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
. 65
~69
I
S
SN
: 208
8-8
6
9
4
65
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
Versi
o
ns of
Switched Relu
ct
ance Generator Design at a
Constant Stator
Configuration
N.V. Grebennikov*
, A.V. Ki
reev**,
* Rostov State Transport Univ
ers
i
ty
, Rostov-on-Don, Russia
** Science and
Technolo
gy
Center “PRIVOD-N
”
,
Rostov-on-Don,
Russia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Sep 26, 2014
Rev
i
sed
D
ec 28
, 20
14
Accepte
d
Ja
n 10, 2015
The investigatio
n of the influence
of the number of phases of switched
reluctance gen
e
rator (SRG) to
the pul
se of
electromagnetic torque was
carri
ed out
. Th
e com
puter m
o
del was cr
eat
ed
. The
am
plitud
e
of torqu
e
ripples
redu
ces
t
o
6 tim
es
with i
n
creas
ing of
the
ripple fr
equency to 5 times,
that
is
m
o
re
ac
ce
ptabl
e
in
terms of requir
e
ments.
Keyword:
C
o
m
put
er m
odel
Num
b
er of
pha
s
es
O
v
er
lap f
actor
Switche
d reluc
t
ance
m
achines
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
:
N.
V. Gre
b
e
n
niko
v,
Ro
stov
State Tran
spo
r
t
Un
iv
ersity,
N
a
rod
nog
oOpo
lch
e
n
i
ya sq.,
Ro
stov
-on
-
D
o
n
,
R
u
ssia, Po
stal co
d
e
:
34
4038
.
Em
a
il: g
r
eb
en
nik
o
v
nv@m
a
i
l
.ru
1.
INTRODUCTION
Switche
d rel
u
ctance m
achines (SRM), de
signe
d as
a hi
gh efficiency
type
of electrom
echanical
ener
gy
c
o
n
v
ert
e
r [
1
]
-
[
5]
, ca
n
be a
ppl
i
e
d
o
n
v
e
hi
cl
es i
n
cl
u
d
i
n
g
rai
l
w
ay
rol
l
i
ng
st
oc
ks.
Electrical
m
a
c
h
in
es u
s
ed
on v
e
h
i
cles op
erate in
sev
e
re
co
nd
itio
ns.
Du
ri
n
g
op
erati
o
n
th
ey
are
affect
ed
by
si
gni
fi
cant
dy
nam
i
c forces res
u
l
t
i
ng f
r
om
vi
brat
i
on an
d sh
oc
k part
i
c
ul
a
r
l
y
at
hi
g
h
ru
n
n
i
n
g s
p
eed
s
.
It
can cause t
o
vari
o
u
s fai
l
u
r
e
s:
wi
res an
d wi
n
d
i
n
g co
nne
ct
i
on di
sr
u
p
t
i
o
n, crac
ki
n
g
an
d i
n
s
u
l
a
t
i
ng m
a
t
e
ri
al
s
dam
a
ge. For t
h
i
s
reas
on
wh
en ch
oo
si
ng electrical
m
achines desi
gn the
r
e
is a ten
d
e
ncy to
u
s
e si
mp
le and
reliab
l
e techn
i
cal so
lu
tion
s
.
Fro
m
th
is p
o
i
nt o
f
v
i
ew th
e
main
ad
v
a
n
t
age o
f
SRM is t
h
e d
e
sign
simp
licity. Th
e roto
r is p
a
ssiv
e
wi
t
h
o
u
t
wi
n
d
i
ng a
nd t
h
e st
a
t
or i
s
equi
p
p
e
d
wi
t
h
wi
ndi
ng
con
s
istin
g
of cen
tered
type co
ils. In
com
p
ariso
n
with ot
her types of electrical
m
achines, SR
M is
m
o
re
so
p
h
i
s
t
i
cat
ed, has
l
e
ss speci
fi
c c
ons
um
pt
i
on
of
coo
p
e
r
an
d
i
n
su
lating
materials. In
case o
f
SRM app
licatio
n
on
the v
e
h
i
cles, it will al
lo
w to
imp
r
ov
e th
e reliab
ility o
f
energy supply syste
m
, to achieve be
t
t
e
r e
n
er
gy
an
d wei
g
ht
-
s
i
ze param
e
t
e
rs
, to re
duc
e the cost and ope
r
ation
expe
nses
. T
h
e
di
sad
v
a
n
t
a
ges
of
SR
M
are
co
nsi
d
e
r
abl
e
el
ec
t
r
om
agnet
i
c
t
o
r
que
ri
ppl
e a
n
d
hi
g
h
er
n
o
i
s
e l
e
vel
.
2.
VERS
IO
NS O
F
SWIT
CHE
D
RELU
CTA
NCE GENE
R
A
TOR
Co
n
s
i
d
er th
e po
ssib
ility to
red
u
c
e th
e torque ripp
le
on
th
e
ex
am
p
l
e o
f
switch
e
d
relu
ctance g
e
n
e
rat
o
r
(SR
G
)
havi
ng
cl
assi
cal
confi
g
u
r
at
i
o
n 1
8
/
1
2
(1
8 t
eet
h at
t
h
e
stator a
nd
12 - at the roto
r).
18 coils located
at the
st
at
or a
r
e
di
vi
d
e
d i
n
t
o
t
h
ree
p
h
ases a
n
d t
h
e
a
ngl
e
bet
w
ee
n
c
o
i
l
s
’ a
x
l
e
s i
s
6
0
°.
In [6] it is said
that «if the ter
m
s
of SRM shoul
d ens
u
re the high sta
b
ility of rotation fre
que
ncy a
nd
l
o
w t
o
r
q
ue
ri
p
p
l
e
, t
h
e
num
ber
of
p
h
ases
sh
oul
d
be c
h
ose
n
as m
a
xim
u
m
pos
si
bl
e»
.
Inc
r
easi
n
g
t
h
e
n
u
m
ber of
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
:
6
5
– 69
66
SRM p
h
a
ses can
b
e
ob
tain
ed b
y
ch
ang
i
ng
th
e nu
m
b
er of t
eeth
at th
e ro
tor wh
ile m
a
in
tain
ing
th
e sam
e
stato
r
with
1
8
teeth
,
it is sp
ecified
by eco
no
m
i
c co
n
s
id
eratio
ns.
C
onsi
d
er t
h
e p
o
ssi
bl
e va
ri
ant
s
of SR
G c
o
n
f
i
g
u
r
at
i
o
n, wi
t
h
st
at
or ha
vi
n
g
1
8
t
eet
h and c
o
i
l
s
di
spos
e
d
at
each
tooth, depe
nding on num
ber
of teeth at the
rotor (
the num
b
er of
teeth at the
rot
o
r is
less tha
n
or e
q
ual
to
18):
a)
18/
18 – a si
ngle
phase m
ach
in
e, with stro
ng
t
o
rqu
e
;
b) 1
8
/
9
– t
w
o
-
pha
se
m
achi
n
e
,
whi
c
h t
o
r
que
ri
ppl
e
is higher than three-phas
e m
achine obtains [6],
with
acco
u
n
t
of th
e fact t
h
at th
is ri
p
p
l
e is
concept
u
ally im
possible t
o
elim
inate [7];
c) 18/
12
– t
h
ree-phase m
achine,
th
e nu
m
b
er
of
stator
teeth
w
a
s
inc
r
ea
sed three
f
ol
d
com
p
ared t
o
basic three-pha
s
e m
achine conf
i
g
uratio
n 6
/
4. It allows t
o
red
u
c
e th
e
no
ise
lev
e
l [6
];
d)
18/16 – ni
ne-phase m
achine wit
h
alternating
polarity
of a
d
jacent
wi
ndi
ngs and strong m
u
tual
i
n
d
u
ct
ance
of
adjace
nt
phase
s. N
o
t
e
t
h
at
t
h
e num
ber
of
p
o
we
r sem
i
cond
uct
o
r de
vi
ces (
PSD
) i
n
t
h
e co
nve
rt
e
r
is increase
d
by
three
tim
e
s com
p
ared to
t
h
e
conve
r
ter
of three-pha
se m
a
c
h
ine.
B
a
sed
on
anal
y
s
i
s
of
SR
G
p
e
rf
orm
a
nce wi
t
h
di
ffe
rent
n
u
m
bers of
r
o
t
o
r
t
eet
h, si
x-
pha
se m
achi
n
e
with
18
/15
configu
r
ation
is p
r
o
p
o
s
ed
fo
r ap
plicatio
n
.
Th
e co
st o
f
th
e co
nverter fo
r th
is k
i
n
d
m
ach
in
e will b
e
m
u
ch
lo
wer than
fo
r
n
i
n
e
-phase
m
ach
in
e: th
e d
e
si
g
n
o
f
co
nv
erter is kn
own
for m
ach
in
e’s supp
ly (Figu
r
e
1)
havi
ng
t
h
e
sam
e
n
u
m
b
ers o
f
P
S
D as
we
ll as fo
r th
r
e
e-p
h
a
se
mach
in
e [8
].
Fi
gu
re
1.
Sc
he
m
e
of si
x-
p
h
as
e SR
G
an
d s
u
p
p
l
y
co
nve
rt
er
(
S
C
–
St
at
i
c
co
nve
rt
er,
C
S
– c
ont
rol
sy
st
em
,
En
co
d
e
r –
ro
t
o
r p
o
s
ition
sen
s
o
r)
Th
e m
a
in
co
nd
itio
n
for eli
m
in
atio
n
o
f
electro
m
ag
n
e
tic to
rqu
e
ri
p
p
l
e in
SRM is p
a
rtial o
v
e
rlapp
i
ng
of m
achi
n
e’s
ope
rat
i
o
n area
s by
adjac
e
nt
pha
ses. T
o
est
i
m
a
t
e
t
h
e poss
i
bl
e ove
rl
ap
pi
ng
of t
h
e
s
e ar
eas, t
w
o
f
acto
r
s ar
e used
[
7
],
[8
]:
1
)
ab
so
lu
te
ov
erlapp
ing
fact
o
r
:
2
/
m
А
,
whe
r
e
m
– num
ber
of
SR
M
p
h
ases;
2) effective
overlapping fa
ctor:
)
(
2
R
S
R
E
N
N
N
,
whe
r
e
R
N
–
num
b
er of
rotor teeth,
S
N
–
num
b
er of st
ator teeth.
Fro
m
th
e fo
rm
u
l
a an
alysis
g
i
v
e
n abov
e, it fo
llo
ws th
at th
e in
crease of abso
lu
te
ove
rl
ap
pi
n
g
fact
or
i
s
pos
si
bl
e u
nde
r
con
d
i
t
i
on
of i
n
creasi
n
g t
h
e n
u
m
ber of pha
ses
,
and t
h
e i
n
c
r
e
a
se of ef
fect
i
v
e ove
rl
ap
pi
n
g
f
act
or
is p
r
ov
id
ed
with
in
creasing
t
h
e nu
m
b
er of
roto
r teeth.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Versi
o
n
s of
Sw
i
t
c
hed
Rel
u
ct
a
n
ce Gene
rat
o
r Desi
g
n
at
a
C
o
nst
a
nt
St
at
or
C
onf
i
g
ur
at
i
o
n
(
N
.V. Gre
b
en
ni
kov)
67
Versi
ons
o
f
S
R
M
con
f
i
g
urat
i
on a
n
d t
h
e
val
u
es
of
o
v
erl
a
p
p
i
n
g fact
ors
ar
e gi
ve
n i
n
Ta
b
l
e 1. Ta
bl
e
1
shows t
h
at the
m
i
nim
a
l
torque ri
pples ta
ke
place wh
e
n
maxim
u
m
pos
sible value
of
pha
se num
b
er, but it
in
creases sign
ifican
tly th
e
q
u
an
tity o
f
PSD
an
d th
e co
st
of co
nv
erter
b
e
co
m
e
s th
e h
i
gh
est. Fro
m
th
e o
t
h
e
r
han
d
, t
h
e l
o
we
st
cost
of t
h
e con
v
e
r
t
e
r i
s
achi
e
ve
d at
t
h
e l
o
west
po
ssi
bl
e
val
u
e
of
phas
e
num
ber (a si
ngl
e
p
h
a
se), bu
t th
is v
a
rian
t is no
t ratio
n
a
l fo
r v
i
b
r
o
acou
s
tic ind
i
cato
rs. Th
e low
to
rq
u
e
ripp
le
of SRG and
t
h
e
co
st
o
f
its co
n
t
ro
l
syste
m
are
mu
tu
ally con
f
lictin
g
criteria,
s
o
t
h
e
p
r
o
p
o
se
d
vari
ant
of
1
8
/
1
5 c
o
n
f
i
g
ura
t
i
on i
s
o
p
tim
al [9
].
Tabl
e 1. Ver
s
i
ons
o
f
SR
M
co
nfi
g
u
r
at
i
o
n
Teeth at
stator
Teeth at
ro
to
r
Nu
m
b
e
r
of
phases
Nu
m
b
e
r
of
coils in the
single phase
Nu
m
b
e
r
of
PSD
Absolute
over
l
apping
f
actor,
А
Ef
f
ective
over
l
apping
f
actor,
E
18
18
1
18
4
0,
5
–
18
9
2
9
8
1
0,
5
18
12
3
6
12
1,
5
1
18
15
6
3
24
(
12)
3
2,
5
18
16
9
2
36
4,
5
4
3.
COMPUTER SIMULATION
To i
nve
st
i
g
at
e di
f
f
ere
n
t
o
p
e
r
at
i
o
n
m
odes
of
SR
G an
d to
d
e
velop
th
e op
tim
a
l
co
n
t
ro
l of
ph
ase
swi
t
c
hi
n
g
, t
h
e
com
put
er si
m
u
l
a
t
o
r o
f
S
R
G el
ect
ri
cal
part
has
be
en de
vel
o
pe
d
i
n
soft
ware
packa
g
e
Matlab
/
Si
m
u
li
n
k
(Fi
g
u
r
e 2), with
acc
ou
nt
o
f
m
u
t
u
al
phase inductance
.
The m
a
nagement of
keys
VT
1…
VT
6 s
w
itching is
pe
rformed by
unit Upra
vlenie, ba
se
d
on recei
ve
d
sig
n
a
ls: w(rad
/
s) – angu
lar freq
u
e
n
c
y
o
f
ro
t
o
r
ro
tation
,
pos –
an
gu
lar
ro
to
r
po
sitio
n
rel
a
tiv
e to
stato
r
, I(A)
–
current value
i
n
SR
G windings.
Th
e i
n
itial su
pp
ly i
m
p
u
l
se
g
o
es to
g
e
n
e
rator
fro
m
p
r
e-ch
arged
cap
acito
r
С
.
Uni
t
s
Sco
p
e w
,
Sco
p
e I(
A)
_
V
(
V
)
,
Sco
p
e M
o
m
e
nt
, Scop
e Fl
ux(
V
*
s)
, S
c
ope
V_
n an
d Sco
p
e I_
n ar
e
desi
g
n
e
d
f
o
r
o
s
ci
l
l
ogram
s recor
d
i
n
g
of t
h
e
fol
l
o
wi
n
g
:
an
gul
a
r
r
o
t
a
t
i
on
fre
que
ncy
o
f
c
u
r
r
ent
a
n
d
v
o
l
t
a
ge i
n
st
at
or
wi
n
d
i
n
gs
o
f
gene
rat
o
r, e
l
ect
rom
a
gnet
i
c
t
o
r
q
ue,
fl
u
x
l
i
nka
ge,
l
o
a
d
vol
t
a
ge an
d l
o
a
d
c
u
r
r
ent
.
Fi
gu
re
2.
C
o
m
put
e
r
m
odel
o
f
si
x-
pha
se SR
G
1
8
/
1
5 c
o
n
f
i
g
u
r
at
i
o
n
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
:
6
5
– 69
68
As a resu
lt of si
m
u
latio
n
it was
o
b
t
ain
e
d
cu
rren
t,
vo
ltage in
SRG
wind
ing
s
an
d
electro
m
ag
n
e
tic
to
rq
u
e
d
e
p
e
n
d
e
n
ces
on
an
gu
lar ro
tor
po
sitio
n fo
r t
h
ree-ph
ase and
si
x
-
p
h
a
se con
f
i
g
uration of SR
G.
Fi
gu
re
3
pre
s
e
n
t
s
t
h
e
di
a
g
ra
m
s
of p
h
ase t
o
rq
ues
(c
ur
ves
1 a
n
d
2
)
a
n
d t
o
t
a
l
el
ect
rom
a
gnet
i
c
t
o
r
ques
(curv
e
s
3
an
d 4) in relativ
e
un
its.
(1
–
t
o
r
q
ue
of
s
i
ngl
e
pha
se
of
SR
G
18/
1
2
,
2
– t
o
r
que
o
f
si
n
g
l
e
p
h
ase
o
f
S
R
G 1
8
/
1
5
,
3
–
t
o
t
a
l
t
o
r
que
o
f
SR
G
18/
12
,
4
– t
o
t
a
l
t
o
r
que
o
f
SR
G
18/
15
)
Fi
gu
re
3.
De
pe
nde
nce
o
f
SR
G
el
ect
rom
a
gnet
i
c
t
o
r
ques
The c
o
m
p
ari
s
on
o
f
el
ect
r
o
m
a
gnet
i
c
t
o
r
q
ues i
s
gi
ve
n i
n
Ta
bl
e
2
wh
i
c
h dem
onst
r
a
t
es t
h
at
t
h
e
fre
que
ncy
of el
ect
rom
a
gnet
i
c
t
o
r
que ri
ppl
es
at
si
x-p
h
ase S
R
G con
f
i
g
urat
i
on i
n
c
r
eases b
y
about
fi
ve t
i
m
es and
am
pl
i
t
ude
of t
o
rq
ue
ri
p
p
l
e
s
de
creases a
p
pr
ox
im
at
ely
by
si
x
t
i
m
e
s.
Tabl
e
2. C
o
m
p
ari
s
o
n
of
el
ect
r
o
m
a
gnet
i
c
t
o
r
q
ues
of
SR
G
di
f
f
ere
n
t
co
n
f
i
g
ur
at
i
o
n
SRG
config
ur
ation
Nu
m
b
e
r
of
SRG phase
Rotor rotation
fr
equency
ω
р
,
rad
/
s
T
o
r
que r
i
pple
fr
equency
,
Hz
M
i
nim
a
l tor
que
value M
MIN
, r.u
Ripple
am
plitude M
A
,
r.u
.
M
A
/ |
M
MIN
|
18/12
3
100
573
–1
0,
469
0,
469
18/15
6
100
2860
–0,
57
0,
081
0,
141
4.
CO
NCL
USI
O
N
R
e
pl
aci
ng t
h
e
rot
o
r ha
vi
n
g
1
2
t
eet
h wi
t
h
t
h
e rot
o
r ha
vi
n
g
15 t
eet
h w
h
i
l
e
m
a
i
n
t
a
i
n
i
ng t
h
e sam
e
st
at
or
an
d pow
er conv
er
ter allo
ws
us to
red
u
ce el
e
c
t
r
om
agnet
i
c
t
o
r
q
ue ri
ppl
e a
p
pr
o
x
i
m
at
el
y
by 6 t
i
m
es.
ACKNOWLE
DGE
M
ENTS
The
prese
n
t
e
d
wo
r
k
ha
s be
en d
e
vel
ope
d
wi
t
h
s
u
p
p
o
rt
of R
u
ssi
an
M
i
ni
st
ry
o
f
E
duc
at
i
on,
gra
n
t
RFMEFI5
761
4X
003
6.
REFERE
NC
ES
[1]
Voron OA, Gre
b
ennikov NV, Zarifian
AA, Petrushin AD. Unde
rcar
switched r
e
luctance gen
e
rator.
Bull
etin of th
e
Russian Research and Design
Institut
e
for el
ectric
. 2009; 1: 132-1
43.
[2]
Swi
t
c
he
d rel
u
ct
anc
e
el
ec
t
r
ic
dri
v
e
for el
ec
t
r
ic
rolli
ng st
oc
k
. Bul
l
et
i
n
of th
e Russian
Research and D
e
sign Institu
te
fo
r
ele
c
tric
. 2002
; 4
4
: 336.
[3]
Kireev AV. El
e
c
trorol
ling com
position with tr
act
ion switched
reluc
t
anc
e
el
ec
tr
ic drive
.
Rol
ling
stock of the
X
X
I
centur
y
. 2008
; 2
0
-22.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Versi
o
n
s of
Sw
i
t
c
hed
Rel
u
ct
a
n
ce Gene
rat
o
r Desi
g
n
at
a
C
o
nst
a
nt
St
at
or
C
onf
i
g
ur
at
i
o
n
(
N
.V. Gre
b
en
ni
kov)
69
[4]
Maged NF Nashed, Samia M Mahmoud, Mohs
en Z El-Sher
i
f,
Emad S Abdel-Alie
m. H
y
steresis C
u
rrent Contro
l o
f
Switched Re
luct
ance Motor
in Aircraf
t
Applic
at
i
ons.
Internation
a
l Journal of
Po
we
r Electronics
and Drive System
.
2014; 4(3): 376-
392.
[5]
S
r
inivas
P
,
P
r
a
s
ad P
VN. Direct Ins
t
an
taneous
Tor
que Contro
l of 4 Phase 8
/
6 Switched R
e
luctance Motor
.
International Jo
urnal of
Powe
r Electronics
and
Drive
System
. 20
11; 1(2): 121-12
8.
[6]
Kuznetsov VA,
Kuz'
mich
evVA.
Switched r
e
lu
ctance motor
,
2003; 68 pp
.
[7]
Krasovskiy
AB, B
y
chkov MG. Investiga
tion of torque ripple in the switc
hed reluctan
ce electric
drive.
E
l
ec
tric
ity
.
2001; 10: 33-43.
[8]
Miller TGE
.
Switch
e
d Reluct
an
ce Motors and
Their Control
.
Oxford Magna
Physics Publishing and Clarend
o
n
Press
. 1993.
[9]
Grebennikov N
V
, Petrushin AD, Reactiv
e switched
electr
ical
machine with r
o
tation
s
y
mmetr
,
Rostov-na-Don
u
,
2012; 13.
BIOGRAP
HI
ES OF
AUTH
ORS
GrebennikovNikolay
was born in Russia, in 1
985. He receiv
e
d the Ph.D. degree in 2012, in
railway
rolling stock from Rost
ov State Transp
ort
Unive
r
sity
.
His c
u
rre
nt re
sea
r
c
h
inte
re
sts:
trac
tion m
o
tors,
switched r
e
lu
cta
n
ce m
a
chines
an
d com
puter
sim
u
lation
.
E-mail: greb
ennikovnv@mail.ru.
Kir
eev Alexan
d
er
wasborn in R
u
ssia in 1974. He received
the P
h
.D. degr
ee in 2
004 in the ar
ea
of ele
c
tri
c
a
l
m
achines
from
S
outh-Rus
s
i
an S
t
a
t
e T
echni
ca
l Univers
i
t
y
.
His
c
u
rrent res
e
arch
inter
e
sts: electrical mach
ines, freque
ncy
conver
t
ers
and c
ontrol s
y
stems.
E-mail: akir
eev
@privod-n.ru.
Evaluation Warning : The document was created with Spire.PDF for Python.