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u
te
t
h
e
m
a
g
n
e
t
i
c
f
l
u
x
a
n
d
r
e
d
u
c
e
lo
c
a
l
s
at
u
r
a
t
i
o
n
a
t
al
i
g
n
e
d
p
o
s
it
i
o
n
s
.
T
h
e
u
s
e
o
f
a
u
n
i
f
o
r
m
a
i
r
g
a
p
wi
t
h
r
o
t
o
r
p
e
r
f
o
r
a
t
i
o
n
s
ca
n
m
i
n
i
m
i
z
e
t
o
r
q
u
e
r
i
p
p
l
e
wi
t
h
o
u
t
p
e
n
a
li
z
i
n
g
t
h
e
a
v
e
r
a
g
e
t
o
r
q
u
e
.
S
u
ch
t
e
c
h
n
i
q
u
e
s
a
r
e
h
i
g
h
l
y
r
e
l
i
a
n
t
o
n
f
i
n
i
t
e
e
l
e
m
e
n
t
a
n
a
l
y
s
is
(
F
E
A
)
i
n
o
r
d
e
r
t
o
p
r
e
d
i
c
t
t
h
e
f
l
u
x
p
a
t
h
s
a
n
d
v
e
r
i
f
y
a
n
y
i
m
p
r
o
v
e
m
e
n
t
i
n
p
e
r
f
o
r
m
a
n
c
e
[
5
]
.
S
i
n
c
e
t
o
r
q
u
e
r
i
p
p
l
e
a
n
d
u
n
e
v
e
n
f
l
u
x
a
l
s
o
e
x
c
i
te
r
a
d
ia
l
f
o
r
c
e
s
p
r
o
d
u
c
i
n
g
v
i
b
r
a
t
i
o
n
a
n
d
a
c
o
u
s
ti
c
n
o
i
s
e
,
r
e
s
e
a
r
c
h
e
r
s
h
a
v
e
i
n
t
e
g
r
at
e
d
s
t
r
u
c
t
u
r
a
l
a
n
d
a
c
o
u
s
t
i
c
m
o
d
e
ls
wi
th
F
E
A
.
I
t
i
s
f
ea
s
i
b
l
e
t
h
a
t
t
h
e
g
e
o
m
e
t
r
i
c
al
c
o
n
s
t
r
u
c
t
io
n
o
p
t
i
m
i
z
a
ti
o
n
t
h
r
o
u
g
h
m
u
l
t
ip
h
y
s
i
c
s
F
E
A
s
i
m
u
l
t
a
n
e
o
u
s
l
y
lo
w
e
r
s
t
o
r
q
u
e
r
i
p
p
le
a
n
d
r
e
d
u
c
e
s
s
o
u
n
d
p
r
e
s
s
u
r
e
l
e
v
e
l
s
,
g
i
v
i
n
g
m
o
r
e
c
o
m
p
l
et
e
i
m
p
r
o
v
e
m
e
n
t
t
o
SR
M
p
e
r
f
o
r
m
a
n
c
e
[
6
]
.
Mo
r
e
in
n
o
v
ativ
e
to
p
o
lo
g
ies
h
av
e
also
b
ee
n
p
r
o
p
o
s
ed
b
ey
o
n
d
co
n
v
en
tio
n
al
d
esig
n
s
,
s
u
ch
as
s
eg
m
en
ted
-
r
o
t
o
r
SR
Ms,
wh
ic
h
im
p
r
o
v
e
f
lu
x
u
n
if
o
r
m
ity
.
Su
ch
m
ac
h
in
es
r
ed
u
ce
f
lu
x
p
at
h
s
an
d
f
lu
x
r
ev
er
s
als
in
th
e
s
tato
r
,
h
en
ce
im
p
r
o
v
i
n
g
to
r
q
u
e
d
en
s
ity
an
d
ef
f
ici
en
cy
.
Xu
et
a
l.
[
7
]
r
ev
iewe
d
th
e
ad
v
an
tag
es
o
f
SS
R
M
s
,
wh
er
ea
s
W
id
m
er
et
a
l.
[
8
]
o
p
tim
ized
a
n
80
-
kW
au
to
m
o
tiv
e
-
s
ca
le
SS
R
M;
to
r
q
u
e
d
en
s
ity
co
m
p
etitiv
en
ess
an
d
r
ed
u
ce
d
r
ip
p
le
wer
e
attain
ed
co
m
p
a
r
ed
to
co
n
v
en
tio
n
al
d
esig
n
s
.
Mo
r
eo
v
er
,
s
im
ilar
s
tr
ateg
ies
ar
e
in
v
esti
g
ated
f
o
r
b
ea
r
in
g
-
less
SR
Ms,
wh
er
e
p
o
le
s
h
ap
in
g
h
as
b
ee
n
ap
p
lied
to
s
im
u
ltan
eo
u
s
ly
b
o
o
s
t
to
r
q
u
e
a
n
d
m
i
n
im
ize
r
ip
p
le
u
n
d
er
c
o
m
b
in
e
d
elec
tr
o
m
a
g
n
etic
an
d
f
o
r
ce
r
e
q
u
ir
em
e
n
ts
[
9
]
.
R
ec
en
t
s
tu
d
ie
s
also
h
ig
h
lig
h
t
ad
v
an
ce
d
o
p
tim
izatio
n
m
eth
o
d
s
,
w
h
ich
c
o
m
b
in
e
p
ar
am
etr
ic
m
o
d
elin
g
with
o
p
tim
izatio
n
s
,
o
r
h
y
b
r
id
tim
e
-
e
f
f
icien
t FE
A
m
o
d
els,
to
ac
ce
ler
ate
th
e
ev
alu
atio
n
o
f
m
a
n
y
d
esig
n
v
ar
iab
les [
1
0
]
.
Mu
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
m
eth
o
d
s
ar
e
also
in
v
esti
g
ated
to
o
b
tain
h
ig
h
er
o
u
tp
u
t
p
o
wer
a
n
d
to
r
q
u
e
in
SR
Ms
[
3
]
.
T
o
ev
alu
ate
th
e
elec
tr
o
m
ag
n
etic
an
d
v
ib
r
o
-
ac
o
u
s
tic
tr
ad
e
-
o
f
f
s
[
1
1
]
,
a
h
y
b
r
id
ac
o
u
s
tic
p
r
ed
ict
io
n
m
o
d
el
h
as
b
ee
n
p
r
o
p
o
s
ed
.
Me
an
wh
ile,
im
p
r
o
v
em
en
ts
in
f
lu
x
d
is
tr
ib
u
tio
n
m
u
s
t
b
e
c
o
-
d
esig
n
e
d
with
cu
r
r
e
n
t
ex
citatio
n
s
tr
ateg
ies to
ac
h
iev
e
r
o
b
u
s
t to
r
q
u
e
-
r
ip
p
le
m
in
im
izatio
n
[
1
2
].
On
th
e
o
th
er
h
a
n
d
,
m
a
n
y
ex
is
tin
g
wo
r
k
s
s
tu
d
ied
th
e
in
v
esti
g
atio
n
an
d
o
p
tim
izatio
n
o
f
th
e
g
eo
m
etr
y
o
f
th
e
SR
Ms,
f
o
cu
s
in
g
o
n
a
s
i
n
g
le
tar
g
et,
s
u
ch
as
to
r
q
u
e
r
ip
p
le
r
ed
u
cti
o
n
,
with
o
u
t
s
im
u
lta
n
eo
u
s
ly
ac
co
u
n
tin
g
f
o
r
ef
f
icien
cy
a
n
d
ac
o
u
s
tic
p
er
f
o
r
m
a
n
ce
[
6
]
.
Oth
er
s
f
o
cu
s
o
n
s
p
ec
if
ic
d
esig
n
v
a
r
iab
les
wh
ile
n
eg
lectin
g
m
an
u
f
ac
tu
r
ab
ilit
y
co
n
s
tr
ain
ts
,
lam
in
atio
n
r
o
b
u
s
tn
ess
,
o
r
p
e
r
f
o
r
m
a
n
ce
co
n
s
is
ten
cy
u
n
d
er
d
if
f
er
en
t
o
p
er
atin
g
co
n
d
itio
n
s
s
u
c
h
as
v
o
ltag
e
v
a
r
iatio
n
,
th
e
r
m
al
e
f
f
ec
ts
,
an
d
h
ig
h
-
s
p
ee
d
tr
an
s
ien
ts
[
1
3
]
.
I
n
t
h
is
p
ap
er
,
SR
M
is
m
o
d
eled
a
n
d
s
im
u
lated
u
s
in
g
th
e
p
ar
am
etr
ic
m
eth
o
d
.
Mo
r
e
p
r
ec
is
ely
,
th
e
s
tato
r
,
r
o
to
r
,
an
d
air
g
a
p
d
esig
n
a
r
e
f
u
r
th
er
im
p
r
o
v
ed
b
y
a
p
p
ly
in
g
th
e
wh
ite
wh
ale
al
g
o
r
ith
m
an
d
in
te
g
r
ated
with
An
s
y
s
Ma
x
well
s
o
f
twar
e.
C
o
n
s
eq
u
en
tly
,
th
e
p
r
ed
icted
r
esu
lts
s
h
o
w
a
b
etter
m
o
to
r
d
e
s
ig
n
,
wh
er
e
th
e
d
is
tr
ib
u
tio
n
a
n
d
f
lo
w
o
f
m
ag
n
etic
f
lu
x
b
etwe
en
its
d
if
f
er
en
t p
a
r
ts
im
p
r
o
v
e
d
,
r
aisi
n
g
t
h
e
to
r
q
u
e
a
n
d
s
u
b
s
eq
u
e
n
tly
,
th
e
o
v
er
all
ef
f
icien
cy
.
2.
A
F
UNDA
M
E
N
T
AL
D
E
S
I
G
N
M
E
T
H
O
D
F
O
R
T
H
E
S
R
M
T
h
e
SR
M
d
esig
n
p
r
o
ce
s
s
f
o
cu
s
es
o
n
th
e
d
eter
m
in
atio
n
o
f
th
e
m
ain
g
eo
m
etr
ic
d
i
m
en
s
io
n
s
,
esp
ec
ially
th
e
in
n
er
an
d
o
u
ter
d
iam
eter
s
,
wh
ich
will
b
e
u
s
ed
as
th
e
b
asis
f
o
r
a
m
o
r
e
d
etailed
d
esig
n
o
f
b
o
th
s
tato
r
a
n
d
r
o
to
r
.
T
h
is
is
f
o
llo
wed
b
y
g
eo
m
etr
ic
d
e
f
in
itio
n
;
th
e
p
e
r
f
o
r
m
a
n
ce
ev
alu
atio
n
is
v
er
if
ied
in
ter
m
s
o
f
elec
tr
o
m
ag
n
etic
t
o
r
q
u
e
an
d
o
v
er
all
ef
f
icien
c
y
.
M
u
lti
-
v
ar
iab
le
in
ter
d
e
p
en
d
e
n
cies
in
h
er
en
tly
af
f
ec
t
t
h
e
ef
f
icien
cy
o
f
th
e
m
o
to
r
,
s
u
ch
as
elec
tr
o
m
a
g
n
etic
a
n
d
co
r
e
lo
s
s
es
d
u
e
to
th
e
i
n
ter
n
al
c
o
n
f
ig
u
r
atio
n
,
s
elec
ted
co
n
s
tr
u
ctio
n
m
ater
ials
,
s
tato
r
win
d
in
g
tech
n
iq
u
e,
an
d
g
eo
m
etr
ical
s
h
ap
in
g
o
f
th
e
p
er
ip
h
er
al
r
o
to
r
ed
g
es
[
1
3
]
,
[1
4
]
.
T
o
e
n
s
u
r
e
ac
cu
r
ac
y
in
p
er
f
o
r
m
a
n
ce
p
r
e
d
ictio
n
,
ANSYS
MA
XW
E
L
L
s
o
f
twar
e
is
e
m
p
lo
y
ed
to
p
e
r
f
o
r
m
two
-
d
im
en
s
io
n
al
f
in
ite
elem
e
n
t
an
aly
s
is
(
FEA)
,
u
s
in
g
th
e
d
ev
elo
p
e
d
m
o
to
r
m
o
d
el
with
th
e
c
h
ar
ac
ter
is
tics
s
p
ec
if
ied
in
T
ab
le
1
.
Mo
r
eo
v
er
,
th
e
w
h
ale
o
p
tim
izatio
n
alg
o
r
ith
m
(
W
OA)
is
in
teg
r
at
ed
in
to
th
e
d
esig
n
f
r
am
ewo
r
k
to
s
ea
r
ch
f
o
r
th
e
o
p
tim
al
v
alu
es o
f
th
e
k
ey
d
esig
n
v
ar
iab
les.
T
h
e
g
eo
m
etr
y
o
f
th
e
s
tato
r
an
d
r
o
to
r
lam
in
atio
n
s
s
ig
n
if
ican
t
ly
af
f
ec
ts
th
e
m
ag
n
etic
p
er
f
o
r
m
an
ce
an
d
ef
f
icien
cy
o
f
s
witch
ed
r
elu
cta
n
ce
m
o
to
r
s
(
SR
Ms)
.
Op
tim
ized
p
r
o
f
iles
ca
n
r
ed
u
ce
co
r
e
lo
s
s
es,
im
p
r
o
v
e
f
l
u
x
d
is
tr
ib
u
tio
n
,
an
d
en
h
an
ce
to
r
q
u
e
[1
5
]
.
T
h
e
s
tato
r
an
d
r
o
to
r
wer
e
m
o
d
eled
in
Ma
x
well
s
o
f
twar
e
u
s
in
g
th
e
p
ar
am
etr
ic
m
eth
o
d
an
d
r
elev
a
n
t
m
ec
h
an
ical
d
esig
n
eq
u
atio
n
s
.
T
h
e
r
o
to
r
s
h
ap
e,
wh
ich
d
e
ter
m
in
es
r
elu
ctan
ce
to
r
q
u
e,
is
d
esig
n
e
d
to
alig
n
with
en
er
g
ized
s
tato
r
p
o
les,
m
in
im
izin
g
m
ag
n
etic
r
esis
tan
ce
an
d
im
p
r
o
v
in
g
o
v
er
all
p
er
f
o
r
m
a
n
ce
[
1
6
]
,
[
1
7
]
.
Fig
u
r
e
1
s
h
o
ws a
cr
o
s
s
-
s
ec
tio
n
o
f
s
tato
r
a
n
d
r
o
to
r
g
eo
m
etr
y
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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&
Dr
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t
I
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N:
2088
-
8
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Is
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alan
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f
p
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m
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ce
g
iv
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ea
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lier
[
1
8
]
.
3.
F
E
M
M
E
T
H
O
DS A
ND
M
A
XWE
L
L
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Q
UAT
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h
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f
in
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elem
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t
m
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(
FEM
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is
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o
f
th
e
m
o
s
t
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o
p
ted
n
u
m
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tech
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tr
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m
a
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c
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m
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t
h
o
d
s
f
a
l
l
s
h
o
r
t
[
1
7
]
.
AN
SY
S
M
A
XW
E
L
L
is
a
s
o
f
t
wa
r
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t
h
a
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-
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a
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l
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x
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n
s
i
ty
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
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s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
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20
2
6
:
167
5
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1
6
8
7
1678
–
f
ield
s
tr
en
g
th
(
B
-
H)
m
ater
ia
l
b
eh
av
i
o
r
,
a
n
d
p
r
e
d
icts
th
e
p
e
r
f
o
r
m
a
n
ce
o
f
a
m
ac
h
in
e
u
n
d
er
ch
an
g
in
g
lo
ad
an
d
ex
citatio
n
co
n
d
itio
n
s
[
19
]
.
T
h
is
co
m
p
u
tatio
n
al
f
r
am
ewo
r
k
allo
ws
d
esig
n
er
s
n
o
t
o
n
ly
to
esti
m
ate
s
tatic
an
d
d
y
n
am
ic
to
r
q
u
e
b
u
t
also
t
o
an
aly
ze
lo
s
s
es,
ef
f
icien
cy
,
a
n
d
th
er
m
al
in
ter
ac
tio
n
s
m
o
r
e
p
r
ec
is
ely
[
2
0
]
b
y
ap
p
ly
in
g
m
ater
ial
p
r
o
p
er
ties
a
n
d
s
ettin
g
b
o
u
n
d
a
r
y
c
o
n
d
itio
n
s
in
s
ev
er
al
s
tep
s
,
as illu
s
tr
ate
d
in
Fig
u
r
e
2
[
2
1
].
FEM
-
b
ased
s
im
u
latio
n
s
ca
n
b
e
in
teg
r
ated
with
o
p
tim
izatio
n
alg
o
r
ith
m
s
s
u
ch
as
W
OA
to
ex
p
lo
r
e
lar
g
e
d
esig
n
s
p
ac
es
an
d
id
e
n
tify
o
p
tim
al
g
e
o
m
etr
ical
c
o
n
f
ig
u
r
atio
n
s
th
at
im
p
r
o
v
e
f
l
u
x
d
is
tr
ib
u
tio
n
a
n
d
ef
f
icien
cy
[
2
2
]
,
[
2
3
]
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el,
s
h
o
wn
in
Fig
u
r
e
3
(
a
)
,
is
an
aly
ze
d
u
s
in
g
n
o
n
lin
ea
r
m
ater
ial
ch
ar
ac
ter
is
tics
,
wh
ile
th
e
co
r
r
esp
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n
d
in
g
m
esh
g
en
e
r
atio
n
u
s
ed
f
o
r
th
e
FEA
is
illu
s
tr
ated
in
Fig
u
r
e
3
(
b
)
.
T
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
f
o
cu
s
es
o
n
k
ey
d
esig
n
p
ar
am
eter
s
,
in
clu
d
in
g
s
tato
r
an
d
r
o
to
r
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o
k
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s
,
s
lo
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m
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,
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d
ai
r
g
ap
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g
th
,
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h
a
n
ce
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e
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tr
o
m
ag
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etic
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m
an
ce
a
n
d
o
v
er
all
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f
ic
ien
cy
o
f
t
h
e
SR
M.
Fig
u
r
e
2
.
FEM
s
tep
s
(
a)
(
b
)
Fig
u
r
e
3
.
SR
M
p
r
o
p
o
s
ed
m
o
d
el
: (
a)
n
o
n
lin
ea
r
m
ater
ial
ch
a
r
ac
ter
is
tics
an
d
(
b
)
m
esh
in
g
an
aly
s
is
f
o
r
SR
M
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
FEA
-
b
a
s
ed
o
p
timiz
a
tio
n
o
f sw
itch
es fo
r
r
elu
cta
n
ce
mo
to
r
s
(
Hib
a
E
s
a
m
A
z
iz
)
1679
4.
WH
AL
E
O
P
T
I
M
I
Z
A
T
I
O
N
AL
G
O
RI
T
H
M
(
WO
A)
T
h
e
p
r
o
p
o
s
ed
W
OA
is
a
r
ec
en
tly
in
tr
o
d
u
c
ed
n
atu
r
e
-
in
s
p
ir
ed
m
etah
eu
r
is
tic
d
ev
elo
p
e
d
b
y
Mir
jalili
an
d
L
ewis
[
2
4
]
,
wh
ich
h
as
b
e
en
in
s
p
ir
ed
by
th
e
b
u
b
b
le
-
n
et
h
u
n
tin
g
s
tr
ateg
y
o
f
h
u
m
p
b
ac
k
wh
ales
[
2
5
]
.
W
OA
h
as
g
ain
ed
s
ig
n
if
ican
t
i
n
ter
est
an
d
b
r
o
ad
c
o
n
s
id
er
atio
n
o
win
g
to
its
s
im
p
licity
,
ef
f
ec
tiv
e
g
l
o
b
al
s
ea
r
ch
ab
ilit
y
,
an
d
its
p
o
ten
tial
f
o
r
b
alan
cin
g
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
wh
ile
s
o
lv
in
g
co
m
p
lex
e
n
g
in
e
er
in
g
o
p
tim
izatio
n
p
r
o
b
lem
s
[
2
6
]
.
I
n
elec
tr
ical
m
ac
h
in
e
d
esig
n
,
t
h
e
in
teg
r
at
io
n
o
f
th
e
W
OA
with
FEA
h
as
alr
ea
d
y
b
ee
n
im
p
lem
en
ted
f
o
r
id
e
n
tify
in
g
o
p
tim
al
g
eo
m
etr
ical
p
ar
am
et
er
s
ca
p
ab
le
o
f
im
p
r
o
v
in
g
p
e
r
f
o
r
m
a
n
ce
m
etr
ics
r
eg
ar
d
in
g
to
r
q
u
e,
ef
f
icien
cy
,
a
n
d
f
lu
x
d
is
tr
ib
u
tio
n
[
2
7
]
,
[
2
8
]
.
Fig
u
r
e
4
illu
s
tr
ates
th
e
p
r
in
ci
p
les
o
f
o
p
er
atio
n
o
f
th
e
W
OA.
T
o
im
p
lem
en
t
W
OA
f
o
r
th
e
p
r
o
p
o
s
ed
SR
M
ef
f
ec
tiv
ely
,
th
r
ee
cr
itical
d
esig
n
v
ar
iab
les
h
av
e
b
ee
n
s
elec
ted
as
o
p
tim
izatio
n
in
p
u
t
s
.
T
h
e
f
ir
s
t
is
s
tato
r
y
o
k
e
wi
d
th
,
wh
ich
is
r
elate
d
t
o
th
e
c
ar
r
y
in
g
ca
p
ac
ity
o
f
m
ag
n
etic
f
lu
x
in
th
e
s
tato
r
,
p
r
ev
en
tin
g
its
co
r
e
f
r
o
m
s
atu
r
atio
n
,
a
n
d
g
en
er
ally
af
f
ec
tin
g
to
r
q
u
e
p
r
o
d
u
ctio
n
a
n
d
ef
f
icien
cy
[
2
7
]
.
T
h
e
s
ec
o
n
d
is
th
e
r
o
to
r
y
o
k
e
wid
th
,
d
ef
in
in
g
th
e
r
etu
r
n
p
at
h
o
f
m
ag
n
etic
f
lu
x
an
d
h
a
v
in
g
a
d
ir
ec
t
ef
f
ec
t
o
n
to
r
q
u
e
ca
p
ab
i
lity
an
d
m
ag
n
etic
lo
ad
in
g
,
p
l
u
s
o
v
er
all
ef
f
icien
cy
in
en
e
r
g
y
co
n
v
er
s
io
n
.
T
h
e
th
ir
d
is
th
e
air
-
g
ap
d
im
en
s
io
n
,
m
o
r
e
d
ec
is
iv
e
in
s
h
ap
in
g
th
e
f
lu
x
lin
k
ag
e,
i
n
d
u
ctan
ce
v
a
r
iatio
n
,
an
d
to
r
q
u
e
r
ip
p
le,
s
in
ce
e
v
en
m
in
o
r
v
a
r
iatio
n
in
th
is
p
ar
am
eter
s
tr
o
n
g
ly
in
f
lu
en
ce
s
th
e
s
m
o
o
t
h
n
ess
o
f
to
r
q
u
e
a
n
d
ef
f
icien
cy
in
t
h
e
m
ac
h
in
e
[
29
]
,
as illu
s
tr
ated
in
T
ab
le
2
.
Fig
u
r
e
4
.
Alg
o
r
ith
m
f
l
o
wch
ar
t
f
o
r
th
e
p
r
o
p
o
s
ed
W
OA
T
ab
le
2
.
T
h
e
v
ar
iab
le
lim
itatio
n
s
f
o
r
th
e
p
r
o
p
o
s
ed
m
o
d
el
V
a
r
i
a
b
l
e
s
S
y
mb
o
l
U
n
i
t
s
R
a
n
g
e
s
W
i
d
t
h
o
f
st
a
t
o
r
y
o
k
e
W
Ys
mm
0
.
3
3
<
W
Ys
<
0
.
9
7
W
i
d
t
h
o
f
r
o
t
o
r
y
o
k
e
W
YR
mm
0
.
3
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b
r2
<
0
.
9
S
t
a
t
o
r
t
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t
h
a
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Ts
mm
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1
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s
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h
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r
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A
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r
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p
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2
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6
5
5.
O
P
T
I
M
I
Z
AT
I
O
N
ST
RAT
E
G
Y
AND
CO
NST
RAIN
T
S
I
n
t
h
e
ANS
YS M
a
x
we
ll
en
v
i
r
o
n
m
en
t,
t
h
e
p
r
e
lim
in
a
r
y
SR
M
g
e
o
m
et
r
y
is
f
ir
s
t
m
o
d
ell
ed
a
n
d
s
im
u
l
ate
d
,
an
d
its
elec
tr
o
m
ag
n
etic
p
er
f
o
r
m
an
ce
is
m
e
asu
r
ed
in
ter
m
s
o
f
to
r
q
u
e
wav
ef
o
r
m
,
o
u
tp
u
t
p
o
wer
,
ef
f
icien
cy
,
p
o
wer
f
ac
to
r
,
an
d
in
p
u
t
cu
r
r
en
t.
T
h
e
ac
cu
r
ac
y
o
f
th
is
an
aly
ti
ca
l
m
o
d
el
is
th
en
v
er
if
ied
b
y
p
er
f
o
r
m
in
g
FEA
to
en
s
u
r
e
th
at
th
e
elec
tr
o
m
a
g
n
et
ic
b
eh
av
io
r
u
n
d
e
r
r
ea
lis
tic
co
n
d
itio
n
s
is
f
aith
f
u
lly
r
ep
r
esen
ted
.
Fo
llo
win
g
th
is
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.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
167
5
-
1
6
8
7
1680
v
alid
atio
n
,
a
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
f
r
am
ewo
r
k
is
u
tili
ze
d
th
at
in
teg
r
ates
th
e
W
OA
with
FEA
ev
alu
atio
n
s
to
s
u
cc
ess
iv
ely
tu
n
e
th
e
ch
o
s
en
d
esig
n
v
ar
iab
l
es
in
th
e
s
ea
r
ch
f
o
r
th
e
m
o
s
t
p
r
o
m
is
in
g
s
ettin
g
.
E
f
f
icien
cy
is
to
b
e
m
ax
i
m
ized
,
an
d
to
r
q
u
e
r
ip
p
le
m
in
im
ize
d
in
th
e
o
p
tim
izatio
n
wh
ile
k
ee
p
in
g
th
e
m
ac
h
in
e
s
tab
le.
Fo
r
en
s
u
r
in
g
f
ea
s
ib
ilit
y
,
T
ab
le
3
d
ef
i
n
es
th
e
o
p
tim
izatio
n
co
n
s
tr
ain
ts
th
r
o
u
g
h
s
p
ec
if
icatio
n
o
f
th
e
b
o
u
n
d
s
o
n
th
e
u
p
p
er
an
d
lo
wer
lim
its
o
f
th
e
v
ar
iab
les
an
d
th
e
id
ea
l
tar
g
et
v
alu
es
o
f
th
e
o
b
jectiv
es,
alo
n
g
with
ass
o
ciate
d
weig
h
t
f
ac
to
r
s
.
T
h
e
s
e
weig
h
ts
(
w
i
)
,
with
in
t
h
e
A
NSYS
o
p
tim
izatio
n
en
v
ir
o
n
m
en
t,
v
a
r
y
b
etwe
en
1
an
d
5
a
n
d
a
r
e
b
ased
o
n
th
e
p
r
io
r
ity
r
a
n
k
in
g
o
f
t
h
e
d
esig
n
e
r
;
th
at
is
,
co
r
r
esp
o
n
d
in
g
ly
lar
g
er
weig
h
ts
(
to
b
e
ass
ig
n
ed
to
h
ig
h
e
r
-
p
r
i
o
r
ity
o
b
j
ec
tiv
es)
d
ictate
s
tr
o
n
g
er
em
p
h
asis
d
u
r
in
g
th
e
s
ea
r
ch
p
r
o
ce
s
s
.
T
ab
le
3
.
Op
tim
izatio
n
co
n
s
tr
ai
n
ts
f
o
r
th
e
p
r
o
p
o
s
ed
(
W
OA)
D
e
scri
p
t
i
o
n
O
p
t
i
mi
z
a
t
i
o
n
c
o
n
s
t
r
a
i
n
t
C
o
n
st
r
a
i
n
t
e
q
u
a
t
i
o
n
Wi
Ef
f
i
c
i
e
n
c
y
%
(
η)
7
9
<
η
<
1
0
0
1
+
(
η
-
i
n
i
t
i
a
l
v
a
l
u
e
)
*
t
a
r
g
e
t
v
a
l
u
e
/
d
i
f
f
e
r
e
n
c
e
v
a
l
u
e
5
To
r
q
u
e
(
T)
4
.
7
7
<
T
<
9
1
+
(T
-
i
n
i
t
i
a
l
v
a
l
u
e
)
*
t
a
r
g
e
t
v
a
l
u
e
/
d
i
f
f
e
r
e
n
c
e
v
a
l
u
e
4
B
(
Te
s
l
a
)
2
<
B
<
4
1
+
(B
-
i
n
i
t
i
a
l
v
a
l
u
e
)
*
t
a
r
g
e
t
v
a
l
u
e
/
d
i
f
f
e
r
e
n
c
e
v
a
l
u
e
3
6.
SI
M
UL
A
T
I
O
N
O
P
T
I
M
I
Z
A
T
I
O
N
R
E
SU
L
T
S AN
D
D
I
S
CUSS
I
O
N
T
h
e
in
itial
p
ar
am
et
r
ic
m
o
d
el
is
cr
ea
ted
in
An
s
y
s
Ma
x
well,
f
o
llo
wed
b
y
v
ar
iab
le
a
n
aly
s
is
an
d
an
o
p
tim
izatio
n
p
r
o
ce
s
s
u
s
in
g
t
h
e
p
r
o
p
o
s
ed
wh
ite
wh
ale
o
p
tim
izatio
n
alg
o
r
ith
m
im
p
le
m
en
ted
in
MA
T
L
AB
.
T
h
e
p
r
ed
icted
r
esu
lts
ar
e
t
h
en
i
n
t
eg
r
ated
b
ac
k
in
to
th
e
An
s
y
s
s
o
f
twar
e
f
o
r
v
alid
atio
n
.
I
t
ca
n
b
e
n
o
ticed
th
at
a
s
ig
n
if
ican
t
in
cr
ea
s
e
in
th
e
v
al
u
e
o
f
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
ca
n
b
e
o
b
tain
e
d
,
as
s
h
o
w
n
in
Fig
u
r
e
5
.
T
h
is
in
cr
ea
s
e
is
d
u
e
to
an
im
p
r
o
v
e
m
en
t
in
th
e
r
o
to
r
y
o
k
e
wid
th
,
as
th
e
o
p
tim
al
v
alu
e
f
o
r
th
e
p
r
o
p
o
s
ed
d
esig
n
is
0
.
3
6
m
m
.
Fu
r
th
e
r
m
o
r
e.
An
i
m
p
r
o
v
e
m
en
t
in
th
e
d
is
tr
ib
u
tio
n
o
f
m
a
g
n
etic
f
lu
x
tr
an
s
m
itted
f
r
o
m
th
e
s
tato
r
to
th
e
r
o
to
r
ac
r
o
s
s
th
e
air
g
a
p
ca
n
b
e
ac
h
iev
e
d
.
I
n
ad
d
itio
n
to
t
h
e
im
p
r
o
v
e
m
e
n
t
o
f
th
e
av
er
a
g
e
to
r
q
u
e,
a
s
ig
n
if
ican
t
r
e
d
u
ctio
n
o
f
th
e
to
r
q
u
e
r
ip
p
le
is
o
b
s
er
v
ed
.
Fro
m
th
e
o
b
tain
ed
cu
r
v
es
in
Fig
u
r
e
6
,
it
ca
n
b
e
s
ee
n
th
at
th
e
in
itial
d
esig
n
h
as
s
ig
n
if
ican
t
d
ip
s
an
d
o
s
cillatio
n
s
in
th
e
to
r
q
u
e,
wh
e
r
ea
s
th
e
o
p
tim
ized
d
esig
n
h
as
s
m
o
o
th
er
to
r
q
u
e
ch
ar
ac
te
r
is
tics
with
f
ewe
r
ab
r
u
p
t
f
lu
ctu
atio
n
s
.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
o
p
tim
ized
to
p
o
lo
g
y
h
as
a
lo
wer
to
r
q
u
e
r
ip
p
le
v
alu
e
o
f
3
6
.
6
%
th
an
th
e
in
itial
d
esig
n
v
alu
e
o
f
5
2
%,
wh
ich
co
n
f
i
r
m
s
th
e
ef
f
ec
tiv
e
n
ess
o
f
th
e
p
r
o
p
o
s
ed
o
p
tim
iz
atio
n
ap
p
r
o
ac
h
.
T
h
is
r
ed
u
ctio
n
o
f
to
r
q
u
e
r
ip
p
le
is
m
ain
ly
attr
ib
u
ted
t
o
th
e
b
etter
d
is
tr
ib
u
tio
n
o
f
th
e
m
ag
n
etic
f
l
u
x
a
n
d
th
e
s
m
o
o
th
er
v
ar
iatio
n
o
f
t
h
e
p
h
ase
in
d
u
cta
n
ce
with
th
e
r
o
to
r
p
o
s
itio
n
.
T
h
u
s
,
th
e
p
r
o
p
o
s
ed
d
esig
n
n
o
t
o
n
ly
im
p
r
o
v
es
th
e
to
r
q
u
e
p
r
o
d
u
ctio
n
b
u
t
also
r
e
d
u
ce
s
th
e
v
ib
r
atio
n
,
ac
o
u
s
tic
n
o
is
e
,
an
d
m
ec
h
a
n
ical
s
tr
ess
,
wh
ich
im
p
r
o
v
es
th
e
o
v
er
all
SR
M
p
er
f
o
r
m
an
ce
.
Fig
u
r
e
7
(
a)
s
h
o
ws
th
e
d
is
tr
ib
u
ted
m
ag
n
etic
f
ield
d
en
s
ity
f
o
r
th
e
b
asic
m
o
d
el
with
a
m
ax
im
u
m
v
alu
e
o
f
(
2
.
2
6
8
7
T
)
,
in
d
icatin
g
a
r
el
ativ
ely
lo
wer
m
ag
n
etic
f
lu
x
d
en
s
ity
.
I
n
co
n
tr
ast,
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u
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7
(
b
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e
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im
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1
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f
o
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er
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a
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ce
o
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s
witch
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m
ac
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Fig
u
r
e
5
.
C
o
m
p
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r
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o
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f
to
r
q
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e
r
esu
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o
r
b
asic a
n
d
o
p
tim
iz
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m
o
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els
B
a
si
c
d
e
s
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g
n
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p
t
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mal
d
e
si
g
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
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lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
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n
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o
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o
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els
(
a)
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)
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u
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.
Ma
g
n
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ield
d
is
tr
i
b
u
tio
n
:
(
a
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b
asic m
o
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n
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al
m
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el
Fig
u
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Air
g
ap
f
l
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lin
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ath
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
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lec
&
Dr
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s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
167
5
-
1
6
8
7
1682
On
th
e
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th
er
h
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n
d
,
t
h
e
an
aly
s
is
o
f
cu
r
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en
t
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o
r
m
ch
ar
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tics
i
s
p
r
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ted
in
Fig
u
r
e
9
.
T
h
e
p
r
ed
icted
r
esu
lts
d
em
o
n
s
tr
ate
im
p
r
o
v
e
d
s
tab
ilit
y
a
n
d
p
er
f
o
r
m
an
ce
o
f
t
h
e
o
p
tim
ized
m
o
d
e
l.
T
h
e
p
ea
k
v
al
u
e
o
f
th
e
cu
r
r
en
t
in
th
e
o
p
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ized
m
o
d
el
is
r
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ce
d
to
5
.
1
6
4
5
A
co
m
p
ar
ed
to
5
.
4
6
0
5
A
in
th
e
b
asic
d
esig
n
.
T
h
is
r
ed
u
ctio
n
in
p
ea
k
cu
r
r
en
t
e
f
f
ec
tiv
ely
m
in
im
izes
cu
r
r
e
n
t
f
lu
ctu
atio
n
s
an
d
c
o
n
tr
ib
u
te
s
to
a
s
ig
n
if
ican
t
en
h
an
ce
m
e
n
t
in
ef
f
icien
cy
.
M
o
r
eo
v
e
r
,
th
e
p
ea
k
cu
r
r
en
t
r
ed
u
ctio
n
d
ec
r
ea
s
es
th
e
s
witch
in
g
s
tr
ess
in
th
e
p
o
wer
s
em
ico
n
d
u
cto
r
d
ev
ices
,
wh
ic
h
lead
s
to
im
p
r
o
v
e
d
r
eliab
il
ity
an
d
r
e
d
u
ce
d
th
er
m
al
lo
a
d
in
g
.
Fu
r
t
h
er
m
o
r
e,
s
m
o
o
th
er
cu
r
r
e
n
t
tr
an
s
itio
n
s
wo
u
ld
h
av
e
th
e
ad
v
an
tag
e
o
f
r
e
d
u
ce
d
elec
tr
o
m
a
g
n
etic
in
ter
f
er
en
ce
(
E
MI
)
,
wh
ich
is
an
im
p
o
r
tan
t
is
s
u
e
i
n
SR
M
d
r
iv
e
s
y
s
tem
s
.
T
h
u
s
,
th
e
p
r
o
p
o
s
ed
g
eo
m
etr
ic
o
p
tim
izatio
n
c
an
n
o
t
o
n
ly
im
p
r
o
v
e
th
e
m
o
to
r
elec
tr
o
m
ag
n
etic
p
er
f
o
r
m
an
ce
,
b
u
t
also
en
h
a
n
ce
th
e
o
v
er
all
ef
f
icien
c
y
a
n
d
s
tab
ilit
y
o
f
t
h
e
co
r
r
esp
o
n
d
in
g
p
o
wer
elec
tr
o
n
i
c
co
n
v
er
te
r
[
3
0
].
T
h
e
ef
f
icien
c
y
o
f
s
witch
ed
r
el
u
ctan
ce
m
o
t
o
r
s
(
SR
Ms)
is
g
r
e
atly
af
f
ec
ted
b
y
d
if
f
er
e
n
t
ty
p
e
s
o
f
p
o
wer
lo
s
s
es
in
s
id
e
th
e
m
ac
h
in
e.
T
h
e
lo
s
s
es
ar
e
u
s
u
ally
class
if
ied
in
to
co
p
p
er
lo
s
s
es,
co
r
e
(
ir
o
n
)
lo
s
s
es
,
an
d
s
tr
ay
lo
s
s
es.
C
o
p
p
er
lo
s
s
es
ar
e
r
elat
ed
to
th
e
r
esis
tan
ce
o
f
t
h
e
s
tato
r
win
d
in
g
s
an
d
ar
e
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
to
t
h
e
m
ag
n
itu
d
e
an
d
wa
v
ef
o
r
m
o
f
t
h
e
p
h
ase
cu
r
r
en
t
[
3
1
]
.
C
o
r
e
l
o
s
s
es
ar
e
ca
u
s
ed
b
y
h
y
s
ter
esis
an
d
ed
d
y
cu
r
r
en
t
ef
f
ec
ts
in
th
e
m
ag
n
etic
m
at
er
ials
an
d
ar
e
v
er
y
s
en
s
itiv
e
to
th
e
f
lu
x
d
e
n
s
ity
d
is
tr
ib
u
tio
n
an
d
s
witch
in
g
f
r
eq
u
e
n
cy
.
Mo
r
eo
v
er
,
leak
ag
e
f
lu
x
,
h
a
r
m
o
n
ic
c
o
m
p
o
n
en
ts
,
an
d
n
o
n
-
id
ea
l
elec
tr
o
m
ag
n
etic
ef
f
ec
ts
ca
u
s
e
s
tr
ay
lo
s
s
es,
wh
ich
ar
e
h
ar
d
to
ac
cu
r
ately
m
o
d
el
b
u
t
co
n
tr
i
b
u
te
to
th
e
o
v
er
all
ef
f
icie
n
cy
d
e
g
r
ad
atio
n
.
A
b
etter
f
lu
x
d
is
tr
ib
u
tio
n
an
d
s
m
aller
cu
r
r
e
n
t
p
ea
k
s
in
SR
Ms
ca
n
g
r
ea
tly
cu
t
d
o
wn
co
p
p
er
an
d
co
r
e
lo
s
s
es,
th
u
s
in
cr
ea
s
in
g
ef
f
icien
cy
an
d
th
er
m
al
p
er
f
o
r
m
an
ce
[
3
2
].
Fig
u
r
e
9
.
L
i
n
e
cu
r
r
en
t o
f
SR
M
Fig
u
r
e
1
0
co
m
p
ar
es
th
e
p
r
ed
i
cted
co
p
p
e
r
lo
s
s
es
b
etwe
en
t
h
e
b
asic
an
d
th
e
o
p
tim
ized
d
esig
n
.
T
h
e
o
p
tim
ized
d
esig
n
s
h
o
ws
a
r
e
d
u
ctio
n
in
th
e
co
p
p
er
lo
s
s
es
to
(
1
2
2
.
9
W)
,
with
th
e
p
ea
k
v
alu
e
f
o
r
t
h
e
b
asic
d
esig
n
r
ea
ch
in
g
(
1
1
6
.
3
W
)
.
Fi
g
u
r
e
s
1
1
a
n
d
1
2
d
ep
ict
th
e
p
r
e
d
icted
r
esu
lts
f
o
r
th
e
s
tr
an
d
e
d
an
d
co
r
e
l
o
s
s
es
o
f
th
e
b
asic
an
d
th
e
o
p
tim
u
m
p
r
o
p
o
s
ed
m
o
d
els
,
r
esp
ec
tiv
ely
.
Stra
n
d
ed
lo
s
s
es
r
ed
u
ce
d
f
r
o
m
(
4
3
W
)
to
(
2
3
.
1
W
)
in
th
e
o
p
tim
al
m
o
d
el
;
th
is
r
ed
u
ctio
n
in
lo
s
s
es
in
d
icate
s
im
p
r
o
v
ed
ef
f
icien
c
y
an
d
b
etter
th
er
m
al
m
an
a
g
em
en
t
in
th
e
o
p
tim
ized
m
o
to
r
d
esig
n
.
Fig
u
r
e
s
1
3
(
a)
an
d
1
3
(
b
)
,
th
e
b
asic
m
o
d
el
h
as
an
ef
f
icien
cy
o
f
7
9
%
an
d
s
h
o
ws
a
g
r
e
at
d
ea
l
o
f
v
ar
iatio
n
,
m
e
an
in
g
th
at
th
e
o
p
er
atio
n
al
s
tab
ilit
y
is
p
o
o
r
,
p
a
r
t
icu
lar
ly
at
lo
w
a
n
d
m
ed
iu
m
s
p
ee
d
s
.
Ho
wev
er
,
th
e
o
p
tim
ized
d
esig
n
g
iv
es
a
h
ig
h
er
ef
f
icien
cy
o
f
ar
o
u
n
d
8
4
%,
wh
ich
im
p
lies
a
m
o
r
e
ef
f
icien
t
en
er
g
y
c
o
n
v
e
r
s
io
n
.
T
h
e
g
ai
n
s
ar
e
d
u
e
to
th
e
im
p
r
o
v
em
en
t
o
f
m
a
g
n
etic
f
l
u
x
d
i
s
tr
ib
u
tio
n
an
d
l
o
w
co
r
e
lo
s
s
an
d
e
n
s
u
r
e
a
m
o
r
e
s
tab
le
p
er
f
o
r
m
a
n
ce
o
f
th
e
SR
M
u
n
d
er
v
ar
iab
le
-
s
p
ee
d
o
p
e
r
at
io
n
.
T
ab
le
4
co
m
p
ar
es
th
e
p
er
f
o
r
m
an
ce
ch
ar
ac
ter
is
tics
o
f
th
e
b
asic
an
d
o
p
tim
ized
m
o
d
els
in
d
etail,
wh
ich
s
h
o
ws
th
e
o
v
er
all
im
p
r
o
v
em
e
n
t
o
b
tain
ed
u
s
in
g
th
e
p
r
o
p
o
s
ed
o
p
tim
izatio
n
te
ch
n
iq
u
e.
I
t
clea
r
ly
in
d
icate
s
th
e
im
p
r
o
v
e
m
en
ts
o
f
k
ey
p
a
r
am
eter
s
lik
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e,
ef
f
icien
c
y
,
an
d
lo
s
s
r
e
d
u
ctio
n
.
T
h
ese
r
esu
lts
v
er
if
y
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
o
p
tim
izatio
n
ap
p
r
o
ac
h
to
im
p
r
o
v
e
th
e
o
v
er
a
ll
p
er
f
o
r
m
an
ce
a
n
d
s
tab
ilit
y
o
f
th
e
SR
M.
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
FEA
-
b
a
s
ed
o
p
timiz
a
tio
n
o
f sw
itch
es fo
r
r
elu
cta
n
ce
mo
to
r
s
(
Hib
a
E
s
a
m
A
z
iz
)
1683
Fig
u
r
e
1
0
.
SR
M
c
o
p
p
er
Fig
u
r
e
1
1
.
SR
M
s
tr
an
d
ed
lo
s
s
es
Fig
u
r
e
1
2
.
SR
M
c
o
r
e
lo
s
s
es
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.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
167
5
-
1
6
8
7
1684
(
a)
(
b
)
Fig
u
r
e
1
3
.
E
f
f
icien
c
y
o
f
SR
M
:
(
a)
e
f
f
icien
c
y
-
t
im
e
an
d
(
b
)
e
f
f
icien
cy
-
s
p
ee
d
T
ab
le
4
.
Ou
tp
u
t c
h
ar
ac
ter
is
tics
f
o
r
th
e
b
asic a
n
d
th
e
p
r
o
p
o
s
ed
m
o
d
el
o
f
th
e
m
o
to
r
M
o
t
o
r
c
h
a
r
a
c
t
e
r
i
st
i
c
s
B
a
si
c
m
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e
l
O
p
t
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mal
m
o
d
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l
U
n
i
t
P
e
r
c
e
n
t
a
g
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f
i
m
p
r
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v
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me
n
t
El
e
c
t
r
i
c
a
l
t
o
r
q
u
e
4
.
7
7
6
.
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m
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5
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−
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9
3
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5
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7
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43
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.
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3
%
7.
CO
NCLU
SI
O
NS
T
h
is
p
ap
er
p
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esen
ted
an
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f
e
ctiv
e
o
p
tim
izatio
n
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f
a
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witch
ed
r
elu
ctan
ce
m
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ased
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FEA.
T
h
e
o
p
tim
izatio
n
was
p
er
f
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m
ed
b
y
ap
p
ly
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n
g
th
e
w
h
ale
o
p
tim
izatio
n
alg
o
r
ith
m
to
im
p
r
o
v
e
th
e
elec
tr
o
m
ag
n
etic
p
er
f
o
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m
a
n
ce
an
d
th
e
o
v
er
all
ef
f
icie
n
cy
.
T
h
e
an
aly
s
is
f
o
cu
s
ed
o
n
th
e
k
ey
p
er
f
o
r
m
an
ce
in
d
icato
r
s
,
s
u
ch
as
elec
tr
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m
ag
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etic
to
r
q
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,
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s
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es
,
an
d
ef
f
icien
cy
,
wh
ich
p
r
o
v
id
ed
a
th
o
r
o
u
g
h
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