Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 4
,
A
ugu
st
2016
, pp
. 13
85
~
1
394
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
4.9
646
1
385
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
/
IJECE
A Modular Approach and Simula
tion of an Asynchronous
Machine
Z
i
neb Mekrin
i, Seddik
Bri
Materials and
In
strumentation
(
M
IM),
High Sch
ool of
Technolo
g
y
, Moulay
Ismail Univ
ersity
, M
e
knes, Moro
cco
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 5, 2015
Rev
i
sed
Feb
26
, 20
16
Accepted
Mar 10, 2016
This ar
ticle pr
esents the modeling
and
simulation o
f
th
e as
y
n
chronou
s
m
achine.
The a
i
m
of this
res
earc
h
is
the m
a
s
t
er
y
of the el
ectr
i
c
a
l,
m
echanic
al
and magnetic behaviors of this type of
m
achine
.
T
h
e Matl
ab/Sim
ulink is used
for
sim
u
lation
two
t
y
pes
of
no-load and a
dditiona
l
lo
ad services in
transition
a
l and
perm
anent ope
ration
.
The Ana
l
ytic
al equ
a
ti
ons describin
g
the
two oper
a
ti
ng s
y
s
t
em
s
are
evalu
a
te
d a
n
d de
v
e
l
o
pe
d
by
a
g
e
n
e
r
a
l
i
z
e
d
model of a three-phase induction
motor.
The simulation r
e
sults presented in
this ar
ticle
confirms that th
e pro
posed
model gave a satisf
actor
y response
in
term
s
of torqu
e
c
h
arac
teris
t
ics
an
d s
p
eed.
Keyword:
abc-qd c
o
nvers
i
ons
Async
h
ronous machine
M
odel
i
n
g
Spee
d
Torque
Copyright ©
201
6 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
:
Zin
e
b Mekr
in
i,
M
a
terials and
I
n
str
u
m
e
ntation (M
IM
)
,
H
i
gh
Scho
o
l
of Techno
log
y
,
Mo
u
l
ay Ism
a
i
l
U
n
i
v
er
sity,
M
e
knes
,
M
o
r
o
cco.
Em
a
il: zin
e
b
.
mek
r
i
n
i@g
m
ail.co
m
1.
INTRODUCTION
One
of the m
o
st comm
on electrical
m
o
tor
used in
m
o
st
appl
i
cat
i
ons
whi
c
h i
s
kn
ow
n a
s
i
n
d
u
ct
i
o
n
m
o
tor. This
motor is als
o
ca
lled as asy
n
chronous
m
o
tor
because it runs at a s
p
ee
d le
ss tha
n
sy
nchronous
sp
eed
b
ecau
s
e th
e ro
tating
m
a
g
n
e
tic field
which
is p
r
odu
ced
in
th
e stato
r
will g
e
n
e
rate flux
in
th
e ro
to
r
wh
ich
will
m
a
k
e
th
e ro
tor to
ro
tate,
b
u
t
du
e to
th
e lag
g
i
n
g
o
f
fl
u
x
cu
rren
t in
th
e ro
tor with
flux
cu
rren
t in
th
e stato
r
,
th
e ro
tor
will nev
e
r reach
t
o
its ro
tatin
g
m
a
gn
etic field
sp
eed
[1
]-[3
]
.
En
erg
y
su
pp
li
ed
to th
e i
n
ductio
n
m
o
to
r is d
i
stribu
ted in th
e two
p
a
rts, th
e fi
rst is in th
e form
o
f
m
echani
cal
ou
t
put
an
d sec
o
n
d
o
n
e i
s
i
n
t
h
e
fo
rm
of l
o
sse
s. Fo
r t
h
e
hi
g
h
pe
rf
orm
a
nce
of t
h
e m
o
t
o
r
l
o
sses
sho
u
l
d
be sm
al
l
,
so t
h
e
o
u
t
p
ut
o
f
m
o
t
o
r
g
o
e
s hi
gh
,
In
d
u
ct
i
on m
o
t
o
r
ef
fi
ci
ency
i
s
depe
nde
nt
o
n
m
a
ny
m
o
t
o
r
param
e
t
e
rs;
ho
weve
r i
t
i
s
a
fu
nct
i
o
n of t
h
e operat
i
ng
s
p
eed an
d ap
pl
i
e
d v
o
l
t
a
ge hei
r
im
pl
em
ent
a
t
i
on i
n
SIMULINK
is o
u
tlin
ed
[4
],[5
]
.
Indu
ctio
n
m
o
to
rs con
s
titu
te
a th
eoretically
in
tere
sting
and
p
r
actically im
p
o
r
tan
t
class o
f
non
lin
ear
sy
st
em
s. They
are
desc
ri
be
d
by
no
nl
i
n
ea
r
di
ffe
re
nt
i
a
l
eq
uat
i
o
n
[
5
]
.
T
h
e v
o
l
t
a
ge a
n
d
t
o
r
que
eq
uat
i
o
ns t
h
at
descri
be t
h
e
d
y
n
am
i
c
beha
vi
or
o
f
a
n
i
n
d
u
ct
i
on m
o
t
o
r
are
t
i
m
e
-vary
i
ng
.
It
i
s
succe
ssf
ul
l
y
use
d
t
o
sol
v
e suc
h
di
ffe
re
nt
i
a
l
equ
a
t
i
ons i
t
can
t
h
us
be m
odel
e
d
by
i
n
t
e
rc
on
nec
t
i
on
of a
p
pr
op
r
i
at
e funct
i
on
bl
ock
s
, eac
h
of
whi
c
h
perform
i
ng a specific m
a
the
m
atical operati
on
[6].
A poly
pha
se wi
n
d
i
ng
(a,
b
,c) ca
n
be r
e
duce
d
t
o
a set
of t
w
o
pha
se
wi
n
d
i
n
g
s
(
q
-
d
)
,
t
h
e st
at
or a
n
d
rot
o
r
vari
a
b
l
e
s (
v
ol
t
a
ges,
cu
rre
nt
s
and
fl
ux
l
i
n
ka
ges)
o
f
a
n
i
n
d
u
ct
i
on
machine are transfe
rre
d to a
refe
rence
fram
e
, which m
a
y
ro
tate at an
y an
gu
lar
v
e
lo
city o
r
rem
a
in
stat
io
n
a
ry
[7
].
Th
is article in
clud
es t
h
e
fo
llo
wi
n
g
section
s
:
- The i
n
t
r
od
uc
t
i
on p
r
ese
n
t
s
t
h
e i
m
port
a
nce
of el
ect
ri
cal
machines in the econom
y
and t
h
e si
m
u
l
a
t
i
on t
ool
s
use
d
i
n
t
h
e
fi
el
d
of
electrical engi
neeri
n
g.
- T
h
e the
o
retical study
of the
asynchronous machine
m
odel.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
13
85
–
1
394
1
386
- Th
e sim
u
latio
n
m
o
d
e
l in
t
h
e
MATLAB
/ Si
m
u
l
i
n
k
.
- T
h
e
results a
n
d disc
ussi
on.
2.
THEORETICAL ANALYSIS
Th
is
research
ai
m
e
d
to
inv
e
stig
ate wh
eth
e
r indu
ctio
n mo
tor
o
p
e
ratio
nal si
m
u
latio
n
s
with
g
e
n
e
ral
eq
u
a
tion
s
cou
l
d
b
e
u
s
ed fo
r co
nd
itio
n m
o
n
ito
ri
n
g
and
d
i
agn
o
s
is of indu
ctio
n
m
o
to
rs. Therefo
r
e, a theoretical
m
o
t
o
r anal
y
s
i
s
was m
a
de
base
d o
n
ge
n
e
ral
i
zed r
o
t
a
t
i
ng
fi
el
d t
h
eo
r
y
and by
m
a
ki
n
g
t
h
e f
o
l
l
o
wi
n
g
assum
p
t
i
ons w
h
i
c
h
a
r
e
c
o
m
m
onl
y
rega
rde
d
as
ap
pr
o
p
ri
at
e [8]
:
-
Th
e m
a
g
n
e
tic
p
e
rm
eab
ility o
f
iron
is con
s
id
ered to
b
e
i
n
fi
n
ite an
d th
e
air-gap
is
v
e
ry
sm
al
l an
d sm
o
o
t
h
.
-
Th
e state
o
f
operatio
n rem
a
in
s far fro
m
m
a
g
n
etic satu
ratio
n.
-
The sel
f-induct
ances a
n
d m
u
tual-inductance
s bet
w
een
stator or rotor
phase
s
are c
o
nstant.
-
Mutual-induct
ances betwee
n the
st
ato
r
and ro
tor
wind
ing
s
are fun
c
tio
ns
of th
e ro
tor
p
o
s
i
tio
n
.
-
Space m
a
gnetic
m
o
tive force
(MMF) and flux profiles are
consi
d
ere
d
to be sinus
o
ida
l
distribute
d
a
nd
hi
g
h
er
ha
rm
oni
cs are
ne
gl
i
g
i
b
l
e
.
Th
e asy
n
chro
no
u
s
m
ach
in
e is rep
r
esen
ted b
y
6
wind
ing
s
3 in
th
e stato
r
an
d 3
i
n
th
e ro
tor as fo
llo
ws:
(
1
)
-
Vsa,
Vs
b a
n
d
Vsc
(V
):
a
-
axi
s
, b
-
a
x
i
s
a
n
d
c-
axi
s
c
o
m
pone
n
t
s of
t
h
e
st
at
or
vol
t
a
ge
ve
ct
or
Vs.
-
V
r
a
,
V
r
b a
n
d
V
r
c (
V
):
a-a
x
i
s
,
b-a
x
i
s
a
n
d
c-a
x
i
s
com
pone
nt
s
of
t
h
e st
at
o
r
v
o
l
t
a
ge vect
or
V
r
.
2.
1.
Electrical equati
on
The
necessa
ry electrical
m
odel of the t
h
ree-
p
h
ase
i
n
d
u
c
t
i
on
m
o
t
o
r was obt
ai
ne
d usi
n
g wel
l
-
doc
um
ent
e
d m
o
t
o
r m
odel
s
[
9
]
.
The m
a
t
r
i
x
f
o
rm
of t
h
e st
at
or
an
d
rot
o
r
v
o
l
t
a
ge eq
uat
i
o
ns
:
(2
)
The a
p
propriate subsc
r
ipts as
, bs
, cs, ar
, br
, a
n
d cr
, th
e
vo
ltag
e
eq
uatio
n
s
of th
e m
a
g
n
e
tically co
up
led
stato
r
an
d ro
tor circu
its can
b
e
written as
fo
ll
o
w
s:
(3
)
Th
is m
a
th
e
m
a
tical
m
o
d
e
l is
a syste
m
o
f
six
d
i
fferen
tial eq
u
a
tion
s
with
co
efficien
ts fun
c
tion
s
p
e
ri
o
d
i
cal
o
f
time, reso
l
u
tion
is d
i
fficu
lt ev
en
with
th
e use
o
f
th
e
nu
m
e
ric
a
l to
o
l
.
To
rem
e
d
y
th
is prob
lem
we u
s
e th
e three-ph
ase to
t
w
o-a
x
i
s
vol
t
a
ge
t
r
a
n
sfo
r
m
a
t
i
on .Th
e
co
nve
rsi
o
n
of a three-phas
e syste
m
(a,
b,
c) in a
t
w
o-
p
h
a
s
e sy
st
em
(d, q
)
i
s
gi
ve
n
by
:
(4
)
In t
h
e electric
a
l
m
odel, the
two-phase
voltage [Vds
,
Vq
s, Vd
r,
Vqr] is th
e inpu
t and th
e cu
rren
t
vector [i
ds, i
q
s
,
idr, iqr] is the ou
tput vect
or. The
rotor
vol
tage vect
or
is
norm
ally zero
because of t
h
e
short-
ci
rcui
t
e
d
ca
ge rot
o
r wi
n
d
i
n
g,
Vd
r=0
a
n
d
V
q
r
=
0 [1
0]
.
dt
d
*
Vr
r
Ir
Rr
)
3
4
-
ft
cos(2
*
Vsc
)
3
2
-
ft
cos(2
*
Vsb
ft)
cos(2
*
Vs
a
Vm
Vm
Vm
)
3
4
-
ft
cos(2
*
Vrc
)
3
2
-
ft
cos(2
*
Vrb
ft)
cos(2
*
Vra
Vm
Vm
Vm
dt
d
*
Vs
s
Is
Rs
dt
d
Vcs
dt
d
Vbs
dt
d
Vas
cs
RsIcs
bs
RsIbs
as
RsIas
d
t
d
Vcr
dt
d
Vbr
dt
d
Var
cr
RrIcr
br
RrIbr
ar
RrIar
)
2
3
2
3
(
3
2
)
2
1
2
1
(
3
2
Vsc
Vsb
Vsa
Vsq
Vsc
Vsb
Vsa
Vsd
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Modular
Approac
h
and Si
mul
a
tion
of an Async
h
r
o
nou
s
Mac
h
ine (Zine
b
Mekri
n
i)
1
387
‘
(5)
-
Ids
,
I
q
s
(
A
):
d-
axi
s
a
n
d
q
-
axi
s
com
pone
nt
s
o
f
t
h
e
st
at
or
cu
rr
ent
vect
ors
Is
.
-
Id
r,
I
q
r
(A
):
d-
axi
s
a
n
d
q
-
axi
s
com
pone
nt
s
o
f
t
h
e
r
o
t
o
r c
u
r
r
e
nt
vect
ors
I
r
.
-
Rr (
Ω
): rotor
resistance.
-
Rs (
Ω
)
:
ro
to
r
resistan
ce.
-
s
,
r
:(rad
/ s): stator an
d ro
to
r Ele
c
trical Heart
b
e
a
t.
-
s
,
r
: stator a
n
d
rot
o
r
fluxes
linka
ge.
2.
2.
Ma
gne
t
ic Equ
a
ti
on
In
m
a
trix
no
tatio
n
,
th
e
flux
lin
k
a
g
e
s
of th
e stato
r
and
ro
t
o
r
wind
ing
s
m
a
y
b
e
written
in term
s o
f
the
winding inductances a
n
d the
c
u
r
r
ent i
n
the
re
fere
nce
[1
1]
:
(6
)
-
Ls (H): stat
or i
n
ductance
.
-
Lr
(H
): r
o
to
r in
ducta
nce.
-
M (H): Mut
u
al Inductance
bet
w
een the
stator and the
rotor
.
-
Is, Ir: S
t
ator
an
d rot
o
r
c
u
rre
nts.
2.
3.
Equations
of power
and
tor
que
Th
e con
v
e
rsion
s
k
e
ep
in
stan
tan
e
ou
s power
.
Th
e last
p
o
wer will b
e
written
:
(7
)
Th
e
first term
is easily id
en
ti
fiab
le in
j
o
u
l
e
lo
sses; th
e seco
nd term
co
rresp
ond
s t
o
elect
ro
m
a
g
n
e
tic
p
o
wer; th
e th
ird
term
represen
ts th
e
r
efore the electrical power tra
n
sform
e
d int
o
m
echani
cal powe
r
.
In the two-
axis stator re
fe
rence
fram
e, the electrom
a
gne
t
i
c
t
o
rq
ue C
e
i
s
gi
ve
n
by
:
(8
)
-
Ω
s (rad / s): st
ator a
n
gular el
ectrical fre
que
ncy
-
Ce (Nm
)
: Electro
m
a
g
n
e
tic torq
u
e
-
P: Pole
num
b
er
2.
4.
Mech
ani
c
al
E
qua
ti
on
M
echani
cal
pa
rt
o
f
i
n
d
u
ct
i
o
n m
o
t
o
r ca
n
be
descri
be
d
by
(
9
)
,
whe
r
e
i
s
an
g
u
l
a
r
ro
t
o
r
vel
o
ci
t
y
,
J- m
o
m
e
nt
of
i
n
ert
i
a
, C
r
-
m
e
chani
cal
t
o
r
que
, C
e
el
ect
r
o
m
a
gnet
i
c
t
o
r
que
[
12]
.
(9
)
0
*
0
*
*
dt
qr
d
dr
r
Iqr
Rr
Vqr
dt
dr
d
qr
r
Idr
Rr
Vdr
dt
qs
d
ds
s
Iqs
Rs
Vqs
dt
ds
d
qs
s
Ids
Rs
Vds
*
*
Is
Msr
Ir
Lr
Ir
Msr
Is
Ls
*
*
r
*
*
s
]
*
*
[
]
*
*
[
²]
*
²
*
[
Isd
sq
Isq
sd
s
Isq
dt
sq
d
Isd
dt
sd
d
Isq
Rs
Isd
Rs
Pi
)
*
*
(
*
)
*
*
(
*
)
*
*
(
*
)
*
*
(
*
Irq
Isd
Ird
Isq
M
P
Ce
Isd
sq
Isq
sd
P
Ce
Isd
sq
Isq
sd
s
s
s
Pe
Ce
Isd
s
q
Isq
s
d
s
s
Ce
Pe
Cr
Ce
dt
r
d
J
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
13
85
–
1
394
1
388
2.
5.
Induc
tion
motor
slip
an
d efficiency of
as
ynchr
o
nous m
o
tor
Th
e m
o
to
r
slip
b
e
tween
th
e swiv
el
field
an
d th
e
ro
t
o
r is spelt as fo
llows:
(1
0)
The e
f
ficiency
of the m
achine
va
ries
according to t
h
eir
power is
give
n
by:
(1
1)
-
Pa: Ab
so
rb
ed
po
w
e
r
-
Pu: Out
put Power
3.
R
E
SU
LTS AN
D IN
TE
RPRETATIONS
Th
e ind
u
c
tion
mach
in
e m
o
d
e
l i
m
p
l
e
m
en
ted
in
th
is p
a
p
e
r is sh
own
in
Fi
g
u
re 1. It consists o
f
six
m
a
jor
bl
oc
ks:
con
v
e
r
si
o
n
, a
b
c-d
q
, i
n
d
u
ct
i
o
n
m
achi
n
e d
-
q
m
odel
bl
ocks
,
Joul
e st
at
o
r
a
n
d r
o
t
o
r l
o
sses
bl
oc
ks,
slip and e
fficie
n
cy bl
ocks.
Th
e
fo
ll
o
w
i
n
g sub
s
ection
s
will exp
l
ain
each
b
l
o
c
k
.
In th
is m
o
d
e
l t
h
e sim
u
latio
n
starts
with
gene
rat
i
n
g t
h
re
e-p
h
ase st
at
o
r
vol
t
a
ge
s acc
or
di
n
g
t
o
t
h
e e
q
uat
i
o
n
s
(
1
)
,
a
n
d t
h
e
n
t
r
a
n
s
f
o
r
m
i
ng t
h
ese
bal
a
nced
vol
t
a
ge
s t
o
t
w
o p
h
ase
vol
t
a
g
e
s refe
rre
d t
o
t
h
e usi
ng t
r
ans
f
orm
a
t
i
on as i
n
equat
i
o
ns
(4
).
Aft
e
r t
h
at
t
h
e d-
q fl
u
x
l
i
nkage
an
d c
u
rre
nt
eq
uat
i
o
ns
were i
m
pl
em
ent
e
d as t
o
be
de
m
o
n
s
tr
ated belo
w
as i
n
equatio
n
s
(6)
.
Fi
gu
r
e
1
illu
strates th
e
in
tern
al
stru
ct
u
r
e of t
h
e indu
ctio
n m
ach
in
e d-q m
o
d
e
l by wh
ich
t
h
e
flu
x
link
a
g
e
s, cu
rren
t
s
,
t
o
r
que
an
d t
h
e
rot
o
r a
n
gul
a
r
s
p
eed are
calcul
a
ted.
Th
e i
n
du
ction
m
o
to
r was th
e
m
o
to
r of
1
.
5
K
W
p
o
wer
a
n
d
electrical para
meters: nom
inal curre
n
t,
In
3.2A = stator
resistance Rs=
5.72
Ω
, stator inductance
Ls=0.4642
H, rotor resistance, Rr=
4.2
Ω
,
ro
tor
i
n
d
u
ct
ance
, Lr
= 0.
46
1
2
H
,
m
u
t
u
al
i
nduct
a
nce M
=
0.
4
4
H
,
t
h
e si
m
u
l
a
t
i
o
n res
u
l
t
s
are
gi
ven
f
o
r t
h
e i
n
d
u
ct
i
o
n
m
o
tor sy
stem
at diffe
re
nt re
fer
e
nce s
p
ee
d a
n
d
load
to
rq
ue:
N
S
=
15
0
0
tr/m
in a
n
d
Cr =
1
2
Nm
.
Fig
u
re
1
.
In
du
ctio
n
m
ach
in
e
dyn
amic
m
o
d
e
l
i
m
p
l
e
m
en
tatio
n
in Sim
u
lin
k
s
s
g
Pu
Pa
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Modular
Approac
h
and Si
mul
a
tion
of an Async
h
r
o
nou
s
Mac
h
ine (Zine
b
Mekri
n
i)
1
389
0
0.
02
0.
04
0.
06
0.
08
0.
1
-4
00
-3
00
-2
00
-1
00
0
100
200
300
400
Ti
m
e
(
s
)
S
t
at
or
vo
l
t
a
ges
(
V
)
Vs
a
Vs
b
Vs
c
The Fi
gure
2 shows the t
h
ree-pha
se to t
w
o-a
x
is
v
o
l
t
a
ge t
r
a
n
s
f
o
r
m
a
ti
on i
s
ac
hi
e
v
e
d
usi
n
g t
h
e
fol
l
o
wi
n
g
s
u
b-
m
odel
:
F
i
g
u
r
e
2
.
a
b
c-
qd
co
nv
er
s
i
on
s
Whe
r
e
Vas, Vbs, a
n
d
VCs are the three-pha
s
e stat
o
r
vo
ltag
e
s,
wh
ile Vd
s and
Vq
s are t
h
e two
-
ax
is
com
pone
nt
o
f
t
h
e st
at
or
v
o
l
t
a
ge
vect
o
r
V
s
.
The Fi
gu
re
3 s
h
o
w
s t
h
e el
ect
ri
cal
cur
r
e
n
t
,
fl
ux
, t
o
rq
ue a
n
d
rot
o
r
spee
d are
re
pre
s
ents
on the
following
sub-m
odel of asy
n
chronous m
achine
.
Fi
gu
re 3.
Propo
sed
o
v
e
r
a
ll mo
d
e
l
of
an
asynch
r
on
ou
s m
ach
in
e
The
vol
t
a
ge
su
ppl
y
bl
oc
k co
n
s
i
s
t
s
of a t
h
ree
-
p
h
ase si
nus
oi
dal
v
o
l
t
a
ge
ge
nerat
o
r a
n
d t
h
e t
h
ree
-
p
h
ase
si
nus
oi
dal
vol
t
a
ge ge
ne
rat
o
r
i
s
based
o
n
e
q
uat
i
on
(
1
)
a
n
d
t
h
e t
h
ree
p
h
as
e vol
t
a
ges i
s
m
odel
e
d as sh
ow
n i
n
Fi
gu
re 4.
Fi
gu
re 4.
Th
re
e-p
h
ase st
at
or vol
t
a
ge
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
13
85
–
1
394
1
390
0
0.
02
0.
0
4
0.
0
6
0.
08
0.
1
-500
0
500
Ti
m
e
(
s
)
S
t
a
t
o
r
v
o
lta
g
e
s
(
d
,q
)
a
x
is
(V
)
Vs
d
Vs
q
0
1
2
3
4
5
6
-3
0
-2
0
-1
0
0
10
20
30
40
Ti
m
e
(
s
)
St
at
or
c
u
r
r
ent
i
s
d(
A)
The Fi
gure
5
shows t
h
e thre
e-phase to two-a
x
is
vo
ltag
e
tran
sform
a
tio
n
m
ean
s th
e co
nv
er
sion
of
coordinates
from
the three
phases stationa
ry.
Fi
gu
re 5.
T
w
o
–p
hases
’
st
at
or
v
o
l
t
a
ges
The Fi
gu
re
6
p
r
esent
s
t
y
pi
cal
wave
f
o
rm
s rel
a
t
e
d t
o
st
art-u
p
o
f
th
e m
o
to
r.
Mo
to
r starts
u
n
d
e
r
no-lo
ad
co
nd
itio
n and
n
e
x
t
, at t= 1
s
ad
d
ition
a
l lo
ad with
n
o
m
in
al v
a
lu
e
was added
is
1
2
Nm
. Transien
t sim
u
latio
n
d
u
ring
starting o
f
i
n
du
ction
m
o
to
r cu
rren
t
is 2
1
.3
A,
Al
m
o
st 6
ti
mes t
h
e no
m
i
n
a
l v
a
lu
e of th
e
curren
t
. Th
e
m
o
t
o
r has a
st
art
u
p t
i
m
e of ap
pr
o
x
i
m
at
el
y
0.2 s a
n
d t
h
e
st
a
r
t
i
n
g
cu
rre
nt
i
s
t
o
o
l
a
rg
e [
1
2]
. It
can
be
see
n
fr
om
the fi
gure, that
the m
achine
has reac
he
d stea
dy state at
ab
ou
t 0.2 seco
nd
s. S.
K
.
Jain, et
al [
1
3
]
o
b
s
erv
e
s th
e
startin
g
curren
t
is larg
e, in some cases of the ord
e
r
o
f
10
ti
mes th
e rated
v
a
lu
e.
T
h
ere
f
ore, it is
recom
m
ended
t
h
at
red
u
ce
d v
o
l
t
a
ge st
art
i
n
g
m
e
t
hods s
u
c
h
as st
ar/
d
el
t
a
, aut
o
t
r
a
n
sf
o
r
m
e
r, an
d s
o
ft
st
art
m
e
t
hods
be e
m
pl
oy
ed
to reduce the e
x
cess starting
current [6]. The application
of 12
N-m
m
e
c
h
anical loa
d
s at 1 seconds gi
ves an
increase of
c
u
rrents
and sha
r
p drop of
c
u
rre
nts a
f
ter
rem
oval o
f
l
o
ad
at 3
sec.
Fi
gu
re
6.
Si
m
u
l
a
t
i
on o
f
i
n
d
u
ct
i
on m
o
t
o
r
-
st
at
or
cu
rre
nt
I
s
d
The stator current out
put su
b-m
odel is
used to calculate the stat
or curre
n
t am
plitude
according to the
fo
llowing
Figu
re
7
.
After a tran
sien
t p
e
rio
d
o
f
0
.
2
s; th
e resu
lts stato
r
cu
rren
t v
a
ri
es ex
pon
en
tially u
n
til
v
acuu
m
stead
y. It is
o
b
serv
ed
fro
m
Fig
u
r
e
7
t
h
at th
e stator cu
rren
ts are
DC
q
u
a
n
tities in
the stead
y state at 0
.
2
sec. Th
e app
licatio
n
o
f
12
N-m
m
ech
an
ical lo
ad
s at
1
secon
d
s
as illu
strat
e
d
in
Figu
re
6
,
resu
lts in v
e
ry slig
h
t
increase i
n
c
u
rrents.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Modular
Approac
h
and Si
mul
a
tion
of an Async
h
r
o
nou
s
Mac
h
ine (Zine
b
Mekri
n
i)
1
391
0
1
2
3
4
5
6
0
5
10
15
20
25
Ti
m
e
(
s
)
S
t
ato
r
c
u
r
r
en
t I
s
(
A
)
0
1
2
3
4
5
6
-2
0
0
20
40
60
80
10
0
12
0
14
0
16
0
Ti
m
e
(
s
)
R
o
t
o
r s
p
ee
d
w
(r
ad
/
s
)
Fi
gu
re
7.
Si
m
u
l
a
t
i
on o
f
i
n
d
u
ct
i
on m
o
t
o
r
st
at
o
r
c
u
r
r
ent
Is
Fi
gu
re
8 s
h
o
w
s t
h
e e
v
ol
ut
i
on
of t
h
e m
echani
cal
s
p
ee
d d
u
r
i
n
g t
h
e
no
-l
oa
d a
n
d
c
o
u
p
l
e
d
l
o
a
d
si
m
u
latio
n
.
The sp
eed
shows o
s
cillatio
n
s
in th
e first m
o
me
n
t
s of starting, th
en
stab
ilizes at a v
a
lu
e clo
s
e to
157 ra
d/s. since friction
and winda
g
e losses are not taken int
o
account, the m
a
c
h
ine accelerat
es to
synchronous speed
. It can
be seen
from
figure
8, th
at the m
achine ha
s reache
d
stea
dy state at about
0.
2
seco
nd
. T
h
e a
ppl
i
cat
i
o
n
of
1
2
N-m
m
echanical
loads
at 1 seconds
gives
a
resu
lts in sh
arp drop in th
e
m
o
to
r
spee
d f
r
o
m
157
ra
d/
sec t
o
14
0
rad/
sec
an
d a
n
i
n
c
r
ease
i
n
A
f
t
e
r
rem
oval
o
f
l
o
a
d
at
3 sec
[1
3]
.
Qu
i
c
kl
y
,
i
ndi
cat
i
n
g t
h
at
M
A
TLAB
/
Si
m
u
li
nk i
s
an a
p
p
r
op
ri
at
e t
ool
t
o
i
nvest
i
g
at
e
st
eady
-
st
at
e b
e
havi
or
of i
n
d
u
ct
i
o
n
m
o
to
rs as well, th
e ro
to
r t
r
ansien
t sp
eed
v
a
riatio
n
was
be
en selected as
one
of t
h
e m
a
in pa
ram
e
ters to be
m
oni
t
o
red [7]
,
[
13]
.
Fi
gu
re
8.
Ev
ol
ut
i
o
n
o
f
t
h
e m
e
chani
cal
s
p
ee
d
du
ri
n
g
t
h
e
no
-l
oad
an
d c
o
upl
e
d
l
o
a
d
t
e
st
si
m
u
l
a
t
i
o
n
Fi
gu
re
9 sh
o
w
s t
h
e t
o
r
q
ue ca
l
c
ul
at
i
on f
r
om
equat
i
o
n
(8
);
i
t
sho
w
s as a
fu
nct
i
on
o
f
t
i
m
e
s;
ho
weve
r i
t
coul
d al
so be
pl
ot
t
e
d as a
fu
nct
i
o
n of s
p
eed (Fi
g
u
r
e 1
0
)
.
The co
upl
e has t
h
e fi
rst
m
o
m
e
nt
s of st
art
i
n
g
im
port
a
nt
beat
s for a ve
ry
sh
ort
t
i
m
e
i
n
t
e
rval
, bef
o
re st
abi
lizing thereafte
r at a valu
e su
bstan
tially zero
stead
y.
A
loa
d
t
o
rque
(Cr=
12 Nm
)
can be placed on
the
m
achine
at t= 1 s t
o
determ
ine the effe
ct on the accel
eration
ti
m
e
[1
3
]
,[14
]. An
in
crease in
th
e electro
mech
an
ical to
rqu
e
up
to
24
N-m in
sy
m
p
a
t
h
y
with
th
e ap
p
lied
mechanical loa
d
ing.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
13
85
–
1
394
1
392
0
20
40
60
80
10
0
12
0
14
0
16
0
180
-1
0
0
10
20
30
40
50
S
p
eed
(
r
ad
/s
)
T
o
rq
u
e
(N
.
m
)
0
1
2
3
4
5
6
0
5
10
15
20
25
30
35
40
45
50
Ti
m
e
(
s
)
E
l
ectr
o
m
ag
n
e
tic to
r
q
ue
Ce (
N
m
)
0
1
2
3
4
5
6
0
1
000
2
000
3
000
4
000
5
000
6
000
7
000
8
000
9
000
Ti
m
e
(
s
)
Jo
u
l
e
l
o
ss
e
s
P
j
s
(
W
)
0
1
2
3
4
5
6
0
10
0
0
20
0
0
30
0
0
40
0
0
50
0
0
60
0
0
Ti
m
e
(
s
)
J
o
ul
e l
o
s
s
es
P
j
r
(
W
)
Fi
gu
re
9.
To
r
q
ue c
h
aract
e
r
i
s
t
i
c
Th
e
resu
lts of sim
u
lat
i
o
n
are also
g
i
ven fo
r th
e asyn
ch
ro
nou
s m
o
to
r is low slip m
a
ch
in
e; t
h
at is,
rat
e
d
t
o
r
q
ue
i
s
devel
ope
d
at
s
y
nch
r
o
n
ous
s
p
eed a
s
s
h
ow
n
i
n
Fi
g
u
re
9.
T.c.nwodo
[1
2
]
pr
es
e
n
ts
a la
r
g
e r
i
p
p
l
e in
th
e
torqu
e
t
h
is can
’
t
b
e
rem
a
rk
ed
in
ou
ir
m
e
t
h
od
.
Figure
10. T
o
rque
-s
peed cha
r
acteristics
Fig
u
re 11
sh
ows resp
ectiv
el
y j
o
u
l
e lo
sses
o
f
th
e stat
o
r
and
ro
tor, th
ey po
in
t ou
t th
at losses v
a
ry in
th
e tran
sien
t
un
til attain
in
g
o
f
Pjs at
8
000
W
and
Pjr at
50
00
W and b
e
co
m
e
stab
le in
p
e
rm
an
ent area
afterwa
r
ds
0.2
s. T
o
re
duce
joule losses
of the stator is
essen
tial to
red
u
c
e
th
e resistan
ce
o
f
t
h
e
wind
ing
.
Th
ere
are two
m
a
in
ways th
at th
is can
b
e
ach
ieved
–
eith
er
e
n
l
a
rgi
ng t
h
e wi
re diam
eter or increasing t
h
e
stator
len
g
t
h,
with
sev
e
ral altern
atives.
Figure
1
1
.
Joul
e losses
in t
h
e
stator a
n
d rotor winding
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Modular
Approac
h
and Si
mul
a
tion
of an Async
h
r
o
nou
s
Mac
h
ine (Zine
b
Mekri
n
i)
1
393
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
-1.
5
-1
-0.
5
0
0.
5
1
1.
5
Tim
e
(
s
)
R
o
t
o
r
f
l
ux
l
i
n
k
age
Fr
d
(
W
eb)
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
-1.5
-1
-0.5
0
0.
5
1
1.
5
Ti
m
e
(
s
)
R
o
t
o
r
f
l
ux
li
n
k
ag
e Fr
q
(
W
e
b
)
0
1
2
3
4
5
6
-0
.
1
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
Ti
m
e
(
s
)
E
f
fi
ci
en
cy
o
f
a
s
yn
c
h
r
o
no
us m
o
t
o
r
0
1
2
3
4
5
6
-0.
2
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
Ti
m
e
(
s
)
In
ducti
o
n
m
o
tor
sl
i
p
Fi
gu
re
12
s
h
o
w
s t
h
e
fl
ux
φ
,
whi
c
h i
s
ass
u
m
e
d t
o
vary
si
nus
oi
dal
l
y
as f
unct
i
o
n
o
f
t
i
m
e (t
) a
f
t
e
r t
h
e
tran
sien
t, is exp
r
essed in
term
s of its
p
eak instan
tan
e
o
u
s
v
a
l
u
e.
Figu
re
1
2
. R
o
tor
flu
x
φ
r
d
,
φ
rq
Figure 13 s
h
ows the efficiency of
async
h
ronous m
o
tor, the core lo
sse
s can be incl
ude
d in efficiency
cal
cul
a
t
i
ons. S
i
nce t
h
e sh
ort
-
ci
rcui
t
e
d r
o
t
o
r
wi
ndi
ng
s ha
ve s
m
all resista
n
ce, a sm
all s
lip induces a large
cu
rren
t i
n
the ro
tor an
d produces larg
e torque. At
fu
ll rate
d
load,
slip varie
s
fr
om
m
o
re
th
an 5% (Fig
u
r
e 14
).
Fi
gure
13. E
f
ficiency of asy
n
chr
o
nous m
o
tor
Figure
14.
Slip
of
async
h
ronous
m
o
tor
3.
1.
Com
p
ari
s
on
s
t
ud
y
I
n
o
r
d
e
r
to
evalu
a
te th
e m
o
d
e
lisatio
n
o
f
t
h
e asyn
chr
onou
s m
o
to
r
,
th
e f
o
llow
i
ng
com
p
ar
iso
n
is
i
n
t
r
o
d
u
ced
. I
n
refe
rence
[
1
]
,
C
onst
r
uct
i
o
nal
det
a
i
l
s
o
f
vari
ous
s
u
b
-
m
odel
s
f
o
r
t
h
e i
n
d
u
ct
i
on m
o
t
o
r
.
T
h
e
spee
d
an
d torqu
e
resp
on
ses are illustrated
i
n
Figure
8
and
9 acco
r
d
i
ng
t
o
[1
].
In
referen
ce
[6
]
,
th
e sp
eed an
d to
rqu
e
respon
ses are illu
strated
in
Fig
u
re
5
and
6
.
It is clear
from o
u
r
resu
lts th
at th
e sp
eed
an
d
t
o
rqu
e
repo
n
s
e
of
in
v
e
stig
ated
meth
od
is faster
.
A
m
o
to
r sim
i
lar to
th
at used
in
referen
c
e [9
] is sim
u
lat
e
d
b
y
th
e
prop
o
s
ed
m
odel, where
t
h
e c
u
rre
nt is
presente
d i
n
Figure
.6,
we
can re
m
a
rked that
s
t
artup tim
e of
approxim
a
tely 0.2
s
an
d th
e cu
rren
t
is too lar
g
e i
n
startin
g m
o
to
r
,
it is th
e
r
eal case of an indu
ctio
n m
ach
in
e,
wh
ich
isn
’
t
illu
strated
in re
fere
nce
[9].
T
h
e refe
re
nce
[15] prese
n
ts a lar
g
e
ripp
le in
t
h
e torqu
e
; th
is can
be rem
a
rk
ed
fro
m
th
e
resp
o
n
se o
f
ou
r m
e
t
hod, w
h
i
c
h i
s
m
a
i
n
t
a
i
n
ed co
nst
a
nt
. I
n
al
l
of ref
e
re
nce
s
, we ca
n'
t
see
t
h
e j
oul
e l
o
sse
ss;
t
h
e
sl
i
p
an
d e
f
fi
ci
e
n
cy
b
u
t
t
h
e
p
r
o
pos
ed
m
e
t
hod
prese
n
t
s
t
h
e al
l
o
f
t
h
i
s
be
havi
ou
rs.
4.
CO
NCL
USI
O
N
Thi
s
art
i
c
l
e
pr
op
oses
a m
e
t
hod
ol
o
g
y
f
o
r m
odel
i
n
g a
n
d si
m
u
l
a
t
i
on o
f
a
n
asy
n
c
h
ro
n
o
u
s
m
o
t
o
r by
Matlab
.
Th
e
d
e
v
e
l
o
p
e
d
m
o
d
e
l is b
u
ilt fro
m
si
m
p
le su
b
-
m
o
d
e
ls.
Th
e eq
u
a
tion
s
were estab
lish
e
d b
a
sed
equat
i
o
ns
dem
onst
r
at
e be
ha
v
i
or at
st
ea
dy
st
at
e of asy
n
c
h
r
o
no
us m
achi
n
es.
As a
g
ai
n
s
t
i
t
s
sim
u
l
a
t
i
on
i
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
13
85
–
1
394
1
394
d
i
f
f
icu
lt, b
ecau
s
e th
e m
o
d
e
l
is h
i
gh
ly n
onlin
ear
, we
u
s
ed
th
e three-phase vo
ltag
e
tran
sfo
r
m
a
tio
n
with
two
axes t
o
sim
p
lify m
a
ny equations
that
react t
h
e
physical
be
havi
or of t
h
e
machine.
Through the
use
of
Sim
u
link
to
o
l
, w
e
h
a
v
e
d
e
v
e
l
o
p
e
d th
e
ef
f
ects of
no
n-lin
ear
ity in
t
h
e d
y
n
a
m
i
c p
e
r
f
or
m
a
n
ce o
f
inductio
n
m
o
to
r and
g
i
v
e
the
user access to
all internal
varia
b
les getting
a
n
overview of
the
functi
oni
ng
of the
machine
whe
n
st
arting
with
ou
t lo
ad
an
d with an additio
n
a
l ch
ar
g
e
.
The res
u
lts obtained dem
ons
trate the corre
c
tness
o
f
t
h
e
m
odel
devel
o
p
e
d an
d are al
s
o
co
nfi
r
m
e
d
fr
om
t
h
e re
sul
t
s p
u
b
l
i
s
hed
i
n
t
h
e
bi
bl
i
o
g
r
aphy
.
T
h
u
s
,
t
h
e m
odel
devel
ope
d
al
l
o
wed
l
o
ss c
o
nt
r
o
l
o
f
t
h
e
asynchronous machine
and
also the
electrical, m
echanical and
m
a
gnet
i
c
beha
vi
o
r
.
These
asp
ect
s ar
e
i
m
p
o
r
tan
t
fo
r t
h
e i
n
du
strial
use
o
f
an i
n
du
ctio
n
m
ach
in
e.
Fin
a
lly
, th
e si
m
u
la
tio
n
resu
lts prov
id
e i
n
sig
h
t
on
cho
o
si
ng
t
h
e o
r
de
r of
t
h
e asy
n
chronous m
a
c
h
ine.
ACKNOWLE
DGE
M
ENTS
Th
is
work
is
su
ppo
rted
b
y
the presid
en
cy of
the Uni
v
ersity
Moulay Ism
a
il,
Meknes –
M
o
rocc
o.
REFERE
NC
ES
[1]
K.
I.
Shi
, et
a
l
.
, “Modelling
an
d sim
u
lation of
the
three-phase induct
i
on m
o
to
r using Sim
u
lin
k,”
In
t. J.
El
ec
t
.
Enging. Edu
c
, v
o
l. 36
, pp
. 163–1
72, 1999
.
[2]
N. Rahaman an
d
H. V. Govindraju, “Modeling
&
Simulation of
a Three-Phase
Electric Tractio
n Induction Motor
Using Matlab
Simulink,”
International Journ
a
l of Electrica
l
, El
ectronics a
nd Computer Systems (
I
JEECS
)
,
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, pp. 18-25, 2014
.
[3]
S. A
y
asun
and
C. Nwankpa,
“Induction Motor Tests Using
MATLAB/Simulink and
Their
Integr
ation
in
to
Undergraduat
e
E
l
ec
tric
M
ach
iner
y Cou
r
s
e
s
,
”
IEEE transactions o
n
educa
tion
, vol/issue: 48(1), 200
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[4]
E. Anbarasu an
d M. Karthi
keyan, “Modeling of Induction Motor and Fault Analy
s
is
,”
Inter
national Journa
l of
Engineering Science and Inno
va
tive Techno
logy
(
I
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, vol/issue: 2(4)
, 2013
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[5]
E. De
lal
eau
, et
al.
, “Modeling and control of in
duction motors,”
Int. J. Appl.
Ma
th. Comput. Sci
, vol/issue: 11
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,
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, 20
01.
[6]
H. Arabaci and
O. Bilgin, “Squirrel Cage of
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tional Journal of
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p
timization
, vol/issue: 2(3), pp. 3
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.
[7]
S
.
Is
s
ac and
K.
Vanam
a
thi
,
“
M
ode
lling of
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ear Indu
ction
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urnal of So
ft Co
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[8]
B. Liang A.,
et al.
, “Simulation
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lt d
e
tection
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e
induction motors,”
Math
ematics and Computers
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i
on
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o
l/issue: 6
1
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p
. 1-15
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.
[9]
P.
M.
Pa
lpa
n
ka
r
, et al.
, “
A
Gen
e
ral
i
zed
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y
n
a
m
i
c M
odel of
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u
ction Motor
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Ele
c
trica
l
and
E
l
ec
tronics Eng
i
n
eering (
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I-T
EEE)
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[10]
M
.
W
i
eczor
e
k
a
n
d
E. Roso
ł
ows
k
i, “Modelling
of Induction
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c
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e
r S
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, 2010.
[11]
M. Arkan
, et a
l
.
,
“Modelling an
d simulation of
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s
with inter-turn
faults for diagn
o
stics
,
”
Ele
c
tri
c
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r Sy
ste
m
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se
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[12]
T. C
.
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imulation too
l
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es modelling: te
ach
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e
rian Journal o
f
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[13]
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.
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.
J
a
in
,
et
al
., “Modeling and
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l Journal
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.
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[14]
R. Singh,
et al
., “Comparative Stud
y
of PWM C
ontrol and PI C
ontrol of Induction Motor,”
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ectr
i
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l
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, vol/issue: 4(1)
, pp
.
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.
[15]
Mohan K. S and Febin Day
a
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.
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e model ba
s
e
d S
p
eed Es
tim
at
ion S
c
hem
e
s
for S
p
eed Encod
e
rl
es
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