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
. 3
,
Sep
t
em
b
e
r
2015
, pp
. 43
9
~
44
8
I
S
SN
: 208
8-8
6
9
4
4
39
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
A Novel Method for IRFOC of
Three-Phase Induction Motor
under Open-Phase Fault
Mohammad Jann
ati
*
,
Tole Sutikn
o
**, Nik
Rumz
i
Nik
I
d
ris*,
Moh
d
Junaidi Ab
dul Az
iz
*,
* UTM-PROTON Future Driv
e
Laborator
y
,
Faculty
of
Electr
ical Engin
eering
,
U
n
ivers
iti Teknologi Malay
s
ia, Jo
hor
Bahru, Malay
s
ia
** Departmen
t
o
f
Electr
i
cal
Engineerin
g
,
Faculty
of Industrial
Technolog
y
,
Univ
er
sitas Ahmad Dahlan, Yog
y
akar
ta,
Indonesia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 26, 2015
Rev
i
sed
Jun
12,
201
5
Accepted
Jun 26, 2015
This paper investigates
the v
ector control of a star-connected three-phas
e
Induction
Motor
(IM) under
stator winding op
en
-phase fau
l
t. Th
e used vector
control method
is based upon
indirect ro
tor
field-orien
t
ation co
ncepts th
at
have been
adapted for this ty
p
e
of
m
achine. Be
s
i
de the im
plem
enta
tion of
this method in
critical industrial appl
ications,
the proposed method in th
is
paper can be used for vector
co
ntrol
of unbalan
ced 2-phas
e
or single-ph
ase
IM with two m
a
in and
auxi
lia
r
y
windi
ngs.
Simulation
results are provided to
show the op
eration of th
e propos
ed driv
e s
y
s
t
em.
Keyword:
Fi
el
d-
ori
e
nt
e
d
cont
rol
Ope
n
-p
hase fa
ult
Single
-
phase IM
Three
-
phase
i
n
duct
i
o
n m
o
t
o
r
Un
bal
a
nce
d
2
-
pha
se
Vector c
ontrol
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
oham
m
ad Jannat
i
,
Facu
lty of Electri
cal Engineering,
Un
i
v
ersiti Tekn
o
l
o
g
i
Malaysia,
U
T
M Sku
d
a
i,
8
131
0 Joho
r,
Malaysia.
Em
a
il: j
a
n
n
a
ti
m
9
4
@
yah
o
o
.
co
m
1.
INTRODUCTION
Three
-
phase
I
n
duct
i
o
n
M
o
t
o
r
(IM
)
dri
v
es a
r
e o
n
e
of
t
h
e
m
o
st
c
o
m
m
on t
y
pes
of
AC
d
r
i
v
es
use
d
i
n
i
n
d
u
st
ri
al
ap
pl
i
cat
i
ons [
1
]
-
[
3]
.
In s
o
m
e
appl
i
cat
i
ons w
h
e
r
e
cont
i
n
u
o
u
s
o
p
e
rat
i
on i
s
desi
r
a
bl
e o
r
cri
t
i
cal
, suc
h
as in
m
i
litary,
electric vehicle, airc
raft
, a
nd
et
c havi
n
g
a fa
ul
t
-
t
o
l
e
ra
nt
co
nt
r
o
l
sy
st
em
i
s
necessary
.
Ge
neral
l
y
th
e classificatio
n of
fau
lts i
n
th
ree-ph
ase
IM
d
r
i
v
es can
b
e
l
i
sted
as
fo
llows: fau
lts i
n
th
e
in
v
e
rter
[4
],
fau
lts in
the m
echanical or electrical s
e
ns
ors
[5
] and [7] and also
faults in electrical
m
ach
in
e [7]-[11
]
. Fau
lts th
at is
related
to electrical m
ach
in
e is bro
a
d
l
y d
i
scussed
i
n
th
e
literatu
res, th
ese inclu
d
e
stato
r
fau
lts and
ro
t
o
r fau
lts.
No
wa
day
s
Fi
e
l
d-
Ori
e
nt
e
d
C
ont
rol
(F
OC
)
m
e
t
hod
f
o
r
IM
s i
s
b
r
oa
dl
y
ado
p
t
e
d t
o
o
b
t
a
i
n
hi
gh
per
f
o
r
m
a
nce cont
rol
of
IM
dri
v
e sy
st
em
s. The
FOC
re
prese
n
ts a
bet
t
er sol
u
tion to convi
nce industrial
requ
irem
en
ts. In
th
e literatu
re, sev
e
ral app
r
oach
es hav
e
b
e
en
presen
ted
for v
ector
con
t
ro
l o
f
three-ph
ase IM
un
de
r o
p
e
n
-
p
h
a
se fa
ul
t
[1
2]
-
[
20]
.
I
n
[
1
2]
an
d [
1
3]
scal
ar a
n
d
vect
or c
o
nt
r
o
l
t
ech
ni
q
u
es t
o
c
ont
r
o
l
∆
-connecte
d
t
h
ree-
p
h
ase I
M
un
der
o
p
en
-
pha
se fa
ul
t
usi
ng c
u
r
r
e
n
t
co
n
t
rol
l
e
r ha
ve
be
en p
r
o
p
o
se
d. I
n
[
14]
a
not
her
m
e
t
hod
fo
r F
O
C
of
∆
-
c
on
nect
ed
t
h
re
e-p
h
ase
IM
i
n
case o
f
ope
n
-
pha
se fa
ul
t
ba
sed
on
v
o
l
t
a
ge
co
nt
rol
l
e
r
has
bee
n
prese
n
t
e
d
.
It
was di
sc
usse
d
i
n
[14]
, d
u
ri
n
g
o
p
en
-p
hase
faul
t
,
t
h
e l
i
m
i
tat
i
on d
u
e t
o
m
a
xim
u
m
perm
i
ssi
ble
t
o
r
que i
s
ab
out
30% o
f
t
h
e rat
e
d t
o
r
q
ue of t
h
e IM
. In [
1
5]
-[
18]
, se
veral
t
echni
que
s fo
r FO
C
of st
ar-c
o
n
n
ect
e
d
t
h
ree-
p
h
ase m
o
t
o
r u
nde
r o
p
e
n
-
p
hase fa
ul
t
were
pr
op
ose
d
. Ho
we
ver
,
t
h
e
resul
t
s
i
n
[
15]
-[
18]
d
u
e t
o
us
i
ng t
w
o
d
i
fferen
t
transfo
r
m
a
tio
n
m
a
tri
ces fo
r
stato
r
vo
ltag
e
an
d
curren
t v
a
riab
les are sen
s
itiv
e to
v
a
riation
s
o
f
m
o
to
r
p
a
ram
e
ters. In
[19
]
th
e an
alysis o
f
th
e
star-c
onnected three
-
phase
IM i
n
t
h
e open-phase
fault
indicates that,
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
43
9 – 448
44
0
com
p
ensat
e
t
o
r
que
pul
sat
i
o
ns
,
od
d ha
rm
oni
c vol
t
a
ge
s o
f
t
h
e
m
a
gni
t
ude a
n
d p
h
ase an
gl
e
can be i
n
ject
e
d
at
t
h
e
machine term
inal. T
h
ese m
e
thods
ha
ve
bee
n
a
pplied
and im
p
l
e
m
en
ted
to a vo
lts/h
ertz co
n
t
ro
lled IM.
Thi
s
pape
r i
n
v
e
st
i
g
at
es t
h
e
u
s
e o
f
t
h
e sc
he
m
e
i
n
Fi
gu
re
1
fo
r f
eedi
ng a
t
h
ree
-
p
h
ase
IM
un
de
r
ope
n-
pha
se fa
ul
t
.
T
h
i
s
pa
pe
r p
r
es
ent
s
a
vect
o
r
c
ont
rol
st
rat
e
gy
base
d
on
I
ndi
rect
R
o
t
o
r F
O
C
(IR
F
O
C
)
f
o
r t
h
ree-
pha
se IM
un
de
r ope
n
-
p
h
ase f
a
ul
t
.
It
i
nvest
i
g
at
es t
h
e desi
gn
and use o
f
t
h
e
R
F
O vect
or c
ont
rol
i
n
det
a
i
l
.
The
p
r
esen
ted drive syste
m
en
ab
l
e
to
co
n
t
ro
l t
h
ree-ph
ase
IM un
d
e
r no
rm
al
an
d
o
p
e
n-ph
ase fau
lt
con
d
ition
s
.
Th
is
p
a
p
e
r is org
a
n
i
zed
as fo
llows; after th
e in
trod
u
c
tion
in
sect
io
n
1
,
section
2
g
i
v
e
s th
e m
a
th
em
a
tical
m
o
d
e
l of
t
h
ree-
p
h
ase IM
un
der st
at
o
r
w
i
ndi
n
g
ope
n-
p
h
a
se faul
t
.
N
e
xt
,
sect
i
on 3
desc
ri
bes t
h
e
de
vel
opm
ent
of t
h
e
FO
C
al
go
ri
t
h
m
,
fol
l
o
we
d
by
prese
n
t
i
n
g
p
r
op
ose
d
schem
e
for
ve
ct
or c
o
nt
rol
o
f
t
h
ree
-
p
h
ase
I
M
un
de
r
ope
n-
pha
se
fault. T
h
e
perform
ance of the
p
r
op
osed
app
r
o
ach is tested
b
y
sim
u
latio
n
s
with
th
e resu
lts p
r
esen
ted
in
section
4
an
d fi
n
a
lly, co
n
c
l
u
sion
s are
listed
in
section
5
.
Fi
gu
re 1.
Th
re
e-p
h
ase IM
dri
v
e wi
t
h
one
o
p
e
ned
p
h
ase
2.
FAULT
Y
TH
REE-PH
ASE
IM MO
DEL
The
d-
q m
odel
of
t
h
e st
art
-
co
nnect
e
d
t
h
ree-
pha
se IM
u
nde
r st
at
or
wi
ndi
n
g
ope
n-
p
h
ase
f
a
ul
t
can
be
descri
bed
by
t
h
e f
o
l
l
o
wi
ng
eq
uat
i
o
n
s
[
2
0]
:
St
at
or v
o
l
t
a
ge equat
i
o
ns:
s
qr
s
dr
qs
ds
s
qs
s
ds
qs
s
ds
s
s
qs
s
ds
i
i
p
M
p
M
i
i
p
L
r
p
L
r
v
v
0
0
0
0
(
1
)
Ro
to
r vo
ltag
e
eq
u
a
tion
s
:
s
qr
s
dr
r
r
r
r
r
r
r
r
s
qs
s
ds
qs
ds
r
qs
r
ds
s
qr
s
dr
i
i
p
L
r
L
L
p
L
r
i
i
p
M
M
M
p
M
v
v
(
2
)
St
at
or fl
u
x
e
q
u
a
t
i
ons:
s
qr
s
dr
qs
ds
s
qs
s
ds
qs
ds
s
qs
s
ds
i
i
M
M
i
i
L
L
0
0
0
0
(3)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A N
o
vel
Met
ho
d f
o
r I
RFOC
of
Thre
e-P
h
ase
I
n
d
u
ct
i
o
n M
o
t
o
r u
n
d
e
r
Ope
n
-
P
h
a
se F
a
ul
t
(Mo
h
a
m
m
a
d J
a
nn
at
i
)
44
1
R
o
t
o
r
fl
ux
eq
u
a
t
i
ons:
s
qr
s
dr
r
r
s
qs
s
ds
qs
ds
s
qr
s
dr
i
i
L
L
i
i
M
M
0
0
0
0
(
4
)
Tor
q
ue e
quat
i
o
n
s:
r
r
l
e
s
qr
s
ds
ds
s
dr
s
qs
qs
e
B
Jp
pole
T
T
i
i
M
i
i
M
pole
T
2
2
(
5
)
whe
r
e:
dt
d
p
L
L
L
L
L
L
L
M
L
M
ms
ls
qs
ms
ls
ds
ms
qs
ms
ds
,
2
1
,
2
3
2
3
,
2
3
(
6
)
I
n
(1
)-
(6)
,
v
s
ds
,
v
s
qs
are the stator d-q axes vol
t
ages,
i
s
ds
,
i
s
qs
a
r
e the stator d-q axes curre
nts
,
i
s
dr
,
i
s
qr
are
the rot
o
r
d-
q a
x
es cu
rre
nts,
λ
s
ds
,
λ
s
qs
are the s
t
ator d-q a
x
es fluxes a
nd
λ
s
dr
and
λ
s
qr
are the rotor d-q a
x
es fl
uxe
s
in the
stationa
r
y
refe
rence
f
r
a
m
e (su
p
ersc
rip
t
“
s
”).
r
s
and
r
r
indicate the
st
ator a
n
d
rot
o
r
resistances
. L
ds
,
L
qs
,
L
r
,
M
ds
and
M
qs
den
o
t
e
t
h
e st
at
or an
d r
o
t
o
r d
-
q axes sel
f
an
d
m
u
t
u
al
i
nduct
a
nces.
r
is
th
e
m
o
to
r sp
eed
.
T
e
and
T
l
are electromagnetic torque and loa
d
torque.
J
and
B
are the m
o
ment of inerti
a and
viscous
friction
coefficient res
p
ectively. Note that (1
)
-
(
5
) a
r
e ge
neral eq
u
a
tions f
o
r the t
h
ree
-
p
h
ase IM
.
In ot
her w
o
rd
s, they
may represent
either a h
ealthy th
ree-p
h
a
se
IM if
L
ds
=L
qs
=L
s
=L
ls
+
3/
2
L
ms
and
M
ds
=M
qs
=M=
3/
2
L
ms
or a fau
lty
three-phase
IM (three
-phas
e
IM under
st
at
or wi
n
d
i
n
g o
p
en
-
phase
fa
ul
t
)
i
f
L
ds
=L
ls
+
3/2
L
ms
,
L
qs
=L
ls
+
1/
2
L
ms
,
M
ds
=
3/
2
L
ms
and
M
qs
=
√
3/
2
L
ms
.
3.
FIELD-
O
RIE
N
TED CO
NT
ROL OF
FAULTY THREE-PHASE IM
3.
1.
Problem
Am
ong t
h
e
va
ri
o
u
s t
y
pes o
f
t
h
e vect
or c
o
nt
r
o
l
t
echni
q
u
e
s, FOC
m
e
t
hod i
s
m
o
re co
nve
ni
ent
.
In
co
nv
en
tio
n
a
l
Ro
to
r
FOC m
e
th
od
and
i
n
norm
a
l co
n
d
itio
n,
th
e IM equ
a
tio
n
s
are tran
sfo
r
m
e
d
to
th
e
ro
tating
referen
c
e frame. Fo
r th
is
p
u
rpo
s
e, th
e
fo
llowin
g
t
r
an
sfo
r
m
a
t
i
o
n
m
a
trix
is
used
[21
]
:
s
qs
s
ds
mr
mr
mr
mr
s
qs
s
ds
mr
s
mr
qs
mr
ds
i
i
i
i
T
i
i
cos
sin
sin
cos
(
7
)
In (
7
),
θ
mr
is the angle between the stationary refe
re
nce
fram
e and the rotating re
ference fram
e
(in
th
is p
a
p
e
r superscri
p
t “
mr
” indicates that the va
riables are in th
e rotating re
fe
rence fram
e). Since the IM
studie
d
is asy
mme
trical, the
use
of field-ori
e
ntation
pr
inci
ples needs
a s
p
ecial atte
n
tio
n
.
Th
e
asymmetr
y is a
resu
lt
o
f
d
i
fferen
t
d an
d q ax
i
s
p
a
ram
e
ters in
th
e
fau
lty IM
m
o
d
e
l. Th
is asy
mmetry cau
ses an o
s
cillatin
g term
in
th
e fau
lty mach
in
e to
rque [20
]
. It is po
ssib
l
e to
remo
v
e
t
h
e o
s
cillatin
g
term
in
th
e fau
lty m
a
ch
in
e
el
ect
rom
a
gnet
i
c
t
o
r
q
ue
by
usi
n
g
an
ap
p
r
o
p
ri
ate cont
rol
of t
h
e stator c
u
rre
n
ts.
3.
2.
Prop
osed
Me
t
h
od
(u
si
ng
T
r
ans
f
orm
a
ti
on
Ma
tri
x
f
o
r S
t
at
or
Curre
nt
Vari
abl
e
s)
Using
fo
llowing
su
bstitu
tio
n
s
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
43
9 – 448
44
2
qs
qs
ds
ds
qs
ds
QS
qs
ds
DS
i
M
M
i
M
M
j
i
ji
i
i
(
8
)
Th
e electro
m
a
g
n
e
tic torq
u
e
eq
u
a
tion
of fau
l
ty
m
ach
in
e can b
e
written
as
(9
):
qr
QS
ds
qr
DS
ds
dr
QS
ds
dr
DS
ds
e
i
i
jM
i
i
M
i
i
M
i
i
jM
pole
T
2
(
9
)
whi
c
h gi
ves
,
qr
DS
ds
dr
QS
ds
e
i
i
M
i
i
M
pole
T
2
(
1
0
)
As ca
n
be see
n
f
r
o
m
(10)
, fa
ul
t
y
m
achi
n
e t
o
r
q
ue eq
uat
i
o
n
bec
o
m
e
s sim
i
lar heal
t
h
y
m
a
chi
n
e t
o
r
q
u
e
eq
u
a
tion
.
Eq
u
a
tio
n
(8) can
b
e
written
as (11
)
:
qs
ds
qs
ds
qs
ds
QS
DS
i
i
M
M
M
M
j
j
i
i
1
(
1
1
)
Using
fo
llowing
su
bstitu
tio
n
s
,
mr
qs
qs
s
qs
QS
mr
ds
ds
s
ds
DS
mr
mr
i
i
i
i
i
i
i
i
j
sin
cos
1
(12)
Th
e tran
sform
a
tio
n
m
a
trices fo
r th
e
cu
rren
t can
b
e
written
as (1
3).
mr
qs
mr
ds
mr
qs
ds
mr
qs
ds
mr
mr
s
qs
s
ds
i
i
M
M
M
M
i
i
cos
sin
sin
cos
(
1
3
)
The i
nve
rse
of
(1
3)
gi
ves t
h
e
pr
o
pose
d
t
r
ans
f
o
r
m
a
ti
on m
a
t
r
i
x
f
o
r
st
at
or
cu
rre
nt
va
ri
abl
e
s:
s
qs
s
ds
mr
ds
qs
mr
mr
ds
qs
mr
s
qs
s
ds
mr
is
mr
qs
mr
ds
i
i
M
M
M
M
i
i
T
i
i
cos
sin
sin
cos
(
1
4
)
Using
(14
)
, t
h
e n
e
w m
a
th
e
m
at
ical
m
o
d
e
l can
b
e
written
as (1
5) and
(16
)
:
Ro
to
r vo
ltag
e
eq
u
a
tion
s
:
s
qr
s
dr
mr
s
mr
s
r
r
r
r
r
r
r
r
mr
s
s
qs
s
ds
mr
is
mr
is
qs
qs
r
qs
r
ds
mr
s
s
qr
s
dr
mr
s
i
i
T
T
p
L
r
L
L
p
L
r
T
i
i
T
T
p
M
M
M
p
M
T
v
v
T
1
1
(
1
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A N
o
vel
Met
ho
d f
o
r I
RFOC
of
Thre
e-P
h
ase
I
n
d
u
ct
i
o
n M
o
t
o
r u
n
d
e
r
Ope
n
-
P
h
a
se F
a
ul
t
(Mo
h
a
m
m
a
d J
a
nn
at
i
)
44
3
Tor
q
ue e
quat
i
o
n
:
s
qs
s
ds
mr
is
mr
is
ds
qs
T
mr
s
T
mr
s
s
qr
s
dr
s
qs
s
ds
ds
qs
s
qr
s
dr
s
qr
s
ds
ds
s
dr
s
qs
qs
e
i
i
T
T
M
M
T
T
i
i
pole
i
i
M
M
i
i
pole
i
i
M
i
i
M
pole
T
0
0
2
0
0
2
)
(
2
1
1
(
1
6
)
whi
c
h gi
ves
,
Ro
to
r vo
ltag
e
eq
u
a
tion
s
:
mr
qr
mr
dr
r
r
r
r
mr
r
r
mr
r
r
mr
qs
mr
ds
ds
ds
r
mr
ds
r
mr
ds
i
i
p
L
r
L
L
p
L
r
i
i
p
M
M
M
p
M
0
0
(
1
7
)
Tor
q
ue e
quat
i
o
n
:
)
(
2
mr
qr
mr
ds
ds
mr
dr
mr
qs
ds
e
i
i
M
i
i
M
pole
T
(
1
8
)
whe
r
e,
ω
mr
i
s
t
h
e a
n
gul
ar
vel
o
ci
t
y
of
t
h
e
r
o
t
o
r
fi
el
d-
o
r
i
e
nt
ed
refe
rence
f
r
a
m
e
. Fr
om
(17
)
a
n
d
(
1
8),
i
t
c
a
n
be
seen
th
at th
e ro
tor vo
ltag
e
an
d
th
e t
o
rq
u
e
eq
u
a
tion
s
are si
m
ilar to
th
e
h
ealth
y th
ree-p
h
a
se IM equatio
n
s
.
C
onse
q
uent
l
y
,
i
t
i
s
possi
bl
e t
o
co
nt
r
o
l
faul
t
y
m
achi
n
e by
t
h
e som
e
m
odi
fi
cat
i
ons i
n
t
h
e con
v
e
n
t
i
onal
R
F
O
vect
o
r
c
ont
r
o
l
.
3.
3.
RFO
C
Eq
uati
ons
of F
a
ulty
IM
Th
e
ro
t
o
r
FOC
equ
a
tio
n
s
of fau
lty IM b
a
sed on
eq
u
a
tion
s
(1
7) an
d (1
8) ca
n
b
e
written
as (19)-(21)
(to
ob
tain
th
ese equ
a
tio
ns th
e assu
m
p
tio
n
λ
dr
mr
=|
λ
r
|
and
λ
qr
mr
=0 has bee
n
c
o
nsi
d
e
r
ed
):
R
o
t
o
r
fl
ux
eq
u
a
t
i
on:
p
T
i
M
r
mr
ds
ds
r
1
(
1
9
)
Tor
q
ue e
quat
i
o
n
:
mr
qs
r
r
ds
e
i
L
M
pole
T
2
(
2
0
)
Spee
d e
quat
i
on
:
r
r
mr
qs
ds
r
mr
T
i
M
(
2
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
43
9 – 448
44
4
In thes
e equations
,
T
r
is th
e ro
tor ti
m
e
co
n
s
tan
t
(
T
r
=
L
r
/
r
r
). As ca
n be
seen fr
om
(19)
-(
2
1
) t
h
e
st
ruct
u
r
e
of t
h
e
eq
uat
i
ons
o
f
p
r
o
p
o
sed
vect
or
co
nt
rol
fo
r
faulty th
ree-ph
ase IM is th
e sam
e
as equ
a
tion
s
o
f
t
h
e
vector control for health
y three-phase
IM. In summ
ery the com
p
arison
between c
o
nve
n
tional and propos
ed
vect
o
r
c
ont
r
o
l
equat
i
o
ns
i
s
l
i
s
t
e
d i
n
Tabl
e
1.
Tabl
e
1. T
h
e
C
o
m
p
ari
s
on
bet
w
een
C
o
n
v
ent
i
onal
a
n
d P
r
op
o
s
ed
Vect
o
r
C
o
nt
r
o
l
Eq
uat
i
o
ns
Healthy IM
Faulty
IM
Flux equation
p
T
Mi
r
mr
ds
r
1
p
T
Mi
p
T
i
M
r
mr
ds
r
mr
ds
ds
r
1
1
T
o
r
que equation
mr
qs
r
r
e
i
L
M
po
l
e
T
2
mr
qs
r
r
mr
qs
r
r
ds
e
i
L
M
pole
i
L
M
pole
T
2
2
Speed equation
r
r
mr
qs
r
mr
T
Mi
mr
qs
r
r
r
r
mr
qs
ds
r
mr
i
L
M
pole
T
i
M
2
3.
4.
Block
Diagram of Pr
opose
d
IR
FOC for
Faulty T
h
ree-Phase
I
M
Fro
m
th
e resu
l
t
s o
f
(19)-(21
), it
is p
o
ssib
l
e
to
ad
op
t th
e ind
i
rect field
-
orie
nt
ed co
nt
r
o
l
schem
e
for
faul
t
y
t
h
ree
-
ph
ase IM
usi
n
g
cur
r
ent
c
o
nt
r
o
l
l
e
r as s
h
o
w
n i
n
Fi
gu
re
2.
In
Fi
gu
re
2, t
h
e s
w
i
t
c
hes a
r
e c
h
ang
e
d
fr
om
bal
a
nced
m
ode t
o
u
n
b
al
anced
m
ode aft
e
r fa
ul
t
i
s
hap
p
e
ned
.
It can b
e
no
ted th
at 2 to
2
t
r
ansform
a
tio
n
for
st
ato
r
cu
rren
ts
d
u
ring
fau
lt con
d
ition
as is [20
]
:
bs
as
s
qs
s
ds
i
i
i
i
1
1
1
1
2
2
(
2
2
)
Fi
gu
re
2.
B
l
oc
k
di
ag
ram
of p
r
o
p
o
sed
IR
F
O
C
of
heal
t
h
y
an
d
faul
t
y
t
h
re
e-
pha
se IM
4.
R
E
SU
LTS AN
D COMPAR
ISON
S
To
veri
fy
t
h
e
effect
i
v
e
n
ess
o
f
t
h
e
p
r
op
ose
d
m
e
t
hod,
di
f
f
e
r
ent
ca
ses
usi
n
g M
A
TL
AB
s
o
ft
ware
are
sim
u
l
a
t
e
d. R
u
n
g
e-
K
u
t
t
a
al
gori
t
hm
i
s
used f
o
r
sol
v
i
n
g t
h
e
he
al
t
h
y
and fa
ul
t
y
IM
dy
nam
i
c
equat
i
o
ns
. A
n
IM
i
s
fed
fr
om
a SPWM
VS
I.
I
n
t
h
i
s
pa
per i
t
i
s
assum
e
d an i
m
m
e
di
at
e ope
n s
t
at
or wi
ndi
ng
det
ect
i
o
n
.
The
rat
i
n
g
s
an
d p
a
ram
e
ters of th
e sim
u
lat
e
d
m
o
to
r are as fo
llo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A No
vel Met
h
od
for IRFO
C o
f
Th
ree-Pha
s
e
In
du
ction
Mo
tor un
der
O
p
en-Pha
se Fau
l
t
(Mo
h
a
m
m
a
d J
a
nn
at
i
)
44
5
Fi
gu
re
3 s
h
ow
s t
h
e c
o
m
p
ari
s
on
bet
w
een
c
o
nve
nt
i
o
nal
c
o
n
t
rol
l
e
r a
n
d
pr
o
pos
ed
IR
F
O
C
(Fi
g
ure
3
(l
eft
)
:
c
o
n
v
e
n
t
i
onal
a
n
d Fi
gu
r
e
3
(ri
ght
):
p
r
o
pos
ed
).
In
t
h
i
s
fi
g
u
re,
t
h
e
IM
i
s
st
art
i
n
g i
n
t
h
e
bal
a
nce
d
c
o
nd
i
t
i
on.
The
n
a p
h
ase c
u
t
-
of
f fa
ul
t
i
s
int
r
od
uce
d
at
t
=
0.
5s an
d t
h
e
I
M
becom
e
s un
bal
a
nce
d
. Si
m
u
l
a
t
i
on re
sul
t
s
of t
h
e
co
nv
en
tio
n
a
l
an
d pro
p
o
s
ed
con
t
ro
ller illu
strate th
at th
e conv
en
tion
a
l FOC
was
un
ab
le to
co
n
t
ro
l t
h
e
fau
l
ty IM
co
rrectly. Esp
ecially, sig
n
i
fican
t o
s
cillatio
n
s
in
th
e IM to
rq
u
e
an
d
sp
eed are o
b
s
erv
e
d
.
It can
b
e
seen
fro
m
Fi
gu
re
3 t
h
at
t
h
e dy
nam
i
c
per
f
o
r
m
a
nce o
f
t
h
e
p
r
o
p
o
se
d F
O
C
i
n
bot
h
heal
t
h
y
a
n
d
fa
ul
t
y
con
d
i
t
i
ons
i
s
satisfacto
r
y.
Fig
u
re
3
.
Sim
u
latio
n
resu
lts
of th
e conv
en
tion
a
l IRFO
C
(l
ef
t
)
an
d pr
o
p
o
s
e
d
IR
FOC
(ri
g
h
t
);
fr
om
t
op
t
o
bot
t
o
m
:
st
at
or
a-axi
s
c
u
rre
nt
,
el
ect
rom
a
gnet
i
c
t
o
r
q
ue, s
p
ee
d
an
d z
oom
of
s
p
eed
In
Fi
g
u
re 4
,
t
w
o
d
r
i
v
e system
s
are tested
u
n
d
e
r th
e same o
p
e
ratin
g
con
d
ition
s
as fo
llo
ws: a ph
ase
cu
t-o
f
f fau
lt is in
trod
uced
at
t=2
s
, th
e
v
a
lu
e o
f
th
e l
o
ad is
increase
d
from zero to
1
N
.
m
at
t
=
0.5s an
d f
r
om
1
N
.m
to
1
.
3
N
.m
a
t
t=2
s
. Simu
latio
n
resu
lts
sh
ow t
h
at th
e
co
nv
en
tio
n
a
l
vecto
r
con
t
ro
ller canno
t con
t
ro
l th
e
u
n
b
a
lan
c
ed
IM p
r
op
erly (see Figu
re 4 (l
eft)).
As can
b
e
seen
fro
m
Fig
u
re
4
(left), in
t
h
e
fau
lt co
nd
itio
n,
sig
n
i
fican
t
o
s
cillatio
n
is seen
in
t
h
e electro
m
a
g
n
e
tic
torqu
e
an
d m
o
t
o
r
sp
eed
(in
t
h
is case an
d
u
s
ing
co
nv
en
tio
n
a
l co
n
t
ro
ller th
e
oscillatio
n
o
f
electro
m
a
g
n
e
tic to
rq
u
e
at steady state
is ab
o
u
t 0
.
9N.m
aro
u
n
d
th
e
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t
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b
e
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43
9 – 448
44
6
avera
g
e am
ou
n
t
of
1.
3
N
.m
).
B
a
sed
on
Fi
g
u
r
e 4
(
r
i
g
ht
) t
h
e p
r
op
osed con
t
ro
ller is
ab
le t
o
con
t
ro
l bo
th
health
y
an
d fau
lty th
ree-ph
ase
IM even
u
n
d
e
r lo
ad
v
a
riation
s
.
Sim
u
la
tio
n
resu
l
t
s o
f
Figu
re 4
(righ
t
) show t
h
at th
e
p
r
op
o
s
ed
co
n
t
ro
ller red
u
c
es th
e to
rqu
e
oscillatio
n
con
s
id
erab
ly (in
th
is case an
d
u
s
i
n
g
p
r
o
p
o
s
ed
con
t
ro
l
l
er th
e
o
s
cillatio
n
o
f
electro
m
a
g
n
e
tic to
rqu
e
at steady state is ab
ou
t
0
.
3N.m
).
Fig
u
re
4
.
Sim
u
latio
n
resu
lts
of th
e conv
en
tion
a
l IRFO
C
(l
ef
t
)
an
d pr
o
p
o
s
e
d
IR
FOC
(ri
g
h
t
);
fr
om
t
op
t
o
b
o
tto
m
:
ro
tor a-ax
is curren
t
, stato
r
a-ax
is curr
ent, electrom
a
gnetic torque
, s
p
eed and
spee
d error
Evaluation Warning : The document was created with Spire.PDF for Python.
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8-8
6
9
4
A No
vel Met
h
od
for IRFO
C o
f
Th
ree-Pha
s
e
In
du
ction
Mo
tor un
der
O
p
en-Pha
se Fau
l
t
(Mo
h
a
m
m
a
d J
a
nn
at
i
)
44
7
Fi
gu
re
5 s
h
ow
s si
m
u
l
a
ti
on re
sul
t
s
o
f
t
h
e
p
r
o
pos
ed m
e
t
h
o
d
fo
r
heal
t
h
y
an
d
faul
t
y
IM
i
n
t
h
e
di
ffe
re
nt
val
u
es
o
f
refe
r
e
nce s
p
ee
d (ze
r
o/
l
o
w s
p
ee
d a
n
d
hi
gh
s
p
eed
)
.
I
n
Fi
g
u
re
5,
a p
h
ase c
u
t
-
of
f
fa
ul
t
i
s
occ
u
r
r
e
d at
t
=
3s. It
i
s
evi
d
ent
fr
om
Fi
gure 5 t
h
at
usi
ng
pr
o
pose
d
t
ech
n
i
que t
h
e t
h
re
e-
pha
se IM
du
ri
ng
no
rm
al and
ope
n-
p
h
a
se fau
lt con
d
ition
s
can
follo
w th
e
re
feren
ce sp
eed
witho
u
t
an
y ov
ersho
o
t
an
d
stead
y
-
state erro
r. It
can
b
e
seen
fro
m
th
e p
r
esen
ted
si
m
u
la
tio
n
resu
lts th
at th
e dynam
i
c perform
ance of the proposed
fault-t
o
lera
nt
cont
rol of
thre
e-phase IM dri
v
e
is
acce
ptabl
e
.
Fi
gu
re 5.
Si
m
u
l
a
t
i
on
res
u
l
t
of t
h
e
s
p
eed
res
p
ons
e usi
n
g pr
o
pos
ed
IR
F
O
C
5.
CO
NCL
USI
O
N
The r
o
t
o
r fl
u
x
-
o
ri
e
n
t
e
d co
nt
r
o
l
of a fa
ul
t
y
three
-
p
h
ase IM
(t
hree
-p
hase I
M
unde
r o
p
e
n
-
pha
se faul
t
)
was prese
n
t
e
d i
n
t
h
i
s
pap
e
r.
The desi
g
n
of
pr
o
pose
d
c
o
nt
r
o
l
l
e
r
f
o
r
fa
ul
t
y
m
achi
n
e
was di
scuss
e
d
i
n
d
e
t
a
i
l
.
It
was sh
o
w
n t
h
at
t
o
cont
r
o
l
t
h
ree
-
p
h
ase IM
un
der st
at
or
wi
n
d
i
n
g o
p
en
-
pha
se faul
t
i
t
i
s
requi
re
d t
o
use
u
n
b
a
lan
c
ed
tran
sform
a
t
i
o
n
matrix
fo
r stato
r
curren
t
v
a
riab
les to
elimin
ate th
e o
s
cillatin
g
ter
m
o
f
th
e
el
ect
rom
a
gnet
i
c
t
o
r
q
ue. T
h
i
s
pape
r
has
sh
o
w
n
t
h
at
wi
t
h
s
o
m
e
m
odi
fi
cat
i
ons
i
n
t
h
e st
r
u
ct
ure
of
co
n
v
e
n
t
i
onal
RFO con
t
ro
ller for h
ealth
y three-ph
ase
IM it is p
o
ssi
b
l
e to
im
p
l
e
m
en
t co
nv
en
tion
a
l con
t
ro
ller fo
r t
h
ree-p
h
a
se
IM
u
nde
r o
p
e
n
-p
hase fa
ul
t
.
Si
m
u
l
a
t
i
on res
u
l
t
s
sh
ow t
h
at
t
h
e
per
f
o
r
m
a
nce o
f
t
h
e p
r
op
ose
d
vect
o
r
co
nt
r
o
l
l
e
r i
s
sat
i
s
fact
ory
.
T
h
e a
ppl
i
cat
i
o
ns
of
t
h
e
p
r
o
p
o
s
e
d
dri
v
e sy
ste
m
are its use a
s
an em
erge
nc
y schem
e
for
critic
a
l
in
du
strial ap
p
l
i
catio
n
s
and
v
e
cto
r
con
t
ro
l
of
sin
g
l
e-ph
ase
IM with
t
w
o m
a
in
and
aux
iliary wind
ing
s
.
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