TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 12, Decembe
r
2014, pp. 80
6
9
~ 807
6
DOI: 10.115
9
1
/telkomni
ka.
v
12i12.66
93
8069
Re
cei
v
ed
Jun
e
17, 2014; Revi
sed Septe
m
ber
10, 201
4; Acce
pted
Octob
e
r 19, 2
014
Modelling of Faulty Three Phase Induction Motor by
Field Orientation
M. Jannati, N. R. N. Idris, M. J. A. Az
iz
Univers
i
ti T
e
knolo
g
i Mal
a
ysia,
UT
M-PROT
O
N F
u
ture Drive
Lab
orator
y, F
a
cult
y
of Elec
tric
al Eng
i
ne
eri
ng,
Universiti T
e
knol
ogi Ma
la
ysi
a
,
813
10 Sku
dai,
Johor Ba
hru, Mala
ysi
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: Jannatim
94
@
y
ah
oo.com
A
b
st
r
a
ct
T
h
is study inv
e
stigates the s
i
mp
le vect
or co
ntrol of a 3-
ph
ase sq
uirre
l ca
ge Ind
u
ction M
o
tor (IM)
und
er o
p
e
n
-cir
cuit fau
l
t (fault
y
3-p
hase
IM). It w
a
s s
how
n
that it is
ne
ed
ed to
su
pply
the stator
w
i
nd
i
n
g
s
w
i
th unb
ala
n
ce
d curre
nts to re
mov
e
the
osci
ll
ating ter
m
of th
e mach
ine
el
ec
troma
g
n
e
tic tor
que. T
h
e
vecto
r
control system
is based upon
Field-Or
iented Control
(FOC
)
that has been
adapted for
this type of m
a
c
h
ine.
Simulati
on res
u
lts are prov
id
ed to show
t
he oper
ation
of the pr
op
ose
d
dri
v
e system.
Ke
y
w
ords
: sq
uirrel ca
ge 3-
p
hase IM, F
O
C,
ope
n- circuit fa
ult, simp
le
met
hod, si
mu
latio
n
results
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Re
cently, 3-p
hase Indu
ctio
n Motors
(IM
s
)
hav
e
recei
v
ed a g
r
eet a
ttention for el
ectri
c
al
drive appli
c
at
ions [1-5]. Squirrel ca
ge 3-pha
se
IMs h
a
ve several advantag
es f
o
r exampl
e h
i
gh
reliability and robustness.
Open-ci
r
cuit fault is one
of familiar fa
ilures in the
3-phase IM
stator
windi
ng
s. Th
is abn
orm
a
l
conditio
n
h
appe
ns b
e
ca
use of the f
a
ilure
of on
e stator
pha
se
con
n
e
c
tion, inverter fault
s
mitigated by
usin
g fuse
s o
r
many other
reason
s.
The conventi
onal vecto
r
cont
rol
system
s whi
c
h i
s
u
s
ed for he
alth
y IMs drive cannot be
able to work
durin
g fault situations, in practice, t
hey fail in the presence of such faults as op
e
n
-
phase fault (if
a conventional vect
or
cont
rol sy
stem is
applied to th
e faulty IM, oscillations in the
motor to
rqu
e
and
spe
ed
ca
n be o
b
serve
d
[6-1
4]). For
this, a suitabl
e co
ntrol
algo
rithm is
nee
d
e
d
to ensure proper ope
rati
on of t
he
dri
v
e both in h
ealthy and f
aulty con
d
itio
ns. Mo
st of
the
different sol
u
tions propo
sed in the pa
st to
improv
e the perfo
rmance of the 3-ph
ase IM or
unbal
aced 2
-
pha
se IM d
r
i
v
es un
de
r o
pen-ci
rcuit fault [6-18]. In
gene
ral, the
s
e m
e
thod
s
are
based on
usi
ng tran
sfo
r
m
a
tion matri
c
e
s
which
are obtaine
d fro
m
machine
model (i
n [6-18],
several tech
nique
s for
FOC of faul
ty 3-phas
e IM (open
-ph
a
se fault), single-pha
se
IM
(unb
alan
ce
d
2-ph
ase IM
) and
hig
h
p
e
rform
a
n
c
e
FOC of the
s
e ma
chi
n
e
s
usin
g Extend
ed
Kalman Filter (EKF), adapt
ive sliding mo
de and
etc h
a
v
e been pro
p
o
se
d). The
s
e
transfo
rmatio
n
matrices a
r
e
used to modify the con
t
rolling sy
ste
m
due to the fault. It is clea
r the use of
transfo
rmatio
n matrices in
the drive sy
a
s
t
e
m
s
lead
s t
o
sy
st
em
co
mplix
it
y
.
The main co
ntribution of this pa
per i
s
to expand vector cont
rol m
e
thod ba
sed
on FOC
(Field
-O
riente
d
Cont
rol) fo
r 3-p
h
a
s
e IM whi
c
h can
be also a
d
opted for fa
ulty 3-pha
se
IM.
Differently fro
m
the previo
us m
e
t
hod
s f
o
r ve
ctor
con
t
rol of faulty IM (e.g., [6-1
8
]
), the pro
p
o
s
ed
method in
thi
s
pa
per do
no
t used t
r
an
sfo
r
mation
matri
c
e
s
. Thi
s
re
search i
s
o
r
ga
nize
d a
s
follo
ws:
In part 2, m
o
del of he
althy and faulty 3
-
pha
se IM
b
a
sed on
d-q mo
del is
pre
s
e
n
ted. After that, a
brief ove
r
vie
w
o
n
ve
ctor control
equ
atio
ns
fo
r healthy
3-pha
se
IM based on FO
C
a
r
e
presen
ted
in pa
rt 3. Be
sides, th
e mai
n
ide
a
of th
e
prop
os
ed
met
hod fo
r ve
cto
r
control of
3-pha
se IM
und
er
open
-ci
r
cuit fault is expo
u
nded in thi
s
se
ction.
The
simulatio
n
result
s and
copma
r
isi
o
n
s
are
sho
w
n in p
a
rt
4 and part 5
con
c
lu
de
s the pape
r.
2. Machine
mo
del
The dynami
c
model of 3-ph
ase IM can b
e
sho
w
n a
s
followin
g
equ
a
t
ions [19, 20]:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8069 – 80
76
8070
s
qr
s
dr
s
qs
s
ds
r
r
r
r
ms
ms
r
r
r
r
r
ms
r
ms
ms
ms
ls
s
ms
ms
ls
s
s
qs
s
ds
i
i
i
i
dt
d
L
r
L
dt
d
L
L
L
dt
d
L
r
L
dt
d
L
dt
d
L
dt
d
L
L
r
dt
d
L
dt
d
L
L
r
v
v
2
3
2
3
2
3
2
3
2
3
0
2
3
0
0
2
3
0
2
3
0
0
s
qr
s
dr
s
qs
s
ds
r
ms
r
ms
ms
ms
ls
ms
ms
ls
s
qr
s
dr
s
qs
s
ds
i
i
i
i
L
L
L
L
L
L
L
L
L
L
0
2
3
0
0
0
2
3
2
3
0
2
3
0
0
2
3
0
2
3
r
r
l
e
s
qr
s
ds
s
dr
s
qs
ms
e
F
d
t
d
J
Pole
i
i
i
i
L
Pole
2
2
3
2
(1)
(2)
(3)
(4)
Whe
r
e,
v
s
ds
, v
s
qs
, i
s
ds
, i
s
qs
, i
s
dr
, i
s
qr
,
λ
s
ds
,
λ
s
qs
,
λ
s
dr
and
λ
s
qr
are the
d-q axes voltag
es,
current
s,
and
fluxes of the
stator
and
rot
o
r in
the
stat
or
referen
c
e f
r
ame
(sup
erscript
“
s
”)
.
r
s
a
nd
r
r
den
ote t
h
e
stator and rot
o
r
resi
stan
ce
s.
L
ls
an
d
L
ms
denote th
e
stator le
akage
and m
u
tual in
ducta
nces.
r
is
the machine
spe
ed.
τ
e
,
τ
l
, J
and
F
are
electroma
gne
tic torqu
e
, load torq
ue, in
ertia an
d viscous
friction
co
efficient. Th
e e
q
uation
s
that
pre
s
ent th
e d
y
namic
mode
l for 3
-
ph
ase
IM unde
r
ope
n-
circuit fault are also a
s
follo
wing e
quatio
ns [9]:
s
qr
s
dr
s
qs
s
ds
r
r
r
r
ms
ms
r
r
r
r
r
ms
r
ms
ms
ms
ls
s
ms
ms
ls
s
s
qs
s
ds
i
i
i
i
dt
d
L
r
L
dt
d
L
L
L
dt
d
L
r
L
dt
d
L
dt
d
L
dt
d
L
L
r
dt
d
L
dt
d
L
L
r
v
v
2
3
2
3
2
3
2
3
2
3
0
2
1
0
0
2
3
0
2
3
0
0
(5)
s
qr
s
dr
s
qs
s
ds
r
ms
r
ms
ms
ms
ls
ms
ms
ls
s
qr
s
dr
s
qs
s
ds
i
i
i
i
L
L
L
L
L
L
L
L
L
L
0
2
3
0
0
0
2
3
2
3
0
2
1
0
0
2
3
0
2
3
(6)
r
r
l
e
s
qr
s
ds
ms
s
dr
s
qs
ms
e
F
dt
d
J
Pole
i
i
L
i
i
L
Pole
2
2
3
2
3
2
(7)
(8)
The mod
e
l of faulty 3-pha
se IM was o
b
tained
u
s
in
g a
n
approa
ch li
ke that used to obtain
the mod
e
l fo
r a
healthy
3-ph
ase IM
(the mod
e
l of
faulty 3-p
h
a
s
e IM i
s
full
y discu
sse
d
in
Referenc
e [9]).
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Modelling of Faulty Three
Phase Inducti
on
Motor by
Field Ori
entat
ion (M. Jannati)
8071
3.
Rotor Field-Oriented Co
ntrol (RFO
C)
In this sectio
n the convent
ional RF
OC
of healthy 3-pha
se IM and prop
osed method fo
r
RFO
C
of 3-p
hase IM unde
r open
-circuit fault is discu
s
sed.
3.1. RFO
C
of Healthy
3-phase IM
In RFO
C
met
hod, it is n
e
cessary th
e m
a
chi
ne e
quati
ons t
r
an
sfer f
r
om
stator
ref
e
ren
c
e
frame (sup
erscript “
s
”) to t
he
rotating
re
feren
c
e
fram
e (su
perscri
pt “
e
”) [21]. Eq
uation
of 3
-
p
hase
IM voltage
s, fluxes
and
ele
c
trom
agn
etic
torque
in
the
rotating
refe
rence frame
can b
e
exp
r
e
ss
as
foll
ows (in
this
p
ape
r, su
perscript “
e
” i
ndicates that
the eq
uation
s
are in
the
rot
a
ting
referen
c
e
frame. Moreo
v
er, in (9),
ω
e
is the angul
a
r
velocity of the Roto
r Fiel
d-O
r
iente
d
frame) [21]:
e
qr
e
dr
e
qs
e
ds
r
r
r
r
e
ms
ms
r
e
r
r
e
r
r
ms
r
e
ms
ms
ms
e
ms
ls
s
ms
ls
e
ms
e
ms
ms
ls
e
ms
ls
s
e
qs
e
ds
i
i
i
i
dt
d
L
r
L
dt
d
L
L
L
dt
d
L
r
L
dt
d
L
dt
d
L
L
dt
d
L
L
r
L
L
L
dt
d
L
L
L
dt
d
L
L
r
v
v
2
3
2
3
2
3
2
3
2
3
2
3
2
3
2
3
2
3
2
3
2
3
2
3
0
0
(9)
e
qr
e
dr
r
r
e
qs
e
ds
ms
ms
e
qr
e
dr
i
i
L
L
i
i
L
L
0
0
2
3
0
0
2
3
(10
)
e
qr
e
ds
e
dr
e
qs
ms
r
e
i
i
L
L
Pole
2
3
(11
)
In RF
OC
system, the roto
r flux vecto
r
i
s
ali
gned
wit
h
d-axis
(
λ
dr
e
=|
λ
r
| and
λ
qr
e
=0). With
this su
ppo
siti
on Equation
(10) can
be
written as Equat
ion (12
)
:
e
qr
e
dr
r
r
e
qs
e
ds
ms
ms
r
i
i
L
L
i
i
L
L
0
0
2
3
0
0
2
3
0
(12
)
From (1
2),
t
he
e
quation
betwe
en roto
r
curr
ent
s a
n
d
stato
r
cu
rrents
are
obt
ained
as
followin
g
equ
ations:
e
ds
r
ms
r
r
e
dr
i
L
L
L
i
2
3
(13
)
e
qs
r
ms
e
qr
i
L
L
i
2
3
(14
)
Based o
n
(9
)-(1
4) an
d after sim
p
lifying RFOC e
qua
tions for he
al
thy 3-pha
se
IM are
obtaine
d as f
o
llowin
g
equ
a
t
ions [21]:
e
qs
r
r
ms
e
e
qs
r
r
ms
r
e
e
ds
r
ms
r
i
L
L
Pole
i
T
L
i
dt
d
T
L
2
3
2
1
2
3
1
1
2
3
(15
)
(16
)
(17
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8069 – 80
76
8072
In above equ
ations,
T
r
is rotor time co
n
s
tant. Base
d on (15
)
-(1
7
), conve
n
tional
block
diagram of h
ealthy 3-p
h
a
s
e IM ba
sed
o
n
Indire
ct
RF
OC (IRFO
C
) is
a
s
Fig
u
re 1
(the simpl
e
st
way to imple
m
ent the FO
C is to use hystere
s
i
s
cu
rre
n
t controllers
whi
c
h is
us
ed in this
s
t
udy).
Figure 1. Con
v
entional blo
c
k diag
ram of
healthy 3-p
h
a
s
e IM ba
sed
on IRFO
C
In Figu
re
1,
i
ds
e*
,
i
qs
e*
and
τ
e
*
represent
the refere
nce
stat
or
d-
a
x
is c
u
r
r
e
n
t, re
fer
e
nc
e
stator q
-
axis
curre
n
t and referen
c
e to
rq
ue, respe
c
tively. Moreove
r
,
M
=3/
2
L
ms
.
The blo
ck [
T
s
e
]
-1
perfo
rms
sig
nal tran
sform
a
tions from t
he rotati
ng referen
c
e fra
m
e to the stationary refe
rence
frame. Fu
rthe
rmore, the bl
ock [
T
s
]
-1
is 2
to 3 tran
sformation for th
e stato
r
curre
n
t variable
s
(Park
transfo
rmatio
n). In Fi
gure
1, 3-pha
se
IM is
fe
d fro
m
a
conve
n
tional
3-le
g V
o
ltage So
urce
Inverter (VSI) as sh
own in Figure 2. [
T
s
e
] and [
T
s
] are difined a
s
follows [21]:
s
qs
s
ds
e
e
e
e
s
qs
s
ds
e
s
e
qs
e
ds
i
i
i
i
T
i
i
cos
sin
sin
cos
(18
)
cs
bs
as
cs
bs
as
s
s
qs
s
ds
i
i
i
i
i
i
T
i
i
2
3
2
3
0
2
1
2
1
1
3
2
(19
)
Figure 2. 3-le
g Voltage So
urce Inverter
(VSI)
3.2. RFO
C
of fault
y
3-phase IM
Becau
s
e
of the a
s
ymmetry of stator
winding
s in th
e faulty 3-p
h
a
se IM, the
use
of
conve
n
tional
FOC n
eed
s a
spe
c
ial atten
t
ion. The asy
mmetry in the
faulty IM mo
del is a result of
different
d
-
q
para
m
eters. This asymm
e
try
cau
s
e
s
an
oscillating
te
rm in
the m
a
chin
e torque.
It is
possibl
e to remove the oscillating term of faulty
machi
ne torque by mean
s of a suitable control
of the stato
r
q-axis current
. Based
on th
e RF
OC
mod
e
l for h
e
althy
3-ph
ase IM which i
s
d
e
rive
d
previou
s
ly, it is po
ssi
ble to
employ the
RFO
C
p
r
in
ci
p
l
es for ve
ctor control of faulty 3-pha
se
IM.
Assu
ming tha
t
the stator q-ax
is cu
rrent can be impo
se
d as:
s
QS
s
qs
I
i
3
(20
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Modelling of Faulty Three
Phase Inducti
on
Motor by
Field Ori
entat
ion (M. Jannati)
8073
By substitutin
g
(20
)
, the faulty machine
model can be
re-written a
s
:
Rotor flux
equations
:
s
qr
s
dr
r
r
s
QS
s
ds
ms
ms
s
qr
s
dr
i
i
L
L
I
i
L
L
0
0
2
3
0
0
2
3
(21
)
Electrom
agn
etic torqu
e
eq
uation:
s
qr
s
ds
s
dr
s
QS
ms
e
i
i
i
I
L
Po
l
e
2
3
2
(22
)
Equation
(2
1
)
a
nd
(22
)
i
s
equival
ent t
o
t
hat
of the
healthy
3-p
hase IM i
n
whi
c
h th
e
oscillating term does not
exist
in
steady state.
Usi
n
g the stat
or q-axis
current compensation
given by (20),
a novel ve
ct
or
control mo
del c
an b
e
d
e
v
eloped fo
r 3
-
pha
se
IM un
der
open
-circuit
fault. From t
he p
r
op
osed
results
(eq
u
a
t
ions
(10
)
a
n
d
(1
1)), it is
possibl
e to a
dopt the I
R
F
O
C
scheme, a
s
p
r
esented in Fi
gure 3.
Figure 3. Pro
posed blo
c
k diagram of he
al
thy and faul
ty 3-phase IM base
d
on IRFOC
In Figure
3, the blo
ck [
T
s
fa
ult
]
-1
is 2 to 2 transfo
rmatio
n for the stat
or current variable
s
in
the faulty co
n
d
ition which i
s
difine
d a
s
[
9
] (in thi
s
p
a
p
e
r it i
s
a
s
sum
e
d a
cut
-
off fault is
occu
re
d in
phas
e
“c
”)
:
bs
as
bs
as
faul
t
s
s
qs
s
ds
i
i
i
i
T
i
i
1
1
1
1
2
2
(23
)
With the aim
of swit
ched
b
e
twee
n the two
condi
tio
n
s, five switche
s
are u
s
ed in
Figure 3.
These switch
es chan
ge p
o
sition
s on
ce
the faul
t is d
e
tected
(in th
is pap
er, an i
mmediate o
p
e
n
stator
windin
g
detectio
n
is supp
osed a
s
con
s
ide
r
ed i
n
[6-14]).
4. Simulation
Results
To sh
ow th
e useful
ne
ss of the pro
pos
ed alg
o
rit
h
m (Fig
ure
3), MATLAB/M-FILE
simulation are carried out.
At the same
time, a
controlling system based on Figure 2 for
healt
h
y
and fa
ulty 3-pha
se IM i
s
also
sim
u
late
d.
In sim
u
lati
ons the
refe
rence moto
r
speed
(
ω
ref
) and
load torque (
T
l
) are co
nsi
d
ered
as Fig
u
re 4 and Fig
u
re 5 re
spe
c
tively. The simu
lated 3-pha
se
IM
para
m
eters a
r
e listed a
s
fo
llows:
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8069 – 80
76
8074
Figure 4. Vari
ation of rotor
spe
e
d
Figure 5. Vari
ation of load torqu
e
(a)
(b)
(c
)
(d)
(e)
Figure 6. Simulation re
sult
s of the com
p
ar
ison bet
we
en co
nventio
nal IRFO
C (le
ft) and
prop
osed IRF
O
C(rig
h
t) for
vector
control
of heal
thy and faulty 3-pha
se IM, (a) Sta
t
or a-axi
s
curre
n
t, (b) S
peed, (c) Spe
ed error, (d)
Torq
ue, (e
) Z
oom of torqu
e
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Modelling of Faulty Three
Phase Inducti
on
Motor by
Field Ori
entat
ion (M. Jannati)
8075
Two
cases are si
mulated;
Ca
se
(1
): con
v
entional I
R
F
O
C
metho
d
f
o
r
healthy
an
d faulty
3-ph
ase IM b
a
se
d on Fig
u
r
e 2 (th
e
sim
u
lation result
s of this
case
is sh
own in
Figure 6(l
e
ft)) and
Ca
se (2): p
r
o
posed IRF
O
C metho
d
for healthy and
faulty 3-pha
se IM based o
n
Figu
re 3 (t
he
simulat
i
o
n
re
sult
s of
t
h
is
c
a
se i
s
sh
ow
n in Figur
e 6(ri
ght)). In both
ca
se
s,
the 3-pha
se IM started
in the health
y condition a
nd witho
u
t load torq
ue, a
nd then at t=0.3
s
a pha
se cut-off fault is
happ
ened
in
pha
se
“c”. After that at t=1s a
st
e
p
lo
ad torque
eq
ual to 0.3
N
.
m
is
applie
d. As
expecte
d in the healthy co
ndition, the conventio
n
a
l and rop
o
sed controlle
r exhi
bit good tra
c
king
perfo
rman
ce
and
fa
st re
sp
onse without steady-state
error. Sim
u
lat
i
on
re
sults of
Figu
re
6(righ
t)
sho
w
s that t
hat the
actu
a
l
motor spee
d c
an follo
w
and trace
we
ll the refere
n
c
e
sp
eed
even
unde
r loa
d
(see Fig
u
re
6(right-b
)).
Com
pare
d
to
the
conve
n
tional
IRFO
C alg
o
ri
thm, the mot
o
r
spe
ed
of the
propo
se
d
scheme
contain
s
ve
ry lo
w
speed
ri
pple
s
(se
e
Fi
gu
re
6(left-c) an
d
se
e
Figure 6(rig
h
t-c)). Mo
re
ove
r
, usi
ng p
r
op
ose
d
c
ontroll
er, the el
ectromagn
etic to
rque
wavefo
rms
contai
n lo
w ri
pple
s
even
at
the faulty mo
de (se
e
Fig
u
re 6
(right
-e)). The stator cu
rre
nt
waveform
is e
n
larged
to
sh
ow that th
e IM current i
s
n
early
sin
u
s
oid
a
l in
both
healthy
and f
aulty co
nditio
n
s
(se
e
Figu
re
6(ri
ght-a
)). It is sh
own that the
prop
o
s
ed IRFO
C
algorith
m
for vector
control of
healthy an
d
faulty 3-ph
ase IM
ha
s a go
od
sp
eed
con
r
ol
and a
deq
uat
e vecto
r
co
ntrol
cha
r
a
c
teri
stics at wide
ran
ge sp
eed o
p
e
r
ation.
5. Conclu
sion
A simpl
e
Ind
i
rect
Roto
r-Fi
eld O
r
iente
d
Co
nt
rol (IRFOC)
of a squirrel cag
e
3-ph
ase
motor u
nde
r
open
-ci
r
cuit fault wa
s
simu
lated in
the M
A
TLAB environment. It wa
s sho
w
n that i
t
is
essential to
sup
p
ly the stator
q-axis
motor wi
ndin
g
with unb
al
anced curren
t to remove the
oscillating te
rm of the ele
c
t
r
oma
gneti
c
to
rque. F
u
rth
e
rmore, thi
s
un
balan
ce
d con
t
rol is
esse
ntial
to realize a balan
ced IRF
O
C which e
n
able
s
vector
control to be applie
d to the faulty IM. Ba
sed
on the pre
s
e
n
ted re
sults i
n
this pape
r it is po
ssi
ble
to implemen
t high-pe
rformance AC drive
system
s with
a faulty 3-pha
se IM. A prospective
ap
plication of the propo
sed meth
od is its u
s
e a
s
an
schem
e f
o
r th
e
singl
e-pha
se IM
d
r
i
v
e syste
m
s
(the st
ru
cture
of
singl
e-p
h
a
se
IM
with t
w
o
different wi
n
d
ing
s
is
simi
lar to the
3-pha
se IM
u
nder
ope
n-ci
rcuit fa
ult). In future
wo
rks,
experim
ental tests will be condu
cted
to empha
si
ze
th
e sim
u
lation
result
s, which
are
so
far very
promi
s
in
g.
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e
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ala
m
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d
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02-4
046
TELKOM
NI
KA
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14 : 8069 – 80
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