I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
s
(
I
J
P
E
DS
)
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
,
p
p
.
1
5
9
8
~
16
08
I
SS
N:
2088
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
ijp
ed
s
.
v
1
2
.
i3
.
pp
1
598
-
16
08
1598
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Reduction
of t
o
tal
harm
o
nic distor
t
io
n of t
hr
ee
-
pha
se
inverter
using
alterna
te
switching s
trategy
Nur
Arif
a
h Ra
m
li
1
,
Auza
ni J
idi
n
2
,
Z
u
lha
ni Ra
s
i
n
3
,
T
o
le
Su
t
ik
no
4
1
,
2,
3
F
a
c
u
l
ty
o
f
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
,
U
n
iv
e
rsit
i
Tek
n
ik
a
l
M
a
lay
sia
M
e
lak
a
,
M
a
lac
c
a
,
M
a
lay
sia
1,
2
,3
Re
se
a
rc
h
Lab
o
ra
t
o
ry
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dri
v
e
s,
Un
i
v
e
rsiti
Tek
n
i
k
a
l
M
a
lay
sia
M
e
lak
a
,
M
a
l
a
c
c
a
,
M
a
lay
sia
4
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
,
U
n
iv
e
rsitas
Ah
m
a
d
Da
h
lan
,
Yo
g
y
a
k
a
rta,
I
n
d
o
n
e
sia
4
Emb
e
d
d
e
d
S
y
ste
m
a
n
d
P
o
we
r
El
e
c
tro
n
ics
Re
se
a
rc
h
G
ro
u
p
,
Yo
g
y
a
k
a
rta,
In
d
o
n
e
sia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ap
r
1
7
,
2
0
2
1
R
ev
is
ed
J
u
l
7
,
2
0
2
1
Acc
ep
ted
J
u
l
20
,
2
0
2
1
Altern
a
ti
n
g
c
u
rre
n
t
(AC)
e
lec
tri
c
a
l
d
riv
e
s
m
a
in
ly
re
q
u
ire
sm
a
ll
e
r
c
u
rre
n
t
(o
r
to
rq
u
e
)
ri
p
p
les
a
n
d
l
o
we
r
t
o
tal
h
a
rm
o
n
ic
d
ist
o
rti
o
n
(THD)
o
f
v
o
lt
a
g
e
f
o
r
e
x
c
e
ll
e
n
t
d
riv
e
p
e
rfo
rm
a
n
c
e
s.
No
rm
a
ll
y
,
in
p
ra
c
ti
c
e
,
to
a
c
h
i
e
v
e
th
e
se
re
q
u
irem
e
n
ts,
th
e
i
n
v
e
rter
n
e
e
d
s
t
o
b
e
o
p
e
ra
ted
a
t
h
ig
h
sw
it
c
h
in
g
f
re
q
u
e
n
c
y
.
By
o
p
e
ra
ti
n
g
a
t
h
ig
h
sw
it
c
h
in
g
f
re
q
u
e
n
c
y
,
t
h
e
siz
e
o
f
f
il
ter
c
a
n
b
e
re
d
u
c
e
d
.
Ho
we
v
e
r,
th
e
in
v
e
rter
wh
ich
o
f
ten
ly
e
m
p
lo
y
s
i
n
su
late
d
g
a
te
b
ip
o
la
r
tran
sisto
r
(IG
BT)
fo
r
h
ig
h
p
o
we
r
a
p
p
l
ica
ti
o
n
s
c
a
n
n
o
t
b
e
o
p
e
ra
ted
a
t
h
i
g
h
sw
it
c
h
in
g
fre
q
u
e
n
c
y
.
T
h
is
is
b
e
c
a
u
se
,
t
h
e
IG
BT
sw
it
c
h
in
g
fre
q
u
e
n
c
y
c
a
n
n
o
t
b
e
o
p
e
ra
ted
a
b
o
v
e
5
0
k
Hz
d
u
e
t
o
it
s th
e
rm
a
l
re
strictio
n
s.
T
h
is
p
a
p
e
r
p
r
o
p
o
se
s
a
n
a
lt
e
rn
a
te
sw
it
c
h
in
g
stra
teg
y
t
o
e
n
a
b
le
t
h
e
u
se
o
f
IG
BT
fo
r
o
p
e
ra
ti
n
g
th
e
in
v
e
rter
a
t
h
i
g
h
sw
it
c
h
in
g
fre
q
u
e
n
c
y
to
imp
ro
v
e
THD
p
e
rfo
rm
a
n
c
e
s.
In
th
is
stra
teg
y
,
e
a
c
h
IG
BT
i
n
a
g
ro
u
p
o
f
sw
it
c
h
e
s
i
n
t
h
e
m
o
d
ifi
e
d
in
v
e
rter
c
ircu
it
will
o
p
e
ra
te
th
e
sw
it
c
h
in
g
fre
q
u
e
n
c
y
a
t
o
n
e
-
fo
u
rt
h
o
f
t
h
e
in
v
e
rter
sw
it
c
h
in
g
fre
q
u
e
n
c
y
.
Th
e
a
lt
e
rn
a
te
sw
it
c
h
i
n
g
is
imp
lem
e
n
ted
u
sin
g
sim
p
le
a
n
a
lo
g
a
n
d
d
ig
it
a
l
in
te
g
ra
ted
c
ircu
it
s.
K
ey
w
o
r
d
s
:
Alter
n
ate
s
witch
in
g
I
GB
T
I
n
v
er
ter
Switch
in
g
f
r
eq
u
e
n
cy
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
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
:
Au
za
n
i Jid
in
Facu
lty
o
f
E
lectr
ical
E
n
g
in
ee
r
in
g
Un
iv
er
s
ity
T
ec
h
n
ical
Ma
lay
s
ia
Ma
lacc
a
J
alan
Han
g
T
u
ah
J
ay
a,
7
6
1
0
0
Du
r
ian
T
u
n
g
g
al,
Ma
lacc
a,
Ma
lay
s
ia
E
m
ail: a
u
za
n
i@
u
tem
.
ed
u
.
m
y
1.
I
NT
RO
D
UCT
I
O
N
A
th
r
ee
-
p
h
ase
in
v
e
r
ter
is
t
h
e
m
ain
p
a
r
t
in
alter
n
atin
g
cu
r
r
e
n
t
(
AC
)
elec
tr
ical
d
r
iv
es,
wh
ic
h
is
u
s
ed
to
p
r
o
d
u
ce
d
esire
d
m
ag
n
itu
d
e
an
d
f
r
eq
u
e
n
cy
o
f
AC
v
o
ltag
es
f
r
o
m
an
u
n
r
eg
u
lated
o
r
a
r
eg
u
l
ated
d
ir
ec
t
cu
r
r
en
t
(
DC
)
v
o
ltag
e.
T
h
e
DC
v
o
lta
g
e
is
o
b
tain
ed
f
r
o
m
a
r
ec
tif
ier
o
r
a
s
er
ies
o
f
b
atter
ies.
Alo
n
g
with
p
o
wer
elec
tr
o
n
ic
co
n
t
r
o
ller
an
d
ele
ctr
ical
m
ac
h
in
e,
AC
m
o
to
r
d
r
iv
es
is
well
k
n
o
wn
th
r
o
u
g
h
all
s
ec
to
r
s
in
th
e
in
d
u
s
tr
y
.
I
n
ter
m
s
o
f
s
y
s
tem
ef
f
icien
cy
,
co
n
tr
o
llab
ilit
y
an
d
o
v
er
all
p
er
f
o
r
m
an
ce
,
it
ca
n
g
u
a
r
an
tee
f
o
r
ex
c
ellen
t
p
er
f
o
r
m
an
ce
s
.
Fig
u
r
e
1
illu
s
tr
ates
th
e
u
s
e
o
f
th
r
e
e
-
p
h
ase
in
v
er
ter
in
AC
m
o
to
r
d
r
iv
es,
i
n
wh
ich
th
e
in
v
er
ter
ca
n
b
e
p
er
f
o
r
m
e
d
as
v
o
ltag
e
s
o
u
r
ce
in
v
er
te
r
(
VSI
)
an
d
c
u
r
r
en
t
s
o
u
r
ce
in
v
er
te
r
(
C
SI)
.
Sev
er
al
AC
d
r
iv
es
p
er
f
o
r
m
th
e
in
v
e
r
ter
as
VSI
,
f
o
r
ex
am
p
les
in
d
i
r
ec
t
to
r
q
u
e
co
n
tr
o
l
(
DT
C
)
,
s
p
ac
e
v
ec
to
r
m
o
d
u
lat
io
n
(
SVM)
.
T
h
e
ap
p
licatio
n
o
f
VSI
ca
n
b
e
ap
p
lied
in
b
o
th
s
in
g
le
-
p
h
ase
an
d
th
r
ee
-
p
h
ase
ap
p
licatio
n
s
[
1
]
.
Usu
ally
,
VSI
tak
es
p
lace
o
f
th
e
f
u
ll
co
n
v
er
ter
in
m
o
s
t
ap
p
licatio
n
s
[
2
]
.
T
h
ey
a
r
e
wid
ely
u
s
ed
in
p
o
wer
g
en
e
r
atio
n
ap
p
licatio
n
s
,
th
r
ee
-
p
h
ase
UPS
s
y
s
tem
s
an
d
is
lan
d
ed
o
p
er
atio
n
o
f
t
h
r
ee
-
p
h
ase
s
y
s
tem
,
wh
er
e
th
e
b
ala
n
ce
d
th
r
ee
-
p
h
ase
v
o
ltag
e
o
u
tp
u
t
is
r
eq
u
ir
ed
w
h
en
th
e
lo
ad
s
ar
e
u
n
b
alan
ce
d
[
3
]
.
On
th
e
o
th
er
h
an
d
s
,
th
er
e
ar
e
m
an
y
AC
m
o
to
r
d
r
iv
es p
e
r
f
o
r
m
th
e
i
n
v
er
ter
as C
SI,
s
u
ch
as f
ield
-
o
r
ien
ted
co
n
t
r
o
l (
FOC
)
an
d
in
d
u
ctio
n
m
o
t
o
r
.
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:
2
0
8
8
-
8
694
R
ed
u
ctio
n
o
f to
ta
l h
a
r
mo
n
ic
d
i
s
to
r
tio
n
o
f th
r
ee
-
p
h
a
s
e
in
ve
r
te
r
u
s
in
g
a
lter
n
a
te
…
(
N
u
r
A
r
ifa
h
R
a
mli
)
1599
(
a)
(
b
)
Fig
u
r
e
1
.
T
h
e
u
s
e
o
f
in
v
er
te
r
i
n
AC
m
o
to
r
d
r
iv
es,
wh
er
e
in
v
er
ter
p
er
f
o
r
m
ed
as (
a)
v
o
ltag
e
s
o
u
r
ce
in
v
er
te
r
(
VSI
)
,
(
b
)
c
u
r
r
e
n
t so
u
r
ce
i
n
v
er
ter
(
C
SI)
C
SI
is
v
er
y
r
ar
ely
im
p
lem
en
t
ed
alter
n
ativ
e
to
th
e
VSI
b
u
t
q
u
ite
well
k
n
o
wn
f
o
r
its
f
u
n
ctio
n
[
4
]
.
Nev
er
th
eless
,
th
e
s
ig
n
if
ican
t
p
r
ac
tical
ap
p
licatio
n
o
f
C
SI
r
eg
ar
d
in
g
o
f
s
elf
-
co
m
m
u
ted
v
ar
ia
n
t
is
n
o
t
f
o
u
n
d
y
et
[
5
]
.
So
m
e
ap
p
licatio
n
s
h
av
e
a
p
p
lied
C
SI
with
in
d
ep
e
n
d
en
t
d
c
lin
k
to
b
alan
ce
t
h
e
d
c
-
lin
k
cu
r
r
en
ts
with
p
r
o
p
er
co
n
tr
o
l
o
f
th
e
r
ec
tif
ier
s
[
6
]
.
T
h
e
o
u
tp
u
t
o
f
i
n
v
er
ter
is
g
en
e
r
ated
b
y
th
e
AC
v
o
ltag
e
th
at
c
an
b
e
a
v
ar
iab
le
o
r
co
n
s
tan
t d
ep
en
d
i
n
g
o
n
th
e
r
eq
u
ir
em
en
ts
o
f
th
e
ap
p
licatio
n
s
[
7
]
.
T
h
e
AC
o
u
tp
u
t is co
n
tr
o
lle
d
in
d
ep
en
d
en
tly
b
y
VSI
th
at
b
eh
av
e
as
a
v
o
ltag
e
s
o
u
r
ce
th
at
is
r
eq
u
ir
ed
b
y
m
a
n
y
in
d
u
s
tr
ia
l
ap
p
licatio
n
s
.
On
th
e
o
th
er
h
an
d
,
C
SI
p
r
o
d
u
ce
h
ig
h
q
u
ality
cu
r
r
en
t
wav
ef
o
r
m
s
th
at
ar
e
wid
ely
u
s
ed
b
y
m
e
d
iu
m
-
v
o
ltag
e
in
d
u
s
tr
ial
ap
p
licatio
n
s
.
I
n
o
r
d
er
to
p
r
o
d
u
ce
a
s
m
o
o
th
c
u
r
r
en
t
wav
ef
o
r
m
,
VSI
n
ee
d
s
to
g
en
er
ate
AC
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
th
at
is
co
m
p
o
s
ed
w
ith
th
e
d
is
cr
ete
v
alu
es
s
o
th
at
th
e
lo
ad
ca
n
b
e
in
d
u
ctiv
e
at
th
e
h
ar
m
o
n
ic
f
r
e
q
u
en
cies.
VSI
will
g
en
er
ate
lar
g
e
c
u
r
r
en
t
s
p
ik
es
i
n
a
ca
p
ac
itiv
e
lo
a
d
th
at
is
p
r
e
v
en
ted
b
y
in
d
u
ctiv
e
f
ilter
b
et
wee
n
th
e
AC
s
id
e
o
f
VSI
an
d
th
e
lo
ad
.
I
n
th
e
co
n
j
u
n
ctio
n
o
f
th
e
VSI
,
C
SI
p
r
o
d
u
ce
d
lar
g
e
v
o
ltag
e
s
p
ik
es
in
t
h
e
in
d
u
ctiv
e
lo
a
d
.
I
f
th
is
h
ap
p
en
ed
,
ca
p
ac
itiv
e
f
ilt
er
will
b
e
u
s
ed
b
etwe
en
C
SI
at
th
e
AC
s
id
e
an
d
th
e
lo
ad
[
8
]
.
T
o
co
n
tr
o
l
th
e
in
v
er
ter
,
s
o
m
e
asp
ec
ts
n
ee
d
to
b
e
tak
en
in
to
ac
co
u
n
t
s
u
ch
as
th
e
ef
f
icien
cy
o
f
th
e
in
v
er
ter
.
T
h
is
in
clu
d
e
th
e
s
witch
in
g
lo
s
s
es
an
d
h
ar
m
o
n
ic
r
ed
u
ctio
n
th
at
p
r
i
n
cip
ally
d
ep
en
d
e
d
o
n
th
e
m
o
d
u
latio
n
s
tr
ateg
ies
[
9
]
.
T
h
e
in
v
er
ter
co
n
tr
o
l te
ch
n
iq
u
es a
r
e
b
ased
o
n
t
h
e
f
u
n
d
am
e
n
tal
f
r
e
q
u
en
cy
an
d
h
ig
h
s
witch
in
g
f
r
e
q
u
en
cy
.
T
h
e
r
e
g
u
lar
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
m
o
d
u
latio
n
m
eth
o
d
s
ca
n
b
e
d
i
v
id
ed
in
to
two
class
wh
ich
ar
e
o
p
en
lo
o
p
an
d
clo
s
ed
.
Op
en
lo
o
p
is
ap
p
lied
f
o
r
VSI
wh
ile
clo
s
ed
lo
o
p
is
u
s
u
ally
u
s
ed
f
o
r
th
e
C
SI.
T
h
is
p
r
o
p
o
s
ed
r
esear
ch
is
m
ai
n
ly
f
o
cu
s
ed
o
n
o
p
e
n
lo
o
p
wh
i
ch
is
VSI
.
Op
en
lo
o
p
co
n
s
is
ts
o
f
PW
M
tech
n
iq
u
es
s
u
ch
as
s
in
u
s
o
id
al
p
u
ls
e
wid
t
h
m
o
d
u
latio
n
(
SP
W
M)
[
1
0
]
,
s
p
ac
e
v
ec
to
r
p
u
ls
e
wid
t
h
m
o
d
u
latio
n
(
SVPW
M)
[
1
1
]
an
d
th
ir
d
h
a
r
m
o
n
ic
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
T
HPW
M)
[
1
2
]
.
T
h
e
m
o
d
u
latio
n
m
e
th
o
d
s
d
e
v
elo
p
ed
to
co
n
tr
o
l th
e
m
u
ltil
ev
el
in
v
er
ter
s
th
at
ar
e
b
ased
o
n
m
u
lti
-
ca
r
r
ier
o
r
d
er
s
with
PW
M.
SP
W
M
i
s
th
e
m
o
s
t c
o
m
m
o
n
co
n
tr
o
l
s
ch
em
es
th
at
co
n
tr
o
l
th
e
m
u
ltil
ev
el
in
v
er
ter
s
.
I
n
co
n
v
en
tio
n
al
SP
W
M,
a
s
in
u
s
o
id
al
r
ef
er
en
ce
wav
ef
o
r
m
is
co
m
p
ar
e
d
with
a
tr
ian
g
u
lar
ca
r
r
ier
wav
ef
o
r
m
to
g
en
er
ate
s
witch
in
g
s
eq
u
en
ce
s
f
o
r
p
o
wer
s
em
ico
n
d
u
cto
r
in
in
v
er
ter
m
o
d
u
les.
T
h
e
f
u
n
d
am
e
n
tal
f
r
e
q
u
en
cy
SP
W
M
co
n
tr
o
l
m
eth
o
d
was
p
r
o
p
o
s
ed
to
m
in
im
ize
th
e
s
witch
in
g
lo
s
s
e
s
.
T
h
e
m
u
lti
-
ca
r
r
ier
SP
W
M
c
o
n
tr
o
l
m
eth
o
d
s
ar
e
also
im
p
lem
en
ted
to
in
cr
ea
s
e
th
e
p
er
f
o
r
m
an
ce
o
f
m
u
ltil
ev
el
in
v
er
ter
s
an
d
a
r
e
class
if
ied
ac
co
r
d
in
g
to
v
er
tical
o
r
h
o
r
izo
n
t
al
ar
r
an
g
em
e
n
ts
o
f
ca
r
r
ier
s
ig
n
al
[
1
3
]
.
I
ts
s
witch
in
g
s
ch
em
e
is
ea
s
y
to
im
p
le
m
en
t
in
b
o
th
an
al
o
g
u
e
an
d
d
ig
ital
cir
cu
it.
I
n
th
e
s
im
p
lest
f
o
r
m
,
it
in
v
o
lv
es
t
h
e
h
ig
h
s
witch
in
g
f
r
e
q
u
en
c
y
tr
ian
g
u
lar
ca
r
r
ie
r
v
o
ltag
e
with
a
s
in
u
s
o
id
al
m
o
d
u
latin
g
s
ig
n
al
t
h
at
r
e
p
r
esen
ts
th
e
d
esire
d
f
u
n
d
am
e
n
tal
co
m
p
o
n
en
t
o
f
th
e
v
o
ltag
e
w
av
ef
o
r
m
[
1
4
]
.
T
h
e
p
ea
k
m
ag
n
itu
d
e
o
f
th
e
m
o
d
u
latin
g
s
ig
n
al
s
h
o
u
ld
r
em
ain
li
m
ited
to
th
e
p
e
ak
m
a
g
n
itu
d
e
o
f
th
e
ca
r
r
ier
s
ig
n
al
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
is
d
ev
elo
p
ed
b
y
co
n
s
id
er
in
g
t
h
e
s
id
e
b
an
d
h
ar
m
o
n
ics
an
d
m
o
d
u
latio
n
b
an
d
wid
th
in
Simu
lin
k
d
u
r
in
g
s
im
u
latio
n
.
T
h
e
ex
p
er
im
en
tal
v
e
r
if
icatio
n
o
f
th
e
m
o
d
eled
s
y
s
tem
is
an
aly
ze
d
b
y
co
n
tr
o
llin
g
th
e
I
GB
T
m
o
d
u
les with
d
e
v
elo
p
ed
SP
W
M
alg
o
r
ith
m
g
e
n
er
a
ted
b
y
h
ig
h
s
witch
in
g
s
tr
ateg
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
1
5
9
8
–
16
08
1600
SVM
o
r
SVP
W
M
wa
s
o
r
ig
in
ally
d
ev
elo
p
ed
as
v
ec
to
r
ap
p
r
o
ac
h
to
PW
M
f
o
r
th
r
ee
p
h
ase
in
v
er
ter
s
.
I
t
is
a
m
o
r
e
s
o
p
h
is
ticated
tech
n
iq
u
e
f
o
r
g
en
er
atin
g
s
in
e
wav
e
th
at
p
r
o
v
id
es
a
h
i
g
h
er
v
o
ltag
e
to
th
e
m
o
to
r
with
lo
wer
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
T
h
e
m
ain
aim
o
f
an
y
m
o
d
u
latio
n
tech
n
i
q
u
e
is
to
o
b
t
ain
v
ar
iab
le
o
u
tp
u
t
h
av
in
g
a
m
ax
im
u
m
f
u
n
d
a
m
e
n
tal
co
m
p
o
n
en
t
with
m
in
im
u
m
h
ar
m
o
n
ics.
SVPW
M
m
eth
o
d
is
an
a
d
v
an
ce
d
co
m
p
u
tatio
n
in
te
n
s
iv
e
PW
M
m
eth
o
d
[
1
5
]
.
Desp
ite
th
e
ad
v
a
n
ce
m
en
t,
th
e
an
aly
s
is
o
f
th
e
SVPW
M
co
n
tain
ed
a
co
m
p
lex
im
p
lem
en
t
in
th
e
s
o
f
twar
e
co
m
p
a
r
ed
to
SP
W
M
[
1
6
]
.
E
v
en
th
o
u
g
h
th
e
SVPW
M
h
as
m
o
r
e
ad
v
an
tag
e
o
f
less
h
ar
m
o
n
ic
co
n
ten
t,
t
h
e
d
if
f
er
e
n
ce
s
b
etwe
en
t
h
e
t
w
o
m
o
d
u
latio
n
s
ar
e
s
m
all.
T
h
u
s
,
with
in
tan
g
i
b
le
d
if
f
er
en
ce
s
,
SP
W
M
is
ch
o
s
en
as th
e
cir
cu
it is
m
u
ch
s
im
p
ler
t
h
an
SVPW
M
wh
en
ex
ec
u
ted
i
n
th
e
s
o
f
twar
e.
T
h
e
s
in
u
s
o
id
al
PW
M
i
s
th
e
s
i
m
p
lest
m
o
d
u
latio
n
s
ch
em
e
to
u
n
d
er
s
tan
d
b
u
t it
is
u
n
ab
le
to
f
u
lly
u
tili
ze
th
e
av
ailab
le
DC
b
u
s
s
u
p
p
ly
v
o
ltag
e.
Du
e
to
th
is
p
r
o
b
lem
,
t
h
e
T
HPW
M
tech
n
iq
u
e
was
d
ev
elo
p
ed
to
im
p
r
o
v
e
th
e
in
v
er
te
r
p
e
r
f
o
r
m
an
ce
.
T
h
e
s
in
u
s
o
id
al
PW
M
tech
n
iq
u
e
ca
u
s
es
d
ec
r
ea
s
e
m
a
x
im
u
m
ac
h
iev
ab
le
o
u
tp
u
t
v
o
ltag
e.
I
n
th
is
ca
s
e,
an
in
c
r
ea
s
e
o
f
m
ax
im
u
m
ac
h
iev
a
b
le
o
u
tp
u
t
v
o
ltag
e
is
s
tu
d
ied
.
Hen
ce
,
b
y
s
im
p
ly
a
d
d
in
g
a
th
ir
d
h
ar
m
o
n
ic
s
ig
n
al
to
ea
ch
o
f
th
e
r
ef
er
e
n
ce
s
ig
n
als,
it
is
p
o
s
s
ib
le
to
o
b
tain
a
s
i
g
n
if
ican
t
am
p
litu
d
e
in
cr
ea
s
e
at
th
e
o
u
t
p
u
t
v
o
ltag
e
with
o
u
t
lo
s
s
o
f
q
u
ality
[
1
7
]
.
I
t
is
r
em
ar
k
ab
le
t
h
at
th
e
r
ef
e
r
en
ce
s
ig
n
al
r
esu
ltin
g
f
r
o
m
th
e
ad
d
itio
n
o
f
th
e
th
ir
d
(
V3
)
an
d
f
ir
s
t
h
ar
m
o
n
ic
(
V1
)
i
s
s
m
aller
in
am
p
litu
d
e
th
an
t
h
e
f
ir
s
t
h
ar
m
o
n
ic.
At
th
e
o
u
tp
u
t,
t
h
e
o
b
tain
e
d
am
p
litu
d
e
o
f
th
e
f
i
r
s
t
h
ar
m
o
n
ic
i
s
eq
u
al
to
th
e
am
p
litu
d
e
o
f
th
e
f
ir
s
t
h
ar
m
o
n
ic
r
ef
er
en
ce
.
No
te
also
th
at
th
e
t
h
ir
d
h
ar
m
o
n
ic
is
n
o
t
s
ee
n
at
th
e
o
u
tp
u
t
v
o
ltag
e.
Ho
wev
er
,
th
e
p
h
ase
o
f
th
e
th
ir
d
h
ar
m
o
n
ic
in
jecte
d
m
u
s
t
b
e
s
tr
i
ctly
s
y
n
ch
r
o
n
o
u
s
with
t
h
e
p
h
a
s
e
o
f
t
h
e
r
ef
er
en
ce
v
o
ltag
e.
T
h
e
s
y
n
c
h
r
o
n
izatio
n
will
ca
u
s
e
th
e
d
if
f
icu
lty
o
f
t
h
e
in
jecte
d
t
h
ir
d
h
ar
m
o
n
ic
g
en
er
atio
n
[
1
8
]
.
T
h
u
s
,
SP
W
M
tech
n
iq
u
e
is
m
o
r
e
len
ien
t c
o
m
p
ar
e
d
to
t
h
e
T
HPW
M
to
o
b
tain
th
e
T
HD
v
o
lta
g
e
o
f
th
e
m
o
to
r
.
T
h
e
g
r
o
wth
in
AC
m
o
to
r
d
r
iv
e
s
is
d
r
asti
ca
lly
as o
v
er
th
e
p
ast y
ea
r
s
d
u
e
t
o
th
e
f
o
llo
win
g
f
ac
to
r
s
:
-
R
ap
id
tech
n
o
lo
g
y
d
e
v
elo
p
m
e
n
t o
f
m
icr
o
p
r
o
ce
s
s
o
r
in
ca
lcu
latin
g
/ex
ec
u
tin
g
co
m
p
le
x
alg
o
r
ith
m
s
[
1
9
]
,
-
R
ap
id
tech
n
o
lo
g
y
d
ev
el
o
p
m
e
n
t
o
f
s
o
lid
s
tate
s
witch
in
g
d
e
v
ices
wh
ich
ab
le
to
o
p
e
r
ate
th
e
s
witch
in
g
at
h
ig
h
er
p
o
wer
an
d
s
witch
in
g
f
r
eq
u
en
cies
[
2
0
]
,
-
Hig
h
d
em
an
d
f
o
r
in
d
u
s
tr
ial
ap
p
licatio
n
s
,
e.
g
.
elec
tr
ic
v
e
h
icle
ap
p
licatio
n
f
r
ac
tio
n
d
r
iv
es,
au
to
m
atio
n
in
d
u
s
tr
y
[
2
1
]
.
B
ased
o
n
th
e
f
ac
to
r
s
ab
o
v
e
,
i
n
ad
d
itio
n
,
th
er
e
ar
e
s
ev
er
al
r
esear
ch
er
s
u
s
ed
th
e
f
u
lly
o
p
tim
izatio
n
o
f
th
e
in
v
er
ter
s
h
as
in
v
en
ted
t
h
e
to
p
o
lo
g
ies
th
at
u
n
d
er
g
o
n
e
co
n
s
tan
t
ch
an
g
e
wh
ich
th
e
f
ir
s
t
w
as
C
SI
f
o
llo
wed
b
y
VSI
b
ased
o
n
ap
p
licatio
n
[
2
2
]
.
AC
m
o
to
r
d
r
iv
es
g
iv
e
b
en
e
f
its
in
ter
m
o
f
p
r
o
ce
s
s
co
n
tr
o
l
,
s
y
s
tem
s
tr
ess
an
d
en
er
g
y
s
av
in
g
s
[
2
3
]
.
I
t
en
ab
le
s
th
e
u
s
er
s
to
co
n
t
r
o
l
th
e
s
p
ee
d
o
f
m
o
to
r
at
a
co
n
s
tan
t
s
p
ee
d
.
T
h
e
p
r
o
ce
s
s
o
u
tp
u
t
n
ee
d
s
to
m
atch
t
h
e
d
i
f
f
er
en
t
s
y
n
ch
r
o
n
izin
g
p
ar
t
as
to
lo
ck
t
h
e
f
lo
w
b
ec
o
m
e
s
m
o
o
t
h
b
etwe
en
s
u
b
p
r
o
ce
s
s
es
in
th
e
p
r
o
ce
s
s
co
n
tr
o
l.
AC
d
r
iv
e
s
d
o
h
av
e
its
o
wn
d
is
ad
v
an
tag
es.
I
t
ten
d
s
t
o
h
a
v
e
c
o
m
p
lex
it
y
in
th
e
cir
c
u
it
an
d
co
s
tly
co
m
p
ar
ed
to
o
t
h
er
m
o
t
o
r
.
T
h
e
h
o
r
s
ep
o
wer
r
atin
g
e
x
p
en
s
iv
e
is
ex
p
en
s
iv
e
as
it
h
as
a
m
o
d
er
n
tech
n
o
lo
g
y
b
u
ild
in
s
id
e
th
e
d
r
iv
es
[
2
4
]
.
Fo
r
an
ex
am
p
le,
if
th
e
AC
m
o
to
r
ten
d
s
to
r
o
tate
f
aster
th
an
th
e
co
m
m
an
d
AC
d
r
iv
e,
th
e
m
o
to
r
its
elf
will
ac
ts
as
r
eg
en
er
ates
th
at
it
ca
n
p
u
m
p
en
er
g
y
in
to
d
r
iv
e
a
g
ain
.
T
h
e
d
r
iv
e
will
s
h
o
r
t
cir
cu
it if
th
e
en
e
r
g
y
t
h
at
ar
e
r
e
g
en
er
ated
ca
n
n
o
t a
b
s
o
r
b
th
is
e
n
er
g
y
w
h
ich
ca
n
lea
d
au
d
i
b
le
n
o
is
e.
I
n
th
is
r
esear
c
h
m
eth
o
d
,
th
e
m
ain
co
n
ce
r
n
is
to
m
in
im
ize
th
e
T
o
tal
Har
m
o
n
ic
Dis
to
r
tio
n
(
T
HD)
o
f
o
u
tp
u
t
v
o
ltag
e
as
well
as
o
u
t
p
u
t
cu
r
r
en
t,
a
n
d
f
ilter
s
ize.
B
ased
o
n
th
e
r
esear
ch
r
ep
o
r
t
in
[
2
5
]
,
T
HD
ca
n
b
e
m
in
im
ize
b
y
o
p
er
atin
g
th
e
in
v
er
ter
at
h
i
g
h
s
witch
in
g
f
r
eq
u
e
n
cy
with
o
u
t
d
eg
r
a
d
in
g
I
GB
T
s
witch
in
g
p
er
f
o
r
m
an
ce
.
I
n
s
u
ch
way
,
th
e
u
n
d
esire
d
h
a
r
m
o
n
ic
co
m
p
o
n
en
ts
ca
n
b
e
lo
ca
ted
at
h
ig
h
er
f
r
eq
u
e
n
cies
an
d
h
en
ce
s
m
all
f
ilter
s
ize
ca
n
b
e
ef
f
ec
tiv
ely
elim
in
ate
th
e
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
.
I
n
th
is
p
ap
e
r
,
I
GB
T
is
ch
o
s
en
d
u
e
to
its
ad
v
an
tag
e
wh
ic
h
ca
n
o
p
er
ate
at
h
ig
h
er
p
o
wer
ca
p
ab
ilit
y
[
2
6
]
.
Ho
we
v
er
,
I
GB
T
c
an
n
o
t b
e
o
p
er
ated
at
v
er
y
h
ig
h
s
witch
in
g
f
r
eq
u
en
cy
,
i.e
.
ab
o
v
e
5
0
k
Hz
d
u
e
t
o
its
t
h
er
m
al
r
estrictio
n
as
r
e
p
o
r
ted
in
[
2
7
]
.
T
h
is
p
a
p
er
p
r
o
v
id
es
a
s
im
p
le
s
o
lu
tio
n
to
en
ab
le
th
e
u
s
e
o
f
I
GB
T
to
o
p
er
ate
at
v
er
y
h
ig
h
s
witch
in
g
f
r
eq
u
e
n
cy
with
o
u
t
d
eg
r
ad
in
g
its
s
witch
in
g
p
er
f
o
r
m
an
ce
s
.
T
h
e
o
b
jectiv
e
o
f
th
is
p
ap
er
is
to
s
tu
d
y
,
im
p
lem
e
n
t
an
d
im
p
r
o
v
e
th
e
p
e
r
f
o
r
m
an
ce
s
o
f
AC
d
r
iv
es
u
s
in
g
alter
n
ate
s
witch
in
g
an
d
h
ig
h
s
witch
in
g
f
r
eq
u
en
cy
s
tr
ateg
y
.
T
h
e
m
ain
o
b
jectiv
es o
f
th
is
r
ese
ar
ch
ar
e:
-
T
o
r
ed
u
ce
T
HD
o
f
o
u
tp
u
t
v
o
l
tag
e
an
d
cu
r
r
e
n
t
an
d
f
ilter
s
iz
e
b
y
o
p
er
atin
g
th
e
i
n
v
er
ter
at
h
ig
h
s
witch
in
g
f
r
eq
u
e
n
cy
with
o
u
t d
eg
r
a
d
in
g
I
GB
T
s
witch
in
g
p
er
f
o
r
m
an
ce
s
.
-
T
o
d
esig
n
an
‘
Alter
n
ate
Switch
in
g
Stra
teg
y
’
u
s
in
g
an
alo
g
an
d
d
ig
ital
I
C
s
,
wh
ich
allo
ws
I
GB
T
b
ased
in
v
er
ter
to
o
p
er
ate
at
h
ig
h
s
witch
in
g
f
r
eq
u
e
n
cy
.
-
T
o
v
er
i
f
y
th
e
im
p
r
o
v
em
e
n
ts
o
f
th
e
in
v
er
ter
(
i.e
.
r
ed
u
ctio
n
o
f
T
HDs)
th
r
o
u
g
h
s
im
u
latio
n
an
d
h
ar
d
war
e
r
esu
lts
.
2.
P
RO
P
O
SE
D
AL
T
E
RNA
T
E
SWI
T
CH
I
NG
S
T
RA
T
E
G
Y
I
n
o
r
d
e
r
to
im
p
r
o
v
e
AC
d
r
iv
e
p
er
f
o
r
m
an
ce
s
,
s
p
ec
if
ically
in
r
ed
u
cin
g
o
u
tp
u
t
p
h
ase
v
o
ltag
e
T
HD,
it
is
n
ec
ess
ar
y
to
o
p
er
ate
th
e
in
v
er
ter
at
v
er
y
h
ig
h
s
witch
in
g
f
r
e
q
u
en
cy
.
As
d
is
cu
s
s
ed
ab
o
v
e,
th
e
u
s
e
o
f
I
GB
T
in
th
e
in
v
er
ter
cir
cu
it
is
s
tr
o
n
g
l
y
r
ec
o
m
m
e
n
d
ed
d
u
e
its
h
ig
h
-
p
o
wer
o
p
e
r
atio
n
ca
p
ab
ilit
y
.
Ho
wev
er
,
th
e
I
GB
T
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:
2
0
8
8
-
8
694
R
ed
u
ctio
n
o
f to
ta
l h
a
r
mo
n
ic
d
i
s
to
r
tio
n
o
f th
r
ee
-
p
h
a
s
e
in
ve
r
te
r
u
s
in
g
a
lter
n
a
te
…
(
N
u
r
A
r
ifa
h
R
a
mli
)
1601
ca
n
n
o
t
b
e
o
p
er
ated
at
v
e
r
y
h
ig
h
s
witch
in
g
f
r
eq
u
en
cy
,
i.e
.
a
b
o
v
e
5
0
k
Hz.
T
o
e
n
ab
le
th
e
t
h
r
ee
-
p
h
ase
in
v
er
ter
u
s
in
g
I
GB
T
s
to
o
p
er
ate
at
v
er
y
h
ig
h
s
witch
in
g
f
r
eq
u
en
cy
,
an
alter
n
ate
s
witch
in
g
s
tr
ateg
y
is
p
r
o
p
o
s
ed
.
Gen
er
ally
,
in
t
h
is
s
tr
ateg
y
,
th
e
co
n
v
e
n
tio
n
al
in
v
er
ter
ci
r
cu
i
t n
ee
d
s
to
b
e
m
o
d
if
ied
a
n
d
th
e
s
witch
in
g
f
r
e
q
u
en
c
y
as
well
a
s
s
witch
in
g
s
tate
s
f
o
r
s
witch
in
g
ea
ch
I
GB
T
i
s
s
p
l
itted
s
u
ch
th
at
th
e
I
GB
T
s
wit
ch
in
g
f
r
eq
u
en
cy
is
one
-
f
o
u
r
th
o
f
th
e
in
v
er
ter
s
witch
in
g
f
r
eq
u
e
n
cy
.
2
.
1
.
M
o
difica
t
io
n o
f
t
hree
-
ph
a
s
e
inv
er
t
er
circ
uit
T
h
e
m
o
d
if
icatio
n
o
f
th
e
in
v
e
r
ter
cir
cu
it
with
ad
d
itio
n
al
I
GB
T
s
ca
n
b
e
illu
s
tr
ated
in
Fig
u
r
e
2
.
Fo
r
ex
am
p
le,
t
h
e
to
p
I
GB
T
in
L
e
g
3
(
o
r
c
-
p
h
ase)
o
f
th
e
co
n
v
e
n
tio
n
al
th
r
ee
-
p
h
ase
in
v
er
te
r
,
i.
e.
Q5
is
r
ep
r
esen
te
d
as
a
g
r
o
u
p
o
f
f
o
u
r
I
GB
T
s
in
th
e
m
o
d
if
ied
in
v
er
ter
wh
ich
ar
e
co
n
n
ec
ted
in
p
ar
allel,
i.e
.
Q
5
a,
Q5
b
,
Q5
c
an
d
Q5
d
.
T
h
is
m
ea
n
s
ev
er
y
s
in
g
le
I
GB
T
in
th
e
o
r
i
g
in
al
in
v
er
ter
c
ir
cu
it
is
n
o
w
b
ein
g
r
ep
lace
d
w
ith
a
g
r
o
u
p
o
f
f
o
u
r
I
GB
T
s
.
T
h
er
ef
o
r
e,
th
e
m
o
d
if
ied
in
v
er
ter
cir
cu
it c
o
n
s
is
ts
o
f
2
4
I
GB
T
s
.
Fig
u
r
e
2
.
Mo
d
if
icatio
n
o
f
in
v
e
r
ter
cir
cu
it (
a)
t
h
e
co
n
v
en
tio
n
a
l th
r
ee
-
p
h
ase
in
v
er
ter
,
(
b
)
a
g
r
o
u
p
o
f
f
o
u
r
I
GB
T
s
co
n
n
ec
ted
i
n
p
ar
allel
I
n
th
is
way
,
th
e
in
v
e
r
ter
s
witch
in
g
f
r
eq
u
en
cy
ca
n
b
e
d
iv
id
e
d
in
to
f
o
u
r
,
s
o
th
at
e
v
er
y
I
GB
T
in
a
g
r
o
u
p
h
as
a
o
n
e
-
f
o
u
r
th
o
f
in
v
e
r
ter
s
witch
in
g
f
r
eq
u
e
n
cy
.
Fo
r
ex
a
m
p
les,
if
th
e
in
v
er
ter
s
witch
in
g
f
r
eq
u
e
n
cy
is
ch
o
s
en
as
2
0
0
k
Hz,
t
h
er
ef
o
r
e
ev
e
r
y
I
GB
T
in
ea
ch
g
r
o
u
p
h
as
a
s
witch
in
g
f
r
eq
u
e
n
cy
o
f
5
0
k
Hz.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
th
e
in
v
er
ter
s
till
o
p
er
ates
at
s
witch
in
g
f
r
eq
u
en
cy
o
f
2
0
0
k
H
z
as
ea
ch
I
GB
T
in
a
g
r
o
u
p
is
s
witch
ed
alter
n
ately
,
i.e
.
o
n
e
-
by
-
o
n
e
a
n
d
o
n
e
I
GB
T
is
s
witch
ed
at
o
n
e
tim
e.
T
h
e
r
ef
o
r
e,
t
h
e
s
witch
in
g
o
p
er
atio
n
o
f
I
GB
T
is
p
r
ev
en
ted
t
o
o
p
er
ate
b
ey
o
n
d
it
s
lim
itatio
n
an
d
at
th
e
s
am
e
ti
m
e
th
e
r
ed
u
ctio
n
o
f
h
i
g
h
f
r
e
q
u
en
cies
co
m
p
o
n
e
n
ts
o
f
o
u
t
p
u
t v
o
ltag
e
as we
ll a
s
o
u
tp
u
t c
u
r
r
e
n
t c
an
b
e
o
b
tain
e
d
w
ith
s
m
aller
s
ize
o
f
f
ilter
s
.
2
.
2
.
G
ener
a
t
io
n o
f
s
wit
ching
s
t
a
t
es f
o
r
a
lt
er
na
t
e
s
wit
ching
T
h
is
s
ec
tio
n
ex
p
lain
s
th
e
p
r
o
p
o
s
ed
alter
n
ate
s
witch
in
g
s
tr
ateg
y
th
at
allo
ws
th
e
in
v
e
r
ter
to
o
p
er
ate
at
v
er
y
h
ig
h
s
witch
in
g
f
r
eq
u
en
c
y
f
o
r
im
p
r
o
v
in
g
AC
d
r
iv
e
p
e
r
f
o
r
m
an
ce
s
.
Fo
r
s
im
p
lific
atio
n
,
th
e
e
x
p
lan
atio
n
o
f
th
e
p
r
o
p
o
s
ed
s
tr
ateg
y
will o
n
l
y
co
n
s
id
er
f
o
r
s
witch
in
g
alter
n
ately
f
o
r
f
o
u
r
I
GB
T
s
in
a
g
r
o
u
p
,
e.
g
.
as illu
s
tr
ated
in
Fig
u
r
e
2
.
Fig
u
r
e
3
s
h
o
ws
th
e
b
lo
ck
d
iag
r
am
a
n
d
tim
i
n
g
d
iag
r
am
o
f
t
h
e
p
r
o
p
o
s
ed
alter
n
ate
s
witch
in
g
s
tr
ateg
y
f
o
r
s
witch
in
g
I
GB
T
s
Q5
a
,
Q5
b
,
Q5
c
an
d
Q5
d
in
th
e
m
o
d
if
ied
in
v
e
r
ter
with
th
eir
r
esp
ec
tiv
e
s
witch
in
g
s
tates
S
5a
,
S
5b
,
S
5c
,
an
d
S
5d
.
T
h
e
b
lo
c
k
d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
s
tr
ateg
y
h
as
two
m
ai
n
p
ar
ts
,
i.e
.
two
-
b
it
co
u
n
ter
an
d
d
e
m
u
ltip
lex
er
.
T
h
e
p
r
o
p
o
s
ed
alter
n
ate
s
witch
i
n
g
s
tr
ateg
y
em
p
lo
y
s
a
1
-
to
-
4
d
em
u
ltip
lex
er
an
d
a
two
-
b
it
co
u
n
ter
,
wh
er
e
th
e
in
p
u
t
PW
M
s
ig
n
al
S
x=
S
5
i
s
o
b
tain
ed
f
r
o
m
PW
M
g
en
er
ato
r
an
d
t
h
e
o
u
tp
u
t
s
ig
n
als,
i.e
.
S
5a
,
S
5b
,
S
5c
,
an
d
S
5d
ar
e
u
s
ed
to
co
n
tr
o
l
th
e
s
witch
in
g
o
p
er
atio
n
o
f
I
GB
T
s
.
T
h
e
o
p
er
ati
o
n
o
f
t
h
e
p
r
o
p
o
s
ed
Q5a
Q5
b
Q5
c
Q5
d
Q5
S
5a
S
1
S
2
S
3
S
4
S
5
S
6
A
B
C
S
5b
S
5c
S
5d
(a)
(b
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
1
5
9
8
–
16
08
1602
alter
n
ate
s
witch
in
g
s
tr
ateg
y
to
p
r
o
d
u
ce
alter
n
ate
s
witch
in
g
s
tates
ca
n
b
e
illu
s
tr
ated
b
y
tim
in
g
d
iag
r
am
in
Fig
u
r
e
3
(
b
)
.
Fig
u
r
e
4
s
h
o
ws
a
s
im
u
latio
n
m
o
d
el
o
f
two
-
b
it
co
u
n
ter
u
s
in
g
Gr
ay
C
o
d
e
an
d
1
-
to
-
4
d
em
u
ltip
lex
er
f
o
r
p
r
o
d
u
cin
g
alter
n
ate
s
witch
in
g
s
tates,
e.
g
.
S
5a
,
S
5b
,
S
5c
,
an
d
S
5d
.
T
h
e
s
im
u
latio
n
m
o
d
el
r
eq
u
ir
es
two
in
p
u
t
s
wh
ich
ar
e
a
S5
(
PW
M)
s
ig
n
al
an
d
en
ab
lin
g
s
ig
n
al
(
i.e
.
d
esig
n
ated
as
E
N
B
)
,
to
p
r
o
d
u
ce
tw
o
-
b
it
o
u
tp
u
t,
i
.
e.
A
1
(
MSB
)
an
d
A
0
(
L
SB
)
.
T
h
ese
two
-
b
it
o
u
tp
u
ts
ar
e
u
s
ed
to
in
d
ex
th
e
s
elec
tio
n
ta
b
le
g
iv
en
in
T
ab
le
1
,
f
o
r
s
p
litt
in
g
a
PW
M
s
ig
n
al
in
to
f
o
u
r
s
witch
in
g
s
tat
es
in
d
em
u
lt
ip
lex
er
o
p
e
r
atio
n
.
No
te
t
h
at
th
e
en
ab
lin
g
s
ig
n
al
is
s
et
to
lo
g
ic
1
to
ac
tiv
ate
t
h
e
co
u
n
t
in
g
o
p
er
atio
n
.
Fig
u
r
e
3
.
T
h
e
p
r
o
p
o
s
ed
alter
n
ate
s
witch
in
g
s
tr
ateg
y
f
o
r
s
wit
ch
in
g
f
o
u
r
I
GB
T
s
in
a
g
r
o
u
p
:
(
a)
b
lo
ck
d
iag
r
am
(
b
)
tim
in
g
d
iag
r
am
wav
ef
o
r
m
(
a)
(
b
)
Fig
u
r
e
4
.
Simu
latio
n
m
o
d
el
o
f
th
e
p
r
o
p
o
s
ed
alter
n
ate
s
witch
i
n
g
s
tr
ateg
y
f
o
r
c
o
n
tr
o
llin
g
a
g
r
o
u
p
o
f
f
o
u
r
s
witch
es
:
(
a)
t
wo
-
b
it c
o
u
n
ter
(
b
)
1
-
to
-
4
d
em
u
ltip
lex
er
T
ab
le
1
.
Sp
litt
in
g
o
f
PW
M
s
ig
n
als to
p
r
o
d
u
ce
s
witch
in
g
s
tate
f
o
r
ea
c
h
ch
an
n
el
o
u
t
p
u
t
A
d
d
r
e
ss
d
a
t
a
(
f
r
o
m
t
w
o
-
b
i
t
c
o
u
n
t
e
r
)
O
u
t
p
u
t
o
f
d
e
m
u
l
t
i
p
l
e
x
e
r
A
1
(
M
S
B
)
A
0
(
LSB)
S
5a
S
5b
S
5c
S
5d
0
0
S
5
0
0
0
0
1
0
S
5
0
0
1
0
0
0
S
5
0
1
1
0
0
0
S
5
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:
2
0
8
8
-
8
694
R
ed
u
ctio
n
o
f to
ta
l h
a
r
mo
n
ic
d
i
s
to
r
tio
n
o
f th
r
ee
-
p
h
a
s
e
in
ve
r
te
r
u
s
in
g
a
lter
n
a
te
…
(
N
u
r
A
r
ifa
h
R
a
mli
)
1603
T
h
e
two
-
b
it
co
u
n
ter
em
p
l
o
y
s
two
D
F
lip
-
flo
p
an
d
a
N
OT
lo
g
ic
g
ate,
an
d
1
-
to
-
4
d
e
m
u
ltip
lex
er
em
p
lo
y
s
a
s
et
o
f
lo
g
ic
g
ates w
h
ich
is
co
n
s
tr
u
cted
b
ased
o
n
B
o
o
lean
e
x
p
r
ess
io
n
g
iv
e
n
in
(
1
)
.
5
=
1
̅
̅
̅
∙
0
̅
̅
̅
∙
5
5
=
1
̅
̅
̅
∙
0
∙
5
5
=
1
∙
0
∙
5
5
=
1
∙
0
̅
̅
̅
∙
5
(
1
)
W
h
er
e
th
e
B
o
o
lean
ex
p
r
ess
io
n
f
o
r
ea
c
h
s
witch
in
g
s
tate
is
f
u
n
ctio
n
ed
o
f
PW
M
s
ig
n
al
an
d
two
-
b
it a
d
d
r
ess
,
wh
ich
ca
n
b
e
o
b
tain
e
d
f
r
o
m
th
e
d
em
u
ltip
lex
er
o
p
er
atio
n
g
iv
e
n
in
T
ab
le
1
.
3.
E
XP
E
R
I
M
E
N
T
A
L
SE
T
UP
T
h
is
s
ec
tio
n
d
is
cu
s
s
e
s
th
e
e
x
p
er
im
en
tal
s
etu
p
o
f
th
e
p
r
o
p
o
s
ed
alter
n
ate
s
witch
in
g
s
tr
ateg
y
f
o
r
mi
n
im
izin
g
T
HD
o
f
o
u
tp
u
t
v
o
ltag
e.
Fig
u
r
e
5
s
h
o
ws
an
elec
t
r
o
n
ic
cir
c
u
it
o
f
th
e
p
r
o
p
o
s
ed
alter
n
ate
s
witch
in
g
s
tr
ateg
y
f
o
r
co
n
t
r
o
llin
g
f
o
u
r
s
witch
es
in
a
g
r
o
u
p
,
i.e
.
S
5a
,
S
5b
,
S
5c
,
an
d
S
5d
.
T
h
e
two
-
b
it
co
u
n
ter
with
Gra
y
co
d
e
is
im
p
lem
en
ted
u
s
in
g
i
n
teg
r
ated
cir
cu
it
(
I
C
)
m
o
d
el:
MC7
4
HC
7
4
ADG,
an
d
1
-
to
-
4
d
em
u
ltip
lex
er
is
im
p
lem
en
ted
u
s
in
g
I
C
m
o
d
el:
MC7
4
AC
1
3
9
DG.
T
h
e
in
p
u
t
o
f
th
e
cir
cu
it
is
a
P
WM
s
ig
n
al,
e.
g
.
S
5
a
n
d
th
is
s
ig
n
al
is
s
p
litt
ed
in
to
f
o
u
r
s
witch
in
g
s
tates,
i.e
.
S
5a
,
S
5b
,
S
5c
,
an
d
S
5d
,
wh
er
e
ea
ch
s
witch
in
g
s
tate
p
er
f
o
r
m
s
at
one
-
f
o
u
r
th
o
f
th
e
P
WM
s
ig
n
al
f
r
eq
u
e
n
cy
.
Fig
u
r
e
6
s
h
o
ws
two
p
h
o
to
s
o
f
th
e
ex
p
e
r
im
en
tal
s
etu
p
o
f
th
e
p
r
o
p
o
s
ed
alter
n
ate
s
witch
in
g
s
tr
ateg
y
.
Sp
ec
if
ically
,
th
e
m
o
d
if
ied
th
r
ee
-
p
h
ase
in
v
er
te
r
cir
cu
it
co
n
s
is
t
o
f
6
x
4
I
GB
T
s
,
g
ate
d
r
iv
er
an
d
th
e
p
r
o
p
o
s
e
d
alter
n
ate
s
witch
in
g
cir
cu
its
is
s
h
o
wn
in
Fig
u
r
e
6
(
a
)
,
wh
ile
t
h
e
co
m
p
lete
e
x
p
er
im
e
n
t
s
etu
p
is
s
h
o
wn
in
Fig
u
r
e
6
(
b
)
.
A
th
r
ee
-
p
h
ase
r
esis
to
r
b
an
k
is
u
s
ed
as
a
lo
ad
i
n
g
u
n
it
an
d
th
e
P
WM
s
ig
n
als
a
r
e
g
en
e
r
ated
f
r
o
m
d
SP
AC
E
1
1
0
4
co
n
tr
o
ller
b
o
a
r
d
.
(
a)
(
b
)
Fig
u
r
e
5
.
E
lectr
o
n
ic
cir
cu
it
o
f
th
e
p
r
o
p
o
s
ed
alter
n
ate
s
witch
i
n
g
s
tr
ateg
y
:
(
a
)
two
-
b
it c
o
u
n
te
r
(
b
)
1
-
to
-
4
d
em
u
ltip
lex
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
1
5
9
8
–
16
08
1604
(
a)
(
b
)
Fig
u
r
e
6
.
E
x
p
er
im
e
n
tal
s
etu
p
o
f
th
e
p
r
o
p
o
s
ed
alter
n
ate
s
witch
in
g
s
tr
ateg
y
:
(
a
)
alter
n
ate
s
witch
in
g
cir
cu
it,
g
ate
d
r
iv
er
cir
c
u
it a
n
d
th
e
m
o
d
i
f
ied
in
v
er
ter
,
(
b
)
c
o
m
p
lete
ex
p
er
i
m
en
t setu
p
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
So
m
e
ex
p
er
im
en
ts
ar
e
ca
r
r
ie
d
o
u
t
to
v
alid
ate
th
e
T
HD
r
ed
u
ctio
n
in
th
e
p
r
o
p
o
s
ed
m
e
th
o
d
.
T
h
e
ex
p
er
im
en
ts
ar
e
ca
r
r
ied
o
u
t
b
y
ap
p
l
y
in
g
Sin
u
s
o
id
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SP
W
M)
tech
n
iq
u
e
f
o
r
th
r
ee
d
if
f
er
en
t
in
v
er
ter
s
witch
in
g
f
r
eq
u
en
cies,
i.e
.
f
sw=
5
k
Hz,
f
sw=
10
k
Hz
an
d
f
sw=
5
0
k
Hz.
E
ac
h
e
x
p
er
im
en
t
a
p
p
lies
a
d
c
v
o
ltag
e
o
f
5
0
V
a
n
d
a
s
im
p
le
lo
w
p
ass
f
ilter
with
cu
t
-
o
f
f
f
r
eq
u
en
cy
,
f
c
=1
0
k
Hz.
Fi
g
u
r
es
7
a
n
d
8
s
h
o
w
ex
p
er
im
en
t
r
esu
lts
o
f
o
u
tp
u
t
p
h
ase
v
o
ltag
es
an
d
th
ei
r
f
r
e
q
u
e
n
cy
s
p
ec
tr
u
m
s
,
b
ef
o
r
e
a
n
d
af
t
er
f
ilter
in
g
ac
t
io
n
s
,
f
o
r
th
r
ee
d
if
f
er
en
t
s
witch
in
g
f
r
eq
u
en
cies.
Fro
m
th
ese
f
ig
u
r
e
s
,
s
o
m
e
o
b
s
er
v
atio
n
s
ca
n
b
e
m
ad
e
wh
ich
ca
n
b
e
s
tated
ar
e
:
-
T
h
e
wav
e
s
h
ap
e
o
f
o
u
tp
u
t
p
h
a
s
e
v
o
ltag
e
is
clo
s
ely
to
s
in
u
s
o
id
al
wav
e
s
h
ap
e
af
te
r
f
ilter
in
g
ac
tio
n
ap
p
lied
,
p
ar
ticu
lar
ly
at
th
e
h
ig
h
est in
v
e
r
ter
s
witch
in
g
f
r
eq
u
en
cy
,
i.e
.
f
sw=
5
0
k
Hz,
-
H
ar
m
o
n
ic
c
o
m
p
o
n
en
ts
ar
e
l
o
c
ated
at
h
ig
h
er
f
r
eq
u
en
cies
wh
en
th
e
in
v
er
ter
s
wi
tch
in
g
f
r
e
q
u
en
cy
i
n
cr
ea
s
es,
b
ef
o
r
e
a
n
d
af
te
r
f
ilter
in
g
ac
tio
n
ap
p
lied
,
-
O
u
tp
u
t
p
h
ase
v
o
ltag
e
s
ee
m
s
t
o
co
n
tain
i
n
s
ig
n
if
ican
t
h
ar
m
o
n
ic
co
m
p
o
n
e
n
ts
af
ter
f
ilter
in
g
ac
tio
n
is
ap
p
lied
f
o
r
ea
ch
in
v
er
ter
s
witch
in
g
f
r
e
q
u
en
cy
,
an
d
-
T
h
e
f
u
n
d
am
e
n
tal
co
m
p
o
n
en
t
o
f
o
u
tp
u
t
p
h
ase
v
o
lta
g
e
af
ter
f
ilter
is
ap
p
lied
is
less
th
an
th
at
p
r
o
d
u
ce
d
b
ef
o
r
e
t
h
e
f
ilter
is
ap
p
lied
d
u
e
to
lo
w
p
ass
f
ilter
g
ain
.
T
h
u
s
,
it
o
b
v
io
u
s
ly
s
h
o
ws
th
at
th
e
q
u
ality
o
f
o
u
tp
u
t
p
h
ase
v
o
ltag
e
wav
ef
o
r
m
im
p
r
o
v
e
d
if
t
h
e
in
v
er
ter
o
p
er
ates
at
h
ig
h
er
s
witch
in
g
f
r
e
q
u
en
cy
,
an
d
it is
s
ig
n
if
ican
tly
im
p
r
o
v
e
d
af
ter
f
ilter
a
p
p
lied
.
T
ab
le
2
s
h
o
ws
th
e
T
HD
o
f
o
u
tp
u
t
p
h
ase
v
o
ltag
es
co
r
r
esp
o
n
d
in
g
to
th
e
r
esu
lts
o
b
tain
ed
i
n
f
r
eq
u
e
n
cy
s
p
ec
tr
u
m
s
h
o
wn
in
Fig
u
r
e
8
.
Fro
m
th
e
tab
le,
th
e
T
HD
o
f
t
h
e
o
u
tp
u
t p
h
ase
v
o
ltag
e
d
ec
r
ea
s
e
s
wh
en
th
e
in
v
er
te
r
s
witch
in
g
f
r
eq
u
e
n
cy
in
c
r
ea
s
es.
Ob
v
io
u
s
ly
,
th
e
T
HD
o
f
o
u
tp
u
t
p
h
ase
v
o
ltag
e
is
s
ig
n
if
ic
an
tly
m
in
im
ized
t
o
1
0
.
1
5
%
af
ter
t
h
e
f
ilter
is
ap
p
li
ed
an
d
wh
en
th
e
in
v
er
ter
o
p
er
ates
at
th
e
h
ig
h
est
in
v
er
te
r
s
witch
in
g
f
r
eq
u
e
n
cy
.
T
h
is
is
b
ec
au
s
e
th
e
f
ilter
with
lo
w
c
u
t
-
o
f
f
f
r
e
q
u
en
c
y
ca
n
ef
f
ec
tiv
ely
elim
in
ate
an
d
m
in
im
ize
h
ar
m
o
n
ics
at
h
ig
h
er
f
r
eq
u
en
cies.
T
h
er
ef
o
r
e,
th
is
clea
r
ly
s
h
o
ws
th
at
th
e
im
p
r
o
v
em
e
n
t
o
f
o
u
tp
u
t
p
h
ase
v
o
ltag
e
wav
ef
o
r
m
is
d
u
e
to
lo
w
T
HD
as g
iv
e
n
in
T
ab
le
2
.
Mo
r
e
o
v
er
,
th
is
also
h
ig
h
lig
h
ts
th
a
t le
s
s
f
ilter
s
ize
is
r
e
q
u
ir
ed
to
m
in
im
ize
T
HD
f
o
r
im
p
r
o
v
in
g
o
u
tp
u
t
p
h
ase
v
o
ltag
e
wav
ef
o
r
m
if
th
e
in
v
er
ter
o
p
er
ates
at
th
e
h
ig
h
est
s
witch
in
g
f
r
eq
u
e
n
cy
.
T
ab
le
2
.
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
o
f
o
u
tp
u
t p
h
ase
v
o
ltag
es f
o
r
th
r
ee
d
if
f
er
e
n
t switch
in
g
f
r
eq
u
e
n
cies;
b
ef
o
r
e
a
n
d
af
te
r
f
ilter
cir
cu
it is
ap
p
lied
.
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
,
f
sw
(
k
H
z
)
To
t
a
l
H
a
r
mo
n
i
c
D
i
st
o
r
t
i
o
n
(
%)
B
e
f
o
r
e
f
i
l
t
e
r
A
f
t
e
r
f
i
l
t
e
r
5
6
8
.
5
5
4
0
.
1
1
10
6
8
.
5
4
2
7
.
2
0
50
6
7
.
7
5
1
0
.
1
5
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:
2
0
8
8
-
8
694
R
ed
u
ctio
n
o
f to
ta
l h
a
r
mo
n
ic
d
i
s
to
r
tio
n
o
f th
r
ee
-
p
h
a
s
e
in
ve
r
te
r
u
s
in
g
a
lter
n
a
te
…
(
N
u
r
A
r
ifa
h
R
a
mli
)
1605
B
ef
o
r
e
f
ilter
in
g
ac
tio
n
Af
ter
f
ilter
in
g
ac
tio
n
(
a)
(
b
)
(
c)
Fig
u
r
e
7
.
E
x
p
er
im
e
n
t Res
u
lts
o
f
o
u
t
p
u
t p
h
ase
v
o
ltag
e
b
ef
o
r
e
an
d
af
ter
f
ilter
in
g
ac
tio
n
f
o
r
d
if
f
er
en
t switch
in
g
f
r
eq
u
e
n
cies
:
(
a)
1
k
Hz,
(
b
)
1
0
k
Hz
an
d
(
c
)
5
0
k
Hz
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
1
5
9
8
–
16
08
1606
B
ef
o
r
e
f
ilter
in
g
ac
tio
n
Af
ter
f
ilter
in
g
ac
tio
n
(
a)
(
b
)
(
c)
Fig
u
r
e
8
.
E
x
p
er
im
e
n
t Res
u
lts
o
f
o
u
t
p
u
t p
h
ase
v
o
ltag
e
f
r
eq
u
e
n
cy
s
p
ec
tr
u
m
b
ef
o
r
e
an
d
af
ter
f
ilter
in
g
ac
tio
n
f
o
r
d
if
f
er
en
t switch
in
g
f
r
eq
u
en
cie
s
:
(
a)
5
k
Hz,
(
b
)
1
0
k
Hz
a
n
d
(
c
)
5
0
k
Hz,
(
x
-
ax
is
s
ca
le:
1
2
.
5
k
Hz/d
iv
.
)
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
h
as
p
r
o
p
o
s
ed
an
im
p
r
o
v
e
m
en
t
o
f
T
HD
o
f
o
u
tp
u
t
p
h
ase
v
o
ltag
e
b
y
o
p
er
atin
g
t
h
e
in
v
er
ter
at
h
ig
h
s
witch
in
g
f
r
e
q
u
en
c
y
.
I
n
p
r
ac
tice,
I
GB
T
p
o
wer
s
witch
is
n
o
t
r
ec
o
m
m
en
d
e
d
t
o
b
e
a
p
p
lied
at
h
ig
h
s
witch
in
g
f
r
eq
u
en
cy
o
p
e
r
atio
n
d
u
e
to
its
lim
itatio
n
s
,
i.e
.
it
ca
n
n
o
t
o
p
er
ate
a
b
o
v
e
5
0
k
Hz
a
n
d
t
h
er
m
al
r
estrictio
n
.
T
h
is
p
a
p
er
h
as
s
u
g
g
ested
to
ap
p
ly
th
e
p
r
o
p
o
s
ed
alter
n
ate
s
witch
in
g
s
tr
ateg
y
s
o
th
at
I
GB
T
s
ca
n
b
e
em
p
lo
y
ed
f
o
r
h
i
g
h
in
v
e
r
ter
s
witch
in
g
f
r
eq
u
e
n
cy
.
I
n
th
is
s
tr
ateg
y
,
th
e
in
v
e
r
ter
o
p
er
ates
at
h
ig
h
s
witch
i
ng
f
r
eq
u
e
n
cy
,
e
.
g
.
2
0
0
k
Hz,
h
o
w
ev
er
,
ea
ch
I
GB
T
in
a
g
r
o
u
p
o
f
f
o
u
r
s
witch
es
in
th
e
m
o
d
if
ie
d
in
v
er
te
r
cir
cu
it
is
s
witch
ed
alter
n
ately
,
an
d
as
a
r
esu
lt
ea
ch
I
GB
T
o
p
er
ates
at
o
n
e
-
f
o
u
r
th
o
f
th
e
in
v
er
te
r
s
witch
in
g
f
r
eq
u
en
cy
,
e.
g
.
5
0
k
Hz
wh
ich
is
s
till
b
elo
w
its
m
ax
im
u
m
f
r
eq
u
en
cy
.
So
m
e
ex
p
e
r
im
en
t
r
esu
lts
h
av
e
v
er
if
ie
d
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
alter
n
ate
s
witch
in
g
o
p
er
atio
n
to
im
p
r
o
v
e
o
u
tp
u
t
p
h
ase
v
o
lt
ag
e
wav
e
s
h
ap
e
as
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:
2
0
8
8
-
8
694
R
ed
u
ctio
n
o
f to
ta
l h
a
r
mo
n
ic
d
i
s
to
r
tio
n
o
f th
r
ee
-
p
h
a
s
e
in
ve
r
te
r
u
s
in
g
a
lter
n
a
te
…
(
N
u
r
A
r
ifa
h
R
a
mli
)
1607
well
as
T
HD
p
er
f
o
r
m
an
ce
.
T
h
e
m
ain
b
en
ef
it
o
f
th
e
p
r
o
p
o
s
e
d
m
eth
o
d
is
to
f
ac
ilit
ate
th
e
u
s
e
o
f
I
GB
T
in
h
ig
h
p
o
wer
ap
p
licatio
n
s
,
s
u
ch
th
a
t
it
ca
n
b
e
u
s
ed
f
o
r
o
p
er
atin
g
th
e
in
v
er
ter
at
h
ig
h
s
witch
in
g
f
r
eq
u
en
cy
f
o
r
im
p
r
o
v
in
g
T
HD
p
er
f
o
r
m
a
n
ce
s
.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
e
au
th
o
r
s
wo
u
ld
lik
e
to
th
an
k
Min
is
tr
y
o
f
E
d
u
ca
tio
n
Ma
lay
s
ia,
Un
iv
er
s
iti
T
ek
n
ik
al
Ma
lay
s
ia
Me
lak
a
(
UT
eM
)
f
o
r
p
r
o
v
id
in
g
th
e
r
esear
ch
g
r
an
ts
R
AC
E
R
/2
0
1
9
/FKE
-
C
E
R
I
A/F0
0
3
9
8
to
c
o
m
p
lete
th
e
p
a
p
er
.
RE
F
E
R
E
NC
E
S
[1
]
S
.
Kh
a
rj
u
le,
“
Vo
lt
a
g
e
s
o
u
rc
e
i
n
v
e
rter,”
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
E
n
e
rg
y
S
y
ste
ms
a
n
d
Ap
p
li
c
a
t
i
o
n
s
,
2
0
1
5
,
p
p
.
537
-
5
4
2
,
d
o
i:
1
0
.
1
1
0
9
/IC
ES
A.
2
0
1
5
.
7
5
0
3
4
0
7
.
[2
]
Z.
Hu
a
n
g
,
T.
Ya
n
g
,
P
.
G
ian
g
ra
n
d
e
,
S
.
C
h
o
wd
h
u
r
y
,
M
.
G
a
lea
,
P
.
W
h
e
e
ler,
“
An
Ac
ti
v
e
M
o
d
u
lati
o
n
S
c
h
e
m
e
to
Bo
o
st
V
o
lt
a
g
e
Util
iza
ti
o
n
o
f
t
h
e
Du
a
l
Co
n
v
e
rter
Wi
th
a
F
lo
a
ti
n
g
Br
id
g
e
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
I
n
d
u
st
ria
l
El
e
c
tro
n
ics
,
v
o
l.
6
6
,
n
o
.
7
,
p
p
.
5
6
2
3
-
5
6
3
3
,
Ju
l
y
2
0
1
9
,
d
o
i
:
1
0
.
1
1
0
9
/T
I
E.
2
0
1
8
.
2
8
7
3
5
3
9
.
[3
]
M
.
Zh
a
n
g
,
D.
J.
Atk
i
n
so
n
,
B.
Ji,
M
.
Arm
stro
n
g
,
M
.
M
a
,
“
A
Ne
a
r
-
S
tate
Th
re
e
-
Dim
e
n
sio
n
a
l
S
p
a
c
e
Ve
c
to
r
M
o
d
u
latio
n
f
o
r
a
T
h
re
e
-
P
h
a
se
F
o
u
r
-
Leg
V
o
lt
a
g
e
S
o
u
rc
e
In
v
e
rter,”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l.
2
9
,
n
o
.
1
1
,
p
p
.
5
7
1
5
-
5
7
2
6
,
2
0
1
4
,
d
o
i:
1
0
.
1
1
0
9
/T
P
EL
.
2
0
1
3
.
2
2
9
7
2
0
5
.
[4
]
G
.
M
ig
li
a
z
z
a
e
t
a
l
.
,
“
DC
Cu
rre
n
t
Co
n
tr
o
l
f
o
r
a
S
i
n
g
le
-
S
tag
e
Cu
rre
n
t
S
o
u
rc
e
In
v
e
rter
in
M
o
to
r
Dri
v
e
Ap
p
li
c
a
ti
o
n
,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
P
o
w
e
r
El
e
c
tro
n
ics
,
v
o
l.
3
6
,
n
o
.
3
,
p
p
.
3
3
6
7
-
3
3
7
6
,
M
a
rc
h
2
0
2
1
,
d
o
i:
1
0
.
1
1
0
9
/
TP
EL
.
2
0
2
0
.
3
0
1
3
3
0
1
.
[5
]
B.
S
a
h
a
n
,
S
.
V.
Ara
ú
jo
,
C.
N
ö
d
i
n
g
P
.
Zac
h
a
rias
,
“
Co
m
p
a
ra
ti
v
e
Ev
a
lu
a
ti
o
n
o
f
Th
re
e
-
P
h
a
se
Cu
rre
n
t
S
o
u
rc
e
In
v
e
rters
fo
r
G
rid
I
n
terfa
c
in
g
o
f
Distri
b
u
ted
a
n
d
Re
n
e
wa
b
le
E
n
e
rg
y
S
y
ste
m
s,”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
ics
,
v
o
l
.
2
6
,
n
o
.
8
,
p
p
.
2
3
0
4
-
2
3
1
8
,
Au
g
.
2
0
1
1
,
d
o
i:
1
0
.
1
1
0
9
/
TP
EL
.
2
0
1
0
.
2
0
9
6
8
2
7
.
[6
]
L.
Din
g
,
Y.
W.
Li
,
“
S
imu
l
tan
e
o
u
s
DC
C
u
rre
n
t
Ba
lan
c
e
a
n
d
C
o
m
m
o
n
-
M
o
d
e
V
o
lt
a
g
e
C
o
n
tr
o
l
Wi
th
M
u
l
ti
lev
e
l
Cu
rre
n
t
S
o
u
rc
e
In
v
e
rters
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
El
e
c
tro
n
i
c
s
,
v
o
l.
3
3
,
n
o
.
1
1
,
p
p
.
9
1
8
8
-
9
1
9
7
,
No
v
.
2
0
1
8
,
d
o
i:
1
0
.
1
1
0
9
/T
P
EL
.
2
0
1
8
.
2
7
9
0
9
5
0
.
[7
]
I.
Co
lak
,
E.
Ka
b
a
lci,
“
De
v
e
lo
p
in
g
a
n
o
v
e
l
si
n
u
so
id
a
l
p
u
lse
wid
th
m
o
d
u
lati
o
n
(S
P
WM
)
tec
h
n
iq
u
e
t
o
e
li
m
in
a
te
sid
e
b
a
n
d
h
a
rm
o
n
ics
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
4
4
,
n
o
.
1
,
p
p
.
8
6
1
-
8
7
1
,
2
0
1
3
,
d
o
i:
1
0
.
1
0
1
6
/j
.
ij
e
p
e
s.2
0
1
2
.
0
8
.
0
2
4
.
[8
]
Ya
o
w
-
M
in
g
Ch
e
n
,
C
h
i
h
-
Hu
n
g
Hs
ieh
,
Yu
a
n
-
M
in
g
C
h
e
n
g
,
“
M
o
d
ifi
e
d
S
P
W
M
c
o
n
tr
o
l
sc
h
e
m
e
s
fo
r
t
h
re
e
-
p
h
a
se
in
v
e
rters
,
”
4
th
IEE
E
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
P
o
we
r
El
e
c
tr
o
n
ics
a
n
d
Dr
ive
S
y
ste
ms
.
IEE
E
PE
DS
2
0
0
1
-
In
d
o
n
e
sia
.
Pro
c
e
e
d
in
g
s (C
a
t.
N
o
.
0
1
T
H
8
5
9
4)
,
2
0
0
1
,
p
p
.
6
5
1
-
6
5
6
v
o
l.
2
,
d
o
i:
1
0
.
1
1
0
9
/P
EDS
.
2
0
0
1
.
9
7
5
3
9
6
.
[9
]
E.
Ba
b
a
e
i,
S
.
H.
Ho
ss
e
in
i,
G
.
B.
G
h
a
re
h
p
e
ti
a
n
,
“
Re
d
u
c
ti
o
n
o
f
T
HD
a
n
d
l
o
w
o
r
d
e
r
h
a
rm
o
n
ics
with
sy
m
m
e
tri
c
a
l
o
u
t
p
u
t
c
u
rre
n
t
fo
r
sin
g
le
-
p
h
a
se
a
c
/ac
m
a
tri
x
c
o
n
v
e
rters
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
tr
ica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
3
2
,
n
o
.
3
,
p
p
.
2
2
5
-
2
3
5
,
2
0
1
0
,
d
o
i:
1
0
.
1
0
1
6
/j
.
ij
e
p
e
s.2
0
0
9
.
0
7
.
0
0
4
.
[1
0
]
Z.
g
h
u
o
P
a
n
,
F
.
Z.
P
e
n
g
,
“
A
No
v
e
l
S
P
WM
M
e
th
o
d
wit
h
Vo
lt
a
g
e
Ba
lan
c
in
g
Ca
p
a
b
il
i
ty
fo
r
M
u
lt
il
e
v
e
l
Re
c
ti
fier/In
v
e
rter
S
y
ste
m
s,”
AP
E
C
0
7
-
T
we
n
ty
-
S
e
c
o
n
d
A
n
n
u
a
l
I
EE
E
A
p
p
li
e
d
P
o
we
r
El
e
c
tro
n
ics
Co
n
fer
e
n
c
e
a
n
d
Exp
o
siti
o
n
,
2
0
0
7
,
p
p
.
1
1
0
9
-
1
1
1
5
,
d
o
i:
1
0
.
1
1
0
9
/AP
EX.
2
0
0
7
.
3
5
7
6
5
4
.
[1
1
]
D.
V.
Bra
m
h
a
n
a
id
u
,
A.
S
re
e
n
i
v
a
su
lu
,
“
Im
p
lem
e
n
tatio
n
o
f
S
p
a
c
e
Ve
c
to
r
P
u
lse
Wi
d
t
h
M
o
d
u
lat
io
n
Tec
h
n
i
q
u
e
o
n
Th
re
e
P
h
a
se
Two
Lev
e
l
In
v
e
rter,
”
IOS
R
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
,
v
o
l.
1
2
,
n
o
.
3
,
p
p
.
1
4
-
2
4
,
2
0
1
7
,
d
o
i:
1
0
.
9
7
9
0
/1
6
7
6
-
1
2
0
3
0
2
1
4
2
4
.
[1
2
]
M
.
Esa
,
M
.
Ab
d
u
l
,
M
.
Na
wa
z
,
“
THD
a
n
a
ly
sis
o
f
S
P
WM
&
THP
WM
c
o
n
tro
ll
e
d
th
re
e
p
h
a
se
v
o
lt
a
g
e
so
u
rc
e
in
v
e
rter,”
In
ter
n
a
ti
o
n
a
l
Res
e
a
rc
h
J
o
u
rn
a
l
o
f
En
g
in
e
e
rin
g
a
n
d
T
e
c
h
n
o
l
o
g
y
,
v
o
l
.
4
,
n
o
.
1
0
,
p
p
.
3
9
1
-
3
9
8
,
2
0
1
7
,
[On
li
n
e
].
A
v
a
il
a
b
le:
h
tt
p
s://
irj
e
t.
n
e
t/
v
o
l
u
m
e
4
-
issu
e
1
0
.
[1
3
]
J.
Ro
d
rig
u
e
z
,
S
.
Ko
u
ro
,
J.
Re
b
o
ll
e
d
o
,
J.
P
o
n
tt
,
“
A
Re
d
u
c
e
d
S
witc
h
in
g
F
re
q
u
e
n
c
y
M
o
d
u
latio
n
Alg
o
rit
h
m
fo
r
Hig
h
P
o
we
r
M
u
lt
i
lev
e
l
I
n
v
e
rters
,
”
I
E
EE
3
6
t
h
Po
we
r
El
e
c
tro
n
ics
S
p
e
c
ia
li
sts
Co
n
fer
e
n
c
e
,
2
0
0
5
,
p
p
.
8
6
7
-
8
7
2
,
d
o
i:
1
0
.
1
1
0
9
/
P
ES
C.
2
0
0
5
.
1
5
8
1
7
2
9
[1
4
]
P
.
S
.
S
h
e
te,
“
P
e
rfo
rm
a
n
c
e
o
f
S
in
u
so
id
a
l
P
u
lse
W
id
t
h
M
o
d
u
lati
o
n
b
a
se
d
T
h
re
e
P
h
a
se
In
v
e
rter,
”
In
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
o
n
Eme
rg
in
g
Fr
o
n
t
ier
s in
T
e
c
h
n
o
l
o
g
y
f
o
r R
u
r
a
l
Are
a
,
2
0
1
2
,
p
p
.
2
2
-
2
6
.
[1
5
]
G
.
An
n
a
p
u
rn
a
,
G
.
Tu
las
iram
d
a
s,
“
S
imu
latio
n
a
n
d
c
o
m
p
a
riso
n
o
f
S
P
W
M
a
n
d
S
VPW
M
c
o
n
tr
o
l
fo
r
two
le
v
e
l
UPQC,
”
J
o
u
rn
a
l
o
f
T
h
e
o
re
ti
c
a
l
a
n
d
A
p
p
li
e
d
I
n
fo
rm
a
ti
o
n
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
7
8
,
n
o
.
1
,
p
p
.
2
4
-
3
3
,
2
0
1
5
.
[1
6
]
H.
K.
Kim
,
S
.
I.
Ao
,
M
.
A.
Am
o
u
z
e
g
a
r,
“
Tran
sa
c
ti
o
n
s
o
n
e
n
g
i
n
e
e
rin
g
tec
h
n
o
l
o
g
ies
:
S
p
e
c
ial
issu
e
o
f
th
e
w
o
rld
c
o
n
g
re
ss
o
n
e
n
g
in
e
e
ri
n
g
a
n
d
c
o
m
p
u
ter sc
ien
c
e
,”
S
p
rin
g
e
r S
c
ien
c
e
&
Bu
sin
e
ss
M
e
d
ia
,
2
0
1
3
.
2
0
1
4
.
[1
7
]
K.
B.
Na
g
a
sa
i,
T.
R.
Jy
o
th
sn
a
,
“
Ha
rm
o
n
ic
An
a
ly
sis
a
n
d
Ap
p
l
ica
ti
o
n
o
f
P
WM
Tec
h
n
iq
u
e
s
fo
r
Th
re
e
P
h
a
se
In
v
e
rter,”
In
ter
n
a
ti
o
n
a
l
Res
e
a
rc
h
J
o
u
rn
a
l
o
f
E
n
g
i
n
e
e
rin
g
a
n
d
T
e
c
h
n
o
l
o
g
y
,
p
p
.
1
2
2
8
-
1
2
3
3
,
2
0
1
6
.
[1
8
]
B.
Tan
,
Z.
G
u
,
K.
S
h
e
n
,
X.
Din
g
,
“
Th
ird
Ha
rm
o
n
ic
I
n
jec
ti
o
n
S
P
W
M
M
e
th
o
d
Ba
se
d
o
n
Altern
a
ti
n
g
Ca
rrier
P
o
larity
to
S
u
p
p
re
ss
th
e
Co
m
m
o
n
M
o
d
e
Vo
l
tag
e
,
”
IEE
E
Acc
e
ss
,
v
o
l.
7
,
p
p
.
9
8
0
5
-
9
8
1
6
,
2
0
1
9
,
d
o
i:
1
0
.
1
1
0
9
/ACCE
S
S
.
2
0
1
8
.
2
8
9
0
0
1
4
.
[1
9
]
V.
Dy
g
a
lo
,
E.
S
a
ly
k
in
,
V.
Ko
t
o
v
,
“
M
e
th
o
d
s
o
f
De
v
e
lo
p
m
e
n
t
a
n
d
A
d
a
p
tatio
n
o
f
En
g
i
n
e
e
rin
g
M
icro
p
r
o
c
e
ss
o
r
En
g
in
e
Co
n
tr
o
l
U
n
it
in
Re
a
l
Ti
m
e
t
o
En
s
u
re
th
e
P
o
ss
ib
il
it
y
o
f
Re
se
a
rc
h
Wo
rk
i
n
Va
rio
u
s
M
o
d
e
s,”
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
I
n
d
u
stria
l
En
g
in
e
e
rin
g
,
Ap
p
li
c
a
ti
o
n
s
a
n
d
M
a
n
u
fa
c
t
u
rin
g
ICIEA
M
,
2
0
1
9
,
p
p
.
1
-
6
,
d
o
i:
1
0
.
1
1
0
9
/ICI
EAM
.
2
0
1
9
.
8
7
4
3
0
5
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.