aly
s
is
o
f
a
7
-
lev
el
,
9
-
lev
el
C
HB
ML
I
wi
th
a
f
ilte
r
.
T
h
e
o
b
s
er
v
atio
n
s
f
r
o
m
th
e
ab
o
v
e
m
o
d
els ar
e
tab
u
lated
in
T
ab
le
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
1
1
-
22
18
Fig
u
r
e
1
2
.
T
HD
an
aly
s
is
o
f
7
-
lev
el
C
HB
ML
I
Fig
u
r
e
1
3
.
T
HD
an
aly
s
is
o
f
9
-
lev
el
C
HB
ML
I
Fig
u
r
e
1
4
.
Ou
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
o
f
7
-
le
v
el
C
HB
ML
I
wit
h
an
L
C
f
ilter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
a
lysi
s
a
n
d
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imu
la
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n
o
f
7
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l
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el
a
n
d
9
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leve
l c
a
s
ca
d
e
d
H
-
b
r
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mu
lti
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ve
r
ters
(
S
u
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th
a
B
a
n
ka
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19
Fig
u
r
e
1
5
.
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tp
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t
v
o
ltag
e
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ef
o
r
m
o
f
9
-
le
v
el
C
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ML
I
wit
h
an
L
C
f
ilter
Fig
u
r
e
1
6
.
T
HD
an
aly
s
is
o
f
7
-
lev
el
C
HB
ML
I
with
p
ass
iv
e
L
C
f
ilter
Fig
u
r
e
1
7
.
T
HD
an
aly
s
is
o
f
9
-
lev
el
C
HB
ML
I
with
p
ass
iv
e
L
C
f
ilter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
1
1
-
22
20
T
ab
le
1.
T
HD
c
o
m
p
ar
is
o
n
of
7
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lev
el
an
d
9
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lev
el
ML
I
Le
v
e
l
o
f
M
LI
P
a
r
a
me
t
e
r
s
TH
D
v
a
l
u
e
F
u
n
d
a
m
e
n
t
a
l
c
o
m
p
o
n
e
n
t
o
f
o
u
t
p
u
t
v
o
l
t
a
g
e
(
V
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7
-
l
e
v
e
l
M
LI
F
i
x
e
d
D
C
w
i
t
h
o
u
t
L
C
f
i
l
t
e
r
1
3
.
8
2
%
3
0
8
.
4
F
i
x
e
d
D
C
w
i
t
h
L
C
f
i
l
t
e
r
2
.
6
8
%
3
0
0
9
-
l
e
v
e
l
M
LI
F
i
x
e
d
D
C
w
i
t
h
o
u
t
L
C
f
i
l
t
e
r
1
2
.
2
5
%
3
4
9
.
8
F
i
x
e
d
D
C
w
i
t
h
L
C
f
i
l
t
e
r
3
.
2
7
%
4
2
1
.
7
4.
CO
NCLU
SI
O
N
T
h
e
C
HB
ML
I
is
ca
p
ab
le
o
f
p
r
o
d
u
cin
g
s
u
p
er
io
r
q
u
ality
o
u
tp
u
t
wav
ef
o
r
m
s
co
m
p
ar
ed
to
tr
ad
itio
n
al
two
-
lev
el
in
v
er
ter
s
,
wh
ich
h
a
s
co
n
tr
ib
u
ted
to
its
r
is
in
g
p
o
p
u
lar
ity
in
ap
p
licatio
n
s
r
e
q
u
ir
i
n
g
m
ed
iu
m
to
h
ig
h
p
o
wer
.
W
h
en
it
co
m
es
to
ML
I
,
PW
M
tech
n
iq
u
es
ar
e
n
ec
ess
ar
y
to
ac
h
iev
e
th
e
d
esire
d
o
u
t
p
u
t.
I
t
was
d
ec
i
d
ed
to
u
s
e
th
e
lev
el
s
h
if
t
p
u
ls
e
wi
d
th
m
o
d
u
latio
n
(
PW
M)
tech
n
iq
u
e
f
o
r
th
is
p
r
o
ject,
with
a
s
i
n
e
wav
e
s
er
v
in
g
as
th
e
m
o
d
u
latin
g
s
ig
n
al.
T
h
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
H
D)
was
m
ea
s
u
r
ed
to
b
e
1
3
.
8
2
%
f
o
r
th
e
7
-
lev
el
in
v
er
ter
an
d
1
2
.
2
5
%
f
o
r
th
e
9
-
lev
el
in
v
er
ter
,
r
esp
ec
tiv
ely
.
I
t
is
ev
id
en
t
th
at
in
cr
ea
s
in
g
th
e
n
u
m
b
er
o
f
le
v
els
in
th
e
ML
I
lo
wer
s
th
e
T
HD
p
er
ce
n
tag
e
an
d
en
h
an
ce
s
th
e
f
u
n
d
am
e
n
tal
v
o
ltag
e,
wh
ich
s
ig
n
if
ies
im
p
r
o
v
e
d
in
v
er
ter
p
e
r
f
o
r
m
an
ce
.
T
h
e
ef
f
icien
cy
o
f
p
a
s
s
iv
e
f
ilter
s
in
l
o
we
r
in
g
T
HD
is
an
o
th
er
k
ey
tak
ea
way
f
r
o
m
th
is
ef
f
o
r
t.
T
h
r
o
u
g
h
th
e
ex
ec
u
tio
n
o
f
th
e
r
eq
u
ir
ed
c
o
m
p
u
tatio
n
s
,
an
L
C
f
ilter
was
d
esig
n
ed
.
T
h
e
T
HD
v
alu
es
f
o
r
7
-
lev
el
an
d
9
-
lev
el
C
HB
ML
I
s
ar
e
r
ep
o
r
ted
to
b
e
2
.
6
8
%
an
d
3
.
2
7
%,
r
esp
ec
tiv
ely
,
o
n
ce
th
e
p
ass
iv
e
f
ilter
th
at
was c
o
n
s
tr
u
cted
is
in
co
r
p
o
r
ate
d
with
th
e
p
r
o
p
er
DC
in
p
u
t v
o
ltag
e.
Pre
cise a
d
ju
s
tm
en
t o
f
f
ilter
s
is
n
ec
ess
ar
y
to
g
en
er
ate
p
u
r
e
s
in
u
s
o
id
al
wav
e
f
o
r
m
s
o
f
v
o
ltag
e
a
n
d
c
u
r
r
en
t,
wh
ich
will d
ec
r
ea
s
e
T
HD
an
d
en
h
an
ce
ef
f
icien
cy
.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
is
r
esear
ch
wo
r
k
was su
p
p
o
r
ted
b
y
“
W
o
o
s
o
n
g
Un
iv
e
r
s
ity
’
s
Aca
d
em
ic
R
esear
ch
Fu
n
d
in
g
-
2
0
2
4
”
.
RE
F
E
R
E
NC
E
S
[
1
]
C
.
R
.
B
a
l
a
mu
r
u
g
a
n
a
n
d
R
.
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e
sn
r
a
j
,
“
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n
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l
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se
t
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n
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mu
l
t
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e
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i
n
v
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r
,
”
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n
t
e
rn
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
A
p
p
l
i
e
d
P
o
w
e
r
En
g
i
n
e
e
r
i
n
g
(
I
J
A
PE)
,
v
o
l
.
7
,
n
o
.
1
,
p
p
.
2
7
–
3
9
,
2
0
1
8
,
d
o
i
:
1
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.
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9
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/
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j
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p
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.
v
7
.
i
1
.
p
p
2
7
-
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9
.
[
2
]
T.
P
.
S
a
n
u
a
n
d
A
.
X
a
v
i
e
r
,
“
C
a
s
c
a
d
e
d
H
b
r
i
d
g
e
f
i
f
t
e
e
n
l
e
v
e
l
i
n
v
e
r
t
e
r
,
”
I
n
t
e
rn
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
E
n
g
i
n
e
e
r
i
n
g
Re
s
e
a
rc
h
&
T
e
c
h
n
o
l
o
g
y
(
I
J
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,
v
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l
.
4
,
n
o
.
9
,
p
p
.
8
8
0
–
8
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,
[
O
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l
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n
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]
.
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a
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l
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3
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4
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5
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,
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6
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1
3
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[
1
4
]
B
.
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.
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[
1
5
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P
.
K
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