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ag
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etic
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th
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e
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th
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o
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tim
izes
th
e
m
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n
etic
f
lu
x
f
o
r
b
etter
to
r
q
u
e
p
r
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d
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ctio
n
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lo
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g
as
th
e
m
ag
n
et
s
ize
s
ta
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s
with
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th
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t
d
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ter
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en
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ity
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s
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etter
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e
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tp
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d
b
etter
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f
icien
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m
s
th
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b
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tr
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g
th
e
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en
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e
ca
p
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h
e
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ch
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lies
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o
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tim
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in
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th
e
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t
m
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et
s
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s
h
o
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g
h
o
w
th
ey
b
o
o
s
t
elec
tr
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c
v
eh
i
cle
m
o
to
r
s
to
m
ee
t
th
eir
r
eq
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ir
e
m
en
ts
.
Ou
r
test
s
with
f
in
ite
elem
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t
m
eth
o
d
(
FEM
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s
h
o
w
h
o
w
ch
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g
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g
m
a
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et
d
im
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r
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m
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r
eq
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en
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th
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tim
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p
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f
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m
th
ick
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y
4
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5
m
m
wid
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es.
T
h
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tio
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o
o
s
ts
f
lu
x
d
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n
s
ity
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wh
ich
im
p
r
o
v
es
m
o
to
r
to
r
q
u
e
a
n
d
en
er
g
y
ca
p
ac
ity
.
At
th
ese
o
p
tim
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d
im
en
s
io
n
s
,
th
e
en
g
in
e
ac
h
ie
v
ed
9
5
%
ef
f
icien
cy
with
p
r
ec
is
e
f
lo
w
b
ar
r
ier
ad
ju
s
tm
en
ts
th
at
h
elp
ed
in
cr
ea
s
e
to
r
q
u
e
o
u
tp
u
t w
h
ile
r
ed
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ci
n
g
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n
s
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le
elec
tr
icity
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u
tp
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t
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K
ey
w
o
r
d
s
:
C
o
g
g
in
g
to
r
q
u
e
Dy
n
am
ic
p
er
f
o
r
m
a
n
ce
Fin
ite
elem
en
t m
eth
o
d
PMSMs
V
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ty
p
e
T
h
is i
s
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n
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a
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ss
a
rticle
u
n
d
e
r th
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CC B
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SA
li
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se
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C
o
r
r
e
s
p
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A
uth
o
r
:
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m
ed
J
ad
aa
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Ali
T
ec
h
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ical
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n
g
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No
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th
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ical
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s
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s
u
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ate
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m
ail:
ah
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j.a
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u
.
i
q
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
p
er
m
an
e
n
t m
ag
n
et
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
(
PMSM)
is
a
v
ita
l m
em
b
er
in
m
an
y
ap
p
licatio
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s
,
r
an
g
in
g
f
r
o
m
elec
tr
ic
v
e
h
icles
(
E
Vs)
to
r
en
ewa
b
le
e
n
er
g
y
s
y
s
tem
s
.
Par
ticu
lar
ly
as
ca
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s
m
o
v
e
to
w
ar
d
s
elec
tr
ic
p
o
wer
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e
is
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g
r
o
win
g
n
ee
d
to
en
h
an
ce
th
e
ch
ar
ac
ter
is
tics
o
f
elec
tr
ic
m
o
to
r
s
,
m
ain
ly
in
E
Vs
[
1
]
-
[
3
]
.
I
n
th
e
wo
r
ld
o
f
elec
tr
ic
v
eh
icles,
f
in
e
-
tu
n
in
g
th
e
s
ize
o
f
th
e
m
ag
n
ets
in
th
e
r
o
to
r
b
ec
o
m
es
ex
tr
em
ely
s
ig
n
if
ic
an
t
[
4
]
.
T
h
is
tu
n
in
g
n
o
t
ju
s
t
in
f
lu
en
ce
s
th
e
p
r
o
f
ile
o
f
th
e
m
o
to
r
,
it
g
iv
es
th
e
m
o
d
if
icatio
n
b
etwe
en
a
h
ig
h
a
n
d
lo
w
p
er
f
o
r
m
in
g
m
ac
h
in
e
.
Ho
wev
e
r
,
it
is
n
o
t
ju
s
t
ab
o
u
t
th
e
ac
tu
al
le
n
g
th
s
o
f
th
o
s
e
m
ag
n
ets,
it
is
also
im
p
o
r
tan
t
to
an
aly
ze
t
h
e
g
en
er
ated
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tr
o
m
a
g
n
etic
f
o
r
ce
s
,
d
y
n
am
ic
p
er
f
o
r
m
an
ce
,
i
n
ad
d
itio
n
t
o
th
e
m
ec
h
an
ical
s
tr
u
ctu
r
e
o
f
th
ese
m
ac
h
in
es.
E
n
h
an
cin
g
m
o
to
r
e
f
f
icien
cy
,
r
ed
u
cin
g
lo
s
s
es,
an
d
b
o
o
s
tin
g
o
v
er
all
p
er
f
o
r
m
an
ce
ar
e
ess
en
tial
g
o
als
in
o
p
tim
izin
g
th
e
r
o
t
o
r
m
ag
n
e
t’
s
s
tr
u
ctu
r
e.
Ho
wev
er
,
class
ic
al
ap
p
r
o
ac
h
es
f
o
r
s
ch
em
in
g
th
ese
s
tr
u
ctu
r
es
o
f
ten
d
ep
en
d
o
n
s
im
p
le
p
r
o
to
ty
p
es
o
r
tr
ial
-
an
d
-
e
r
r
o
r
m
et
h
o
d
s
[
5
],
[
6
]
.
Me
etin
g
th
ese
r
eq
u
ir
em
e
n
ts
is
co
n
s
id
er
ed
an
ess
en
tial
f
ac
to
r
to
s
u
f
f
icien
tly
u
n
d
er
s
tan
d
h
o
w
th
ese
m
o
to
r
s
wo
r
k
.
E
Vs
r
eq
u
ir
e
h
i
g
h
to
r
q
u
e
d
en
s
ity
(
T
D)
t
o
d
eliv
er
ef
f
ec
tiv
e
an
d
h
ig
h
p
er
f
o
r
m
an
ce
[
2]
-
[
7
]
.
I
n
cr
ea
s
in
g
th
e
th
ick
n
ess
o
f
m
a
g
n
ets
ca
n
d
el
iv
er
h
ea
v
y
m
ag
n
etic
Evaluation Warning : The document was created with Spire.PDF for Python.
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I
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t J Po
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&
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,
Vo
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16
,
No
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2
,
J
u
n
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20
25
:
7
6
9
-
7
79
770
f
ield
s
,
wh
ich
d
eliv
er
a
h
ig
h
er
to
r
q
u
e
d
en
s
ity
.
T
h
is
is
v
ital
f
o
r
ac
co
m
p
lis
h
in
g
th
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p
r
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I
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co
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with
T
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p
o
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d
en
s
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(
PD)
is
also
an
ess
en
tial
f
ac
to
r
in
E
Vs
;
th
ick
er
m
ag
n
ets
g
iv
e
a
h
i
g
h
er
PD
b
y
s
u
p
p
o
r
tin
g
th
e
m
o
t
o
r
to
p
r
o
d
u
ce
m
o
r
e
p
o
wer
with
in
a
ce
r
tain
v
o
lu
m
e
o
r
weig
h
t
r
estra
in
t.
T
h
is
is
im
p
o
r
tan
t
f
o
r
attain
in
g
th
e
p
r
ef
e
r
r
ed
s
p
ee
d
a
n
d
p
er
f
o
r
m
an
ce
in
E
Vs
[
8
]
.
T
ests
h
av
e
s
h
o
wn
th
at
m
ag
n
etic
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
s
(
PMSM)
with
V
-
ty
p
e
m
ag
n
ets
s
ig
n
if
ica
n
tly
af
f
ec
t
t
h
e
to
r
q
u
e
p
e
r
f
o
r
m
a
n
ce
o
f
th
e
m
ac
h
in
e
d
esig
n
.
I
n
n
ewly
u
s
ed
elec
tr
i
c
ca
r
s
,
wh
ich
d
ete
r
m
in
es
th
e
o
v
er
all
ef
f
icien
c
y
o
f
th
e
ca
r
i
s
d
eter
m
in
ed
.
T
h
e
m
ag
n
etic
cir
cu
it
f
o
r
th
is
ty
p
e
o
f
m
o
to
r
is
b
ein
g
d
esig
n
ed
b
y
r
esear
ch
er
s
.
I
t
co
n
tr
ib
u
tes
to
r
ed
u
cin
g
co
g
g
in
g
to
r
q
u
e,
w
h
ich
is
u
n
wan
ted
to
r
q
u
e
th
at
af
f
ec
ts
th
e
m
o
v
e
m
en
t
o
f
th
e
e
n
g
in
e
[
9
]
.
T
h
e
m
o
d
er
n
m
e
th
o
d
s
o
f
r
ese
ar
ch
er
s
,
w
h
i
c
h
is
th
e
r
e
aso
n
f
o
r
wr
it
in
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a
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r
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s
h
o
w
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h
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g
m
a
g
n
eti
c
f
ie
ld
wi
th
in
th
e
ai
r
g
a
p
o
f
t
h
e
en
g
i
n
e
,
w
h
i
c
h
le
a
d
s
t
o
i
m
p
r
o
v
in
g
o
p
er
ati
n
g
ef
f
i
cie
n
c
y
an
d
r
e
d
u
ci
n
g
n
o
is
e
an
d
v
i
b
r
at
io
n
s
f
r
o
m
b
y
r
e
d
u
ci
n
g
t
h
e
r
i
p
p
le
f
a
ct
o
r
o
f
th
e
m
ac
h
i
n
e
t
o
r
q
u
e
.
M
an
y
a
n
al
y
s
es
a
r
e
u
s
e
d
wit
h
co
m
p
u
te
r
s
i
m
u
la
ti
o
n
(
F
E
M
)
t
o
o
p
ti
m
iz
e
g
e
o
m
et
r
i
c
v
a
r
ia
b
l
es
in
th
e
PM
SM,
wi
th
t
h
e
a
n
g
le
an
d
s
p
ac
e
o
f
t
h
e
m
a
g
n
e
ts
.
T
h
is
c
o
n
t
r
i
b
u
tes
to
ac
h
ie
v
i
n
g
an
i
d
e
al
b
a
la
n
c
e
b
e
t
wee
n
h
i
g
h
t
o
r
q
u
e
an
d
lo
w
e
n
er
g
y
i
n
g
est
in
g
,
w
h
i
ch
i
n
c
r
e
ases
t
h
e
e
f
f
ici
en
c
y
o
f
t
h
e
m
o
to
r
an
d
e
x
te
n
d
s
i
ts
l
if
eti
m
e
,
p
a
r
ti
cu
la
r
l
y
i
n
c
h
a
n
g
in
g
o
p
e
r
ati
n
g
l
o
c
ati
o
n
s
s
u
c
h
as
i
n
ele
c
tr
i
c
c
ar
s
[
1
0
]
.
T
h
e
d
i
m
e
n
s
i
o
n
s
o
f
r
o
t
o
r
m
a
g
n
ets
i
n
PM
SMs
p
l
ay
a
n
i
m
p
o
r
t
a
n
t
r
o
le
d
u
r
i
n
g
t
h
e
d
esi
g
n
s
t
ag
e
d
u
e
to
t
h
ei
r
d
i
r
e
ct
e
f
f
ec
t
o
n
t
h
e
m
o
to
r
'
s
p
e
r
f
o
r
m
a
n
c
e.
T
h
e
s
ize
an
d
s
h
ap
e
o
f
th
e
m
ag
n
ets
ar
e
th
e
k
ey
p
ar
am
eter
s
th
at
im
p
ac
t
th
e
to
r
q
u
e,
p
o
wer
d
e
n
s
ity
,
an
d
ef
f
icien
cy
o
f
th
e
m
o
t
o
r
.
Pre
v
i
o
u
s
Stu
d
ies
h
ad
s
h
o
wn
th
at
ad
ju
s
tin
g
th
e
PM
d
im
en
s
io
n
s
,
s
p
ec
if
ically
th
e
wid
th
an
d
d
e
p
th
,
co
u
ld
s
ig
n
if
ica
n
tly
af
f
ec
t
th
e
to
r
q
u
e
f
ea
tu
r
es
an
d
to
tal
ef
f
icien
cy
o
f
PMSMs
[
11
]
.
I
n
PMSMs,
th
e
m
ass
an
d
len
g
th
o
f
th
e
PM
s
tr
u
ctu
r
es
h
av
e
a
d
is
tin
g
u
is
h
ed
i
m
p
ac
t
o
n
th
e
to
r
q
u
e,
ef
f
icien
c
y
,
an
d
p
o
we
r
d
en
s
ity
o
f
th
e
m
o
to
r
.
Stu
d
ies
h
av
e
v
er
i
f
ied
th
at
ex
te
n
s
iv
e
m
ag
n
et
s
ca
les
an
d
f
ewe
r
m
ag
n
ets
p
e
r
p
o
le
ca
n
lead
t
o
h
ig
h
er
m
o
to
r
to
r
q
u
e
,
wh
ile
u
s
in
g
h
e
av
ier
m
ag
n
ets
ca
n
im
p
r
o
v
e
m
o
to
r
e
f
f
icien
cy
[
1
1
]
.
Ad
d
itio
n
ally
,
th
e
d
iam
eter
,
len
g
th
,
an
d
tu
r
n
s
p
er
c
o
il
o
f
t
h
e
m
ac
h
in
e
ar
e
s
er
io
u
s
p
ar
a
m
eter
s
th
at
af
f
ec
t
to
r
q
u
e,
p
o
wer
,
a
n
d
ef
f
icien
c
y
,
wh
e
r
e
th
e
th
r
ee
f
ac
to
r
s
i
n
cr
ea
s
e
with
m
ac
h
in
e
len
g
th
.
Nev
e
r
th
eless
,
a
lim
ited
in
cr
ea
s
e
in
ef
f
icie
n
cy
an
d
p
o
wer
m
ay
n
o
t
b
e
co
n
s
id
er
ed
in
t
h
e
lin
ea
r
ly
in
cr
ea
s
in
g
to
r
q
u
e.
T
h
is
em
p
h
asizes
th
e
d
if
f
ic
u
lt
r
elatio
n
s
h
ip
b
etwe
en
m
ag
n
et
d
im
en
s
io
n
s
an
d
PMSM
p
er
f
o
r
m
an
ce
[
1
2
]
,
[
1
3
]
.
Mo
r
eo
v
er
,
th
e
elec
tr
o
m
ag
n
etic
f
ea
tu
r
es
o
f
V
-
ty
p
e
PMSMs
ar
e
d
if
f
icu
lt
t
o
lin
k
to
o
t
h
er
i
s
s
u
es
lik
e
m
ag
n
et
s
h
ap
e
,
s
ize,
s
tato
r
teet
h
,
an
d
f
lu
x
b
a
r
r
ier
s
.
Mo
d
if
y
in
g
th
e
d
im
en
s
io
n
s
o
f
th
e
r
o
to
r
a
n
d
s
tato
r
,
i
n
clu
d
in
g
th
e
n
u
m
b
e
r
o
f
s
tato
r
win
d
in
g
tu
r
n
s
in
ea
ch
co
il
,
m
ay
p
r
o
d
u
ce
v
a
r
iatio
n
s
in
elec
tr
o
m
ag
n
etic
f
ea
tu
r
es
an
d
p
er
f
o
r
m
an
ce
r
esu
lts
.
Mo
d
if
y
in
g
th
e
p
er
f
o
r
m
a
n
ce
o
f
PMSMs
b
y
ch
an
g
i
n
g
d
im
en
s
io
n
s
lik
e
len
g
th
,
d
iam
eter
,
an
d
tu
r
n
s
p
er
c
o
il
ca
n
b
e
u
tili
ze
d
to
o
p
tim
ize
elec
tr
o
m
ag
n
etic
to
r
q
u
e,
d
ev
elo
p
ed
p
o
wer
,
an
d
ef
f
icien
c
y
in
th
e
ab
s
en
ce
o
f
wid
e
r
e
d
esig
n
in
g
,
th
o
u
g
h
ca
r
e
f
u
l
asp
ec
ts
o
f
m
ec
h
an
ical
r
estrictio
n
s
an
d
elec
tr
o
m
ag
n
etic
p
er
f
o
r
m
an
ce
a
r
e
ess
en
tial
[
1
4
]
,
[
1
5
]
.
I
n
s
u
m
m
a
r
y
,
th
e
d
i
m
en
s
io
n
s
o
f
r
o
to
r
m
ag
n
ets
in
V
-
ty
p
e
PMSMs
h
av
e
a
s
u
p
er
f
icial
in
f
lu
e
n
ce
o
n
p
er
f
o
r
m
an
ce
p
ar
a
m
eter
s
(
to
r
q
u
e,
e
f
f
icien
cy
,
an
d
p
o
we
r
d
en
s
ity
)
.
Op
tim
izin
g
m
ag
n
et
d
im
en
s
io
n
s
is
a
v
er
y
im
p
o
r
tan
t
asp
ec
t
f
o
r
h
ig
h
-
p
er
f
o
r
m
in
g
P
MSM
s
.
E
x
ten
s
iv
e
m
ag
n
et
d
im
en
s
io
n
s
,
lo
w
n
u
m
b
er
o
f
m
a
g
n
ets/
p
o
les
,
a
n
d
s
u
itab
le
len
g
th
a
n
d
d
iam
eter
ad
ju
s
tm
en
ts
ar
e
ess
en
tial
f
ac
to
r
s
in
ac
c
o
m
p
lis
h
in
g
p
r
ef
er
r
ed
m
o
to
r
ch
ar
ac
ter
is
tics
[
16]
-
[
1
8
]
.
I
n
th
e
cu
r
r
e
n
t
s
tu
d
y
,
a
p
ar
a
m
etr
ic
in
v
esti
g
atio
n
was
co
n
d
u
cted
u
s
in
g
ANSYS
s
o
f
twar
e
,
p
r
o
v
i
d
in
g
ap
p
r
ec
iate
d
in
s
ig
h
ts
in
to
th
e
ef
f
ec
ts
o
f
w
id
th
an
d
th
ick
n
ess
v
ar
iatio
n
s
o
n
th
e
p
er
f
o
r
m
an
ce
o
f
V
-
ty
p
e
PMSM.
T
h
e
r
esu
lts
h
ig
h
lig
h
ted
th
e
ef
f
ec
t
o
f
o
p
tim
izin
g
m
a
g
n
et
d
im
en
s
io
n
s
to
attain
g
r
e
ater
m
o
to
r
p
er
f
o
r
m
an
ce
,
with
th
e
b
est
d
im
en
s
io
n
s
id
en
tifie
d
as
5
-
6
m
m
wid
th
an
d
3
5
-
4
0
m
m
th
ick
n
ess
.
T
h
ese
r
esu
lts
co
n
tr
ib
u
te
to
t
h
e
im
p
r
o
v
e
m
e
n
t
o
f
PMSM
d
esig
n
a
n
d
o
p
ti
m
izatio
n
f
o
r
n
u
m
er
o
u
s
en
g
in
ee
r
in
g
r
eq
u
ests
.
I
n
ad
d
itio
n
,
f
l
u
x
b
a
r
r
ier
(
FB
)
v
ar
iatio
n
p
lay
s
an
ess
en
tial
r
o
le
i
n
en
h
a
n
cin
g
th
e
d
ev
elo
p
ed
to
r
q
u
e,
ef
f
icien
cy
,
a
n
d
m
in
im
izin
g
r
ip
p
le
to
r
q
u
e
o
f
V
-
ty
p
e
PMSM.
B
y
ad
ju
s
tin
g
th
e
FB
with
in
th
e
m
o
to
r
d
esig
n
,
s
ev
er
al
ad
v
an
ta
g
es
ca
n
b
e
ac
c
o
m
p
lis
h
ed
.
FB
ca
n
b
e
o
p
tim
ized
to
im
p
r
o
v
e
th
e
m
ag
n
etic
f
l
u
x
d
is
tr
ib
u
tio
n
wi
th
in
th
e
m
o
to
r
.
B
y
s
u
itab
ly
in
s
er
tin
g
a
n
d
m
o
d
eli
n
g
th
ese
b
ar
r
ier
s
,
th
e
m
ag
n
etic
f
lu
x
p
ath
s
ca
n
b
e
e
f
f
ec
tiv
e
ly
m
ax
im
izin
g
th
e
in
ter
ac
tio
n
b
etwe
en
th
e
s
tato
r
an
d
r
o
to
r
Flu
x
es.
T
h
is
o
p
tim
iz
atio
n
im
p
r
o
v
es
t
h
e
to
r
q
u
e
g
en
e
r
atio
n
a
n
d
i
n
cr
ea
s
es
th
e
o
v
er
all
p
er
f
o
r
m
a
n
ce
.
Als
o
,
v
ar
iatio
n
o
f
FB
h
elp
s
in
d
ec
r
e
asin
g
m
ag
n
etic
co
r
e
lo
s
s
es with
in
th
e
m
o
to
r
,
lik
e
h
y
s
ter
esis
an
d
ed
d
y
cu
r
r
e
n
t
lo
s
s
es.
B
y
s
u
itab
ly
d
esig
n
in
g
th
e
FB
,
th
ese
lo
s
s
es
ca
n
b
e
ab
at
ed
,
co
n
s
eq
u
en
tial
i
n
en
h
an
ce
d
e
f
f
icien
cy
.
A
d
d
itio
n
ally
,
o
p
tim
izin
g
th
e
FB
ca
n
r
e
d
u
ce
th
e
co
g
g
in
g
t
o
r
q
u
e,
wh
ic
h
m
ea
n
s
in
cr
ea
s
in
g
ef
f
icien
cy
b
y
r
ed
u
cin
g
t
h
e
p
o
wer
r
eq
u
ir
e
d
to
ca
n
ce
l
r
elu
cta
n
ce
ef
f
ec
ts
th
r
o
u
g
h
m
o
to
r
o
p
e
r
atio
n
.
In
th
e
s
am
e
m
an
n
er
,
FB
ch
an
g
e
ca
n
ass
is
t
in
r
ed
u
cin
g
th
e
r
ip
p
le
to
r
q
u
e
ef
f
ec
t,
wh
ich
is
p
r
o
d
u
ce
d
d
u
e
to
f
lu
ctu
atio
n
in
d
ev
elo
p
e
d
to
r
q
u
e
th
r
o
u
g
h
m
o
to
r
r
o
tatio
n
[
1
9
]
-
[
2
1
]
.
W
h
en
FB
is
o
p
tim
ized
,
th
e
m
ag
n
eti
c
f
lu
x
d
is
tr
ib
u
tio
n
b
ec
o
m
es
m
o
r
e
u
n
if
o
r
m
,
g
en
e
r
atin
g
a
s
m
o
o
t
h
to
r
q
u
e.
T
h
e
r
ed
u
ctio
n
i
n
to
r
q
u
e
r
i
p
p
le
in
cr
ea
s
es
th
e
o
v
er
all
p
er
f
o
r
m
an
ce
,
p
ar
ticu
lar
ly
f
o
r
a
p
p
licatio
n
s
th
at
n
ee
d
ac
cu
r
ate
co
n
tr
o
l a
n
d
s
m
o
o
t
h
o
p
e
r
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
P
a
r
a
metric a
n
a
lysi
s
o
n
th
e
effec
t o
f V
-
typ
e
r
o
to
r
ma
g
n
et
g
eo
metry
…
(
A
h
med
Ja
d
a
a
n
A
li
)
771
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
T
h
e
s
h
ap
e
o
f
r
o
to
r
m
ag
n
ets
an
d
s
tato
r
s
lo
ts
co
n
s
id
er
ab
ly
af
f
ec
ts
th
e
ef
f
icien
cy
an
d
p
er
f
o
r
m
an
ce
o
f
PMSMs.
Dif
f
er
en
t
r
o
to
r
s
tr
u
c
tu
r
es
af
f
ec
t
m
o
to
r
o
p
e
r
atio
n
f
ac
to
r
s
as
co
g
g
in
g
to
r
q
u
e
,
d
ev
elo
p
ed
to
r
q
u
e,
b
ac
k
E
MFs,
an
d
to
tal
elec
tr
o
m
ag
n
etic
f
ea
tu
r
es
o
f
th
e
m
o
to
r
.
Fo
r
ex
am
p
le,
u
s
in
g
a
s
lo
t
s
lice
m
ad
e
o
f
co
m
p
o
s
ite
m
ater
ials
o
r
in
s
er
tin
g
is
o
late
d
m
ag
n
etic
m
ater
ials
in
s
lo
ts
ca
n
d
ec
r
ea
s
e
e
d
d
y
cu
r
r
en
t
l
o
s
s
es
an
d
im
p
r
o
v
e
elec
tr
o
m
ag
n
etic
p
e
r
f
o
r
m
an
ce
[
2
2
]
-
[
2
4
]
.
Fu
r
th
e
r
m
o
r
e,
asy
m
m
etr
ic
s
lo
t
p
o
s
itio
n
s
ca
n
d
ev
e
lo
p
to
r
q
u
e
f
ea
tu
r
es
an
d
th
e
to
tal
elec
tr
o
m
ag
n
etic
p
er
f
o
r
m
an
ce
b
y
ad
ju
s
tin
g
th
e
s
lo
t
asy
m
m
etr
y
[
1
6
]
.
Als
o
,
th
e
wid
th
an
d
d
ep
t
h
o
f
s
ec
o
n
d
ar
y
s
lo
ts
in
th
e
s
tato
r
c
an
alter
th
e
d
is
tr
ib
u
tio
n
o
f
m
o
to
r
in
ter
n
al
lo
s
s
,
ir
o
n
lo
s
s
,
an
d
PM
ed
d
y
cu
r
r
en
t
lo
s
s
,
p
r
o
v
id
e
d
th
at
v
is
io
n
s
f
o
r
m
o
to
r
d
esig
n
[
1
7
]
.
Ov
er
all,
o
p
tim
izin
g
s
tato
r
s
lo
t
s
h
ap
es
is
cr
u
cial
f
o
r
en
h
a
n
cin
g
th
e
ef
f
icien
cy
a
n
d
p
e
r
f
o
r
m
an
c
e
o
f
PMSMs.
No
wad
ay
s
,
m
o
r
e
r
esear
ch
ef
f
o
r
ts
h
av
e
p
o
in
ted
o
u
t
th
e
s
ig
n
if
ican
ce
o
f
r
o
to
r
m
ag
n
et
o
p
tim
izatio
n
in
in
cr
ea
s
in
g
PMSM
p
er
f
o
r
m
a
n
ce
.
T
h
e
im
p
ac
t
o
f
m
ag
n
et
d
i
m
en
s
io
n
s
o
n
PMSM
ef
f
icien
cy
s
ev
er
al
s
tu
d
ies
h
av
e
s
o
u
g
h
t
to
ex
p
a
n
d
u
p
o
n
th
is
f
o
u
n
d
atio
n
al
k
n
o
wled
g
e
.
T
h
e
i
n
f
lu
en
ce
o
f
m
ag
n
et
s
h
ap
e
o
n
m
o
to
r
e
f
f
icien
cy
also
ca
u
s
es a
r
ed
u
ctio
n
i
n
th
e
co
g
g
in
g
to
r
q
u
e
an
d
im
p
r
o
v
es
to
r
q
u
e
d
en
s
ity
[
4
]
.
T
h
e
p
h
y
s
ical
len
g
th
o
f
r
o
to
r
m
ag
n
ets
in
in
ter
io
r
p
e
r
m
an
en
t
m
ag
n
et
s
y
n
c
h
r
o
n
o
u
s
m
o
to
r
s
(
I
PMSMs)
h
as
a
g
r
ea
t
e
f
f
ec
t
o
n
th
eir
p
er
f
o
r
m
an
ce
.
Var
io
u
s
r
o
to
r
m
ag
n
e
t
d
esig
n
s
,
s
u
ch
as
s
in
u
s
o
id
al,
e
cc
en
tr
ic,
V
-
s
h
ap
ed
,
Nab
la
-
s
h
ap
ed
,
a
n
d
s
eg
m
e
n
te
d
b
r
id
g
e,
in
f
lu
en
ce
k
ey
p
er
f
o
r
m
an
ce
i
n
d
icato
r
s
lik
e
to
r
q
u
e
ca
p
ab
ilit
y
,
to
r
q
u
e
r
ip
p
le,
ef
f
icien
c
y
,
an
d
f
lu
x
d
e
n
s
ity
d
is
tr
i
b
u
tio
n
[
1
8
]
-
[
2
5
]
.
O
p
tim
al
r
o
to
r
s
tr
u
ctu
r
es
ca
n
b
e
o
b
tain
ed
b
y
f
in
e
-
tu
n
in
g
o
f
p
er
m
an
e
n
t
m
ag
n
et
d
im
en
s
io
n
s
.
Acc
o
r
d
in
g
p
r
ev
io
u
s
ly
m
en
tio
n
ed
ty
p
es
o
f
PM,
th
e
th
ick
n
ess
,
m
ag
n
et
ar
r
an
g
em
e
n
t,
an
d
p
o
le
ar
c
to
p
o
le
p
itch
r
atio
,
lead
in
g
to
en
h
an
ce
d
to
r
q
u
e,
e
f
f
icien
cy
,
an
d
f
lu
x
wea
k
e
n
in
g
ca
p
ab
ilit
y
o
v
e
r
a
wid
e
s
p
ee
d
r
an
g
e
[
2
0
]
.
As
m
en
tio
n
e
d
ea
r
li
er
,
f
in
ite
elem
e
n
t
an
aly
s
is
(
FE
A)
is
n
o
r
m
ally
th
e
m
eth
o
d
e
m
p
lo
y
e
d
to
in
v
esti
g
at
e
th
e
ef
f
ec
ts
o
f
r
o
to
r
m
ag
n
et
d
i
m
en
s
io
n
s
v
ar
y
in
g
o
n
th
e
PMSMs
elec
tr
o
m
ag
n
etic
p
er
f
o
r
m
an
ce
,
e
n
ab
lin
g
th
e
u
tili
ze
d
o
f
s
u
itab
le
r
o
to
r
g
eo
m
etr
y
s
tr
u
ctu
r
es
f
o
r
I
n
ter
io
r
PMSMs
in
elec
tr
ic
v
eh
icles
an
d
o
t
h
er
a
p
p
licatio
n
s
[
2
1
]
,
[
2
2
]
.
Fu
r
t
h
er
m
o
r
e,
d
ev
elo
p
m
en
t
s
in
co
m
p
u
tatio
n
al
m
et
h
o
d
s
,
s
u
ch
as
f
i
n
ite
elem
en
t
an
aly
s
is
(
FEA)
,
h
a
v
e
allo
we
d
r
esear
ch
er
s
to
d
is
co
v
er
th
e
c
o
m
p
lex
s
tr
u
ctu
r
e
o
f
m
ac
h
in
e
g
eo
m
etr
ies
in
m
o
r
e
d
etail
[
1
0
]
.
FEA
em
p
lo
y
e
d
to
o
p
tim
ize
d
im
en
s
io
n
s
to
r
ed
u
ce
th
e
lo
s
s
es
an
d
en
h
an
ce
to
r
q
u
e
ch
ar
ac
te
r
is
tics
,
r
ec
en
t
wo
r
k
s
h
a
v
e
b
ee
n
u
s
ed
t
o
in
v
esti
g
ate
th
e
elec
tr
ic
m
ac
h
in
es
b
ased
o
n
ad
v
a
n
ce
d
o
p
tim
izatio
n
alg
o
r
ith
m
s
.
A
g
en
etic
alg
o
r
ith
m
is
em
p
lo
y
ed
to
o
p
tim
ize
m
o
to
r
s
h
ap
es,
r
ea
ch
in
g
s
ig
n
if
ican
t
im
p
r
o
v
em
en
ts
in
th
e
ef
f
icien
cy
an
d
s
u
p
p
r
ess
io
n
o
f
to
r
q
u
e
r
ip
p
le
[
1
1
]
-
[
2
6
]
.
Ad
d
itio
n
ally
,
t
h
e
p
r
e
v
io
u
s
wo
r
k
s
h
i
g
h
lig
h
t
th
e
s
ig
n
if
ican
ce
o
f
co
n
s
id
er
in
g
th
er
m
al
ef
f
ec
ts
in
m
ac
h
in
e
o
p
tim
izatio
n
.
W
ith
E
Vs
p
u
s
h
in
g
t
h
e
b
o
r
d
e
r
s
o
f
m
o
to
r
p
er
f
o
r
m
an
ce
,
th
e
r
m
al
co
n
t
r
o
l
b
ec
o
m
es
a
s
er
io
u
s
is
s
u
e
[
1
2
]
.
Als
o
,
r
ese
ar
c
h
h
as
f
o
c
u
s
ed
o
n
th
e
i
n
f
lu
en
c
e
o
f
m
a
n
y
t
y
p
es
o
f
m
at
er
ials
o
n
m
o
t
o
r
p
er
f
o
r
m
a
n
ce
.
T
h
e
e
f
f
ec
t
o
f
i
n
s
u
l
ati
o
n
m
a
ter
ials
o
n
co
n
d
u
ct
o
r
s
'
lo
s
s
es
a
n
d
t
h
e
r
m
al
b
e
h
av
io
r
h
as
b
ee
n
i
n
v
est
ig
ate
d
,
e
m
p
h
asi
zin
g
th
e
s
i
g
n
i
f
ic
a
n
ce
o
f
m
a
te
r
i
al
c
h
o
i
ce
i
n
im
p
r
o
v
i
n
g
m
o
to
r
e
f
f
ici
en
c
y
[
1
3
]
.
T
h
e
p
o
p
u
l
ar
it
y
o
f
u
s
in
g
p
er
m
a
n
e
n
t
m
a
g
n
ets
i
n
el
ec
tr
ic
v
e
h
i
cl
es
h
a
s
s
o
a
r
ed
o
wi
n
g
t
o
t
h
e
ir
k
n
ac
k
f
o
r
i
m
p
r
o
v
in
g
m
o
t
o
r
d
y
n
am
ic
p
er
f
o
r
m
a
n
c
e
an
d
h
ig
h
ef
f
i
cie
n
c
y
.
A
m
o
n
g
t
h
e
v
ar
io
u
s
p
e
r
m
a
n
e
n
t
m
ag
n
et
(
PM
)
co
n
f
ig
u
r
a
ti
o
n
s
,
th
e
V
-
ty
p
e
PM
h
as
g
ai
n
e
d
a
m
o
s
t
r
em
a
r
k
a
b
l
e
att
en
ti
o
n
d
u
e
t
o
i
ts
a
d
v
a
n
ta
g
es
i
n
r
e
d
u
ci
n
g
t
o
r
q
u
e
f
l
u
ct
u
ati
o
n
s
an
d
im
p
r
o
v
i
n
g
t
h
e
o
v
e
r
all
v
eh
icl
e
p
e
r
f
o
r
m
a
n
c
e.
B
asi
ca
l
ly
,
t
h
e
V
-
t
y
p
e
P
M
is
a
p
p
r
o
p
r
iat
e
f
o
r
th
e
t
y
p
e
o
f
i
n
te
r
i
o
r
p
e
r
m
a
n
e
n
t
m
a
g
n
et
(
I
P
M)
s
y
n
c
h
r
o
n
o
u
s
m
o
t
o
r
s
,
i
n
cl
u
d
i
n
g
a
r
o
to
r
p
r
e
p
ar
ed
wit
h
V
-
s
h
ap
e
d
p
o
les
[
2
3
]
,
[
2
7
]
.
T
h
is
ad
v
a
n
ce
d
c
o
n
f
i
g
u
r
ati
o
n
p
r
o
d
u
c
es
a
m
o
r
e
r
eli
ab
le
d
is
t
r
i
b
u
ti
o
n
o
f
m
a
g
n
e
tic
f
l
u
x
,
w
h
i
ch
ca
u
s
es
a
d
ec
r
e
ase
i
n
t
o
r
q
u
e
v
a
r
i
ati
o
n
s
a
n
d
an
i
n
c
r
e
ase
i
n
p
o
we
r
o
u
t
p
u
t.
It
is
im
p
o
r
ta
n
t
to
n
o
te
t
h
at
,
c
o
m
p
ar
ed
to
o
t
h
er
ty
p
es
o
f
I
P
M
m
o
t
o
r
s
,
th
e
V
-
t
y
p
e
p
e
r
m
an
en
t
m
a
g
n
e
t
d
is
p
la
y
s
l
o
w
c
o
g
g
i
n
g
t
o
r
q
u
e
,
e
x
t
r
a
e
n
h
a
n
ci
n
g
t
h
e
o
v
e
r
all
p
e
r
f
o
r
m
a
n
ce
o
f
E
Vs
.
W
i
d
e
s
t
u
d
i
e
s
i
n
r
e
c
e
n
t
y
e
a
r
s
h
av
e
f
o
c
u
s
e
d
on
t
h
e
a
p
p
l
i
c
a
t
i
o
n
o
f
V
-
t
y
p
e
P
M
s
i
n
E
Vs
.
S
t
u
d
i
es
h
a
v
e
s
h
o
w
n
t
h
a
t
t
h
e
s
e
m
a
g
n
e
ts
c
a
n
s
i
g
n
i
f
i
ca
n
t
l
y
i
m
p
r
o
v
e
t
h
e
s
t
a
b
i
li
t
y
o
f
t
o
r
q
u
e
i
n
E
V
s
,
r
e
s
u
l
t
i
n
g
i
n
a
r
e
l
i
ab
l
e
a
n
d
f
i
n
e
r
d
r
i
v
i
n
g
s
k
i
l
ls
.
M
o
r
e
o
v
e
r
,
i
t
i
s
f
o
u
n
d
a
n
i
n
c
r
e
a
s
e
i
n
t
h
e
P
M
m
o
t
o
r
e
f
f
i
c
ie
n
c
y
a
n
d
p
o
w
e
r
o
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t
p
u
t
i
s
f
o
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n
d
,
w
h
i
c
h
r
e
s
u
l
t
s
in
a
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o
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p
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e
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e
n
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v
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n
h
a
n
c
e
m
e
n
t
in
t
h
e
a
c
ce
l
e
r
a
ti
o
n
a
n
d
d
r
i
v
i
n
g
r
a
n
g
e
o
f
E
V
s
[
2
4
]
,
[
2
5
]
.
I
n
g
e
n
e
r
a
l
,
t
h
e
V
-
t
y
p
e
PM
i
s
c
o
n
s
i
d
e
r
e
d
t
h
e
p
r
e
f
e
r
r
e
d
c
h
o
i
c
e
f
o
r
E
V
s
.
I
t
h
a
s
t
h
e
a
b
i
l
it
y
t
o
m
i
t
i
g
a
t
e
f
l
u
c
t
u
a
t
i
o
n
s
i
n
d
e
v
e
l
o
p
e
d
t
o
r
q
u
e
,
i
n
c
r
e
a
s
e
p
r
o
d
u
c
e
d
m
e
c
h
a
n
i
c
a
l
o
u
t
p
u
t
p
o
w
e
r
,
a
n
d
e
n
h
a
n
c
e
e
f
f
i
c
i
e
n
c
y
.
T
h
e
w
i
d
e
r
e
s
e
a
r
c
h
s
h
o
we
d
t
h
at
t
h
e
u
s
e
o
f
V
-
t
y
p
e
P
M
s
i
n
E
Vs
h
a
s
g
e
n
e
r
at
e
d
f
a
v
o
r
a
b
l
e
o
u
t
c
o
m
e
s
i
n
te
r
m
s
o
f
i
n
c
r
e
a
s
i
n
g
o
v
e
r
a
ll
v
e
h
i
c
l
e
p
e
r
f
o
r
m
a
n
c
e
[
2
6
]
,
[
2
7
]
.
PMSM
r
ep
r
esen
tatio
n
u
s
in
g
th
e
f
in
ite
elem
en
t
m
eth
o
d
(
FEM
)
is
an
elec
tr
o
m
ag
n
etic
an
al
y
s
is
p
r
o
ce
s
s
in
wh
ich
th
e
m
o
to
r
is
d
iv
id
ed
in
to
s
m
all
p
ar
ts
ca
lled
“e
lem
e
n
ts
”.
E
ac
h
elem
en
t
s
ig
n
if
ies
a
v
er
y
s
m
all
s
h
ar
e
o
f
th
e
m
o
to
r
co
n
s
tr
u
ctio
n
,
f
o
r
ex
a
m
p
le
,
a
p
e
r
m
an
en
t
m
ag
n
et,
s
ta
to
r
,
o
r
air
g
a
p
,
an
d
elem
en
tar
y
b
eh
av
io
r
eq
u
atio
n
s
ar
e
ap
p
lied
to
it
to
d
eter
m
in
e
h
o
w
m
ag
n
etic
f
ield
s
an
d
elec
t
r
ical
cu
r
r
en
ts
in
ter
r
elate
th
r
o
u
g
h
th
e
PMSM.
W
e
ca
n
s
tar
t
with
th
e
e
q
u
atio
n
s
,
t
h
en
th
e
m
o
d
elin
g
s
tep
s
,
with
e
ac
h
s
tag
e
as
th
e
m
a
g
n
etic
p
o
te
n
tial
f
ield
eq
u
atio
n
(
J
=
∇
×
(
1
/
μ
)
∇
×
A
)
)
.
T
h
is
eq
u
atio
n
is
b
ased
o
n
t
h
e
m
ag
n
etic
p
o
ten
tial th
eo
r
y
,
wh
er
e
th
e
m
ag
n
etic
p
o
ten
tial
v
ar
iab
le
is
u
s
ed
f
o
r
ea
s
y
id
en
tific
atio
n
o
f
th
e
m
ag
n
etic
f
lu
x
in
s
id
e
th
e
m
o
t
o
r
.
T
h
is
eq
u
atio
n
is
s
o
lv
e
d
at
th
e
lev
el
o
f
ea
ch
elem
en
t
o
f
th
e
m
o
d
el
g
en
er
atin
g
n
etwo
r
k
.
W
h
er
e
A:
I
t
r
ep
r
esen
ts
th
e
m
ag
n
etic
v
ec
to
r
p
o
ten
tial
f
o
r
ea
c
h
p
o
in
t in
s
id
e
th
e
m
o
to
r
.
μ
:
r
ep
r
esen
ts
th
e
m
ag
n
etic
p
er
m
ea
b
ilit
y
o
f
th
e
m
ater
ial
(
p
e
r
m
ea
b
ilit
y
)
a
n
d
ca
n
v
ar
y
d
e
p
en
d
i
n
g
o
n
th
e
m
ater
i
als
u
s
ed
,
s
u
ch
as
p
er
m
a
n
en
t
m
ag
n
ets
o
r
ir
o
n
p
ar
ts
.
J
r
ep
r
e
s
en
ts
cu
r
r
en
t
d
en
s
ity
,
wh
ich
is
ze
r
o
in
s
id
e
a
p
er
m
an
en
t
m
ag
n
et.
Af
ter
ca
lcu
latin
g
t
h
e
m
ag
n
etic
f
lu
x
d
e
n
s
ity
,
A,
it
is
u
s
ed
to
ca
lcu
lat
e
th
e
m
ag
n
etic
f
lu
x
d
en
s
ity
B
=
∇
×
A
,
f
l
o
w
d
en
s
ity
B
is
th
e
p
r
im
ar
y
v
ar
iab
le
b
y
w
h
ich
t
h
e
s
tr
en
g
t
h
o
f
th
e
m
ag
n
etic
f
ield
ac
r
o
s
s
th
e
ar
m
atu
r
e
p
o
les
an
d
m
ag
n
ets
is
an
aly
ze
d
an
d
d
eter
m
in
e
d
.
W
h
er
e
Far
ad
ay
’
s
law
f
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
7
6
9
-
7
79
772
in
d
u
ce
d
v
o
ltag
e
in
th
e
win
d
in
g
’
s
in
d
u
ce
d
v
o
ltag
e
is
b
ased
o
n
th
is
law,
wh
ich
d
escr
ib
es
h
o
w
ch
an
g
in
g
m
ag
n
etic
f
lu
x
p
r
o
d
u
ce
s
a
v
o
ltag
e
in
th
e
co
il
(
e
=
−
dt
d
Φ
=
−
N
dt
dB
)
wh
er
e
e:
in
d
u
ce
d
v
o
lta
g
e,
an
d
d
e
p
en
d
s
o
n
t
h
e
r
ate
o
f
ch
an
g
e
in
m
ag
n
etic
f
lu
x
d
en
s
ity
.
Φ
:
m
ag
n
etic
f
lu
x
,
wh
ich
is
c
alcu
lated
as
th
e
in
teg
r
al
o
f
th
e
f
lu
x
d
e
n
s
ity
ac
r
o
s
s
th
e
s
u
r
f
ac
e
o
f
th
e
c
o
il.
N:
T
h
e
n
u
m
b
e
r
o
f
tu
r
n
s
,
wh
ich
d
ir
ec
tly
af
f
ec
ts
th
e
am
o
u
n
t
o
f
in
d
u
ce
d
v
o
ltag
e.
T
h
e
to
r
q
u
e
g
en
er
ated
b
y
th
e
PMSM
is
ca
lcu
lated
u
s
in
g
th
e
f
o
l
lo
win
g
r
elatio
n
s
h
ip
)
T
=
2
3
×
p
×
(
ψ
×
i
)
wh
er
e
T
:
r
ep
r
esen
ts
th
e
r
esu
ltin
g
to
r
q
u
e.
p
:
Nu
m
b
e
r
o
f
p
o
la
r
p
air
s
.
ψ:
b
in
d
in
g
f
lu
x
f
o
r
ea
ch
p
h
ase.
i:
T
h
e
cu
r
r
en
t
p
ass
in
g
th
r
o
u
g
h
th
e
win
d
in
g
s
[
2
6
]
-
[
2
8
]
.
T
o
d
ete
r
m
in
e
th
e
i
n
f
lu
en
ce
o
f
r
o
to
r
m
ag
n
et
d
im
en
s
io
n
s
o
n
th
e
lo
s
s
f
ield
d
is
tr
ib
u
tio
n
o
f
th
e
PMSMs,
th
e
v
ar
iatio
n
law
o
f
th
e
elec
tr
o
m
ag
n
etic
f
ield
ca
n
b
e
an
aly
ze
d
ac
cu
r
ately
.
B
ased
o
n
Par
k
-
tr
a
n
s
f
o
r
m
atio
n
,
th
e
s
u
p
p
lied
v
o
ltag
e
an
d
d
ev
elo
p
e
d
elec
tr
o
m
a
g
n
etic
t
o
r
q
u
e
o
f
th
e
3
-
p
h
ase
PMSM
in
th
e
d
-
q
r
e
p
r
esen
tatio
n
ca
n
b
e
s
tated
as
(
1
)
a
n
d
(
2
)
[
2
9
]
.
=
+
−
(
1
)
=
+
+
(
−
)
(
2
)
W
h
er
e
vd
,
vq
,
id
,
iq
,
Ld
,
Lq
ar
e
th
e
a
p
p
lied
v
o
ltag
e,
cu
r
r
en
t
,
an
d
in
d
u
ctan
ce
in
d
-
q
-
f
r
am
e
,
r
esp
ec
tiv
ely
,
R
is
th
e
ar
m
atu
r
e
r
esis
tan
ce
,
ω
e
is
th
e
elec
tr
ical
an
g
u
lar
s
p
ee
d
o
f
th
e
r
o
tated
m
ag
n
etic
f
ield
,
an
d
λ
PM
is
th
e
l
in
k
ag
e
f
lu
x
p
r
o
d
u
ce
d
b
y
th
e
PM.
T
h
e
FEM
ca
n
b
e
u
s
ed
to
ac
cu
r
ately
i
n
v
esti
g
ate
th
e
elec
tr
o
m
a
g
n
etic
r
elatio
n
s
h
ip
o
f
th
e
PMSM,
wh
er
e
th
e
tr
an
s
ien
t f
i
eld
eq
u
atio
n
o
f
th
e
PMSM
ca
n
b
e
g
iv
e
n
b
y
(
3
)
an
d
(
4
)
[
3
0
]
,
[
3
1
]
.
(
1
)
+
(
1
)
=
−
(
−
−
)
(
3
)
1
1
−
1
2
=
(
4
)
T
h
e
s
im
u
lated
r
eg
io
n
,
A
th
e
m
ag
n
etic
v
ec
to
r
p
o
ten
tial
(
W
b
/
m
)
,
J
is
th
e
cu
r
r
en
t
d
e
n
s
ity
,
μ
i
s
th
e
p
er
m
ea
b
ilit
y
,
σ
is
th
e
co
n
d
u
ctiv
ity
,
Js
is
th
e
e
q
u
iv
alen
t
c
u
r
r
en
t
d
en
s
ity
o
f
t
h
e
p
er
m
a
n
en
t
m
a
g
n
et,
S
1
is
th
e
b
o
u
n
d
ar
y
co
n
d
itio
n
o
f
th
e
p
e
r
m
an
en
t
m
ag
n
et,
μ
1
a
n
d
μ
2
a
r
e
th
e
p
e
r
m
ea
b
ilit
y
o
f
th
e
two
m
ed
iu
m
o
n
th
e
b
o
u
n
d
a
r
y
o
f
t
h
e
p
e
r
m
an
e
n
t
m
ag
n
et.
B
y
m
er
g
in
g
t
h
e
ex
te
r
n
al
elec
tr
ic
cir
cu
it
an
d
co
m
p
u
ted
m
o
d
el
o
f
PMSM
elec
tr
o
m
ag
n
etic
f
ield
,
t
h
e
eq
u
atio
n
o
f
th
e
f
ield
cir
cu
it c
o
u
p
led
m
o
d
el
ca
n
b
e
ex
p
r
ess
ed
as [
2
2
]
-
[
3
2
]
.
=
+
+
(
∬
+
−
∬
−
)
(
5
)
W
h
er
e
v
s
an
d
i
s
ar
e
th
e
p
h
ase
v
o
ltag
e
an
d
p
h
ase
cu
r
r
e
n
t,
r
esp
ec
tiv
ely
,
R
s
is
th
e
to
tal
s
tato
r
r
esis
tan
ce
,
L
e
is
th
e
en
d
win
d
in
g
in
d
u
ctan
ce
,
l
s
tk
i
s
th
e
s
tack
len
g
th
o
f
th
e
co
r
e,
S
turn
is
th
e
cr
o
s
s
-
s
ec
tio
n
a
r
ea
o
f
o
n
e
tu
r
n
,
S
+
a
n
d
S
−
ar
e
th
e
p
o
s
itiv
ely
an
d
n
e
g
ativ
ely
to
tal
ar
ea
s
o
f
o
r
ien
te
d
co
il
.
As
s
tated
in
(
1
)
,
t
h
e
t
wo
v
ar
iab
le
t
o
r
q
u
e
co
m
p
o
n
en
ts
o
f
PM
m
ac
h
in
es
ar
e
av
ailab
le.
T
h
e
f
ir
s
t
co
m
p
o
n
en
t
is
in
f
lu
en
ce
d
b
y
th
e
r
o
to
r
ex
citatio
n
PM
f
lu
x
,
wh
er
e
its
v
alu
e
is
h
ig
h
ly
af
f
ec
ted
by
th
e
p
r
o
p
e
r
ties
of
th
e
PM
m
ater
ial
,
lik
e
s
ize,
m
ax
im
u
m
e
n
er
g
y
p
r
o
d
u
ct
o
f
f
lu
x
d
e
n
s
ity
B
,
an
d
f
lu
x
in
ten
s
ity
H.
W
h
ile
th
e
s
e
c
o
n
d
co
m
p
o
n
en
t
,
ca
lled
r
elu
cta
n
ce
to
r
q
u
e,
d
e
p
en
d
s
o
n
th
e
s
alien
cy
r
atio
o
f
th
e
r
o
to
r
r
elu
ctan
ce
,
it
is
c
o
m
p
u
t
ed
b
y
two
co
m
p
o
n
en
ts
/
.
T
h
e
f
ix
ed
ter
m
co
m
p
o
n
en
ts
ar
e
p
h
ase
n
u
m
b
er
an
d
p
o
le
p
air
n
u
m
b
er
.
=
2
2
[
Ψ
+
(
−
)
]
(
6
)
Th
e
d
ev
elo
p
ed
elec
tr
o
m
ag
n
eti
c
to
r
q
u
e
o
f
i
n
t
e
r
n
a
l
PM
m
ac
h
in
es
m
ay
be
ap
p
r
o
x
im
ately
d
eter
m
in
ed
by
v
ar
y
in
g
(
1
)
to
co
m
p
r
is
e
t
h
e
d
-
q
o
f
t
h
e
f
l
u
x
a
s
s
tated
in
(
2
)
[
2
6
]
-
[
3
3
]
.
_
=
3
2
2
(
−
)
(
7
)
T
h
e
s
t
u
d
y
o
f
th
e
P
MSM
m
o
d
e
l
is
b
as
ed
o
n
a
V
-
t
y
p
e
PM
m
o
t
o
r
u
s
e
d
i
n
an
el
ec
t
r
i
ca
l
v
e
h
ic
le
p
r
o
v
i
d
ed
b
y
t
h
e
ANSYS
s
o
f
twa
r
e
l
ib
r
a
r
y
.
I
t
h
as
4
p
o
les
a
n
d
2
4
s
l
o
ts
w
ith
c
h
o
r
d
ed
w
in
d
i
n
g
s
l
o
c
ate
d
i
n
th
e
s
ta
to
r
s
e
cti
o
n
.
I
n
t
h
e
r
o
t
o
r
c
o
r
e
,
a
s
i
n
g
le
-
l
a
y
e
r
,
V
-
t
y
p
e
PM
s
li
ce
s
a
r
e
in
tr
o
d
u
c
ed
i
n
t
o
t
h
e
r
a
d
ia
l
h
o
le
at
ea
ch
p
o
l
e
ar
ea
.
D
u
e
t
o
th
e
c
o
n
s
tr
u
cti
o
n
o
f
th
e
PM
m
o
to
r
,
a
co
m
p
l
ete
m
o
d
el
,
t
h
e
d
im
en
s
io
n
p
a
r
a
m
ete
r
s
o
f
t
h
e
m
o
t
o
r
is
g
i
v
e
n
i
n
T
a
b
le
1
.
T
h
e
m
a
g
n
et
wi
d
t
h
(
w
=
2
0
-
6
0
m
m
)
a
n
d
m
a
g
n
et
d
e
p
t
h
(
d
=
2
-
6
m
m
)
.
T
h
e
f
lu
x
b
a
r
r
ie
r
o
f
t
h
e
r
o
to
r
m
a
g
n
et
h
as
v
ar
ie
d
i
n
t
h
e
r
a
n
g
e
o
f
(
1
-
3
m
m
)
.
T
h
e
r
es
ea
r
c
h
o
b
je
cti
v
e
o
f
t
h
is
s
tu
d
y
is
t
o
co
m
p
r
e
h
e
n
s
i
v
el
y
i
n
v
esti
g
a
te
th
e
in
f
l
u
e
n
c
e
o
f
r
o
t
o
r
m
a
g
n
et
d
im
e
n
s
i
o
n
s
v
a
r
ia
ti
o
n
o
n
t
h
e
p
er
f
o
r
m
an
ce
o
f
p
e
r
m
a
n
e
n
t
m
ag
n
e
t
s
y
n
ch
r
o
n
o
u
s
m
a
ch
in
es
(
PMSMs
)
.
I
n
d
e
tai
l,
t
h
e
w
o
r
k
aim
s
to
cla
r
i
f
y
h
o
w
v
ar
iat
io
n
s
in
r
o
to
r
m
a
g
n
et
g
eo
m
e
tr
y
,
i
n
cl
u
d
i
n
g
wi
d
t
h
,
d
e
p
t
h
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
P
a
r
a
metric a
n
a
lysi
s
o
n
th
e
effec
t o
f V
-
typ
e
r
o
to
r
ma
g
n
et
g
eo
metry
…
(
A
h
med
Ja
d
a
a
n
A
li
)
773
f
l
u
x
b
a
r
r
ie
r
w
id
th
,
a
n
d
m
ag
n
e
t
b
r
i
d
g
e
i
m
p
ac
t
,
o
n
th
e
ele
ct
r
o
m
a
g
n
eti
c
p
e
r
f
o
r
m
a
n
c
e,
l
o
s
s
es
d
is
t
r
i
b
u
ti
o
n
,
t
o
r
q
u
e
ch
ar
ac
t
er
is
ti
cs,
a
n
d
o
v
er
all
e
f
f
ic
ie
n
c
y
o
f
PM
SMs.
B
y
c
o
n
d
u
ct
in
g
a
s
y
s
t
em
ati
c
an
al
y
s
is
an
d
co
m
p
a
r
is
o
n
o
f
d
i
f
f
er
e
n
t r
o
t
o
r
d
im
e
n
s
i
o
n
s
[
3
4
]
,
[
3
5
]
.
T
h
e
s
t
u
d
y
t
r
i
es
t
o
p
r
o
v
i
d
e
v
al
u
a
b
l
e
u
n
d
er
s
ta
n
d
i
n
g
i
n
t
o
th
e
o
p
ti
m
a
l d
esi
g
n
p
a
r
a
m
e
te
r
s
f
o
r
m
ax
im
i
zi
n
g
m
o
t
o
r
ef
f
i
cie
n
cy
a
n
d
m
i
n
i
m
iz
i
n
g
c
o
g
g
i
n
g
t
o
r
q
u
e
wh
ile
m
ai
n
ta
in
in
g
ac
c
e
p
ta
b
l
e
to
r
q
u
e
c
r
e
ati
o
n
,
m
i
n
i
m
al
l
o
s
s
es
,
a
n
d
s
ta
b
l
e
o
p
er
ati
o
n
.
Fu
r
t
h
er
m
o
r
e
,
t
h
e
r
ese
ar
ch
ai
m
s
c
o
m
p
r
i
s
es
e
x
p
lo
r
e
t
h
e
t
as
k
s
r
el
ate
d
to
d
i
f
f
e
r
e
n
t
m
ag
n
e
t
co
n
f
i
g
u
r
a
ti
o
n
s
,
as
wel
l
as
r
ec
o
g
n
i
zi
n
g
c
h
an
ce
s
f
o
r
ad
d
i
tio
n
a
l
o
p
ti
m
iz
ati
o
n
im
p
r
o
v
e
m
e
n
t
a
n
d
en
h
an
ci
n
g
t
h
e
p
e
r
f
o
r
m
an
ce
o
f
PMS
M.
Fi
g
u
r
e
1
s
h
o
ws
t
h
e
s
te
p
s
i
n
v
o
lv
ed
i
n
th
e
p
r
o
ce
s
s
o
f
r
e
p
r
ese
n
t
in
g
t
h
e
e
f
f
e
ct
o
f
V
-
s
h
ap
ed
r
o
t
o
r
m
a
g
n
et
g
e
o
m
et
r
y
o
n
th
e
d
y
n
a
m
i
c
p
er
f
o
r
m
a
n
c
e
o
f
p
e
r
m
an
e
n
t
m
ag
n
e
t
s
y
n
c
h
r
o
n
o
u
s
m
o
t
o
r
s
(
P
MSM
s
)
u
s
i
n
g
t
h
e
f
i
n
i
te
ele
m
e
n
t
m
et
h
o
d
(
FEM
)
.
T
h
e
p
r
o
c
ess
b
e
g
i
n
s
b
y
d
e
f
i
n
i
n
g
t
h
e
b
asic
m
o
to
r
m
o
d
e
l,
t
h
en
th
e
g
e
o
m
etr
y
o
f
th
e
V
-
s
h
a
p
e
d
m
ag
n
et
s
is
d
esi
g
n
e
d
.
Fo
ll
o
we
d
b
y
f
o
r
m
i
n
g
t
h
e
n
et
wo
r
k
(
Me
s
h
i
n
g
)
a
n
d
ap
p
l
y
i
n
g
e
lec
t
r
o
m
a
g
n
e
tic
eq
u
ati
o
n
s
.
A
f
t
er
t
h
at
,
t
h
e
cu
r
r
e
n
t
is
f
e
d
i
n
t
o
t
h
e
s
tat
o
r
c
o
ils
s
o
t
h
e
eq
u
a
ti
o
n
s
ar
e
s
o
l
v
e
d
n
u
m
e
r
i
ca
lly
u
s
i
n
g
F
E
M
,
a
n
d
t
h
e
d
y
n
am
ic
p
er
f
o
r
m
a
n
ce
is
a
n
al
y
ze
d
t
o
o
b
tai
n
t
h
e
r
es
u
lts
.
I
f
p
e
r
f
o
r
m
a
n
c
e
i
m
p
r
o
v
e
m
e
n
t
is
n
ee
d
e
d
,
t
h
e
p
r
o
ce
s
s
ca
n
b
e
r
ep
e
ate
d
wit
h
d
esi
g
n
m
o
d
i
f
i
ca
t
io
n
s
.
T
h
r
o
u
g
h
th
is
r
esear
ch
,
th
e
s
tu
d
y
o
b
jectiv
es
to
ad
d
to
th
e
d
ev
elo
p
m
e
n
t
o
f
m
o
to
r
d
esig
n
an
d
o
p
tim
izatio
n
s
ch
em
es,
with
im
p
licatio
n
s
f
o
r
s
ev
er
al
ap
p
licati
o
n
s
s
u
ch
as
E
Vs
r
en
ewa
b
le
en
e
r
g
y
s
y
s
tem
s
(
R
E
S),
an
d
in
d
u
s
tr
ial
r
o
b
o
tics
.
R
o
to
r
m
ag
n
et
s
tr
u
ctu
r
e
o
f
th
e
PMSM
was
p
ar
am
etr
ically
s
u
g
g
e
s
ted
,
in
clu
d
in
g
th
e
v
ar
iatio
n
s
o
f
m
ag
n
et
d
ep
t
h
f
ir
s
t,
th
en
m
a
g
n
et
wid
t
h
an
d
f
in
all
y
ch
an
g
e
o
f
b
o
th
wid
th
an
d
d
e
p
th
.
T
h
e
ef
f
ec
ts
o
f
d
if
f
er
en
t
d
ep
th
-
wid
t
h
d
im
en
s
i
o
n
s
o
n
th
e
c
o
g
g
i
n
g
to
r
q
u
e,
d
-
q
r
elu
ctan
ce
s
,
an
d
b
ac
k
E
MF
o
f
th
e
PMSMs
wer
e
in
v
esti
g
ated
u
s
in
g
t
h
e
FEA
m
eth
o
d
a
n
d
th
e
ANSYS
E
lectr
o
n
ics
s
o
f
twar
e
u
s
in
g
a
v
o
ltag
e
s
o
u
r
ce
an
d
b
o
th
o
f
s
tatic
an
d
tr
an
s
ien
t
an
aly
s
is
o
p
tio
n
s
ettin
g
.
Als
o
,
th
e
o
p
t
im
al
wid
th
/d
ep
th
r
atio
an
d
r
elatio
n
L
_
d
q
also
d
eter
m
in
ed
.
Als
o
,
f
l
u
x
b
a
r
r
ier
(
FB
)
in
V
-
ty
p
e
PMSMs
o
f
f
er
s
a
u
s
ef
u
l
m
eth
o
d
to
im
p
r
o
v
e
th
e
m
o
to
r
p
e
r
f
o
r
m
an
ce
[
3
6
]
,
[
3
7
]
.
B
y
ca
r
ef
u
lly
co
n
tr
o
llin
g
th
e
FB
,
it
ca
n
in
cr
ea
s
e
d
ev
elo
p
ed
to
r
q
u
e,
i
n
cr
ea
s
e
ef
f
ici
en
cy
,
an
d
m
in
im
ize
th
e
to
r
q
u
e
r
ip
p
le,
wh
ich
lead
s
to
o
b
tain
ef
f
icien
t a
n
d
r
eliab
le
m
o
to
r
o
p
er
at
io
n
in
s
ev
er
al
a
p
p
licatio
n
s
.
Fig
u
r
e
1
.
Flo
w
c
h
a
r
t o
f
t
h
e
s
tep
s
in
v
o
lv
ed
in
th
e
p
r
o
ce
s
s
o
f
r
ep
r
esen
tin
g
th
e
e
f
f
ec
t o
f
V
-
s
h
ap
ed
r
o
tatin
g
m
ag
n
et
g
e
o
m
etr
y
3.
RE
SU
L
T
S AN
A
L
YS
I
S
I
n
th
e
c
u
r
r
en
t
s
tu
d
y
,
a
3
-
p
h
ase,
4
-
p
o
le
,
1
2
0
-
Hz,
3
6
0
0
r
p
m
,
V
-
T
y
p
e
PMSM
is
u
s
ed
as
th
e
o
b
ject
o
f
th
e
ar
ticle.
Sev
er
al
in
v
esti
g
atio
n
s
h
av
e
b
ee
n
im
p
lem
e
n
ted
to
s
tu
d
y
th
e
in
f
lu
en
ce
o
f
th
e
PM
d
im
en
s
io
n
ch
a
n
g
e
o
n
th
e
m
ag
n
etic
f
lu
x
d
is
tr
ib
u
tio
n
.
T
h
e
m
o
to
r
p
a
r
am
eter
s
ar
e
in
cl
u
d
ed
in
T
ab
le
1
.
I
t
is
p
o
s
s
ib
le
t
o
g
et
th
e
m
ag
n
etic
f
lu
x
d
is
tr
ib
u
tio
n
b
ased
o
n
th
e
t
r
an
s
ien
t f
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[
3
8
]
,
[
3
9
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
7
6
9
-
7
79
774
T
h
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p
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m
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ased
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4
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Evaluation Warning : The document was created with Spire.PDF for Python.
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4
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DATA AV
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[
1
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[
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