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20
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Desig
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P
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Pu
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wid
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latio
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T
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c
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CC B
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C
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Kis
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Par
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Dep
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E
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Facu
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T
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An
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Un
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p
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k
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m
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co
m
1.
I
NT
RO
D
UCT
I
O
N
Po
wer
elec
tr
o
n
ics
is
a
cr
u
cial
f
ield
in
m
o
d
er
n
tech
n
o
lo
g
y
,
i
m
p
ac
tin
g
a
wid
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r
an
g
e
o
f
ap
p
l
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s
b
y
en
ab
lin
g
e
f
f
icien
t
co
n
v
er
s
io
n
an
d
co
n
tr
o
l
o
f
elec
tr
ical
p
o
we
r
[
1
]
,
[
2
]
.
Po
wer
elec
tr
o
n
ics
p
lay
s
a
v
ital
r
o
le
i
n
m
o
d
er
n
tech
n
o
lo
g
y
,
en
ab
lin
g
ef
f
icien
t
en
er
g
y
c
o
n
v
er
s
io
n
,
c
o
n
tr
o
l,
a
n
d
m
a
n
ag
em
e
n
t
ac
r
o
s
s
a
wid
e
r
an
g
e
o
f
ap
p
licatio
n
s
.
I
ts
im
p
ac
t
is
s
ee
n
in
r
en
ewa
b
le
e
n
er
g
y
s
y
s
tem
s
,
elec
tr
ic
v
eh
icles,
s
m
ar
t
g
r
id
s
,
i
n
d
u
s
tr
ial
au
to
m
atio
n
,
co
n
s
u
m
e
r
elec
tr
o
n
ics,
telec
o
m
m
u
n
icatio
n
s
,
ae
r
o
s
p
ac
e,
h
ea
lth
ca
r
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r
ail
t
r
an
s
p
o
r
tatio
n
,
a
n
d
th
e
in
ter
n
et
o
f
th
in
g
s
[
3
]
,
[
4
]
.
A
s
tech
n
o
lo
g
y
c
o
n
tin
u
es
t
o
ad
v
an
ce
,
t
h
e
im
p
o
r
tan
ce
o
f
p
o
wer
elec
tr
o
n
ics
in
ac
h
iev
in
g
e
n
er
g
y
ef
f
icien
c
y
,
r
eliab
ilit
y
,
an
d
s
u
s
tain
ab
ilit
y
will o
n
ly
g
r
o
w
[
5
]
.
Po
wer
elec
tr
o
n
ics
is
a
b
r
an
ch
o
f
elec
tr
ical
en
g
in
ee
r
in
g
th
at
f
o
cu
s
es
o
n
th
e
c
o
n
v
e
r
s
io
n
,
c
o
n
tr
o
l,
a
n
d
co
n
d
itio
n
in
g
o
f
elec
tr
ic
p
o
we
r
u
s
in
g
elec
tr
o
n
ic
d
e
v
ices
[
6
]
.
I
t
p
lay
s
a
c
r
itical
r
o
le
in
m
o
d
er
n
tech
n
o
lo
g
y
b
y
en
ab
lin
g
e
f
f
icien
t
an
d
p
r
ec
is
e
m
an
ag
em
e
n
t
o
f
elec
tr
ical
en
er
g
y
,
wh
ich
is
ess
en
tial
f
o
r
a
wid
e
r
a
n
g
e
o
f
ap
p
licatio
n
s
f
r
o
m
in
d
u
s
tr
ial
s
y
s
tem
s
to
co
n
s
u
m
er
elec
tr
o
n
i
cs
[
7
]
,
[
8
]
.
Po
wer
elec
tr
o
n
ics
is
a
d
y
n
am
ic
a
n
d
ess
en
tial
f
ield
th
at
u
n
d
e
r
p
in
s
m
o
d
er
n
elec
tr
ical
en
g
in
ee
r
in
g
an
d
tec
h
n
o
lo
g
y
[
9
]
,
[
1
0
]
.
B
y
en
ab
lin
g
ef
f
icien
t
co
n
v
er
s
io
n
an
d
co
n
tr
o
l
o
f
el
ec
tr
ical
p
o
wer
,
it
s
u
p
p
o
r
ts
a
wid
e
ar
r
ay
o
f
a
p
p
licatio
n
s
th
at
im
p
r
o
v
e
en
er
g
y
ef
f
icien
cy
,
r
eliab
ilit
y
,
an
d
p
e
r
f
o
r
m
an
ce
[
1
1
]
,
[
1
2
]
.
As
tech
n
o
lo
g
y
a
d
v
an
ce
s
an
d
th
e
d
em
an
d
f
o
r
s
u
s
tain
ab
le
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
2
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8
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I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
2
4
9
-
5
2
5
7
5250
en
er
g
y
s
o
lu
tio
n
s
g
r
o
ws,
th
e
r
o
le
o
f
p
o
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elec
tr
o
n
ics
will
b
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o
m
e
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m
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s
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t
[
1
3
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[
1
4
]
.
Mo
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co
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v
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te
r
s
(
MM
C
s
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r
ep
r
esen
t
a
s
ig
n
if
ican
t
ad
v
an
ce
m
e
n
t
in
p
o
wer
e
lectr
o
n
ics,
o
f
f
er
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g
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m
e
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o
u
s
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tag
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ess
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r
o
win
g
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em
an
d
s
o
f
m
o
d
e
r
n
elec
tr
ical
s
y
s
tem
s
[
1
5
]
,
[
1
6
]
.
T
h
eir
u
n
iq
u
e
m
o
d
u
lar
ar
ch
it
ec
tu
r
e
an
d
o
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lex
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b
ilit
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ak
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t
h
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n
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is
p
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s
ab
l
e
in
v
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io
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s
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ig
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-
v
o
ltag
e
an
d
h
ig
h
-
p
o
wer
ap
p
l
icatio
n
s
[
6
]
,
[
1
7
]
.
MM
C
s
p
l
ay
a
cr
u
cial
r
o
le
in
m
o
d
er
n
p
o
wer
elec
tr
o
n
ics,
o
f
f
er
in
g
u
n
p
ar
alleled
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v
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ter
m
s
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f
s
ca
lab
ilit
y
,
ef
f
icien
cy
,
an
d
f
lex
ib
ilit
y
[
1
8
]
,
[
1
9
]
.
As
th
e
d
e
m
an
d
f
o
r
ef
f
icien
t
an
d
r
eliab
le
p
o
w
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n
v
er
s
io
n
c
o
n
tin
u
es
to
g
r
o
w,
MM
C
s
will
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em
ain
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co
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s
to
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e
tech
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lo
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v
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g
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ca
p
ab
ilit
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f
p
o
wer
elec
tr
o
n
ic
s
y
s
tem
s
[
2
0
]
,
[
2
1
]
.
MM
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s
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ly
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o
n
ics
d
u
e
to
th
eir
s
ca
lab
ilit
y
,
ef
f
icien
cy
,
an
d
s
u
p
er
i
o
r
p
er
f
o
r
m
an
ce
i
n
h
i
g
h
-
v
o
ltag
e
a
n
d
h
i
g
h
-
p
o
wer
a
p
p
licatio
n
s
.
Her
e
a
r
e
th
e
k
ey
r
ea
s
o
n
s
wh
y
MM
C
s
ar
e
im
p
o
r
tan
t to
d
ay
:
[
2
2
]
a.
Scalab
ilit
y
an
d
f
lex
i
b
ilit
y
:
MM
C
s
co
n
s
is
t
o
f
s
u
b
m
o
d
u
les
th
at
ca
n
b
e
ad
d
e
d
o
r
r
e
m
o
v
e
d
to
a
d
ju
s
t
th
e
v
o
ltag
e
an
d
p
o
wer
lev
els,
m
a
k
in
g
th
em
h
ig
h
ly
s
ca
lab
le
an
d
f
lex
ib
le
f
o
r
v
ar
io
u
s
ap
p
licat
io
n
s
[
2
3
]
.
T
h
ey
ca
n
b
e
tailo
r
ed
f
o
r
s
p
ec
if
ic
n
ee
d
s
in
in
d
u
s
tr
ies
r
an
g
i
n
g
f
r
o
m
r
en
ewa
b
le
en
er
g
y
in
teg
r
atio
n
to
elec
tr
ic
v
eh
icle
ch
ar
g
i
n
g
[
2
4
]
.
b.
Hig
h
ef
f
icien
cy
:
MM
C
s
o
p
er
ate
at
lo
wer
s
wi
tch
in
g
f
r
eq
u
en
cies,
wh
ich
r
ed
u
ce
s
s
witch
in
g
lo
s
s
es
an
d
im
p
r
o
v
es
o
v
e
r
all
ef
f
icien
cy
[
2
5
]
.
T
h
e
y
p
r
o
d
u
ce
a
h
ig
h
-
q
u
ality
o
u
tp
u
t
wav
ef
o
r
m
with
lo
wer
h
ar
m
o
n
ic
d
is
to
r
tio
n
,
m
in
im
izin
g
th
e
n
ee
d
f
o
r
a
d
d
itio
n
al
f
ilter
in
g
[
2
6
]
.
As
a
r
esu
lt
o
f
t
h
eir
m
o
d
u
la
r
d
esig
n
,
s
ca
lab
ilit
y
,
an
d
h
i
g
h
ef
f
icien
cy
,
MM
C
s
ar
e
ex
ten
s
iv
ely
em
p
lo
y
ed
i
n
h
ig
h
-
v
o
ltag
e
d
ir
ec
t
cu
r
r
en
t
(
HVDC)
tr
an
s
m
is
s
io
n
,
r
en
ewa
b
le
en
e
r
g
y
in
te
g
r
atio
n
,
an
d
g
r
id
-
tied
ap
p
licatio
n
s
.
Nev
er
th
eless
,
co
n
v
en
tio
n
al
m
o
d
u
latio
n
m
eth
o
d
s
f
o
r
MM
C
s
,
s
u
ch
as
ca
r
r
ier
-
b
ased
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
o
r
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
(
SVM)
,
m
ay
f
ac
e
co
n
s
tr
ain
ts
s
u
c
h
as
h
eig
h
ten
ed
h
ar
m
o
n
ic
d
is
to
r
tio
n
,
d
im
in
is
h
ed
d
y
n
am
i
c
r
esp
o
n
s
iv
en
ess
,
a
n
d
i
n
tr
icate
im
p
lem
en
tatio
n
at
h
ig
h
er
s
witch
in
g
f
r
eq
u
e
n
cies.
T
h
er
e
is
a
r
eq
u
ir
em
en
t
f
o
r
c
o
n
tem
p
o
r
ar
y
m
o
d
u
latio
n
m
et
h
o
d
i.e
.
p
h
ase
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
m
o
d
u
latio
n
m
eth
o
d
th
at
s
p
ec
if
ically
ta
r
g
e
t
th
ese
co
n
s
tr
ain
ts
,
g
u
ar
an
teei
n
g
o
p
tim
ized
p
er
f
o
r
m
an
ce
,
in
cr
ea
s
ed
h
ar
m
o
n
ic
ch
ar
ac
ter
is
tics
,
an
d
ef
f
ec
tiv
e
r
eg
u
latio
n
at
b
o
th
h
i
g
h
an
d
lo
w
f
r
eq
u
e
n
cies.
2.
P
RO
P
O
SE
D
M
E
T
H
O
D
2
.
1
.
P
ha
s
e
o
pp
o
s
it
io
n dis
po
s
it
io
n
m
o
du
la
t
io
n t
ec
hn
iqu
e
T
h
e
p
h
ase
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
(
POD)
m
o
d
u
latio
n
tech
n
iq
u
e
is
a
m
eth
o
d
o
f
co
n
tr
o
llin
g
th
e
s
witch
in
g
o
f
p
o
wer
elec
tr
o
n
ic
s
in
MM
C
s
to
ac
h
iev
e
h
ig
h
-
q
u
ality
o
u
tp
u
t
wav
ef
o
r
m
s
with
r
ed
u
ce
d
h
ar
m
o
n
ic
d
is
to
r
tio
n
[
2
7
]
.
2
.
2
.
Wo
r
k
ing
princip
le
o
f
P
O
D
m
o
du
la
t
io
n
in
M
M
C
s
At
ea
ch
m
o
m
e
n
t
in
tim
e,
th
e
POD
tech
n
iq
u
e
g
en
er
ates
P
W
M
s
ig
n
als
b
y
co
m
p
ar
i
n
g
th
e
r
ef
er
en
ce
wav
e
with
a
s
in
g
le
ca
r
r
ier
wh
i
ch
is
illu
s
tr
ated
in
Fig
u
r
e
1
.
T
h
e
b
asic
cy
cle
is
s
ep
ar
ated
i
n
to
s
ix
p
a
r
ts
in
o
r
d
e
r
to
p
r
o
d
u
ce
t
h
e
s
in
g
u
lar
ca
r
r
ie
r
f
o
r
m
o
d
u
latio
n
.
T
h
e
r
ef
er
en
ce
s
ig
n
al
is
co
m
p
ar
e
d
to
th
e
c
ar
r
ier
s
ig
n
als.
Su
b
-
m
o
d
u
les
ar
e
in
t
r
o
d
u
ce
d
wh
e
n
th
e
r
ef
er
e
n
ce
s
ig
n
al
ex
ce
e
d
s
th
e
ca
r
r
ier
s
ig
n
al
.
W
h
en
th
e
r
ef
er
en
ce
s
ig
n
al
is
lo
wer
th
an
th
e
ca
r
r
ier
s
ig
n
al,
th
e
s
u
b
-
m
o
d
u
les
ar
e
s
k
ip
p
ed
.
I
n
PW
M,
th
e
ca
r
r
ier
s
ig
n
als
f
o
r
th
e
u
p
p
e
r
an
d
lo
wer
ar
m
s
u
n
d
er
g
o
in
v
e
r
s
io
n
to
m
ain
tain
a
co
n
s
is
ten
t
s
u
m
o
f
v
o
ltag
es
in
b
o
th
ar
m
s
.
T
h
is
tech
n
iq
u
e
ef
f
ec
tiv
ely
m
in
im
izes
v
o
ltag
e
r
ip
p
le
an
d
h
ar
m
o
n
ic
d
is
to
r
tio
n
[
2
8
]
.
Fig
u
r
e
1
.
Sig
n
al
r
ep
r
esen
tatio
n
o
f
p
h
ase
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Desig
n
a
n
d
imp
leme
n
t
a
tio
n
o
f a
mo
d
ern
mo
d
u
la
tio
n
tech
n
i
q
u
e
fo
r
mo
d
u
la
r
…
(
K
is
h
o
r
e
P
a
r
a
p
elly
)
5251
2
.
2
.
1
.
T
hree
m
o
des
o
f
wo
r
k
i
ng
T
h
r
ee
m
o
d
es o
f
wo
r
k
in
g
ar
e
a
s
f
o
llo
ws:
a.
Su
b
m
o
d
u
le
a
r
r
an
g
em
en
t
:
An
MM
C
co
n
s
is
t
s
o
f
m
u
ltip
le
s
u
b
m
o
d
u
les
(
SMs)
in
ea
ch
p
h
ase
leg
.
E
ac
h
SM
ca
n
g
e
n
er
ate
a
v
o
ltag
e
o
f
eith
er
Vd
c
(
s
u
b
m
o
d
u
le
in
s
er
ted
)
o
r
0
(
s
u
b
m
o
d
u
le
b
y
p
ass
ed
)
.
T
h
e
s
u
m
o
f
th
e
v
o
ltag
es o
f
all
in
s
er
ted
s
u
b
m
o
d
u
les d
eter
m
in
es th
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
MM
C
[
2
9
]
.
b.
C
ar
r
ier
d
is
p
o
s
itio
n
:
th
e
ca
r
r
ie
r
s
ig
n
als
ar
e
d
is
p
o
s
ed
s
u
ch
t
h
at
th
o
s
e
ab
o
v
e
t
h
e
ze
r
o
r
ef
e
r
en
ce
(
p
o
s
itiv
e
ca
r
r
ier
s
)
ar
e
in
p
h
ase,
wh
ile
th
o
s
e
b
elo
w
th
e
ze
r
o
r
e
f
er
en
ce
(
n
eg
ativ
e
ca
r
r
ier
s
)
ar
e
1
8
0
d
eg
r
ee
s
o
u
t
o
f
p
h
ase
with
th
e
p
o
s
itiv
e
ca
r
r
ier
s
.
T
h
is
ar
r
an
g
em
en
t
h
elp
s
in
r
ed
u
cin
g
s
p
ec
if
ic
h
a
r
m
o
n
ic
co
m
p
o
n
e
n
ts
in
th
e
o
u
tp
u
t
v
o
ltag
e
[
3
0
]
,
[
3
1
]
.
c.
PW
M
g
en
er
atio
n
:
th
e
s
in
u
s
o
id
al
r
ef
er
en
ce
s
ig
n
al
is
co
m
p
a
r
ed
with
ea
ch
o
f
th
e
ca
r
r
ier
s
to
g
en
er
ate
th
e
g
atin
g
s
ig
n
als
f
o
r
th
e
s
u
b
m
o
d
u
les.
W
h
en
th
e
r
ef
e
r
en
ce
s
ig
n
al
is
g
r
ea
ter
th
an
a
ca
r
r
ier
,
th
e
co
r
r
esp
o
n
d
in
g
s
u
b
m
o
d
u
le
is
in
s
er
ted
in
to
th
e
cir
cu
it;
o
th
er
wis
e,
it is
b
y
p
ass
ed
[
3
2
]
.
Fig
u
r
e
2
d
ep
icts
r
ef
er
en
ce
s
ig
n
al
:
T
h
is
b
lo
ck
g
en
er
ates
th
e
d
esire
d
s
in
u
s
o
id
al
wav
ef
o
r
m
th
at
th
e
MM
C
aim
s
to
p
r
o
d
u
ce
at
th
e
o
u
tp
u
t.
a.
C
o
m
p
ar
ato
r
:
C
o
m
p
a
r
es
th
e
r
ef
er
en
ce
s
ig
n
al
with
th
e
ca
r
r
ier
s
ig
n
als.
Sep
ar
ate
co
m
p
ar
ato
r
s
ar
e
u
s
ed
f
o
r
th
e
u
p
p
er
a
n
d
lo
wer
ar
m
s
.
b.
Su
b
-
m
o
d
u
le
co
n
t
r
o
l
lo
g
ic
:
B
a
s
ed
o
n
th
e
c
o
m
p
ar
at
o
r
'
s
o
u
tp
u
t,
th
is
lo
g
ic
d
ec
id
es
wh
eth
er
e
ac
h
s
u
b
-
m
o
d
u
le
s
h
o
u
ld
b
e
i
n
s
er
ted
o
r
b
y
p
ass
ed
.
c.
Up
p
er
an
d
lo
wer
ar
m
s
:
E
ac
h
ar
m
h
as
its
ca
r
r
ier
s
ig
n
al;
th
e
u
p
p
er
ar
m
'
s
ca
r
r
ier
is
a
tr
ian
g
u
lar
wav
ef
o
r
m
,
wh
ile
th
e
lo
wer
ar
m
'
s
ca
r
r
ier
i
s
an
in
v
er
ted
tr
ia
n
g
u
lar
wav
ef
o
r
m
(
p
h
ase
o
p
p
o
s
itio
n
)
.
d.
Su
b
-
m
o
d
u
les
: T
h
ese
ar
e
co
n
t
r
o
lled
b
ased
o
n
th
e
lo
g
ic
s
ig
n
al
s
to
s
y
n
th
esize
th
e
d
esire
d
o
u
tp
u
t v
o
ltag
e
.
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
am
r
ep
r
e
s
en
tatio
n
o
f
p
h
ase
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
2
.
3
.
Wo
r
k
ing
o
pera
t
io
n o
f
m
o
du
la
r
m
ulti
co
nv
er
t
er
T
h
e
MM
C
o
p
er
ates
b
y
d
y
n
am
ically
in
s
er
tin
g
an
d
b
y
p
ass
in
g
s
u
b
-
m
o
d
u
les
in
ea
ch
ar
m
to
s
y
n
th
esize
th
e
d
esire
d
o
u
tp
u
t v
o
ltag
e
an
d
cu
r
r
en
t.
T
h
e
u
s
e
o
f
ad
v
an
ce
d
m
o
d
u
latio
n
tec
h
n
iq
u
es lik
e
P
OD
h
elp
s
to
ac
h
iev
e
h
ig
h
-
q
u
ality
o
u
t
p
u
t
with
r
ed
u
ce
d
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
T
h
e
m
o
d
u
lar
n
atu
r
e
o
f
MM
C
s
allo
ws
f
o
r
s
ca
lab
ilit
y
,
r
ed
u
n
d
an
cy
,
an
d
ea
s
e
o
f
m
ain
t
en
an
ce
,
m
a
k
in
g
th
e
m
id
ea
l f
o
r
h
ig
h
-
p
o
wer
ap
p
licatio
n
s
[
3
3
]
.
2
.
3
.
1
.
Wo
rk
ing
princip
le
T
h
e
MM
C
o
p
er
ates
b
y
in
s
er
t
in
g
o
r
b
y
p
ass
in
g
s
u
b
-
m
o
d
u
le
s
in
ea
ch
ar
m
to
s
y
n
th
esize
th
e
d
esire
d
o
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
en
t.
Fig
u
r
e
3
illu
s
tr
ated
an
MM
C
ty
p
ically
co
n
s
is
ts
o
f
t
h
r
ee
p
h
ase
s
(
f
o
r
a
th
r
ee
-
p
h
ase
s
y
s
tem
)
,
an
d
ea
ch
p
h
ase
h
as a
n
u
p
p
e
r
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d
a
lo
wer
a
r
m
,
ea
ch
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n
tain
in
g
s
u
b
-
m
o
d
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les co
n
n
ec
ted
in
s
er
ies.
R
e
fe
r
e
n
c
e
S
i
gn
al
C
om
p
ar
ato
r
(
>
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e
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r
e
n
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e
>
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ar
r
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e
r
S
i
gn
al
U
p
p
e
r
A
r
m C
ar
r
i
e
r
S
i
gn
al
Tr
i
an
gu
l
ar
Low
e
r
A
r
m
C
ar
r
i
e
r
S
i
gn
al
I
n
ve
r
te
d
S
u
b
M
od
u
l
e
C
on
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ol
Logi
c
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r
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r
m S
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b
M
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l
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i
n
s
e
r
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/
b
yp
as
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on
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ol
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m
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l
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i
n
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e
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as
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)
O
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tp
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t V
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
7
0
8
I
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C
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p
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15
,
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.
6
,
Decem
b
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r
20
25
:
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2
4
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5
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5252
Fig
u
r
e
3
.
B
asic
s
tr
u
ctu
r
e
o
f
an
MM
C
2
.
4
.
M
a
t
hema
t
ica
l
m
o
dellin
g
a
nd
o
pera
t
io
n
Fig
u
r
e
4
d
e
p
icts
th
e
MM
C
,
wh
ich
co
n
s
is
ts
o
f
s
u
b
-
m
o
d
u
les
p
er
ar
m
,
with
u
p
p
e
r
an
d
lo
we
r
ar
m
s
in
ea
ch
p
h
ase.
E
ac
h
s
u
b
-
m
o
d
u
le
co
n
tain
s
a
ca
p
ac
ito
r
th
at
s
to
r
es
v
o
ltag
e.
T
h
e
ca
p
ac
ito
r
v
o
lt
ag
e
is
co
n
tr
o
lled
to
m
ain
tain
a
d
esire
d
r
ef
er
e
n
ce
v
o
ltag
e.
T
h
er
e
is
ar
m
in
d
u
ctan
ce
in
ea
ch
p
h
ase
t
h
at
co
n
tr
ib
u
tes
to
f
ilter
in
g
th
e
o
u
tp
u
t c
u
r
r
en
t.
Fig
u
r
e
4
d
e
p
icts
MM
C
m
ath
em
atica
l
m
o
d
ellin
g
with
POD
in
wh
ich
T
r
ian
g
le
p
u
ls
es
h
as
p
r
esen
ted
in
th
is
ar
ticle.
L
et
co
n
s
id
er
,
,
,
,
ar
e
in
p
u
t
DC
v
o
ltag
e,
cu
r
r
en
t,
r
esis
tan
ce
an
d
I
n
d
u
cta
n
ce
s
.
An
d
u
p
p
er
an
d
lo
wer
v
o
ltag
es
ar
e
1
,
2
,
3
an
d
1
,
2
,
3
.
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d
u
p
p
er
an
d
lo
wer
ar
m
cu
r
r
en
ts
ar
e
1
,
2
,
3
an
d
1
,
2
,
3
.
T
h
e
u
p
p
er
ar
m
v
o
ltag
e
is
=
∗
(
1
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T
h
e
lo
wer
ar
m
v
o
ltag
e
is
=
∗
(
2
)
W
h
er
e
_
,
ar
e
u
p
p
er
,
l
o
wer
ca
p
a
cito
r
v
o
ltag
es.
T
h
e
u
p
p
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ar
m
cu
r
r
e
n
t is
=
(
3
)
T
h
e
lo
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ar
m
cu
r
r
e
n
t
=
(
4
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T
o
tal
ca
p
ac
ito
r
cu
r
r
en
t
=
+
2
(
5
)
T
o
tal
ar
m
cu
r
r
en
t
−
(
6
)
Fro
m
Fig
u
r
e
5
co
n
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p
a
n
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s
is
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u
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=
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(
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=
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(
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ig
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ly
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is
(
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ess
io
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=
+
+
+
+
(
9
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=
(
∗
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+
(
∗
)
+
+
+
(
1
0
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W
h
er
e
is
au
x
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v
o
ltag
e
o
f
d
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es in
ar
m
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6
A
rm
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rm
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rm
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8
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10
L
11
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12
Va
AC
AC
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N:
2088
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u
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Stru
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ed
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Fig
u
r
e
5
.
Simu
lin
k
m
o
d
el
f
o
r
p
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o
p
o
s
ed
to
p
o
l
o
g
y
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n
th
e
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n
tex
t
o
f
n
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n
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co
m
p
l
em
en
tar
y
s
witch
in
g
,
q
u
asi
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s
tates
ef
f
ec
tiv
ely
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y
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ass
o
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e
ar
m
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im
u
ltan
eo
u
s
ly
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e
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f
u
lly
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h
en
th
e
o
u
tp
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t
v
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e
r
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h
es
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d
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ativ
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icate
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th
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itiatio
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o
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ain
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witch
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i
n
th
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ar
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o
th
th
e
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e
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f
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n
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lo
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im
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u
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ly
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h
u
s
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e
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m
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er
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as
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e
co
n
d
u
it
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o
r
th
e
cu
r
r
e
n
t
d
u
r
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g
th
e
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u
tp
u
t
p
h
ase.
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e
d
io
d
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in
t
h
e
u
p
p
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ar
m
'
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n
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ito
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s
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r
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ito
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DC
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
2
4
9
-
5
2
5
7
5254
3.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
I
n
th
is
a
r
ticle
h
as
b
ee
n
d
o
n
e
d
esig
n
an
d
a
n
aly
ze
a
POD
-
b
a
s
ed
s
ev
en
-
lev
el
MM
C
f
o
r
ef
f
icien
t
an
d
r
eliab
le
co
n
tr
o
l
o
f
a
p
er
m
a
n
en
t
m
ag
n
et
s
y
n
ch
r
o
n
o
u
s
m
o
t
o
r
(
PMSM)
,
with
t
h
e
aim
o
f
im
p
r
o
v
in
g
s
y
s
tem
p
er
f
o
r
m
an
ce
in
ter
m
s
o
f
p
o
w
er
q
u
ality
,
h
ar
m
o
n
ic
r
e
d
u
ctio
n
,
an
d
ef
f
icien
c
y
in
h
ig
h
-
p
er
f
o
r
m
an
ce
i
n
d
u
s
tr
ial
ap
p
licatio
n
s
.
T
h
is
ar
ticle
f
o
cu
s
ed
o
n
th
e
co
n
tr
o
l
s
tr
ateg
y
(
POD)
,
th
e
b
en
ef
its
o
f
a
s
ev
en
-
l
ev
el
MM
C
s
u
ch
as
r
ed
u
ce
d
h
ar
m
o
n
ic
d
is
to
r
tio
n
a
n
d
b
etter
v
o
ltag
e
co
n
tr
o
l,
an
d
th
e
o
p
tim
izatio
n
o
f
th
e
PMSM
o
p
er
atio
n
.
Fig
u
r
e
5
d
ep
icts
th
e
Simu
lin
k
m
o
d
e
l
o
f
POD
b
ased
s
ev
en
lev
el
MM
C
with
PMSM
an
d
T
ab
le
1
r
e
p
r
esen
ts
th
e
co
n
f
ig
u
r
atio
n
a
n
d
p
a
r
am
eter
s
r
eq
u
ir
em
e
n
ts
f
o
r
th
e
d
r
iv
e
.
T
ab
le
1
.
T
h
e
co
n
f
ig
u
r
atio
n
an
d
p
ar
am
eter
s
r
e
q
u
ir
em
e
n
ts
f
o
r
th
e
d
r
iv
e
No
.
o
f
P
h
a
ses
Th
r
e
e
Emf
(
b
a
c
k
)
W
a
v
e
f
o
r
m
S
i
n
e
w
a
v
e
R
o
t
o
r
S
a
l
i
e
n
t
p
o
l
e
S
p
e
c
i
f
y
R
o
u
n
d
r
o
t
o
r
I
n
p
u
t
(
M
e
c
h
)
To
r
q
u
e
Tm
S
t
a
t
o
r
p
h
.
r
e
s
i
st
a
n
c
e
1
.
6
o
h
m
s
F
l
u
x
l
i
n
k
a
g
e
0
.
1
8
5
2
Fig
u
r
e
6
s
h
o
ws
th
e
v
ar
iatio
n
o
f
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
(
T
e)
o
f
an
in
d
u
ctio
n
m
o
to
r
d
r
iv
e
o
v
er
a
s
h
o
r
t p
er
io
d
.
W
h
ich
r
e
p
r
esen
ts
−
I
n
itial
to
r
q
u
e
o
s
cillatio
n
s
:
At
th
e
b
e
g
in
n
in
g
(
0
t
o
0
.
0
1
s
ec
o
n
d
s
)
,
th
e
to
r
q
u
e
s
h
o
ws
s
m
all
o
s
cillatio
n
s
.
T
h
is
m
ig
h
t b
e
d
u
e
to
i
n
itial tr
an
s
ien
ts
as th
e
m
o
to
r
s
tar
ts
u
p
o
r
r
ea
cts to
a
s
u
d
d
en
lo
a
d
ch
a
n
g
e.
−
I
n
cr
ea
s
in
g
a
m
p
litu
d
e:
As
tim
e
p
r
o
g
r
ess
es,
th
e
am
p
litu
d
e
o
f
th
e
to
r
q
u
e
o
s
cillatio
n
s
in
cr
ea
s
es,
r
ea
ch
in
g
h
ig
h
er
v
alu
es
to
wa
r
d
s
th
e
en
d
o
f
th
e
o
b
s
er
v
e
d
p
e
r
io
d
.
T
h
is
i
n
d
icate
s
a
ch
a
n
g
e
in
t
h
e
o
p
er
a
tin
g
co
n
d
itio
n
s
,
p
o
s
s
ib
ly
an
in
cr
ea
s
e
in
l
o
ad
o
r
a
r
esp
o
n
s
e
to
c
o
n
tr
o
l a
ctio
n
s
.
−
Stead
y
-
s
tate
o
s
cillatio
n
s
:
B
ey
o
n
d
0
.
0
2
s
ec
o
n
d
s
,
th
e
o
s
cillatio
n
s
in
th
e
to
r
q
u
e
b
ec
o
m
e
m
o
r
e
p
r
o
n
o
u
n
ce
d
an
d
s
ee
m
t
o
s
tab
ilize
in
a
m
p
li
tu
d
e,
s
u
g
g
esti
n
g
th
e
m
o
to
r
m
i
g
h
t
b
e
r
ea
ch
i
n
g
a
s
tead
y
-
s
tate
co
n
d
itio
n
u
n
d
er
p
er
io
d
ic
lo
a
d
v
ar
iatio
n
s
.
Fig
u
r
e
6
d
ep
icts
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
(
T
e)
v
ar
iatio
n
s
o
f
an
i
n
d
u
ctio
n
m
o
to
r
d
r
iv
e
o
v
er
a
s
h
o
r
t
p
er
io
d
.
T
h
e
i
n
itial
s
m
all
o
s
cillatio
n
s
f
o
llo
wed
b
y
i
n
cr
ea
s
in
g
an
d
s
tab
ilizin
g
to
r
q
u
e
r
ip
p
les
i
n
d
icate
th
e
m
o
to
r
'
s
d
y
n
am
ic
r
esp
o
n
s
e
to
co
n
tr
o
l
ac
tio
n
s
an
d
lo
ad
ch
an
g
es.
An
aly
zin
g
th
ese
to
r
q
u
e
v
a
r
i
atio
n
s
is
v
ital
f
o
r
o
p
tim
izin
g
m
o
to
r
p
e
r
f
o
r
m
an
ce
an
d
im
p
r
o
v
in
g
co
n
tr
o
l stra
teg
ies to
ac
h
iev
e
s
m
o
o
th
a
n
d
ef
f
i
cien
t o
p
er
atio
n
.
Fig
u
r
e
7
d
ep
icts
th
e
r
o
to
r
an
g
l
e
(
θm
)
v
ar
iatio
n
s
o
f
an
in
d
u
ctio
n
m
o
to
r
d
r
iv
e
o
v
er
a
s
h
o
r
t
p
e
r
io
d
.
T
h
e
in
itial
g
r
ad
u
al
in
cr
ea
s
e
f
o
llo
w
ed
b
y
a
s
tead
y
in
cr
ea
s
e
with
p
er
io
d
ic
o
s
cillatio
n
s
in
d
icate
s
th
e
m
o
t
o
r
'
s
s
tar
t
-
up
p
h
ase
an
d
s
tab
le
o
p
er
atio
n
u
n
d
er
co
n
tr
o
l.
Fig
u
r
e
8
d
ep
icts
th
e
r
o
to
r
s
p
ee
d
(
ω
m
)
v
a
r
iatio
n
s
o
f
an
in
d
u
ctio
n
m
o
to
r
d
r
iv
e
o
v
er
a
s
h
o
r
t
p
er
io
d
.
T
h
e
in
itial
s
m
all
o
s
cillatio
n
s
f
o
llo
wed
b
y
i
n
cr
ea
s
in
g
am
p
l
itu
d
e
an
d
p
er
io
d
i
c
o
s
cillatio
n
s
in
d
icate
th
e
m
o
to
r
'
s
d
y
n
am
ic
r
esp
o
n
s
e
d
u
r
i
n
g
ac
c
eler
atio
n
an
d
u
n
d
e
r
co
n
tr
o
l.
Fig
u
r
e
9
d
e
p
icts
s
ev
en
le
v
el
in
v
er
ter
v
o
ltag
e
lin
e
v
o
ltag
e
an
d
p
h
ase
v
o
ltag
e
g
iv
e
n
to
in
d
u
cti
o
n
m
o
to
r
d
r
iv
e
with
p
ea
k
-
to
-
p
ea
k
1
0
0
0
V.
T
h
e
s
tep
p
ed
n
atu
r
e
o
f
th
e
wav
ef
o
r
m
ac
h
iev
es
h
ig
h
e
r
p
o
wer
q
u
ality
an
d
lo
wer
h
ar
m
o
n
ic
d
is
to
r
tio
n
c
o
m
p
ar
ed
to
tr
ad
itio
n
al
two
-
le
v
e
l in
v
er
ter
s
.
B
y
in
cr
ea
s
in
g
th
e
n
u
m
b
er
o
f
lev
els,
th
e
o
u
tp
u
t w
av
e
f
o
r
m
b
ec
o
m
es sm
o
o
th
er
,
cl
o
s
ely
r
esem
b
lin
g
a
s
in
e
wav
e
.
Fig
u
r
e
1
0
d
ep
icts
th
e
p
r
o
p
o
s
ed
POD
-
b
ased
s
ev
en
-
lev
el
MM
C
co
m
b
in
ed
with
a
PMS
M
d
em
o
n
s
tr
ates
s
ig
n
if
ican
t
ad
v
an
ce
m
en
ts
in
co
n
tr
o
l
p
er
f
o
r
m
an
ce
,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
ac
h
iev
es
r
e
m
ar
k
ab
ly
lo
w
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
,
r
ed
u
ce
d
to
less
th
an
2
%,
wh
ich
is
a
s
u
b
s
tan
tial
im
p
r
o
v
em
en
t
o
v
er
tr
ad
itio
n
al
tech
n
iq
u
es
s
u
ch
as
s
p
ac
e
v
ec
t
o
r
PW
M
(
SVPW
M)
an
d
ca
r
r
i
er
-
b
ased
PW
M
(
C
B
PW
M)
,
wh
ich
ex
h
ib
it
T
HD
lev
els
o
f
ap
p
r
o
x
im
ately
1
0
-
2
0
%.
T
h
is
r
ed
u
ctio
n
in
T
HD
is
p
r
im
ar
ily
attr
ib
u
ted
to
t
h
e
m
u
lti
-
lev
el
to
p
o
lo
g
y
an
d
th
e
p
h
ase
-
s
h
if
ted
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
POD
-
PW
M)
s
tr
ateg
y
,
wh
ich
ef
f
ec
tiv
el
y
ca
n
ce
ls
h
ar
m
o
n
ics
an
d
d
eliv
er
s
s
m
o
o
th
er
v
o
ltag
e
o
u
tp
u
ts
.
I
n
ter
m
s
o
f
t
o
r
q
u
e
r
ip
p
le,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
ex
ce
ls
w
ith
v
alu
es
b
elo
w
1
%
-
2
%,
s
i
g
n
if
ican
tly
o
u
tp
er
f
o
r
m
in
g
tr
a
d
itio
n
al
a
p
p
r
o
ac
h
es,
wh
ich
o
f
ten
ex
ce
e
d
1
0
%
-
2
0
%.
T
h
is
lo
w
r
ip
p
l
e
en
h
a
n
ce
s
m
o
t
o
r
s
m
o
o
th
n
ess
an
d
r
ed
u
ce
s
v
ib
r
atio
n
s
,
m
ak
in
g
th
e
s
y
s
tem
i
d
ea
l
f
o
r
h
i
g
h
-
p
e
r
f
o
r
m
an
ce
a
p
p
licatio
n
s
s
u
ch
as
elec
tr
ic
v
eh
icles
an
d
in
d
u
s
tr
ial
au
to
m
atio
n
.
C
o
m
p
ar
ed
t
o
alter
n
ativ
e
ad
v
an
ce
d
m
eth
o
d
s
lik
e
C
ascad
ed
H
-
B
r
id
g
e
MM
C
,
th
e
POD
-
b
ased
s
ev
en
-
lev
el
MM
C
ac
h
iev
es
s
im
ilar
to
r
q
u
e
r
i
p
p
le
r
e
d
u
ctio
n
wh
ile
o
f
f
e
r
in
g
a
s
im
p
ler
an
d
m
o
r
e
co
s
t
-
ef
f
ec
ti
v
e
d
esig
n
.
Ov
er
all,
th
e
p
r
o
p
o
s
ed
s
y
s
tem
en
s
u
r
es
ex
ce
p
tio
n
al
p
er
f
o
r
m
a
n
ce
in
b
o
th
T
HD
a
n
d
to
r
q
u
e
r
i
p
p
le
m
etr
ics,
d
eliv
er
in
g
h
ig
h
p
r
ec
is
io
n
,
ef
f
icien
cy
,
a
n
d
d
y
n
am
ic
r
es
p
o
n
s
e.
T
h
is
m
ak
es
th
e
POD
-
b
ased
Sev
en
-
L
ev
el
MM
C
with
PMSM
a
s
u
p
e
r
io
r
ch
o
ice
f
o
r
ap
p
licatio
n
s
r
eq
u
ir
in
g
s
tr
in
g
en
t
p
er
f
o
r
m
an
ce
s
tan
d
ar
d
s
an
d
o
p
er
atio
n
al
r
eliab
ilit
y
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Desig
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t
a
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f a
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Fig
u
r
e
6
.
R
ep
r
esen
tatio
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o
f
el
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tr
o
m
ag
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etic
to
r
q
u
e
Fig
u
r
e
7
.
R
ep
r
esen
tatio
n
o
f
r
o
to
r
an
g
le
Fig
u
r
e
8
.
R
ep
r
esen
tatio
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o
f
r
o
to
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s
p
ee
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Fig
u
r
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9
.
R
ep
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esen
tatio
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o
f
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e
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en
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ter
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Fig
u
r
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.
C
o
m
p
ar
ativ
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a
n
aly
s
is
4.
CO
NCLU
SI
O
N
T
h
e
POD
m
o
d
u
latio
n
tec
h
n
iq
u
e
is
a
h
i
g
h
ly
ef
f
ec
tiv
e
m
eth
o
d
f
o
r
c
o
n
tr
o
llin
g
MM
C
s
,
s
ig
n
if
ican
tly
en
h
an
cin
g
th
eir
p
e
r
f
o
r
m
an
ce
in
h
ig
h
-
v
o
ltag
e
an
d
h
ig
h
-
p
o
wer
ap
p
licatio
n
s
.
B
y
u
tili
zin
g
m
u
ltip
le
p
h
ase
-
o
p
p
o
s
ed
ca
r
r
ier
s
ig
n
als,
POD
m
o
d
u
latio
n
ac
h
ie
v
es
lo
w
T
HD
an
d
h
ig
h
-
q
u
ality
o
u
t
p
u
t
wav
ef
o
r
m
s
.
T
h
is
m
o
d
u
latio
n
s
tr
ateg
y
n
o
t
o
n
ly
im
p
r
o
v
es
p
o
wer
q
u
ality
b
u
t
als
o
en
s
u
r
es
b
alan
ce
d
s
witch
in
g
ac
tio
n
s
,
wh
ich
ar
e
cr
u
cial
f
o
r
t
h
e
lo
n
g
ev
ity
an
d
r
eliab
ilit
y
o
f
th
e
c
o
n
v
e
r
ter
c
o
m
p
o
n
en
ts
.
POD
m
o
d
u
latio
n
'
s
ab
ilit
y
to
r
ed
u
ce
ev
en
-
o
r
d
er
h
ar
m
o
n
ics
an
d
m
a
n
ag
e
th
er
m
al
a
n
d
elec
tr
ical
s
tr
ess
es
ef
f
icien
tly
m
ak
es
it
p
ar
ticu
lar
ly
s
u
itab
le
f
o
r
d
em
an
d
in
g
ap
p
licatio
n
s
s
u
ch
as
r
en
ewa
b
le
en
er
g
y
in
teg
r
ati
o
n
,
HVDC
tr
an
s
m
is
s
io
n
,
in
d
u
s
tr
ial
m
o
to
r
d
r
iv
es,
an
d
elec
tr
ic
v
eh
icle
s
y
s
tem
s
.
T
h
e
tech
n
iq
u
e'
s
in
h
er
en
t
s
ca
lab
ilit
y
an
d
f
lex
ib
ilit
y
f
u
r
th
er
co
n
tr
ib
u
te
to
its
im
p
o
r
tan
ce
,
allo
win
g
MM
C
s
to
b
e
ea
s
ily
a
d
ap
ted
to
v
a
r
io
u
s
p
o
wer
lev
els
an
d
s
y
s
tem
r
e
q
u
i
r
em
en
ts
.
T
h
e
POD
m
o
d
u
latio
n
tec
h
n
iq
u
e
is
an
ess
en
tial
ad
v
an
ce
m
en
t
in
t
h
e
co
n
tr
o
l
o
f
MM
C
s
,
p
r
o
v
id
in
g
a
r
o
b
u
s
t
s
o
lu
tio
n
f
o
r
m
o
d
er
n
p
o
wer
elec
tr
o
n
ics
ch
allen
g
es.
I
ts
im
p
lem
en
tatio
n
lead
s
to
im
p
r
o
v
e
d
ef
f
icie
n
cy
,
r
eliab
ilit
y
,
an
d
0
10
20
30
40
T
r
a
d
i
t
i
o
n
a
l
T
ec
h
n
i
q
u
es
S
p
a
c
e Ve
c
t
o
r
PW
M
(
S
VPW
M
)
Ca
r
r
i
er-B
a
s
ed
PW
M
(
CB
PW
M
)
Ca
s
c
a
d
ed
H
-
B
r
i
d
g
e (
CHB
)
MMC
PO
D
-
b
a
s
ed
S
even
-
L
ev
el
M
M
C (
Pr
o
p
o
s
ed
M
et
h
o
d
)
T
o
t
a
l
h
a
r
m
o
n
i
c
d
i
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in
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