Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol.
5, No. 6, Decem
ber
2015, pp. 1284~
1
291
I
S
SN
: 208
8-8
7
0
8
1
284
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 Novel Meth
od for Vect
or Cont
rol of Faulty Three-Phase IM
Dri
v
es Based on FOC Method
M
o
hammad
Ja
nna
t
i
*
, N
i
k
R
u
mzi N
i
k Idris*
,
Mo
hd Juna
idi
A
b
dul Azi
z
*
,
To
le Sut
i
kno**
* UTM-PROTON Future Driv
e
Laborator
y
,
Faculty
of
Electr
ical Engin
eering
,
U
n
ivers
iti Teknologi Malay
s
ia, 81
310
Skudai, Johor
Bahru, M
a
lay
s
ia
** Departmen
t
o
f
Electr
i
cal
Engineering
,
Un
iv
ersitas Ahmad Dah
l
an, Yog
y
akarta,
Indonesia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
n 20, 2015
Rev
i
sed
Au
g
22
, 20
15
Accepte
d
Se
p 8, 2015
This paper prop
oses a novel method for vecto
r
control of f
a
ulty three-ph
as
e
Induction Motor
(IM) drives based on Fi
eld-Oriented Control (F
OC) method.
The perform
an
ce ch
ara
c
ter
i
s
t
i
c
s
of the pr
e
s
ented driv
e s
y
s
t
em
ar
e
investigated at health
y
and
op
en-phase fault co
nditions.
The
simulation of
the case stud
y
is
carried out b
y
using
the Matlab/M-File software for a star-
connected thr
ee-
phase IM. The
results
show the better p
e
rformance of th
e
proposed drive
s
y
stem especially
in r
e
duction
of motor speed and torque
oscilla
tions dur
i
ng open-phase
f
a
ult
opera
ting
.
Keyword:
FOC
Op
en-Phase Fau
lt
Sp
eed
an
d To
rq
u
e
Oscillatio
n
s
Stat-Connecte
d
Three
-
P
h
ase I
n
duct
i
o
n
M
o
t
o
r
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. Jann
ati,
UTM
-
PR
OT
O
N
F
u
tu
re
Dri
v
e
Lab
o
rat
o
ry
,
Faculty of Electrical
En
gi
nee
r
i
n
g
,
Un
i
v
ersiti Tekn
o
l
o
g
i
Malaysia,
8
131
0 Sk
ud
ai,
Jo
hor
Bah
r
u
,
Malaysia.
Em
a
il: j
a
n
n
a
ti
m
9
4
@
yah
o
o
.
co
m
1.
INTRODUCTION
The Fi
el
d-
Ori
e
nt
ed C
o
nt
rol
(F
OC
) m
e
t
h
o
d
i
s
wi
del
y
u
s
ed
fo
r i
m
pl
em
ent
i
ng
hi
g
h
per
f
o
r
m
a
nce
vect
o
r
c
ont
r
o
l
of t
h
ree
-
phase
In
d
u
ct
i
o
n
M
o
t
o
r
(IM
)
dri
v
es.
The
FOC
t
e
c
h
ni
q
u
e
di
vi
de
s I
M
st
at
or c
u
r
r
e
n
t
s
i
n
t
o
fl
u
x
an
d t
o
r
q
u
e
pro
d
u
ci
n
g
co
m
ponent
s. T
h
e
t
o
rq
ue i
s
pr
op
ort
i
o
nal
t
o
t
h
e pr
o
duct
o
f
t
h
es
e t
w
o per
p
e
n
di
cul
a
r
com
pone
nt
s an
d t
h
ey
can be t
r
eat
ed se
parat
e
l
y
. Thi
s
m
eans t
h
at
t
h
e cont
r
o
l
of t
h
ree
-
p
h
as
e IM
i
s
t
r
ansf
o
r
m
e
d
in
to
a con
t
ro
l syste
m
si
milar t
o
th
e con
t
ro
l of DC
m
ach
in
e. Gen
e
rally, th
ere are t
w
o
po
ssib
ilities fo
r th
e FOC
technique. T
h
e
y
are: Roto
r
Fi
el
d-
Ori
e
nt
e
d
C
ont
rol
(R
F
O
C
)
an
d St
at
o
r
Fi
el
d-
Ori
e
nt
ed C
o
nt
r
o
l
(S
FOC
)
[
1
]
.
In s
o
m
e
indust
r
ial applications, suc
h
as i
n
el
ectri
c vehicle,
space e
xpl
orati
o
n,
and etc the
cont
rol
of
faulty electrical m
achines is ve
ry im
portant [2]. T
h
es
e
ap
p
lication
s
need
a fau
lt-to
l
e
ran
t
con
t
ro
l
meth
o
d
wh
ereb
y
th
e op
eration
o
f
the
driv
e
sy
st
em
can
not
be i
n
t
e
rr
upt
e
d
by
a
faul
t
y
co
n
d
i
t
i
on m
o
st
l
y
for
s
a
fet
y
reaso
n
s
.
The
c
ont
rol
of
faul
t
e
d m
achi
n
e, h
o
we
ve
r, i
s
cl
e
a
rl
y
di
ffe
re
nt
f
r
om
t
h
e cont
ro
l
of
heal
t
h
y
m
achi
n
e.
By u
s
in
g
t
h
e stan
d
a
rd
con
t
rol strateg
i
es to
fau
lted
m
ach
ine, sign
ifican
t
oscillatio
n
s
in
th
e m
o
to
r sp
eed
and
to
rq
u
e
ou
tpu
t
will b
e
d
e
v
e
l
o
p
e
d [3
]-[5
].
In case
of open-phase fa
ult, in
[6]-[12], s
o
m
e
m
e
thods
to control fa
ulted m
u
lti-phas
e
IMs and
faul
t
e
d
pe
rm
anent
m
a
gnet
s
y
nch
r
o
n
ous
m
o
t
o
rs
ha
ve
be
en
pr
o
pos
ed
.
These
m
e
t
hod
s are
l
i
m
i
t
e
d t
o
t
h
ese
cust
om
i
zed or
speci
al
i
zed m
a
chi
n
es a
nd a
p
p
l
i
cat
i
ons. I
n
[
5
]
,
[13]
t
w
o t
echni
que
s fo
r F
O
C
of t
h
ree
-
pha
se IM
un
de
r o
p
en
-
p
h
a
se faul
t
ha
ve
been
pre
s
ent
e
d
.
These t
e
c
hni
q
u
es are
o
n
l
y
appl
i
cabl
e
t
o
vec
t
or-c
o
n
t
r
ol
l
e
d
m
o
t
o
r
dri
v
es base
d o
n
c
u
r
r
ent
-
co
nt
r
o
l
l
e
d Vol
t
a
ge So
urce
I
nve
rt
e
r
(
V
S
I
)
.
I
n
[
1
4
]
,
[1
5]
di
ffe
ren
t
m
e
t
hods
base
d o
n
vol
t
a
ge
co
nt
r
o
l
l
e
r fo
r ve
ct
or
cont
rol
of t
h
r
ee-p
h
ase
IM
u
nde
r
ope
n
-
p
h
a
s
e faul
t
have
been
p
r
o
p
o
se
d
.
Th
e
dra
w
back
o
f
t
h
ese t
ech
ni
qu
es i
s
t
h
at
t
h
es
e m
e
t
hods
are
n
o
t
g
o
o
d
fo
r
hi
g
h
per
f
o
r
m
a
nce
vect
o
r
c
ont
ro
l
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
A N
o
vel
Met
h
o
d
f
o
r Vect
o
r
C
ont
r
o
l
of
Fa
ul
t
y
Thr
ee-P
h
ase
IM
Dri
ves B
a
s
e
d
on
F
O
C
…
(
M
o
h
a
m
m
a
d J
a
nn
at
i
)
1
285
appl
i
cat
i
o
ns as i
n
t
h
ese t
echni
que
s due t
o
t
h
e
usi
ng t
w
o di
f
f
e
rent
t
r
ans
f
or
m
a
t
i
on
m
a
t
r
i
c
es, t
h
e dri
v
e sy
s
t
em
i
s
sen
s
itiv
e
to
m
o
to
r p
a
ram
e
ters v
a
riation
s
.
Thi
s
st
u
d
y
sh
ows t
h
e t
h
ree
-
pha
se IM
eq
u
a
t
i
ons u
n
d
er
o
p
en
-
phase
faul
t
can be m
odel
e
d as t
w
o
bal
a
nce
d
f
o
r
w
ard a
nd
back
w
a
rd e
quat
i
o
ns
. B
a
sed o
n
t
h
i
s
,
a novel
F
O
C
m
e
t
hod f
o
r t
h
ree-
pha
se IM
un
de
r
ope
n
-
p
h
ase i
s
prese
n
t
e
d
.
The
con
f
i
g
urat
i
o
n
of t
h
e
used c
o
nve
rt
er f
o
r
fee
d
i
n
g t
h
ree
-
p
h
a
s
e IM
du
ri
n
g
ope
n
-
p
h
a
se fau
lt is
sh
own
in
Fi
g
u
re 1
.
Du
ring
fau
lt co
nd
itio
n
as sh
own
in
this fig
u
re, th
e
mid
-
po
in
t of DC-l
i
nk
vol
t
a
ge s
h
oul
d
be co
nne
ct
ed t
o
t
h
e ne
ut
ral
p
o
i
n
t
o
f
t
h
e m
a
chi
n
e as
di
scuss
e
d i
n
[
1
6]
. Thi
s
pape
r i
s
o
r
ga
ni
ze
d
as fo
llows: Aft
e
r in
tro
d
u
c
tion in
sectio
n
1
,
i
n
section
2,
d
-
q m
odel
of
he
al
t
h
y
and
faul
t
y
t
h
ree-
pha
se I
M
s is
prese
n
t
e
d
.
Ne
x
t
, sect
i
on
3 des
c
ri
bes t
h
e
de
ve
l
opm
ent
of t
h
e
FOC
al
g
o
ri
t
h
m
,
fol
l
owe
d
by
p
r
esent
i
n
g
pr
o
p
o
se
d
schem
e
. The
p
e
rf
orm
a
nce o
f
t
h
e p
r
ese
n
t
e
d
m
e
t
hod i
s
a
n
al
y
zed an
d c
h
ec
ked
usi
n
g
M
a
t
l
a
b s
o
ft
ware i
n
sect
i
o
n
4 a
n
d
sect
i
o
n
5
co
ncl
u
des t
h
e
pape
r.
Fi
gu
re 1.
C
o
nfi
g
u
r
at
i
o
n of
t
h
e use
d
c
o
n
v
ert
e
r fo
r feedi
n
g
t
h
r
ee-p
h
ase IM
d
u
ri
ng
o
p
e
n
-
pha
se
fa
ul
t
2.
MO
DELIN
G
OF
HE
ALTH
Y AN
D
FAUL
TY THREE-PHASE
IMs
The d
-
q m
odel
of h
eal
t
h
y
an
d fa
ul
t
y
t
h
ree-
pha
se IM
s in t
h
e stationa
ry refere
nce fram
e
(supers
c
ript
“
s
”)
ca
n be des
c
ri
be
d by
t
h
e f
o
l
l
o
wi
ng
eq
uat
i
ons
[
13]
:
(
1
)
In (1
),
v
s
ds
,
v
s
qs
are the stator
d-q a
x
es voltage
s,
i
s
ds
,
i
s
qs
are the stator d-q a
x
es currents
,
i
s
dr
,
i
s
qr
are the
rot
o
r d-q axes
currents
,
λ
s
ds
,
λ
s
qs
are the stator d-q a
x
es fluxes and
λ
s
dr
,
λ
s
qr
are the rotor d-q axes
fluxes.
r
ds
,
r
qs
,
r
r
indicate the
s
t
ator a
n
d rotor
d-q a
x
es
resist
ances.
L
ds
,
L
qs
,
L
r
,
M
d
,
M
q
de
n
o
t
e
t
h
e
st
at
or a
n
d
r
o
t
o
r
d-
q a
x
es sel
f
and m
u
tual inductances
.
r
is
th
e m
o
to
r sp
eed
.
τ
e
,
τ
l
a
r
e el
ect
rom
a
gnet
i
c
t
o
r
que a
n
d l
o
a
d
t
o
rq
ue.
J
,
F
are
the
m
o
m
e
nt
of i
n
ert
i
a
and vi
sc
ous
fri
ct
i
o
n co
effi
ci
ent
res
p
e
c
t
i
v
el
y
.
It
can be not
e
d
t
h
at
Equat
i
o
n (
1
)
can be
descri
bed heal
thy three
-
phas
e IM if,
r
ds
=
r
qs
=r
s
,
L
ds
=L
qs
=
L
s
=
L
ls
+1.5
L
ms
,
M
d
=
M
q
=1.5
L
ms
and three-pha
s
e IM
u
n
d
e
r
op
en
-phase f
a
u
lt if
,
r
ds
=
r
qs
=r
s
,
L
ds
=L
ls
+1.5
L
ms
,
L
qs
=
L
ls
+0.5
L
ms
,
M
d
=1
.5
L
ms
,
M
q
=
√
3/
2
L
ms
[13
]
(
L
ls
an
d
L
ms
are leaka
g
e a
n
d m
u
tual induc
tances re
specti
v
ely).
3.
PROP
OSE
D
METHO
D
F
O
R
VECT
OR
CO
NTR
O
L
OF HE
ALTH
Y
AN
D F
A
UL
TY I
M
s
In t
h
i
s
sect
i
o
n,
a m
e
t
hod
f
o
r
vect
o
r
co
nt
r
o
l
of t
h
ree
-
p
h
ase
IM
ba
sed
o
n
ext
e
n
d
ed
m
odel
of
IM
as
sho
w
n i
n
(
1
)
i
s
pre
s
ent
e
d.
It
i
s
o
b
v
i
o
us
t
h
i
s
m
e
t
hod
can
be u
s
ed
f
o
r
heal
t
h
y
m
a
chi
n
e i
f
,
r
ds
=
r
qs
=r
s
,
L
ds
=L
qs
=
L
s
=
L
ls
+1.5
L
ms
,
M
d
=
M
q
=1.5
L
ms
and
fau
lty m
ach
in
e if,
r
ds
=
r
qs
=r
s
,
L
ds
=L
ls
+1.5
L
ms
,
L
qs
=
L
ls
+0
.5
L
ms
,
M
d
=1.5
L
ms
,
M
q
=
√
3/
2
L
ms
. T
h
e
pr
o
pose
d
m
e
t
hod
i
s
based
o
n
i
ndi
rect
R
F
OC
an
d
di
rect
R
F
OC
m
e
t
hods.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1284 –
1291
1
286
In RFOC strat
e
gy it is neces
sary that the
m
o
tor
equations tra
n
sfe
r
to t
h
e rotating
re
ference
fram
e
.
Fo
r th
is
pu
rpo
s
e, th
e t
r
an
sfo
r
matio
n
m
a
tr
ix
as show
n in
(2
) is u
s
ed
[1
]:
(2)
I
n
(2
),
su
p
e
r
s
cr
ip
t “
e
” i
ndicat
es the e
q
uations a
r
e in th
e
r
o
tating
re
fere
n
ce fram
e
. Als
o
, “
θ
e
” is t
h
e
angle
betwe
e
n the stationary
refe
re
nce fra
m
e and
rotati
ng
refe
rence
f
r
a
m
e. Usi
n
g
(2
),
t
h
e e
quat
i
ons
o
f
I
M
(Equation
(1)), can
be
obtaine
d
as
(3) and
(4):
(3
)
Whe
r
e,
(4)
In (
3
),
“
ω
e
” is
th
e angu
lar
v
e
lo
city o
f
t
h
e ro
t
o
r
field
o
r
ie
nted re
fere
nce
fra
m
e
. As it is se
en f
r
o
m
(3)
,
i
n
ge
neral
,
E
q
uat
i
o
n
(
3
) i
n
cl
ude
s t
w
o set
o
f
eq
uat
i
o
ns
(f
o
r
wa
rd
eq
uat
i
o
ns:
su
pe
rscri
p
t
“+
e
” and
bac
k
wa
rd
eq
u
a
tion
s
: su
perscri
p
t “-
e
”). Each of equations re
pre
s
e
n
ts an e
q
u
a
tion
wh
ere
ro
tat
e
s in
th
e fo
rward
or
back
wa
rd
di
rec
t
i
on as
sh
o
w
n
i
n
Fi
gu
re
2.
e
e
e
e
e
s
T
cos
sin
sin
cos
e
qr
e
dr
e
qs
e
ds
e
qr
e
dr
e
qs
e
ds
v
v
v
v
e
qr
e
dr
e
qs
e
ds
q
d
q
d
r
e
q
d
r
e
q
d
q
d
q
d
e
qs
ds
qs
ds
qs
ds
e
q
d
e
q
d
qs
ds
e
qs
ds
qs
ds
v
v
v
v
e
qr
e
dr
e
qs
e
ds
r
r
r
r
e
q
d
q
d
r
e
r
r
e
r
r
q
d
r
e
q
d
q
d
q
d
e
qs
ds
qs
ds
qs
ds
e
q
d
e
q
d
qs
ds
e
qs
ds
qs
ds
e
qs
e
ds
i
i
i
i
dt
d
M
M
M
M
M
M
dt
d
M
M
dt
d
M
M
M
M
dt
d
L
L
r
r
L
L
M
M
dt
d
M
M
L
L
dt
d
L
L
r
r
i
i
i
i
dt
d
L
r
L
dt
d
M
M
M
M
L
dt
d
L
r
M
M
dt
d
M
M
dt
d
M
M
M
M
dt
d
L
L
r
r
L
L
M
M
dt
d
M
M
L
L
dt
d
L
L
r
r
v
v
0
0
2
2
0
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0
0
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
A N
o
vel
Met
h
o
d
f
o
r Vect
o
r
C
ont
r
o
l
of
Fa
ul
t
y
Thr
ee-P
h
ase
IM
Dri
ves B
a
s
e
d
on
F
O
C
…
(
M
o
h
a
m
m
a
d J
a
nn
at
i
)
1
287
Fi
gu
re
2.
(a
):
F
o
r
w
ar
d a
n
d st
a
t
i
ona
ry
refe
re
n
ce fram
e
s (s
up
erscri
pt “+
e
”: forward, supe
rs
cript “
s
”:
statio
n
a
r
y
),
(b): Back
w
a
r
d
an
d statio
nary
ref
e
rence
f
r
am
es (su
p
e
r
scri
pt “-
e
”: backwa
rd,
supersc
r
ipt “
s
”:
st
at
i
onary
)
Fi
gu
re
3.
B
l
oc
k
di
ag
ram
of p
r
o
p
o
sed
m
e
t
hod
fo
r
vect
o
r
c
o
nt
r
o
l
o
f
heal
t
h
y
and
fa
ul
t
y
m
achi
n
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1284 –
1291
1
288
As it
is seen from
(3), the str
u
ct
ure of t
h
e forwa
r
d and ba
ckwar
d
equat
i
ons are sim
i
l
a
r to t
h
e R
F
OC
equat
i
ons
of
heal
t
h
y
t
h
ree-phase IM
.
C
o
nseque
nt
l
y
,
it
is p
o
ssib
l
e to co
n
t
ro
l fau
lty
m
ach
in
e u
s
in
g
two
devel
ope
d R
F
OC
alg
o
r
ith
m
s
. The
bl
ock
di
agram
of pr
op
osed R
F
OC
fo
r vect
or
co
nt
ro
l
of fa
ul
t
y
m
a
chi
n
e i
s
show
n i
n
Fi
g
u
r
e
3. In t
h
i
s
fi
gu
re, an i
ndi
rect
R
F
OC
al
g
o
r
it
hm
and a di
rect
R
F
OC
alg
o
r
it
hm
are used t
o
cont
rol
faul
t
y
IM
(i
ndi
rect
R
F
OC
al
g
o
r
ith
m
t
o
cont
rol
fo
rwar
d
equat
i
ons an
d
di
rect
R
F
OC
alg
o
r
ith
m
t
o
cont
rol
backwar
d
eq
ua
t
i
ons). In
Fi
gu
r
e
3, i
n
o
r
der t
o
al
t
e
rnat
el
y
swit
ched bet
w
een
t
h
e for
w
ard a
n
d back
ward
st
at
es, a
swi
t
c
h i
s
used
where
b
y
t
h
i
s
swi
t
c
h wi
l
l
consecut
i
v
el
y change posi
t
i
ons i
n
each sam
p
li
ng t
i
m
e
. It
can be
not
e
d
th
at th
is fig
u
r
e can
b
e
u
s
ed
fo
r bo
th
h
ealth
y an
d
fau
lty th
ree-p
h
a
se
IMs. Th
e p
a
ram
e
te
rs o
f
m
o
to
r which
are
needed t
o
be c
h
ange
d f
r
om
heal
t
h
y
m
ode
t
o
faul
t
y
m
ode are show
n i
n
Fi
g
u
re 3
.
In t
h
e pr
op
osed schem
e
for vect
or cont
r
o
l
of faul
t
y
m
ach
i
n
e an Ext
e
nde
d Kalm
an Fi
lter (EKF) i
s
u
s
ed
to
esti
m
a
t
e
th
e ro
to
r flu
x
in
th
e d
i
rect R
F
OC. Fo
r th
e
p
u
r
p
o
s
e
o
f
ro
to
r flux
esti
mat
i
o
n
,
th
e d
-
ax
is an
d
q-
axis of stator curre
nts as well
as d-axis and
q-axis of
rotor
fluxes are chose
n
as the
state v
a
riables. Using these
st
at
e vari
abl
e
s,
i
t
i
s
possi
bl
e t
o
express t
h
e st
a
t
e space
m
odel
i
n
t
h
e form
of
Equat
i
on (
5
) a
nd
(6):
(5)
(6)
In t
h
ese equat
i
ons,
x
,
y
and
u
are t
h
e sy
st
em
st
at
e
m
a
t
r
i
x
, sy
st
em
out
put
m
a
t
r
i
x
and sy
st
em
i
nput
matr
ix
. Also
,
A
,
B
and
C
are
t
h
e sy
st
em
, i
n
put
and
out
p
u
t
m
a
t
r
ices respectively.
The matrices
of
x
,
y
,
u
,
A
,
B
and
C
i
n
eq
uat
i
ons (
5
) a
n
d
(6
)
are gi
ven as
fol
l
ows:
T
qr
dr
qs
ds
i
i
x
(7a)
T
qs
ds
i
i
y
(
7
b
)
T
qs
ds
v
v
u
(
7
c
)
1
0
0
2
0
1
2
0
0
0
1
0
0
1
dt
M
M
dt
M
M
dt
dt
A
q
d
r
q
d
r
r
r
(
7
d
)
T
B
0
0
0
0
0
0
0
0
(
7
e
)
0
0
1
0
0
0
0
1
C
(7f
)
The steps of the EKF algorithm
can be form
ulated as [15]:
1
)
Esti
m
a
t
i
o
n
of th
e Erro
r Covarian
ce Matrix
:
(
8
)
2
)
Co
m
p
u
t
atio
n
of K
a
lm
an
Fi
lter G
a
in
:
(
9
)
3) U
pdat
e
o
f
t
h
e Erro
r Cova
ri
ance Mat
r
i
x
:
(
1
0
)
4) St
at
e Est
i
m
a
t
i
on:
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN
:
208
8-8
7
0
8
A Novel
Met
h
o
d
f
o
r Vect
o
r
C
ont
r
o
l
of
Fa
ul
t
y
Thr
ee-P
h
ase
IM
Dri
ves B
a
s
e
d
on
F
O
C… (
M
o
h
a
m
m
a
d J
a
nn
at
i
)
1
289
In these equations,
P
,
Q
and
R
are the covariance
m
a
trices
of the no
ises.
To begi
n the calculation, the
in
iti
al v
a
lu
es o
f
th
e sta
t
e v
a
ri
ab
les an
d
erro
r co
v
a
rian
ce
m
a
trices n
eed
to
b
e
id
en
tified
.
In
th
is w
o
rk
, th
e in
itia
l
values of m
a
trices
P
,
Q
and
R
for est
i
m
a
ti
on
of r
o
t
o
r
fl
ux a
r
e obt
ai
ned f
r
o
m
t
h
e t
r
i
a
l
and error
pr
ocess.
4.
SIM
U
LATI
O
N
RESULTS
AN
D CO
MP
ARI
SIO
N
S
In
th
is sectio
n
si
m
u
la
tio
n
results fo
r
4
75W
att star-co
n
n
ected th
ree-ph
ase IM is carried
out to
v
a
lid
ate
t
h
e pro
posed c
ont
rol
st
rat
e
gy
. The sim
u
l
a
t
i
o
n i
nvest
i
g
at
i
on i
s
m
a
i
n
ly
focused on t
h
e m
o
tor speed an
d t
o
rq
ue
respo
n
ses. Tw
o di
ffe
rent
cases usi
ng Mat
l
a
b/
M-Fi
l
e
soft
ware are sim
u
l
a
t
e
d:
Fi
gu
re
4.
Si
m
u
l
a
t
i
on res
u
l
t
s
o
f
t
h
e
co
n
v
ent
i
o
nal
(l
eft
)
a
n
d
p
r
o
p
o
sed
(
r
i
g
ht
)
m
e
t
hod
s f
o
r
v
ect
or c
o
nt
rol
o
f
h
ealth
y and
fau
lty th
ree-ph
ase IMs; fro
m
to
p
to bo
tto
m: R
o
tor
a
-
ax
is
cu
rre
n
t
,
S
t
a
t
or
a-
axis
c
u
rr
en
t,
El
ect
rom
a
gnet
i
c
t
o
r
q
ue, Z
o
om
o
f
electrom
a
gnetic torque,
Speed
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1284 –
1291
1
290
1) Fi
g
u
r
e 4(l
e
f
t
):
vect
or co
nt
r
o
l
of heal
t
h
y
a
nd fa
ul
t
y
t
h
ree
-
p
h
ase IMs d
r
i
v
e base
d o
n
con
v
e
n
t
i
onal
IR
FOC
(t
he c
o
nve
nt
i
o
nal
IRF
O
C m
e
t
h
o
d
base
d
on
vol
t
a
ge
co
nt
r
o
l
l
er has
bee
n
f
u
l
l
y
di
scusse
d i
n
[1]
)
.
2)
Fi
g
u
r
e
4(
ri
g
h
t
)
:
vect
o
r
c
o
n
t
rol
of
heal
t
h
y
an
d
fa
ul
t
y
t
h
r
ee-p
h
ase
IMs
dri
v
e
base
d
on
Fi
g
u
re
3
(
p
ro
po
s
e
d
FOC)
.
Ru
ng
e–
Ku
tta alg
o
rith
m
is
u
s
ed
fo
r
so
l
v
in
g
t
h
e
h
ealthy an
d
fau
lty
th
ree-ph
ase
IMs d
y
n
a
m
i
c
equat
i
o
ns
. A
n
IM i
s
fe
d
fr
om
a Si
ne
Pul
s
e
W
i
dt
h
Mo
dul
a
t
i
on (
S
P
W
M)
VSI
.
In t
h
e si
m
u
l
a
t
i
on t
h
e
r
e
fere
nc
e
sp
eed
is 500
rp
m
.
In
th
is
p
a
p
e
r it is assumed
an
imme
d
i
ate op
en-ph
a
se fau
lt
d
e
tectio
n
.
Th
e rating
s
and
p
a
ram
e
ters o
f
t
h
e sim
u
lated
mo
tor are:
In
Figu
re 4, it
is sup
p
o
s
ed
that th
e op
en
-pha
se fau
lt h
a
p
p
en
ed at t=2
s
(fro
m
t=0
s
to
t=2
s
→
h
ealth
y
con
d
i
t
i
on a
nd
fr
om
t
=
2s t
o
t=7s
→
fau
lty con
d
ition
)
. In
th
i
s
test, th
e v
a
lu
e o
f
th
e lo
ad
is: fro
m
t=0
s
to
t=0
.
5s,
T
l
=0
N.m
;
fro
m t=0
.
5
s
to
t=2
s
, T
l
=1
N.m
;
from t=2
s
to
t=2
.
2
s
, T
l
=0
N.m
;
fro
m
t=2
.
2
s
to
t=7
s
, T
l
=2
N.
m.
B
a
s
e
d
on
Fi
g
u
re
4(l
e
f
t
), si
m
u
l
a
ti
on r
e
sul
t
s
o
f
t
h
e c
o
nve
nt
i
o
nal
contro
ller confirm th
at th
e con
v
e
n
tio
n
a
l co
n
t
ro
l
l
er is
una
ble to control the fa
ulty IM correc
tly. It can
b
e
seen
th
at fro
m
th
e p
r
esen
ted
sim
u
l
a
tio
n
resu
lts th
at th
e
dynam
i
c perform
a
nce of the
propose
d
faul
t-tolerant c
o
ntroller is accept
a
bl
e. As can
be seen
from
F
i
gure
4(
ri
g
h
t
)
,
t
h
e
pr
op
ose
d
F
O
C m
e
t
h
o
d
pr
o
duces
fewe
r
ri
p
p
l
e
s i
n
t
h
e
spee
d a
n
d t
o
rq
ue
res
p
o
n
ses.
As
can
b
e
see
n
b
y
u
s
ing
co
nven
tio
n
a
l co
n
t
roller, th
e electro
m
a
g
n
e
tic to
rqu
e
o
s
cillatio
n
at stead
y state
is ab
ou
t 1N
.m at an
avera
g
e am
ount of
2N.m
but by usi
ng
propos
ed c
ont
roll
er, the electro
magnetic torque oscillation
reduce
d
not
a
b
l
y
by
abo
u
t
0.
3N
.m
at
an ave
r
age am
ount
o
f
2
N
.m
. Sim
u
l
a
t
i
on resul
t
s sho
w
t
h
e be
t
t
e
r perf
orm
a
n
ce of
t
h
e p
r
op
ose
d
t
e
chni
que
f
o
r
ve
ct
or c
o
nt
rol
o
f
faul
t
e
d
m
achi
n
e i
n
bot
h t
r
a
n
si
ent
an
d
st
eady
st
at
e.
5.
CO
NCL
USI
O
N
In t
h
i
s
pa
pe
r,
a vect
or c
ont
r
o
l
st
rat
e
gy
fo
r
st
a
r-connected three
-
phase
IM
d
r
i
v
es un
der op
en-ph
a
se
fau
lt b
a
sed
o
n
RFO
C
is p
r
op
o
s
ed
an
d
sim
u
lated
.
It w
a
s
sh
own
th
at the fau
lty
m
ach
in
e equ
a
tion
s
in
th
e
rotating re
fere
nce fram
e can be classified as
two s
e
t of
bal
a
nced
eq
uat
i
o
ns
(f
or
wa
rd a
n
d
back
wa
rd e
q
ua
t
i
ons)
.
Based o
n
t
h
i
s
,
a no
vel
vect
o
r
co
nt
r
o
l
t
echn
i
que
usi
n
g t
w
o
devel
ope
d RF
OC al
go
ri
t
h
m
s
was p
r
op
ose
d
. The
resu
lts sho
w
the go
od
p
e
rfo
r
man
ce of th
e propo
sed driv
e syste
m
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