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
)
V
o
l.
10, N
o.
2, June
2
01
9, pp.
653~
6
6
1
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
2.pp
6
53-
66
1
ļ²
653
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
A simple switching on-tim
e
calcu
lation revision in multilevel
inverter-space vector modulati
o
n
to achieving exte
n
de
d voltage
boun
dary operation
Bh
ar
atiraj
a
C
.
1
, R
.
K.
P
on
gian
n
a
n
2
,
A
d
e
d
ay
o Y
u
su
ff
3
,
Mo
hd Ta
riq
4
, Te
l
u
gu
M
add
i
l
e
ti
5
,
Th
ar
w
i
n
k
u
m
ar
6
1,
2
,
6
D
epartm
en
t o
f
El
ectrical and
El
ectro
ni
cs E
ngineeri
n
g
,
S
RM Ins
t
i
t
ute of S
cience and
Tech
nol
og
y,
I
nd
i
a
1,
3
Dep
artm
ent
o
f
El
e
ct
rical En
g
ineerin
g,
U
niversit
y
of
S
ou
th A
f
r
i
ca, So
u
th
A
f
r
i
ca
4
D
epart
m
en
t
o
f
E
lectri
cal Eng
ineering
, Ali
garh Mu
s
lim
U
n
i
v
ersit
y,
Ind
ia
5
S
reen
id
hi
I
nsti
tut
e
o
f
S
c
ience
a
n
d
Techn
o
l
ogy
, In
d
i
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
M
ay
3
0
, 2
018
Re
vise
d S
e
p 20,
201
8
A
c
c
e
pte
d
D
ec 3,
201
8
In
i
n
v
e
rte
r
sā
p
ul
se
w
idth
m
od
ul
a
t
io
n
te
c
h
niqu
e
s
(
P
W
M)
t
h
e
S
p
a
c
e
V
ecto
r
PW
M
(SVPWM)
is
a
s
m
a
rt
c
ontest
a
nt
d
u
e
t
o
it
s
direct
c
o
n
t
r
ol
i
n
nature
w
ith
vari
abl
e
s
whi
c
h
pro
v
i
d
e
th
e
s
t
raig
ht
f
o
r
ward
f
i
nds
t
o
each
i
nve
rt
er
s
witchi
ng
vect
or.
Th
e
in
dust
r
ial
dri
v
es
a
re
a
cq
uai
n
t
i
ng
t
o
u
s
e
S
V
PW
M
owin
g
ext
e
nded
sp
eed
ā
t
o
rq
ue
r
e
g
i
o
n
operat
i
o
n
s.
H
ow
ever,
t
h
e
e
x
t
e
nd
ed
S
VPW
M
o
p
erati
o
n
is
u
s
e
s
mu
ch
m
at
hem
a
ti
cal
c
al
cul
a
ti
on
to
p
red
i
ct
t
h
e
s
w
i
t
c
h
i
n
g
on-t
i
m
e
s,
wh
ich
dem
a
nd
s
hi
gh
d
i
gital
p
l
atf
o
rm
.
In
o
rder
t
o
reduce
th
is
c
a
lcul
at
i
o
n
in
th
is
p
ap
er
a
s
i
m
pl
e
on
-time
calcul
a
ti
on
bas
e
d
S
V
PW
M
is
p
ro
po
sed
.
The
pro
p
o
s
ed
S
VPW
M
i
s
dev
e
lo
ped
f
o
r
three-level
mul
til
evel
i
n
v
erter
a
nd
th
e
sp
ace
p
e
rsp
ectiv
e
of
v
ect
or
a
nal
y
s
i
s
are
est
a
blished
an
d
exp
l
ai
ned.
T
he
o
v
e
r
m
o
d
u
l
a
tio
n
enh
a
nces
t
he
p
ro
per
po
wer
ut
ilizati
o
n
cap
a
c
it
y
o
f
v
o
lt
age
so
urce
in
vert
er
t
hereby
i
m
p
rov
e
t
he
i
n
v
ert
e
r
o
u
t
put
voltag
e
a
n
d
l
o
a
d.
This
p
roposed
m
e
th
od
t
a
il
ed
t
he
s
im
il
ar
m
at
h
e
m
a
ti
cal
p
ra
ctice
as
c
o
n
v
e
nt
ional
t
wo
-level
S
V
PW
M
f
o
r
calcu
lati
ng
s
ecto
r
i
dent
ifi
catio
n
and
t
r
ian
g
le
d
et
erm
in
at
i
o
n.
T
h
e
app
r
oach
f
i
nds
t
h
e
c
i
r
cular
an
d
hex
a
g
o
n
a
l
bo
un
dary
o
n-tim
e
b
a
se
d
on
t
he
st
raigh
t
forward
reference
vect
or
p
os
iti
on
ide
n
tificat
ion
and
ca
lcu
l
ates
di
rectl
y
t
he
s
wi
tchin
g
p
ul
se
p
att
e
rns
f
o
r
th
e
in
vert
e
r
d
ev
ic
es
us
in
g
an
exp
r
ess
i
on
b
ased
o
n
th
e
d
e
f
i
n
i
tion
of
t
he
d
u
t
y
cy
cle.
T
h
e
p
erf
o
rm
ance
of
t
h
e
pro
p
o
s
ed
S
VM
i
s
sim
u
l
a
ted
b
y
M
ATL
A
B
11.
b
si
m
u
l
a
tio
n
so
ftw
a
re
a
n
d
val
i
d
a
ted
with
l
ab
orato
r
y
s
e
t
u
p
2
k
W
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12
s
w
itch
n
e
ut
ral
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lamped
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1
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P
s
quirrel
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in
du
ctio
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v/f
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t
ro
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r
iv
e.
T
h
e
s
im
u
l
ati
on
and
exp
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rim
e
nt
al
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e
s
u
l
ts
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l
o
s
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r
e
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c
o
nfir
ming
t
he
a
dv
a
n
ta
g
e
s
of
t
h
e
p
ro
po
se
d
SVM
me
th
od
.
T
h
e
pro
p
o
sed
sch
e
m
e
can
b
e
ext
e
n
d
ed
t
o
n-l
e
vel
in
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e
r
a
nd
als
o
a
p
p
li
cabl
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to
cascad
ed
H-b
r
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logy
K
eyw
ord
s
:
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e
utra
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p
o
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nt
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lam
p
ed
(
N
P
C)-
MLI
O
v
er
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la
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o
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Pu
l
s
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d
t
h
m
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p
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t
or
p
ul
se
w
id
th
Mo
du
la
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on te
c
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que
Th
re
e-l
e
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e
l
mu
l
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inv
e
r
t
e
r
Co
pyri
gh
t Ā© 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:
Bha
r
atira
j
a
C
h
ok
k
a
lin
ga
m,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
and
El
ect
ro
ni
c
s
Eng
in
e
e
ring
,
S
R
M Inst
i
t
u
t
e
of
S
cie
n
ce
an
d T
ech
no
l
o
g
y
, 603
2
03,
Ind
ia.
E-m
a
il : bha
rat
i
raja
.c@
k
tr.
s
rm
univ.
ac.
in
1.
I
N
TR
OD
U
C
TI
O
N
In
r
e
c
e
n
t
y
ea
rs,
mu
l
t
il
ev
el
i
n
v
e
rt
ers
(M
LIs)
h
a
v
e
b
een
w
i
d
e
l
y
u
se
d
i
n
t
he
a
rea
of
h
igh-
pow
er
me
dium-v
ol
ta
g
e
a
pp
l
i
c
a
t
i
ons.
They
o
ffer
a
s
e
t
o
f
fe
a
t
ures
t
hat
a
r
e
w
e
l
l
s
u
i
te
d
t
o
h
ig
h-v
o
lta
ge
d
r
i
ve
s
ys
t
e
ms
an
d
po
wer
sy
stem
a
p
p
l
i
c
a
t
i
ons
s
u
c
h
as
HVDC
t
ran
s
mi
ssio
n
,
r
eact
i
ve
pow
er
c
ompe
nsa
tio
n
e
q
u
i
pm
en
t
[1,
2]
.
The
N
e
u
t
ral
P
o
in
t
C
l
am
pe
d
(NP
C
)
has
be
e
n
m
ain
l
y
use
d
M
LI
f
o
r
m
o
t
o
r
con
t
ro
l
an
d
P
V
a
pp
lica
tio
ns
[
3-6]
.
To
c
on
tro
l
t
he
N
P
C
-
M
LI
,
amon
gs
t
var
i
o
u
s
m
odula
t
i
o
n
t
e
c
h
n
i
que
s,
S
V
PWM
is
a
n
a
t
t
r
a
c
ti
ve
c
a
n
dida
t
e
due
t
o
Evaluation Warning : The document was created with Spire.PDF for Python.
ļ²
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
6
5
3
ā
6
61
65
4
t
h
e
fo
llo
wi
n
g
meri
t
s
[
7
-
9
]
.
It
d
i
r
ect
ly
u
se
s t
h
e
co
n
t
rol
v
a
ri
ab
le
g
i
v
en b
y th
e
c
o
ntro
l
s
y
s
t
e
m
and id
e
n
tifie
s ea
ch
switc
h
i
n
g
v
ec
t
o
r
a
s
a
p
oi
nt
i
n
c
o
m
p
le
x
spa
c
e
.
I
t
is
u
se
fu
l
in
i
mp
r
o
vin
g
D
C
l
i
nk
volt
a
ge
u
t
i
l
i
z
a
t
ion
,
r
e
d
u
c
in
g
c
o
mm
uta
t
i
on
l
o
sse
s
a
n
d
T
o
t
a
l
H
ar
monic
D
i
stor
ti
o
n
(
TH
D
)
[
10-
1
5
]
.
The
S
V
P
W
M
tr
e
a
ts
s
inus
oi
d
a
l
v
o
l
t
a
g
e
as
c
ons
t
a
n
t
a
m
p
l
i
t
ude
v
ect
o
r
r
o
t
a
ti
n
g
a
t
c
onsta
nt
f
r
e
que
n
c
y
wi
th
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e
f
ere
n
ce
v
o
lt
ag
e
v
e
c
t
or
V
*
,
de
fi
ne
d
by
V
*
=|
V
*
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e
jw
t
,
r
o
ta
t
e
s
ar
o
und
t
h
e
c
e
n
tr
e
of
t
he
s
pac
e
v
e
c
tor
d
i
ag
ra
m
at
a
n
a
n
gul
a
r
f
re
qu
en
cy
Ļ
=
2
Ļf
sys
.
T
he
s
pac
e
v
e
c
t
o
r
dia
g
r
a
m
of
a
ny
n
-
l
e
v
e
l
i
n
v
e
r
t
er
c
ons
ists
o
f
si
x
sectors,
n
3
switching
states
a
nd
a
gain
e
ac
h
se
ctor
c
o
n
si
sts
of
(
n
ā
1)
2
t
ri
an
gl
es
[
1
6
].
B
ase
d
u
pon
t
h
e
v
al
u
e
o
f
m
odu
la
tio
n
i
n
de
x,
i
t
is
c
l
a
ssif
i
e
d
a
s
li
nea
r
m
odu
la
tio
n
a
n
d
o
v
e
r
m
o
d
u
l
a
tio
n.
O
ver
m
odu
l
a
t
i
o
n
e
nha
n
c
e
s
t
he
pr
ope
r
pow
er
u
t
i
l
i
z
at
ion
of
i
ns
t
a
l
l
e
d
c
apa
c
i
t
y
o
f
v
o
l
t
a
ge
s
our
c
e
in
ve
r
t
er
.
The
i
m
p
l
em
en
tat
i
on
of
S
V
P
WM
f
or
m
u
lti
le
ve
l
in
v
e
rter
s
is
c
o
n
s
i
de
red
com
p
le
x
.
T
his
c
o
m
p
le
xi
t
y
i
s
exp
e
ct
ed
t
o
in
c
r
ea
se
f
u
r
th
e
r
i
n
th
e
o
v
er
m
odu
la
tio
n
r
e
gi
o
n
d
ue
t
o
t
h
e
no
n
l
i
n
ea
r
i
t
y
o
f
this
r
e
g
i
on.
I
n
th
e
o
v
er
m
o
d
u
l
a
t
i
o
n
r
a
n
g
e
,
t
he
t
r
a
jec
t
or
y
o
f
t
he
r
e
fe
renc
e
ve
c
t
or
i
s
n
o
t
c
o
mple
t
e
l
y
c
irc
u
la
r
,
it
is
a
c
om
bi
na
ti
o
n
o
f
c
ir
c
u
l
a
r
a
nd
he
x
a
go
na
l
tr
a
j
e
c
t
o
r
y.
T
he
m
a
xim
u
m
ou
t
p
u
t
v
o
l
t
a
ge
c
a
n
b
e
incr
ease
d
up
to
2
V
d
c
/
Ī
[
1
6,
17]
.
T
h
e
al
go
ri
t
h
m
p
r
op
o
s
ed
i
n
B
e
i
g
[
7
]
t
o
ope
r
a
te
t
he
i
nv
er
te
r
i
n
t
he
o
v
e
r
modula
t
io
n
z
one.
The
r
e
f
e
r
e
n
c
e
s
a
m
p
l
e
s
w
h
i
c
h
a
r
e
c
l
o
s
e
r
t
o
t
h
e
m
e
d
i
u
m
a
n
d
lar
g
e
ve
c
t
or
s
a
r
e
move
d
to
w
a
r
d
s
t
h
e
i
r
r
e
spec
ti
ve
n
ear
e
s
t
m
e
d
i
um
a
n
d
n
e
a
r
e
s
t
l
a
r
g
e
v
e
c
t
o
r
s
.
T
h
i
s
v
e
c
t
o
r
se
l
e
c
t
i
on
is
b
a
s
ed
up
o
n
t
he
a
ngle
c
o
r
r
ecti
o
n
f
a
c
t
or
[
15]
.
I
n
S
eo
et
.
a
t
.
[
16]
p
r
o
p
o
se
d
a
schem
e
f
or
a
t
hr
ee
-
leve
l
i
nver
t
e
r
b
ase
d
o
n
t
w
o-
leve
l
S
V
P
W
M
.
T
he
3
-
l
e
v
e
l
S
V
M
d
i
a
gr
a
m
is
d
i
v
ide
d
i
n
t
o
s
i
x
tw
o-
l
e
ve
l
s
p
ac
e
ve
ct
or
d
ia
gr
am
s
[22,
33]
.
McG
r
a
t
h
et
a
l
.
,
[
17]
e
x
p
l
a
i
ns
t
he
b
e
h
av
i
o
r
of
t
he
k
e
y
m
u
l
t
i
l
e
v
el
c
ar
r
i
er
b
as
e
d
P
W
M
m
e
t
h
o
d
s
f
o
r
di
o
d
e
cla
m
pe
d
,
casc
a
ded,
a
n
d
f
lyi
ng
ca
pac
i
t
o
r
s
t
o
p
o
l
og
i
e
s
in
t
h
e
o
v
er
m
odula
t
i
o
n
r
e
gi
o
n
.
Mo
n
d
al
[
1
8
]
pe
r
f
or
m
s
S
VPW
M
b
a
s
e
d
o
v
e
r
modula
t
i
on
on
a
thr
e
e-
le
ve
l
N
P
C
i
nver
t
e
r
.
T
h
e
o
n
-
t
i
m
e
c
a
l
c
u
l
a
t
i
o
n
e
q
u
a
t
i
o
n
s
di
ff
er
f
or
e
ver
y
t
r
i
a
n
gu
lar
secti
o
n.
D
ue
t
o
inc
r
ea
sed
com
p
uta
t
i
o
n
a
l
c
omp
l
ex
i
t
y,
it
i
s
c
u
m
ber
s
om
e
t
o
e
xte
n
d
th
is
s
c
h
em
e
to
a
n
-le
v
e
l
i
n
v
e
rter.
Amit
ku
ma
rgup
ta
[
9]
,
the
sc
h
e
m
e
easi
l
y
deter
m
i
n
e
s
t
he
l
oc
a
t
i
on
of
t
h
e
r
e
f
e
ren
c
e
v
e
c
t
o
r
a
nd
calculates
on
-times.
Saeed
i
fard
[
19]
u
ses
c
l
a
s
s
i
fic
a
tio
n
a
l
gor
i
t
h
m
in
o
ver
m
o
du
l
a
t
i
o
n
r
a
nge
f
or
S
VPWM
o
f
a
thr
ee-
l
e
ve
l
NPC
in
v
e
rter
a
nd
s
imil
ar
i
m
p
le
m
e
n
t
a
t
ion
is
d
one
b
y
bhar
a
tir
a
j
a
et
.a
l
.,
in
[
2
1
]
.
I
t
i
s
no
t
clear
,
how
i
t
ca
n
be
e
xte
n
de
d
t
o
a
n
-
l
eve
l
i
n
v
e
r
t
e
r
.
I
n
over
m
odu
l
a
tio
n
[
1
9-
2
1
,
29,
30]
m
odi
f
y
the
t
r
ajec
tor
y
o
f
r
e
fer
e
nce
v
e
c
t
or
b
y
usi
n
g
lo
ok
u
p
t
a
b
le
s
.
T
he
aut
hor
K
.
M
.
K
w
on
et
.al
.
[20]
e
x
t
e
n
ds
h
is
ope
r
a
ti
o
n
i
n
to
t
he
o
v
e
r
modu
la
ti
o
n
r
e
g
i
o
n,
t
he
d
if
f
i
c
u
lt
y
i
s
t
he
tim
in
g
calc
u
la
ti
o
n
s
whic
h
i
n
vo
l
v
e
som
e
tr
i
g
o
n
o
me
tr
ic
f
unc
tio
ns.
I
n
t
his
pa
pe
r
,
a
s
im
ple
S
V
P
W
M
s
c
hem
e
f
o
r
a
3
-
L
e
v
e
l
N
P
C
-
M
L
I
w
a
s
d
e
v
e
l
o
p
e
d
t
o
ope
r
a
te
t
he
i
nv
er
ter
in
t
he
e
n
tir
e
m
odula
t
i
o
n
r
e
gion.
F
i
gur
e
1
sh
ow
s
N
P
C
topo
l
o
g
y
a
n
d
F
igur
e
2
s
how
s
the
S
V
PWM d
i
ag
r
a
m
o
f
a 3
-lev
el in
v
e
r
t
er.
F
i
gur
e
1.
S
chem
atic
d
i
a
gr
am
f
or
a
3
-
phase
3
-
l
eve
l
N
P
C
i
nve
r
t
e
r
Fig
u
r
e
2
.
S
V
D
fo
r a th
ree-lev
e
l
inv
e
rte
r
2.
MO
DE OF
O
P
ERATIO
NS
In
S
VP
WM,
the
t
h
re
e-pha
se
v
o
lta
ge
r
e
f
er
ence
i
s
gi
ve
n
as
a
v
o
lta
ge
r
e
f
er
ence
v
e
c
t
o
r
V
*
[13
]
.
Th
e
m
odu
la
tio
n
ind
e
x is de
f
i
n
ed a
s,
Mīµ
ī
ī°
ī
ī°
ī±
ī±
ī±®
ī°·
ī±©
ī±Ŗ
ī±
ī±¦
(1
)
ā
1,
2
ā
1,
3
ā
1,
1
V
L2
[
1
1
-
1
]
V
M1
[
10-
1]
[
10
0
]
,[
0-
1-
1]
[
1
01]
,
[
0-
1
0
]
[
0
0
1
]
,
[-1
-1
0
]
[0
1
1
}
,
[
-1
0
0
]
[
010]
,[
-
1
0
-
1]
[1
1
0
],[0
0
-
1
]
V
M2
[
0
1
-
1
]
[-1
1
0
]
V
M3
[
-
10
1]
V
M4
V
M5
[0-1
1
]
V
M6
[
1-
10]
V
L3
[-
1
1
-
1]
V
L5
[-1
-1
1
]
V
L2
[-1
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1
]
[
00
0]
,
[
11
1
]
[
-
1
-
1
-
1
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V
Z
V
S1
V
S4
V
S5
ā
1,0
V
L4
[
-1
1
-
1]
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
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65
5
Th
e
ra
ng
e
f
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om
0
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o
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907
i
s
c
all
e
d
as
l
i
n
e
a
r
modu
l
a
ti
o
n
a
nd
0
.
90
7
t
o
1
.0
i
s
t
e
rme
d
a
s
ov
e
r
modu
la
ti
o
n
r
a
nge.
I
n
l
ine
a
r
range
t
he
m
a
x
im
um
obt
a
i
n
a
b
l
e
vo
l
t
a
g
e
i
s
90.7
%
o
f
t
h
e
six
-
st
ep
v
al
u
e
.
It
can
b
e
incre
a
se
d
furt
h
e
r
by prope
rl
y ut
iliz
i
n
g the
D
C
l
ink
ca
pac
i
t
y
th
ro
ug
h o
v
e
r
m
odu
la
tio
n.
2.1.
Lin
e
ar
M
od
u
l
at
ion
( 0 ā¤ M.I<
0.907
)
The
F
i
g
u
r
e
3
(
a)
s
hows
se
c
t
o
r-1
o
f
spa
c
e
v
ector
d
i
a
gram
,
t
h
e
t
i
p
P
of
t
h
e
r
e
f
ere
n
ce
ve
c
t
o
r
c
an
b
e
loca
te
d i
n
a
n
y
of the
4 tria
ng
l
e
s
(
Ī
10
-Ī
13
).
T
he ob
j
e
c
t
ive
he
re
i
s
to
i
de
nt
i
f
y
the
tria
ng
le
i
n
w
h
ic
h the
p
o
in
t
P
is
loca
te
d.
I
n
the
li
nea
r
m
od
u
l
at
i
o
n
t
h
e
trajec
t
o
r
y
o
f
t
h
e
re
fer
e
n
ce
v
ec
t
o
r
is
e
ntire
l
y
c
i
rc
ular
a
nd
it
i
s
a
l
w
a
ys
lie
s
in
si
de
t
he he
x
a
g
o
n
.
2.2.
Ove
r
M
od
u
l
at
i
o
n
-
I (
0
.907 ā¤
M.
I<
0
.9535)
The
m
a
x
i
m
u
m
al
low
a
ble
le
n
g
t
h
o
f
t
h
e
re
fe
re
nce
ve
c
t
or
h
a
ppe
ns
w
h
en
i
t
t
o
uc
hes
the
bo
u
ndar
y
o
f
hexa
gon.
A
n
y
fur
t
her
i
n
c
r
ea
se
i
n
t
h
e
M
.
I
c
a
uses
t
he
r
e
f
er
ence
v
ec
t
o
r
to
b
e
pa
rt
i
a
lly
o
uts
i
de
t
he
h
exag
o
n
w
h
ic
h is te
r
m
e
d a
s
over
m
odula
t
i
on [
1
6].
2.3.
Ove
r
M
od
u
l
at
i
o
n
-
II (0.
953
5 ā¤
M.
I<
1
)
O
n
c
e
o
ver
m
odu
la
ti
o
n
-I
has
r
e
a
c
hed
t
h
e upp
e
r
l
im
it,
o
ve
r
m
odu
la
tio
n-
II
becom
e
s
ac
tiv
e.
U
nde
r
o
v
er
modu
la
ti
o
n
-II
t
he
e
sse
nt
ia
l
fe
ature
i
s
t
ha
t
the
par
tic
u
l
ar
acti
ve
v
ol
ta
ge
v
e
c
t
or
t
hat
is
c
l
o
ses
t
t
o
t
h
e
sta
t
or
vo
lta
ge r
efe
r
en
c
e
ve
c
tor
i
s
u
se
d gra
d
ual
l
y
lo
nge
r
and l
o
n
g
er
t
i
me
p
e
r
io
ds [18
].
(a)
(
b
)
(c)
F
i
gure
3.
S
V
M
d
i
a
gram
for se
c
to
r-1
; (
a
)
l
i
ne
a
r
modu
la
ti
o
n
m
ode,
(
b)
O
VM m
ode-I
, (c) O
V
M
m
ode-
I
I
3.
OPE
R
A
T
ION
OF 3
-LEV
E
L
INVERTE
R
O
VE
R
MODULAT
ION REGIO
N
3.1.
Over
mod
u
lat
i
on-I
I
n
t
he
o
ver
mod
u
l
at
i
on
r
a
n
g
e
s
how
n
in
F
i
gure
3
(
b
),
t
he
t
rajec
t
o
r
y
of
t
he
r
efe
r
enc
e
v
ector
i
s
no
t
c
o
m
p
l
e
t
e
l
y
c
i
r
c
u
l
a
r
b
u
t
a
c
o
m
b
i
n
a
t
i
o
n
o
f
c
i
r
c
u
l
a
r
a
n
d
h
e
x
a
g
o
n
a
l
t
ra
j
e
ct
o
r
y.
S
ec
t
o
r
ide
n
ti
fica
ti
on
a
n
d
t
r
ian
g
le
deter
m
i
n
at
i
o
n
a
r
e
sam
e
f
or
b
ot
h
t
h
e
trajec
to
r
i
e
s
a
nd
t
h
e
y
a
re
d
if
fe
r
on
ly
i
n
on
t
i
m
e
c
a
l
c
u
l
ati
on
e
q
u
a
t
i
on
s.
T
h
e
trans
i
t
i
on
from
c
i
rcular
t
r
a
jec
t
or
y
t
o
t
he
h
e
x
ago
n
t
ra
je
ct
ory
i
s
determ
i
n
ed
by
the
tra
n
sit
i
on
a
n
gle
ī
ī®¼
.F
or
ī
ī®¼
ā¤
ī
<
Ī
/3 ā
ī
ī®¼
,
the
v
e
ctor
m
oves
o
n
h
e
x
a
g
on
t
r
ac
k
a
nd
f
o
r
re
m
a
in
i
ng
par
t
o
f
t
h
e
s
ector
on
circ
ular
t
rac
k
,
whe
r
e
ī
ī®¼
is gi
ven
b
y
t
he
(
2) w
hic
h
te
l
ls
t
hat t
h
e
va
l
u
e of
ī
ī®¼
is
c
ons
ta
nt f
or a
give
n
m
od
ula
t
ion
i
nde
x.
ī
īÆ
īµļŗ
ī
6
ļ»
ā
īµc
o
s
ī¬æī¬µ
ļŗī
ļŗ2
ā
3
īÆ
ā
ļ»ļ»
(
2
)
3.1.
1.C
i
rc
u
l
ar
t
raj
ect
ory
F
o
r
app
l
y
i
ng
t
he
S
V
P
WM
t
e
c
hn
i
que,
f
i
r
s
tl
y
i
t
i
s
req
u
ire
d
t
o
d
e
t
ermi
n
e
t
he
s
ec
to
r
wh
i
c
h
th
e
vol
t
a
ge
vec
t
or
i
s
w
i
thi
n
.
F
o
r
any
g
i
v
e
n
re
fer
e
nce
ve
ctor,
the
a
n
g
l
e
Ī³
an
d
its
s
ec
t
o
r
of
o
pe
rat
i
o
n
S
k
c
a
n
b
e
d
e
t
e
r
m
i
n
e
d
by us
i
n
g (3)
and
(4)
respec
ti
v
e
l
y
,
Ī³īµr
e
m
ļŗ
Īø
6
0
ā
ļ»
(3)
S
ī©
īµi
n
t
ļŗ
Īø6
0
āļ»
īµ 1
(4)
A
f
ter
the
sec
t
o
r
i
den
t
ifica
t
io
n
the
t
r
i
a
ng
l
e
d
ete
r
mina
t
i
o
n
i
s
t
h
e
m
o
s
t
i
m
po
rt
an
t
on
e
.
E
ac
h
s
ect
o
r
i
n
the
3-
l
e
ve
l
in
v
e
rter
c
a
n
b
e
sp
l
i
t
i
n
t
o
f
o
u
r
t
r
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SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
653
ā
6
61
65
6
ty
pe
1
-
ba
se
s
i
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e
of
t
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t
r
i
a
n
g
l
e
is
a
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b
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om
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t
t
o
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s
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T
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l
e
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10
,
Ī
11
,
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13
,
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y
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1
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2
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d.
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the tria
n
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the
sm
a
ll
vec
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or
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V
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ca
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n
by us
i
n
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o
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n
te
ger
s
k1 a
n
d k
2
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re
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ne
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y
the
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rd
i
n
at
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s
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, V
Ī²
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as,
ī
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īµī
ī
ī
ļŗ
ī
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īµ ī
ī°
ā
3
ā
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(
5
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ī
ī¬¶
īµī
ī
ī
ļŗ
ī
ī°
ā
ā
ļ»
(
6
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K
1
r
epre
sents
t
h
e
p
a
r
t
o
f
t
h
e
se
ct
or
b
e
t
w
e
e
n
t
he
t
wo
l
ine
s
j
o
i
ni
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g
t
h
e
ve
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c
e
s
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te
d
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dista
n
c
e
h
a
n
d
i
n
cli
n
e
d
a
t
120
ā¦
wi
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h
r
e
s
p
ect
t
o
Ī±-axis.
F
rom
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Figure4,
K
1
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s
ig
ni
fi
es
t
ha
t
th
e
p
o
i
nt
V
*
i
s
b
e
l
o
w
t
h
e
l
i
n
e
X
1
X
2
.
k
1
=
1
s
ig
ni
fies
t
ha
t
poi
nt
V
*
i
s
b
et
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en
l
i
n
e
X
1
X
2
and
line
X
3
X
5
.
K
2
r
ep
re
sen
t
s
t
h
e
p
a
rt
o
f
th
e
se
c
t
o
r
betw
ee
n
t
h
e
t
w
o
line
s
j
oi
n
i
n
g
t
he
v
ertice
s
,
separ
a
te
d
b
y
d
is
t
a
n
ce
h
an
d
para
l
l
e
l
t
o
Ī±-
axi
s
.
k
2
=0
s
i
gnif
i
e
s
t
h
a
t
the
p
o
i
n
t
P
i
s
betw
ee
n
line
X
0
X
3
a
nd
l
i
n
e
X
2
X
4
.
k
2
=
1
s
ig
ni
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es
t
h
a
t
t
h
e
poi
nt
V
*
i
s
a
bove
l
i
n
e
X
2
X
4
.
G
e
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etrica
l
l
y,
the va
l
u
e
s o
f
K
1
and K
2
ar
e
a
n inter
s
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c
t
i
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n of tw
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re
c
tan
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lar re
gio
n
s w
h
i
c
h is e
i
t
her
a
tr
i
a
n
g
l
e
or r
hombus
a
s show
n in
F
i
gur
e
4.
F
i
gure
4.
3
-lev
el
S
VP
WM sec
tor-1 w
i
t
h su
b
-
tria
ngle
s
K
now
i
n
g
the
va
lue
s
o
f
k
1
a
nd
k
2
t
h
e
c
o
ordi
na
tes
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V
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,
V
Ī²i
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of
t
he
r
efer
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n
ce
vec
t
or
a
re
d
eter
min
e
d
[1
0]
by,
ī
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ī°
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ī¬µ
īµ 0
.
5
ī
ī¬¶
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7
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ī
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īµīø
ī°
īµī
ī¬¶
ā
(
8
)
for
k
1
=1
a
nd
k
2
=
0
,
the
com
m
on
in
tersec
ti
on
i
s
rhom
bu
s
w
h
ic
h
is
t
he
c
o
m
bina
t
i
o
n
o
f
t
w
o
tria
ng
le
s
Ī
1
a
nd
Ī
2
.
the
t
r
i
a
n
g
l
e
w
he
re
t
he
r
efere
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ce
p
o
i
nt
i
s
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n
b
e
d
e
t
e
rm
i
n
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d
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y
t
h
e
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mpa
r
i
s
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V
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ā¤ā
3
V
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3V
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s
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r
u
e
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h
e
n
t
h
e
p
o
i
n
t
V
*
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w
i
t
h
i
n
t
h
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ng
le
Ī
1
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p
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,
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Ī
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t
ype-2).
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h
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c
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ula
r
trajec
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Ā
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11
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1
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K
2
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1
K
2
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0
X0
X2
X3
X4
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Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
ļ²
A sim
p
le s
w
i
t
c
h
i
n
g
on-
tim
e calc
u
l
a
tio
n re
vi
sion i
n
m
u
l
tile
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e
l
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e
r
t
e
r-sp
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t
o
r ā¦
(Bh
a
ra
t
i
r
a
j
a
C)
65
7
3.1.
2.Hex
a
g
o
n
a
l t
r
aje
c
tor
y
I
f
t
he
a
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ī
,
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t
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iti
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a
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(17)
The
se
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t
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u
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a
n
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m
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i
n
t
he
s
i
m
i
l
ar
m
anne
r
of
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irc
u
lar
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to
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y
.
The
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ch
o
f
the
t
r
ia
ngle
o
f
t
he
s
ma
ll
v
ec
tor
(
V
*
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ca
n
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n
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rro
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d
d
o
w
n
b
y
us
in
g
t
w
o
i
n
te
gers
k
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k
2
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d
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a
s
ī
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2
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18)
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ā
ā
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(
19)
by k
now
in
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h
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1
a
nd k
2
the
val
ue
o
f the tria
ngle
num
ber ca
n b
e
ob
t
a
i
ne
d by us
i
n
g the
(
2
0)
a
nd t
h
e
coor
di
na
tes
of
t
he
sma
l
l
v
ect
o
r
V
s
a
r
e
give
n by t
h
e
(21)
a
nd
(
22).
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ī¬µ
ī¬¶
īµ 2
ī
ī¬¶
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5
ī
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(
22)
on t
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r
to
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l i
nver
t
e
r
a
nd ar
e
dete
rm
ined b
y
usin
g
t
h
e
(2
3)
-(25_
.
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ļŗīø
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ā
3
ā
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(23)
ī
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īµī¶
īƦ
īµī
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(24)
ī
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īµ0
(25)
3.2.
Over
mod
u
lat
i
on
-
11
Ā
O
n
c
e
over
modu
la
ti
o
n
-I
has
r
eac
hed
t
h
e
u
p
p
er
lim
it,
ove
r
m
odula
t
i
on
-II
b
e
c
o
me
s
ac
ti
ve.
S
w
i
t
chi
ng
in o
ver
m
odula
t
i
o
n-II
is c
h
aracteriz
e
d
by
a h
o
l
d
a
n
g
l
e
ā
īÆ
[21]
, defined
a
s
ī
īÆ
īµ
1
0.
5
ļŗ
1.
0
5
īµ
1
īÆ
ā
ļ»
(26)
Fo
r
ī
īÆ
ā¤
ī
<
Ī
/3 ā
ī
īÆ
,
the
vec
t
or
m
ove
s
o
n
h
e
x
a
g
on
tr
ack
a
n
d
th
e
on-
tim
e
c
a
lc
ula
t
ion
is
s
am
e
as
t
ha
t
dur
in
g
th
e
he
x
a
g
o
na
l
t
r
aject
o
r
y
in
ove
r
m
o
dula
t
i
o
n
m
ode
I
a
nd
fo
r
r
e
main
i
ng
part
o
f
the
se
ctor
i
.
e
.,
ī
īÆ
ā¤
ī
<
Ī
/3 ā
ī
īÆ
an
d
0
ā¤
ī
<
ī
īÆ
a
nd
Ī
/3
ā
ī
īÆ
ā¤
ī
<
Ī
/3
t
h
e
vec
t
or
i
s
he
ld
a
t
one
o
f
the
la
r
g
e
vec
t
or
.In
F
i
gur
e
3
(
c
)
t
he
squ
a
re
dots
at
t
he
p
o
i
n
t
s
4ā,
3
ā,
2
ā
and
1ā
r
eprese
nt
t
he
r
e
f
er
e
nce
vec
t
or
s
a
m
ples
i
n
o
v
er
m
odu
l
a
tio
n
m
ode
II.
The
sam
p
le
s
4
ā
,3ā
a
re
c
loser
to
t
he
l
arge
v
e
c
t
or
L
1
a
nd
t
h
ey
a
re
m
ove
d
tow
a
rds
t
h
e
l
a
r
g
e
vec
t
or
L
1
a
nd
t
h
e
sam
p
l
e
s 2ā,
1
ā, ar
e
cl
o
se
r to
t
he large vector L
2
and
t
h
e
y
a
re
m
ove
d tow
a
rd
s
t
h
e
lar
g
e ve
c
t
or L
2
.
I
f
t
he
r
e
f
ere
n
ce
v
ec
to
r
m
a
ke
s
an
a
ngle,
0īµī
īµ
ī
6
ā
t
hen
the
ve
ct
or
i
s
held
a
t
l
a
rge
vec
t
or
L
1
as
show
n in F
igur
e 3
(c
)
a
n
d
the on-
t
i
m
e
e
qua
t
i
ons
a
r
e
ī
īÆ
īµī¶
īƦ
,ī
īÆ¢
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,
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f
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e
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L
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as
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igur
e3.
(c
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n
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the on-
t
i
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ons
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r
e
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F
i
gure
5 sh
ow
the
f
l
o
w
c
ha
rts
for
ent
i
re
m
od
ula
t
io
n i
n
d
e
x f
o
r li
nea
r
a
nd o
v
er
m
odula
t
i
o
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ļ²
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
653
ā
6
61
65
8
F
i
gure
5. Ma
i
n
flow
c
h
ar
t
for
ent
i
re
m
odu
la
ti
on i
n
dex
4.
SIMU
L
A
TION
A
ND
E
XPE
R
IMENTAL
RE
S
U
LT
S
The
pe
rform
a
n
c
e
of
t
he
p
r
o
p
o
se
d
S
V
M
ha
ve
b
e
e
n
i
nve
s
t
i
g
a
t
e
d
a
n
d
si
mul
a
t
e
d
by
M
ATLAB
11
.b
f
o
r
12
s
w
i
tch
N
P
C-MLI
w
i
t
h
3
00V
D
C-
lin
k,
t
w
o
1
00ĀµF
c
a
pac
i
t
o
r,
5
kH
Z
sw
i
t
ch
i
n
g
fr
eque
nc
y
fe
d
1.
5
H
P
squ
i
r
r
el
c
a
g
e
3-
p
h
ase
in
d
u
ct
io
n
mo
t
o
r
ope
n
lo
op
v/f
c
o
n
t
ro
l
dri
ve.
F
u
rthe
r
t
h
e
s
i
mul
a
t
i
o
n
i
s
e
x
ten
d
e
d
t
o
lab
o
ra
tory
s
cal
e
expe
rime
n
t
a
l
pow
er
circ
u
it
i
s
show
n i
n
F
i
g
ur
e
6.
3
l
e
ve
l
N
P
C
M
L
I
DS
O
FP
GA
B
o
a
r
d
Is
o
l
a
t
i
o
n
Tr
an
s
f
o
r
me
r
F
i
gure
6.
E
xpe
rim
e
nta
l
se
t
u
p
-
SV
M
based
3 Leve
l N
P
C-MLIF
P
G
A
S
P
A
RTEN I
II
The
pr
o
pose
d
ove
r
mo
d
u
la
t
i
o
n
S
V
P
WM
a
lg
ori
t
hm
i
s
pro
g
ram
m
e
d
in
V
eril
og
Hard
wa
re
D
e
s
c
r
i
p
tiv
e
Lang
u
a
g
e
(
VHDL)
co
d
e
a
nd
s
y
n
th
esi
z
ed
i
n
mi
n
i
mu
m
co
mp
ut
at
i
o
n
a
l
l
oad
using
S
P
ARTAN
āI
II-3AN
ā
X
C
3S
4
00
F
P
GA
f
am
il
y
bo
a
r
d
[
1
6
]
.
The
al
gor
it
hm
i
s
t
e
st
e
d
o
n
a
3-
le
ve
l
N
P
C
l
a
b
o
rat
o
ry
p
r
o
tot
y
pe
i
nve
r
t
er
w
ith
3
00V
D
C-l
i
n
k
,
tw
o
1
00
Āµ
F
capa
c
i
t
o
r
,
5kH
z
sw
it
chi
n
g
fre
q
uen
c
y
f
e
d
1
.
5
H
P
s
q
u
i
r
r
e
l
c
a
g
e
3
-
p
h
a
s
e
in
duc
t
i
on
mo
to
r
open
l
o
op
v/
f
con
t
rol
dr
ive
.
F
igure
7
sh
ow
s
the
l
i
n
e
v
o
l
t
a
g
e
f
o
r
a
3
-
l
e
v
e
l
N
P
C
-
M
L
I
f
o
r
0
.
9
0
7
,
0.95
7,
and
0.9
9
m
odu
la
tio
n
i
n
de
x re
spect
i
v
ely.
5.
RESULT
D
ISCUSSION
F
i
gure
8
d
e
p
ic
ts
t
he
M
.
I
v
er
sus
line
vo
l
t
a
g
e
for
a
1.5
H
P
s
qu
irr
el
c
age
3-
pha
se
i
n
d
u
c
t
i
o
n
m
o
t
o
r
fed
from
a
N
P
C
M
LI
f
or
t
he
p
ro
p
o
se
d
S
V
M
sc
h
e
m
e
i
ncl
u
din
g
ove
rmo
d
u
l
a
ti
o
n
.
F
r
om
t
he
g
r
a
ph
i
t
w
a
s
o
b
s
e
r
ved
tha
t
t
he
o
ut
p
u
t
line
v
o
lta
ge
i
s
24
8V
a
t
M
=
0.
8.and
a
t
t
he
M
=
0
.
9
52
i
t
wa
s
f
oun
d
th
at
t
h
e
o
utp
u
t
lin
e
v
ol
t
a
g
e
i
s
M,
a
n
g
l
e
C
a
l
c
ul
at
i
o
n of
S
e
c
t
o
r a
n
d A
n
gl
e
Li
ne
a
r
Mod
u
l
a
t
i
o
n
OV
M
-
I
OV
M
-
I
I
Go
t
o
C
i
r
c
u
l
a
r
Ī±
c C
al
cu
l
a
t
i
o
n
Ī±
h
C
al
cu
l
a
t
i
o
n
Go
t
o
O
V
M-
I
Ī±
h
c
o
n
di
t
i
o
n
chec
k u
s
i
n
g
E
q
.2
Ī±
h
a
ngl
e
ch
eck
G
o
t
o he
xa
go
n
U
si
n
g
E
q
.
27
&
2
8
Sw
i
t
ch
i
n
g o
n
t
i
m
e
c
a
l
c
u
l
at
i
o
n
s
Ye
s
No
Ā
OV
M
-
I
Ī¾
C
a
l
c
u
l
a
t
i
o
n
Us
i
n
g
E
q
.
9
G
o
t
o C
i
r
c
ul
ar
G
o
t
o h
e
xagon
On
t
i
m
e
mo
d
i
f
i
c
a
ti
o
n
Ī¾
r
a
n
ge
chec
k
Ī±
c
<
<
Ļ
/3
-Ī±
c
S
w
itc
h
in
g
v
e
c
t
o
r
Ma
p
p
i
n
g
S
w
i
t
chi
n
g ve
c
t
o
r
Map
p
i
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
ļ²
A sim
p
le s
w
i
t
c
h
i
n
g
on-
tim
e calc
u
l
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tio
n re
vi
sion i
n
m
u
l
tile
v
e
l
inv
e
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t
e
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ra
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65
9
27
9
V
.
T
he
refor
e
i
t
i
s
e
vi
de
n
t
t
hat
t
h
e
o
u
t
put
v
o
l
t
a
ge
o
f
t
h
e
i
nver
t
e
r
g
e
t
s
i
n
cre
a
sed
a
s
t
he
ope
rat
i
n
g
va
lue
of
M m
oves t
o
w
a
r
d
s the
ove
r mod
u
l
at
i
o
n
re
gio
n
.
(a)
(b)
(c)
F
i
gure
7. S
how
s the
line
v
o
l
t
a
ge
f
or a
3-le
v
e
l
NP
C
-
M
LI
for
(a
)
0
.
907,
(
b)
0
.957,
(
c) 0.
9
9
M
a
re
s
pe
ct
i
v
el
y
30
0
60
0
90
0
12
00
15
00
0.6
0
.
8
0
.9
Mo
t
o
r
S
p
e
e
d
(
N
r
)
0.
95
0.
99
0.
4
N
r
=
1
28
2
R
P
M
N
r
=
1
39
6
R
P
M
N
r
=
1
41
1 R
P
M
N
r
=
1
42
2
R
P
M
L
i
n
e
ar
m
od
u
l
at
i
o
n
O
v
e
r
m
od
u
l
at
i
o
n
M
F
i
gure
8.
Mo
t
o
r
spee
d
ver
sus
M
.
for a 3-lev
el NP
C
-MLI
.
Tab
l
e
1.
S
imula
t
i
o
n vs
h
ardw
a
r
e resul
t
s at
d
i
f
fere
n
t
M.I
v
al
ues
M
.
I
Si
m
u
la
tion
re
sul
t
s output
m
o
to
r
v
o
l
tag
e
sp
e
e
d
H
a
rdwa
r
e
r
e
s
ult
s
o
utput
m
otor
volta
ge
s
pee
d
0.
800
248
9
2
8
246
92
7
0.
906
260
1
2
87
257
12
82
0.
938
273
1
4
01
272
13
96
0.
952
280
1
4
13
279
14
11
0.
998
293
1
4
23
291
14
22
F
u
n
d
a
m
en
t
a
l
V
o
l
t
a
g
e
=2
5
7
V
ab
150
V
/
D
i
v
F
u
n
d
am
e
n
t
a
l
V
o
l
t
ag
e
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79
V
ab
15
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v
Ā
V
ab
1
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i
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u
n
d
a
m
en
t
a
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l
t
a
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e
=
2
9
1
Evaluation Warning : The document was created with Spire.PDF for Python.
ļ²
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
653
ā
6
61
66
0
6.
CONCL
U
S
ION
Th
is
p
a
p
er
p
r
o
p
o
se
s
a
s
i
mple
S
VPWM
t
ec
h
n
iq
ue
f
o
r
c
alcu
la
t
i
n
g
t
h
e
o
n
-t
im
es
i
n
t
h
e
e
n
t
i
re
modu
la
ti
o
n
r
eg
io
n,
t
h
e
on-
tim
es
calc
u
l
a
tio
n
is
b
ase
d
o
n
on-
tim
e
c
a
l
c
u
l
a
tio
n
for
tw
o-l
e
ve
l
S
V
P
W
M.
A
s
im
ple
me
tho
d
o
f
c
a
l
c
u
la
t
i
n
g
on-
t
i
m
e
s
in
t
he
o
ver
modu
la
ti
o
n
r
an
ge
i
s
use
d
,
hen
c
e,
a
s
olu
t
i
o
n
t
o
c
om
ple
x
e
q
u
a
tio
ns
and
l
o
ok
up
ta
b
l
es
a
re
n
o
t
r
eq
uire
d.
T
he
p
ro
pos
ed
a
l
gor
it
h
m
c
an
be
a
p
p
l
i
e
d
to
a
v
ari
e
ty
o
f
m
o
d
u
l
a
ti
on
val
u
e
s
and
it
c
a
n
b
e
e
a
si
l
y
a
p
p
l
i
ca
ble
for
an
y
le
ve
l
i
n
verter
a
nd
to
a
l
l
th
e
t
y
p
e
s
of
m
ul
ti
le
v
e
l
top
o
lo
gi
es.
Th
e
expe
r
i
me
n
t
a
tio
n
va
lida
t
i
n
g
th
e
prop
ose
d
R
P
W
M.
&
A
I
can
b
e
exte
n
de
d
to
a
b
r
o
ad
r
ange of
a
p
p
l
icat
i
o
n
s
s
uc
h
as dr
i
ve
rles
s v
e
hi
c
l
e
s
.
REFE
RENCES
[1]
J.
R
odr
i
g
uez,
J
.-
S.
L
ai
,
and
F.
Z
.
Peng,
āMu
ltile
vel
invert
er
s:
A
s
u
r
vey
o
f
t
o
pologies
,
contro
l,
a
n
d
a
pp
li
cati
ons
ā,
IEEE Tr
ans
.
Ind
.
El
ectron
.
Vo
l.
49,
N
o.
4
,
pp.
7
2
4
ā7
38,
A
u
g
.
2
002.
[2]
H.
A
bu
-Rub
,
J.
H
ol
ts,
J
.
R
o
d
r
ig
ue
z
,
a
nd
G
.
Ba
o
m
ing
,
ā
M
e
diu
m
v
ol
t
a
ge
m
u
l
ti
lev
e
l
co
nv
erters,
st
a
t
e
of
t
he
a
rt
,
chal
len
g
es and
r
equ
i
rem
e
nt
s
i
n
i
n
dus
tri
a
l
ap
pl
ica
t
ions,
ā
IEE
E
Tr
a
n
s.
Ind.
El
ectr
on.
,
Vo
l.
5
7,
N
o
.
8
,
p
p.
2
5
8
1
ā
2
5
96,
Aug.
2
010
.
[3]
C.
B
harati
ra
ja,
R.
S
elvaraj,
T
.
R
.
C
h
e
ll
ia
h,
J
.
L.
M
un
da
,
M.
T
a
ri
q
,
a
nd
A.
I
.
Masw
ood,
ā
Desi
gn
and
Im
pl
e
m
entatio
n o
f
F
ou
rth
Arm
fo
r
Elimi
n
ation
of
B
earing
Current
i
n
NP
C-MLI-Fed
I
nd
ucti
on
M
ot
or D
riv
e
,
ā
IE
EE
T
r
a
n
s
a
ction
s
on
Ind
u
st
ry
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ppli
c
a
t
ions
,
V
ol.
54,
N
o
.
1
,
pp
.
7
4
5
ā754,
J
an
.
20
18
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[4]
C.
B
harati
raja,
S
.
J
eevan
anth
an
,
J.L.
M
u
n
d
a
,
an
d
R.
L
ath
a
,
ā
I
m
p
ro
ved
S
V
PWM
v
ector
s
el
ection
app
r
oa
ches
i
n
OVM
re
gion
t
o
re
du
c
e
c
o
mmo
n-
mod
e
v
ol
ta
g
e
f
or
t
h
r
e
e
-
le
v
e
l
ne
u
t
ra
l
po
in
t
c
l
a
m
pe
d
i
n
v
e
r
t
e
r
,
ā
International
Jou
r
n
a
l
o
f
El
ectr
i
cal P
o
wer
&
E
n
ergy
Syst
ems
, Vo
l
.
7
9
,
N
o.
1
,
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97
,
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01
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G.
P
r
ak
ash
,
C
.S
ubram
ani
,
C
.
Bha
r
at
iraj
a,
a
nd
M
.S
hab
i
n,
ā
A
l
o
w
c
o
st
s
i
ngle
p
h
ase
g
r
id
c
on
ne
cted
r
edu
c
e
d
s
w
i
t
c
h
P
V
i
nv
erter
b
a
sed
on
T
i
m
e
F
r
am
e
S
w
itchi
ng
S
chem
e,ā
Inter
n
a
t
i
onal Jour
na
l
of El
ec
t
r
i
c
al
Power
&
E
n
er
gy
Sys
t
em
s
,
Vo
l
.
77
,
p
p
. 1
00
-11
1
, M
arch
20
1
6
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[6]
C.Bharat
iraj
a,
S
.Jeev
anan
than
,
Lat
h
a,
R
.,
ā
F
PGA
b
a
sed
practi
cal
i
m
p
lem
e
ntati
on
of
N
P
C
-ML
I
w
it
h
SV
PWM
f
o
r
a
n
a
uto
n
o
m
ou
s
op
e
r
a
t
io
n
P
V
s
y
s
te
m
w
i
th
c
a
p
a
c
i
tor
ba
la
nc
in
gā
,
Int
e
rna
t
i
o
n
a
l
Jour
nal of
Electrica
l Po
wer an
d
En
erg
y
Sys
t
ems
, V
ol
.
6
1
,
p
p
.
489
-50
9
,
Oc
t
201
4
.
[7]
Abd
u
l
Ra
hi
ma
n
Be
ig
,
āSy
n
c
h
ro
niz
e
d
S
VP
WM
a
lg
ori
t
h
m
f
or
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l
a
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i
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i
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l
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s
w
i
t
c
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g
f
r
equ
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ncy
m
e
dium
-vo
l
t
a
ge
t
hree-lev
e
l
VS
I,
ā
IEEE
T
r
an
s.
In
d
.
Electro
n.
,
Vo
l. 5
9,
N
o. 12
, Dec. 20
1
2
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C.
B
h
a
rat
i
raj
a
,
T.
B
.
P
r
asad
,
and
R.
L
at
ha,
āCo
m
parat
i
ve
r
eal
iz
at
ion
o
f
d
ifferen
t
S
VPW
M
s
ch
emes
i
n
li
near
m
o
d
u
l
a
ti
on
u
s
ing
F
P
GA,
ā
2
0
0
8
IEEE
R
e
g
i
o
n
8 In
ter
natio
nal Co
nf
eren
ce
on
Com
p
u
t
atio
nal Tech
no
lo
gies
i
n
El
ectrica
l
a
n
d
El
ectro
n
i
cs E
n
g
i
neerin
g
, Novosibi
r
sk Sci
en
tific Ce
n
tre
, No
v
o
s
ibir
sk
, Rus
sia
.
21
-25
Ju
l
y
2
00
8.
[9]
Ami
t
K
um
ar
G
up
ta
a
nd
Ash
win
M
.
K
h
a
mb
adk
o
n
e
,
āA
G
eneral
S
p
ace
Ve
ctor
P
W
M
A
lgorith
m
f
o
r
Mul
tilevel
In
ve
rte
r
s,
I
n
c
lud
i
n
g
O
p
e
ra
tion
i
n
Ove
r
m
od
ula
tio
n
Ra
n
g
e
,
ā
IE
EE
Tran
s.
o
n
Power E
l
ectr
on.
,
V
o
l
.
2
2
,
N
o
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Ma
rc
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07
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C.
B
harat
i
raj
a
,
P
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S
anj
e
ev
ik
u
m
ar,
an
d
F
.
B
laab
jerg
,
"
C
ri
ti
ca
l
I
n
vest
iga
t
io
n
an
d
Com
p
arativ
eAn
a
lys
i
s
o
f
A
d
v
an
ced
PW
M
T
echn
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q
u
esf
o
rTh
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ee-P
h
as
eT
hree-Lev
e
l
N
P
C-M
L
I
Dri
v
es,ā
El
ectric P
o
we
r
Com
pon
ent
s
and
S
y
s
t
em
s
.
Vol.
46
,
N
o
.
3
,
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p
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269
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eb
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20
1
8
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Bharat
iraja,
C
.,
H
arish
,
S
.,
M
unda,
J
.
L.
,
(.
..
),
S
riram
K
um
ar,
M
.
,
B
ha
t
i
,
V
.
ā
A
P
W
M
s
t
r
a
te
g
i
e
s
f
or
d
io
d
e
a
ss
is
te
d
NP
C-ML
I
t
o
o
b
t
ain
m
a
x
i
m
u
m
v
o
l
t
age
g
a
in
f
or
E
V
app
l
icat
io
n
ā,
In
tern
atio
nal Jou
r
n
a
l
o
f
P
o
wer Elect
ro
n
i
cs
an
d
Dr
ive S
y
s
t
ems
(
I
JPED
S
)
,
Vol.
8
, N
o.
2
,
p
p
.
7
67
-774,
J
un
e
20
17.
[12]
S
a
nt
hak
u
m
a
r,
C
.,
S
hi
vakum
ar,
R.
,
B
harat
i
ra
ja,
C.
,S
anj
e
ev
ik
um
ar,
P.
ā
Car
r
i
e
r
sh
if
t
i
ng
a
l
g
orithms
f
o
r
t
he
m
i
t
i
g
a
t
ion
of
c
i
r
cula
t
i
n
g
c
urren
t
i
n
di
od
e
cl
am
ped
M
L
I
f
e
d
ind
u
ctio
n
m
o
t
o
r
d
r
i
v
e
ā
,
Int
e
rn
atio
na
l
Jou
r
na
l of Po
wer
El
ectr
onics
an
d
D
r
ive Sys
t
em
(IJP
E
D
S
)
s
, Vo
l
.8
,
No
.2,
pp
.
84
4-8
5
2
, Ju
n
e 2
0
1
7
.
[13]
C
.
B
h
a
r
a
t
i
r
a
j
a
,
K
.
V
.
R
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S
.
P
.
R
a
o
,
R
.
P
a
l
a
n
i
s
a
m
y
,
a
n
d
S
.
J
e
e
v
a
n
a
n
t
h
a
n,
ā
Critical
E
val
u
ati
o
n
o
f
S
V
P
WM
S
chem
e
f
o
r
Capaci
tor
balancing
in
N
P
C
-MLI,ā
IET Chen
na
i 3r
d Inte
rn
atio
nal Con
f
e
r
en
ce on S
u
st
a
i
na
bl
e
E
n
er
gy a
n
d
Int
e
ll
ig
ent Systems
(
S
E
I
SCO
N
2
0
12)
,
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ndia,
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D
ec.
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012
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C.
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h
a
rati
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m
ar,
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u
nda
,
L
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N
orum,
and
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R
agh
u
,
ā
M
i
t
i
g
atio
n
of
C
i
r
cu
latin
g
Current
i
n
Di
od
e
clam
ped
M
L
I
f
e
d
Ind
u
ct
ion
M
o
t
o
r
D
r
ive
Us
ing
Carrier
S
h
i
ft
i
n
g
PWM
T
echn
i
qu
es,ā
Le
ct
ur
e Not
e
s in
El
ectrica
l E
n
g
i
n
eer
in
g
,
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p
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7
1
ā83,
D
ec.
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017.
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C
Bharati
r
aja,
N
S
ri
rams
a
i
,
ā
I
n
v
est
i
g
a
ti
on
of
t
he
C
om
m
o
n
M
o
d
e
V
ol
tage
f
or
a
N
e
u
tral
-Point-C
l
a
mped
M
ultilevel
In
ve
rte
r
D
riv
e
a
n
d
i
t
s
I
nn
ov
a
t
i
v
e
El
im
in
a
tion
thro
ug
h
S
V
P
W
M
Sw
i
t
c
hi
ng
-State
R
edu
n
d
a
ncy
ā
,
Interna
t
ional
Jou
r
n
a
l
o
f
Po
we
r Elect
ronics
and
Dri
ve Sys
t
em
s
(I
J
P
E
D
S
)
,
V
o
l.
3
,
N
o
.
7,
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9
2
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ec
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J.
H
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S
e
o,
C
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C
ho
i,
a
nd
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S
.
Hy
un
,
ā
A
n
ew
s
im
plified
s
p
ace-
vect
or
p
wm
m
et
hod
f
or
t
h
r
ee
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i
n
v
ert
e
rs,ā
IEEE
Trans
.
Po
wer E
l
ectron.
,
Vol
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6
,
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u
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B.
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McG
r
a
t
h
an
d
D.
G
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H
o
lm
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ā
S
inu
s
oid
a
l
PWM
of
m
ult
i
l
e
vel
i
n
v
ert
e
rs
i
n
t
h
e
ov
er
m
od
ul
ation
reg
i
on
,
ā
Proc
.
IEEE 33
rd
A
n
nu
. Po
werE
l
ectron
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S
p
ec. Co
nf
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P
E
S
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u
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S
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K
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M
ond
al,
B.
K
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Bo
s
e
,
ā
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pa
ce
vect
or
p
uls
e
w
i
d
t
h
m
od
ul
a
tion
of
t
h
r
e
e
-
le
v
e
l
in
ve
rte
r
e
x
t
e
n
di
ng
o
pe
ra
tion
in
to
ov
er
m
od
ul
a
tio
n
regio
n
,
ā
I
E
EE
T
r
ans.
P
o
wer
E
l
e
c
tron
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04
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ar.
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S
aeedi
f
ard,
A
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R.
B
akhs
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G
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J
o
os,
an
d
P
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J
ain
,
ā
E
x
t
e
nd
ing
t
h
e
op
erati
ng
rang
e
o
f
t
he
n
eu
ro
-co
m
p
u
ti
ng
o
f
t
h
ree-
level
inverters
into
o
ve
r
mo
du
lat
i
on
r
egio
n,
ā
Pro
c
.
IEEE 38
th
In
d.
Ap
p
l
.
Con
f
.
,
V
o
l.
1
,
p
p
.
67
2ā6
77
.
v
ect
o
r
clas
sificati
on space ve
ct
or m
o
dul
ati
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rith
m Oct
.
20
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[20]
Ky
ou
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-Mi
n
Kwo
n,
J
a
e
-M
o
on
Lee,
J
i
n
-M
o
k
L
ee,
M
.
ā
O
ver
m
o
d
u
l
a
ti
on
S
ch
em
e
o
f
T
hree-Level
In
vert
ers
for
Vect
or
C
o
n
t
r
o
lled
In
du
cti
on
M
o
tor
D
r
ives,
ā
Jo
urnal
of
P
o
wer Elect
ro
ni
cs
,
Vo
l. 9
,
No. 3
,
May
2
0
0
9
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[21]
C.
B
harati
raja,
S.
J
eev
anant
h
an
a
n
d
J
L
m
u
nda
ā
Ti
min
g
C
orrecti
o
n
A
lgo
r
ith
m
fo
r
SVP
W
M
Ba
se
d
Diod
e
-
Cla
m
pe
d
MLI
Ope
r
a
t
e
d
i
n
o
v
e
rmod
ula
t
io
n
Re
gion
ā
,
IEEE
j
ourn
a
l o
f
Se
lected
to
pi
cs in
P
o
wer
El
ectr
onics
a
ppl
icati
ons
.
Vol. 6
,
No
. 1
,
p
p
. 23
3
-
24
5,
Mar.
2
0
1
8
[22]
C.
B
harati
raja,
P.
S
an
jeev
ikum
ar,
an
d
F
.
B
l
aabjerg
,
"
C
ri
tical
I
n
v
estig
ati
o
n
and
Co
m
p
arati
v
e
Anal
y
s
is
o
f
Ad
van
ced
PW
M
Tech
ni
quesf
or
T
h
r
ee-P
h
aseT
hree-Lev
e
l
NP
C-M
L
I
D
r
ives
ā
,
Elect
ri
c P
o
wer
Co
mp
onen
t
s
and
Syst
ems
.
Vo
l
.
46
,
N
o
.
3
,
p
p
.
258ā
269
,
F
eb
.
20
1
8
[23]
C.Bharat
iraj
a,
S
.Jeev
a
n
ant
h
an
.,
Lat
h
a,
R
.,
ā
F
P
GA
based
practi
c
a
l
implemen
t
a
ti
on
of
N
PC-M
LI
w
ith
S
VP
WM
f
or
a
n
a
uto
n
o
m
ou
s
op
e
r
a
t
io
n
P
V
s
y
s
te
m
w
i
th
c
a
p
a
c
i
tor
ba
la
nc
in
gā
,
Int
e
rna
t
i
o
n
a
l
Jour
nal of
Electrica
l Po
wer an
d
En
erg
y
Sys
t
ems
, V
ol
.
6
1
,
p
p
.
489
-50
9
,
Oc
t
201
4
[24]
C.
B
h
a
rati
ra
ja,
Harsh
a
vard
han
Reddy
,
N
.
S
ri
R
am
sai
,
a
n
d
S
unkava
l
li
Satya
Sais
u
m
a
āFPGA
B
a
sed
Desi
gn
a
nd
V
a
li
da
t
i
o
n
o
f
A
s
y
mme
tr
ic
a
l
R
e
d
uc
e
d
S
wi
tc
h
M
u
l
t
i
le
v
e
l
I
n
v
e
r
t
e
r
,
ā
Int
e
rn
atio
na
l
Jo
ur
na
l o
f
Po
wer El
ectro
n
i
cs an
d
Dr
ive S
y
s
t
em
(
I
JP
EDS)
,
Vo
l
. 7
,
No. 2
, p
p
. 34
0
-3
4
8
, Ju
n
e 2
0
1
6
.
[25]
C.Bharat
iraj
a,
S
.
J
e
ev
anan
th
an,
S,
R
.
L
a
tha,
a
nd
V
.M
oh
an,
āVect
or
s
el
e
c
tio
n
app
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oach-b
ased
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ex
a
g
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t
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resi
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sp
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ctor
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ur
ren
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r
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ase
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o
r
v
o
ltag
e
b
al
anci
ng
,ā
IET Powe
r
El
ectr
onics
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,
V
ol.
9,
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o.
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Bharat
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C
.,
S
an
jeevi
k
u
m
ar,
P
.
,
M
a
h
e
sh
,
S
w
ath
i
m
a
la,
A
.
S
.
,
R
agh
u
,
S
.
ā
An
a
l
y
s
is,
design
a
nd
inves
t
i
g
a
t
ion
on
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new
s
i
ngle-p
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as
e
sw
it
ched
q
u
a
si
Z
-s
ou
rce
in
verter
f
or
pho
to
volt
aic
ap
pl
icati
o
n
ā
,
in
In
ter
n
a
t
i
onal Jou
r
na
l o
f
Po
wer
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ectr
onics
an
d
D
r
ive Sys
t
ems
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S
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C.
B
h
a
rat
i
raj
a
,
Red
d
y
,
H.
S
r
i
R
amsai
,
N
,
Sa
i
s
uma,
S
.S.
āF
PG
A
ba
sed
desi
gn
a
nd
v
ali
d
at
ion
of
a
s
y
mm
etri
cal
redu
ced
s
wit
c
h
m
u
lti
l
ev
el
i
n
v
ert
e
rā
,
Inter
n
a
t
i
onal Jo
ur
nal
o
f
Power
El
e
c
t
r
o
n
i
c
s an
d D
r
i
v
e
S
y
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ems
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C.Bharat
iraj
a,
S
.Ragh
u
,
an
d
K.R.
S
.
Rao,
"
Comp
ara
t
iv
e
analy
s
is
o
f
d
iff
e
ren
t
P
W
M
t
ech
ni
ques
to
r
edu
c
e
t
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o
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ol
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-
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t
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o
r
v
ariab
l
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sp
eed
i
ndu
cti
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driv
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Int
e
rn
ation
a
l
Jo
u
r
n
a
l of Po
wer
E
l
ect
ronics a
nd Dri
ve System
s
(
I
JP
EDS)
, Vo
l
3
,
No 1
,
p
p
. 1
05
-11
6
, March
20
1
3
.
[29]
C.Bharat
iraj
a,
R
.Lat
ha,
S
.
S
.
Dash
,
R.Gulati,
R
,
an
d
P
.
V
S
h
arm
a
,
āA
3
D-S
V
P
W
M
alg
o
rit
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m
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i
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FP
GA
IP-core
im
plement
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ti
on
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o
r
ML
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o
perating
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modulatio
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ra
n
g
eā,
I
n
t
e
rn
ation
a
l
R
eview
of
E
l
ectrical
Engi
neering
, vo
l
.8
,
n
o
. 3
p
p.
9
47
-96
1
,2
01
3.
[30]
C.
B
h
a
ratiraj
a,
S
.
J
eevan
a
n
th
an
a
n
d
S
.
S
.
D
as
h,
"
A
V
ecto
r
S
elec
ti
on
A
p
p
roach
B
ased
o
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C
o
n
t
rol
Deg
r
ee
of
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r
eedo
m
t
o
P
r
ovi
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D
C-L
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nk
Vo
lt
a
g
e
Balanci
n
g
in
D
io
de
C
lamp
ed
M
u
l
t
ilevel
Inverter",
Int
e
r
n
at
ion
a
l
Review
o
f
El
ectrica
l E
n
g
i
n
eer
in
g
, Vo
l
.8
, N
o. 1 p
p
. 39
ā 5
1
,
J
an
-Feb
2
0
1
3
.
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