Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 63
4
~
64
0
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p63
4-6
40
6
34
Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
The effect of static and dy
namic eccentricities on the
performance of flu
x
reversa
l permanent magnet machine
Ahl
a
m
Lu
aib
i
Sh
ur
aij
i
Ele
c
tro
m
ech
anic
al Eng
i
n
e
ering
Dep
a
rtm
e
nt
, Un
iv
e
r
sit
y
of
Te
c
h
n
o
lo
gy
,
Ira
q
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
Au
g 9
,
20
19
Re
vise
d Oc
t
9, 2
019
Acc
e
pt
e
d
Fe
b 7, 2
0
2
0
Th
is
study
in
v
e
s
t
ig
ates
the
e
ffec
t
o
f
static
an
d
dy
nami
c ec
cen
trici
t
ies
o
n
th
e
perfo
rman
ces of
flux
r
e
v
e
rsa
l
p
e
rmanen
t m
a
gne
t (F
RP
M
)
mach
in
e with
ev
en
rotor p
o
l
e
numb
e
r,
i.
e.
F
R
P
M
m
ach
in
e with
12/
10
stato
r
/rotor
c
o
mbin
ation
.
No
-lo
a
d an
d
lo
a
d
p
e
rform
anc
e
s
of the
m
achin
e
are
in
ves
t
ig
ated
un
der thr
e
e
rotor op
eratin
g
con
d
i
tions
in
clud
in
g
cen
tr
icity, sta
t
ic
ec
ce
ntrici
ty
and
dy
nami
c
ec
cen
tr
icity
.
Th
e
inv
e
st
igatio
n h
a
s
been
carri
ed ou
t us
in
g 2D
-F
EA
.
It
has
b
een
rev
e
aled
th
a
t
th
e 1
2
/
1
0
FRP
M
mach
in
e
un
d
e
r no
rm
a
l
o
p
er
ating
con
d
ition
h
a
s
n
o
un
balan
ced m
a
gn
eti
c
forc
e,
d
u
e
to the ev
en po
le
nu
mber
o
f
t
h
e
rot
o
r. On th
e o
t
h
e
r h
a
nd, su
ch
un
d
e
si
ra
b
l
e fea
t
ur
e wo
u
l
d be
pre
s
e
n
te
d i
n
t
h
e
12/1
0
FRPM
m
a
c
h
in
e
a
s
a
re
su
lt o
f
th
e e
x
i
s
t
i
n
g
of sta
tic
an
d
dy
na
m
i
c
ecc
ent
r
i
c
it
ies
.
B
o
th
st
a
t
i
c
and
dy
n
a
mic
ecc
en
tric
m
a
ch
in
es ex
hibit
un
balan
ced
thr
e
e-ph
ase
flux
lin
k
age
as
well
as
back
-EM
F
.
M
o
reo
v
er,
thre
e
operating
conditions of
t
h
e investi
g
at
ed
machine
have the
same fundament
a
l
c
o
gg
in
g t
o
rq
u
e
ha
rm
o
n
ic
.
Ho
wev
e
r,
lo
w
o
r
de
r ha
rm
o
n
ic
s
are
e
x
ist
e
d i
n
t
h
e
static and
d
yna
mic centr
ic ma
ch
in
es
an
d are
not
fo
un
d
in
the c
e
ntri
c
mach
ine.
F
u
rthe
rmore,
ab
ou
t 16
% les
s
to
rqu
e
r
i
pp
le d
e
liv
e
red
b
y
the
c
e
ntri
c
mach
ine
co
mp
ar
ed w
i
th
b
o
th
s
t
at
ic
an
d d
y
n
a
mic
c
o
unterpar
t
s.
Ke
yw
ords:
D
y
n
a
mic
e
ccen
tr
ic
it
y
Fl
ux
re
ver
s
al
p
e
rma
n
ent
mag
n
e
t
machi
n
e
S
t
a
tic
e
c
c
e
n
tr
ic
ity
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
Ahl
a
m
L
u
a
i
bi
S
h
urai
j
i
,
El
ect
romec
h
a
n
i
cal
Engi
ne
eri
n
g De
pa
rt
me
nt
,
Uni
v
ersi
t
y
o
f
Tech
nol
og
y,
Ba
gh
da
d, Ira
q.
Ema
i
l
:
a
h
la
ml
y2
009
@y
ah
oo
.co
m
1.
IN
TR
O
DUCTION
S
t
at
or pe
rma
n
e
n
t ma
g
n
e
t
(S
P
M
)
ma
chi
n
es
ha
ve
rece
i
v
e
d
ma
ny a
t
te
nti
o
ns, si
nce
t
h
e
c
onsi
d
era
b
l
e
a
c
h
i
ev
eme
n
t on
t
h
e p
e
rma
n
en
t m
a
g
n
e
t
ma
t
e
ri
al
s [
1
-5
].
Th
e
i
d
ea
o
f
s
u
c
h
ma
c
h
i
n
es was
f
i
r
s
t i
n
trod
uc
ed
by
Ra
uch a
n
d
Jo
h
n
so
n [6
]. T
h
e
S
P
M
mac
h
i
n
e
s
a
r
e
ge
neral
l
y
c
l
a
s
si
fie
d
to t
h
re
e t
ype
s, w
h
i
c
h are
do
u
b
ly
sa
li
ent
perma
n
e
n
t
ma
gne
t
(D
SP
M
)
mac
h
ine
s
,
fl
u
x
re
ve
rsal
pe
rm
ane
n
t
ma
gnet
(F
RP
M
)
ma
c
h
i
n
es a
n
d
sw
it
ch
flu
x
perma
n
e
n
t
ma
gnet
(S
FP
M) ma
chi
n
e
s
. Ha
v
i
ng
bot
h e
x
ci
t
i
ng s
o
urc
e
s
(t
h
e
cop
p
er
a
n
d t
h
e pe
rma
n
ent
mag
n
et
)
on t
h
e st
at
or
may
be
co
nsi
d
ere
d
as t
h
e
ma
in
dist
i
n
g
u
i
s
h
e
d feat
u
r
e
of
suc
h
ma
chi
n
es
[7
-1
0
]
. D
u
e
t
o
t
h
is
f
e
a
t
u
r
e, t
h
e
SPM ma
ch
in
e
s
po
ss
ess
th
e a
d
van
t
ag
e
s
o
f
si
mp
le
, p
a
ss
i
v
e an
d
ligh
t
ro
tor
str
u
c
t
u
r
e. Th
er
efo
r
e
,
t
h
ese t
o
p
o
lo
gi
es co
op
erat
e t
h
e fe
at
ure
s
of re
luc
t
a
n
ce
a
n
d pe
rmane
n
t
mag
n
et
ma
c
h
i
n
es.
The
c
o
nc
ept
o
f
t
h
e FR
P
M
ma
chi
n
e
was p
r
e
s
e
n
te
d
i
n
[1
1
]
.
The
ma
c
h
i
n
e
was desi
gne
d a
s
a
si
ngl
e-p
h
a
se
gene
rat
o
r.
It
was
conc
l
ude
d t
h
at
t
h
e machi
n
e
ha
s
t
h
e
ad
va
nta
g
es
of u
n
co
mpl
i
c
a
t
e
d an
d st
ron
g
rot
o
r
st
ruc
t
u
r
e
w
i
t
h
sma
l
l
i
n
e
r
t
i
a
,
h
i
g
h
sp
e
e
d
a
b
ilit
y
an
d
f
a
u
l
t t
o
l
e
r
a
n
c
e
,
wh
ile
[1
2]
d
i
s
c
ussed
mu
lt
iph
a
se FR
PM
ma
c
h
i
n
es
in
wh
i
c
h
3-p
h
a
se
FR
PM
machi
n
e wa
s de
sig
n
e
d
a
n
d
a
n
al
yzed
by
2
D
-fini
t
e
el
ement
a
n
a
l
ysi
s
(FE
A
). It
was
con
f
irme
d t
h
a
t
suc
h
machi
n
e
i
s
s
u
it
abl
e
f
o
r
hig
h
a
s
w
e
l
l
a
s
l
o
w s
p
ee
d
ap
pl
ic
at
io
ns a
n
d i
t
s
si
m
p
le
struct
ure a
nd c
o
n
s
e
q
ue
nt
ly
l
o
w
man
u
fac
t
u
r
i
n
g
coast
ma
ke
t
h
e F
R
P
M
ma
chi
n
e
a
g
o
o
d
c
a
ndi
dat
e
f
o
r
man
y
a
ppli
c
a
t
ions
.
More
ove
r
,
t
h
re
e
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
o
w
Elec &
Dri Sy
st
I
SSN
: 2
0
8
8
-8
69
4
T
h
e ef
fe
ct
of
st
at
i
c
a
n
d
dy
n
a
m
i
c
ecc
ent
r
ic
i
t
i
e
s o
n
t
h
e
perf
orm
a
nc
e of
fl
u
x
…
(A
hl
a
m
Lu
ai
bi
Sh
ur
aij
i
)
6
35
pha
se
F
R
P
M
gene
rat
o
r
was
desi
g
n
e
d
f
o
r
a
u
tom
o
t
i
ve
s
e
c
t
or
i
n
[
1
3]
. It
wa
s del
i
v
er
e
d
t
h
at
the
ge
n
e
ra
t
o
r
has
l
o
w
tr
a
n
si
e
n
t
t
i
m
e
a
n
d a
l
mo
s
t
c
onst
a
nt
o
u
tp
ut
v
o
l
t
a
ge
wi
t
h
f
a
st
s
p
ee
d c
h
an
ge.
F
u
rt
he
r
m
o
r
e
,
[
1
4]
p
r
o
pos
ed
ro
to
r po
le
s p
a
iri
n
g
te
chn
i
qu
e to
r
e
d
u
c
e
coggi
n
g
t
o
rq
u
e
of
t
h
e
FRPM
m
ach
in
e
.
To
min
i
m
i
z
e
t
h
e f
l
ux
-
l
e
a
k
ag
e
on t
h
e r
o
t
o
r p
o
l
es of t
h
e
F
R
P
M
ma
c
h
i
n
e
,
[
1
5]
pl
ace
d
fl
u
x
ba
r
r
i
e
r
on t
h
e
edge
s o
f
t
h
e r
o
t
o
r
p
o
l
e
s,
w
h
i
l
e
[1
6]
i
n
t
r
o
d
u
ce
d
a
n
e
w st
ruct
ure
o
f
the
P
M
fo
r
t
h
e
FR
PM ma
c
h
i
n
e
k
n
o
wn
as i
n
s
e
t
FR
PM
ma
ch
i
n
e whe
r
e
t
h
e
PM
is
pl
ac
ed in
pa
ra
ll
el
on
t
h
e
st
a
t
or o
f
the
F
R
P
M
ma
chi
n
e,
t
o
e
n
hance
t
h
e per
f
o
r
ma
nce
of the
c
o
nv
e
n
ti
onal
co
rr
esp
ond
ing
.
I
t
w
a
s
st
ate
d
th
a
t
th
e
in
s
e
t
F
R
P
M
t
opo
lo
gy
sho
w
s a
b
e
tte
r p
e
rfo
rma
n
c
e
co
mpa
r
ed
t
o
t
h
e e
x
ist
i
n
g
c
o
unte
r
pa
r
t
.
I
n
addi
t
i
o
n
,
th
e
F
R
PM a
nd
DS
PM ma
chi
n
es
wer
e
c
o
m
p
ar
e
d
i
n
t
e
r
m
s o
f
po
we
r
de
n
s
i
t
y
i
n
[
1
7]
.
I
t
wa
s
del
i
v
er
ed tha
t
t
h
e
hig
h
e
r
pow
e
r
de
n
s
i
t
y wa
s
obt
ai
n
e
d b
y
t
h
e
F
R
P
M
mac
h
i
n
e
c
o
mpa
r
ed
to
th
e D
S
PM
c
o
un
te
rp
ar
ts. A
d
d
iti
o
n
a
l
l
y
,
F
R
P
M
ma
c
h
i
n
e
w
ith
fu
ll
p
i
tch
w
i
n
d
i
ng
w
a
s
in
t
r
o
d
u
ced
in [1
8
]
,
to
e
nha
nce
t
h
e m
a
c
h
ine
p
o
we
r
den
s
i
t
y.
B
e
si
de
s,
d
-
q eq
ui
val
e
n
t
ci
rc
uit
of
t
h
e
FR
P
M
wi
th
f
u
l
l
pi
t
c
h
wi
n
d
i
n
g
an
d
co
n
c
en
tr
ate
d
win
d
i
ng
w
e
r
e
d
r
i
v
en
in
[1
9]
. Mo
r
e
ov
er
, [20
]
a
n
ly
sied
and
comp
ar
ed
t
h
e p
e
rfro
man
c
es
o
f
FRP
M
ma
ch
i
n
e
w
ith
t
w
o
PM a
r
r
a
n
g
me
n
t
s, i.e
.
N
S
-N
S and NS
-SN
.
I
t
w
a
s
show
n th
at th
e
NS
-SN arr
a
ng
eme
n
t
h
a
d
hi
g
h
er
spee
d a
n
d
to
r
q
ue t
h
an
t
h
a
t
o
f
t
h
e
N
S
-
N
S
.
Li
ke
ot
he
r P
M
ma
c
h
i
n
es
,
FR
PM
mac
h
i
n
es
wi
l
l
ex
peri
e
n
ce
e
cce
nt
ri
ci
ty i
n
whi
c
h
b
o
t
h
sta
t
o
r
a
n
d
r
o
t
o
r
ce
nt
e
r
s
are
n
o
t
c
o
i
n
ci
ded
,
due
t
o
t
h
e
ma
nuf
ac
t
u
r
i
ng i
m
pe
rf
ect
i
o
n
.
I
t
sh
o
u
l
d
be
poi
nt
ed
o
u
t
t
h
at
th
e
ec
cen
tr
ic
ity
i
s
cl
ass
i
f
i
ed
i
n
to sta
t
i
c
a
n
d
d
y
n
a
mic ec
cen
t
r
i
c
it
ie
s [21
-
2
4
]
.
In
st
at
ic
e
c
c
e
n
tr
ic
ity
the ro
to
r
mo
ves ar
ou
nd
i
t
s ow
n ce
nte
r
and
mini
m
u
m
ai
r-
ga
p
bet
w
ee
n
t
h
e
st
at
o
r
a
n
d t
h
e
rot
o
r i
s
st
at
i
onar
y
.
I
n
c
o
ntr
a
st
,
i
n
dyna
mi
c
e
c
c
e
n
tr
ic
it
y
t
h
e
mi
nimu
m
a
i
r
-
g
a
p
bet
w
ee
n t
h
e
sta
t
or
a
n
d
t
h
e
r
o
t
o
r
r
o
t
a
t
e
s a
r
ou
nd
t
h
e
st
at
or
c
e
n
t
e
r
,
w
h
ile
t
h
e
r
o
t
o
r
r
e
vo
lv
e
s
ar
ou
nd it
s own
ce
n
t
e
r
. Th
e
exci
tin
g
o
f
th
e
e
c
c
e
n
t
ri
ci
ty
is n
e
g
a
ti
v
e
l
y
aff
e
ct
in
g
t
h
e
perfo
rma
n
ce
s o
f
PM
ma
c
h
i
n
es
,
si
nc
e i
t
l
e
ads t
o
u
nba
l
a
nced
ma
g
n
et
ic
f
o
rce
,
whic
h
re
s
u
lt
s i
n
noi
s
e
an
d
vibra
t
ion.
The
be
ha
viors
of t
h
e
ro
tor P
M
a
n
d the
SFPM
machine
s
ha
ve
be
e
n
inte
nse
l
y i
nve
stiga
t
ed
unde
r
th
e
ro
to
r e
c
cen
tr
ic
ity
c
ond
i
tio
n
.
Ho
wev
e
r, th
e
im
p
a
c
t
of
th
e
ro
tor
ecc
en
t
r
i
c
it
y
on
th
e
p
e
rfo
rman
c
e
s o
f
t
h
e FR
PM ma
chi
n
e
ha
s
not
be
en
re
po
rt
ed
yet
.
T
h
ere
b
y
,
i
n
t
h
is st
u
d
y
th
e
effec
t
o
f
the
rot
o
r e
cce
ntric
i
t
i
e
s on
t
h
e pe
rf
o
r
ma
nc
e o
f
s
u
ch
mac
h
i
n
e
w
i
l
l
be c
o
mp
rehe
nsive
l
y
i
nve
st
iga
t
ed.
I
t
i
s
wo
rt
h
me
nt
i
oni
n
g
t
h
at
2
D
-F
E
A
i
s
ut
i
l
i
z
ed t
o
de
sign
an
d
a
n
al
y
z
e
t
h
e
un
de
rst
u
dyi
ng
ma
c
h
i
n
e
.
2.
MAC
H
INE DESC
RIPTI
O
N
T
h
e s
p
e
c
if
ic
at
io
n
s
o
f
t
h
e 12
/1
0
F
R
PM
m
a
ch
in
e
ar
e sh
o
w
n
i
n
T
a
b
l
e
1
.
On
th
e o
t
h
e
r ha
n
d
,
a cr
oss-
se
ct
iona
l
of
t
h
e u
nde
rst
u
d
y
i
n
g
ma
c
h
i
n
e
i
s
depi
ct
ed
i
n
F
i
gu
re
1.
It
ca
n
be
se
e
n
t
h
a
t
t
h
e F
R
P
M
mac
h
ine
is
c
o
n
s
t
r
ue
d
wi
t
h
sal
i
e
nt
pol
e
r
o
to
r
made
o
f
i
r
on,
whi
l
e
bot
h w
i
ndi
ngs a
n
d
the
P
M
s
are
l
o
ca
te
d o
n
t
h
e
st
a
t
or
.
Ea
ch st
at
o
r
t
o
o
t
h ha
s tw
o P
M
s wi
th o
p
p
o
s
i
t
e
pol
a
r
i
t
y
. I
t
s
h
o
u
l
d
be
not
e
d
t
h
at
t
h
e wi
n
d
i
ngs
a
r
e
c
once
n
tr
at
ed
wi
n
d
i
n
gs,
w
h
i
c
h ar
e
mor
e
p
r
e
f
er
a
b
l
e
,
si
nce
the
y
le
ad
t
o
l
e
ss c
oppe
r
usag
e r
e
sul
t
i
n
g i
n
c
o
p
p
e
r
l
o
ss r
e
d
u
ct
i
o
n
,
a
n
d
mac
h
i
n
e
ef
fi
ci
ency
i
m
p
r
o
v
e
m
e
n
t.
Tabl
e 1. Desi
g
n
pa
ra
met
e
r
s
P
a
ra
met
e
rs
Va
lu
es
St
a
t
o
r
p
ole
num
ber
12
Rotor
pole num
be
r
10
Ai
r-
g
ap le
n
g
th (mm
)
0.
5
O
u
ter
r
a
dius of
st
ator
(m
m)
45
Inne
r r
a
di
us of sta
t
or
(
m
m
)
27.
75
Sha
f
t r
a
dius (
m
m
)
10
Z
-
dire
ct
ion len
g
th (
m
m)
50
Spe
e
d (
r
pm
)
500
P
M
thic
kness (m
m)
3
Fig
u
r
e
1
.
FRP
M
mach
i
n
e con
f
i
g
ur
atio
n
3.
PE
RFO
R
MA
NC
ES
C
O
MP
AR
IS
O
N
3.
1.
No
-
l
o
a
d
No
-l
oa
d pe
r
f
o
r
m
a
n
ces of
t
h
e
1
2
/
1
0
FR
P
M
ma
chi
n
e
a
r
e
c
o
mpa
r
ed
at
t
h
ree
o
p
e
r
a
t
in
g
c
o
n
d
it
i
o
ns,
ce
n
t
r
i
c
ity
,
sta
tic
e
c
cen
tr
ic
ity
a
n
d
d
y
n
a
mi
c
e
c
c
e
n
t
ri
ci
ty
.
Fig
u
r
e
2 sho
w
s th
re
e-ph
ase fl
ux
li
nk
ag
e
w
a
ve
f
o
rm
s
for
the
m
ach
ine
un
der
h
e
a
l
t
h
y
(
c
en
tri
c
)
as
w
e
l
l
as sta
t
i
c
an
d
dyn
a
m
i
c
e
c
c
e
n
t
ri
cs con
d
itio
n
s
,
w
h
en
th
e
ro
to
r
r
o
ta
te
s 3
6
0
el
ect
ri
c
a
l
deg
r
e
e
s
. N
o
t
a
bly
,
th
e
ce
n
t
r
i
c
ma
c
h
i
n
e
del
i
v
er
s
ba
l
a
nce
d
th
r
e
e
-
pha
se fl
u
x
l
i
nka
ge
wa
ve
f
o
r
m
s.
I
n
cont
rast
,
bot
h
st
at
i
c
a
n
d d
y
n
a
m
i
c
e
cce
ntr
i
c
ma
chi
n
es ha
ve u
n
e
qua
l
f
u
nd
a
m
ent
a
l
va
l
u
es f
o
r
t
h
ei
r
f
l
u
x
l
i
n
k
a
ge,
bec
a
use
of
the
ir
re
gul
ar
ai
r
ga
p,
w
h
i
c
h
i
s
cause
d
b
y
the
rot
o
r
ec
ce
nt
ri
ci
t
y
.
H
e
nce
,
t
h
e p
h
ases,
w
h
i
c
h ha
ve coi
l
s
fac
i
ng t
h
e
n
a
r
r
o
w ai
r
ga
p
sh
ows hi
g
h
e
r
fl
u
x
l
i
nka
ge
c
o
m
p
ar
e
t
o
t
h
e
s
e
h
a
vi
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
6
3
4
–
640
63
6
coi
l
s
fac
i
n
g
t
h
e
wi
de
ai
r ga
p. It
must
be
me
nt
i
one
d
t
h
at
t
h
e di
ffe
r
e
n
c
e
s
b
e
t
w
e
e
n
t
h
e
fu
nda
me
nt
al
val
u
es a
r
e
sma
l
l
a
n
d
c
a
n
be ne
gle
c
t
e
d
.
This i
s
beca
use
the
u
nde
rst
u
dyi
ng
mac
h
i
n
e
si
ze
is smal
l
and
has a s
m
al
l
ai
r ga
p
(0
.5mm).
F
u
rt
h
e
rmo
r
e,
t
h
re
e
-
p
h
a
s
e ba
ck
-E
MF of t
h
e thre
e ope
ra
ti
n
g
co
ndi
ti
o
n
s
a
r
e i
l
l
u
st
rat
e
d i
n
Fig
u
re
3. As
con
s
eq
ue
n
c
es
of
ba
la
nced
a
n
d
unba
l
a
nce
d
f
l
ux l
i
n
k
a
g
e
w
a
vefor
m
s t
h
e h
e
a
l
thy a
nd e
c
c
e
n
t
r
i
c
mac
h
i
n
es
sh
ow
bal
a
nc
e
d
a
n
d
u
nbal
a
nc
ed
th
re
e-p
h
ase bac
k
-EMF wa
vefo
rms, respect
i
v
el
y. M
o
re
ove
re
, t
h
e
p
r
edi
c
t
e
d
c
o
g
g
in
g
t
o
rque
wa
vef
o
rms a
nd t
h
e
F
F
T for t
h
e ma
chi
n
e w
i
t
h
th
re
e ope
ra
ti
n
g
c
o
n
d
it
i
o
n
s
a
r
e c
o
m
p
are
d
i
n
F
i
gu
re
4.
Ob
vi
o
u
sl
y,
t
h
e
cent
r
i
c
a
n
d e
c
c
e
nt
ri
c
mac
h
i
n
e
s
ha
ve t
h
e s
a
me
fu
nda
me
n
t
al
harmo
n
i
c
(
6
th
ha
rm
onic
)
. l
o
w
order
ha
rm
oni
c
s
(1
st, 2
n
d
a
n
d 5t
h)
are
pre
s
ent
e
d i
n
b
o
t
h
s
t
at
i
c
and d
y
n
a
m
i
c
e
cce
ntric
con
d
i
t
i
o
n
s
,
wh
i
l
e t
h
ey
a
r
e
no
t e
x
c
ite
d f
o
r
c
e
n
tr
ic
co
nd
iti
o
n
.
Th
e
centr
ic
m
a
c
h
in
e
ex
h
i
b
its
sy
mm
e
t
ric
a
l
c
o
gg
in
g
to
rqu
e
,
how
ev
e
r
bo
th
sta
t
ic
and
d
yna
mic
e
cce
nt
ri
c
mac
h
ine
s
have
a
s
y
mmet
r
i
c
a
l
cog
g
i
n
g t
o
rq
ue
.
(a
)
(b
)
(c
)
(d
)
(e
)
(f)
F
i
gu
re
2. Fl
u
x
l
i
nka
ge
for th
re
e o
p
era
t
i
n
g
c
o
ndit
i
o
ns,
(a
)
Wave
form he
al
t
hy c
o
n
d
i
t
ion
.
(b
)
F
F
T
h
e
al
t
h
y
c
o
nd
iti
o
n
, (c
)
W
a
v
e
fo
r
m
sta
tic
ec
ce
n
t
r
i
c
ity
,
(d)
FF
T st
ati
c
e
c
c
e
n
t
ri
ci
ty
, (
e
)
Wa
v
e
for
m
dyn
a
m
ic
e
c
cen
tr
i
c
it
y
,
(f) FF
T dy
nam
i
c ecc
ent
r
i
c
i
t
y
-0
.
0
1
-0
.
0
0
5
0
0.
0
0
5
0.
01
0
6
0
1
20
1
8
0
2
40
3
0
0
3
60
F
L
U
X
-L
I
N
K
A
G
E
(W
b
)
P
O
S
I
TI
O
N
(
ELEC
.
D
E
G
R
EE)
A
B
C
0
0
.
002
0
.
004
0
.
006
0
.
008
02468
1
0
1
2
1
4
F
L
U
X
-
L
I
N
KA
GE
(W
b
)
H
A
RM
O
N
I
C
O
RDE
R
S
A
B
C
-0
.
0
1
-0
.0
0
5
0
0.
0
0
5
0.
01
0
6
0
1
2
0
18
0
2
4
0
30
0
3
6
0
F
L
U
X
-L
I
N
KA
GE
(
W
b
)
P
O
S
I
TI
O
N
(
E
LEC.
D
E
G
R
EE)
A
B
C
0
0.002
0.004
0.006
0.008
02
46
8
1
0
1
2
1
4
F
L
UX-
L
I
N
K
AG
E
(
W
b
)
HA
R
M
ON
I
C
OR
D
E
R
S
A
B
C
-0
.
0
1
-0
.
0
0
5
0
0.
00
5
0.
0
1
0
6
0
1
20
1
8
0
2
40
3
0
0
3
6
0
F
L
UX-L
I
N
K
AG
E
(
W
b
)
P
O
S
I
TI
O
N
(
ELEC.
D
E
G
R
EE)
A
B
C
0
0.
002
0.
004
0.
006
0.
008
0
2
4
6
8
10
12
14
F
L
UX
-
L
I
N
KAGE
(
W
b
)
H
A
RM
O
N
I
C
O
RDE
RS
A
B
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
The
ef
f
e
c
t
of
st
ati
c
a
n
d
dy
n
a
m
i
c
ec
ce
ntri
ci
t
i
e
s
o
n
t
h
e
perf
orm
a
nce
of
f
l
u
x
…
(A
hla
m
Lu
ai
bi
Sh
ur
aij
i
)
6
37
(a
)
(b
)
(c
)
(d
)
(
e
)
(
f
)
F
i
gure
3.
B
a
c
k
-E
MF
fo
r t
h
ree
o
p
era
t
in
g c
o
n
d
it
i
ons
, (a
) Wa
veform
heal
t
h
y
co
ndi
t
i
o
n
, (b) F
F
T
heal
t
h
y
c
o
nd
iti
o
n
, (c
)
W
a
v
e
fo
r
m
sta
tic
e
c
c
e
n
tr
ic
ity
,
(d)
FF
T st
ati
c
e
c
c
e
n
t
ri
ci
ty
, (
e
)
Wa
v
e
for
m
dyn
a
m
ic
e
c
cen
tr
i
c
it
y
,
(f) FF
T dy
nam
i
c ecc
ent
r
i
c
i
t
y
(a
)
(b
)
Fi
g
ure
4
.
Co
gg
in
g
to
r
q
ue c
o
m
p
a
r
i
s
on,
(
a
)
Waveform,
(
b
)
FFT
-5
-2
.
5
0
2.
5
5
0
6
0
1
20
1
8
0
2
40
3
0
0
3
60
B
ACK
-
E
M
F
(V)
P
O
S
I
TI
O
N
(
E
LEC.
D
E
G
R
EE)
A
B
C
0
1
2
3
4
1357
9
1
1
1
3
1
5
B
A
C
K
-E
M
F
(V
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
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6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
6
3
4
–
640
63
8
3.2.
On
-
l
oad
Ele
c
tr
o
m
agn
e
tic
to
rq
u
e
wave
fo
rm
s
o
f
th
e
F
R
P
M
ma
chi
n
e w
ith
th
re
e o
p
e
r
a
ting
c
o
n
d
i
ti
on
s are
com
p
are
d
i
n
Fi
gu
re 5.
More
o
v
er
,
t
o
rque
rip
p
l
e
fo
r
t
h
e ma
chi
n
e
wit
h
t
h
e ment
i
one
d
o
p
e
r
a
t
i
n
g
c
o
n
d
i
t
i
o
n
s are
il
lu
str
a
te
d
i
n
Fi
g
u
re
6
.
Al
th
ou
gh
th
e ma
ch
i
n
e
s
h
a
v
e
th
e
sam
e
a
v
e
r
a
g
e
e
l
e
c
t
r
o
mag
n
e
t
i
c tor
q
u
e
fo
r th
e
thr
e
e
ope
ra
t
i
n
g
c
o
nd
i
t
i
ons,
the
c
e
nt
ri
c mac
h
ine
sh
ows
t
h
e
l
o
west
tor
q
ue
ri
p
p
l
e
fol
l
ow
e
d
b
y
dy
na
mi
c
e
c
c
e
nt
ri
c an
d
t
h
e
st
at
i
c
ecc
en
t
r
i
c
ma
chi
n
e
ha
s
t
h
e
hig
h
e
s
t
t
o
r
que
ri
ppl
e.
F
i
gu
re
5.
To
rq
ue
c
o
m
p
aris
on
F
i
gu
re 6.
To
r
que
rip
p
l
e
co
mp
ari
s
o
n
3.3.
U
nba
lan
c
ed
m
a
g
n
et
ic
fo
r
ce
U
s
ua
ll
y,
fo
r t
h
e e
l
ect
ri
ca
l
ma
chi
n
es
,
the
el
e
c
t
roma
gne
t
i
c
forc
e c
onsi
s
t
s
of ra
dia
l
a
n
d ci
rc
umfere
n
c
e
com
p
o
n
e
n
t
s
. The
s
e c
o
mp
one
nts ca
n
be cal
c
u
l
a
t
e
d base
d
o
n
t
h
e
M
a
x
w
el
l
st
ress me
t
h
o
d
[25
]
.
∗
°
(1
)
°
∗
(2
)
wh
e
r
e
an
d
a
r
e t
h
e ra
di
al
an
d ci
rc
umfe
re
nc
e com
p
o
n
e
n
t
s
of t
h
e el
ec
trom
agne
t
i
c
f
o
rc
e
,
whil
e
and
re
pre
s
ent
the
ra
di
al
a
n
d c
i
rcum
fere
nce
c
o
mpo
n
e
n
t
s
o
f
t
h
e ai
r-
ga
p flu
x
densi
t
y
.
Mo
re
ove
r,
°
is
th
e
a
i
r
perme
a
bi
li
t
y
.
In
t
h
e rot
a
ry
permane
n
t ma
gnet
m
a
c
h
i
n
e
s
,
t
h
e el
ec
tro
m
a
gnet
i
c
t
o
rq
ue
i
s
cont
ri
b
u
t
e
d
b
y
t
h
e c
i
rcu
m
fe
re
nce
f
o
rce
,
w
h
e
n
t
h
e
sta
t
or wi
ndi
ng
s
are e
x
ci
t
e
d.
In
co
nt
rast
,
the
ra
di
al
forc
e
has
n
o
c
ont
ri
but
io
n
t
o
t
h
e e
l
e
c
t
r
om
agnet
i
c
t
o
que
,
ho
we
ve
r, i
t
l
e
ads to
u
n
b
al
anc
e
d
ma
g
n
et
ic
fo
rce
tha
t
ca
uses
vib
r
a
t
io
n a
nd
noi
se
.
Th
e
summa
ti
on
o
f
th
e r
a
d
i
a
l
f
o
r
c
e
fo
r
th
e
id
e
a
l
c
e
n
t
r
i
c PM
ma
c
h
i
n
es wi
th
ev
en
ro
tor
p
o
l
e
is
z
e
ro,
ho
w
e
v
e
r
th
e
ex
i
s
ting
of
t
h
e e
c
c
e
n
t
ri
ci
ty
i
n
t
h
ese
ma
c
h
i
n
es ma
k
e
s
the su
mmat
i
o
n
of su
ch
fo
rc
e to b
e
unb
a
l
a
n
ced
.
In
t
h
is sec
t
ion t
h
e
un
bal
a
n
ced
m
a
gne
ti
c f
o
rce
for t
h
e ma
c
h
i
n
e
wi
t
h
th
ree o
p
e
rat
i
ng c
o
ndi
ti
ons
for
b
o
t
h
n
o
-l
oad
and
l
o
ad
wil
l
be
p
r
edi
c
t
e
d
b
y
2D-FEA
.
Th
e
p
r
e
d
i
c
t
e
d
u
n
b
a
l
ance
d
ma
gn
et
i
c
fo
rce
for
o
n
e
el
ec
tric
al
c
y
c
l
e
at
ce
ntric
,
sta
t
i
c
a
n
d
dy
namic
e
c
c
e
n
tric
it
y c
o
nd
i
t
i
ons for n
o
-l
o
a
d a
n
d l
o
a
d
c
o
ndi
t
i
o
n
s
are
c
o
mpa
r
ed
in
Fi
gu
re
s
7-
8,
re
s
p
ect
i
v
el
y
.
Ob
vi
o
u
sl
y
,
t
h
e e
x
ci
ti
ng
o
f
ec
cent
r
i
c
res
u
lt
s i
n
u
n
b
a
l
a
n
c
e
d ma
g
n
et
i
c
force
wi
t
h
a
v
e
r
a
g
e
of
abo
u
t
96
N
a
n
d
98 N
fo
r no
-
l
oa
d
a
n
d loa
d
,
res
p
ec
ti
vel
y
.
The ce
nt
ri
c
m
achi
n
e
has n
o
un
b
a
l
a
nce
d
ma
gnet
i
c
fo
rc
e a
t
n
o
-l
oa
d as wel
l
as l
o
ad o
p
e
r
at
i
n
g
.
On t
h
e ot
her
h
a
nd
, t
h
e
va
l
u
e
s
of
un
bal
a
n
c
ed
mag
n
et
i
c
forc
e
wit
h
th
e
e
c
c
e
n
t
r
i
c
-
di
sta
n
ce
fo
r bo
t
h
mach
in
es und
er t
h
e
m
e
n
tion
e
d co
nd
iti
o
n
s
a
r
e
l
i
ste
d
in
Tab
l
e
2
.
C
l
ea
r
l
y,
it
ca
n
be
se
e
n
t
h
at
t
h
e
un
bal
a
nce
d
mag
n
et
i
c
fo
rce
i
n
cre
a
s
es a
s
t
h
e e
cce
ntric
-
di
sta
n
ce
. B
o
th
st
a
t
i
c
an
d
d
yna
mi
c
e
c
c
e
n
tr
ic
s ma
ch
in
e
s
h
a
v
e
the sa
me
v
a
lu
es
o
f
th
e
u
n
b
a
lanc
ed
mag
n
e
t
i
c for
c
e at
low va
lu
e
o
f
th
e e
cce
n
t
r
i
c
di
st
anc
e
.
Ho
w
e
ver, at
hi
gh
va
l
u
e
o
f
s
u
c
h
fe
at
u
r
e t
h
e
sta
t
i
c
e
cce
nt
r
i
c
mac
h
i
n
e
s
h
o
w
s
sli
g
ht
ly
hi
gh
e
r
un
bal
a
nc
e
d
ma
gne
ti
c val
u
e c
o
mpa
r
e
d
t
o
t
h
e
dy
na
mi
c c
o
u
n
t
e
rpa
r
t
.
It
i
s
wo
rt
h me
n
t
i
o
n
i
ng t
h
at
t
h
e ec
c
e
nt
ri
c
di
st
anc
e
is
de
fi
ned
b
y
(3)
∆
(3
)
wh
e
r
e
i
s
t
h
e
ec
ce
n
t
r
i
c
-
d
i
sta
n
c
e
,
∆
re
p
r
ese
n
ts the
di
spl
a
ce
me
nt
bet
w
e
e
n
t
h
e
rot
o
r c
e
n
te
r t
o
t
h
e st
at
or
ce
nt
e
r
a
n
d
ai
r-ga
p
l
e
ngt
h.
2.
5
3
3.
5
0
6
0
1
2
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18
0
2
4
0
30
0
3
6
0
TO
R
Q
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N
m
)
P
O
S
I
TI
O
N
(
ELE
C
.
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n
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n
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m
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c
20
21
22
23
24
25
26
27
cen
t
r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
The
ef
f
e
c
t
of
st
ati
c
a
n
d
dy
n
a
m
i
c
ec
ce
ntri
ci
t
i
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s
o
n
t
h
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perf
orm
a
nce
of
f
l
u
x
…
(A
hla
m
Lu
ai
bi
Sh
ur
aij
i
)
6
39
Fi
gu
re
7. C
o
m
p
ari
s
o
n
of u
n
b
al
ance
d
ma
gn
e
t
i
c
forc
e
f
o
r
thr
e
e op
e
r
ati
n
g
co
nd
it
ion
s
at
no
-
l
o
a
d
Fi
gu
re
8. Com
p
aris
on
o
f
u
n
b
a
l
a
nc
ed ma
gne
ti
c
force
fo
r t
h
re
e
o
p
era
t
i
ng c
o
n
d
it
i
o
ns
at
l
o
a
d
Ta
b
l
e
2
.
V
a
l
u
e
of
u
n
b
a
la
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ced
ma
gn
et
ic
fo
r
ce fo
r
d
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ff
e
r
en
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en
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c
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c
e
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r
bo
t
h
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at
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n
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o
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c
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(
m
m
)
U
nbala
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d
m
a
g
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e
(
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)
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CO
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h
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a
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o
u
t
16
%
hi
g
h
er t
o
rque
ri
pple
for
bot
h st
at
i
c
a
n
d
d
y
n
a
mic
ec
ce
nt
ri
c
ma
c
h
i
n
es
co
mpa
r
ed
t
o
t
h
e
hea
l
th
y m
a
c
h
ine
.
I
n
a
d
d
i
tion
,
th
e
v
a
lu
e o
f
th
e
u
n
b
a
l
a
n
c
ed
m
a
g
n
e
ti
c fo
rc
e
i
n
cr
e
a
se
s
w
ith
th
e
in
cre
a
s
ing
o
f
th
e
ec
cen
tr
ic
d
i
sta
n
c
e
.
RE
FERE
NC
E
S
[1]
W.H
.
Tai
,
M
.
C Tsai, Z.L
G
a
in
g
,
P
.
W
H
u
an
g,
a
n
d
Y
.
S
Hs
u,
“No
v
el
s
t
ator
d
e
s
i
g
n
of
do
ub
le sa
lien
t p
e
rman
en
t
magn
e
t
mo
tor,
”
IE
EE Tra
n
s
.
on
Ma
gn
e
tic
s
,
Vo
l.
50
, No
.
4
,
A
p
ril
20
14
.
[2]
H.
Mi
ng
ji
e a
nd
X.
We
i,
“
N
o
v
e
l
si
ng
le
pha
se
dou
b
l
y
sa
li
en
t p
e
rmanen
t
mag
n
e
t
ma
chin
e w
ith
as
ymmetric
s
t
ato
r
po
les
,
”
IEEE Tr
an
s. on Ma
gn
etics
,
Vo
l. 5
3
,
No
.
6,
pp.
1
-
5, Jun
e
20
17
.
[3]
X.
Zh
u,
W
.
Hu
a
,
M.
Ch
e
n
g
a
n
d
G.
Z
h
a
ng,
"An i
m
p
r
ov
e
d
c
onfig
u
r
a
t
i
o
n
fo
r co
gg
in
g
to
rqu
e
re
d
u
c
tio
n
in
fl
ux-
revers
al perm
an
en
t m
a
gn
et ma
c
h
ines,"
20
16
IEEE
Co
nfe
r
e
n
ce
o
n
El
ec
tro
m
a
g
n
e
tic
F
i
e
l
d
Comput
at
io
n
(CEF
C)
,
Mi
a
m
i
,
FL, 2
016
.
[4]
Las
k
aris
an
d
A.
G. Klad
as,
"
I
ntern
a
l P
e
rm
an
ent
M
a
gn
et M
o
to
r D
e
sign for
El
ect
ric
Vehic
l
e
Driv
e,"
IEEE
Tran
s.
on
Ind
u
s
t
rial E
l
ec
tr
on
ics
, Vo
l
.
57
,
No
. 1
,
p
p
.
138
-
1
4
5
,
Jan
.
20
10
.
[5]
Y.
Li
, H
.
Y
a
ng
,
H
.
Lin
and
H
.
Zh
eng
,
"
C
om
parat
i
v
e
S
t
u
d
y
o
f
Ad
van
c
ed
S
t
ator
Int
e
rior
P
e
rman
en
t M
a
gn
e
t
M
achines,"
20
19 IE
EE
Inte
rn
at
ion
a
l
E
l
e
c
t
r
ic
Machi
ne
s
&
Driv
e
s
Co
nf
e
r
e
n
ce
(IEM
D
C
)
, Sa
n Di
e
go,
C
A
,
USA, pp.
26
6-2
72,
20
19
.
[6]
S
.
E.
Rau
c
h
and
L.
J.
Jo
hn
son
,
“
D
esign
princ
i
p
l
e
s
of
fl
u
x
-s
witchi
ng
alt
e
rna
t
ors,
”
in A
I
E
E
Trans
.
,
Vol
.
7
4
, No.
3
,
p
p
.
12
61
–12
68
, J
a
n
u
ary
,
1
9
5
5
.
[7]
X.
Li
u, D. W
u
,
Z
.
Q. Zh
u
,
A. P
r
id
e
,
R.
P De
o
dha
r, a
nd T.
Sa
sa
ki, “
E
f
fi
c
i
en
cy
im
pro
v
emen
t of
s
w
itch
ed
flu
x
P
M
memory
m
a
ch
in
e ov
er
in
terio
r
P
M
machin
e fo
r EV/HEV A
p
p
l
ic
atio
ns,
”
IE
EE Tran
s.
on
ma
g
n
e
t
ic
s
,
Vo
l.
50,
No.
11
,
No
v 2
014.
[8]
H. Y. Li
and
Z.
Q.
Zhu,
“A
na
lysis of flux
rev
e
rsal
p
e
rm
an
ent
ma
gn
et
mach
in
es w
i
th
d
i
f
f
eren
t co
n
s
eq
uen
t
po
le
P
M
to
po
lo
gi
es
,”
IEEE Tran
s. o
n
M
agne
t
i
c
s
, V
o
l
.
5
4
,
N
o
.
11
,
No
v
201
8.
[9]
K.
Xie
,
D
.
Li,
R
.
Q
u
,
Y
.
Gao
and
Y
.
P
a
n
,
"
A
nov
el
f
l
u
x
r
e
v
e
rsa
l
P
M
M
achine
w
i
t
h
Halb
ach
array
magn
e
t
s
in
s
t
ato
r
slot op
ening
,
"
20
th
Inte
rn
at
io
nal Co
nfe
r
e
n
c
e
o
n
E
l
ec
t
r
i
c
a
l
Ma
c
h
in
e
s
an
d S
y
ste
m
s (ICE
M
S
)
,
S
y
dn
e
y
, NS
W, pp
.
1
-
6,
20
17
.
0
50
10
0
15
0
0
6
0
1
2
0
18
0
2
40
3
0
0
3
60
U
N
B
A
LA
N
C
ED
M
A
G
N
E
T
I
C
F
O
R
C
E
(N
)
PO
S
I
TI
O
N
(
ELEC.
D
E
G
R
E
E
)
ce
n
t
ri
c
e
c
ce
n
t
ri
c
-
s
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a
t
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e
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e
nt
r
i
c
-
dy
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m
i
c
0
50
10
0
15
0
20
0
0
6
0
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20
1
8
0
2
4
0
3
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3
60
U
N
B
A
LA
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ED
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A
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C
F
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R
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(N
)
PO
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I
O
N
(
ELEC.
D
E
G
R
EE)
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n
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t
r
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i
c
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
6
3
4
–
640
64
0
[10]
Z.
Z.
Wu
, Z.
Q
.
Zh
u
an
d
H.
L
.
Zhan
,
"
C
ompar
a
tiv
e
An
aly
s
is
o
f
P
a
rtitioned
S
t
a
t
or
F
l
ux
Rev
e
rs
a
l
PM
Mach
in
es
Ha
vi
ng
Frac
tiona
l
-
Slo
t
Non
ove
rl
a
ppin
g
a
n
d
In
te
g
e
r-Sl
o
t Ov
e
r
la
p
p
in
g
W
i
n
d
i
n
g
s
,
"
IEEE Tra
n
s
.
on
E
n
e
r
gy
Conversion
,
Vo
l.
3
1
,
No
.
2
,
p
p
.
776
-7
88
, Jun
e
2016
.
[11]
R. P
.
D
e
o
d
h
a
r
,
S
.
An
ders
so
n, I
.
Bo
ld
e
a
an
d
T.
J.
E. M
iller
,
"Th
e
flu
x
-r
ev
ersa
l
mach
ine:
a
new
brus
hless
dou
bl
y-
salien
t per
m
an
en
t-mag
n
e
t m
ach
ine,"
IEEE
Tra
n
s.
on
In
du
st
ry
Ap
pl
ic
at
io
ns
,
V
o
l. 33
,
No.
4
,
p
p
.
92
5-9
34,
Jul
y
-
Au
gu
st, 19
97
.
[12]
C.
Wan
g
,
S
.
A.
N
a
sar
and
I. Bo
ld
ea
, "
T
hree-p
h
a
se f
l
u
x
r
e
vers
al
ma
chine
(F
R
M
),"
I
E
E Pro
cee
di
ng
s - Ele
c
t
r
ic
P
o
wer App
l
ic
a
t
i
o
ns
,
Vo
l. 14
6, No.
2
,
pp.
1
3
9
-1
4
6
,
Ma
rc
h, 19
99
.
[13]
C. X. W
a
ng
, I.
Bo
ld
ea
a
n
d S
.
A
.
Nasar,
"
C
har
a
c
t
erization
of th
r
e
e
p
h
as
e
flux
rev
e
rsal
m
ach
in
es a
s
an au
to
m
o
tive
generat
o
r,"
IEEE Tran
s.
on
En
ergy
Co
nv
e
r
si
on
,
V
o
l. 1
6
,
N
o
.
1,
p
p
.
74
-80
,
M
a
r
c
h,
200
1.
[14]
T.
H
e
ou
ng
K
i
m,
S
.
H
.
Wo
n,
K
.
Bong
and
J. L
e
e
,
“Red
u
c
tio
n
in
cogg
in
g torqu
e
in
fl
u
x
rev
e
rs
al
mach
ine b
y
ro
to
r
tee
t
h p
a
ir
i
n
g
”
IEE
E
Tran
s.
on M
a
gn
e
t
ic
s
,
Vol.
4
1
, No. 10
, pp
3
964
-39
6
6
,
Oct
o
b
e
r,
20
05.
[15]
T.
H
e
o
u
n
g
Ki
m
an
d J. Lee
“A stud
y of the des
i
g
n
for th
e
fl
u
x
reversal
ma
ch
ine,”
I
E
EE T
r
a
n
s
.
on Ma
gn
eti
c
s
,
Vol
.
4
0
, No. 4, p
p
.
20
53
-20
5
5
,
July
,
2
0
04.
[16]
T
H
.
Kim,
"
A
st
ud
y o
n
th
e
de
sign
o
f
a
n
in
set
p
e
rm
a
n
e
n
t
m
a
gne
t
ty
p
e
flu
x
reve
rsa
l
ma
c
h
i
n
e,
"
IEE
E
Tr
ans.
on
Ma
gn
etics
, V
o
l
.
45
, N
o
.
6,
pp.
28
59
-286
2,
Ju
ne
, 2
0
0
9
.
[17]
J.
zh
a
n
g
,
M
.
Ch
en
g,
W. Hu
a an
d X. Zh
u
,
“Ne
w
ap
pro
a
ch
to
po
wer equa
tio
n
for comp
ariso
n
of do
ubly sa
lien
t
ele
c
trical mach
in
es,”
in
Pr
oc.
I
E
EE
I
n
d
u
s
t
ry
App
l
i
c
at
io
ns An
nu
l
meet
in
g
,
p
p
.
1
178-1
1
8
5
,
2
0
0
6
.
[18]
D.
S. Mor
e
a
n
d
B.
G.
Fe
rn
a
nde
s,
"
P
owe
r
d
e
n
s
i
t
y
im
p
r
ov
e
m
e
n
t o
f
th
re
e
p
h
a
s
e fl
ux
re
ve
rsa
l
m
a
c
h
in
e wi
th d
i
st
ri
bu
te
d
wind
in
g,"
I
E
T El
ectric P
o
wer Appl
ic
ations
,
Vo
l.
4,
No
.
2,
pp
. 1
09-1
2
0
,
Fe
b
r
ua
ry, 20
1
0
.
[19]
D.
S
.
Mo
re
, H
.
K
a
lluru
and
B.
G.
F
e
rn
an
des,
"
d
-q
equ
i
v
a
lent
c
i
rcuit r
e
p
r
esen
ta
tion
o
f
th
re
e-ph
as
e f
l
ux
rev
e
rs
a
l
mach
i
n
e
wi
th
f
u
l
l
p
itch
win
d
i
n
g
,
”
in
Pro
c
. IEE
E
Po
wer
Ele
c
tro
n
ics Sp
ecial
is
ts
Co
nferen
ce
, R
h
odes
,
pp
. 120
8
-
12
14
, 2
008
.
[20]
M.
H. Rem
l
a
n
,
R.
Aziz
a
nd S.
Sa
li
m
i
n,
” Co
m
p
a
r
i
s
o
n
of diffe
ren
t
m
a
g
n
et a
rra
nge
m
e
n
t
o
n
p
e
rfo
r
m
a
n
ce o
f
fl
ux
revers
al
p
e
rman
ent m
a
gn
et (F
RP
M
)
mach
in
e,”
In
te
rna
t
i
o
nal Jo
urna
l o
f
Po
wer
Electro
nics a
n
d
Dr
ive
Syst
e
m
(IJP
E
DS)
, Vol.
1
0
,
No. 3, pp
. 1207
-1
21
4,
Se
ptem
b
e
r,
2
0
1
9
.
[21]
J. Y.
Son
g
, K.
J.
Ka
n
g
,
C. H.
Ka
n
g
a
n
d G.
H
.
Ja
n
g
, "
C
og
gi
ng t
o
rq
ue a
n
d
un
ba
l
a
n
c
e
d
m
a
g
n
e
t
ic
p
u
l
l
due
to
simultan
eo
us
ex
is
ten
ce o
f
d
y
n
a
m
i
c
and
s
t
atic
eccen
tri
c
it
ies
an
d un
ev
en
magn
eti
zation
in
per
m
anen
t
magn
et
motors
,
"
IE
E
E
Tran
s.
on
Ma
gn
etic
s
,
Vo
l.
53
,
No
.
3,
pp
.
1
-
9,
M
a
rc
h
20
17
.
[22]
H.
M
a
hmou
d
,
N.
Bianch
i,
M.
D
e
g
a
no,
M
.
A
l
-A
n
i
an
d
C.
Gerad
a
,
"
E
c
cent
r
ic
Re
luctan
ce
and
P
e
rmanen
t M
a
gn
et
S
y
n
c
hron
ou
s Machin
es Comp
ariso
n
,"
IEEE T
r
ans
.
on
In
dus
tr
y A
p
p
l
ication
s
,
Vo
l.
54
,
No.
6,
p
p
.
57
60
-57
7
1
,
Nov
.
-
Dec.
201
8.
[23]
J.
H
o
n
g
, S
.
B.
Lee, C. Kral
and
A
.
Hau
m
e
r
, "D
e
t
ec
tio
n
of
a
i
rgap
ec
cen
tric
ity
for
perman
en
t
mag
n
e
t s
y
n
c
hron
ou
s
m
o
to
rs b
a
se
d
on t
h
e
d-a
x
is
in
duc
t
a
n
c
e,
"
8
t
h IEEE
S
y
mp
osiu
m o
n
Di
ag
no
st
ic
s
f
o
r El
ectrical
Machines, P
o
w
e
r
Ele
c
tr
onics &
D
r
ives
, p
p
.
37
8-384,
Bo
lo
gna
,
2
0
1
1
.
[24]
Y.
Li
,
Z
.
Zhu
,
G.
Li and D. Wu,
"Ana
lytical
s
y
n
t
h
e
sis o
f
air-g
ap
f
i
eld
in
perm
an
ent
mag
n
e
t
mach
in
es w
i
th
ro
t
o
r
e
c
c
e
n
tric
i
t
y
by su
pe
rp
osi
t
i
o
n
me
th
od
,
"
2
015
I
EEE In
ter
n
a
t
iona
l M
a
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e
tics
Co
nferen
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e
(INTE
RM
AG)
,
Beiji
ng
,
20
15
.
[25]
Z
.
Q
.
Z
h
u
,
Z
.
P
.
X
i
a
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L
.
J
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u
,
a
n
d G.
W
.
Jewel
l
,
“Analyti
cal modeli
ng and
fi
n
i
te-
e
le
ment
co
mpu
t
at
io
n of r
a
d
i
al
vibratio
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forc
e
in frac
t
ion
a
l-s
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o
t
perm
anen
t-
ma
gn
et bru
s
h
l
es
s
mach
in
es,”
IEEE
Tran
s.
In
du
stry
Ap
p
lic
at
io
ns
,
Vol
.
4
6
, n
o
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5
,
p
p
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08
–1
91
8, S
e
p
t
e
m
be
r
/
O
c
t
obe
r,
2
0
10.
BIBLIOGRAPHY OF
AUTHO
R
Ahl
a
m L
u
ai
bi
Sh
u
r
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e
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v
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h
e
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r
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n
E
n
gi
neeri
n
g
Edu
c
a
t
i
o
n
a
l Tec
h
no
logy
/
El
e
c
t
r
i
c
a
l
Eng
i
ne
e
r
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n
g
,
fr
om
U
n
i
v
e
r
sity
o
f
Te
ch
no
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B
a
gh
da
d,
Ira
q, in
1
9
9
8
a
n
d
2
004,
res
p
ec
t
i
v
e
l
y, a
n
d
t
h
e
P
h
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. de
g
r
ee
in el
ec
t
r
i
cal
e
ngi
ne
eri
n
g
from
The
U
n
i
v
ersi
t
y
of
She
f
fi
el
d,
S
h
e
f
fie
l
d,
U.K.
, i
n
2
0
1
7
. S
h
e
is
cu
rr
en
t
l
y a le
ct
u
r
e
r
at
t
h
e
Un
iv
ers
ity
o
f
Te
ch
no
l
ogy
/ Elec
tr
o
m
e
c
h
a
n
i
c
a
l
Eng
i
n
e
eri
ng
de
pa
rt
me
nt
.
H
e
r re
se
arc
h
i
n
t
e
re
st
s
i
n
c
l
ude
t
h
e
de
si
gn
o
f
pe
rmane
n
t
-
ma
g
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e
t
ma
chi
n
es
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