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.3
,
No
.3
, Sep
t
em
b
e
r
20
13, pp
. 251
~258
I
S
SN
: 208
8-8
6
9
4
2
51
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
Implementation of MATLAB Based Flux Linkage
Charact
eris
t
ics
Model
of
8/
6 SRM
Yo
gesh
P
a
h
a
r
i
ya
1
,
Re
kesh
S
axe
na
2
1
Electrical & Electronics
Engg
.,
Techno
crats
Institute of
Technolog
y
& Scien
ce, Bhopal,
India
2
Electrical Eng
i
n
eering
Depar
t
me
nt,
at SGSITS, Indore,
India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 23, 2012
Rev
i
sed
Jun
29,
201
3
Accepte
d
J
u
l 27, 2013
This paper is describes the method of
measuring the flux link
a
ge versus
current and ro
to
r position of
SRM for
submersible pump a
pplication. Th
e
knowledge of
flux linkag
e
char
acteris
tics
of motor is
utilized
for
determination o
f
performance
of moto
r, desig
n
of conver
t
er
and rotor
position. Proposed exper
i
mental se
tup is f
i
nding the flu
x
linkage
c
h
a
r
ac
te
ri
st
ic
s of mot
o
r a
nd t
h
ei
r
modeling in
MATLAB is also designed
using Fourier cosine coefficients.
Develop
e
d
m
odel is com
p
ared with
experimental res
u
lts an
d
validate
MATLAB model.
Keyword:
Fl
ux
l
i
nka
ge
Su
bm
ersi
bl
e Pum
p
Fourier Coe
ffi
cient
Sim
p
son’s
Rul
e
Copyright ©
201
3 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
:
Yo
ges
h
Pa
ha
ri
y
a
Depa
rt
m
e
nt
of
El
ect
ri
cal
and
El
ect
roni
cs
E
n
gi
nee
r
i
n
g,
Techn
o
c
rats Institu
te o
f
Techn
o
l
o
g
y
& Scien
ce,
A
n
and
N
a
g
a
r
,
Bh
op
al
(
M
P)
In
d
i
a,
462
021
Em
a
il: yp
ah
ariya@yah
o
o
.
com
1.
INTRODUCTION
Swi
t
c
he
d
rel
u
c
t
ance m
o
t
o
r
dri
v
es
hav
e
bec
o
m
e
t
h
e su
b
j
ect
of c
o
nsi
d
e
r
a
b
l
e
at
t
e
nt
i
on
bec
a
use
of
t
h
ei
r
in
h
e
r
e
n
t
ad
v
a
ntag
es in
v
a
r
i
able sp
eed
m
o
to
r d
r
i
v
e system
.
D
u
e to
lack of
an
y
w
i
nd
ings o
r
br
ush
e
s
on
the
ro
t
o
r,
SRM is an
ex
cep
tion
a
lly rob
u
s
t stru
ct
u
r
e, a wi
d
e
sp
eed
rang
e can
op
erate in
v
e
ry h
o
s
tile env
i
ronmen
ts
[1]. The switched reluctance
m
achine
(SR
M
) can be use
i
n
a vari
et
y
of vari
a
b
l
e
-s
pee
d
ap
pl
i
cat
i
ons
suc
h
as
fans
,
pum
ps,
h
a
nd
-t
o
o
l
s
, ce
nt
ri
fu
ges
,
m
achi
n
i
n
g s
p
i
n
dl
es,
and
el
ect
ri
c ve
hi
cl
es.
The s
u
bm
ersible pum
p
is an
e
m
erging a
pplic
ation
fo
r a
g
riculture
in rural
areas. The
s
e
rural areas
are
always sufferi
ng
from
poor quality of power s
u
pply
and this causes
the fre
que
nt breakdown and poor
per
f
o
r
m
a
nce of c
o
n
v
e
n
t
i
o
n
a
l
i
nduct
i
o
n
m
o
t
o
r. The Swi
t
c
he
d R
e
l
u
ct
ance M
o
t
o
r p
o
ssesses
uni
que
ch
aracteristics th
at th
e m
o
t
o
r
h
a
s
fau
lt to
leran
ce cap
ab
ility, ab
ility
t
o
con
tinu
e
operatio
n
d
e
sp
ite fau
l
t
e
d
wi
n
d
i
n
gs
or
i
n
vert
er
ci
rc
ui
t
r
y
[
2
,
3]
. T
h
e m
a
gnet
i
c
i
nde
pe
nde
nce
o
f
t
h
e
m
o
t
o
r p
h
ases
and
t
h
e ci
rcui
t
o
f
t
h
e
i
nve
rt
er
p
h
ases
pe
rm
it
t
h
e S
w
i
t
c
hed
Relu
ctan
ce M
o
tor
d
r
ive to
con
tin
u
e
op
eration
with
o
n
e
or m
o
re
fau
lted
pha
ses with
re
duce
d
ca
pacity. The
SRM is a cost eff
ective
and rugge
d
machine
du
e t
o
the a
b
se
nce
of a
ny
m
a
gnet
i
c
so
ur
ce i
n
i
t
s
rot
o
r [4]
.
T
h
e SR
M
can pe
rf
orm
wel
l
i
n
t
h
e su
bm
ersi
bl
e pum
p ap
pl
i
cat
i
on
due i
t
s
uni
que
cha
r
act
eristics.
Th
e stand
a
rd
SR p
o
l
e
n
u
m
b
e
r n
o
t
ation
will b
e
u
s
ed, e.g
.
a 6
/
4
m
o
to
r
h
a
s 6
stato
r
po
les
an
d
4
ro
t
o
r
poles
, a
n
d a cl
assical SR m
o
tor is de
fine
d as
[5]:
a)
A
n
inn
e
r ro
tor
b)
M
o
re st
at
or
po
l
e
s t
h
an rot
o
r
pol
es
, i
n
part
i
c
ul
ar a t
h
ree p
h
a
se
m
o
t
o
r has
a basi
c pol
e pa
t
t
e
rn o
f
6/
4,
a
fo
ur
-
pha
se 8/
6, et
c.
c)
One
t
o
ot
h pe
r pol
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
IJPE
DS
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
3
:
25
1 – 2
5
8
25
2
d)
A
sh
or
t p
itch
e
d
w
i
nd
ing
r
ound
each
stator
po
le
e)
Possi
bl
e
m
u
l
t
i
pl
es of t
h
e sam
e
basi
c pol
e pat
t
e
rn
, e.g
.
a 12/
10 i
s
t
w
o r
e
peat
s of t
h
e 6/
4 p
o
l
e
p
a
ttern
f)
Possi
bl
e i
n
t
e
r
p
ol
e p
r
oject
i
o
ns
(heat spi
k
es) on the
stator
g)
At least thre
e
phases
The
kn
o
w
l
e
d
g
e
of
fl
u
x
l
i
n
ka
ge ch
aract
eri
s
t
i
cs i
s
necessa
ry
fo
r
pr
ope
r
des
i
gn
of c
o
nve
rt
e
r
sy
st
em
and
per
f
o
r
m
a
nce anal
y
s
i
s
of t
h
e
SR
M
.
The
fl
u
x
l
i
nka
ge an
d i
n
duct
a
nce
pr
ofi
l
e of t
h
e SR
M
depe
n
d
s
on t
h
e
rot
o
r
p
o
s
ition
and
ph
ase curren
t
. Th
e fam
i
l
y
o
f
th
e flu
x
link
a
g
e
ch
aracteristics (fo
r
d
i
fferen
t
ro
tor p
o
sitio
n
s
) can
b
e
det
e
rm
i
n
ed i
n
l
a
bo
rat
o
ry
us
i
ng
Si
m
pon’s
⅓
ru
le [6
].
Th
e M
A
TLAB
m
o
d
e
lin
g of sam
e
m
o
to
r is also
desi
g
n
e
d
.
2.
MAT
H
EM
AT
ICAL
S
R
M
MO
DEL
Precise com
p
utation of the nonlinea
r m
a
gnetic ch
aracteri
s
tic at an arbi
tr
ary rotor
pos
ition and a
current is c
r
itical whe
n
perform
ance
p
r
edi
c
t
i
ons,
si
m
u
l
a
ti
ons
, com
put
er
-ai
d
e
d
desi
g
n
s
,
t
o
r
q
ue c
ont
r
o
l
an
d
sen
s
o
r
less contro
l of th
e swi
t
ch
ed
reluctance
m
o
tor
(SR
M
) drives a
r
e
carried out. T
h
e nonlinear
magnetic
ch
aracteristics in
th
e SRM are th
e fu
n
c
tion
s
o
f
bo
th
th
e
ro
to
r
po
sitio
n
and th
e curren
t
. To
im
p
l
e
m
en
t a
ccu
rat
e
sim
u
l
a
t
i
on an
d
real
-t
i
m
e cont
rol
,
t
h
e
desi
gn
ers
have
t
o
de
vel
o
p
no
vel
t
e
chni
que
s t
o
ca
l
c
ul
at
e preci
sel
y
t
h
e
no
nl
i
n
ea
r m
a
gnet
i
c
cha
r
act
eri
s
t
i
c
s of
t
h
e
SR
M
bot
h
o
n
l
i
n
e
an
d
of
fl
i
n
e
[7]
.
The SRM drive syste
m
sim
u
lation is m
u
ch
m
o
re
com
p
lex tha
n
ac &
dc
m
o
tor drive
s
because its
o
p
e
ration
a
l regio
n
is m
o
stly n
o
n
lin
ear.
The
no
n
lin
earity is in
tro
d
u
c
ed
b
y
th
e
fo
llowing
t
h
ree fact
o
r
s:
1.
Th
e
no
n
lin
ear
B-H ch
aracteri
s
tics o
f
th
e m
a
g
n
e
tic m
a
terial
.
2.
The de
pe
nde
nc
e of p
h
ase fl
u
x
l
i
nkages o
n
b
o
t
h t
h
e rot
o
r p
o
s
i
t
i
on and c
u
r
r
e
n
t
m
a
gni
t
ude
whi
l
e
i
n
o
t
h
e
r m
ach
in
es it is d
e
p
e
nd
en
t on
ly on
cu
rrent
m
a
g
n
itu
de.
3.
The
si
ngle source of
e
x
citation.
B
y
usi
ng t
h
e p
r
o
p
o
sed m
e
t
h
o
d
a de
vi
at
i
o
n o
f
t
h
e c
u
r
r
ent
sl
ope
, w
h
i
c
h i
s
n
o
t
i
n
fl
uence
d
b
y
t
h
e
m
o
t
o
r
spee
d can
be
deri
ved
.
The
devi
at
i
o
n o
f
t
h
e cu
rre
nt
sl
o
p
e i
s
o
n
l
y
rel
a
t
e
d t
o
i
n
put
d.c.
v
o
l
t
a
ge a
nd sel
f
inductance of m
o
tor. As a
result the self inductance
of
the m
o
tor can be precisely estim
a
te
by detecti
ng
current slope
[8].
SR
M
m
odel
s
are gene
ral
l
y
m
a
de u
p
of t
h
re
e part
s:
the electrical
m
odel, torque cha
r
act
eristics and
mechanical m
odel. T
h
e electri
cal circuit for
o
n
e pha
se of SR
M
i
s
sh
ow
n
i
n
Fi
gu
re 1.
Ap
pl
y
i
ng
Ki
rc
hh
o
ff
v
o
l
t
a
ge l
a
w t
h
us
v
o
l
t
a
g
e
gi
ve
n
by
E
q
u
a
t
i
on
(1
).
d
t
i
d
ir
v
)
,
(
(
1
)
Whe
r
e R is
phase resistance
and
)
,
(
i
i
s
m
a
gnet
i
c fl
u
x
i
s
gi
ve
n
by
E
quat
i
o
n
(2
).
i
i
L
i
)
,
(
)
,
(
(
2
)
Whe
r
e
)
,
(
i
L
is t
h
e ph
ase ind
u
c
t
a
n
ce, wh
ich varies as a
functio
n
o
f
ro
tor po
sitio
n (du
e
to
v
a
ryin
g
relu
ctan
ce) and ph
ase cu
rren
t
(du
e
t
o
m
a
g
n
e
tic satu
ration
)
.
Sol
v
e
Eq
uat
i
o
n (
1
) t
o
cal
c
u
l
a
t
e
m
a
gnet
i
c
fl
ux
at
va
ri
o
u
s
r
o
t
o
r an
gl
es a
n
d c
u
r
r
ent
m
a
gni
t
ude
s f
r
om
m
easures st
at
o
r
vol
t
a
ges
,
c
u
r
r
e
nt
s a
n
d
resi
st
a
n
ce as
gi
ven
i
n
Eq
uat
i
o
n (
3
).
dt
ir
v
i
)
(
)
,
(
(
3
)
Figure
1. Electrical M
odel
o
f
One
P
h
ase of
SRM
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Im
pl
eme
n
t
a
t
i
o
n
of
MAT
L
AB
Base
d Fl
ux Li
n
k
age
C
h
ar
act
e
ri
st
i
c
s Model
o
f
8/
6
SRM
(
Y
o
g
e
sh P
a
ha
ri
ya)
25
3
Th
e electrical
m
o
d
e
l o
f
t
h
e SRM can
b
e
com
p
ared
with d.c. m
o
to
r
b
y
sub
s
titu
tin
g (2
) in
(1) as fo
llo
ws:
dt
i
i
L
d
ir
v
)
)
,
(
(
dt
i
L
d
i
dt
di
i
L
ir
))
,
(
(
)
,
(
d
i
L
d
dt
d
i
dt
di
i
L
ir
))
,
(
(
)
,
(
d
i
L
d
i
dt
di
i
L
ir
))
,
(
(
)
,
(
(
4
)
There a
r
e m
a
ny approache
s
for m
odeling the SRM,
su
ch as l
o
ok
u
p
-t
abl
e
t
echni
que
s, m
a
gnet
i
c
eq
u
i
v
a
len
t
ci
rcu
it an
alysis, cub
i
c-sp
lin
e in
terp
o
l
a
tions and fin
ite-ele
m
e
n
t
an
alysis
(FEA).
Mag
n
e
tic
equi
val
e
nt
-ci
r
c
u
i
t
anal
y
s
i
s
and FEA are c
o
m
put
at
i
onal
l
y
i
n
t
e
nse an
d cu
bi
c-s
p
l
i
n
e i
n
t
e
r
pol
at
i
o
ns an
d l
o
o
k
u
p
-
tab
l
e tech
n
i
q
u
es requ
ire
numero
u
s
flux
-li
n
k
a
g
e
cu
rren
t
-
p
o
s
ition
data, wh
ich
are
o
b
tain
ed
eith
er t
h
rou
g
h
expe
ri
m
e
nt
s or
usi
n
g
FE
A,
w
h
i
c
h a
r
e t
i
m
e-inef
fect
i
v
e a
n
d
t
e
di
ou
s [
9
,
1
0
]
.
3.
DIRE
CT
FL
U
X
LI
NK
AGE METHO
D
Th
e fl
u
x
link
a
g
e
ch
aracterist
i
cs o
f
SRM d
e
p
e
nd
on
th
e
roto
r po
sition
and
th
e ex
cited
stato
r
ph
ase
current. T
h
e ideal flux linka
ge cha
r
acteristics of SRM a
r
e
r
e
prese
n
t
e
d
i
n
F
i
gu
re 2.
Th
e fl
ux
lin
k
a
g
e
characterist
i
cs at alig
n
e
d
p
o
s
ition
ar
e rep
r
esen
ted,
wh
en
th
e stat
o
r
in
t
e
rpo
l
ar ax
i
s
co
in
cid
e
s with th
e ro
tor in
terpo
l
ar ax
is and
th
e
flux
link
a
g
e
ch
aracteristic at u
n
a
lign
e
d po
sitio
n is also
represe
n
ted. T
h
e flux linka
ge characteristics at the
in
ter
m
ed
iate p
o
s
itio
n
sh
own
,
as th
e ro
tor po
sitio
n
is
ch
ang
e
d
fro
m
u
n
a
lign
e
d
p
o
sitio
n
t
o
align
e
d
p
o
s
ition
till th
e ov
erlap
o
f
t
h
e
p
o
l
e app
r
o
a
ch
ed
[11
,
12
].
Th
e
p
h
ase indu
ctan
ce
of th
e SRM d
e
p
e
n
d
s
on
b
o
t
h
th
e ex
citatio
n
cu
rren
t and
ro
t
o
r po
sitio
n. The
measurem
ent
of inductance
can be
perf
ormed
wh
ile th
e p
h
a
se
wind
ing
is ex
cited
wi
th
th
e app
r
o
p
ri
ate d
.
c.
cur
r
ent
.
T
h
e m
easurem
ent
o
f
fl
u
x
l
i
n
kages
c
a
n
be i
m
pl
em
ent
e
d i
n
t
w
o
wa
y
s
:
1.
By ap
p
l
ying
a
co
nstan
t
v
o
ltage to
p
h
a
se
w
i
nd
ing
an
d m
eas
u
r
i
n
g th
e
r
i
sing cur
r
e
n
t
.
2.
First establishi
ng a steady st
ate d. c
.
curre
nt
in the wi
ndi
ng and the
n
m
easuri
n
g the
decaying
current
when the circ
u
it is
d
e
n
e
rg
ized.
A sim
p
lified
measu
r
em
en
t circu
it fo
r
SRM fl
u
x
li
n
k
a
g
e
ch
aracteristics is sh
own
in Figure 3
.
Wh
en
a
v
o
ltage pu
lse ap
p
lied to
an
y
p
h
a
se
o
f
th
e
SRM wh
ile all o
t
h
e
r
ph
ases
a
r
e
open the
voltage
gi
ve
n by
E
quat
i
on (
5
) [
9
]
.
(
5
)
λ
(
6
)
Fi
gu
re 2.
I
d
eal
Fl
ux
Li
n
k
a
g
e
Characteristics
of SRM
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
IJPE
DS
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
3
:
25
1 – 2
5
8
25
4
Whe
r
e ‘V
m
’ vo
l
t
a
ge
acr
oss p
h
a
se
wi
ndi
ng
‘R
m
’
r
e
sistance of
th
e ph
ase
w
i
nd
ing
‘
λ
’ is
flux
link
a
g
e
From
t
h
e Equa
t
i
on (6
) fl
u
x
l
i
nka
ge can be c
a
l
c
ul
at
ed fr
om
any
num
eri
cal i
n
t
e
grat
i
o
n t
echni
que t
h
e
abo
v
e e
q
uat
i
o
n
i
s
pe
rf
orm
e
d b
y
usi
n
g
Si
m
p
son
’
s
1/
3
r
d
rul
e
.
3.
1.
Si
mpso
n’s
⅓
Rule
Sim
p
so
n’s
1/
3
r
u
l
e
i
s
one
o
f
t
h
e
p
o
pul
a
r
m
e
t
hod
o
f
nu
m
e
ri
cal
i
n
t
e
gr
at
i
on a
n
d i
t
i
s
use
d
f
o
r t
h
e
measurem
ent of
definite i
n
tegrals.
∫
Y
(
x)
dx
=h
/3[Y
0
+
4Y
1
+
2Y
2+4
Y
3
+
-
-
-
-
-
-
-
---
--
--
--
--
--
-
2Y
n-
2
+
4
Y
n-
1
+
Yn
]
(
7
)
In E
q
uat
i
on
(
7
)
Y(
x) i
s
t
h
e
fu
nct
i
on a
n
d
Y0
, Y
1
……
……. t
h
e
val
u
es o
f
f
u
nct
i
o
n at
speci
fi
e
d
in
terv
als and
h
is th
e in
terv
al
p
e
ri
o
d
.
The p
r
o
p
o
se
d m
e
t
hod ha
s be
en t
e
st
ed usi
n
g an ex
pe
ri
m
e
nt
al
0.5
-
k
W
4
2
-
V
f
o
u
r
-
p
has
e
8/
6 SR
M
dri
v
e,
whi
c
h i
s
desi
g
n
f
o
r su
b
m
ersi
bl
e pum
p
and
f
u
rt
he
r s
p
eci
fi
cat
i
on o
f
m
o
t
o
r i
s
m
e
nt
ione
d i
n
Tabl
e
1. T
h
e
d
c
r
e
sistan
ce
o
f
m
o
to
r ph
ase w
i
nd
ing
is
measu
r
ed using
V
o
ltm
eter
-
A
mmeter
m
e
t
h
od
and
it is f
ound
3.
32
1
ohm
s.
Tabl
e 1.
M
o
t
o
r
S
p
eci
fi
c
a
t
i
ons of
SR
M
Su
bm
ersi
bl
e
Pum
p
Para
m
e
ter
Value
Nu
m
b
er
of phase
4
Nu
m
b
er
of Stator
poles
8
Nu
m
b
e
r
o
f
ro
to
r p
o
les
6
Stator
I
nner
dia
m
eter
50
m
m
Rotor
outer
diam
eter
49
m
m
Stack length
102
m
m
Stator ar
c
10
mm
Rotor
ar
c
08
m
m
Air
g
ap length
0.
3
m
m
Shaf
t Dia
m
ete
r
19
mm
The expe
rim
e
n
t
al setup is shown in Fi
gure 4. An
IGBT is
use
d
as a switching de
vice in each phas
e
of
SR
M
.
Free
wheel
i
n
g
di
od
e i
s
co
n
n
ect
ed
acros
s t
h
e
m
o
tor
wi
ndi
ng
f
o
r
di
ssi
pat
e
s
t
h
e
st
ore
d
e
n
er
gy
and
a
n
Fi
gu
re
4.
E
x
p
e
ri
m
e
nt
al
Set
u
p
Fi
gu
re
3.
Si
m
p
l
i
f
i
e
d M
easu
r
i
n
g C
i
rc
ui
t
f
o
r
S
R
M
Fl
ux
Li
n
k
a
ge C
h
aract
eri
s
t
i
c
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
Im
pl
eme
n
t
a
t
i
o
n
of
MAT
L
AB
Base
d Fl
ux Li
n
k
age
C
h
ar
act
e
ri
st
i
c
s Model
o
f
8/
6
SRM
(
Y
o
g
e
sh P
a
ha
ri
ya)
25
5
R
-
C
snu
b
b
er c
i
rcui
t
i
s
used f
o
r t
h
e
pr
ot
ect
i
on
of t
h
e s
w
i
t
c
hi
n
g
de
vi
ce I
G
B
T
. A
v
o
l
t
a
ge p
u
l
s
e ap
pl
i
e
d b
y
t
u
r
n
i
n
g o
n
t
h
e
swi
t
c
h a
nd t
h
e vol
t
a
ge
an
d
cur
r
ent
wave
f
o
rm
s are reco
r
d
ed
d
u
ri
ng s
h
ort
du
rat
i
on t
h
ro
u
g
h
d
i
g
ital
storag
e o
s
cillo
scop
e. A d
i
g
ital
storag
e o
s
cillo
scope (TDS
21
00
TEKTR
ONIX) is u
s
ed
t
o
acqu
ire and
st
ore t
h
e c
u
r
r
e
n
t
an
d
v
o
l
t
a
ge
wave
f
o
rm
s di
g
i
t
a
l
l
y
.
A m
echani
s
t
’
s
di
vi
di
ng
head
(
i
nde
xi
n
g
hea
d
)
i
s
u
s
ed
t
o
h
o
l
d
t
h
e
rot
o
r
i
n
p
o
s
i
t
i
on a
g
ai
nst
h
i
gh t
o
r
q
ue
pr
o
duce
d
du
ri
ng t
h
e e
xpe
ri
m
e
nt
cur
r
ent
.
Any
one
o
f
t
h
e ph
ase i
s
co
n
n
ect
ed t
o
dc
s
u
p
p
l
y
w
h
i
l
e
al
l
ot
her
pha
ses o
p
en
. T
h
e cu
rre
nt
an
d
vol
t
a
ge
wave
f
o
rm
s across t
h
e phase
wi
n
d
i
ng a
r
e capt
u
re
i
s
DSO as s
h
o
w
n i
n
Fi
gu
re
5 a
n
d
Fi
gu
re
6.
Di
gi
t
a
l
l
y
st
ored
vo
l
t
a
ge an
d c
u
r
r
e
nt
wa
ve
fo
rm
i
s
appl
i
e
d i
n
Eq
uat
i
o
n
(
6
&
7)
t
o
calcu
late th
e fl
u
x
lin
k
a
g
e
at
differen
t
cu
rren
t
lev
e
ls
o
f
a 0.5k
w 8
/
6
SRM is ob
tain
ed.
Tabl
e 2. Fl
u
x
Li
nka
ge
C
h
ara
c
t
e
ri
st
i
c
s
Cu
rren
t
in
Am
p
Flux Linkage in
mWb at
Different Rotor Position
0 deg
8 deg
16 deg
25 deg
30 deg
0 0
0
0
0
0
0.
5 1.
2
1.
8
2.
4
2.
7
4.
8
0.
948
2
3
3.
9
4.
8
6.
8
1.
481
3.
3
3.
9
5
6.
6
9.
8
2.
104
4.
5
5
7.
2
9.
3
13.
4
2.
667
5.
7
6.
6
8.
7
11.
7
16.
1
3.
289
6.
6
7.
8
11
14.
4
19.
5
3.
763
7.
5
8.
5
12.
3
16.
8
22.
2
4.
44
8.
7
10
15
20
26.
7
5.
03
9.
6
11
17.
4
23
30
5.
68
10.
7
12.
6
19.
2
26
35.
1
6.
45
11.
7
13.
5
22.
8
30.
8
39.
8
7.
04
13
15.
2
25
34
44.
6
7.
51
14
16.
6
26.
9
37
47.
3
8.
01
15
17.
9
28.
5
39.
7
50
8.
51
16
19.
3
30
41.
8
52
9.
01
16.
5
20.
5
31.
5
43.
5
54
9.
51
17
21
33.
1
45
55.
8
10
18.
1
22.
4
34
46
57.
3
10.
5
19.
1
22.
9
35.
6
46.
8
58
11
19.
6
24
36.
5
47.
5
58.
5
12.
68
22.
2
27.
2
38.
2
48.
5
58.
8
Th
e
flux
lin
kag
e
at equ
a
lly sp
aced
ro
tor po
sitio
n
s
b
e
t
w
een un
align
e
d
to
align
e
d
p
o
s
ition
s
are
reco
rde
d
as
gi
ven i
n
Tabl
e
2.
The fl
u
x
l
i
n
ka
ge cha
r
act
eri
s
t
i
c
s of t
h
e m
o
t
o
r
based
o
n
ex
pe
ri
m
e
nt
s i
s
shown i
n
Fi
gu
re 7.
Fig
u
re 6
.
Vo
ltag
e
Acro
ss
t
h
e Mo
to
r
Ph
ase W
i
nd
ing
Fig
u
r
e
5
.
Cur
r
e
n
t
thr
oug
h th
e
Mo
to
r Ph
ase
W
i
nd
ing
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
IJPE
DS
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
3
:
25
1 – 2
5
8
25
6
4
.
MODELLING OF SRM FLUX
LINK
AGE CHARACTERISTI
CS IN
MATL
AB
Th
e m
o
d
e
lin
g is m
o
tiv
ated
b
y
th
e n
e
ed
for accu
rate
d
r
i
v
e perfo
r
m
a
n
ce esti
m
a
te to
su
pp
ort op
ti
m
i
zed
ex
citatio
n
and
co
n
t
ro
l. In
t
h
is reg
a
rd
on
e
o
f
th
e m
o
st ch
allen
g
i
n
g
asp
ects
o
f
m
o
d
e
lin
g the driv
e is th
e an
alytic
represen
tatio
n
o
f
t
h
e m
o
to
r,
wh
ich
co
n
t
ains sp
atial an
d
m
a
g
n
e
tic
n
o
n
lin
earities. Th
e m
o
d
e
lin
g appro
a
ch
u
s
ed
h
e
re is
b
a
sed on
ch
aracteristics o
f
ex
isti
n
g
m
o
to
r.
Once the
SRM is m
odeled a
n
alytically, a general
exp
r
essi
on
f
o
r
t
o
r
que
, po
wer
pr
o
duct
i
o
n
a
n
d
l
o
sses can
be
deri
ve
[
1
0]
.
The fl
ux linka
ge curre
nt characteristics are use
d
to
represe
n
t the coupling be
tween t
h
e electrical and
mech
an
ical termin
als o
f
th
e
m
o
to
r. Th
e m
a
g
n
e
tic saturatio
n
is
v
e
ry im
p
o
rtan
t to
th
e
h
i
g
h
p
e
rfo
r
m
a
n
ce o
f
th
e
SRM dri
v
e.
The piece wis
e
linearization
of the m
a
gnetic char
acteristic
s has accuracy limitations and the SRM
d
r
i
v
e m
o
d
e
lin
g
req
u
i
rem
e
n
t
s
m
a
k
e
s sen
s
e to
fin
d
an
analytic ex
p
r
essio
n
for flux
link
a
g
e
/cu
r
ren
t
/
p
o
s
itio
n
d
a
ta. Th
e
g
o
a
l
o
f
th
is an
alytic ex
pression
is to
p
r
ov
ide all o
f
th
e flux
link
a
g
e
cu
rren
t in
fo
rm
atio
n
for ev
ery
ro
t
o
r
p
o
s
ition
in
on
e su
mmary eq
u
a
tion
th
at
is si
m
p
le,
m
a
t
c
h
e
s th
e ex
p
e
ri
men
t
al d
a
ta can
b
e
con
n
ected to
a
phy
si
cal
i
n
t
e
r
p
ret
a
t
i
on. F
r
om
t
h
e ex
peri
m
e
nt
al
dat
a
of SR
M
,
a fu
nct
i
on
of fl
u
x
l
i
nka
ge
i
s
chose
n
as s
u
m
m
a
r
y
Equ
a
tio
n (8
).
Th
e co
efficien
t
s
a,
b
and
c i
n
Equ
a
tio
n (8
) to v
a
ry w
ith ro
tor
p
o
s
ition
,
consid
ering
t
h
e
physical
significa
nce t
h
at can
be attac
h
ed to
eac
h
of
these c
o
efficients [10].
,
1
(
8
)
The fl
ux l
i
n
ka
ge cu
rre
nt
rel
a
t
i
ons
hi
p f
o
r ea
ch p
h
ase
of the
m
o
tor is the sam
e
except for the angula
r
depe
n
d
ence
t
a
kes i
n
t
o
acco
u
n
t
t
h
e
phy
si
cal
i
n
t
e
rp
ol
ar s
p
a
c
i
ng.
The i
nhe
rent
peri
odi
c st
ruct
ure
of t
h
e
SR
M
i
s
gi
ve
n i
n
t
h
e va
ri
at
i
ons o
f
t
h
e coef
fi
ci
ent
s
a, b an
d c
m
a
y
b
e
repre
s
ent
e
d by
Fo
uri
e
r c
o
s
i
ne seri
es of t
h
e form
in
Eq
u
a
tion
s
(9, 10
, 11).
∑
cos
∝
(
9
)
∑
co
s
∝
(
1
0
)
∑
co
s
∝
(
1
1
)
Whe
r
e
a
k
, b
k
an
d c
k
represen
ts
th
e k
th
Fou
r
ier co
efficien
t
o
f
th
e
fittin
g
co
efficien
t. Th
e
period
icity o
f
th
e Fourier series is d
e
p
e
nd
en
t on
,
which is the
num
b
er of electrical
cycles seen
by each
phase
.
For the
expe
ri
m
e
nt
al
SR
M
,
= 6
.
The Fou
r
ier co
efficien
ts listed
i
n
Tab
l
e
3 are
use
d
to ge
ne
ra
te the coefficient a,
b
and c
as de
scr
i
bed at
al
l
rot
o
r
p
o
si
t
i
ons
. T
h
ere
f
o
r
e F
o
uri
e
r coe
ffi
ci
ent
i
n
Ta
bl
e 3
des
c
ri
be
d t
h
e m
a
gnet
i
c
st
ruct
u
r
e o
f
t
h
e
expe
ri
m
e
nt
al
SR
M
.
Eq
uat
i
o
n (
8
) i
s
a
pp
lied
fo
r ex
perim
e
ntal SRM
with
coefficients a, b and
c
as sho
w
n i
n
F
i
gu
re 8. T
h
e
sim
u
l
a
t
e
d fl
ux
l
i
nkage c
h
ara
c
t
e
ri
st
i
c
s of expe
ri
m
e
nt
al
SR
M
are prese
n
t
e
d i
n
Tabl
e 4.
Fi
gu
re
7.
Ex
pe
ri
m
e
nt
al
Fl
ux
Li
nka
ge C
h
ara
c
t
e
ri
st
i
c
s of
SR
M
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Im
pl
eme
n
t
a
t
i
o
n
of
MAT
L
AB
Base
d Fl
ux Li
n
k
age
C
h
ar
act
e
ri
st
i
c
s Model
o
f
8/
6
SRM
(
Y
o
g
e
sh P
a
ha
ri
ya)
25
7
Tabl
e
3.
Fo
uri
e
r C
o
e
ffi
ci
ent
s
f
o
r
Ex
pe
ri
m
e
ntal
SR
M
Tabl
e
4.
Si
m
u
lat
e
d Fl
ux
Li
n
k
a
ge C
h
aract
eri
s
t
i
c
s
Curren
t
I
Flux Linkage in
mWb at
Different Rotor Position
Unaligned
8 Degree
16 Degree
25 Degree
Aligned
0
0
0
0 0 0
1
1.
92
2.
355
5.
41
7.
78
8.
59
2
3.
25
4.
56
10.
32
15.
36
17.
15
3
5.
69
6.
67
14.
71
20.
69
23.
01
4
7.
57
9.
45
19.
13
25.
94
28.
95
5
9.
53
11.
17
23.
12
31.
17
34.
33
6
11.
46
13.
33
26.
94
35.
87
39.
51
7
13.
3
15.
49
30.
33
40.
26
43.
94
8
15.
46
17.
55
33.
73
44.
38
48.
05
9
16.
99
19.
64
36.
89
47.
74
51.
73
10
18.
95
21.
85
39.
88
51.
24
55.
22
11
20.
8
23.
93
42.
62
54.
12
58.
16
5.
CO
NCL
USI
O
N
The Switched
Reluctance Motor dri
v
e has
excellent perform
ance chara
c
teristics with
v
a
riation
in
spee
d, phase c
u
rrent,
num
b
er of stat
or and ro
tor po
les.
Th
e m
o
to
r is ab
le to
g
i
v
e
s th
e ch
aracterist
i
cs o
f
in
du
ctio
n m
o
to
r,
d
c
shu
n
t
m
o
to
r or series m
o
to
r
o
r
co
m
b
in
atio
n
o
f
m
o
to
rs.
Thi
s
pa
per has
been p
r
esent
e
d ex
peri
m
e
nt
al fl
ux l
i
nka
ge c
h
aract
eri
s
t
i
c
s o
f
su
bm
ersi
bl
e
pum
p SR
M
.
Obtaine
d
res
u
lts are acce
ptable for sim
u
lation of SR
M
drive and its c
o
ntrol stra
tegy i
n
s
ubm
ersible
pum
p
appl
i
cat
i
o
n. F
u
rt
her M
A
TL
A
B
m
odel
fo
r sa
m
e
m
o
t
o
r has
devel
ope
d
usi
n
g F
o
u
r
i
e
r se
ri
es cosi
ne c
o
ef
fi
ci
ent
s
.
The acc
ur
acy
o
f
t
h
e
m
odel
has
ve
ri
fi
ed
wi
t
h
e
xpe
ri
m
e
nt
al
resul
t
s
an
d t
h
ey
have
val
i
d
at
ed
t
h
e m
odel
.
REFERE
NC
ES
[1]
AD Cheok, N
Ertugrul. Computer B
a
sed Auto
mated Te
st Mea
s
urem
ent S
y
ste
m
For Determ
ining Magnet
i
z
a
ti
o
n
Charac
teris
t
ics
of S
w
itched Re
luct
ance M
o
tors
.
IEEE Transactions on Instrumentation
&
M
e
asurement
. 20
01;
50(3): 690-696
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[2]
Yogesh Pahariya, R
a
kesh Sax
e
na, Bh
im Singh. Switched
Relu
ctan
ce Motor
D
r
ive: A New C
oncept in Var
i
able
S
p
eed Drive
.
I
E
EMA Journal.
2
005; 25(10): 72–
76.
k a
b
c
0 43.
309
1
-
0
.
0792
1.
2648
1 33.
872
7
-
0
.
0415
-
0
.
6771
2 -
3
.
4927
0.
0211
-
0
.
0168
3 -
0
.
7585
-
0
.
0124
0.
0376
4 -
0
.
141
0.
0039
0.
0027
5 -
0
.
8969
-
0
.
0021
0.
0307
6 0.
1335
-
0
.
0013
0.
0107
7 -
0
.
2167
0.
0011
-
0
.
0016
8 0.
3225
-
0
.
0014
-
0
.
0038
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I
S
SN
:
2
088
-86
94
IJPE
DS
V
o
l
.
3, N
o
. 3,
Se
pt
em
ber 20
1
3
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5
8
25
8
[3]
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eph
e
ns. Faul
t De
tec
t
ic
a
nd Man
a
gem
e
nt S
y
s
t
em
for
Fault-
Tol
e
ran
t
S
w
itched
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ct
a
n
ce Motor
Drive
s
.
IEEE Transactio
ns on
Industry Applications
. 199
1; 27(6): 1098-1
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[4]
Chris S Edrington, B Fahimi, M Kris
hnamurt
h
y
. An Autocalibrating Inducta
n
ce Model for Switched Relctan
ce
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I
EEE Transactio
ns on
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. 200
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[5]
HC Lovatt. Ana
l
ytic
al Model of
A Cl
as
s
i
cal S
w
itch
e
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ctan
c
e
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[6]
A Ferrero, A Raciti. A Digital Method for
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ination Of Magnetic Character
i
s
tic Of Variab
le Reluctance Motor
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4): 604-608.
[7]
XD Xue, KWE
Cheng, SL Ho. A Self Training
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Method to Calculate the Ma
gnetic C
h
aracteristics for
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e
luc
t
ance
Motor Driv
e.
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E
EE Transactions on Magn
etics
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[8]
Tian Hua, Ch
in
g Gua Chen. Implementation
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orless Switched Relu
ctan
ce Drive with Self Inductance
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ating
Te
ch
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IE
EE I
n
d
u
s
t
r
i
al El
ec
tr
oni
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[9]
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n, JF Chen.
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m
p
lified Flux-
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r Switched-R
e
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ce Motors
.
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ec
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y, JH Lang. Mod
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r Va
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e
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ct
anc
e
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EE Proc
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c
tri
c
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r
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90; 137(5): 314-
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[11]
V Ramnar
y
a
nnan, L Venkatesha,
Debi Prasad P
a
nda. Flux Link
age Ch
aracte
r
i
st
ic of
Switched
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anc
e
Mot
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r.
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t
em
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e
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[12]
H Cailleux
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Chenadec. Com
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ari
s
on of Measurem
ent Methods t
o
Determ
ine th
e Ele
c
trom
agnet
i
c
Charact
eris
t
i
cs
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w
itched Reluct
anc
e
M
o
t
o
rs
.
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r
ive Design an
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tions (
E
PE Chap
ter drives)
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994: 639-644.
BIOGRAP
HI
ES OF
AUTH
ORS
Dr. Yogesh Pahari
ya
is present
l
y
working
as Pr
ofessor & Direc
t
or in T
echno
cr
ats Institu
te of
Techno
log
y
& Science, Bhopal, India since Ap
r
il 2012. He co
mpleted his B. E. in Electr
i
cal
Engineering fro
m
Shri
G. S. In
stitute of Techn
o
log
y
& Sci
e
nce, Indore in 199
1, M. Tech
. in
Energ
y
Manag
e
ment from School of Energ
y
& Environmental Studies, D
e
vi Ahily
a
bai
University
, Indo
re in 1994
and P
h
. D. from Shri
G.
S. Institute of
Technol
og
y
& Science,
Indo
re
under Rajeev Gandhi T
echnolog
ical University
, B
hopal, in
2011.
Dr. Pahariy
a
started his
car
eer f
r
om Industr
y
Wo
ckhardt Limited, India.
He worked 4
y
r
s in
industr
y
and holded various positions in his 15
yr
s of teaching
ex
perien
ce. He pu
blished 16 nos.
research
pap
e
rs in national & Internation
a
l Journ
a
ls & Confer
ences.
He is Fellow Mem
b
er of Institu
tion of Eng
i
neer
s (India), Kolk
at
a and Indi
an Socie
t
y of Ligh
t
Engineers, New Delhi (ISLE)
. Life Member of
Indian S
o
cie
t
y for
Tec
hnical Education (ISTE)
,
New Delhi. Sen
i
or Mem
b
er, Int
e
rnat
ional Asso
ciation of Computer Sc
ien
ce and
Information
Techno
log
y
(IA
CSIT), Singapor
e and
Member,
In
ternational Association
of
En
gineers, Hong
Kong.
His research
ar
eas are
El
ectr
i
cal Driv
es, En
erg
y
Auditing
,
Energ
y
Mana
gem
e
nt, Power
E
l
ec
t
r
onic
s
et
c
.
Dr. Rakesh Sa
xena
is present
l
y
working as
pr
ofessor & He
ad in Shri
G.
S. Institut
e
o
f
Techno
log
y
and
Science, Indor
e since 1987. He co
mpleted h
i
s B. E.
in Electrical Engin
eer
ing
from Jiwaji University
, Gwalior
in 1984, M. E. in Power Electronics in 1987
and Ph. D. in
Power Electron
ics & Driv
es in
2
003 from Devi
Ahily
a
bai University
, Indor
e.
He has published several r
e
sear
ch
papers
in n
a
tio
nal
& in
tern
atio
nal
journals
and
conferen
ces.
His
res
ear
ch a
r
e
a
s
are
E
l
e
c
tri
cal
Drives
, P
o
wer
E
l
ec
tronics
,
Digi
t
a
l Con
t
rol,
High
Voltage
et
c.
Evaluation Warning : The document was created with Spire.PDF for Python.