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.
10~18
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
5
9
1
/ij
ped
s
.
v10
.
i
1.pp
1
0
-1
8
10
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 constant switchi
n
g fre
quency o
f
direct torque contro
l
of b
rushless DC motor
Yusn
i
d
a
Ta
rmi
z
i
1
,
Au
zan
i
Jidin
2
, Kasru
l Ab
dul
Kar
i
m
3
,
T
o
le
Sutik
n
o
4
1,
2
,
3
F
acu
lty
of
Elec
t
r
ical
En
g
i
n
eerin
g,
U
nivers
iti Tekn
ik
al M
a
l
ay
sia
M
elak
a, M
alaysia
1,
2
,
3
El
ectrical
M
a
c
hi
ne D
esi
g
n
,
P
o
w
er El
ectron
i
cs and
Dri
ves
Rese
arc
h
Grou
p,
C
eRIA,
U
T
eM,
M
a
l
a
ysi
a
4
D
e
partm
e
n
t
o
f El
ectri
cal E
ng
in
eeri
n
g
, Univ
e
rsitas
Ah
m
ad Dah
la
n
,
I
nd
on
esi
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
A
ug
9,
201
8
Re
vise
d N
ov
1
2
,
201
8
A
c
c
e
pte
d
D
ec 3,
201
8
Th
is
p
ap
er
d
i
s
c
u
sses
abo
u
t
di
re
ct
t
orq
u
e
co
nt
rol
o
f
B
rushl
e
ss
D
C
m
o
to
r
by
injecting
the
tr
i
a
ngular
wavef
o
rm
a
n
d
u
s
i
n
g
P
I
c
o
n
t
r
o
l
l
e
r
i
n
o
r
d
e
r
to
r
e
duc
e
th
e
t
o
rq
ue
a
nd
obt
ain
con
s
t
a
nt
switch
i
ng
freq
u
en
cy.
Brus
hl
ess
D
C
m
o
t
o
r
ar
e
w
i
d
e
ly
u
s
e
d
in
a
p
p
l
i
c
a
ti
on
s
wh
i
c
h
r
e
qu
ir
e
wi
d
e
r
a
n
ge
o
f
sp
e
e
d
a
nd
t
orq
u
e
con
t
ro
l
becaus
e
o
f
robu
st
,
lo
ng
er
l
if
esp
a
n,
f
aster
to
rque
r
esp
o
n
s
e
and
a
b
le
t
o
op
erate
at
h
igh
sp
eed.
Un
li
ke
c
on
ven
t
i
onal
th
re
e
p
h
as
e
DTC
of
i
nd
uction
m
achi
n
e
(IM
)
,
the
prop
os
ed
D
T
C
a
pp
roa
c
h
i
n
trodu
ces
t
w
o
phas
e
c
o
nd
uct
i
on
m
o
d
e
.
Besi
des
th
at,
t
h
e
m
a
g
n
itude
f
l
ux
is
c
onsid
ered
c
o
n
s
t
ant
i
n
which
the
resu
lts
o
n
l
y
g
a
in
s
from
co
ns
tant
t
o
r
que
r
egi
o
n
.
T
hu
s,
t
he
f
lu
x
c
o
n
t
r
o
l
lo
op
i
s
elimina
t
ed
w
hil
e
i
mp
le
m
e
n
t
t
h
i
s
s
c
hem
e
.
Usi
ng
t
he
t
ri
ang
u
lar
wa
ve
fo
rm
t
h
a
t
will
b
e
com
p
are
wit
h
actual
torq
ue,
t
h
e
prop
er
s
wit
c
hi
ng
p
at
ter
n
can
b
e
sel
ected
t
o
con
t
ro
l
th
e
g
e
nerat
e
d
to
rque
a
n
d
r
e
duci
n
g
co
m
m
u
tati
o
n
t
orqu
e
ripp
le
.
The
torq
ue
r
e
s
po
nse
de
p
e
n
d
s
on
t
h
e
s
p
e
e
d
o
f
th
e
sta
t
o
r
fl
ux
li
nkag
e
wh
ich
i
s
d
i
r
ectly
c
ont
rol
l
ed
b
y
sel
ectin
g
app
r
op
riate
vo
lt
age
s
p
ace
v
ectors
f
r
o
m
a
l
o
o
k
-
u
p
t
a
b
l
e
t
o
m
a
k
e
s
u
r
e
t
h
e
t
o
r
q
u
e
e
r
r
o
r
w
i
t
h
i
n
t
h
e
b
a
n
d.
T
he
val
i
dit
y
o
f
t
h
e
p
r
op
osed
c
o
n
t
r
o
l
s
ch
eme
f
o
r
co
ns
tan
t
s
witchi
ng
fre
q
ue
n
c
y
a
n
d
re
d
u
c
e
torq
ue
r
ip
ple
a
r
e
v
e
rifie
d
t
h
r
ou
gh
si
m
u
l
a
tio
n a
n
d e
x
pe
ri
m
e
nt
al res
u
lts.
K
eyw
ord
s
:
BL
D
C
CS
F
DTC
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:
K
a
srul
A
bd
ul
K
arim
,
Fa
cult
y
o
f
E
l
e
c
t
rica
l
En
gine
erin
g,
U
n
i
v
ersi
ti
T
e
k
ni
ka
l Ma
la
ysia
M
ela
k
a,
H
a
ng
Tua
h
Ja
y
a,
7610
0 D
u
ria
n
T
u
n
g
g
a
l
,
M
e
laka,
Ma
lays
ia.
Em
ail:
kasru
l
@u
t
e
m.
edu.
my
1.
I
N
TR
OD
U
C
TI
O
N
Th
e
Bru
s
hl
e
sss
D
i
r
ec
t
Cu
rre
n
t
(BLDC)
m
o
t
or
b
e
c
o
m
e
pop
ul
a
r
a
nd
g
ra
du
a
l
l
y
r
e
p
la
c
i
ng
c
o
n
ve
n
t
i
o
na
l
D
C
m
a
c
hi
ne
d
rives
in
m
a
n
y
ind
u
s
t
rial
a
p
p
lica
t
i
ons
s
u
c
h
as
a
p
p
l
i
a
n
ce
s,
a
ut
om
o
t
i
v
e
,
c
o
n
sum
e
r,
a
e
r
ospace
,
i
n
s
t
r
u
m
e
n
t
a
n
d
o
t
h
e
r
s
.
T
h
e
B
L
D
C
m
o
t
o
r
i
s
e
l
e
c
t
r
i
c
a
l
l
y
c
o
m
m
u
t
a
t
e
d
b
y
p
o
w
e
r
s
w
i
t
c
h
e
s
i
n
s
t
e
a
d
o
f
b
r
u
s
h
e
s
i
n
order
to
i
m
p
ro
ve
t
he
r
e
l
i
a
bil
i
t
y
a
n
d
d
u
r
a
b
i
l
ity
o
f
t
h
e
u
n
it.
F
o
r
ins
t
anc
e
,
t
h
e
e
l
e
c
t
rica
l
c
o
mm
utat
i
on
ha
ppe
ne
d
w
ith
p
e
r
m
a
ne
n
t
m
a
gne
t
ro
t
o
r
and
s
t
a
t
or
c
oi
s
l
i
n
a
prope
r
se
que
n
c
e
.
The
fo
rce
acti
ng
o
n
t
he
r
otor
c
aus
e
s
it
t
o
rota
te w
hen t
h
e
a
r
m
a
ture coil
s
a
re sw
i
tc
hed e
l
ectr
o
n
i
ca
l
l
y by t
rans
ist
o
r
a
t
the rig
h
t
fiels po
l
es.
The
H
a
ll effec
t
sens
ors
is
u
se
d
to
d
e
t
ec
t
the
c
u
rre
nt
c
om
muta
tio
n
p
o
i
n
t
s
tha
t
o
cc
ur
e
ve
ry
60
e
l
e
c
t
rica
l
degre
e
s.
T
he
re
fore
,
t
h
re
e
sen
s
o
r
s
ha
s
b
een
p
l
a
ced
i
n
t
o
t
h
e
st
at
o
r
i
n
t
h
e
mot
o
r
wi
th
1
2
0
d
e
g
ree
la
g
w
i
t
h
r
es
pe
ct
t
o
the
ot
he
r
tw
o
sens
ors.
T
hese
s
ensors
a
r
e
n
a
m
ed
a
s
H
a
ll
A
,
H
a
ll
B
an
d
H
a
ll
C
.
G
e
n
e
rall
y,
w
hene
ve
r
r
o
t
o
r
m
a
gne
t
i
c
po
les
pass
nea
r
t
he
h
a
l
l
-
effect
s
e
n
sor,
a
h
i
g
h
o
r
l
ow
s
igna
l
w
ill
b
e
corr
espo
nd
ed
w
he
n
t
h
e
N
o
rt
h
or
S
out
h
P
o
le
i
s
pass
in
g
nea
r
t
he
s
ens
o
rs.
N
o
ted
th
at,
t
h
e
N
o
rt
h
p
o
le
s
i
g
n
a
l
is
in
d
i
ca
t
e
s
to
‘
1’
a
n
d
t
he
S
outh
P
o
le
t
o
‘0’[1].
U
n
l
i
ke
i
n
duc
t
i
on
mo
t
o
r,
B
L
D
C
o
p
e
r
ates
i
n
t
w
o-
p
h
a
s
e
c
o
n
d
u
ct
i
o
n
m
o
d
e
w
h
ic
h
m
eans
on
l
y
t
w
o
p
hases
con
d
u
ct
a
t
an
y
ins
t
a
n
t
of
tim
e.
T
he
p
roce
ss
oc
c
u
rs
i
n
o
r
de
r
to
co
n
t
rol
t
o
rque
by
ke
epi
n
g
the
sta
t
or
f
lu
x
lin
ka
ge
a
m
p
li
t
ude a
lmost
c
o
n
s
ta
n
t
b
y
e
lim
in
a
tin
g the
flu
x
con
tr
o
l
. S
i
nce
t
h
e fl
u
x
c
o
n
t
r
ol is cons
ta
nt, t
h
ere
ar
e
a
fe
w
al
g
o
rit
h
ms
n
ee
de
d
for
the
pr
o
pose
d
c
on
t
r
o
l
s
c
h
e
m
e.
A
s
c
o
n
c
l
usio
n
,
o
n
l
y
t
o
r
q
ue
i
s
be
ing
c
o
nt
r
o
l
w
h
i
l
e
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
A
sim
p
le co
ns
tan
t
sw
i
t
c
h
ing
fre
q
uency
o
f
d
i
r
ect t
o
rq
ue co
nt
ro
l
of
br
ush
l
e
ss (Y
us
ni
d
a
T
a
rm
i
z
i)
11
the
s
t
a
t
or
f
lu
x
lin
ka
ge
i
s
ke
pt
c
ons
t
a
nt
on
p
u
rp
ose.
F
urthe
r
m
o
r
e
,
by
u
s
in
g
z
e
ro
v
olta
ge
v
ec
tor
sug
g
es
ted
in
[2],
t
he
e
lec
t
r
o
ma
gn
e
t
i
c
t
or
qu
e
w
i
l
l
d
ec
rea
s
e
w
h
ich
gi
ve
s
o
m
e
o
pp
or
tun
i
t
y
s
uc
h
a
s
g
e
n
e
r
a
ting
m
o
re
freque
n
t
and
la
rger
s
pi
ke
s
for
t
h
e
p
h
ase
vol
ta
ge
s.
T
h
i
s
ef
fec
t
w
ill
de
t
e
ri
orat
e
t
h
e
tra
j
e
c
t
ory
of
t
he
s
tat
o
r
flu
x
lin
ka
ge l
oc
us.
The
BLD
C
m
ot
or
p
r
o
vide
m
any
ad
va
nta
g
e
s
s
uch
as
h
ighe
r
effic
i
e
n
c
y
a
n
d
re
li
ab
il
i
t
y,
h
a
v
e
lo
ng
er
lifes
pan,
r
ob
ust,
f
aster
tor
que
r
e
s
ponse
,
a
n
d
a
bl
e
to
oper
a
te
a
t
hi
ghe
r
spee
d
[3]
.
M
ore
ove
r,
t
he
ir
p
o
p
u
l
arit
y
is
als
o
a
ss
is
ted
d
u
e
to
d
ec
l
i
ni
n
g
c
ost
as
w
e
l
l
as
i
nc
rea
s
i
n
g
f
unc
t
i
o
na
lit
y.
B
LD
C
ca
n
be
s
m
a
ller
an
d
li
gt
her
as
there
w
e
re
b
r
u
sh
le
ss
t
y
p
e
w
i
t
h
t
he
s
a
m
e
pow
er
out
pu
t
to
b
e
use
d
f
o
r
a
pp
l
i
cati
o
n
wh
ere
sp
a
c
e
i
s
l
i
m
i
t
ed
.
Th
e
BL
D
C
h
as
a
n
o
n
-
s
in
us
oi
da
l
back-
E
M
F
w
hic
h
i
s
ne
arl
y
t
rape
z
o
i
d
a
l
or
r
ec
tan
g
u
l
ar
s
h
a
pe
o
f
w
a
ve
fo
rm
f
or
st
a
t
or
pha
se
c
urr
e
nt
d
ue
t
o
ma
g
n
e
t
d
isp
l
a
c
e
m
e
nt
a
nd
c
once
n
t
r
ate
d
w
i
nd
i
ng.
T
he
ref
o
re,
par
t
ic
ula
r
c
o
n
tro
l
appr
oa
ch
i
s
re
qu
ired
i
n
order
to
d
e
v
e
l
o
p
c
o
n
sta
n
t
m
u
tua
l
t
or
que
[
4].
H
o
w
e
ve
r,
B
LD
C
ha
s
a
m
a
j
o
r
dr
aw
ba
ck
w
h
ic
h
duri
n
g
opera
ti
o
n
p
r
o
d
u
ce
l
a
r
ge
t
orq
u
e
r
i
pp
le
a
n
d
varia
b
le
i
n
v
e
r
te
r
sw
it
c
h
in
g
freq
u
enc
y
.
D
e
sp
ite
ma
chine
s
t
ruc
t
ur
e,
t
he
i
np
u
t
s
ys
tem
due
t
o
sw
it
c
h
i
n
g
te
c
h
ni
que
s
a
n
d
p
ha
se
c
urr
e
nt
c
om
muta
ti
on
t
h
at
c
om
es
from
pow
e
r
e
lectro
nic
si
d
e
is t
h
e
ma
in re
a
son
fo
r
torq
ue
w
ave
f
o
rm
becom
es im
p
erfection.
O
v
e
r
t
he
p
a
s
t
t
h
r
ee
dec
a
d
es,
D
i
re
ct
T
or
que
C
on
tro
l
(
D
T
C)
s
chem
e
s
has
be
en
p
ro
p
o
se
d
b
y
[
5]
f
or
in
duc
t
i
on
m
a
c
h
i
n
e.
S
ince
t
he
b
e
g
in
n
i
n
g
,
it
h
as
b
ee
n
de
ve
l
ope
d
a
nd
p
r
e
s
en
t
e
d
w
i
t
h
s
i
m
pli
c
i
t
y
,
g
ood
perform
ance
a
nd
r
o
bus
tne
ss
[6].
I
t
ga
ine
d
p
o
p
u
lar
i
t
y
a
m
o
n
g
t
he
rese
arc
h
er
a
s
i
t
o
ffe
r
s
exce
l
l
e
n
t
dy
nam
i
c
perform
ance
w
hic
h
c
om
para
b
l
e
t
o
t
ha
t
o
b
t
a
i
ne
d
i
n
t
he
D
C
drive
s
an
d
ro
bust
t
o
m
o
t
or
p
ara
m
e
t
er.
D
TC
o
f
BL
D
C
w
i
t
h
n
o
n
-
s
i
nus
o
i
da
l
ba
ck-EMF
i
s
pr
o
pos
ed
i
n
[7],
[
8].
The
s
t
at
or
f
l
u
x
a
n
d
e
l
e
c
tro
m
agnet
t
o
rq
ue
w
er
e
ob
ta
ine
d
from
tw
o-le
ve
l
a
n
d
t
h
e
r
e-
l
e
ve
l
h
y
st
er
esis
c
on
tro
l
le
r
r
es
p
e
c
t
i
v
ey
b
y
co
mp
a
r
in
g
t
h
e
st
ato
r
f
l
ux
link
a
g
e
and
e
s
t
i
ma
ted
elec
tr
oma
gne
t
i
c
torq
ue
w
i
t
h
the
i
r
dem
a
n
d
s
val
u
e.
There
f
ore
,
t
o
sat
i
sfy
t
h
e
fl
ux
a
n
d
tor
q
u
e
dem
a
nd
s,
t
he
s
u
ita
b
l
e
v
o
l
t
a
g
e
ve
ct
or
a
re
s
e
l
e
c
t
e
d
fr
om
a
l
o
ok-
u
p
tab
l
e
eit
h
er
t
o
incr
ease
or
d
ec
rea
s
e
the
t
o
r
q
u
e
o
r
t
h
e
s
a
m
e
t
i
m
e
t
o
e
i
t
h
e
r
i
n
c
r
e
a
s
e
o
r
d
e
c
r
e
a
s
e
t
h
e
s
t
a
t
or
f
lu
x.
O
th
er
t
ha
n
t
h
a
t
,
a
t
h
r
oug
h
i
nve
st
iga
t
i
on
on
t
he
m
a
n
y
sw
it
c
h
i
n
g
tec
hni
q
u
e
in
D
T
C
,
e
s
pecia
lly
i
n
re
duc
i
n
g
t
o
rq
ue
r
ip
ple
a
n
d
pro
v
i
de
a
c
o
n
s
t
an
t
sw
it
c
h
i
n
g fre
q
uenc
y,
bef
ore form
ula
t
i
ng t
h
e pr
o
pose
d
c
on
trol
ler
strate
g
y.
O
bv
io
us
ly,
the
used o
f spac
e
v
e
ct
or
modu
la
ti
o
n
(
S
V
M
)
i
s
c
onsi
d
er
a
s
the
most
p
o
p
u
lar
va
ria
t
ions
i
n
DTC
wh
eth
e
r
f
o
r
i
n
d
u
ct
ion
mo
to
r
(
I
M)
a
nd
brus
hle
ss
D
C
m
ot
or
(
BLD
C
).
H
ow
ever
,
this
t
ec
h
n
i
q
u
e
w
h
ic
h
nor
ma
l
l
y
r
e
f
e
r
r
e
d
t
o
a
D
T
C
-
S
V
M
n
e
e
d
s
m
a
j
o
r
modi
fic
a
t
i
on
s
on
t
h
e
or
ig
ina
l
D
TC
s
truc
t
u
r
e
.
Be
side
s
th
a
t
,
som
e
o
t
h
er
t
e
c
hn
i
que
a
lso
ha
s
bee
n
p
ro
p
o
s
e
d
b
y
rese
arc
h
er
t
o
im
prove
t
he
D
T
C
p
er
form
an
ce
w
hile
p
ut
t
i
n
g
s
om
e
ef
forts
w
h
i
c
h
r
e
tai
n
s
the
sim
p
l
e
s
truc
tu
r
e
o
f
D
T
C
schem
e
.
Bec
a
u
se
o
f
th
at,
the
schem
e
s
r
e
quire
m
a
c
hi
ne
p
a
r
am
e
t
e
r
i
n
o
r
d
e
r
t
o
d
e
s
i
g
n
t
h
e
p
r
o
p
e
r
P
I
con
t
ro
l
l
ers.
R
ece
ntl
y
,
t
h
e
u
s
e
of
m
u
l
tile
v
e
l
i
n
verte
r
h
a
s
g
a
i
ne
d
muc
h
a
t
t
e
n
t
i
on
d
u
e
t
o
its
a
dva
nta
g
e
s
in
pro
v
i
d
i
ng
gr
eater
n
um
ber o
f
v
o
l
t
a
ge
vec
to
r
s
,
low
e
r sw
itc
hi
n
g
los
s
a
nd
low
e
r harm
on
i
c
s. H
ypo
the
tica
lly,
the
grea
ter
the
nu
m
b
er
o
f
v
o
lta
g
e
v
ec
tors,
the
m
o
re
o
p
t
i
o
n
are
g
i
v
e
n
t
o
s
e
l
e
c
t
t
h
e
m
o
s
t
o
pt
i
m
al
v
olta
ge
v
e
c
tors
i
n
order
t
o
i
mpr
o
ve
t
h
e
D
TC
p
e
r
form
anc
e
.
H
o
w
e
ver
,
t
he
m
ul
ti
l
e
ve
l
i
n
v
e
r
ter
m
a
y
com
p
li
c
a
t
e
t
h
e
DTC
str
u
c
t
ure
and
gi
ve
s
om
e
prob
lem
s
s
uc
h
as
r
equire
me
nt
o
f
i
s
o
l
a
t
ed
D
C
vo
lt
a
ges
in
C
H
M
I,
t
he
i
nba
lanc
e
neu
t
ral
or
ca
paci
t
o
r’s
v
o
l
tage
i
n
NPCM
I.
I
n
the
v
i
ew
o
f
t
h
is
s
cena
r
i
o
,
th
i
s
pa
per
i
n
it
ial
l
y
p
rop
o
s
e
s
us
in
g
P
I
c
ontr
o
l
l
e
r
and
in
jec
t
i
o
n
t
r
i
a
n
g
u
la
r w
a
vefor
m
i
n
order
to
a
chieve
t
orq
u
e
r
i
p
p
le-f
ree
operation of BLD
C
motor.
2.
B
A
SIC
S
T
RU
CTURE
2.1.
Math
emat
i
c
al
M
od
ell
i
n
g
of
BLDC
Motor
A
prec
i
s
e
stud
y
of
t
he
B
LD
C
o
p
er
at
i
o
n
i
s
m
ade
in
o
rde
r
t
o
stu
d
y
a
n
d
un
der
s
t
a
nd
t
h
e
dy
nam
i
c
beha
v
i
or
o
f
t
h
e
D
T
C
dri
v
e
.
M
o
d
e
l
l
i
n
g
BLD
C
m
o
t
or
r
equ
i
res
t
w
o
eq
ua
t
i
o
n
s
wh
ic
h
a
r
e
e
l
ectr
i
ca
l
a
nd
me
cha
n
ic
al e
q
u
a
t
ion.
Brus
h
l
e
ss
D
C m
o
t
o
r
equa
tio
n
can
b
e
e
xpress
ed
a
s fol
l
o
w
s:
Ele
c
t
rica
l
equa
ti
o
n
:
(
1
)
=
i
nsta
nta
n
eo
u
s
of
k
–
p
h
a
s
e
v
ol
t
a
g
e
=
i
nsta
nta
n
eo
u
s
of
k
–
phase
c
urr
e
nt
=
i
nsta
nta
n
eo
u
s
of
k
–
phase
b
ac
k-em
f
vol
ta
ge
=
k
–
p
h
a
se resi
s
t
a
n
ce
=
k
-p
h
a
se
ind
uc
t
a
n
c
e
The
mode
l
of a
rm
ature
w
i
nd
i
n
g
for
BLD
C
mot
or c
an
b
e c
l
e
a
rly
ex
p
res
s
es
a
s
f
o
llows
based
(1):
(
2
)
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
:
10
–
18
12
(
3
)
(
4
)
Bru
s
hl
e
ss
DC
m
o
t
o
r
e
qu
at
io
n
wi
t
h
1
20
o
c
o
nduc
tio
n
an
g
l
e
and
trape
z
o
i
d
a
l
b
ac
k-
EM
F
w
a
vef
o
rm
c
an
be
e
xpres
sesd
a
s,
(
5
)
(
6
)
(
7
)
wher
e,
=
ba
c
k
EMF
c
on
s
t
a
n
t of o
ne
pha
se
=
e
lec
t
rica
l
rotor
angle
=
r
otor
spee
d
M
e
ch
ani
cal
equ
a
t
i
o
n:
N
e
xt, m
ec
hani
ca
l
equa
t
i
on w
h
e
r
e
invo
l
v
e
to
rque,
ang
u
lar
v
e
loc
i
t
y a
nd f
r
i
c
t
i
on of the
rotor are
show
n. T
h
e
to
t
al of t
o
rq
ue
t
ha
t
pro
duce
d
for
ea
c
h
p
h
a
s
e c
a
n
b
e
re
p
r
es
en
t
e
d as
b
e
l
o
w
:
,
,
(
8)
.
,
(
9
)
,
.
(
10)
wher
e,
,
i
s
the torq
ue
fa
c
t
o
r.
2.2.
D
i
rec
t
Tor
q
u
e
C
on
trol
o
f B
L
D
C
Mot
or
The
F
i
gur
e 1 s
how
s the
struc
t
ur
e of D
T
C
of BLD
C
m
otor
. The
s
t
at
or flu
x
in t
he v
o
l
ta
ge
ve
c
t
o
r l
o
ok-
up
ta
ble
i
s
s
e
l
e
c
ted
as
-
z
e
ro
o
r
con
s
ta
n
t
w
h
ile
t
he
t
orq
u
e
e
rro
r
is
s
electe
d
b
ase
d
i
n
differ
e
nce
of
e
rror
leve
l
betw
ee
n
the
a
c
t
ua
l
t
o
r
q
ue
a
nd
t
he
r
efere
n
ce
t
o
rq
ue.
The
dir
ect
torque
c
ontrol
of
B
LDC
motor
i
s
e
x
p
l
a
ine
d
i
n
[9],
f
or
t
w
o
p
h
a
se
c
on
duc
t
i
on
w
it
h
o
n
l
y
t
orq
u
e
co
ntr
o
l
l
o
o
p
.
The
selec
t
i
o
n
of
v
o
l
tage
v
ec
tor
is
d
e
p
e
nds
on
t
h
e
t
o
rq
u
e
e
rro
r
wh
i
c
h
co
me
s
fro
m
t
h
e
di
ff
e
r
e
n
c
e
b
et
we
en
e
sti
m
at
ed
to
rque
a
nd
r
e
f
e
r
en
ce
t
o
r
q
u
e
.
Wh
en
t
he
tor
que
e
r
r
or
t
o
u
che
s
t
he
u
p
p
e
r
o
r
low
e
r
hys
t
e
re
si
s
ba
nd,
a
n
app
r
opr
i
a
te
v
ol
t
a
ge
v
ec
tor
is
s
elec
ted
w
h
e
t
her
t
o
reduc
e
or
i
ncre
ase
it
respec
tiv
e
l
y.
T
orq
u
e
er
ror
stat
us
from
c
o
mpa
r
at
ors
is
r
equired
in
o
r
d
er
t
o
de
ter
m
i
n
e
t
h
e
appr
opr
i
a
t
e
v
o
l
t
a
ge
v
e
c
t
o
r
w
h
e
r
e
i
t
c
a
n
b
e
‘1’
or
‘
-
1
’.
W
hen
t
o
rque
s
ta
t
u
s
i
s
‘
1’
o
r
po
si
ti
ve,
me
ans
t
h
at
t
he
t
o
rq
u
e
e
rro
r
t
ou
c
h
es
t
h
e
uppe
r
h
y
s
t
e
resi
s
ba
n
d
a
n
d
ac
tu
al
t
o
r
qu
e
sh
oul
d
d
e
c
r
ea
se
a
nd
t
hu
s
v
o
l
t
a
g
e
v
ec
t
o
r
op
p
o
site
t
o
th
e
dire
c
t
i
on
o
f
r
ota
t
i
o
n
o
f
r
ef
ere
n
ce
sta
t
or
f
lu
x
i
s
c
h
o
se
n
a
s
s
ho
wn
i
n
Fi
gu
re
3
o
r
el
se
i
f
th
e
t
o
r
q
u
e
e
r
r
o
r
s
t
a
t
u
s
i
s
‘
-
1
’
o
r
n
e
g
a
t
i
v
e
,
t
h
i
s
m
e
a
n
s
t
h
a
t
t
h
e
t
o
rq
ue
e
rror
touc
he
s
the
low
e
r
hyste
resis
b
a
nd
a
n
d
ac
t
u
a
l
t
or
que
h
as
t
o
be
d
e
c
re
a
s
ed
s
o
t
h
e
vol
t
a
ge
s
pace
v
ec
t
o
r
i
n
the
dir
ect
io
n
o
f
r
o
t
at
i
o
n
of
t
he
a
c
t
ua
l
s
t
at
or
f
l
ux
v
e
c
t
o
r
i
s
s
el
ec
te
d
.
T
h
e
s
el
e
c
ti
o
n
o
f
t
h
e
re
sp
ect
i
v
e
vo
l
t
a
g
e
vec
t
or
a
lso
depe
n
d
s
o
n
t
he
s
e
c
t
o
r
g
i
ven
fr
o
m
sect
or
1
unt
i
l
s
ector
6
i
n w
h
ic
h
the r
o
t
o
r
is p
re
sent. T
h
u
s,
t
h
e
bas
i
s
of
t
h
i
s
sw
itch
i
ng ta
b
l
e
i
s
g
ive
n
as
Table
1.
The
F
i
gur
e 2
show
s t
h
e si
x n
onzer
o vo
lta
ge
vectors (
-
)
that sha
pe the
a
x
e
s of a hexago
n
a
l
and
fe
ed
e
le
c
t
rica
l
pow
er
t
o
t
h
e
l
o
a
d
.
The
an
gle
be
tw
ee
n
a
ny
a
d
j
a
ce
n
t
t
w
o
n
o
n
-
zer
o
vo
ltage
v
ec
t
o
r
s
o
r
a
l
so
kn
ow
n
a
s
a
ctive
vo
lta
ge
v
ec
tors
i
s
6
0
d
egr
ees,
w
h
ile
t
w
o
z
e
r
o
v
ol
t
a
ge
v
ect
ors
(non-a
c
tive
vo
l
t
age
v
e
c
t
or)
(
and
) a
r
e
at the
orig
i
n an
d
ap
pl
y z
e
ro
vol
tag
e
to the
loa
d
.
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
A
sim
p
le co
ns
tan
t
sw
i
t
c
h
ing
fre
q
uency
o
f
d
i
r
ect t
o
rq
ue co
nt
ro
l
of
br
ush
l
e
ss (Y
us
ni
d
a
T
a
rm
i
z
i)
13
F
i
gure
1.
S
truc
t
u
r
e
of D
T
C o
f
B
L
D
C
mot
o
r
Fi
g
u
r
e 2
.
Sel
ec
t
i
on
o
f
vo
l
t
a
g
e
sp
a
ce
v
ect
o
r
s to
inc
r
ea
se
or
dec
r
ea
se
torque
The
Ta
ble
1
s
h
ow
s
t
h
e
v
o
l
ta
g
e
v
e
c
t
o
r
selec
t
i
on
for
BLD
C
m
otor
a
cc
ordi
ng
t
o
s
ta
tor
f
l
u
x
and
t
o
rqu
e
e
r
r
o
r
s
.
N
o
t
e
d
t
h
a
t
,
o
n
l
y
t
h
e
y
e
l
l
o
w
c
o
l
o
u
r
i
s
u
s
e
d
b
e
c
a
u
s
e
t
h
e
f
l
u
x
f
o
r
B
L
D
C
m
o
t
o
r
i
s
a
s
s
u
m
e
d
a
s
z
e
r
o
or c
ons
t
a
n
t
.
Ta
b
l
e 1.
V
olta
ge
v
ec
tor
selec
t
i
o
n ta
ble
F
l
ux
T
o
r
que
S
e
c
tor
1
2
3
4
5
6
1
1
V
1
V
2
V
3
V
4
V
5
V
6
-1
V
6
V
1
V
2
V
3
V
4
V
5
0
1
V
2
V3 V4
V5 V6
V1
-1
V
5
V6 V1
V2 V3
V4
-1
1
V
3
V
4
V
5
V
6
V
1
V
2
-1
V
4
V
2
V
3
V
4
V
5
V
6
2.3.
In
je
ction
of
C
arr
i
e
r
W
av
e
f
o
r
m
The
tor
que
e
r
r
o
r
is
t
he
i
np
ut
f
or
l
o
o
k
-up
t
a
b
l
e
as
t
he
r
e
s
ul
ts
from
d
i
f
fer
e
nce
be
tw
ee
n
car
rie
r
w
a
ve
form
a
nd
a
c
tua
l
t
or
q
u
e
.
I
njec
tio
n
of
car
rier
w
ave
f
orm
t
e
ch
n
iq
ue
i
s
co
nce
p
tua
l
ly
e
a
s
y
t
o
u
n
d
e
r
st
a
n
d.
T
he
ma
them
at
i
c
al
c
o
n
c
e
p
ts
b
eh
i
nd
t
h
is
t
ec
hn
ique
r
ea
s
oni
ng
a
re
s
im
pl
e
.
T
h
i
s
tec
hni
q
u
e
(
inje
ct
ion
c
a
rr
ier
w
a
ve
form
)
is
i
m
p
lem
e
n
t
ed
a
nd
e
x
pla
i
ne
d
in
[
1
0
]
for
in
d
u
ct
ion
m
o
t
o
r.
A
s
im
i
l
ar
a
ppr
oac
h
i
s
use
d
i
n
t
h
i
s
pape
r.
I
n
do
i
n
g
so,
the
t
r
i
a
n
g
u
l
a
r
w
aveform
freque
nc
y
m
u
s
t
s
et
at
h
igh
val
u
e
i
n
o
r
d
er
t
o
re
duce
ou
t
p
u
t
t
orq
u
e
r
i
p
p
l
e
h
e
n
c
e
f
a
s
t
e
r
t
o
r
q
u
e
r
e
s
p
o
n
s
e
.
F
o
r
P
I
c
o
n
t
r
o
l
l
e
r
,
i
t
i
s
n
ec
essary
t
o
m
a
ke
s
ure
tha
t
t
he
g
a
i
n
va
lue
s
o
f
and
a
re re
s
t
r
i
c
t
e
d so t
ha
t
the
a
b
sol
u
te
s
lo
pe
o
f
Tc not
t
o
ex
ce
ed
t
h
e
abs
o
l
u
te sl
o
pe
o
f th
e
triang
u
l
ar
(
carrier
)
w
a
ve
form
. F
i
g
u
re
3
show
s t
h
e
typ
i
c
a
l
w
a
v
efor
m
for
consta
nt fr
e
q
ue
nc
y t
o
rque
c
o
n
tro
lle
r (
C
F
T
C)
.
F
i
gure
3.
Typ
i
cal
w
avef
orm
of
t
he
c
o
n
st
n
t
fr
e
que
nc
y t
o
rq
u
e
c
ont
ro
ll
er
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
:
10
–
18
14
3.
MEASUR
E
M
ENT S
ETUP
Ta
b
l
e
2
show
s
P
a
rame
t
e
rs
o
f
BLD
C
M
o
t
or.
F
i
g
u
r
e
4
s
how
s
dia
g
r
a
m
for
torq
ue
a
nd
c
o
nsta
n
t
sw
it
c
h
i
n
g
freq
ue
nc
y
se
tu
p.
S
pe
ed
s
e
n
s
o
r
(H
all
Ef
fec
t
)
will
me
as
ure
the
speed
r
pm
w
hich
w
i
l
l
b
e
s
h
o
w
n
b
y
di
gita
l
spee
d
i
ndic
a
t
or.
dS
P
A
CE
1
1
0
4
i
s
c
o
n
t
ro
l
l
er
boa
rd
t
ha
t
b
e
e
n
used
t
o
t
r
a
n
sf
er
d
at
a
f
r
o
m
B
LDC
moto
r
and
al
low
s
t
he
d
a
t
a
to
b
e
pre
s
e
n
t
in
o
sc
i
l
l
o
s
c
ope
a
n
d
C
on
t
r
ol
d
es
k
from
c
ompu
ter.
1
5
V
is
s
up
p
l
i
e
d
t
o
t
he
curr
ent
se
nsor
w
hic
h
fu
n
c
t
i
o
n
t
o
s
e
n
se
t
he
c
ur
rent va
l
ue
a
c
c
u
ra
t
e
l
y
f
o
r
p
h
a
s
e
a
a
n
d
b
i
n
t
h
e
B
L
D
C
m
o
t
o
r
a
s
i
t
is
i
mp
orta
nt
t
o
calc
u
la
te
t
h
e
v
a
l
ue
o
f
est
i
ma
t
e
d
tor
que.
1
00V
–
1
5
0
V
i
s
s
up
p
l
ie
d
t
o
t
he
B
LD
C
m
o
tor
fr
om
pow
er
sup
p
l
y.
F
i
gure
4.
S
c
h
e
m
ati
c
for e
xpe
rim
e
nt se
t
up
Ta
bl
e
2
.
Pa
r
am
et
e
r
s o
f
B
LDC
mo
t
o
r
B
a
ldor’
s
B
L
D
C
M
o
t
o
r
(
25P0
02B
002
)
C
ontrol
Sy
stem
Torque
H
y
s
t
e
r
e
sis Ba
nd
0.
1
N
m
Flux
H
y
st
e
r
e
s
is
Ba
n
d
0.
1
Wb
S
a
m
p
li
ng T
i
m
e
50
µs
G
e
ne
ra
l
P
a
ra
m
e
te
r
s
C
ont.
S
t
a
l
l
T
or
que
Lb-In
(
N
-
M
)
:
18.
50
(
2
.
10)
C
ont.
S
ta
ll
C
ur
re
nt
:
1.
5
Pe
a
k
T
or
que
L
b-
In
(
N
-
m
)
:
55.
5
(6.
3
)
E
l
e
c
t
r
i
c
al
P
ar
a
m
e
t
e
r
s
T
o
rque
C
onsta
nt
L
b-
I
n
/A
m
p
(
N-
m
/
Am
p):
15.
50
(
1
.
75)
V
o
lta
g
e
c
onst
a
nt
v
/
r
/s
(
V
/
K
R
PM
):
150.
00
0
(1
06.1
)
Re
sist
a
n
ce
26.7
Induc
t
a
n
c
e
(
m
H
)
106.
3
M
ech
a
n
i
c
a
l
P
a
r
am
et
er
I
n
e
r
ti
a
Lb
-
I
n-
s
2
(
kg
-
c
m
2
):
0
.
0024
(2.
72)
Spee
d a
t
3
20
B
u
s Volt
s
(
R
PM
):
1800
Pol
e
p
a
i
r
s
2
F
e
ed
b
a
ck
D
ev
i
s
e
Ha
ll
S
en
s
o
r
I
n
c
r
emen
t
a
l
En
co
d
e
r
4.
SIMU
L
A
TION
R
ESULT
S
I
n
t
h
i
s
e
x
perim
e
nt,
t
h
ree
sc
he
m
e
s
wer
e
t
ested
und
e
r
three
diffe
rent
s
p
e
e
d
o
p
e
rat
i
on
s,
i
.e
.
l
o
w
sp
e
e
d,
midd
le
s
pe
ed
a
nd
h
i
g
h
s
peed.
The
e
x
perim
e
nt
f
or
e
ach
s
c
h
em
e
w
a
s
p
e
r
for
m
e
d
u
si
ng
tor
que
c
o
n
t
r
o
l
l
o
op,
i
n
w
h
ic
h the
a
n
g
u
l
ar
v
e
l
oc
i
t
y of BLD
C
m
o
tor
w
a
s
set at
a
rou
nd the
t
h
ree
le
ve
ls of spe
e
d
ope
rat
i
o
n
s by a
p
pl
yin
g
appr
opr
i
a
t
e
l
oa
d
t
o
r
que.
The
rest pa
r
am
eter
contro
l
va
lues f
o
r
e
ach
s
chem
e
were give
n
i
n
Table
3.
Tab
l
e
3. P
a
r
ameter
c
on
tro
l
for
e
ach
s
chem
e
C
ontrol
S
c
h
e
m
e
s
(a
) D
T
C
(b
) C
SF
R
e
fe
re
nc
e
t
o
rq
u
e
,
T
re
f
0
.9
N
m
0
.
9
N
m
Sa
mpling ti
me
, T
s
50
µs
50
µs
Torque
h
y
s
te
re
sis b
a
ndw
idth,
H
B
T
0
.
09 Nm
-
C
u
r
r
e
n
t hy
st
e
r
e
s
is ba
ndwidth, HB
i
0
.
059
2
N
m
-
PI
t
or
q
u
e
c
ontrol:
P
ro
p
o
rtio
n
a
l g
a
in
, K
pT
I
n
t
e
g
r
a
l g
a
in
, K
iT
-
-
2.
67
50
Ca
rrie
r
f
r
e
que
n
c
y, f
sw
-
3125
H
z
Pe
a
k
of ca
rrie
r
, V
tri
-
100
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
A
sim
p
le co
ns
tan
t
sw
i
t
c
h
ing
fre
q
uency
o
f
d
i
r
ect t
o
rq
ue co
nt
ro
l
of
br
ush
l
e
ss (Y
us
ni
d
a
T
a
rm
i
z
i)
15
F
i
gure
5
sh
ow
s
t
h
e
e
x
perim
e
nta
l
r
e
s
u
l
ts
o
f
m
o
t
o
r
to
r
q
ue,
tor
que
e
r
r
o
r
a
n
d
a
-
phase
c
urre
nt
f
or
e
a
c
h
schem
e
,
at
l
o
w
s
pe
e
d
,
me
dium
s
pee
d
a
n
d
h
i
gh
s
pe
e
d
.
F
i
g
u
r
e
6
s
h
o
w
s
t
he
z
o
o
me
d
ima
g
e
for
pre
s
e
n
t
i
ng
clea
rer
r
e
sult
s
in
h
i
g
hli
g
h
t
i
ng
the
im
prove
m
e
nt/e
ffe
c
t
.
It
c
an
be
o
bserve
s
tha
t
t
he
r
ip
p
l
e
si
z
e
s
o
f
t
or
que
i
n
pro
pose
d
C
S
F
s
che
m
e
a
r
e
re
duce
d
c
om
par
e
t
o
D
T
C
sc
h
e
me
.
The
impr
ovem
e
n
t
s
o
b
t
a
i
ne
d
i
n
t
he
p
rop
o
se
d
CS
F
at
t
he
l
ow
-
s
pe
ed
o
pera
ti
on
w
ere
a
l
s
o
v
erifie
d
i
n
t
he
c
ase
o
f
me
d
i
um
a
n
d
h
ig
h
spe
e
d
opera
t
i
o
n
s.
F
ig
ure
5
(b)
a
nd
F
i
g
u
re
6
(
b)
s
how
t
he
e
x
p
e
r
ime
n
t
a
l
r
e
su
l
t
s
for
t
h
e
c
a
se
o
f
t
h
e
m
e
d
i
um-
s
pee
d
ope
r
a
tion,
w
h
ile
F
ig
ur
e
5
(c
)
and
F
i
g
u
r
e
6
(
c)
s
how
s
the
e
x
perim
e
n
t
al
r
e
s
u
lts
f
or
t
he
c
ase
of
t
he
h
i
g
h-spee
d
o
p
e
r
ati
on.
T
he
t
y
p
es
o
f
w
a
ve
form
s
ob
t
a
i
n
e
d
a
n
d
t
or
que
r
efere
n
ce
a
p
p
l
ie
d
in
t
h
e
se
f
i
gure
s
ar
e
same
a
s
the
case
o
f
low-
speed
opera
tio
n.
T
he
onl
y
di
fire
nt
i
s
t
h
at
t
he
l
e
v
e
l
o
f
s
p
ee
d
oper
a
ti
on
,
wh
i
c
h
ca
n
b
e
not
i
c
ed
b
y
ob
s
e
rvi
n
g
th
e
cy
cl
e
peri
od
o
f
the
c
u
rre
nt
a
t
t
h
e
sa
me
time
sca
l
e
.
N
ot
e
d
t
ha
t,
t
he
g
re
ater
n
u
m
be
r
of
c
yc
le
i
n
d
i
c
a
t
e
s
hi
g
j
e
r
s
p
e
ed
opera
tio
ns.
A
ppa
ren
t
l
y
,
t
o
rq
u
e
o
r
c
u
rr
ent
ri
pp
le
i
s
reduce
d
f
or
e
very
l
e
v
e
l
o
f
spee
d
o
p
e
rati
on,
i
.e
.
regard
less
of
s
pe
e
d
o
pe
rat
i
o
n
s.
DTC
CS
F
(a)
(b)
(c)
F
i
gure
5. Expe
rime
nt
a
l
re
s
u
l
t
s
of
tor
que
c
o
n
t
ro
l for
D
T
C and
CS
F
at (
a)
l
o
w
spee
d
, (
b) m
edium
spee
d and
(c)
hi
g
h
spe
e
d
ope
rati
ons
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
:
10
–
18
16
DTC
CS
F
(a)
(b)
(c)
F
i
gure
6. Expe
rime
nt
a
l
re
s
u
l
t of zo
o
m
-
im
age
for
D
T
C and
CS
F
at
(
a
)
l
o
w
spee
d,
(
b
)
m
ed
ium
spee
d and
(c)
hi
g
h
spe
e
d
ope
rati
ons
I
n
or
d
e
r
t
o
d
e
t
e
r
mine
t
he
d
o
m
ina
n
t
sw
i
t
c
h
ing
fr
eq
ue
nc
y
for
e
a
c
h
s
h
em
es,
the
fr
eq
ue
nc
y
s
p
ec
t
r
um
o
f
a
torq
ue
w
a
v
e
f
orm
at
0
.9
N
m
as
m
e
n
t
i
o
n
ed
i
n
Ta
b
l
e
3
was
pl
o
t
te
d
a
s
de
spic
te
d
i
n
F
i
gur
e
7.
I
t
can
b
e
c
l
e
a
rl
y
seen
t
ha
t
the
p
r
opose
d
C
S
F
r
esu
lts
i
n
a
dom
ina
n
t
harm
on
i
c
c
ompo
ne
nt
a
s
it
s
ca
rrie
r
freque
nc
y,
i
.e
.
f
sw
=
3
125
H
z
.
This
i
n
d
ic
ate
s
t
hat
the
sw
itc
hi
n
g
freq
u
e
n
c
y
of
i
nv
ert
e
r
is
c
o
nsta
n
t
a
t
t
h
e
car
rier
fre
que
ncy,
w
h
i
l
e
D
TC
exh
i
bi
t
scat
ter
e
d
ha
rm
on
i
c
c
ompo
ne
nt
s
due
t
o
h
y
ster
es
is
o
per
a
ti
o
n
.
N
o
te
t
hat
t
h
e
sca
t
t
e
red
har
m
onic
com
p
o
n
e
n
t
s
s
how
t
he
s
w
itc
hi
ng
freque
nc
i
e
s
base
d
o
n
h
yste
resis
c
o
n
tr
olle
r
are
u
npr
edic
ta
b
l
e;
t
ha
t
vary
ac
cord
in
g t
o
th
e
opera
tin
g
co
nd
iti
o
n
s.
DTC
CS
F
(a)
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
A
sim
p
le co
ns
tan
t
sw
i
t
c
h
ing
fre
q
uency
o
f
d
i
r
ect t
o
rq
ue co
nt
ro
l
of
br
ush
l
e
ss (Y
us
ni
d
a
T
a
rm
i
z
i)
17
(b)
(c)
F
i
gure
7.
F
re
quenc
y
sp
e
c
t
ru
m
of
t
orque
w
avef
orm
for
D
T
C a
n
d
CS
F
a
t (a)
low
spee
d,
(
b) m
e
d
ium
spee
d a
nd
(c) hig
h
spee
d
oper
a
ti
ons
5.
CONCL
U
S
ION
I
n
conc
l
u
si
on,
t
he
d
irec
t
t
o
r
que
c
on
tro
l
d
r
i
ve
h
a
s
b
ee
n
i
m
pl
e
m
e
n
ted
for
Brus
hle
ss
D
C
M
otor
t
o
reduc
e
tor
q
ue
r
i
p
ple
a
nd
imp
r
ove
v
a
r
ia
b
l
e
freque
ncy
b
y
r
e
p
l
a
c
i
n
g
t
h
e
t
o
r
que
h
y
s
ter
e
sis
con
t
ro
ller
w
i
t
h
t
he
Cons
ta
nt
S
w
i
tc
hin
g
F
re
que
n
c
y
(CS
F
)
in
t
h
e
b
as
ic
D
TC
s
chem
e.
I
n
th
i
s
r
esea
rch,
t
he
c
om
paris
on
o
f
o
u
t
pu
t
tor
que
a
nd
sw
i
t
ch
i
ng
freq
ue
n
c
y
be
tw
ee
n
D
T
C
h
y
s
t
er
esis-
b
ase
d
a
n
d
D
TC-CS
F
w
ere
e
xpe
r
i
me
nt
e
d
i
n
seve
ral
con
d
i
t
i
on
s
(
lo
w
,
m
edium
an
d
hi
g
h
o
per
a
t
i
on)
o
f
m
o
t
o
r
h
a
d
be
en
pr
ese
n
ted.
B
a
s
e
d
on
the
resu
lts,
it
p
rove
n
tha
t
a
t
an
y co
n
d
i
tio
n, t
he CS
F
me
t
ho
d ca
n
re
duce
d
torq
u
e ri
pple
a
nd pro
v
i
d
ed a
c
on
st
a
n
t
sw
it
c
h
i
n
g fre
q
uen
c
y
for
D
T
C
dr
ive
.
F
ina
l
ly,
it
ca
n
be
c
o
n
c
l
u
d
e
d
t
he
D
T
C
w
it
h
C
S
F
me
n
t
hod
w
a
s
s
u
c
c
e
ssfu
l
l
y
i
mp
l
e
me
nt
ed
u
si
ng
BL
D
C
m
otor.
ACKNOW
LEDG
E
MEN
T
S
Th
e
aut
h
ors
wo
u
l
d
l
i
k
e
t
o
th
an
k
M
i
n
i
s
t
r
y
o
f
Ed
u
cati
o
n
M
a
l
a
ysi
a
,
U
n
i
ve
rsi
t
i
T
e
kn
ik
a
l
M
a
l
ay
sia
M
e
l
a
ka
(
U
T
e
M
)
f
o
r
p
r
o
v
id
in
g
t
h
e
res
e
a
r
ch
g
ra
n
t
P
JP
/20
1
7
/
FK
E/H
I
12
/
S
01
53
8
a
nd
FRG
S
/
2
/20
14/
TK03/UTEM
/
0
3
/
2
/
F0
023
9.
REFE
RENCES
[1]
M
.
B
arcaro
,
“
Perf
o
r
m
a
nce
Evaluat
i
o
n
o
f
an
I
n
t
egrat
E
d
S
tarter
A
lte
rna
t
or
u
s
i
n
g
a
n
Inte
rior
P
e
r
ma
ne
n
t
M
a
g
ne
t
M
achi
n
e,”
IE
T El
ectro
n
i
c on
Power A
ppli
e
d
,
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.
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,
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53
9-5
4
6
, 2
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T.
Y
o
on,
“
M
a
g
n
et
icall
y
I
nd
uced
V
ibratio
n
in
a
P
erman
e
nt
-M
agnet
Brushle
s
s
DC
M
otor
w
ith
S
y
mme
tric
P
o
l
e
-
Sl
ot
Co
nfig
ura
t
io
n,”
IEEE T
r
an
sa
c
tions
on
M
a
g
n
e
ti
cs
,
vol.
4
1
,
pp.
2
1
7
3
-
21
79,
2
0
0
5
.
[3]
Z.
Q
.
Z
h
u
and
D.
H
ow
e,
“
In
fl
u
e
n
c
e
of
D
es
ig
n
P
a
ram
e
ters
o
n
C
ogg
i
ng
T
o
r
qu
e
in
P
e
r
ma
n
e
nt
M
ag
ne
t
Ma
c
h
ine
s
,”
IEEE Transac
t
i
on
E
n
ergy Conversion
,
vo
l.
1
5
,
p
p
.
4
0
7
–
4
1
2
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J.
H
ur
a
nd
B
.
W.
K
im,
“
R
o
t
or
S
hap
e
D
esi
g
n
o
f
a
n
In
teri
or
P
M
t
y
p
e
BL
DC
M
oto
r
f
or
I
mp
rov
i
n
g
M
echani
cal
Vi
bration
and
EMI
Ch
aracteri
s
tics,
”
Jou
r
na
l of El
e
c
t
r
i
c
al
En
g
i
neeri
n
g
an
d
T
ech
no
log
y
, vo
l
.
5
, p
p.
46
2
–
4
6
7
,
2
01
0
.
[5]
Z.
Q
.
Z
hu,
M
.
L
.
M
oh
d
Jamil,
a
n
d
L
.
J.
W
u,
“
Infl
uen
c
e
of
S
lot
a
n
d
P
o
l
e
N
u
mb
er
C
om
bi
na
t
i
ons
on
Un
balan
ced
M
a
gn
etic
F
o
r
ce
i
n
P
erm
a
nent
M
agn
e
t
M
achin
es,”
En
e
r
gy
Co
nv
e
r
sio
n
Con
g
r
e
ss a
n
d
Ex
po
si
tion
(ECC
E
)
,
20
11
IEEE
,
p
p
.
1
-8
,
2011
.
[6]
S
.
M
.
Jaf
a
riS
h
iadeh,
M
.
Ardeb
ili,
“
T
h
r
ee-Dimen
s
i
onal
Fi
nite-El
e
me
n
t
-M
od
e
l
I
nv
e
s
tiga
t
i
o
n
o
f
A
xia
l
-F
lu
x
P
M
BLD
C
M
achi
n
es
w
ith
S
i
m
il
ar
P
ol
e
an
d
S
l
ot
C
om
bi
na
ti
on
f
o
r
E
lectr
ic
V
e
h
ic
l
e
s
,
”
P
o
wer an
d En
e
r
gy Con
f
eren
ce a
t
Illino
i
s (
PECI
)
,
2015
IEEE
,
pp.
1
-4,
2
01
5.
[7]
K.
O
.
S
u
ng
,
C.
S
.
Ho
ng
,
an
d
P
.
H
an
,
“F
l
ux
Fl
uctu
ati
o
n
s
i
n
Rotor
C
ore
Acco
rdin
g
to
P
o
l
eSl
o
t
Comb
in
a
t
i
on,”
2
012
IEEE
V
e
hicl
e
Power and
Propu
l
s
i
on
Con
f
erence
,
p
p
.
1
04
5-10
47
, 2
01
2.
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
:
10
–
18
18
[8]
L.
M
a,
M
.
S
a
n
a
da,
S
.
M
ori
m
o
t
o
and
Y.
T
akeda,
"
P
r
edi
c
ti
on
o
f
I
ro
n
l
o
s
s
i
n
rot
a
ting
m
ach
ines
w
ith
ro
tat
i
on
a
l
l
oss
in
clu
d
e,"
IEEE Tr
an
sa
ctio
ns on
M
a
g
n
e
ti
cs
,
v
o
l.
3
9,
pp.
2
0
3
6
-
20
4
,
2
00
3.
[9]
S
a
l
i
h
B
a
r
i
s
O
z
t
u
r
k
,
H
.
A
.
T
o
l
i
y
a
t
,
“
D
i
r
e
c
t
T
o
r
q
u
e
C
o
n
t
r
o
l
o
f
B
r
us
hl
e
s
s
DC
M
ot
or
w
ith
N
o
n
-S
inu
s
oid
a
l
Back-
EMF”,
E
l
ect
r
i
c
M
a
c
hin
e
s
&
Dr
ives Co
nf
erence (
I
EM
D
C
)
,
20
07
[10]
Ji
d
i
n
,
A
.,
I
d
r
i
s
,
N.
R
.
N.,
Ya
t
i
m,
A
.
H
.
M
.
,
S
u
tik
no
,
T.
a
n
d
E
l
b
u
luk
,
M
.
E.,
“S
imp
l
e
Dy
nami
c
Ov
erm
odu
latio
n
S
t
rat
e
g
y
f
o
r
F
as
t
T
o
rqu
e
C
on
tro
l
i
n
DTC
of
I
nducti
on
M
ach
in
es
w
ith
C
onstant-
S
w
i
t
ching-
Fre
q
ue
n
c
y
C
o
n
t
ro
lle
r”
,
IEEE Transac
t
i
ons
Indu
stry Appl
i
c
ation,
vo
l. 47
, p
p
.
2
28
3-2
2
9
1
,
2
01
0.
[11]
V
.
M
o
s
t
a
f
a
,
N
.
A
r
n
e
,
N
.
R
o
b
e
r
t
,
D.
L
.
Robert
a
nd
R
.
Terje,
“
In
f
luen
ce
of
P
o
l
e
and
S
l
o
t
C
om
bin
a
ti
ons
o
n
Mag
n
etic
F
o
rces
a
n
d
V
ib
ratio
n
i
n
L
ow
-S
p
eed
P
M
Wind
G
en
e
r
at
ors
,
”
IE
EE
T
r
an
sa
c
t
ion
s
on
M
a
gn
e
t
ic
s
,
vo
l
.
5
0,
p
p
. 1-1
1
, 2
01
4.
[12]
P
.
M
.
Li
ndh
,
H.
K
.
J
u
ssi
l
a
,
M
.
N
i
e
m
e
l
a
,
A.
P
ar
vi
ai
nen
,
a
n
d
J
.
P
y
r
ho
nen,
“
Co
m
p
ariso
n
o
f
co
n
cen
trated
w
i
nding
perm
anen
t
m
a
gn
et
m
o
t
ors
wit
h
e
m
b
edd
e
d
and
s
u
rf
ace-m
o
u
n
t
e
d
rot
o
r
m
a
g
n
e
t
s
,
”
I
E
E
E
T
r
a
n
sa
c
tio
n
s
on
Mag
ne
tic
s
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J.
Y
an
g
,
G
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L
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W
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Zh
ao,
Q
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C
he
n,
Y
.
Jian
g
,
L
.
Sun
,
et
a
l
.
,
“Q
uan
t
itati
ve
c
om
p
a
ris
on
f
o
r
f
r
act
ion
a
l-slot
con
centrat
ed-w
ind
i
n
g
c
on
fi
gu
rati
on
s
of
p
erm
a
nent
-m
agnet
v
e
rnier
m
achi
n
es,
”
IEEE Tran
sac
t
io
ns o
n
Mag
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t
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S.
U
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Ch
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B
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W
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D.
K
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Ho
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J
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Y
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L
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“
F
r
a
c
ti
on
al
s
l
o
t
con
cent
r
ated
w
i
ndin
g
perm
anen
t mag
n
et
sy
n
ch
rono
us
m
achi
n
e w
i
t
h
co
n
s
e
quen
t
pol
e rot
o
r
f
o
r
l
o
w
s
p
e
ed
d
i
r
ect
d
r
i
v
e
,
”
IEEE T
r
an
sa
c
t
i
ons
o
n
Mag
ne
tic
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vo
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a
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A
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E
l
s
e
r
o
u
g
i
,
“
A
n
i
m
p
roved
perform
ance
di
rec
t
-dri
ve
p
erm
a
nent
m
a
gn
et
w
i
nd
g
e
nerato
r
us
ing
a
n
o
v
e
l
si
ngle
lay
e
r
win
d
i
n
g
l
a
yout
,”
IEE
E
Tra
n
s
a
cti
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K
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J
u
n
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“
N
u
m
erical
i
nv
est
i
ga
t
i
o
n
o
n
torque
h
ar
monics
r
educti
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n
o
f
interi
or
P
M
sy
nch
r
ono
us
m
o
t
or
w
it
h
co
ncentrated
w
i
nding
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”
I
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H
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“
F
i
n
i
t
e
E
l
e
m
e
n
t
C
o
m
p
u
t
a
t
i
o
n
of
M
ag
neti
c
Vibrat
io
n
S
o
urces
i
n
1
0
0
k
W
t
w
o
F
r
actio
nal
-
s
l
o
t
I
nt
erior
P
e
rman
ent
M
a
gn
et
M
ac
h
i
nes
f
o
r
S
h
i
p
,”
I
E
E
E
Tran
sa
c
t
io
ns o
n
Mag
n
e
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M
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EL-Re
f
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“
F
r
acti
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t
C
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n
cent
r
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in
di
ngs
S
y
n
ch
ro
no
us
P
erm
a
nen
t
M
a
g
net
M
achi
n
es
:
Opportunities an
d chal
lenges,
”
IE
E
E
T
r
a
n
s
a
ct
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Ind
u
stri
a
l
El
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M
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EL
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f
aie,
“
F
r
acti
onal
-
s
l
ot
c
o
n
cen
trated
-wi
n
d
i
ng
s
:
A
p
ara
di
gm
s
hift
i
n
elect
rical
m
achi
n
es
,”
i
n
P
r
oceed
ing
IEEE WE
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D
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Lib
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J.
S
oulard
,
“
Inves
tig
a
t
i
o
n
o
n
P
ole-slo
t
C
o
m
b
i
nati
o
n
s
f
o
r
P
e
rm
anent
-
M
a
gnet
M
ach
ines
w
ith
Con
centrat
ed W
in
din
g
s,” i
n
Pro
ceedin
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Y.
S
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of
P
M
Bru
s
hles
s
M
achin
es
h
av
in
g
a
F
r
ac
t
i
o
n
al
N
um
ber
o
f
S
l
o
ts
Pe
r Po
l
e
,”
IEE
E
Tr
an
sa
ctio
ns on
M
a
g
n
e
ti
cs
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G.
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and
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G
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“
Magn
eti
c
r
ad
ial
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rce
d
e
ns
it
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of
t
he
P
M
m
ach
in
e
w
i
t
h
1
2
-
teet
h/10-p
o
l
e
s
wi
ndin
g
topology
,
”
i
n
Proceed
ing
IEEE IEM
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M
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D
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P
r
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,
a
n
d
G
.
G
r
e
z
z
a
n
i
,
“
D
e
s
i
g
n
c
on
sid
e
ration
s
f
o
r
f
r
acti
onal-s
l
ot
w
i
n
d
i
n
g
c
o
nfig
ura
t
io
ns
o
f
syn
c
h
r
on
ou
s
ma
c
h
ine
s
,”
I
EEE Tran
sa
c
t
io
ns
on
In
d
u
str
i
a
l
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F
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a
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Kh
a
m
i
s and M.
N
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sam,
“
Imp
r
ov
e
m
ent o
f
T
orq
u
e
Den
s
ity
S
po
ke
T
yp
e
BL
DC
M
o
t
o
r
U
si
ng
New
H
o
llow
Ro
tor
To
po
lo
gy,
”
Intern
atio
nal Review of
Electrica
l
En
gi
neeri
ng (
I
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A
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J
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i
,
S
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To
l
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a
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M
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s
am,
“Des
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H
ollow-Ro
tor
Brus
hles
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DC
M
o
t
or,
”
In
ter
n
a
t
io
nal Jou
r
n
a
l
o
f
Po
wer El
ectr
o
n
i
cs a
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S
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st
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M
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t
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h
i
,
a
nd
T.
O
kits
u
,
“
Torque
C
har
act
eristics
of
I
P
M
S
M
w
i
t
h
Spoke
and
Axial
Type
M
ag
nets,
”
SPEEDAM
201
2 - 2
1
s
t
In
tern
atio
nal Sym
p
o
s
i
u
m o
n
P
o
wer
Electro
ni
cs, E
l
ectrical D
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and
G.
H
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Kan
g
,
"A
s
tu
d
y
o
n
i
ron
lo
ss
a
n
aly
s
i
s
m
eth
od
con
s
i
d
erin
g
t
h
e
harm
o
n
ics
o
f
t
he
f
lux
den
s
it
y
wavef
o
rm
u
sin
g
i
ron
l
o
ss
curv
es
t
ested
on
E
p
s
tein
s
ampl
es
,"
IEEE T
r
a
n
s
a
c
t
ions on
M
a
gnetics
,
v
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