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.
4, D
e
c
e
m
ber
201
9,
pp.
1705~
17
13
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp1705-1713
1705
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 novel reg
ion selection
approac
h of SVPWM for a three-level
NPC inverter used in electric vehicle
D
e
b
a
njan
R
oy
,
S
a
n
a
tan
Kum
a
r,
M
ad
hu
S
in
gh
Depa
rtem
ent o
f
E
lectr
i
ca
l E
n
gi
neer
in
g,
Na
t
iona
l
Insti
t
u
t
e o
f
Te
ch
nol
ogy
,
In
di
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
Mar
4
,
201
9
Re
vise
d A
p
r
14,
201
9
Ac
ce
p
t
ed
J
un
2
2
,
2
019
Th
is
p
aper
c
onfers
an
i
nv
estigat
io
n
o
f
a
s
pace
v
ect
or
m
o
d
u
l
a
tio
n
based
control
s
t
rat
e
gy
o
f
induc
t
i
o
n
m
o
tor
using
a
t
h
re
e-level
inverte
r
f
o
r
electri
c
veh
i
cl
e
ap
pl
ication
.
T
h
e
p
ropo
sed
co
nt
roller
us
es
a
s
im
ple
v/f
cont
rol
wit
h
a
no
vel
S
V
PW
M
tech
ni
qu
e.
A
n
e
w
m
e
t
hod
f
o
r
r
eg
ion
s
e
lection
o
f
S
VP
WM
f
o
r
a
m
u
l
t
i
l
e
v
e
l
i
n
v
e
r
t
e
r
i
s
i
m
p
l
e
m
e
n
t
e
d
f
o
r
t
h
e
c
l
o
s
e
d
-
l
o
o
p
s
y
st
em.
P
r
evi
ously
t
he
r
egi
o
n
s
e
lection
proced
ure
was
n
o
t
co
nsidered
b
y
m
o
s
t
o
f
t
h
e
researcher
i
n
the
literat
u
re
f
or
d
eveloping
the
P
W
M
al
gori
t
hm.
T
h
i
s
a
p
p
roach
is
b
ased
on
s
o
me
a
lg
ebraic
e
qu
a
t
i
ons.
Th
e
re
m
a
rk
abl
e
p
oi
nt
h
ere
i
s
that
i
t
is
id
entical
t
o
al
l
the
rem
a
in
in
g
s
e
ctors
.
H
en
ce
cal
cul
a
ti
on
c
o
m
pl
e
x
i
t
y
reduces
by
m
aki
n
g
it
a
s
i
m
p
l
er
i
m
p
lem
e
nt
ati
on.
T
his
m
e
th
od
can
b
e
app
l
i
ed
t
o
any
nu
m
b
er
o
f
lev
e
ls.
T
h
e
p
o
t
e
ncy of
t
he prop
o
s
e
d
co
nt
roll
er
i
s
v
a
l
i
d
a
t
e
d
t
hrou
gh
th
e
M
A
TLAB/SIM
U
L
INK
e
n
viron
m
e
n
t.
T
he
p
erf
o
rman
ce
o
f
t
h
e
o
verall
sy
st
e
m
i
s
in
sp
ected
t
h
r
ou
gh
transien
t
and
st
eady
-
s
t
at
e
anal
ys
is
.
T
h
e
neu
t
ral
p
o
int
b
a
la
nc
e
o
f
t
he
3
L
NPC
in
ve
rte
r
i
s
e
s
ta
b
l
i
s
he
d
b
y
a
dop
ting
p
roper
sw
it
chin
g
sequ
ences
.
K
eyw
ord
s
:
Elec
tric
V
ehic
le
(EV
)
F
i
xed
V
/
F
Co
n
t
ro
l
S
p
a
ce
V
e
c
t
or
P
ul
se
w
id
t
h
Mo
du
la
ti
on (
S
V
P
WM)
Three
-
leve
l
(
3L
) I
nverter
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:
De
b
a
nj
an
Roy
,
D
e
pa
rtem
ent o
f
E
lectr
i
c
a
l E
n
gi
nee
r
in
g,
N
a
ti
ona
l N
a
tio
na
l
Ins
tit
ut
e of Te
c
h
n
o
l
og
y,
Jam
s
hed
pur,
Jhark
h
a
nd-
8
3
1
014,
Ind
ia
Em
ail:
deba
n
j
a
n
ro
y8
8@
gm
ai
l
.
c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
D
u
e
t
o
a
lim
it
ed
r
e
s
our
ce
fo
r
oil
a
n
d
to
r
e
duce
t
h
e
air
p
o
l
l
u
ti
on,
e
l
e
c
t
r
i
c
ve
h
i
cles
e
m
e
r
g
ed
a
s
an
alter
n
a
t
e
a
n
d
re
li
a
b
l
e
s
o
l
u
tio
n for th
e
trans
p
ort ind
u
s
t
ry. Se
l
ect
i
o
n of trac
t
i
o
n mo
t
o
r pla
y
s a
n
imp
orta
n
t
ro
l
e i
n
the
e
l
e
c
tr
ic
p
rop
u
l
s
i
on
sys
t
e
m
.
D
e
pend
in
g
on
vari
o
u
s
p
e
rform
anc
e
charact
e
ristics
[
1
]
dif
f
e
rent
t
raction
motors
a
re
g
rade
d
in
t
he
s
ca
l
e
o
f
five.
IM
a
nd
P
M
S
M
a
re
t
he
b
es
t
ca
nd
id
a
t
es
f
o
r
t
ra
ct
io
n
a
p
pl
i
c
ati
ons
a
s
i
t
h
a
s
lo
w
c
o
st
,
ma
t
u
re
t
ec
hno
lo
gy
a
nd
l
ess
ma
i
n
t
e
n
a
nce
[
2
,
3
]
.
A
de
tai
l
e
d
c
om
paris
on
be
tw
ee
n
t
r
ac
ti
o
n
m
oto
r
dri
v
es
a
re
c
om
pare
d
in
[
4]
a
t
sam
e
v
e
h
i
c
l
e
s
pec
i
fica
ti
o
n
s
and
d
i
m
e
n
si
ons.
Th
ou
gh
P
MSM
i
s
a
d
v
a
nt
ag
e
o
u
s
d
u
e
t
o
h
i
gh
p
ower
d
en
si
ty
,
l
e
ss
l
o
ss
a
nd
h
igh
eff
i
ci
en
cy
,
t
h
ey
ar
e
r
e
stric
t
ed
d
ue
t
o
less
a
v
ai
l
a
b
i
l
i
t
y
of
r
are
-
ea
rth m
a
gne
ts a
nd h
i
gher
cos
t
[5]
.
To
c
o
n
t
ro
l
t
h
e
vo
lta
ge
a
nd
fre
que
ncy
vol
ta
ge
s
o
u
rce
i
nve
rter
s
a
re
p
referr
ed
over
cu
r
r
ent
source
in
verter
s
f
o
r
i
t
s
fast
d
y
n
a
m
ic
r
espon
se
b
ec
a
u
se
n
o-l
i
n
e
i
nd
uct
o
r
i
s
u
se
d
as
i
n
t
h
e
c
a
se
o
f
CSI.
D
e
p
en
di
ng
on
the
p
o
l
e
vo
lta
ge
, inve
rters are
c
a
te
gor
ize
d
a
s tw
o le
ve
l
an
d a
b
o
v
e
t
w
o
le
ve
l i.
e. m
u
l
t
ile
ve
l
i
nver
t
e
r
s. In c
a
se o
f
tw
o-le
ve
l
i
n
ve
r
t
er
h
ig
he
r
b
l
o
c
ki
n
g
v
o
l
t
a
ge,
fr
eque
nc
y
,
s
w
i
tch
i
n
g
an
d
c
ond
u
c
ti
on
l
o
s
s
e
s
a
r
e
ex
t
r
e
m
e
l
y
h
i
gh
.
These
losse
s
are
dissi
p
a
t
e
d
b
y
a
heat
s
in
k.
F
or
d
i
ssi
pa
t
i
n
g
t
hi
s
la
rge
a
m
ou
n
t
o
f
pow
er
t
he
r
eq
u
i
rem
e
nt
o
f
a
hea
t
s
i
nk
a
nd
c
o
st
o
f
co
ol
in
g
sys
t
e
m
w
il
l
i
n
c
r
ease,
w
hi
c
h
w
i
l
l
i
n
c
r
ea
se
t
he
s
pa
ce
re
q
u
i
r
e
m
ent
a
s
w
el
l
.
H
ence
,
t
h
e
ov
era
l
l
si
z
e
o
f t
h
e
sy
st
e
m
wi
l
l
i
n
c
r
ea
se
wh
i
ch
i
s no
t
a g
o
o
d
pr
act
ice
for
trac
t
i
o
n
d
ri
ves or elec
t
ric ve
hic
l
es.
H
e
r
e
,
m
u
lt
ile
v
e
l
i
nver
t
e
r
s
com
e
i
nt
o
pla
y
a
s
a
solu
tio
n
t
o
t
h
i
s
p
r
o
b
l
e
m
.
M
a
i
n
l
y
b
e
c
a
u
s
e
i
t
h
e
l
p
s
t
o
l
o
w
e
r
t
h
e
bl
oc
ki
ng
v
o
l
t
a
ge
p
er
d
ev
ice
w
h
ic
h
red
u
ce
s
the
l
o
sse
s
c
o
m
pare
d
t
o
t
w
o
-
l
e
ve
l
i
n
ver
t
e
r
[
6-9].
Th
ou
g
h
v
e
c
t
o
r
con
t
ro
l
i
s
b
es
t
su
ite
d
for
t
r
act
io
n
a
p
p
lic
at
ion
[6],
t
he
f
ixe
d
V
/
F
c
ontr
o
l
is
p
er
form
ed
i
n
t
h
i
s
p
a
p
e
r
f
or
l
ow
c
o
s
t
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 V
ol.
10,
N
o.
4
, Dec
201
9 :
1
7
0
5
– 1
713
1
706
and
simp
le
i
m
p
lem
e
n
t
a
t
io
n
w
ith
p
r
opose
d
S
VP
WM
t
ech
ni
q
u
e
a
s
v
ect
o
r
c
on
trol
m
e
t
h
od
is
m
ore
c
o
mplex
i
n
com
p
aris
on w
i
th V
/
F
c
o
n
trol.
A
ne
w
algori
t
hm
for ne
u
tral po
i
nt
ba
la
nc
i
n
g
w
a
s repor
t
e
d
in [
1
0
]
. In that
paper
,
M
a
md
an
i
’
s
f
u
zzy
l
ogi
c
c
o
nt
rol
l
er
b
a
s
ed
c
o
n
t
ro
l
sch
e
me
i
s
p
r
ese
n
ted
t
o
i
m
p
rove
o
v
e
rall
s
ys
t
e
m
pe
rfor
m
anc
e
for
a
3L
i
nve
r
t
er.
A
com
p
ar
i
s
on
is
i
n
v
est
i
g
a
t
e
d
w
i
t
h
a
n
d
w
it
ho
u
t
t
h
e
ne
utra
l
p
o
in
t
ba
l
a
nci
n
g
al
gor
ithm
.
A
no
ve
l
tec
h
n
i
q
u
e
f
or
r
egi
on
ide
n
tific
a
tio
n
o
f
S
VP
WM
f
or
a
3
L
in
v
e
r
t
e
r
i
s
i
nt
rodu
ce
d
a
n
d
i
m
pl
emen
t
e
d
in
[
1
1
,
1
2
]
und
e
r
o
p
e
n
loo
p
op
erat
io
n
of
a
n
i
n
d
u
c
ti
on
m
oto
r
.
A
si
m
p
l
i
f
ied
S
V
P
W
M
a
l
gor
i
t
hm
i
s
i
m
ple
m
ented
furt
her
i
n
[
1
3
]
w
h
er
e
seve
n
se
gm
ent
se
q
u
e
n
c
e
is
i
m
p
lem
e
nt
ed
f
or
3
L
in
ve
rter
[
12]
a
nd
a
d
e
t
a
ile
d
c
o
m
p
a
r
i
s
o
n
i
s
i
nv
e
s
ti
g
a
t
e
d
wi
th
s
wit
c
hi
ng
se
qu
en
ce
w
h
e
re
a
l
l
t
h
e
r
e
dund
a
n
t
s
t
a
t
e
s
w
e
r
e
u
s
e
d
.
P
r
o
p
e
r
s
w
i
t
c
h
i
n
g
s
e
q
u
e
n
c
e
s
in
S
V
P
WM
t
e
c
h
n
i
que
p
la
ys
a
c
ruc
i
a
l
p
a
r
t
f
o
r
ne
utra
l
poi
n
t
b
ala
n
c
e
i
n
mu
lti
l
e
v
e
l
i
n
v
e
rt
er
w
i
t
hout
i
nt
ro
du
c
i
ng
any
e
x
tra
con
t
rol
l
er.
[
1
4
]
prese
n
ts
t
he
m
ode
l
l
i
ng
of
a
n
elec
tri
c
v
e
h
ic
le
(
EV
)
sup
p
o
rte
d
b
y
i
n
d
u
c
tio
n
mot
o
r
an
d
3L
N
P
C
/d
i
ode
c
l
a
mpe
d
i
nve
rter.
A
fixe
d
V
/
H
z
c
on
tro
l
s
t
r
ateg
y
w
a
s
u
s
e
d
i
n
t
h
a
t
p
a
p
e
r
w
h
i
l
e
t
h
e
i
n
v
e
r
t
e
r
i
s
gate
d
b
y
a
S
i
n
uso
i
da
l
P
u
l
s
e
Wi
dth
Mo
du
la
ti
o
n
.
H
e
re
,
a
close
d
l
o
op
f
i
x
ed
V
/
F
c
ont
rol
i
s
a
ch
iev
e
d
wit
h
t
he
no
ve
l
re
g
i
on
s
ele
c
t
i
o
n
a
ppr
o
a
c
h
a
n
d
e
ffe
c
tive
n
e
ss
of
t
he
p
r
o
pos
e
d
c
o
n
t
rol
l
e
r
i
s
i
nve
st
iga
t
e
d
t
hro
u
g
h
s
te
a
dy-
st
a
t
e a
nd tra
n
si
ent
resp
on
ses o
f
the
i
n
duc
t
i
o
n
m
otor.
The
p
a
p
e
r
co
n
s
i
s
ts
f
o
u
r
di
ff
ere
n
t
sec
t
i
o
ns.
S
e
c
t
io
n
t
w
o
addre
s
s
e
s
t
he
c
on
tro
l
s
truc
tu
re
u
sed
for
con
t
ro
l
lin
g
t
h
e
trac
t
i
on
m
o
t
or
.
Thi
s
s
e
c
t
ion
ha
s
su
bsec
tio
n
w
h
i
c
h
d
i
s
c
u
s
s
e
s
t
h
e
p
r
o
p
o
s
e
d
S
V
P
W
M
a
l
g
o
r
i
t
h
m
whic
h
em
pl
oy
es
n
o
v
el
r
e
g
io
n
i
d
en
t
i
fica
ti
o
n
a
p
p
roa
c
h
wh
e
r
ea
s
sim
ula
tio
n
r
e
sul
t
s
a
r
e
show
n
i
n
s
ec
tio
n
t
h
ree
.
F
i
nal
l
y
,
t
h
e
pa
p
e
r
presents a
sig
n
i
f
i
c
a
n
t c
o
nc
lu
d
i
n
g
o
b
s
e
r
va
ti
o
n in sec
tio
n
fo
ur.
2.
CONT
ROL S
T
RUC
T
URE
I
n
t
h
i
s
pa
pe
r,
a
n
i
n
d
u
c
tio
n
m
o
t
o
r
is
c
on
t
r
ol
le
d
b
y
a
P
WM
m
ult
i
l
ev
el
i
nv
ert
e
r.
A
n
i
n
v
e
rte
r
i
s
f
e
d
by
a
dc
s
up
p
l
y
w
h
ic
h
i
s
c
on
ve
rte
d
by
a
t
h
re
e
p
h
ase
a
c
r
e
c
t
i
f
ie
r.
H
e
r
e,
a
f
ixe
d
V
/F
s
tra
t
e
gy
i
s
u
se
d
f
o
r
co
n
t
ro
ll
ing
the
t
r
ac
ti
o
n
m
ot
or.
S
p
e
e
d
c
o
n
t
ro
l
l
e
r
c
om
pr
i
s
e
s
o
f
a
P
I
c
on
t
r
ol
l
e
r
w
h
i
c
h
g
e
n
erat
e
s
s
l
i
p
co
mp
en
sat
i
o
n
as
exp
l
a
i
ne
d
in
(
1)
a
n
d
t
he
n
g
e
ts
s
um
me
d
u
p
w
i
t
h
m
e
a
s
ur
ed
r
o
t
or
s
p
ee
d.
N
e
x
t
t
h
a
t
s
i
gna
l
is
c
onve
r
t
ed
t
o
fre
que
nc
y
to
p
r
o
d
u
ce
com
m
a
n
d
ed
s
t
a
tor
vo
l
t
a
g
e.
∗
(
1
)
P
I
-c
ontr
o
lle
r
is
t
u
n
ed
u
sin
g
Z
ie
g
l
e
r
–N
ich
o
l
s
me
tho
d
w
her
e
K
p
a
nd
K
i
v
a
l
ue
s
ar
e
obta
i
ne
d
a
t
r
ated
l
o
ad
c
on
di
ti
on
[1
1
]
.
At
f
i
r
st
,
th
e
Ki
i
s
se
t
to
z
e
r
o
a
n
d
K
p
i
s
grad
ua
l
l
y
i
n
c
r
ea
se
d
t
o
its
u
lt
ima
t
e
ga
in
K
p
*
a
t
w
h
ic
h
the
c
o
n
t
r
o
l
l
oop
o
u
t
p
u
t
osc
i
l
l
a
t
e
s
w
i
t
h
a
c
onsta
nt
a
m
p
lit
ude.
(
T
u),
the
osci
lla
ti
o
n
p
e
r
i
od
a
nd
K
p
a
r
e
use
d
t
o
fi
n
d
o
ut
t
he
p
ro
port
i
o
n
a
l
a
nd
i
n
te
gral
g
ai
ns
b
as
e
d
o
n
t
he
t
y
p
e
o
f
t
h
e
c
o
n
t
r
o
l
l
er.
The
r
ef
ore,
t
h
e
pro
port
i
ona
l
a
nd
in
te
gra
l
g
a
i
ns
(
k
p
a
nd
k
i
)
fo
r
pa
rtic
u
l
ar
P
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trol
ler
(sp
e
e
d
c
o
n
t
r
oller
)
a
re
f
ound
0.4
5
ku
a
nd
1.25
(K
p
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u
),
respec
t
i
v
e
l
y.
The
o
v
e
r
a
l
l
s
y
stem
i
mp
lem
e
nta
tio
n
i
s
d
e
p
ic
te
d
in
t
he
f
i
g
ure
be
l
o
w
.
Th
en
d
e
r
i
v
ed
v
olt
a
g
e
a
nd
fre
que
nc
y
fro
m
t
he
f
ix
e
d
V
/
F
c
ontro
l
l
e
r
i
s
fed
to
S
V
P
WM
b
loc
k
f
or
g
ener
at
i
o
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g
ate
p
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s
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3L
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n
F
i
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re 1.
F
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r
e
1
.
A
3-ph
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duc
t
i
o
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m
ot
or V
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z
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m
plem
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tat
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on
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i
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s
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l
e
ve
l
NP
C
in
v
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r
t
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r
SV
P
W
M
/
BC
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W
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Ge
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r
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r
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H
z
3-p
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n
d
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c
t
i
o
n
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t
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f
o
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|
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W
sl
i
p
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o
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W
r
Fr
eq
u
e
n
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t
e
r
W
s
+
+
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I
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for A three
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S
V
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T
E
CHNIQ
U
E FOR
3
L
I
NVE
RTER
Im
plem
enta
ti
on
of
S
VP
WM
t
e
c
h
n
i
q
u
e
for
a
mul
t
i
l
e
v
e
l
i
n
v
er
t
e
r
i
s
mor
e
c
om
p
l
e
x
t
ha
n
a
tw
o-
lev
e
l
i
n
v
e
r
t
e
r
.
S
o
,
i
t
r
e
q
u
i
r
e
s
a
d
i
f
f
e
r
e
n
t
a
p
p
r
o
a
c
h
t
o
d
e
a
l
w
i
t
h
i
t
.
M
a
p
p
i
ng
ba
se
d
co
nce
p
t
f
o
r
MLI
is
v
e
r
y
p
o
p
u
l
a
r
a
nd
pr
ese
n
t
e
d
in
[
1
5
]
.
A
c
once
p
t
of
r
ever
se
m
appi
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is
a
l
s
o
pr
e
sen
t
e
d
i
n
[
1
6]
f
or
a
f
i
v
e-
le
vel
a
nd
a
se
v
e
n-
leve
l
N
P
C
i
n
v
e
r
t
er
.
MLI
top
o
lo
gy
deal
w
it
h
a
nu
m
b
er
o
f
r
e
dunda
n
t
st
a
t
e
s
w
h
i
ch
r
ep
resen
t
t
h
e
s
ame
sp
a
ce
v
e
c
t
o
r
.
F
o
r
a
3
L
i
n
v
e
r
t
e
r
,
a
m
o
n
g
2
7
s
p
a
c
e
v
e
c
t
o
r
s
,
t
h
e
r
e
a
r
e
s
i
x
num
ber
s
o
f
t
h
e
l
a
r
g
e
ve
ctor
,
six
n
u
mb
e
r
s
of
the
m
e
d
i
um,
tw
e
l
ve
n
um
ber
s
o
f
sh
or
t
ve
c
t
or
s
a
nd
t
h
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e
e
n
u
m
b
er
s
o
f
ze
r
o
/
n
u
ll
vec
t
or
s
w
h
ic
h
f
o
r
m
a
h
e
x
ag
o
n
a
l
str
u
c
t
ur
e
a
s
s
h
o
w
n
i
n
the
F
i
gur
e
2.
E
a
c
h
s
e
ctor
h
a
s
f
our
r
egi
o
n
s.
A
f
t
e
r
r
eg
i
o
n
i
d
enti
fi
ca
t
i
on
,
t
h
e
re
fere
n
c
e
ve
ct
or
i
s
gener
a
ted
b
y
e
m
p
l
o
yin
g
n
e
a
r
e
st
t
h
r
e
e
s
pac
e
v
ec
t
o
r
s
.
H
e
n
ce,
r
egio
n
ide
n
ti
fica
ti
o
n
h
as
a
n
in
flue
ntia
l
e
ffe
c
t
on
p
u
ls
e
gen
e
r
a
tio
n.
T
he
r
e
a
r
e
v
er
y
fe
w
pu
b
l
i
c
a
t
io
ns
a
r
e
a
v
a
il
ab
l
e
o
n
r
e
gio
n
i
d
e
nti
f
i
c
at
ion
i
n
t
he
li
ter
a
tur
e
.
A
n
ove
l
r
e
gio
n
i
de
nt
i
f
ica
t
io
n
me
t
hod
is
i
n
t
r
o
d
u
c
e
d
in
[
1
1
,
12]
.
Ea
ch
s
ec
tor
ha
s
f
our
r
e
g
i
ons.
A
f
t
e
r
r
e
gi
on
ide
n
tif
i
c
atio
n,
t
he
r
ef
e
r
enc
e
v
e
c
t
or
i
s
ge
ne
r
a
te
d
b
y
e
m
p
l
o
y
i
n
g
n
e
a
r
e
s
t
t
h
r
e
e
s
p
a
c
e
v
e
c
t
o
r
s
.
H
e
n
c
e
,
r
e
gi
on
ide
n
tif
i
c
atio
n
ha
s
an
i
nf
l
u
en
t
i
al
e
ffe
ct
o
n
pu
lse
ge
ne
r
a
t
i
o
n
.
A
d
e
t
a
i
l
e
d
a
n
a
l
ys
is
h
as
b
e
e
n
per
f
o
r
m
e
d
in
di
ffere
n
t
m
o
d
u
l
at
ion
in
de
x.
I
n
t
h
is
p
aper
,
t
h
i
s
m
e
t
ho
d
is
f
ur
th
e
r
i
mpl
e
m
e
n
t
e
d
f
or
c
lose
d-
loo
p
c
o
n
tr
ol
f
or
ve
h
i
c
u
l
a
r
a
p
pli
c
atio
n.
T
he
m
e
t
h
o
d
i
s
d
i
scu
s
s
e
d
i
n
d
e
t
a
i
l
in
t
he
c
om
ing
sect
io
n.
2V
DC
/3
V
DC
/6
V
DC
/2
x
y
1
2
3
4
1
2
3
4
V
0
V
1
00
0
1
1
1
V
13
V
DC
/3
V
7
V
14
V
2
V
3
V
15
V
8
0-
1-
1
1
0
0
0
0
-
1
1
0
-
1
1
1
-
1
0
1
-
1
-
1
1
-
1
0
1
0
1
0
-
1
S
ect
o
r
2
V
27
V
25
V
19
1-
1-1
V
20
F
i
gur
e
2.
H
e
x
ago
n
a
l
s
pa
ce
v
e
c
t
or
r
e
p
r
e
se
nta
t
i
o
n
of
a
3
L
inve
r
t
e
r
F
i
gur
e
3.
Repr
e
se
n
t
at
ion
o
f
r
egi
o
ns
f
or
s
e
c
tor
1
in
x-
y
p
l
ane
3.
1.
Pro
p
o
s
ed reg
io
n
identifica
t
i
o
n
met
h
o
d
A
ne
w
m
e
th
od
f
or
r
eg
io
n
i
d
e
n
t
i
f
i
c
a
t
io
n,
b
a
s
ed
o
n
a
l
gebr
a
i
c
e
q
u
a
ti
o
n
s
t
o
l
o
cat
e
t
h
e
po
sit
i
on
o
f
t
h
e
V
re
f
i
s
pr
ese
n
te
d
in
t
hi
s
sec
t
io
n.
F
ig
ur
e
3
dep
i
c
t
s
tw
o
su
c
cessi
ve
se
c
t
o
r
s
(
s
e
c
tor
1
a
nd
se
ct
or
2
)
a
nd
it
s
c
o
r
r
e
spo
n
d
i
n
g
r
e
gi
ons
o
f
a
th
r
e
e-
l
e
vel
i
n
ver
t
e
r
.
A
ll
t
h
e
s
i
x
se
ct
or
s
o
f
t
he
h
e
x
a
g
o
n
a
r
e
s
ymm
e
tr
y
in
n
a
t
ur
e
.
H
e
nce
,
t
he
m
e
t
ho
d
of
r
egi
o
n
i
d
en
t
i
f
i
ca
ti
o
n
f
or
a
s
e
c
t
o
r
ca
n ea
s
i
l
y
be
a
p
p
li
ed to
o
t
her
sec
t
or
s.
T
he nul
l
ve
ctor
s
a
r
e
loc
a
te
d
a
t
t
he
o
r
i
gin
o
f
t
he
s
pac
e
v
e
c
t
o
r
dia
g
r
a
m.
C
oo
r
d
ina
t
e
s
o
f
o
t
h
er
v
ec
tors
i
n
t
h
at
s
ec
t
o
r
ca
n
b
e
a
c
qu
ir
ed
f
r
o
m
a
2-
di
m
e
n
s
i
o
n
a
l
x-
y
p
l
ane
as
i
l
l
ustr
a
t
e
d
i
n
F
i
gur
e
3
.
T
h
e
x
c
o
m
pon
ent
of
t
h
e
r
e
f
ere
n
ce
sp
a
ce
ve
ct
or
(
x
1
)
i
s
i
n
p
h
ase
w
i
t
h
t
he
s
tar
t
i
n
g
ve
ctor
i
n
t
h
a
t
s
e
c
t
or
a
nd
y
c
o
m
pone
n
t
i
s
pe
r
p
en
dic
u
lar
to
t
h
a
t
x
co
mp
on
en
t
.
T
he
t
a
(
)
r
e
pr
esent
s
t
he
a
n
g
le
b
etw
e
e
n
t
he
s
t
a
r
t
i
ng
a
n
d
t
h
e
r
e
fer
e
nce
v
ect
or.
The
c
o
ord
i
n
a
t
e
s
o
f
a
b
o
v
e-
m
e
nt
i
one
d
spac
e
vec
t
o
r
s
ar
e
give
n
i
n
t
he
T
a
b
l
e
1
.
The
me
th
od
i
s
base
d
o
n
m
ai
nl
y
tw
o
a
l
ge
br
aic
e
q
ua
ti
on
s.
B
ot
h
r
e
p
r
e
s
e
n
t
t
h
e
e
q
u
a
t
i
o
n
o
f
a
s
t
r
a
i
g
h
t
li
ne.
F
i
r
s
t
one
c
an
b
e
o
b
t
a
i
ne
d
by
j
oi
n
i
n
g
t
w
o
p
o
i
n
t
s
i.
e.
c
oor
dina
tes
of
V
1
a
n
d
V
2
.
S
i
m
i
la
r
l
y
se
c
o
n
d
str
a
ig
ht
li
ne
can
b
e
acq
uir
e
d
by
j
o
in
in
g
V
1
a
nd
V
7
.
B
o
th
t
he
e
qua
t
i
ons
a
re
writte
n
a
s
(2)
and
(3)
11
3
(
3
)
DC
V
x
y
(
2
)
22
3
3
()
DC
V
x
y
(
3
)
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 V
ol.
10,
N
o.
4
, Dec
201
9 :
1
7
0
5
– 1
713
1
708
Tab
l
e
1. T
h
e
c
oor
dina
te of i
n
div
i
d
u
a
l
spa
ce
vec
t
or
s
in x-
y
p
l
a
n
e f
o
r se
cto
r
1
S
p
ac
e
Vec
t
or
C
a
t
e
gory
C
oor
di
na
te
(
X
,
Y
)
V
25
,
V
26
,
V
27
null
(
0
,
0
)
V
1
,
V
19
S
hort
3,0
V
13
L
a
r
g
e
2
3,0
V
7
M
e
d
i
u
m
2
,
3
6
V
14
L
a
r
g
e
3
,
3
3
V
2
,
V
20
Short
6
,
3
6
The
refere
nce
vect
or
V
re
f
h
as tw
o
c
omp
one
nts
1
re
f
x
VC
o
s
(
4
)
1
re
f
yV
S
i
n
(
5
)
N
o
w
,
by
insert
in
g
the
va
l
u
e
o
f
x
1
in
e
qu
at
ion
(2
)
an
d
(3
),
t
he
v
alue
s
for
y
11
a
nd
y
22
c
an
b
e
o
b
ta
i
n
ed
a
s
gi
ve
n
bel
o
w
-
1
11
3)
3
(
D
C
V
x
y
(
6
)
1
22
3
(
)
3
D
C
V
x
y
(
7
)
The
(
5
),
(
6)
,
(7
)
and
x-y
c
o
mpone
n
t
o
f
V
re
f
a
re
u
se
d
to
i
de
n
t
i
f
y
t
h
e
re
gi
ons
b
a
s
e
d
o
n
so
m
e
c
ri
teri
a.
T
he
criter
i
a
for
r
e
g
i
o
n
i
de
nti
f
ica
t
i
on
a
r
e
for
m
ula
t
e
d
i
n
Ta
bl
e
2.
D
ue
t
o
sym
m
e
t
ric
nat
u
re
b
e
t
ween
a
ll
t
h
e
se
ctors,
the m
e
th
o
d
r
em
ains t
he
s
a
m
e
a
s
s
ector
1
e
xcept
the
x-y
co
ord
i
na
t
e
i
s
s
h
if
te
d
b
y
6
0
.
Ta
b
l
e
2.
Crit
e
ri
a
for
regio
n
ide
nt
i
f
ica
tio
n i
n
a
ny sec
t
or
Re
gion
C
ondition
1
1
0/
6
DC
xV
a
nd
06
0
Or
1
/6
DC
Vx
a
nd
11
1
yy
2
1
/6
DC
Vx
a
nd
11
1
3/
6
DC
yy
V
Or
1
/2
DC
Vx
a
nd
22
1
3/
6
DC
yy
V
3
1
/2
DC
Vx
a
nd
12
2
yy
Or
1
/2
DC
Vx
a
nd
03
0
4
I
f
a
bove
thr
e
e
c
onditions a
r
e
not s
a
t
i
s
fie
d
the
n s
e
l
e
ct
r
e
gion
4
3.2.
V
e
ctor
s
equence
an
d
D
w
ell time
c
a
l
c
u
lat
i
o
n
s
The
ve
c
t
or
s
e
que
nce
o
f
a
ny
r
egi
o
n
s
h
o
u
l
d
m
a
i
n
t
a
i
n
t
he
f
ol
low
i
ng
c
r
i
t
e
r
i
a
;
a
)
I
n
a
n
y
s
e
q
u
e
n
c
e
,
cha
nge
over
be
tw
ee
n
s
t
a
t
es
a
llow
s
t
h
e
o
n
l
y
o
n
e
sw
i
t
c
h
i
ng
i.e.
a
tra
n
si
t
i
o
n
f
r
o
m
1
t
o
-
1
or
v
i
c
e-
ve
rsa
i
s
pro
h
i
b
i
t
e
d
.
b)
Ter
minal
st
a
t
e
of
a
n
y
c
urre
nt
s
am
ple sh
ou
l
d
be
t
he i
n
i
ti
a
l
s
ta
te of t
h
e
u
p
c
o
ming
sa
mp
le.
The
d
i
f
f
er
en
t seque
n
c
es
f
or di
f
fere
n
t
r
e
g
ion
s
in
se
c
t
or
1
ar
e
t
ab
ul
ari
z
ed
i
n
Ta
bl
e
3
.
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
A nov
e
l
regi
o
n
se
l
e
c
t
i
on
Ap
pr
oac
h o
f
SVPW
M for A
t
h
re
e-
l
e
v
e
l NP
C i
n
ver
ter
…
(D
e
b
a
n
j
an
R
o
y)
1
709
Tab
l
e
3.
V
ector
s
equenc
es o
f re
gions
(
1,
2
, 3,
4) in sec
t
or 1
Re
gi
on
V
e
c
t
or
S
e
q
u
e
n
c
e
1
V
19
↔
V
20
↔
V
26
↔
V
1
(0-1-
1
)
(00
-
1
)
(000
) (100)
2
V
19
↔
V
20
↔
V
7
↔
V
1
(
0
-1-1)
(0
0
-
1
)
(
1
0
-
1
)
(
100
)
3
V
19
↔
V
13
↔
V
7
↔
V
1
(0
-
1
-
1
)
(
1
-1
-
1
)
(1
0
-
1
)
(
10
0)
4
V
20
↔
V
7
↔
V
14
↔
V
2
(
0
0
-
1)
(
10
-1
)
(
1
1-
1)
(
11
0
)
The
s
p
a
ce
ve
c
t
or
d
iagr
am
t
ha
t
i
s
s
h
o
w
n
i
n
F
i
g
u
r
e
2
c
a
n
b
e
use
d
t
o
c
a
l
c
u
l
a
t
e
t
h
e
t
i
m
e
f
o
r
e
a
c
h
s
e
c
t
o
r
(I
to
V
I).
E
ach
s
ector
has
f
o
ur
r
egio
ns
(
1
t
o
4
),
a
s
sh
ow
n
in
F
i
g
u
r
e
3
,
w
i
t
h
t
h
e
s
w
i
t
c
h
i
n
g
s
t
a
t
e
s
o
f
a
l
l
v
e
c
t
o
r
s
.
The
s
u
m
of
t
h
e
v
o
ltage
m
ul
t
i
pl
ie
d
b
y
t
he
i
n
t
e
r
va
l
o
f
c
h
o
se
n
sp
a
ce
v
e
c
t
or
e
qua
l
s
t
he
p
ro
duc
t
of
t
he
r
efe
r
enc
e
vo
lta
ge
V
re
f
a
nd
sa
mp
li
n
g
p
er
i
o
d
T
s
.
To
i
l
l
u
s
tra
t
e
,
w
he
n
r
e
fe
renc
e
vo
l
t
ag
e
is
l
oc
a
t
e
d
i
n
regi
on
2
of
s
e
c
t
or
I
t
h
e
n
t
h
e
n
e
a
r
e
s
t
v
e
c
t
o
r
s
t
o
ref
e
ren
c
e
vo
lt
ag
e
a
r
e
V
1
,
V
7
,
and
V
2
a
s
show
n
i
n
F
i
g
ure
3
and
4,
a
n
d
t
he
n
e
x
t
equa
t
i
o
n
s e
x
p
l
ain
the
re
lat
i
on
sh
ip be
t
w
e
en
t
i
m
es a
nd vo
lt
a
g
es.
The
v
o
l
t
-sec
b
a
lanc
e e
qua
t
i
on
for
regi
on
2
i
s
17
2
**
*
*
ab
c
r
e
f
s
V
T
VT
VT
V
T
(8)
Whe
r
e
T
a
,
T
b
and
T
c
are
t
he times f
or
V
1
, V
7
, a
nd V
2
resp
e
c
ti
v
e
ly
.
B
y
pu
t
tin
g
t
h
e
va
lue
s
o
f
V
1
,
V
7
, and
V
2
respec
t
ive
l
y
w
e
g
et,
*(
c
o
s
6
0
s
i
n
6
0
)
*
33
3
co
s
3
0
s
i
n
3
0
*
*
3
dd
ab
d
cr
e
f
s
VV
TT
V
TV
T
(9)
abc
s
TT
T
T
(10)
F
r
om
e
qua
ti
on
(
9)
r
eal
p
art
a
n
d
ima
g
i
n
a
r
y
pa
rt
c
a
n
b
e
de
ter
m
ine
d
a
nd
us
in
g
e
qua
t
i
on
(
8),
(9)
and
(10)
w
e
ob
tai
n
ed
t
he
r
e
quir
e
d
dw
ell
t
i
m
i
n
g
s
for
t
h
e
v
o
l
t
a
g
e
vec
tor
s
i
n
r
e
gi
o
n
2
.
S
i
m
i
l
a
r
l
y,
d
w
e
ll
timi
n
gs
f
or
di
ffe
re
nt r
eg
io
n
s
a
re
c
alcula
t
e
d
as show
n
in
T
able
4
.
Ta
b
l
e
4.
S
w
i
tc
hi
n
g
tim
es for se
c
t
o
r 1
Re
gi
on
S
p
a
ce
Vec
tor
s
D
w
e
ll T
i
me
/ Swit
ching T
i
me
1
V
1
, V
19
2
3
V
26
1
2
3
V
20
2
V
1
, V
19
12
V
7
2
3
1
V
20
1
2
3
3
V
1
, V
19
2
2
3
V
7
2
V
13
2
3
1
4
V
14
2
1
V
7
2
3
V
2
,
V
20
2
2
3
Wher
e,
s
T
is
t
he s
a
m
pli
n
g t
i
me
.
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 V
ol.
10,
N
o.
4
, Dec
201
9 :
1
7
0
5
– 1
713
1
710
s
T
=
abc
TT
T
Mo
du
lat
i
on I
nde
x (MI
)
=
3*
/
ref
D
C
VV
F
i
gure
4
s
how
s
seve
n
se
gm
ent
se
q
u
e
n
ce
s
o
f
r
e
g
ions
i
n
se
c
t
or
1
.
As
m
enti
o
n
ed
ear
lie
r,
o
n
l
y
a
swi
t
c
h
is
o
pe
rate
d
i
n
e
ve
ry
s
ta
t
e
c
ha
nge
ove
r.
T
he
v
ector
s
e
que
nce
s
f
or
o
the
r
r
eg
i
ons
i
n
sec
t
or
1
a
re
s
how
n
i
n
T
ab
le
3.
T
he dw
e
lli
n
g
tim
es for t
he
v
ect
ors
of se
c
t
o
r 1
are a
r
ra
nge
d
in Ta
b
le 4.
V
26
00
0
V
20
00
-
1
T
s
/2
T
s
/2
T
s
V
1
10
0
V
19
0-1-1
V
19
0-1-1
V
26
00
0
V
20
00
-
1
T
a
/4
T
c
/2
T
b
/2
T
a
/2
T
b
/2
T
c
/2
T
a
/4
V
az
V
bz
V
cz
V
7
10
-1
V
20
00
-
1
T
s
/2
T
s
/2
T
s
V
1
10
0
V
19
0-
1
-
1
V
19
0-
1-1
V
7
10
-1
V
20
00
-
1
T
a
/4
T
c
/2
T
b
/2
T
a
/2
T
b
/2
T
c
/2
T
a
/4
V
az
V
bz
V
cz
(a)
(b
)
V
7
10
-
1
V
13
1-1
-
1
T
s
/2
T
s
/2
T
s
V
1
10
0
V
19
0-
1
-
1
V
19
0-1
-
1
V
7
10
-
1
V
13
1-
1
-
1
T
a
/4
T
c
/2
T
b
/2
T
a
/2
T
b
/2
T
c
/2
T
a
/4
V
az
V
bz
V
cz
V
14
11
-
1
V
7
10
-
1
T
s
/2
T
s
/2
T
s
V
2
11
0
V
20
00
-
1
V
20
00
-
1
V
14
11
-
1
V
7
10
-
1
T
a
/4
T
c
/2
T
b
/2
T
a
/2
T
b
/2
T
c
/2
T
a
/4
V
az
V
bz
V
cz
(c)
(
d
)
F
i
gure
4.
S
eve
n
segm
e
n
t
sw
i
t
c
hi
n
g
seq
ue
nce
s
f
or
(
a) re
g
i
o
n
1, (
b) regio
n 2
,
(c
)
r
egion 3,
(d)
re
gi
on
4 o
f
s
ect
or
1
4.
SIMU
L
A
TION
O
UT
COMES
I
n
t
h
i
s
se
c
t
i
on,
t
he
p
r
o
p
o
se
d
S
V
P
W
M
a
lg
or
i
t
hm
i
s
exa
m
i
n
ed
t
hr
ou
g
h
t
h
e
s
im
ul
a
tio
n
resu
lts.
The
con
t
ro
l
sc
hem
e
h
a
s
a
lrea
d
y
d
e
p
ic
te
d
ea
lier
in
t
he
F
i
gure
1.
T
he
n
e
u
t
r
a
l
p
o
i
n
t
b
a
l
a
n
c
e
f
o
r
3
L
N
P
C
i
n
v
e
r
t
e
r
i
s
als
o
i
n
v
e
s
t
i
ga
t
e
d.
T
he
a
n
a
lys
i
s
of
t
he
o
vera
l
l
s
ystem
ha
s
b
e
en
p
e
r
f
orm
e
d
un
der
tr
ans
i
e
n
t
a
n
d
ste
a
d
y
-
state
con
d
i
t
i
on
s. Th
e
overa
l
l
s
i
m
u
l
ated peri
o
d
is di
v
ide
d
i
n
t
o th
re
e
subse
c
t
ions
i.e.
spe
e
d
r
e
sp
ons
e, torq
u
e re
spo
n
se
and
stea
d
y
s
t
a
te
r
e
s
ponse
.
S
p
eed
r
esp
o
n
se
d
e
f
i
n
es
a
c
ha
n
g
e
i
n
s
p
e
ed
w
he
rea
s
a
c
ha
nge
i
n
tor
q
ue
r
e
p
r
e
se
nts
tor
que
r
esp
ons
e.
T
he
p
ara
m
e
t
ers use
d
ar
e
jot
ted d
o
w
n
b
e
l
o
w
.
DC b
u
s
vol
t
a
ge
,
V
DC
= 3
53 V
No
mi
n
a
l
Po
wer=
4
K
W
.
R
a
ted S
p
eed=
1
430
r
.p.m.
R
s
=
1
.405
,
R
r
=1.
3
9
5
,
L
m
=0.1722 H
a
nd
L
ls
=L
lr
=0.005839 H.
Swi
t
c
hi
ng
fre
qu
en
cy
, f
sw
= 5
kH
z.
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
A nov
e
l
regi
o
n
se
l
e
c
t
i
on
Ap
pr
oac
h o
f
SVPW
M for A
t
h
re
e-
l
e
v
e
l NP
C i
n
ver
ter
…
(D
e
b
a
n
j
an
R
o
y)
1
711
4.1.
Sp
eed
resp
o
nse
Th
e
sy
st
e
m
i
s
i
n
it
i
a
l
l
y
op
era
t
ed
w
it
h
a
ref
e
r
e
n
c
e
sp
eed
o
f
7
0
0
r
.
p.
m
and
a
refe
renc
e
tor
que
o
f
1
0
Nm.
At
t
=
4
s
ref
e
re
n
c
e,
s
p
e
e
d
i
s
in
c
r
e
a
s
ed
f
ro
m
7
0
0
t
o
1000
r
.p
.
m
keepi
n
g
refere
nce
t
o
rque
c
on
sta
n
t
a
t
10
N
-
m
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
5
(
a
)
.
T
h
e
s
y
s
t
e
m
d
e
p
o
r
t
m
e
n
t
i
s
d
e
p
i
c
t
e
d
d
u
ri
ng
t
h
e
spee
d
c
h
a
n
g
e
i
n
F
i
g
u
r
e
5
(
a
).
T
he
me
ntio
na
ble
p
o
in
t
is
t
ha
t
t
h
e
r
o
t
o
r
spee
d
foll
ow
s
i
t
s
refere
nce
v
a
l
u
e
v
e
r
y
ac
cura
te
ly
a
nd
ve
rifi
es
t
he
effec
t
i
v
e
n
e
s
s
o
f
t
he
s
ug
ge
ste
d
S
V
P
W
M
a
lgo
r
it
hm
.
In
F
igur
e
5(b)
e
l
ec
t
r
oma
g
n
e
ti
c
to
rque
r
i
ppl
e
sh
o
w
n
a
s
2
.4
N
m
.
N
e
utra
l
p
o
i
n
t bala
nc
in
g of
N
P
C
i
s
a
l
so in
v
es
tiga
t
e
d
.
D
u
ri
ng
t
he
s
peed
r
e
s
po
nse
ca
pa
cit
o
rs v
o
l
tage
r
ip
p
l
e
is
s
how
n
in
F
i
gure
5(c
)
w
hic
h
i
s
ab
o
u
t
6.
7
V
in
t
ra
ns
i
e
n
t
a
nd
u
nder
s
t
ea
dy
s
t
a
t
e,
r
ip
p
l
e
com
e
s
d
o
w
n
t
o
5.8
V
.
The
pr
op
ose
d
a
lg
ori
t
h
m
kee
p
s
t
h
e
dc
b
us
v
ol
t
a
ge
b
a
l
a
n
ce
d
at
a
p
ar
t
i
c
u
l
a
r
tolera
nce
l
e
vel
of
5
%
t
h
a
t
o
f
t
h
e
to
t
a
l
D
c
bus vo
l
t
a
ge
s
h
o
w
n
i
n
F
i
gure
5(c
)
.
4.2.
T
o
rqu
e
resp
o
nse
A
t
t
=9s
r
e
fe
re
nc
e,
t
or
que
i
s
inc
r
ea
se
d
from
10
N
m
t
o
1
5
ke
ep
in
g
s
peed
c
on
sta
n
t
a
t
1
000
r
.p
.m.
Fi
g
u
r
e
6
(
a
)
s
ho
ws
r
o
t
o
r
s
p
e
ed
b
e
h
av
iou
r
i
n
t
o
rqu
e
r
e
s
pons
e.
D
u
r
i
ng
t
h
i
s
t
ra
nsit
i
o
n,
t
h
e
s
peed
d
ro
ps
f
r
o
m
10
0
0
r.p.
m.
t
o
95
6.6
7
r
pm
a
nd
set
t
l
es
it
d
o
w
n
w
i
t
h
i
n
0
.
2
5
sec
o
n
d
s.
F
igure
6(b)
s
how
s
the
e
l
e
c
trom
agne
t
i
c
tor
que
b
e
h
av
i
o
ur
o
f
t
h
e
sys
t
e
m
.
The
e
l
e
c
tr
o
m
agnet
i
c
t
o
rq
u
e
r
ip
p
l
e
i
s
restr
i
cte
d
t
o
2.
8
N
m
.
unde
r
st
e
a
d
y
s
ta
t
e
.
F
r
om F
ig
ure
6(c)
the
capa
c
i
t
o
r
s V
o
ltage
r
i
p
p
l
es a
re
i
nve
s
tig
ate
d
at
t
=9s as
w
ell as
i
n a
st
e
a
dy s
t
ate
.
4.3.
St
ead
y
s
tate
respon
s
e
I
n
s
tea
d
y
state
,
t
he
r
o
t
or
r
ot
a
t
e
s
a
t
10
0
0
r
p
m
.
F
i
gur
e
7(
a)
a
n
d
F
i
g
ur
e
8(
a
)
s
how
s
the
s
t
at
or
c
urren
t
and
s
t
a
t
or
v
o
l
t
a
ge
r
espe
c
tive
l
y.
F
i
gur
e
7(
b)
ill
us
trates
t
he
F
F
T
a
n
al
y
s
i
s
o
f
t
h
e
st
ato
r
c
u
r
re
n
t
.
Th
e
%THD
o
f
the
l
i
ne
c
ur
ren
t
a
t
35.
7
H
z
i
s
c
a
lcu
l
a
t
e
d
i
n
F
i
gure
7(
b).
The
i
nv
e
r
t
e
r
swit
chi
n
g
fre
qu
enc
y
i
s
ma
int
a
i
n
ed
a
t
5
KHz
.
Th
e
h
a
rmo
n
i
c
s
s
ee
m
a
s
s
id
eb
an
d
s
a
nd
c
on
c
e
n
t
r
at
ed
a
t
th
e
sw
i
t
c
h
ing
fre
que
nc
y
and
it
s
mu
lt
i
p
l
e
s
i.e
.
surrou
n
d
i
n
g
5
K
H
z
,
10
K
H
z
,
15
K
H
z
e
tc
.
F
i
gure 8(a)
d
e
p
i
c
t
s
ph
a
s
e to
p
ha
se
v
o
lta
ge of
the
3L i
nv
e
r
ter
w
h
ic
h
is
f
e
d
t
o t
h
e
sta
t
or
of
the
i
n
d
u
c
t
i
on
m
o
tor
an
d
F
i
gure
8(b)
s
ho
w
s
s
t
h
e
F
F
T
a
n
al
ys
is
o
f
p
h
a
s
e to
pha
se
v
o
l
t
a
ge
.
Th
e
e
ffe
ct
o
f
l
o
ad
v
ari
a
t
i
o
n
at
c
on
st
an
t
spe
e
d
(f
requ
e
n
cy)
o
n
d
i
f
fere
nt
pow
e
r
q
ua
li
ty
i
n
d
i
ces
a
r
e
stud
ie
d.
V
ariatio
n
in
l
i
n
e-l
i
n
e
vo
l
t
a
g
e,
c
ur
rent,
%
T
H
D
of
l
i
n
e
v
o
lta
g
e
a
nd
c
u
r
r
ent
are
also
s
t
u
d
i
ed
f
o
r
di
ffe
re
nt loa
d
dem
a
nd i.
e. 25
%
,
50%,
75%
a
nd 10
0%
o
f r
a
ted
l
o
a
d
. Effe
c
t o
f
l
oad va
ria
t
i
o
n o
n
dc
li
n
k
vo
l
t
a
ge
rip
p
le
a
n
d
t
orq
u
e
r
i
pp
le
i
s
tab
u
la
te
d
i
n
T
a
b
le
5
.
It
i
s
se
e
n
f
r
om
t
he
T
a
b
le
5
t
ha
t
s
t
at
or
c
u
rrent
T
H
D
is
b
elo
w
5%
w
h
i
c
h
obe
ys
I
EE
E
5
19
s
t
a
n
dard.
I
t
c
a
n
b
e
se
en
f
r
o
m
the
Ta
b
l
e
5
t
h
a
t
as
l
oa
d
i
n
crea
se
s
st
at
o
r
c
u
rrent
i
n
c
r
ea
se
s
bu
t
dc
l
ink
volt
a
g
e
r
i
ppl
e
a
l
so
i
n
c
re
ase
s
.
To
rq
u
e
r
i
p
ple
dec
r
ese
s
a
s
l
o
ad
i
ncre
ases.
%
T
HD
of
S
tator
vo
lta
ge
a
l
s
o
d
ecr
ease
s
w
ith
i
ncre
asi
n
g
loa
d
.
F
r
om
t
he
se
o
bser
va
tio
ns,
th
e
prop
ose
d
S
VP
W
M
a
l
gor
it
h
m
f
or
EV
system
ha
s
ver
y
g
o
od p
o
w
er
quali
t
y
per
form
anc
e
for v
a
r
yi
ng l
oa
d.
(a)
(b)
(c)
F
i
gure
5.
S
pe
ed r
espo
nse
:
(a
)
r
otor
spee
d
, (
b) e
lectrom
a
g
n
e
tic
tor
que,
(c
) capac
i
t
or
s
vo
lta
g
e
.
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 V
ol.
10,
N
o.
4
, Dec
201
9 :
1
7
0
5
– 1
713
1
712
(a)
(b)
(c)
Figure
6.
T
orque
response: (a) ro
t
o
r sp
eed
, (
b
) e
l
e
c
t
r
o
m
ag
net
i
c
torque,
(c)
capacito
r
s
voltage.
(a)
(b)
Figure
7.
(
a) Sta
t
o
r
cur
r
ents
,
(b)
THD of stator current
(
a
)
(b)
F
i
gure
8.
(a
)
Lne
vo
l
tage,
(b)
TH
D
of
l
ine
v
o
l
ta
ge
Tab
l
e
5
.
P
e
rform
ance
of
pow
e
r
qual
ity
i
ndic
e
s
und
er
var
yin
g
l
oa
d o
p
er
at
ion
Lo
a
d
(
%)
V(
L-
L)
(r
m
s
)
(V
)
I (r
m
s
)
(A
)
%
T
H
D
D
C
l
ink
volta
g
e
ripple
(V
)
R
i
ppl
e
in
t
orque
(Nm
)
V
I
25
251.
7
3.
976
3
7.
38
3
.
65
5.
13
3
50
251.
34
5
.
954
3
5.
61
2
.
48
7
3
.
2
75
251.
2
8.
184
3
4.
68
1
.
48
9.
82
2
.
2
26
100
251.
13
10.
9
33.
57
`
1.
61
12.
395
2
.
5
3
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
A nov
e
l
regi
o
n
se
l
e
c
t
i
on
Ap
pr
oac
h o
f
SVPW
M for A
t
h
re
e-
l
e
v
e
l NP
C i
n
ver
ter
…
(D
e
b
a
n
j
an
R
o
y)
1
713
Tab
l
e
6. P
e
r
form
ance
of pow
e
r
qual
i
t
y
i
nd
i
c
e
s
und
er
va
r
yin
g
s
pe
e
d
(
fr
equ
e
ncy)
o
per
a
t
i
on
S
p
eed
(r
pm
)
F
r
e
q
ue
nc
y
(H
z
)
V
(r
m
s
)
%
TH
D
DC
l
ink
volta
g
e
ripple
(V
)
R
i
ppl
e
in
t
orque
(Nm
)
V
I
800
28.
57
251.
77
3
9
.
5
6
.
1
1
9
4
.
18
1
000
35.
7
251.
27
3
5
.
3
2
1.
84
7
.
9
5
2
.
33
1
200
42.
4
251.
06
2
5
.
8
6
2.
01
8
.
2
5
3
.
53
1
400
49.
95
250.
92
24.
3`
3
.
0
2
6.
95
2
.
7
5
5.
CO
NC
L
U
S
I
O
N
A
new
m
e
tho
d
of
S
V
P
W
M
f
or
3
L
i
n
ver
t
e
r
h
as
b
e
e
n
p
re
sente
d
f
or
e
l
ec
t
r
ic
v
eh
ic
le
a
p
p
lic
ati
on.
A
4
k
W
i
ndu
ct
io
n
mo
t
o
r
i
s
c
on
si
d
e
re
d
as
t
ra
c
tio
n
mot
o
r
a
n
d
si
mul
a
t
e
d
i
n
t
he
M
A
TLA
B/
S
I
MU
LINK
p
la
tform
.
Inves
t
i
g
a
tio
n
o
f
s
pe
ed
a
n
d
t
or
que
r
esp
onse
o
f
t
he
s
ys
tem
va
lida
t
e
d
th
e
eff
ect
iv
en
ess
o
f
t
he
p
re
se
nt
ed
s
ch
eme.
In
s
t
e
a
d
y
s
t
a
t
e
,
t
he
c
a
p
ac
it
ors
v
o
lta
ge
r
i
ppl
e
s
w
e
r
e
also
l
i
m
it
e
d
t
o
a
t
o
le
rable
va
l
u
e
.
%
TH
D
of
t
he
o
u
t
pu
t
vo
lta
ge
a
nd
ou
t
p
u
t
c
urr
e
nt
o
f
the
3L
i
nver
t
e
r
i
n
t
h
e
stea
d
y
s
ta
te
a
ls
o
e
s
t
a
bl
i
s
hed
t
h
e
ef
fic
a
c
y
o
f
t
h
e
pr
esen
t
e
d
S
V
P
W
M a
l
gor
i
t
hm
.
In fut
ur
e,
t
he ha
r
dw
ar
e
i
m
plem
en
tat
i
on
of
t
h
i
s
pr
o
p
o
s
e
d
w
o
rk
w
ill b
e
a
cha
l
l
e
ngi
ng
ta
s
k.
REFE
RENCES
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qib
Ja
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Yihu
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Hu
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b
i
n
g
Wa
n
g
a
nd
L
i
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J
ia
n
g
,
“Con
fig
u
r
a
tion
s
a
n
d
Con
t
rol
o
f
T
ra
c
t
io
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4
Mo
to
rs
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El
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c Veh
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c
l
es
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Va
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Ra
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“Ec
o
n
o
m
i
c
a
n
d
Effic
i
e
n
t
I
n
d
ucti
on
Mo
t
o
r
Cont
roller
f
o
r
E
l
ect
r
i
c
Vehi
cle
usi
n
g
Im
pro
v
ed
S
calar A
lg
orit
h
m
”,
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st
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Inte
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Po
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l
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ronics, In
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Nass
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C
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iff
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ren
t
e
lect
ric
m
o
t
o
rs
i
n
t
h
e
e
l
ect
ric
vehi
cles
”,
18
th
In
t
e
rna
t
i
o
n
a
l
Conferen
ce on
El
ectrica
l
M
a
ch
i
n
es
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m
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Gian
m
a
rio
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e
ll
e
g
ri
no,
A
lf
redo
V
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B
arb
a
ra
B
o
azzo
a
n
d
Pa
o
l
o
Guglielmi,
“
Compari
s
on
o
f
Indu
cti
o
n
and
P
M
Sy
n
c
hro
n
o
u
s
M
otor
D
r
i
v
e
s
for
EV
A
pp
lic
a
t
io
n
Inc
l
ud
ing
De
sign
E
x
am
ples
”,
IEEE
T
r
a
n
s
a
ctio
ns on In
du
st
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Appl
i
c
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,
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,
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P
.
X
ue
a
nd
J
.
Li
n
,
“
Di
scu
s
s
i
on
on
t
he
r
ar
e
e
a
rt
h
reso
urces
a
nd
its
d
evel
opment
p
o
t
e
nti
a
l
of
I
n
n
er
M
o
n
g
o
l
i
a
of
Chin
a”, i
n
Pr
oc
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h
an
g
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G
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rgescu
.
“
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o
w
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l
os
s
an
aly
s
is
o
f
t
w
o-l
e
vel
and
t
h
ree-lev
e
l
neut
r
a
l
poi
nt
c
l
a
m
p
ed
i
n
v
ert
e
rs
f
o
r
a
w
i
n
d
pum
p
st
orage
sy
st
em”,
I
n
Proc.
o
n
IEEE
12t
h Int.
Conf.
on O
p
timiz
a
tion
o
f
Elect
ri
cal an
d
Elect
ronic E
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t
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v
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1
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9
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[7]
R.
M
acke,
“
Multilevel
NPC
i
nverter
f
or
l
ow-vo
ltage
a
pplicat
ion
s
”,
I
n
Pr
oc.
IEEE
14
th
Eur
o
p
e
an
Co
nf
.
on
Po
wer
Elect
ro
n
i
cs
A
pplica
t
i
o
n
s
,
Birmingh
am,
UK
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Z
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C
h
e
n
,
L
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Y
u
an
,
an
d
Z
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Z
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a
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,
“
P
o
w
e
r
l
o
s
s
e
s
i
n
2
-
a
n
d
t
h
r
e
e
-
l
e
vel
t
h
ree-ph
ase
p
h
o
t
o
voltai
c
i
nvert
ers
eq
ui
pp
ed
w
it
h
IGBT's”,
i
n
Pr
oc
.
IEEE
15th
In
t.
Co
nf.
on
El
ectr
i
ca
l
M
a
chi
n
es
and S
y
st
ems
,
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p
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r
o, Japan
,
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12
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R.
T
ei
chm
a
nn
a
nd
S
.
Bern
et,
“
A
c
o
m
paris
o
n
of
t
hree-l
e
vel
conv
er
ter
v
e
rsu
s
t
wo
-level
c
on
vert
e
r
s
f
o
r
lo
w-volt
a
ge
driv
es,
t
r
acti
on,
a
nd
u
t
i
l
ity
a
p
p
l
i
cati
o
n
s
”,
IEEE
Tr
ans
.
on Indus
t
r
y
A
p
pl
i
c
ati
ons
,
Vo
l.
4
1
,
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o.
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85
5-
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M
a
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R.
T
homas
N
a
t
h
e
nas
and
G
e
or
g
i
os
A
da
m
i
d
i
s,
“
A
new
app
r
oach
f
or
S
VPW
M
o
f
a
three-l
e
vel
in
vert
er-ind
uction
motor
f
e
d-neut
ra
l
po
int
balancing
al
gori
thm”,
Simula
ti
on M
o
d
e
l
in
g
Pr
ac
t
i
ce a
nd Theo
ry
,
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l
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9
,
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1
7
,
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2.
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D
Ro
y,
M
S
i
n
g
h
a
n
d
T
R
o
y
,
“A
N
ov
el
A
p
p
ro
ach
f
o
r
S
pace
V
ecto
r
B
a
sed
PW
M
Al
gor
ithm
f
o
r
Di
ode
Clam
pe
d
Three
level
V
S
I
F
e
d
In
du
cti
on
M
o
t
o
r
D
r
iv
e”,
In
tern
a
t
io
nal Jo
ur
nal o
f
Powe
r
El
ectr
onics
a
n
d D
r
i
ve Sys
t
e
m
s
(IJPED
S0
, Vo
l
.
8
,
N
o
.
4
,
p
p
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53
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5
4
7
, 2
01
7.
[12]
Deban
j
an
R
o
y
a
nd
T
apas
R
o
y
,
“
A
n
ew
t
ech
ni
q
u
e
t
o
i
m
p
lem
e
n
t
c
on
ve
nt
io
nal
a
s
w
ell
as
a
dv
a
n
ced
P
ul
se
W
i
d
th
Mo
du
latio
n
techn
i
q
u
es
f
o
r
m
ulti-lev
el
i
n
v
erter”,
IEEE
6
t
h
In
dia
Inte
rn
a
t
ion
a
l
C
o
nfe
r
e
n
c
e
on
P
o
we
r
E
l
e
c
tron
ic
s
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P
E
)
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D
e
b
a
n
j
a
n
R
o
y
a
n
d
M
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d
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u
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i
n
g
h
,
“
A
s
i
m
p
l
i
f
i
e
d
s
p
a
c
e
v
e
c
t
o
r
p
u
l
s
e
wi
d
t
h
mo
d
u
latio
n
fo
r
t
h
ree
phas
e
t
hree
-lev
el
dio
d
e
cl
am
ped
i
n
v
e
rter”,
1
s
t IE
EE
Int
e
rnati
o
n
a
l
Co
nf
eren
ce on S
m
a
r
t
gri
d
s
,
Po
wer a
n
d
Adva
nced
Co
nt
ro
l
Engineeri
n
g
(
I
C
S
PA
C
E
)
,
B
a
ng
a
l
o
r
e
, Ind
ia
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2
6
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30
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Mari
o
A
.
G
o
n
zal
ez
and
Mi
gu
el
F
.
Escal
ante,
“Tracti
o
n
S
y
stem
f
or
a
n
EV
B
ased
o
n
In
du
ctio
n
M
o
to
r
and
3-Lev
e
l
NPC
Inverter
M
ultilevel
Con
v
ert
e
rs”,
1
2
t
h
I
E
E
E
I
n
te
rn
at
io
na
l
Power Elect
ron
i
cs
Congress
,
S
a
n
L
u
i
s
P
oto
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i,
Mex
i
co
,
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p
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873-7
7
,
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01
0
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Anees
h
M
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a
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S
.,
A
n
i
sh
G
op
in
ath
an
d
M.
R
.
Baij
u
,
“
A
Si
m
p
l
e
S
p
ace
Vecto
r
P
W
M
G
enerat
ion
S
c
hem
e
f
or
An
y Ge
ne
ra
l n-
Le
ve
l Inv
e
rte
r
”
,
IEEE T
r
a
n
s
a
c
t
ions
on
Ind
u
stri
a
l
El
ectr
onics
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64
9-1656
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S
ush
eela,
P
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S
a
tis
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K
u
m
a
r
an
d
S
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K
.
S
h
arm
a
,
“Gen
erali
zed
A
lg
or
ith
m
o
f
R
e
ve
rse
M
a
pp
in
g
b
a
se
d
S
V
P
W
M
Stra
te
gy
f
or
D
io
de
C
la
mpe
d
M
u
l
til
evel
I
nv
erters”,
IEEE Tr
an
sactio
ns on
In
dustr
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Ap
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ons
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09/TIA.
2018
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2
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9
0
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