In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
Vol.
10, No.
1, Mar
ch 2019,
pp.
58~65
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
5
9
1
/ij
ped
s
.
v10
.
i
1.pp
5
8
-6
5
58
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Coupled random PWM
tech
ni
q
u
e for dual inverter fed
induction m
otor drive
S
y
ed
Mu
n
var
A
li
1
,
V.
Vijaya Kumar Red
d
y
2
,
M
.
S
u
r
ya
Ka
la
v
a
t
h
i
3
1,
2
Ins
t
i
t
u
t
e of
S
cience
and
Techn
o
l
ogy
, In
di
a
3
E.E
.
E. Dep
artment
,
J
N
T
UH
,
India
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Jun 12,
2018
Re
vise
d S
e
p 24,
201
8
A
c
c
e
pte
d
N
ov 2,
201
8
Du
al
i
nv
erter
f
e
d
i
ndu
cti
o
n
m
o
tor
driv
es
p
rov
i
de
m
ore
adv
a
ntag
e
s
in
c
ontrast
with
o
t
h
er
m
ulti
level inverter d
riv
e
s. Cou
pled
PWM
techn
i
q
u
es p
ro
vid
e
g
ood
st
and
a
rd
o
f
outp
u
t
voltag
e
t
han
the
decou
p
l
e
d
PW
M
tech
niq
u
es
f
o
r
dual
invert
er
c
onfi
guration.
I
n
this
p
aper
a
n
a
ly
sis
o
f
o
pen
-
en
d
w
i
n
d
in
g
i
n
d
u
cti
on
m
o
t
o
r
by
cou
p
l
e
d
ran
d
o
m
P
WM
s
i
gnals
a
nd
d
eco
up
led
S
V
PW
M
si
gn
als
w
a
s
carried
o
u
t
.
In
du
cti
o
n
m
o
t
o
r
b
y
r
an
do
m
PWM
t
echn
i
qu
e
generate
l
ow
acou
s
t
i
c
noise
a
nd
e
l
ectrom
a
g
n
eti
c
i
n
t
erf
e
ren
ce
t
o
n
ear
b
y
s
y
st
ems.
T
h
e
perf
o
r
man
ce
ev
a
l
uatio
n
o
f
t
he
d
rive
w
s
s
i
m
p
l
e
m
e
nted
i
n
M
A
TLAB/
s
i
m
uli
nk
an
d the resul
t
s
were p
resen
t
e
d
.
K
eyw
ord
s
:
Co
upl
e
d
PWM
Deco
up
l
e
d
SVPW
M
Dual i
nve
r
t
er
Ind
u
ct
i
on m
o
to
r
Vect
o
r
co
n
t
r
ol
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
S
y
ed
M
unv
a
r
A
l
i
,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
a
n
d
El
ect
ro
ni
c
s
Eng
in
e
e
ring
,
N
.
B.K
.
R. Inst
i
t
u
te o
f S
c
ience
a
nd Tec
h
n
o
lo
g
y
,
Vid
y
aNaga
r
,
And
h
ra
Pr
a
desh,
India.
Em
ail:
sye
d
mu
nva
ra
li
@gma
i
l
.
c
om
1.
I
N
TR
OD
U
C
TI
O
N
Wit
h
t
he
p
ro
gr
ess
in
t
e
c
h
n
o
l
ogy
elec
tric
d
r
i
ve
s
a
r
e
attai
n
ing
i
mport
a
nce
in
e
le
c
t
rica
l
v
e
hic
l
es.
O
n
ac
cou
n
t
o
f
l
i
t
t
l
e
m
ain
t
ena
n
c
e
and
l
o
w
wei
g
ht
t
o
vo
lum
e
r
atio
I
n
du
ct
io
n
mo
t
o
r
f
e
d
A
C
d
riv
e
s
a
r
e
pop
ul
ar
w
h
en
c
om
pare
d
w
i
t
h
D
C
m
o
tor
dr
ive
s
[
1]
.
To
i
ncre
ase
t
h
e
dy
na
mic
r
espo
nse
o
f
t
he
se
d
r
i
ve
s
for
ele
c
t
rica
l
v
e
hi
cl
e
a
ppl
i
cat
ion
s
d
e
c
ou
pl
ed
f
l
u
x
c
ont
ro
l
me
t
h
od
s
l
i
k
e
ve
ct
o
r
c
o
n
t
ro
l
a
n
d
di
r
e
c
t
t
orq
u
e
m
etho
ds
a
re
u
se
d
[
2
]-[
4
].
T
ho
ugh
v
e
c
to
r
c
ont
rol
i
n
v
o
lve
s
m
uc
h
o
f
tra
nsform
atio
ns
but it g
i
ve
s low
s
t
ea
dy
s
ta
te ri
p
p
l
e
.
H
enc
e
in
th
i
s
p
a
p
er
f
oc
us
i
s
give
n o
n
v
e
c
tor
co
ntro
l
l
e
d
in
d
u
ct
ion
mo
tor
(IM)
drives
[5].
Re
gu
lar
tw
o-
le
vel
i
nver
t
e
r
f
e
d
v
ec
tor
co
ntr
o
l
l
e
d
I
M
dri
v
e
s
g
e
n
e
rat
e
poor
q
u
a
l
i
ty
o
f
out
put
v
o
l
t
a
g
e
,
hi
gh
c
o
mm
on
m
ode
v
o
l
t
a
ge
(
CMV
)
a
nd
m
o
r
e
o
v
er
t
he
y
a
r
e
sui
t
ab
le
f
or
l
ow
p
ower
a
ppli
cations
[
6]-[10
]
.
Mu
lt
ile
ve
l
in
v
e
r
t
e
r
f
ed
I
M
dri
v
es
a
re
p
ossi
ble
so
l
u
ti
on
f
or
h
i
g
h
p
o
w
e
r
a
p
p
lic
a
t
i
ons.
D
i
ffer
ent
m
u
lti
le
ve
l
in
verter
c
on
fig
u
rat
i
o
n
s
l
i
ke
H
-
b
ridge
,
c
a
pac
itor
c
l
a
m
pe
d,di
ode
cla
m
pe
d
m
u
lti
le
ve
l
i
nve
r
t
e
s
a
n
d
dua
l
inve
r
t
er
con
f
ig
ura
tio
ns
a
re
d
isc
u
sse
d
i
n
l
i
t
er
at
ure
for
go
o
d
q
ua
l
ity
o
f
out
put
volt
a
ge
a
n
d
lo
w
C
M
V
[
1
1
]
-[
1
4
]
.
Amo
ng
t
h
ese
mu
ltil
ev
el
i
nv
ert
e
r
co
nf
ig
u
r
a
t
ion
s
d
u
a
l
i
n
v
e
rt
er
f
e
d
ope
n
e
nd
I
M
d
rive
o
ffer
s
m
a
ny
a
dva
n
t
a
g
e
s
l
i
k
e
fre
e
from
c
apa
c
i
t
or
bala
n
c
i
n
g
i
ssue
s
,
sim
p
l
e
desi
g
n a
nd o
p
er
at
io
n
[1
5].
Di
ff
e
r
e
n
t
P
W
M
t
e
c
hni
qu
e
s
a
re
e
mp
lo
ye
d
for
t
h
e
c
o
n
t
ro
l
of
d
ual
i
nverter
f
e
d
I
M
d
rive
[
16]
-[
18].
A
ll
the
s
e
P
W
M
t
e
c
hni
que
s
a
r
e
class
i
fie
d
a
nd
ca
n
be
p
er
form
ed
b
a
s
e
d
on
s
ca
l
a
r
c
a
rrie
r
a
n
d
s
pa
ce
v
ec
to
r
appr
oa
ches.
S
p
ac
e
vec
t
or
b
a
s
ed
P
W
M
t
ec
hn
i
q
ue
s
pr
ov
i
d
e
f
r
ee
dom
i
n
se
le
cti
n
g
vol
ta
ge
v
e
c
tors
[
19]-
[
20
].
A
s
the
P
W
M
t
e
c
h
ni
q
u
es
a
r
e
i
mp
lem
e
nt
e
d
a
t
high
sw
i
t
ch
i
ng
fre
que
ncy,
h
igh
a
m
oun
t
of
h
a
r
m
o
nic
s
a
re
obs
e
r
ved
in
h
a
r
m
o
n
i
c
spe
c
tr
um
o
f
o
u
tp
u
t
v
olta
ge
a
nd
c
u
rr
ents
a
t
m
u
ltip
le
s
of
s
w
itc
h
i
ng
freq
u
enc
y
.
Th
is
c
ause
s
ac
oust
i
c
n
o
i
s
e
and
m
a
y
a
l
s
o
c
ause
i
nterfere
n
ce
t
o
t
he
n
ear
b
y
s
y
st
e
m
s.
T
o
o
v
e
rc
o
m
e
t
h
ese
p
r
obl
ems
di
ff
eren
t
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
C
oup
led ra
n
dom
PWM techn
i
que for d
u
a
l
in
v
e
rter
fe
d in
du
c
tio
n m
o
tor dri
v
e
(
S
yed Munv
ar
Al
i)
59
rand
om
P
WM te
c
h
n
i
q
u
e
s
w
e
r
e ide
n
tif
i
e
d for
the
inve
rters.
In t
h
i
s pa
per co
ns
tan
t
sw
i
tc
hi
n
g
fr
e
q
u
e
n
c
y
ra
n
d
o
m
P
W
M
tec
h
n
i
qu
e
i
s
i
m
p
lem
e
n
t
ed
f
or
v
ect
or
c
on
tro
l
l
e
d d
u
a
l
i
nve
r
t
e
r
f
e
d
IM drive.
2.
FIELD ORIENT
E
D
CO
NTROL
OF DU
A
L INVERTE
R
C
ONFIG
U
R
A
T
I
ON
S
e
pa
ratel
y
e
xc
ite
d
D
C
m
o
t
ors
have
f
a
s
t
t
r
ans
i
en
t
re
spon
s
e
b
ec
au
se
o
f
i
nde
pe
nde
n
t
c
o
n
tr
ol
o
f
bot
h
tor
que
a
n
d
f
lu
x
b
y
a
rm
ature
c
u
rre
nt
a
nd
fi
l
e
d
curr
en
t.
B
u
t
t
he
s
e
moto
rs
h
a
v
e
hi
gh
w
ei
g
h
t
t
o
v
o
l
u
m
e
ra
t
i
o
a
nd
als
o
r
equ
i
re
f
r
e
que
n
t
m
a
i
nte
n
a
n
ce
.
On
t
he
o
t
h
er
s
i
d
e
i
n
d
u
c
t
i
o
n
m
o
tor
dr
iv
es
h
ave
l
o
w
w
e
ig
h
t
t
o
vo
lum
e
r
a
t
i
o
and
does
no
t
r
e
qu
ire
fr
eque
nt
m
ai
nt
e
n
a
n
c
e
but
h
a
v
e
poor
t
r
a
nsie
n
t
r
espo
nse.
T
o
i
n
cre
a
se
t
he
t
ra
nsie
nt
perform
ance
o
f
t
h
e
i
n
duc
t
i
o
n
m
otor
d
ri
ve
i
nde
p
e
nde
n
t
c
o
n
tr
ol
o
f
t
or
que
a
nd
fl
u
x
c
o
n
tr
ol
m
e
t
hod
ne
e
d
t
o
b
e
in
t
r
od
uc
ed
by
us
i
n
g
vec
t
or
c
o
n
tr
ol tec
h
n
iq
ue
.
I
n
v
ec
tor
co
nt
rol
o
f
i
n
duc
t
i
o
n
m
o
tor
dri
v
e
to
g
e
n
era
t
e
i
nde
pe
nd
e
n
t
t
o
rque
a
n
d
f
lux
compo
n
e
n
ts
st
a
t
or
c
urre
n
t
is resol
v
e
d
in d
-
a
x
i
s
c
urre
nt
c
om
po
ne
nt
(
I
ds
)
a
n
d
q-a
x
is curr
e
nt
c
omp
o
n
en
t
(I
qs
)
and
rotor
f
l
ux i
s
t
o
b
e
re
so
lv
ed
a
s
d
-
ax
i
s
f
lux
c
o
mp
on
e
n
t
(
dr
)
and
q-a
x
i
s
f
lu
x
com
p
o
n
e
n
t
(
qr
).
T
he
e
l
e
c
t
rom
a
gne
t
i
c
t
o
rq
ue
expre
ssi
on
i
n
t
he
f
orm
of
d
-q
qua
dra
n
t
s
o
f
a
n
i
n
d
u
c
t
i
on
m
o
t
o
r
c
an
b
e
exp
r
esse
d
a
s
i
n
(1
).
B
l
o
ck
d
i
a
gra
m
o
f
vec
t
or
con
tro
l
l
e
d dua
l
i
n
v
e
r
t
e
r
f
e
d
open
en
d w
i
n
d
i
n
g in
d
u
ct
ion
m
o
t
o
r
driv
e
as show
n
i
n
F
igure
1.
F
i
gure
1.
B
l
o
c
k
d
i
a
gram
of vec
t
or
c
o
n
t
r
ol
le
d
dua
l i
nver
t
e
r
fed
o
p
e
n
end
w
i
nd
in
g i
n
d
u
c
t
io
n m
o
tor dri
v
e
ds
qr
qs
dr
r
m
e
i
i
L
L
P
T
2
2
3
(1
)
In
s
e
p
arat
e
l
y
ex
c
i
t
e
d
DC
m
o
t
o
r
d
ri
ve
b
ot
h
t
h
e
cu
rre
n
t
co
mp
on
en
t
s
(
t
or
que
a
nd
f
l
u
x
c
o
n
t
ro
l
l
i
n
g
curr
ent
c
o
mp
o
n
e
n
ts)
w
i
ll
be
i
n
ort
h
og
o
n
al
a
nd
w
i
ll
be
i
n
D
C
qua
n
t
i
t
i
es
.
H
e
nc
e
i
n
d
u
c
tio
n
mo
t
o
r
q
u
a
n
t
itie
s
expre
s
se
d
i
n
s
ync
hro
n
ous
r
e
f
ere
n
ce
f
r
a
m
e
w
i
l
l
a
ppea
r
i
n
D
C
f
orm
a
nd
b
o
t
h
a
r
e
ma
de
t
o
be
i
n
ort
h
o
g
o
n
a
l
.
Whe
n
t
he r
otor
flu
x is a
l
i
g
n
e
d
t
o sy
nchro
n
o
u
s
r
efe
r
enc
e
fra
m
e
r
otor
q
-ax
i
s
flu
x
qr
= 0
bec
o
m
e
s
ze
ro.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
58
–
65
60
H
e
nc
e
t
h
e
t
o
r
q
ue
e
xpr
e
ssi
on
c
a
n
be
m
odi
f
i
e
d
a
s
in
(
2)
ds
m
r
qs
r
r
m
I
L
i
L
L
P
T
whe
r
e
)
(
2
2
3
(2
)
F
r
om
(
2)
it
i
s
obse
r
ve
d
t
h
a
t
b
y
co
n
t
r
o
ll
ing
I
ds
f
l
u
x
c
a
n
b
e
c
o
ntr
o
lle
d
a
n
d
by
c
on
tr
o
l
l
i
n
g
I
qs
tor
que
c
a
n
b
e
c
o
n
t
r
oll
e
d
.
Hen
ce
i
nd
ep
end
e
nt
con
t
r
o
l
o
f
t
o
r
q
u
e
and
f
lux ca
n
b
e
a
c
hie
v
e
d
i
n
vec
t
or
c
on
tr
o
lle
d
I
M
d
r
i
v
e
.
For
the
r
e
fe
renc
e
fram
e
t
r
a
nsform
ati
o
n
p
h
ase
an
g
l
e
(θ
s
)
nee
d
t
o
be
e
st
i
m
ate
d
.
Bas
ed
o
n
t
h
e
e
s
tim
ati
on
of
t
hi
s
pha
se
a
ng
le
v
e
c
t
or
c
o
n
tr
ol
t
e
c
h
n
i
q
u
es
a
r
e
d
i
vide
d
i
n
to
t
w
o
t
y
p
es
a
s
d
i
r
e
c
t
v
ec
tor
con
t
r
o
l
an
d
i
ndi
r
e
c
t
v
e
c
t
o
r
c
on
t
r
o
l
.
I
n
d
i
r
ect
v
ect
o
r
m
e
t
hod
θ
s
i
s
ge
ner
a
te
d
u
s
i
ng
ha
ll
s
e
n
sor
a
n
d
in
i
n
d
ir
e
c
t
v
e
c
t
o
r
c
o
n
t
r
o
l
it
i
s
cal
c
u
l
a
t
e
d from
rot
o
r pos
i
tio
n
ang
l
e
an
d sl
ip a
s
i
n
(
3
)
.
s
sl
r
sl
r
s
dt
)
(
(
3
)
The
b
l
ock
dia
g
r
a
m
of
t
he
d
ua
l
i
nver
t
e
r
f
e
d
I
M
dr
ive
is
s
h
o
w
n
in
F
i
gur
e.
1
.
I
n
F
i
gur
e.
1
r
e
fe
r
e
nc
e
I
*
ds
a
nd
I
*
qs
a
r
e
c
al
cula
te
d
fr
om
t
he
s
pee
d
a
nd
fl
ux
c
o
ntr
o
l
l
er
s.
T
he
se
a
r
e
com
p
a
r
e
d
w
i
t
h
ac
t
u
al
I
ds
a
n
d
I
qs
.
I
ds
a
nd
I
qs
a
r
e
o
b
t
ai
ne
d
fr
om
t
he
a
c
t
ua
l
t
h
r
e
e
p
h
a
s
e
c
u
r
r
e
nts,
w
hic
h
a
r
e
t
he
n
tr
a
n
sf
or
m
e
d
in
t
o
sy
nc
hr
on
o
u
s
r
e
fe
r
e
nc
e
f
r
a
m
e
.
The
cur
r
e
nt
e
r
r
or
c
omm
a
nd
gener
a
tes
i
n
pu
t
r
e
f
e
r
e
nce
sig
n
a
l
s
f
o
r
P
W
M.
I
n
P
W
M
b
l
o
c
k
d
i
f
f
e
r
en
t
c
o
u
p
le
d
P
W
M
tec
h
niq
u
es
c
a
n
b
e
i
m
plem
en
t
e
d
for
dua
l
i
n
v
e
r
t
e
r
c
on
f
i
g
u
r
a
ti
o
n
a
s
i
n
s
ect
i
on
3.
3.
COUPLE
D
PWM
T
E
CHNIQ
U
E FO
R
D
UAL INVER
T
E
R
C
ONFIG
U
R
A
T
I
ON
T
o
g
en
e
r
at
e
sp
ac
e
v
ecto
r
P
WM
p
u
l
s
e
s
fo
r
du
al
i
nv
e
r
t
e
r
t
w
o
ap
p
r
o
a
c
h
e
s
a
r
e
g
e
n
e
r
a
l
l
y
f
o
l
l
o
w
e
d
.
O
n
e
w
a
y
i
s
t
o
d
i
r
e
c
t
l
y
s
yn
the
s
i
z
e
pu
lses
f
or
t
w
o
i
n
v
er
te
r
s
i
n
a
d
e
c
ou
p
l
ed
m
an
n
e
r
i
n
w
hi
c
h
t
he
s
pa
ce
p
la
ne
o
f
th
e
two
inve
r
t
ers
form
s
a
c
o
n
v
e
n
t
i
ona
l
two
le
ve
l
sp
ace
p
la
n
e
e
ach
w
it
h
8
p
o
ss
ib
le
s
w
i
t
c
hi
n
g
s
ta
tes.
S
o
6
4
sw
itc
h
i
n
g
s
ta
t
e
c
om
bina
ti
on
s
a
r
e
possi
ble
to
s
y
n
t
hes
i
ze
r
e
qui
r
e
d
v
o
l
t
a
ge
f
or
t
h
e
i
n
duc
t
i
o
n
m
otor
.
I
n
t
he
se
co
nd
a
p
pr
oa
ch,
P
W
M
puls
e
s ar
e
syn
t
hesi
ze
d
tr
ea
tin
g b
o
t
h
i
nver
ter
s
i
n a cou
p
l
ed m
a
n
ner.
T
ha
t is, swi
t
c
h
in
g
pu
ls
es
f
or
t
he
t
w
o
in
v
er
te
r
s
ar
e
s
y
n
t
he
s
i
z
e
d
f
r
o
m
thr
e
e
le
ve
l
p
ul
se
s.
A
t
ot
al
o
f
27
s
w
i
t
c
hi
ng
s
t
a
t
e
s
a
r
e
p
o
ssib
l
e
to
g
e
n
er
a
t
e
thr
e
e
l
e
ve
l
o
u
t
p
ut
v
o
l
t
a
ge.
T
h
e
27
sw
i
t
ch
i
ng
s
t
ate
s
o
f
a
t
h
r
e
e-
leve
l
i
nve
r
t
e
r
i
n
a
d-
q
ax
is
s
pac
e
ve
ct
or
p
l
a
ne
a
r
e
s
h
o
w
n
i
n
F
i
g
u
r
e
2
.
The
sw
i
t
c
h
i
n
g
s
t
a
t
e
s
o
f
i
n
v
erter
fo
r
g
e
n
e
rating
a
ref
e
r
e
n
c
e
vo
ltag
e
V
re
f
in
a
n
i
ns
tan
t
a
n
eo
us
f
a
s
hi
o
n
u
si
n
g
n
ea
r
e
st
v
o
l
ta
ge
v
e
c
t
or
s
in
a
ll
t
h
e
s
i
x
s
e
c
t
o
r
s
a
r
e
t
o
b
e
s
y
n
t
h
e
s
i
z
e
d
b
a
s
e
d
o
n
a
n
a
l
g
o
r
i
t
h
m
.
T
he
s
a
lie
nt
f
ea
tur
e
s
o
f
s
pace
v
ec
tor
a
l
gor
it
hm
a
r
e
i
)
st
a
r
tin
g
an
d
e
ndi
ng
s
t
a
te
i
n
ev
e
r
y
sa
m
p
l
i
n
g
pe
r
i
od
m
u
st
b
e
sa
me,
i
i
)
not
m
or
e
t
h
a
n
o
ne
s
ta
te
s
ho
u
l
d
c
h
ange
du
ring
e
very
st
a
t
e
t
ra
n
s
iti
on
.
Ther
e
ar
e
di
ff
er
e
n
t
w
a
ys
t
o
sy
nthe
siz
e
th
e
ne
ar
e
s
t
sw
i
t
c
hi
n
g
s
t
at
e
s
.
In
t
h
e
p
re
se
nt
m
et
h
od
th
e
switc
h
i
n
g
s
t
a
te
s
for
the
tw
o
i
nver
t
e
r
s
ar
e
sy
nt
hes
i
z
e
d
from
thr
e
e
l
e
v
e
l
s
w
i
tc
h
i
n
g
s
ta
tes
i
n
a
c
oup
le
d
fa
sh
io
n.
The
a
p
pr
oac
h
r
e
duces
t
he
i
nhe
r
e
nt
c
omp
l
e
x
i
t
y
i
n
v
o
l
ved
i
n
s
e
l
ec
t
in
g
the
t
h
re
e
le
vel
sw
i
t
c
h
i
n
g
st
a
t
e
s
b
y
sh
ifti
n
g
t
he
V
re
f
i
nt
o
a
n
a
ppr
o
p
r
i
a
t
e
tw
o-
le
ve
l
s
u
b
he
xa
go
n.
T
he
r
e
a
r
e
s
i
x
o
u
t
e
r
s
ub
he
xa
go
ns
w
i
t
h
ce
n
t
r
e
s
as
V
7
,
V
8
,
.
....
.
.
.,
V
12
(
H
1
, H
2
,...
.
.
.
,
H
6
)
and
one
i
nner
su
b
hexa
g
on
w
i
th
c
e
n
tr
e
V
0
(
H
0
).
F
i
gur
e
2.
S
w
i
t
c
hin
g
s
t
a
t
e
s
a
nd
their
spa
ce
ve
c
t
or
l
ocat
i
o
n
s
o
f
a
cou
p
l
ed i
n
v
er
t
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
C
oup
led ra
n
dom
PWM techn
i
que for d
u
a
l
in
v
e
rter
fe
d in
du
c
tio
n m
o
tor dri
v
e
(
S
yed Munv
ar
Al
i)
61
Th
e
p
r
o
c
e
s
s
of
s
y
n
th
e
s
i
z
ing
th
e
swit
chi
n
g
s
t
a
t
es
o
f
t
h
e
t
w
o
inv
e
r
t
e
rs
i
s
as
f
oll
o
ws
.
Du
e
t
o
t
h
e
symm
etry
o
f
a
l
l
s
u
b
hexa
g
ons
t
he
s
a
m
e
e
x
p
l
ana
t
ion
is
v
al
i
d
f
or
V
ref
l
o
cate
d
i
n
a
n
y
of
t
he
o
u
t
e
r
s
ub
h
exa
g
on
s.
I
t
i
s
a
s
s
u
m
e
d
t
h
a
t
t
h
e
t
i
p
o
f
t
h
e
V
re
f
lies
in
s
e
c
t
o
r-1
o
f
H
1
.
The
s
u
b
he
x
a
go
n
i
n
w
h
i
c
h
V
re
f
lies
is
i
de
nt
i
f
ie
d
f
r
o
m
d
-
q
a
x
i
s
c
o
m
p
o
n
e
n
t
s
(
V
d
,
V
q
)
of
V
Re
f
u
s
i
n
g
(
4
)
.
H
e
r
e
α
i
s
t
h
e
a
n
g
l
e
m
a
d
e
b
y
V
ref
w
i
t
h
r
e
s
p
e
c
t
t
o
d
-
a
x
i
s
.
O
n
ce
t
he
s
u
b
h
exa
g
o
n
i
s
i
d
e
n
tif
i
e
d,
t
he
t
ai
l
o
f
t
he
V
ref
i
s
s
h
ifte
d
from
V
0
t
o
V
7
.
The
s
h
ift
e
d
or
n
ew
r
efe
r
enc
e
vec
t
or
V
re
f
,,n
d
e
f
i
n
e
d
b
y
(
5
)
i
s
d
e
c
o
m
p
o
s
e
d
i
n
t
o
i
t
s
d
i
r
e
c
t
a
n
d
q
u
a
d
r
a
t
u
r
e
a
x
is
c
omp
one
nt
s
(
V
dn
,
V
qn
).
N
ow
sect
or
i
de
n
tif
i
c
atio
n
i
s
d
o
n
e
i
n
a
s
imi
l
ar
w
ay
a
s
d
one
f
or
i
de
n
t
i
fy
in
g
t
h
e
sub
he
xa
g
on.
K
now
i
ng
the
s
e
c
t
or,
sub
he
xa
go
n
t
h
e
op
t
i
ma
l
sw
itc
hi
ng
s
tates
(f
or
a
g
i
v
e
n
P
W
M
s
e
q
ue
nce)
t
o
syn
t
hes
i
ze
t
he
r
e
f
er
ence
v
e
c
tor
i
n
an
a
ver
a
ge
s
w
itc
hi
ng
per
i
o
d
a
re
i
de
n
t
i
f
ie
d fr
o
m
t
he
lo
o
k
-u
p
Ta
b
le
1
.
1
(
4)
,
=
(
5)
I
n
c
on
ve
nti
ona
l sp
a
c
e
vec
t
or
P
WM
m
eth
o
d
, four
n
ea
rb
y
s
w
itc
hi
n
g
sta
t
es
gener
al
l
y
r
e
f
er
red as acti
v
e
st
a
t
e 1,
a
ctive state
2 an
d two zer
o states are
s
yn
t
h
es
ized ba
s
ed on t
h
e posi
t
i
o
n of the s
h
i
fted refere
n
ce vec
t
or
,
,
.
T
h
e
t
i
m
e
t
o
b
e
d
w
e
l
l
e
d
i
n
a
s
w
i
t
c
h
i
n
g
s
t
a
t
e
i
s
c
a
l
c
u
l
a
t
e
d
m
a
i
n
ta
i
n
i
n
g
the
pr
inc
i
ple
of
v
o
l
t
-
seco
nd
bala
nc
e
a
n
d
a
r
e
gi
ve
n
b
y
(
6)
,
(7)
a
nd
(8)
.
T
he
s
yn
t
h
es
is
o
f
t
h
e
s
w
i
t
c
h
i
n
g
s
t
a
t
e
s
f
o
r
t
h
e
t
w
o
i
n
v
e
r
t
e
r
s
f
r
o
m
t
h
re
e
l
e
v
e
l
inve
rt
e
r
s
wi
t
c
hi
ng
st
at
e
s
i
s
ex
pla
i
n
e
d
th
rou
g
h
Tabl
e
2
.
T
ab
le
2
s
h
o
ws
t
he
s
yn
t
h
es
is
o
f
co
up
le
d
P
W
M
p
ul
s
e
s
w
h
e
n
V
Ref
l
i
e
s
in
s
e
c
t
o
r
-
1
o
f
H
1
.
Tab
l
e
1.
S
ynth
e
sis
o
f
c
ou
p
l
ed
inver
t
e
r
sw
itc
hi
n
g
sta
tes
(swit
c
h
on-1,
of
f-0)
T
h
ree
Le
v
e
l
Inve
rte
r
S
witc
hing
sta
t
e
s
Sw
it
c
h
ing
sta
t
e
s
S
w
i
t
c
hing
sta
t
e
s
of
i
nve
rte
r
-I
o
f
inve
rte
r
-II
+
1
0
0
0
or
1
0
o
r
1
-
0
1
.
∗
(
6
)
.
∗
(
7
)
(
8)
Here
T
1
,
T
2
a
r
e
t
h
e
t
i
m
e
s
t
o
b
e
d
w
e
l
l
e
d
b
y
t
h
e
t
w
o
i
n
v
e
r
t
e
r
s
i
n
a
c
t
i
v
e
s
t
a
te
1
a
nd
2
re
s
p
ect
i
v
e
l
y
a
s
gi
ve
n
i
n
Tab
le 2. In
r
andom
P
W
M
g
e
n
era
t
i
o
n
t
h
e ze
ro-state
distr
i
b
u
t
ion fa
ctor
is
ra
nd
omly ge
n
era
t
ed. Th
e
ti
m
e
t
o
be
l
a
p
se
d
in
z
e
r
o
sta
t
e
1
(T
Z1
)
and
zero
s
t
a
t
e
2
(
T
Z2
)
i
s
d
ivi
d
e
d
i
n
t
h
e
ra
tio
o
f
1
a
m
o
n
g
tw
o
z
e
ro
s
tates
,
g
ive
n
i
n
(9)
and
(
10).
H
e
nc
e
i
s
the
time
to
b
e
dw
elle
d
by
the
tw
o
inve
r
t
e
r
s
in
z
e
r
o
state
1
an
d
ze
ro
s
ta
te
2
r
espect
i
v
el
y.
T
s
is
t
he
t
ime
perio
d
o
f
ha
l
f
t
h
e
sw
i
t
c
h
ing
cyc
l
e.
D
iv
is
io
n
o
f
z
e
r
o
sta
t
e
ti
m
e
s
gene
ra
te
n
um
erous
P
WM
m
e
t
h
ods.
F
o
r
inst
anc
e
,
c
o
n
v
en
t
i
ona
l
sp
ac
e
v
e
c
t
or
P
W
M
p
u
l
s
e
s
a
r
e
ge
nera
t
e
d
w
i
t
h
equa
l
d
i
v
i
s
i
on
of
zer
o sta
t
e
dur
ati
o
n
,
0
.5
.
(
9
)
1
(
1
0
)
Ta
b
l
e
2.
Ran
do
m
distri
bu
t
i
o
n
of
zer
o sta
t
e in
ve
rter
s
w
i
tc
hi
n
g
t
im
es
Swit
c
h
ing T
i
me
s
Th
r
ee
L
e
v
e
l
I
nve
r
t
e
r
S
w
i
t
c
hing
sta
t
e
s
S
w
i
t
c
hing
sta
t
e
s
S
w
i
t
c
h
ing
st
a
t
e
s
o
f
inve
r
t
e
r
-
I
o
f
inve
rte
r
-II
T
1
0
-1
-1
0
0
0
0
1
1
T
2
1
-1
-1
1
0
0
0
1
1
T
Z
1
-0
-
1
1
0
0
0
0 1
(1
-
T
Z
1
-0
-
0
1
0
0
0
0 0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
58
–
65
62
4.
RESULT
S
A
N
D
DISCU
SSIO
N
The
ana
l
ys
is
a
nd
s
i
mu
lat
i
on
of
c
ou
p
l
e
d
P
W
M
t
ec
hni
qu
e
for
vec
t
or
c
on
tro
l
led
dua
l
i
n
ve
rter
f
e
d
i
ndu
c
tio
n
moto
r
d
r
iv
e
wa
s
pe
rfo
rmed
i
n
MATLAB/
S
i
muli
nk
a
nd
r
e
s
u
lts
w
er
e
prese
n
te
d.
T
he
p
ara
m
e
t
ers
use
d
f
or
s
imu
l
a
t
i
on
st
ud
ies
are
inp
u
t
D
C
vo
ltage
o
f
60
0V
w
hic
h
i
s
s
h
a
red
as
300V
t
o
ea
c
h
i
nve
rt
e
r
,
I
nduc
ti
on
m
o
t
o
r
par
a
m
e
ters
a
r
e
R
s
=
1
.57
Ω
,
R
r
=
1
.
2
1
Ω
,
L
s
=0.17H
,
L
r
=0.
17H
,
L
m
=
0
.
1
6
5
H
,
J
=
0.
08
9
K
g
.
m
2
.
The
co
ntro
l
si
g
n
al
s of b
ot
h S
V
P
W
M
and R
P
W
M
ar
e
ge
n
era
t
e
d
w
it
h a
sw
i
t
c
hi
ng
f
re
qu
enc
y
o
f
3
k
H
z
.
The
t
r
ans
i
e
n
t
a
n
d
s
t
ea
d
y
s
ta
te
r
esu
lts
o
f
p
o
le
v
o
l
ta
ge
,
re
sulta
n
t
phase
v
o
l
tage,
C
M
V
,
t
hre
e
p
hase
c
u
rre
n
t
s,
s
pe
e
d
a
nd
t
o
rq
ue
w
i
t
h
S
V
P
W
M
an
d
Ra
nd
om
P
WM
a
t
a
refer
e
n
c
e
s
pee
d
o
f
1
2
00
RP
M
a
r
e
sh
ow
n
in
F
i
g
ure
3.
F
rom
the
re
s
u
lts
s
how
n
i
n
F
i
gur
e
4
it
is
p
e
r
ce
i
v
e
d
t
hat
ma
g
n
itu
de
o
f
vo
l
t
a
g
e
l
e
ve
ls
g
e
n
era
t
e
d
i
n
a
l
l
t
h
e
v
o
l
t
a
g
e
pl
o
t
s
is
s
a
m
e
w
i
t
h
b
ot
h
the
P
W
M
tec
hni
q
u
es.
Be
c
a
u
se
o
f
Ra
nd
om
P
W
M
t
e
c
h
n
i
que
onl
y
ch
a
n
g
e
i
n
p
u
l
s
e
po
si
ti
on
i
s
ob
serv
ed
.
He
n
ce
on
l
y
s
li
ght
c
h
a
ng
e
in
t
ot
al
h
a
r
mo
ni
c
d
i
st
o
r
ti
on
i
s
o
b
serv
e
d
w
h
e
r
e
a
s
S
VP
W
M
t
ech
n
i
q
u
e
gene
rate
m
ore
TH
D
at
n
earby
har
m
on
ics
of
s
w
itc
h
i
n
g
f
reque
nc
ies
b
o
t
h
i
n
vo
l
t
age
a
n
d
c
u
rr
ent
m
a
g
n
itude
s
tha
n
t
he
R
a
n
d
o
m
P
W
M
tec
h
niq
u
e
s
,
b
u
t
t
h
e
THD
at
o
th
er
h
a
r
mo
n
i
c
freque
nc
ies
m
a
y
i
n
cr
ease
or
d
ecr
ease.
B
ec
ause
o
f
re
d
u
c
tio
n
THD
a
t
n
ear
by
harm
on
ics
of
s
w
i
tc
hin
g
freque
nc
ies a
c
ous
tic
s
n
o
ise
a
n
d
elec
tro
n
i
c
m
a
gne
tic
i
nte
rfe
renc
e t
o
n
ea
rby
sy
st
ems al
s
o
d
e
c
re
as
es.
(i)
(ii)
F
i
gure
3a.
Res
u
l
t
s
o
f
dua
l
inv
e
rter
f
e
d
i
n
duc
t
i
o
n
m
ot
or
d
riv
e
w
ith coupl
e
d
P
W
M
tec
hnique,
S
V
PWM;
(i) stating transi
en
t
s
(i
i
) st
e
a
d
y
st
at
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Co
upl
e
d
rand
om PWM t
e
c
h
niq
u
e
fo
r dua
l
inv
e
rt
er f
e
d
i
nduct
i
on
mo
to
r d
r
iv
e (S
ye
d
Mu
n
v
a
r
Ali
)
63
(i
)
(
i
i
)
(b
)
F
i
g
u
r
e
3b.
Resul
ts
o
f
dua
l
i
n
v
e
r
t
er
f
e
d
i
n
duc
t
i
o
n
m
otor
d
r
i
v
e
w
i
t
h
c
ou
pl
ed
P
W
M
t
ech
niq
u
e
,
R
PW
M
;
(i) stati
n
g tra
n
sien
ts (
ii
)
stea
d
y
s
t
a
t
e
(i
)
(
i
i
)
F
i
gur
e
4a.
Res
ults
o
f
dua
l
inv
e
r
t
er
f
e
d
i
n
duc
t
i
o
n
m
ot
or
d
r
i
v
e
w
i
t
h
co
up
le
d
P
W
M
tec
h
n
i
qu
e
S
V
P
W
M
;
(
i
)
vol
t
a
ge
T
H
D
(
ii)
c
ur
r
e
nt
T
H
D
(i)
(
i
i
)
F
i
g
u
r
e
4b.
Resul
ts
o
f
dua
l
i
n
v
e
r
t
er
f
e
d
i
n
duc
t
i
o
n
m
otor
d
r
i
v
e
w
ith
cou
pled
P
W
M
t
ech
niq
u
e,
RPW
M;
(i
)
v
o
l
t
a
g
e
T
HD
(
i
i
)
c
u
rr
e
n
t
TH
D
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
58
–
65
64
5.
CONCL
U
S
ION
The
dua
l
i
n
ve
rter
f
e
d
i
nd
uc
ti
on
m
o
t
o
r
dri
v
es
o
f
f
er
s
m
a
ny
ad
va
nt
a
g
es
l
i
k
e
f
r
ee
f
ro
m
n
e
ut
ral
poin
t
fl
uc
tua
t
io
ns
a
n
d
c
apac
itor
ba
la
nci
n
g
i
s
s
u
es
w
hen
c
o
mpar
e
d
w
ith
o
t
her
mul
tile
ve
l
i
n
vert
e
r
t
op
o
l
o
g
i
es.
D
u
rin
g
fa
il
ure
o
f
a
ny
i
nve
rt
er
t
he
d
ual
i
n
verter
f
e
d
i
n
d
u
ct
i
o
n
m
o
tor
d
r
i
ve
o
pe
r
a
tes
w
i
th
r
e
duc
ed
o
u
t
p
u
t
v
olta
ge
.
More
ove
r,
t
he
v
ect
or
c
o
n
t
ro
l
t
e
ch
n
i
q
u
e
a
l
s
o
p
r
ovi
de
f
a
s
t
tra
n
s
i
en
t
resp
o
n
s
e
o
f
t
h
e
dri
v
e.
F
rom
the
re
su
l
t
s
it
i
s
in
ferr
ed
t
hat
w
i
t
h
t
he
c
ou
p
l
ed
r
andom
P
WM
t
e
c
h
n
i
que
s
for
dua
l
i
nve
r
t
er
f
ed
i
nd
uc
t
i
on
mot
o
r
dri
v
e
TH
D
at
nea
r
b
y
s
w
i
t
c
h
i
ng
fre
que
n
c
y
h
a
rm
onics
a
re
r
educe
d
.
T
h
i
s
l
eads
t
o
t
he
l
o
w
e
r
ing
in
a
co
u
s
t
i
c
no
ise
an
d
e
l
e
c
tr
o
ma
gnet
i
c i
n
ter
f
ere
n
ce
to nea
r
b
y
sys
tem
s
.
REFE
RENCES
[1]
F
.
B
l
a
schk
e
“T
h
e
p
rin
c
ipl
e
o
f
fiel
d
orien
t
atio
n
as
a
p
p
li
ed
t
o
t
h
e
n
ew
t
rans
vecto
r
c
l
o
sed
l
oop
c
o
n
t
r
ol
s
yst
e
m
f
o
r
rot
a
ti
ng-fi
eld m
achi
n
es,
"
S
i
em
ens Revi
e
w
, p
p 2
1
7
-
22
0, 1
97
2.
[2]
]
Has
i
f
A
z
iri
,
F
izat
ul
A
i
n
i
P
a
tako
r,
M
arizan
S
ulaim
a
n,
Z
ulh
i
sy
a
m
S
a
ll
eh
,
“
C
o
m
paris
o
n
P
e
rf
ormances
o
f
In
d
i
rect
F
i
el
d
Ori
e
n
t
ed
C
on
trol
f
or
T
h
r
ee-P
h
ase
In
duct
i
o
n
M
ot
or
D
ri
ves
”
,
Inter
nati
onal J
o
ur
nal
o
f
P
o
wer Elect
ro
n
i
cs
an
d
Dr
ive S
y
s
t
e
m
(
I
JPEDS)
,
vo
l.
8
,
n
o
.
4
,
p
p
.
1
682
–169
2,
201
7.
[3]
M
d
.
Ra
s
h
ed
ul
I
s
l
am
,
M
d
.
M
a
ru
fu
l
Islam
,
M
d
.
K
amal
H
o
s
s
a
in
,
Pi
ntu
K
um
ar
S
ad
h
u
,
“
P
e
rfo
rm
anc
e
A
nal
y
si
s
o
f
a
DT
C
and
S
V
M
Based
F
i
el
d-O
r
ient
ati
o
n
Co
n
t
ro
l
In
du
cti
on
M
o
t
o
r
Dri
v
e”,
International Journal
of
Power
El
ectro
n
i
cs
a
n
d
Dr
ive S
y
s
t
em
(
I
JPEDS)
,
v
o
l.
5
,
n
o
.
3
,
pp
.
3
3
6
–343,
2
0
1
5
.
[4]
S
a
ty
a
Naray
a
na,
P
.
S
urek
ha,
P
.
V
ij
aya
P
r
as
un
a,
“
A
New
F
O
C
Ap
pro
ach
o
f
In
duct
i
o
n
M
oto
r
D
rive
Usin
g
D
TC
S
t
r
a
t
e
g
y
f
o
r
t
h
e
M
i
n
i
m
i
z
a
t
i
o
n
o
f
C
M
V
”
,
Inter
nati
o
n
a
l Jo
ur
nal
o
f
P
o
wer
Elect
ronics
an
d Drive Sys
t
em
(
I
JPEDS)
,
v
o
l.
3
,
no
. 2
,
p
p
.
2
41
–2
50
, 20
1
3
.
[5]
J.
M
.
D
.
M
u
r
phy
an
d
M.
G
.
Egan,
“
A
c
o
m
pariso
n
o
f
P
WM
s
t
r
a
t
egi
e
s
f
or
i
nver
ter
f
e
d
induction
mot
o
r
s
,
”
IE
E
E
Tran
s. In
d
.
Ap
pl
.
,
vol.
IA
-19
,
n
o. 3
,
p
p.
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69
, M
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198
3.
[6]
J.
H
o
l
tz,
“
P
u
lse w
i
dthm
o
dulation—A
s
u
rv
ey,
”
I
E
E
E
Tran
s.
In
d. Ele
c
t
ro
n
.
,
vo
l
.
3
9
,
n
o
. 5
, p
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41
0
–4
20
,
Dec. 19
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2
.
[7]
A.
M
.
Hava,
R.
J
.
Kerkm
a
n
,
a
nd
T.
A
.
Lip
o
,
“A
h
i
gh
perf
orm
a
nc
e
g
e
neral
i
zed
d
is
con
t
in
uo
us
P
WM
a
lg
ori
t
hm
s,
”
IEEE
Trans. Ind
.
Appl
.
,
v
o
l.
34,
n
o.
5
,
p
p
.
105
9–10
71
,
M
ay
/
J
u
n
.
199
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[8]
E
.
R
.
C
.
D
a
S
i
l
v
a
,
E
.
C
.
D
o
s
S
a
n
t
o
s
,
a
n
d
C
.
B
.
J
a
c
o
b
i
n
a
,
“
P
u
l
s
e
w
idth
m
odulatio
n
strat
e
g
i
es,”
IE
E
E
Ind
.
E
l
ectro
n.
Mag
.
,
v
o
l
.
5
, no
. 2
,
p
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. 3
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45
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n
. 20
1
1
.
[9]
A.
M
.
Hav
a
a
nd
N
.
O.
C
e
t
i
n
,
“A
g
enerali
zed
s
calar
P
W
M
a
ppro
c
h
w
it
h
eas
y
im
pl
e
m
entatio
n
feat
ures
f
or
t
hree-
ph
ase t
h
ree w
i
re v
olt
a
ge s
ou
rce in
vert
ers,”
IEEE Trans. Power Elect
ron.
,
v
o
l
. 26
, n
o. 5
, p
p.
13
8
5
–
1
3
9
5
, May 2
01
1
.
[10]
K.
S
at
yanaray
a
na,
B.
A
n
j
an
eyu
l
u,
K
.
S
i
v
a
P
ras
a
d,
“
P
e
rf
orm
a
n
ce
I
mpro
ve
m
e
nt
o
f
Mu
l
t
i
Le
ve
l
Inv
e
rter
f
ed
V
ect
or
Controlled
Induction
Mo
t
o
r
Drive
f
o
r
L
o
w
S
p
ee
d
O
p
erat
ion
s
”,
Int
e
rn
atio
na
l
Jo
ur
na
l o
f
Po
wer El
ectro
n
i
cs and
Dr
ive S
y
s
t
e
m
(
I
JPEDS)
,
v
o
l
.
4
,
n
o
. 1
, p
p.
51
–
6
0
,
2
01
4.
[11]
J
o
s
é
R
o
d
r
í
g
u
e
z
,
J
i
h
-
S
h
e
n
g
L
a
i
, "
M
u
ltil
e
v
e
l
In
verters
:
A
S
urv
e
y
of
T
o
polo
g
i
e
s,
C
on
tro
l
s
,
a
n
d
A
p
p
l
i
cations
"
IEEE
T
r
a
n
s.
Ind.
E
l
e. ,
V
o
l
.
49,
No
.
4
, p
p
7
2
4
-
737
,
A
ug
20
02
.
[12]
S
.
K
ouro
,
M
.
Malin
owsk
i,
K
.
Gop
a
kum
ar,
J.
P
ou,
L
.
G.
F
ran
q
u
e
lo,
B
.
W
u
,
J
.
R
o
d
rig
u
ez,
M
.
A.
P
erez,
a
nd
J
.
I.
Leo
n
,
“
R
ecent
ad
van
ces
a
nd
i
nd
us
trial
app
l
ications
o
f
m
u
ltil
eve
l
co
nv
erters,
”
IE
EE
Tr
an
s.
Ind
.
Electr
on.
,
vol.
57
,
no
.
8
,
pp
.
2
5
5
3–258
0,
A
ug.
2
01
0
.
[13]
Y.
Z
h
a
ng
,
Z
.
Z
hao
,
a
nd
J.
Z
hu,
“
A
hy
bri
d
P
WM
app
l
i
e
d
to
h
ig
h
-
po
w
er
t
hree-l
e
vel
invert
er-fed
induction-m
o
t
o
r
dri
v
es,
”
I
EEE Trans.
Ind
.
Elect
ron.
,
v
o
l
. 58
,
n
o
. 8
,
p
p
. 34
0
9
–
3
4
2
0
, Aug
. 20
1
1
.
[14]
Grai
n
P
.
A
da
m
,
S
tep
h
en
J
.
Fi
nn
ey,
Ah
med
M.
M
as
sou
d
,
and
Barry
W
.
Wil
l
i
a
ms,
“
C
apacit
o
r
Balan
c
e
Iss
u
es
o
f
t
h
e
Di
ode-
Cl
amped
Multilevel
Inv
e
rter
O
perated
in
a
Q
uasi
T
wo-S
t
a
te
M
o
d
e”,
IEEE Tr
an
s.
on Inl
.
E
l
ectro
nic
s
,
Vol.
5
5
, No
. 8
,
Aug
u
st 2
00
8.
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H.
S
te
m
m
l
e
r
an
d
P.
G
ug
genb
ac
h,
“
Conf
igu
r
ati
o
n
s
o
f
hig
h
-p
ow
e
r
v
o
lt
age
so
urce
inv
e
rter
d
ri
ves,
”
i
n
Pr
oc.
5t
h Eur.
Conf.
P
o
wer E
l
e
c
tr
on. App
l
.
, Br
i
g
h
to
n,
U.
K
., p
p
.
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–
1
4
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r
1
99
3
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V.T.
S
o
m
asekhar,
S
riram
a
S
r
i
n
i
va
s
,
a
nd
K
om
muru
K
rant
i
Kumar
“Ef
f
ect
o
f
Ze
ro
-Vect
or
P
lacem
ent
in
a
D
u
a
l-
In
ve
rte
r
F
e
d
O
p
e
n-En
d
Wind
ing
In
du
c
t
io
n
Moto
r
Driv
e
w
ith
A
lte
rn
ate
Su
b-H
e
x
a
g
onal
Cen
t
er
P
W
M
S
witchin
g
S
c
hem
e”
IEEE T
r
ans
.
Pow
e
r
El
ectro.,
V
ol.
23,
No
.
3
,
pp.
1
58
4-1
591
,
M
ay
2
0
08.
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B.
V
enu
g
o
p
al
R
ed
dy,
V
eeramra
j
u
T
im
urala
S
o
m
a
s
e
kh
ar,
an
d
Yen
duri
K
aly
a
n
“
D
eco
upl
ed
S
p
ace-V
e
c
t
or
P
WM
Stra
te
g
i
e
s
f
or
a
F
ou
r-Le
v
e
l
A
sy
mme
tric
a
l
O
p
e
n-En
d
W
i
n
d
i
ng
I
n
d
u
c
ti
on
M
o
t
or
D
riv
e
w
it
h
W
a
ve
fo
rm
S
ymm
e
tri
e
s”
IEEE
Trans. Ind
.
Elect
ron
.
,
Vo
l
.
5
8
, No
. 11
, pp
.
5
13
0-5
1
4
1
,
Nov
.
20
11
.
[18]
M.
H
a
r
sh
a
Va
rdh
a
n
Re
dd
y,
T
.
Bra
h
m
a
na
n
d
a
R
e
dd
y,
B
.
Ra
v
i
n
d
ra
n
a
th
Reddy
,
M
.
S
ury
a
kal
a
v
a
ti
"
Red
u
cti
o
n
of
Com
m
o
n
M
ode
V
olt
a
ge
i
n
Asym
m
e
tri
c
a
l
D
u
a
l
Inv
e
rter
C
onfigu
r
ati
o
n
U
s
i
n
g
Disc
on
tinu
ou
s
Mod
u
la
t
i
n
g
S
ig
na
l
Based
PW
M T
e
c
h
ni
qu
e"
J
o
ur
na
l
of P
o
wer
El
ectr
oni
cs
,
Vo
l
.
15
,
No. 6
,
p
p
. 15
2
4
-
1
53
2, Nov
e
m
ber 2
0
1
5
.
[19]
Abd
u
l
Ra
hi
ma
n
Be
ig
“
Sy
nc
h
r
on
iz
e
d
S
VP
WM
a
lg
ori
t
hm
f
or
t
h
e
o
v
e
r
m
od
ul
a
t
ion
re
gion
o
f
a
low
sw
itc
h
i
n
g
f
r
equ
e
ncy
med
i
um
volt
a
ge
t
hree
level
VS
I”
I
E
EE Tr
ans
.
Ind
.
E
l
ec
tron.
,
V
ol.
59
,
No
.
1
2,
pp.
4
5
4
5
-
455
4,
D
ec.
2
01
2
.
[20]
S
o
u
m
itra
Das
and
G.
N
aray
anan
“
An
alyti
c
al
c
losed
–f
o
r
m
ex
pres
s
i
o
n
f
or
t
h
e
h
armo
ni
c
disto
r
tio
n
corres
p
o
ndi
ng
t
o
th
e
no
vel
s
w
i
t
ching
seq
u
en
ce
fo
r
th
e
neu
t
ral-p
o
i
n
t
-
cl
am
ped
inv
e
rt
ers
”
IEEE
Trans
.
Ind.E
l
ectron
.
,
V
o
l
.
6
1
,
N
o
.
9
,
pp
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4
4
8
5
-
44
97,
Sept
.
2
0
14.
Evaluation Warning : The document was created with Spire.PDF for Python.
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P
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Co
upl
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BIOGRAPHI
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Red
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RE
C
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n
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.
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r
eceived
P
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rom
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rangl
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curren
tly
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Direct
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Evaluation Warning : The document was created with Spire.PDF for Python.