Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
6, N
o
. 1
,
Mar
c
h
20
15
,
pp
. 86
~91
I
S
SN
: 208
8-8
6
9
4
86
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
The Swit
ched Rel
u
ctan
ce Electr
ic Machine with Constructive
Asym
etry
A. Petru
s
hin,
M.
Tc
havych
alov, E.
Miros
h
nichenko
Chair “Electric
Rolling Sto
c
k”,
Rostov State
Tr
ansport University
, Rostov-on-Do
n, Russia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 21, 2014
R
e
vi
sed Dec 3,
2
0
1
4
Accepted Dec 22, 2014
Res
u
lts
of res
e
a
r
ches
of forc
es
of a unil
a
te
ral
att
r
act
ion of a ro
tor
to a s
t
a
t
or
of switched relu
ctan
ce elec
tric
machines taking
into account un
evenness of
an air gap ar
e given. It is offered
for
configuratio
ns of
magnetic s
y
stems with
weak magnetic communication between th
e coils making a phase to carr
y
ou
t
a suppl
y
o
f
coi
l
s in para
lle
l or in
dependen
t
l
y
fro
m
each other
for
reduct
i
on of
not com
p
ens
a
t
e
d
forces
of
a uni
la
tera
l a
ttr
act
ion o
f
a
rotor
to
a s
t
at
or.
Keyword:
Magnetic syste
m
Noise
Switche
d reluc
t
ance
m
achine
Unb
a
lan
c
ed
unilateral
attracti
o
n
Vibratio
n
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
M
.
Tcha
vy
chal
ov
,
Ch
air “Electric Ro
llin
g Sto
c
k”,
Ro
stov
State Tran
spo
r
t
Un
iv
ersity,
2
N
a
rod
nog
o
O
p
o
l
ch
en
iya sq
., Ro
st
o
v
-o
n-D
o
n
,
344
038
,
Ru
ssia.
Em
a
il: ch
av
ych
a
lov
-
m
a
x
i
m@yand
ex.ru
1.
INTRODUCTION
The
o
ry
of
swit
ched rel
u
ctanc
e
m
achines (SRM)
was
in good progres
s
. As
a res
u
lt
SR
M
technical
and
ec
on
om
i
c
i
nde
xes a
r
e
o
n
a l
e
vel
o
f
t
h
e
best
t
r
a
d
i
t
i
onal
electric m
achines
with circul
ar air ga
p m
a
gnetic
field
.
Howev
e
r th
ere are
u
n
so
lv
ed
prob
lem
s
. On
e o
f
the
m
o
st d
i
fficult to
so
lv
e is v
i
bro
a
cou
s
tic in
d
e
x
e
s
devel
opm
ent
.
Tak
i
ng
in
to
acco
un
t th
e lo
st in
v
a
lu
e of h
i
g
h
q
u
a
lity p
o
w
er electro
n
i
c it is
p
o
s
sib
l
e no
w to
set an
d
to
sol
v
e
ne
w
pr
obl
em
s of S
R
M
el
ect
ro
mechanical c
h
a
r
acteristics de
ve
l
o
pm
ent
.
The i
m
provem
e
nt
o
f
vi
b
r
oac
o
ust
i
c
i
nde
xes
i
s
am
ong
o
f
t
h
em
.
An
alytical rev
i
ew of SRM
noise an
d v
i
b
r
atio
n
red
u
c
tion
i
m
p
l
ies th
at p
r
ob
lem
is in
tricat
e and
do
no
t
h
a
v
e
sim
p
le solu
tio
n
s
.
Um
b
r
ella ap
pro
a
ch
is n
ecessary to fin
d
ou
t th
e facto
r
s acting on
th
e SRM
v
i
bratio
n
and
noise. One of those factors is force of unilateral a
ttractio
n
ro
tor to
stato
r
. It is v
a
riab
le and
tak
e
s p
l
ace
p
r
actically always. Th
e m
a
in
cau
se
o
f
u
n
ilat
e
ral attractio
n
i
s
m
a
rg
in
to
leran
ce on
p
a
rts
o
f
SRM. Th
e
fo
rce o
f
u
n
ilateral attractio
n
is m
o
re i
n
sm
all air g
a
p SRMs b
e
caus
e
o
f
great
er
di
s
s
ym
m
e
t
r
y
of m
a
gnet
i
c
sy
st
em
[
1
]
.
2.
R
E
SEARC
H M
ETHOD
SR
M
m
a
gnet
i
c
sy
st
em
s are
di
st
i
n
ct
i
n
nu
m
b
er of phase
s, t
oot
h
s
an
d coi
l
s
. The m
o
st of SR
M
ha
s
weak m
a
gnet
i
c
cou
p
l
i
n
g bet
w
een
p
h
ases
and t
h
e m
a
gnet
i
c
fl
ux i
s
co
m
m
on fo
r al
l
t
oot
h
s
o
f
o
n
e
pha
s
e
(Fig
ure
1
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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S
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4
The Switche
d Reluctance
Ele
c
tric
Machi
n
e w
i
t
h
C
o
n
s
t
r
uct
i
ve Asymet
ry (
A
. Pet
r
ushi
n)
87
(a)
(b
)
Fi
gu
re
1.
Di
st
ri
but
i
o
n
o
f
m
a
gn
et
i
c
fi
el
d l
i
n
es
of
SR
M
;
a)
6/
4
,
b
)
1
8
/
1
2
SRM ro
t
o
r is
always sh
ifted in
no
m
a
tter
wh
ich
sid
e
wit
h
in t
o
leranc
e.
Whe
n
t
h
e air
gap is
rathe
r
sm
a
ll ev
en
small sh
ift o
f
the ro
tor is th
e cau
s
e of
o
ccu
rren
ce of th
e
forces o
f
un
ilateral attractio
n
stato
r
to
rot
o
r.
It
i
s
di
f
f
i
c
ul
t
t
o
ca
ncel
out
t
h
o
s
e f
o
rce
s
by
c
u
r
r
e
n
t
re
gul
at
i
o
n i
n
se
p
a
rat
e
coi
l
s
bec
a
use
of
com
m
o
n
fl
ux
in
trad
itio
n
a
l
SRM co
nfigu
r
at
io
n
s
.
Howev
e
r, it is po
ssi
b
l
e
to
do in
“sho
r
t
-
f
l
ux
”
SRM wh
er
e separ
a
te
p
h
a
se
co
ils h
a
v
e
separate flux
[2
],
[3
].
It will redu
ce th
e
b
e
aring
assem
b
ly lo
ad
an
d
will increase th
e m
a
rg
in
o
f
safety.
Let
us
co
nsi
d
e
r
m
a
gnet
i
c
sy
st
em
on
Fi
g
u
re
2
[
2
]
.
P
h
ase
c
o
i
l
s
are
set
at
an
12
0
de
gree
s an
gl
e
a
n
d
pr
o
duce
o
n
c
o
m
i
ng fl
uxes
.
Fi
gu
re
2.
Di
st
ri
but
i
o
n
o
f
m
a
gn
et
i
c
fi
el
d l
i
n
es
of
SR
M
1
2
/
9
It is ratio
n
a
l to co
nn
ect ph
ase co
ils in
p
a
rallel with
po
wer
su
pp
ly in
SRM
co
nfigu
r
ation
s
lik
e shown
at Fig
u
re 2. In
th
at case con
s
t
r
u
c
tiv
e
d
i
ssymmetry will b
e
co
m
p
en
sated
b
y
cu
rren
ts i
n
th
e p
h
a
se co
ils. Smaller
air gap m
eans less coil induc
tance. As a re
s
u
lt coil curre
nt
will grow fast
er in the
coil with the sm
aller air
g
a
p. Differen
t
cu
rren
t
i
n
p
h
a
se
co
ils will
p
r
od
u
c
e th
e
rad
i
al force co
un
terbalan
cin
g
th
e roto
r.
Th
e calcu
lation
s
were carried
ou
t fo
r m
a
g
n
e
tic syste
m
with
con
n
ection
ph
ase co
ils in
p
a
rallel and
with
co
nn
ection
in series. To
create th
e con
s
tru
c
tiv
e
u
nbal
a
nce t
h
e
r
o
t
o
r
was
vert
i
cal
l
y
m
oved. F
o
r
ex
am
pl
e
m
o
v
i
n
g
th
e ro
t
o
r i
n
0
.
05
mm
(25
%
of
n
o
m
in
al air g
a
p
)
in
alig
n
po
sitio
n the in
du
ctance
o
f
co
il A is
2
.
3
3
2
m
H
and the inductance of coils B and C is 1.921 m
H
. The
di
ffe
rence in inductance is 17%. Num
e
ric values of
coi
l
i
n
d
u
ct
a
n
ce
we
re c
o
m
put
er cal
cul
a
t
e
d
by
fi
ni
t
e
el
em
ent
a
ry
m
e
t
hod.
Mathem
a
tical
m
odel of
SRM phase
with c
o
i
l
s co
n
n
ected
in ser
i
es is as fo
llo
w
s
[4
]-
[6
]:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
8
6
– 91
88
ω
,
=
dt
d
θ
,
T
B
T
J
=
dt
d
ω
,
θ
θ
i,
ψ
ω
R
i
v
θ
i,
L
=
dt
di
L
1
1
(
1
)
W
h
er
e
:
i –
p
h
a
s
e
cu
rr
en
t,
A
;
L(i,
θ
) – phase
inductance
,
H;
θ
– ro
tor
p
o
s
itio
n,
rad
;
v – vol
t
a
ge
, V;
R
– phase resis
t
ance, Ohm
;
ω
–
r
o
t
a
t
i
o
n
f
r
e
que
ncy
,
ra
d/
s;
ψ
(i,
θ
) – fl
u
x
l
i
nka
ge,
Wb;
J –
eq
ui
val
e
nt
m
o
m
e
nt
of
i
n
e
r
t
i
a
, k
g
·
m
2
;
B –
friction
ratio
;
T – electrom
a
gnetic torque,
Nm;
T
L
– l
o
ad torque, Nm
;
Whe
n
t
h
e
phas
e coils are c
o
nnected i
n
paral
l
el th
ere
is no
mag
n
e
tic
couplin
g
b
e
tween
ph
ase
co
ils. It
is possible t
o
calculate phas
e coil c
u
rren
ts in
d
e
p
e
n
d
en
tly. Ph
ase
vo
ltage is app
lied
t
o
all ph
ase co
ils at th
e
sam
e
t
i
m
e. Co
n
s
eq
u
e
n
tly for
co
il curren
t
s it
can
b
e
written
:
ω
,
=
dt
d
θ
,
T
B
T
+
T
+
T
J
=
dt
d
ω
d
θ
θ
i,
ψ
ω
R
i
u
θ
i,
L
=
dt
di
d
θ
θ
i,
ψ
ω
R
i
u
θ
i,
L
=
dt
di
d
θ
θ
i,
ψ
ω
R
i
u
θ
i,
L
=
dt
di
L
c
b
a
c
pc
c
c
c
b
pc
b
b
b
a
pc
a
a
a
1
,
1
,
1
,
1
(
2
)
Whe
r
e:
Rpc – phase
coil
resistance, Ohm
.
3.
R
E
SU
LTS AN
D ANA
LY
SIS
To com
pute SRM param
e
ters by Equation (1) an
d (2) t
h
e accepted as
sum
p
tion is to neglect the
m
u
t
u
al
phase c
o
u
p
l
i
n
g.
Fo
r m
a
gnet
i
c
sy
st
em
u
nde
r
di
scu
ssi
on
(
F
i
g
ure
2
)
m
a
gnet
i
c
p
h
as
e co
upl
i
n
g
i
s
u
s
ual
l
y
taken int
o
account. Howeve
r to recei
ve qualitative result of co
m
p
arison of series and pa
rallel phase coils
connection t
h
at assum
p
tion ca
n
be acce
pted
because
onl
y t
h
e
diffe
re
nce
of c
o
il curre
n
ts i
s
estim
a
ted.
C
a
l
c
ul
at
i
ons were
car
ri
ed out
i
n
SIM
U
LIN
K
/
M
A
TLA
B [7
].
SRM ph
ase m
o
d
e
s fo
r
ser
i
es
and
p
a
r
a
llel conn
ectio
n
o
f
ph
ase co
ils ar
e
show
n
in
Figur
e
3
an
d 4
as fo
llow
s
.
Fi
gu
re
3.
SIM
U
LI
N
K
m
odel
of
SR
M
p
h
ase
wi
t
h
se
ri
es-c
on
nect
ed c
o
i
l
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
The Switche
d Reluctance
Ele
c
tric
Machi
n
e w
i
t
h
C
o
n
s
t
r
uct
i
ve Asymet
ry (
A
. Pet
r
ushi
n)
89
Fi
gu
re
4.
SIM
U
LI
N
K
m
odel
of
SR
M
ph
ase with
p
a
rallel-co
nn
ected
co
ils
In
itial d
a
ta fo
r
co
m
p
u
t
atio
n
s
i
n
th
e
form
o
f
tab
l
e
ψ
(i,
θ
)
were receive
d for
SRM rotor
uni
lateral shift
t
o
25%
, 5
0
% and
75%
of desi
gne
d ai
r ga
p (0
,0
5;
0,
1
и
0,1
5
m
m
)
. The sim
u
l
a
t
i
on was ca
r
r
i
e
d o
u
t
fo
r no
m
i
nal
lo
ad
SRM op
er
atio
n on
a ro
t
a
tio
n
f
r
e
qu
en
cy o
f
100
rad
/
s. D
C
link
vo
ltag
e
f
o
r
ser
i
es
ph
ase co
ils co
nn
ection
was 60
V
,
fo
r paral
l
e
l
co
n
n
ec
t
i
on – 20
V
.
As
a
res
u
l
t
t
h
e de
pen
d
e
n
ci
es
i
(
θ
) we
re recei
ve
d
(Figure
5).
(a)
(b
)
Fi
gu
re 5.
R
e
sul
t
s
of
SR
M
m
o
d
e
l
i
ng (a –
se
ri
es-co
n
n
ect
ed p
h
a
se
coi
l
s
, b – p
a
ral
l
e
l
-
co
nnect
ed pha
se
c
o
i
l
s
)
u
n
d
e
r
ro
tor
sh
i
f
t 0.05
, 0.1 and 0
.
15
mm
Sub
s
equ
e
n
t
to th
e resu
lts of SRM ph
ase
m
o
d
e
lin
g
fo
rces o
f
un
ilateral ro
t
o
r attractio
n
were
cal
cul
a
t
e
d
by
f
i
ni
t
e
el
em
ent
a
ry
m
e
t
hod
(Fi
g
ure
6
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
8
6
– 91
90
Fig
u
re
6
.
Th
e fo
rce of
u
n
ilateral ro
t
o
r t
o
stator attr
action (1
– se
ries-c
onne
cted phase
coil
s, 2 – parallel-
connected phas
e coils)
und
er r
o
t
o
r
sh
if
t 0
.
05,
0.1
and
0
.
15
mm
As can be see
n
from
t
h
e Fi
gure 6 wi
t
h
seri
e
s
phase
co
ils co
nn
ection
wh
en
th
e cu
rren
t is eq
u
a
l in
all
p
h
a
se co
ils t
h
e
force
o
f
un
ilateral ro
to
r attractio
n
is
rath
er mo
re t
h
an in
case o
f
p
a
rallel phase co
ils co
nn
ectio
n
wh
en
co
il cu
rren
t
d
e
p
e
nd
from air g
a
p
d
i
stan
ce. Conn
ecting
ph
ase co
ils in
p
a
rallel it is
p
o
s
sib
l
e to
redu
ce th
e
force
of unilateral rotor attract
ion i
n
3 tim
es
at the avera
g
e.
It is p
o
ssib
l
e to
redu
ce th
e fo
rce of un
ilateral ro
tor attractio
n
in
SRM with
relativ
ely lo
w m
a
g
n
e
tic
co
up
ling
b
e
tween
ph
ase co
ils b
y
o
p
e
rati
n
g
in
artificia
l
m
a
gnet
o
m
ovi
ng
f
o
rce
di
ssy
m
m
e
t
r
y
m
ode. In t
h
i
s
case
every
p
h
ase c
o
i
l
i
s
suppl
i
e
d
b
y
si
ngul
a
r
sem
i
con
duct
o
r s
w
i
t
ch. It
i
s
re
qui
r
e
d t
o
i
n
c
r
ease
cur
r
ent
i
n
c
o
i
l
whe
r
e
the air
ga
p
distance is la
rge
r
a
n
d to dec
r
ease
current i
n
c
o
il
with
sm
aller air
g
a
p.
It is also po
ssib
l
e in
cl
osed
-
loop c
ont
rol s
y
ste
m
using t
h
e sens
or
of
ra
dial dis
p
lacement to im
ple
m
ent active m
a
gnetic levitation of the
ro
tating
ro
t
o
r an
d to
un
lo
ad
the b
e
aring
s
.
Thu
s
t
h
e
v
i
b
r
ati
o
n
an
d no
ise
will b
e
redu
ced
.
4.
CO
NCL
USI
O
N
The speci
al
t
y
of t
h
e SR
M
m
a
gnet
i
c
sy
st
em
s whe
r
ei
n t
h
e
pha
se coi
l
s
ha
ve n
o
m
a
gnet
i
c
cou
p
l
i
ng
rend
er po
ssi
b
l
e to
redu
ce th
e fo
rce
of un
ilateral attractio
n
ro
t
o
r t
o
stator co
nn
ectin
g th
e
ph
ase co
ils in
p
a
rallel.
In t
h
is case t
h
e ne
gative
fee
dbac
k
betwee
n the
air
ga
p
distance a
n
d unbala
nced forc
e of unilateral rot
o
r
attractio
n
will b
e
v
a
lid. In
th
e case o
f
sup
p
l
y
i
n
g
p
h
a
se co
il b
y
sin
g
u
l
ar semico
n
d
u
c
tor switch
it is p
o
s
sib
l
e to
com
p
ensate the forces
of unilateral attraction alm
o
st
co
m
p
le
tely in
th
e sam
e
way t
h
at in
activ
e
mag
n
e
tic
b
eari
n
g. Creat
in
g
con
d
ition
s
for
b
eari
n
g
u
n
l
o
a
d is es
pecially relev
a
n
t
fo
r
h
i
gh-du
ty electric mach
in
es
o
p
e
rating
in
extrem
e
d
u
t
y cycles. Pro
p
o
s
ed
so
lu
tion
s
will mak
e
po
ssi
b
l
e to
redu
ce th
e SR
M v
i
b
r
o
activ
ity an
d
noi
se
as c
o
n
s
e
que
nce.
ACKNOWLE
DGE
M
ENTS
The w
o
r
k
i
s
sup
p
o
rt
e
d
by
The
M
i
ni
st
ry
of
education
and science
of Russia.
Agree
m
ent
№
1
4
.604
.2
1.0040
, i
d
en
tif
ier
RFMEFI
6041
4X
00
40
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
The Switche
d Reluctance
Ele
c
tric
Machi
n
e w
i
t
h
C
o
n
s
t
r
uct
i
ve Asymet
ry (
A
. Pet
r
ushi
n)
91
REFERE
NC
ES
[1]
Petrushin AD, Iljasova EE, Inve
s
tigation of
the
ef
fect of unev
e
n air gap on
the v
a
lue of unilatera
l attr
act
ion
forc
e of
the ro
tor
to th
e s
t
ator
s
w
itched
re
luct
ance
e
l
ec
tri
c
m
achine.
Newsp
aper of
VElNI
I
,
2011; 2: 84-93.
[2]
Petrushin AD, Grebennikov N
V
. Reactive sw
itch
e
d
electr
i
c
machine with r
o
tation
a
l s
y
mmetr
y
.
P
a
t
e
nt
RF
№
2450410,
201
2.
[3]
Miller
TJE, He
ndershot JR. D
e
sign of
Brushl
ess Perm
anent-Magnet Motors,
Magna Physics Publishing an
d
Glarendon Press.
OXFORD. 1994; 512.
[4]
Krishnan R. Switch
e
d relu
ct
anc
e
m
o
tor drives:
m
odeli
ng, simu
lation
,
an
aly
s
is, design,
and ap
plications.
Mag
na
Physics Publishing
. 2001; 416.
[5]
Ghousia SF. I
m
pact analy
s
is
of dwell angles on curre
nt shape and torque in switched
reluctance motors.
International jou
r
nal of pow
er
electronics and dr
ive systems
. 201
2; 2(2): 160-169.
[6]
S
r
inivas
P
,
P
r
as
ad VN. Direct I
n
s
t
antan
e
ous
torque
control of 4
phase 8/6 switch
e
d reluctan
ce motor.
Internat
ion
a
l
journal of power
electr
onics and
drive systems
. 2
011; 1(2): 121-1
68.
[7]
W
a
dnerkar VS
. P
e
rform
ance a
n
al
y
s
is
of s
w
itc
hed relu
ct
an
ce motor;
design, modeli
ng and simulation of 8/6
switched r
e
lu
cta
n
ce m
o
tor
.
Jo
urnal of Theoretical and
Applied I
n
formation Tech
nology
. 2008; 11
: 1118-1124.
BIOGRAP
HI
ES OF
AUTH
ORS
Alexander
Petru
s
hin, Doctor
of
Engeneering
,
Head
of
the “Electr
i
c rolling
Stock” chair, Rostov
S
t
ate
Trans
port
Univers
i
t
y
.
Re
ci
eved P
h
D in
19
87, DoE
in 199
9. Science in
ter
e
sts: switch
e
d
reluc
t
anc
e
m
o
tor
drive
,
op
tim
iza
t
ion of
its
constru
c
tion
,
m
a
th
em
ati
cal
sim
u
lation
.
Maxim Tchav
y
c
h
alov, PhD,
As
s
i
s
t
ant P
r
ofes
s
o
r of th
e “
E
l
ectr
i
c rol
ling S
t
o
c
k”
cha
i
r,
Ros
t
ov
S
t
ate
Trans
port
Univers
i
t
y
. R
e
c
i
eved P
h
D in 20
14. S
c
ien
ce
int
e
r
e
s
t
s
:
s
w
itched
re
luct
ance
m
o
tor
drive, computer
simulation, sensor
less contro
l, control op
timization.
Ekat
erina
M
i
ros
hnichenko
, T
e
a
c
h
ing as
s
i
s
t
ant
of
the
“
E
le
ctri
c ro
l
ling S
t
ock
”
chai
r, Ros
t
ov S
t
ate
Transport Universit
y
. Sci
e
nce
inter
e
sts: switche
d reluctance motors, vibratio
n and noise in
switched r
e
lu
cta
n
ce m
o
tors.
Evaluation Warning : The document was created with Spire.PDF for Python.