Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 2
,
A
p
r
il
201
6, p
p
.
45
8
~
46
7
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
2.9
011
4
58
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
High P
e
rf
orm
a
nce Vector Cont
rol of 3-Ph
as
e IM
Dri
v
es u
nder
Open-Ph
a
se Fault Based on EK
F for Rotor Flux Estimation
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
Elec
trical Engin
eering
,
U
n
iver
siti Teknologi Malay
s
ia,
81310 Skudai, Johor Bahru, Malay
s
ia
** Departmen
t
o
f
Electr
i
cal
Engineer
ing
,
Faculty
of Industr
ial
Technolog
y
,
Univ
er
sitas Ahmad Dahlan,
Yog
y
ak
arta 555
164, Indonesia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 12, 2015
Rev
i
sed
No
v
25
, 20
15
Accepted Dec 16, 2015
This paper
prop
oses a novel
flu
x
observer bas
e
d on Ext
e
nded
Kalm
an Filter
(EKF) for high
performance vector c
ontrol of
3-
phase Induction
Motor (IM)
drives under stator winding open
-
phase fa
ult. Th
e presented flux
estimation
combines the In
direct Rotor
Field-Or
iented Con
t
rol (IRFOC) method. The
rotor flux
is ob
tain
ed from
tw
o m
odified
EKF with two d
i
ff
erent
stato
r
currents (forwar
d and backwar
d
stator
curr
ents).
The proposed technique
can
s
i
gnific
a
ntl
y
r
e
d
u
ce th
e DC-offs
et probl
em
on the pure in
tegr
ator
as
s
o
ciat
ed
with the basic IRFOC
method. The Ma
tlab simulation results confirm the
validity
of
th
e pr
oposed strateg
y
.
Keyword:
3-P
h
ase
I
n
duct
i
on M
o
t
o
r
EKF
Flux Obse
rve
r
IRFOC
Ope
n
-Ph
a
se Fa
ult
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
:
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: m
_
j
a
n
n
atyy@yah
o
o
.co
m
1.
INTRODUCTION
Recently, 3-phase Induction
Motors
(IMs)
have
bee
n
ext
e
nsively
devel
ope
d
due t
o
their low c
o
st,
h
i
gh
reliab
ility
and
g
ood
p
e
rform
a
n
ce.
Field
-
Orien
t
ed
C
o
n
t
ro
l (FOC) tech
n
i
q
u
e
fo
r 3-p
h
a
se IM
drives h
a
s
dra
w
n m
u
ch interest am
ong researche
r
s due
to its accur
acy and superi
or dynam
i
cs
. Generally, there a
r
e two
p
o
s
sib
ilities fo
r th
e FOC techn
i
qu
e b
a
sed
on o
r
ien
t
ation
o
f
th
e ro
tating
frame;
th
ey are:
Ro
to
r Field-Orien
t
ed
C
ont
r
o
l
(R
F
O
C
)
an
d St
at
or
Fi
el
d-O
r
i
e
nt
e
d
C
o
nt
r
o
l
(S
FOC
)
. The
w
a
y
of fl
ux
p
o
si
t
i
on i
s
cal
cul
a
t
e
d
det
e
rm
i
n
es t
h
e t
y
pe of FOC
;
Di
rect
Fi
el
d-
Ori
e
nt
ed C
o
nt
rol
(
D
F
O
C
)
a
nd I
n
di
rect
Fi
el
d-
Ori
e
nt
e
d
C
ont
r
o
l
(IFOC). Th
e
basic FOC strateg
i
es still h
a
v
e
so
m
e
d
r
awb
a
ck
s su
ch
as co
mp
lex
ity an
d
sensitiv
ity
to
th
e m
o
to
r
param
e
ter vari
ations s
u
c
h
as
rot
o
r
a
n
d stator resista
n
ces.
More
ove
r, t
h
e
basic FOC algorithm
cannot
be
used
for so
m
e
ab
norm
a
l co
n
d
itio
ns in
3
-
ph
ase
IM d
r
i
v
es. On
e o
f
th
e m
o
st co
mm
o
n
typ
e
s
o
f
abno
rm
al c
o
nd
itio
ns
i
n
3-
p
h
ase IM
dri
v
es i
s
op
en
-
pha
se fa
ul
t
[1]
.
B
y
appl
y
i
ng t
h
e basi
c F
O
C
t
echni
que
s t
o
a faul
t
e
d
3-
p
h
as
e IM
(3-ph
a
se IM
un
d
e
r stat
o
r
wi
n
d
i
n
g
op
en
-phase fau
lt),
significan
t oscillati
o
n
s
in th
e m
o
to
r sp
eed and
t
o
rqu
e
out
put
will be devel
ope
d.
To
solve t
h
is problem
, som
e
m
o
dified
vector c
ont
rol m
e
t
hods
have
bee
n
introduce
d
t
o
i
m
prove
t
h
e
per
f
o
r
m
a
nce of
t
h
e
3-
p
h
ase
I
M
dri
v
es
u
nde
r
o
p
en
-
phase
fa
ul
t
[
2
]
-
[
7
]
.
Th
e k
e
y issu
e
o
f
th
e IR
FOC
co
n
t
ro
lled
3
-
ph
ase IM driv
es is th
e esti
ma
tio
n
of ro
t
o
r
flu
x
. A m
o
st
po
p
u
l
a
r m
e
t
hod t
o
obt
ai
n t
h
e i
n
fo
rm
ati
o
n
of rot
o
r fl
ux
i
n
IR
FOC
m
e
t
h
o
d
i
s
usi
n
g
a pure i
n
t
e
g
r
at
i
o
n
.
Howev
e
r, using
a
pu
re i
n
tegratio
n
for th
e roto
r
flux
estim
at
io
n
is
sen
s
itiv
e to
d
i
fferen
t
k
i
n
d
s
of
p
r
ob
lems su
ch
as DC-o
ffset
p
r
ob
lem
.
To
so
lv
e t
h
is prob
lem
,
m
a
ny
r
e
searche
r
s
ha
ve ad
d
r
esse
d
im
pro
v
em
ent
on t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
45
8 – 4
6
7
4
59
est
i
m
a
ti
on
of
r
o
t
o
r fl
ux
i
n
3-
pha
se IM
d
r
i
v
es [
8
]
-
[
14]
.
H
o
we
ve
r, t
h
ese
m
e
t
hods
can
n
o
t
be
use
d
f
o
r
faul
t
y
m
achi
n
e as t
h
e
s
e m
e
t
hods a
r
e
desi
gne
d
base
d
on
heal
t
h
y
3
-
pha
se IM
eq
ua
t
i
ons.
In
th
is
p
a
p
e
r, two
m
o
d
i
fied
Ex
ten
d
e
d
Kal
m
an
Filter (EKF) algo
rithm
s
in
o
r
d
e
r t
o
ro
tor flux
estim
a
tion are
replace
d the pure inte
grat
or. It is shown th
at th
e fau
lted
mach
in
e stator cu
rren
ts in
t
h
e ro
tating
refe
rence
frame can be classified as
forward
an
d
b
a
ck
ward
cu
rren
ts. Based
on
th
is sim
p
l
i
city
to
co
n
t
ro
l
fau
lty
3-
p
h
ase IM
, t
w
o m
odi
fi
ed I
R
FOC
al
go
rithm
s
are used. T
h
ese two curre
n
ts
(f
or
war
d
a
nd
back
wa
rd c
u
r
r
ent
s
)
are u
s
ed
f
o
r e
s
t
i
m
a
ti
on
of t
h
e
fo
rwa
r
d an
d
ba
ckwa
r
d
r
o
t
o
r
fl
uxe
s u
s
i
n
g E
K
F al
g
o
ri
t
h
m
.
The
pr
op
ose
d
m
e
t
h
o
d
can
sign
ifican
tly red
u
c
e th
e
DC-o
ffset pro
b
le
m
o
n
th
e
pu
re
integrator ass
o
ciated
w
ith
the IRFOC of fau
lty 3-
pha
se IM
dri
v
es. T
h
e si
m
u
l
a
t
i
on st
u
d
y
i
s
c
a
rri
ed
o
u
t
wit
h
a 475W sta
r
-connected 3-phase
IM. T
h
e
results
confirm
the effectivenes
s
of
t
h
e pr
op
ose
d
f
l
ux o
b
se
rve
r
w
h
en
a
ppl
i
e
d
t
o
t
h
e IR
F
O
C
of
a
fa
ul
t
y
3
-
pha
se
IM
dri
v
e. T
h
i
s
pa
per i
s
o
r
ga
ni
ze
d as f
o
l
l
o
ws:
Aft
e
r i
n
t
r
o
d
u
ct
i
on i
n
sect
i
o
n
1, i
n
sect
i
o
n 2
,
t
h
e d-
q m
ode
l
of a
faul
t
y
st
ar-c
on
nect
ed
3-
pha
s
e
IM
i
s
prese
n
t
e
d.
Ne
xt
, se
ct
i
on 3
descri
bes t
h
e
devel
o
pm
ent
of t
h
e IR
FOC
al
go
ri
t
h
m
for vect
o
r
cont
rol
of a faul
t
e
d
m
achi
n
e. T
h
e p
r
op
ose
d
m
e
t
hod
for r
o
t
o
r fl
u
x
est
i
m
a
ti
on of a
faul
t
y
3-phase IM is analyzed in se
ction 4. T
h
e perform
a
n
ce of
the prese
n
te
d strategy is checked
using Matlab/M-
File so
ft
ware in
section
5
and sectio
n 6 con
c
lu
d
e
s th
e
p
a
p
e
r.
2.
FAULT
Y
ST
AR
-C
ON
NE
C
TED 3
-
PH
AS
E IM
MO
DE
L
The d
-
q m
odel
of st
ar-c
o
n
n
ect
ed 3-
p
h
ase
IM
un
de
r o
p
e
n
-
p
hase fa
ul
t
i
n
t
h
e st
at
i
ona
r
y
refere
nce
fram
e
(su
p
ersc
ript “
s
”
)
ca
n
be
sh
ow
n
by
t
h
e
fol
l
o
wi
n
g
e
q
ua
t
i
ons
[5]
:
(
1
)
whe
r
e,
v
s
ds
and
v
s
qs
are the stator d-q a
x
es
voltages
,
i
s
ds
,
i
s
qs
,
i
s
dr
and
i
s
qr
are the stator and rotor d-q axes
currents
,
λ
s
ds
,
λ
s
qs
,
λ
s
dr
and
λ
s
qr
are the
stator a
n
d rotor
d-q a
x
es
fluxes.
L
ds
,
L
qs
,
L
r
,
M
d
and
M
q
i
n
dicate the
st
at
or an
d r
o
t
o
r
d-
q a
x
es s
e
l
f
an
d m
u
t
u
al
i
nduct
a
nces.
r
ds
,
r
qs
and
r
r
are the stator and rotor d-q axe
s
resistances.
r
is the m
achine spee
d.
τ
e
and
τ
l
are
electromagnetic torque and loa
d
t
o
rque
.
J
and
F
ar
e
th
e
m
o
m
e
nt
of i
n
ert
i
a
an
d vi
sc
ous
f
r
i
c
t
i
on c
o
ef
fi
ci
ent
res
p
ect
i
v
el
y
.
M
o
r
e
ove
r,
r
ds
=
r
qs
=r
s
,
L
ds
=L
ls
+3/2
L
ms
,
L
qs
=
L
ls
+1/2
L
ms
,
M
d
=3/2
L
ms
and
M
q
=
√
3/
2
L
ms
[5]
(
L
ls
and
L
ms
are leaka
g
e a
n
d m
u
tual induc
tances re
specti
v
ely).
3.
VECTO
R
CO
NTROL
OF
A F
AULT
Y
S
T
AR
-C
ON
NE
CTED
3-
PH
A
S
E IM
In t
h
i
s
pa
per
,
a
m
e
t
hod t
o
co
n
t
rol
fa
ul
t
y
m
a
chi
n
e
base
d o
n
IR
FOC
i
s
pre
s
ent
e
d.
I
n
R
F
O
C
st
rat
e
gy
i
t
is n
ecessary t
h
at th
e m
o
to
r equ
a
tion
s
tran
sfer t
o
the ro
tatin
g referen
ce
fram
e
. Fo
r th
is
pu
rp
ose, th
e
tran
sform
a
t
i
o
n
matrix
as sh
ow
n i
n
(
2
)
i
s
used
[
15]
:
(2
)
wh
ere, su
p
e
rscrip
t “
e
” in
d
i
cates th
e eq
u
a
tion
s
are in
th
e ro
ta
ting re
fere
n
ce fram
e (in this pap
e
r, “
θ
e
” is th
e
angle
betwee
n
the stationa
ry refere
nce fram
e
an
d r
o
t
a
t
i
ng
r
e
fere
nce f
r
am
e. Fu
rt
he
rm
ore,
“
ω
e
” is th
e ang
u
l
ar
e
e
e
e
e
s
T
cos
sin
sin
cos
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Hi
g
h
Perf
or
ma
nce Vect
or C
o
nt
rol
of
3-P
h
as
e IM
Dri
ves
u
n
d
er
Op
en
-P
has
e Fa
ul
t
Ba
sed
on
…
(M. Ja
nna
ti)
46
0
velocity
of the
rot
o
r field
-
orie
nted re
fere
nce
fram
e
).
Usi
n
g
equat
i
o
n (
2
), e
quat
i
o
n (
1
), ca
n be
obt
ai
ned
as (3
)-
(7
):
(3
)
(4
)
(5
)
(6
)
(7
)
As can be see
n
, equat
i
o
n (
3
) i
n
cl
u
d
es t
w
o se
t
of equat
i
o
ns
(t
he t
e
rm
s wi
th su
persc
r
i
p
t
“+
e
” and the
term
s
with
su
p
e
rscrip
t “-
e
”). Each t
e
rm
r
e
present
s
a
he
al
t
h
y
3-phase
IM
equat
i
on.
C
onseq
uent
l
y
, vect
or
cont
rol
of
a 3
-
phase
IM
u
nde
r o
p
en
-p
hase f
a
ul
t
usi
ng t
w
o
m
odi
fied R
F
O
C
al
gori
t
h
m
s
is possi
bl
e.
The
bl
ock
diagram
of RFOC fo
r a
faulty
m
o
tor is sho
w
n as
Figu
re
1
.
In
Fig
u
re
1,
RFOC (1
) is u
s
ed to c
o
m
p
ensate th
e
term
s with
superscri
p
t “+
e
”
a
n
d
R
F
OC
(
2
) i
s
us
e
d
t
o
c
o
m
p
ens
a
t
e
the
term
s
with superscri
p
t
“-
e
”.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
45
8 – 4
6
7
4
61
Fi
gu
re
1.
B
l
oc
k
di
ag
ram
of R
F
OC
fo
r a
fa
ul
t
y
m
o
t
o
r
In Fig
u
re
1 [
5
]
:
1
1
1
1
2
2
s
T
(8)
Not
i
ce t
h
at
,
Fi
gu
re
1 ca
n be
u
s
ed f
o
r he
al
t
h
y
3-
p
h
ase IM a
s
well. T
h
e nece
ssary m
odifications
whic
h
ar
e n
eed
ed
i
n
o
r
d
e
r
to
con
t
rol
h
ealth
y
m
o
to
r
ar
e
as gi
ve
n i
n
Tabl
e 1.
B
a
sed o
n
Fi
gu
re 1
and Ta
bl
e 1,
duri
n
g
norm
a
l
condi
t
i
on, t
h
e
out
p
u
t
of R
F
OC
(
2
) i
s
zero. O
n
t
h
e ot
her ha
nd, i
n
no
rm
al
condi
t
i
on t
h
e pro
pose
d
s
c
hem
e
is the sa
m
e
as
basic RFOC scheme.
Tabl
e
1. T
h
e
n
ecessary
m
odi
f
i
cat
i
ons
whi
c
h
are
neede
d
i
n
o
r
de
r t
o
co
nt
r
o
l
heal
t
h
y
m
o
t
o
r i
n
Fi
gu
re
1
Norm
al
condition
ms
ls
s
qs
ds
ms
q
d
s
qs
ds
L
L
L
L
L
L
M
M
M
r
r
r
2
3
,
2
3
,
2
1
2
1
2
1
2
1
2
1
1
2
3
2
3
0
3
2
s
T
4.
ROTOR
FL
UX
ESTIMATION OF A
FAULTY
STA
R
-
C
O
NNE
CTED 3-P
H
A
S
E
I
M
USI
N
G
E
K
F
I
n
th
is wo
rk
, t
w
o m
odi
fi
ed E
K
F al
go
ri
t
h
m
s
are used
to
estimat
e th
e ro
to
r
flu
x
e
s in
th
e RFOC (1) and
R
F
O
C
(
2
)
.
T
h
e
EKF i
s
a
n
est
i
m
at
or w
h
i
c
h c
a
n be
use
d
f
o
r
bot
h l
i
n
ear a
n
d
no
nl
i
n
ea
r sy
st
em
s. F
o
r
t
h
e
p
u
r
p
o
s
e
of r
o
t
o
r
fl
uxes
est
i
m
a
t
i
on, t
h
e
st
at
or current
s
as wel
l
as
rotor fluxes are c
h
osen as th
e state variables. The
state
space
m
odel of an IM can
be e
xpresse
d in
the
form
of equations (9) a
n
d (10):
(9)
(10)
where
A
,
B
and
C
are t
h
e sy
st
em
m
a
t
r
i
x
, i
nput
m
a
t
r
i
x
and o
u
t
put
m
a
t
r
i
x
.
x
,
u
and
y
are th
e syste
m
s
t
a
t
e
matrix
,
sy
st
em
i
nput
m
a
t
r
i
x
and sy
st
em
out
put
m
a
t
r
ix. The m
a
t
r
ices of
x
,
y
and
u
i
n
equat
i
ons
(9)
and (
1
0
)
are gi
ven as
fo
llo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Hi
g
h
Perf
or
ma
nce Vect
or C
o
nt
rol
of
3-P
h
as
e IM
Dri
ves
u
n
d
er
Op
en
-P
has
e Fa
ul
t
Ba
sed
on
…
(M. Ja
nna
ti)
46
2
(
1
1
)
(
12)
(
13)
B
a
sed on e
quat
i
on (
4
), t
h
e m
a
tri
ces of
A
1
,
B
1
and
C
1
i
n
eq
uat
i
ons (
9
) an
d (
1
0) are
obt
ai
ned
as (1
4a)-(
14c
):
(14a
)
(
1
4
b
)
(
1
4
c
)
whe
r
e,
(
1
4
d
)
M
o
reove
r,
based o
n
eq
uat
i
on
(5),
t
h
e m
a
t
r
i
c
es of
A
2
,
B
2
and
C
2
i
n
equat
i
ons
(9
) an
d (
1
0
)
ar
e obt
ai
ned as
(
15a)
-
(
15c
)
:
(
15a
)
T
qr
dr
qs
ds
i
i
x
T
qs
ds
i
i
y
T
qs
ds
v
v
u
dt
L
r
dt
r
dt
L
r
M
M
dt
r
dt
L
r
dt
L
r
M
M
dt
L
k
M
M
r
dt
L
k
M
M
r
dt
L
M
M
r
r
r
k
dt
L
k
M
M
r
dt
L
k
M
M
r
dt
L
M
M
r
r
r
k
A
r
r
r
r
r
q
d
r
r
r
r
r
q
d
r
s
q
d
r
r
s
q
d
r
r
q
d
r
qs
ds
s
r
s
q
d
r
r
s
q
d
r
r
q
d
r
qs
ds
s
1
2
0
1
0
2
2
2
2
2
1
1
0
2
2
0
2
2
1
1
2
2
2
2
2
2
1
T
s
s
dt
k
dt
k
B
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
C
r
q
d
qs
ds
s
L
M
M
L
L
k
2
2
2
1
0
0
2
0
1
2
0
0
0
1
0
0
1
2
dt
M
M
dt
M
M
dt
dt
A
q
d
r
q
d
r
r
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
45
8 – 4
6
7
4
63
(
1
5
b
)
(
15c
)
B
a
sed on (14a)
-(1
5c), t
w
o EK
F al
gori
t
h
m
s
can be used t
o
est
i
m
a
te rot
o
r fl
uxes i
n
t
h
e R
F
OC
(1) and
R
F
OC
(2).
Th
e bl
ock di
ag
ra
m
of t
h
e fl
ux
obser
ver base
d
on E
K
F i
s
sh
own
i
n
Fi
gu
re
2. It
can
be no
t
e
d t
h
at
Fi
gure
2 can
be al
so used
for
h
eal
t
h
y
m
achi
n
e by
onl
y
chan
gi
ng i
n
t
h
e m
o
t
o
r
param
e
t
e
rs as l
i
s
ted i
n
Tabl
e 1.
Fi
gure
2. B
l
ock di
agram
of t
h
e fl
ux
obser
ver
based
on E
K
F
for
hi
gh
per
f
or
m
a
nce vect
or cont
rol
of a fa
ul
t
y
mo
t
o
r
Th
is EKF alg
o
rith
m
is co
m
p
u
t
ed
in
to
th
ree
main
step
s as e
q
u
a
tio
n
s
(1
6)-(1
8
)
[12
]
:
1-P
r
e
d
i
c
t
i
on:
(1
6)
2
-
C
o
m
p
u
t
atio
n of Kalm
an
Filt
er
Gain
:
(1
7)
3-
Up
dat
e
:
(1
8)
whe
r
e,
R
and
Q
a
r
e the
covariance m
a
trices of the
noises.
5.
SIMULATION RESULTS
In
th
is section
si
m
u
latio
n
resu
lts for a 47
5W star-c
onnect
ed 3-phase
IM is
p
r
esen
ted
to
v
a
lid
ate the
per
f
o
r
m
a
nce o
f
t
h
e p
r
op
ose
d
st
rat
e
gy
. The
sim
u
l
a
t
i
ons ar
e carri
ed
o
u
t
b
a
sed o
n
Fi
gu
re
1 an
d Fi
g
u
r
e
2 an
d
usi
n
g M
a
t
l
a
b/
M
-
Fi
l
e
so
ft
war
e
. R
u
nge
-
K
ut
t
a
al
go
ri
t
h
m
i
s
considere
d
t
o
solve t
h
e
h
ealth
y and
fau
lty 3
-
ph
ase
IM equ
a
tio
ns.
In
t
h
e sim
u
lati
o
n
s
th
e
3
-
ph
ase IM is
fed
from a co
nv
en
tion
a
l SPWM VSI. Fo
r
sim
p
lify
i
n
g
th
e
sim
u
l
a
t
i
ons o
f
t
h
e pr
o
p
o
sed
m
e
t
hod, t
h
e ba
ckwa
r
d
com
p
o
n
ent
s
i
n
Fi
g
u
r
e
1 ha
ve
been
rem
oved (
A
s c
a
n
b
e
seen
fr
om
equ
a
t
i
ons
(3
)-
(
5
)
,
t
h
e st
at
o
r
vol
t
a
ge e
q
u
a
t
i
ons
h
a
ve e
x
t
r
a
t
e
rm
s d
u
e t
o
t
h
e
ba
ckwa
r
d
c
o
m
ponent
s
.
Si
nce t
h
e bac
k
wa
r
d
com
ponent
s are
pr
o
p
o
r
t
i
o
nal
t
o
t
h
e di
f
f
ere
n
ce of t
h
e resi
st
a
n
ces, m
u
t
u
al
and sel
f
in
du
ctan
ces, it is p
o
ssib
l
e to n
e
g
l
ect th
em). In
th
is wo
rk
, it is assu
med
an
immed
i
ate o
p
e
n-p
h
a
se fau
l
t
detection. T
h
e
param
e
ters of t
h
e sim
u
lated 3-phase
IM a
r
e:
T
B
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
C
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Hi
g
h
Perf
or
ma
nce Vect
or C
o
nt
rol
of
3-P
h
as
e IM
Dri
ves
u
n
d
er
Op
en
-P
has
e Fa
ul
t
Ba
sed
on
…
(M. Ja
nna
ti)
46
4
Fi
gu
re 3 s
h
o
w
s t
h
e sim
u
l
a
t
i
on res
u
l
t
s
of t
h
e pr
op
ose
d
m
e
t
h
o
d
base
d o
n
Fi
gu
re 1 a
nd
Fi
gu
re 2 f
o
r
vect
o
r
co
nt
r
o
l
of a
heal
t
h
y
3-
pha
se IM
. Fi
g
u
re
3 (a
) sh
o
w
s t
h
e st
at
or a-a
x
i
s
cu
rre
nt
, Fi
gu
re 3
(b
) s
h
o
w
s t
h
e
tor
que
resp
o
n
s
e
and Fi
gu
re 3
(c) s
h
o
w
s the
m
o
tor speed
. I
n
Fig
u
re
3, the
refere
nce s
p
ee
d an
d loa
d
are
set to
3
00r
p
m
an
d 0.5
N
.m
r
e
sp
ectively.
(a)
(b
)
(c)
Fi
gu
re
3.
Si
m
u
l
a
t
i
on res
u
l
t
s
o
f
t
h
e
p
r
o
p
o
se
d
m
e
t
hod
f
o
r
vec
t
or c
o
nt
rol
o
f
a
heal
t
h
y
3-
p
h
as
e IM
;
(a
):
St
at
o
r
a-
axis c
u
r
r
ent,
(
b
): Electrom
a
gn
etic torq
ue,
(c
): Spee
d
As ca
n
be
see
n
fr
om
Fi
gu
re
3,
a
si
n
u
soi
d
al
fo
rm
of t
h
e
st
at
or
a-a
x
i
s
cur
r
ent
i
s
obs
erve
d
d
u
ri
ng
o
p
e
ration
o
f
the m
o
to
r. M
o
reo
v
e
r, th
e t
o
rque in
creases acc
o
r
d
i
ng
ly to
t
h
e app
lied
l
o
ad.
In th
is test, th
e real
spee
d can
foll
ow t
h
e re
fere
nce spee
d
w
ithou
t an
y ov
er
shot an
d
stead
y
-
s
t
a
te er
r
o
r
.
A
s
men
tio
n
e
d b
e
fo
r
e
t
h
e
structure of the prese
n
ted controller
(Fi
g
ur
e 1) d
u
ri
n
g
n
o
r
m
a
l condi
t
i
o
n
i
s
t
h
e sam
e
as basi
c R
F
OC
m
e
t
hod
whi
c
h i
s
use
d
f
o
r
vect
or c
o
nt
r
o
l
o
f
a
heal
t
h
y
3-
p
h
ase
IM
.
Fi
g
u
re
4 sh
o
w
s t
h
e com
p
ari
s
o
n
bet
w
e
e
n
t
h
e basi
c an
d
pr
op
ose
d
m
e
tho
d
s f
o
r vect
o
r
co
nt
rol
of
heal
t
h
y
and
fa
ul
t
y
3-p
h
ase m
achi
n
es (
F
i
g
ur
e 3-l
e
ft
:
basi
c cont
rol
l
e
r an
d
Fi
gu
re 3
-ri
ght
:
pro
p
o
se
d co
nt
rol
l
e
r
base
d o
n
Fi
g
u
r
e
1 an
d Fi
g
u
re
2). Fi
gu
re 3 (
a
) sh
ow
s t
h
e st
at
or a-a
x
i
s
cu
r
r
ent
,
Fi
gu
re 3
(b
) sh
o
w
s t
h
e
m
o
t
o
r
to
rq
u
e
, Fi
g
u
r
e
3
(
c
) show
s t
h
e estim
ated
t
o
rqu
e
an
d Figu
r
e
3 (d
) show
s the m
o
to
r
sp
eed
.
I
n
Figur
e
3
,
t
h
e
refe
rence s
p
ee
d an
d l
o
a
d
a
r
e
set
t
o
5
5
0
r
pm
and
1
N
.m
resp
ect
i
v
el
y
.
In Fi
gu
re
4, i
t
i
s
su
pp
ose
d
t
h
at
a
n
ope
n
-
pha
se fa
ult is
happe
ne
d in pha
s
e “c” a
n
d at t=0.5s.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
45
8 – 4
6
7
4
65
(a)
(b
)
(c)
(d
)
Fi
gu
re
4.
Si
m
u
l
a
t
i
on res
u
l
t
s
o
f
t
h
e
basi
c
(l
eft
)
a
n
d
p
r
o
p
o
se
d
(ri
ght
) m
e
t
hod
s f
o
r
vect
or c
o
nt
r
o
l
o
f
heal
t
h
y
and
faulty
3
-
p
h
ase
IM
s; (a
): Stato
r
a-a
x
is c
u
r
r
e
n
t, (
b
):
El
ect
rom
a
gnet
i
c
t
o
r
que
,
(c
): Estim
ated
electrom
a
gnetic
t
o
r
que
, (
d
):
S
p
eed
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Hi
g
h
Perf
or
ma
nce Vect
or C
o
nt
rol
of
3-P
h
as
e IM
Dri
ves
u
n
d
er
Op
en
-P
has
e Fa
ul
t
Ba
sed
on
…
(M. Ja
nna
ti)
46
6
B
a
sed o
n
t
h
e
prese
n
t
e
d
res
u
l
t
s
of t
h
e Fi
g
u
r
e 4, t
h
e basi
c
R
F
O co
nt
r
o
l
l
e
r i
s
una
bl
e t
o
cont
r
o
l
t
h
e
faulty
3
-
p
h
ase
IM
co
rrectly
(s
ee Fig
u
re
4
(d
)
-
left).
It ca
n
b
e
seen
t
h
at in
com
p
ariso
n
with
th
e b
a
sic con
t
ro
ller,
th
e p
e
rf
or
m
a
n
ce o
f
th
e pr
oposed
f
a
u
lt-
to
ler
a
n
t
str
a
teg
y
in
b
o
t
h
tr
an
sien
t an
d
stead
y
-
s
tate co
nd
itio
n
s
is g
o
o
d
.
As
ca
n be ob
serve
d
fr
om
Fi
gu
re 4 (b
), t
h
e
p
r
op
ose
d
R
F
OC
t
ech
ni
q
u
e pr
od
uces
f
e
wer ri
p
p
l
e
s
i
n
t
h
e
electro
m
a
g
n
e
tic to
rqu
e
.
Using
b
a
sic co
n
t
ro
l
l
er, th
e p
e
ak
to p
eak
electro
mag
n
e
tic torqu
e
o
s
cillatio
n
at stead
y-
state is abo
u
t
1
.
8
N
.m
b
u
t
b
y
u
s
i
n
g pro
p
o
s
ed
tech
n
i
q
u
e
, the p
e
ak
t
o
p
e
ak electro
m
a
g
n
e
t
i
c to
rq
u
e
o
s
cillatio
n
red
u
ce
d
by
ab
out
1
N
.m
. M
o
r
e
ove
r, t
h
e est
i
m
a
t
e
d t
o
r
que
i
s
ob
tain
ed
sim
i
lar to
the real
IM to
rq
u
e
(see
Fig
u
re
4(c
)
-
r
i
g
ht
).
I
n
t
h
e si
m
u
l
a
t
i
on r
e
sul
t
s
o
f
Fi
gu
r
e
4
(c)
-ri
g
h
t
, t
h
e esti
m
a
ted
to
rq
u
e
is ob
tain
ed fro
m
th
e estimate
d
rot
o
r
fl
u
x
. It
c
a
n be c
o
ncl
u
d
e
d t
h
at
t
h
e
per
f
o
r
m
a
nce of t
h
e pr
o
pose
d
ob
serve
r
t
o
est
i
m
at
e t
h
e rot
o
r
fl
ux
i
n
b
o
t
h
n
o
rm
al an
d
o
p
e
n-ph
ase
fau
lt con
d
ition
s
is satisfactory.
Fi
gu
re
5 sh
o
w
s t
h
e si
m
u
l
a
t
i
on
resul
t
s
of t
h
e p
r
op
ose
d
m
e
t
h
o
d
ba
sed
o
n
Fi
gu
re
1 an
d
Fi
gu
re
2 f
o
r
vect
o
r
co
nt
r
o
l
of a 3
-
phase m
achi
n
e
un
der
o
p
en
-
phase
faul
t
con
d
i
t
i
on. Fi
gu
re 5
(a) s
h
o
w
s t
h
e t
o
rq
ue r
e
sp
ons
e
of a
faulty
m
o
tor a
n
d Fig
u
re
5 (
b
) s
h
ow
s th
e
m
o
tor s
p
eed
o
f
a
f
a
u
lty m
o
t
o
r.
In
Fi
gure 3, the re
fere
nce
spe
e
d
an
d lo
ad
ar
e set to
120
0rp
m
a
n
d 1N
.m
r
e
sp
ectiv
ely.
(a
)
(b)
Fi
gu
re
5.
Si
m
u
l
a
t
i
on res
u
l
t
s
o
f
t
h
e
p
r
o
p
o
se
d
m
e
t
hod
f
o
r
vec
t
or c
o
nt
rol
o
f
a
fa
ul
t
y
3-
pha
se
IM
;
(a
):
Electrom
a
gnetic tor
q
ue,
(b
): S
p
eed
As ca
n be
see
n
from
Figure
5, t
h
e torque i
n
crease
s
accordingly to the a
pplied
loa
d
.
In this test, the
r
e
f
e
r
e
n
c
e sp
eed
can
also fo
llo
w th
e
r
e
f
e
r
e
nce sp
eed
w
ith
ou
t an
y stead
y
-
s
tate er
r
o
r
.
Figur
e 5 show
s t
h
e good
per
f
o
r
m
a
nce o
f
t
h
e
p
r
op
ose
d
st
rat
e
gy
fo
r
vect
o
r
c
ont
rol
o
f
t
h
e
fa
ul
t
y
m
o
t
o
r i
n
t
h
e
hi
g
h
spee
d a
n
d
l
o
a
d
co
nd
itio
n.
6.
CO
NCL
USI
O
N
In t
h
i
s
pa
pe
r,
a n
ovel
hi
g
h
p
e
rf
orm
a
nce st
r
a
t
e
gy
t
o
c
ont
r
o
l
st
ar-co
n
n
ect
e
d
3-
pha
se IM
dri
v
es
un
der
ope
n
-
p
h
ase
fau
l
t
based
on
IR
FOC
i
s
p
r
o
p
o
s
e
d an
d si
m
u
l
a
ted. T
o
re
d
u
ce t
h
e DC
-o
ffs
et
p
r
o
b
l
e
m
wi
t
h
t
h
e basi
c
IRFOC strategy, two
m
o
d
i
fied
EKF algo
ri
th
m
s
with
tw
o di
ffe
re
nt
st
at
or c
u
r
r
ent
s
(f
o
r
wa
rd a
n
d bac
k
wa
r
d
stator curre
nts
)
to estim
ate r
o
tor flux a
r
e used. T
h
e
pr
o
p
o
se
d o
b
se
rve
r
can be
use
d
f
o
r 3
-
p
h
ase
IM
dri
v
es
du
ri
n
g
no
rm
al
and
o
p
e
n
-
pha
s
e
faul
t
c
o
n
d
i
t
i
ons
by
onl
y
c
h
angi
ng
i
n
t
h
e
m
o
t
o
r param
e
ters. T
h
e
res
u
l
t
s
sh
ow
th
e goo
d p
e
r
f
or
m
a
n
ce o
f
t
h
e
p
r
op
o
s
ed
dr
iv
e syste
m
f
o
r v
e
cto
r
con
t
r
o
l
of
a f
a
u
lty star
-
c
onn
ected
3-
ph
ase I
M
.
REFERE
NC
ES
[1]
M. Jannati
, et
al
.
, "Modeling
of
Balanced
and
Unbalanced
Thr
ee-Phase
Induction Motor und
er Balanced and
Unbalanced Su
pply
Based
on
Winding Function Method",
In
ternational Jour
nal of
Electrica
l and Computer
Engineering (
I
JECE)
, vol. 5
,
pp
. 644-655, 2015.
[2]
A.
Say
e
d-Ahmed and N.
A.
Demerdash,
"F
ault
-Toler
ant Oper
a
tion of Del
t
a-C
onnect
ed S
cal
ar
- and Vector
-
Controlled
AC
Motor Drives",
I
EEE Transactio
ns
on Power
Electronics
, vol. 27
, pp. 3041-3049,
2012.
[3]
A.
Saleh
, et al
.
, "Fault tolerant
field orien
t
ed co
ntrol of inductio
n motor for
loss of one inverter
phase with re-
s
t
arting
cap
abi
lit
y",
In I
E
EE International S
y
mposium
on Industrial Electronics (
I
SIE 2007)
, pp
. 1
340-1345, 2007
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
45
8 – 4
6
7
4
67
[4]
Y. Zhao and T
.
A. Lipo, "Modeling and con
t
rol
of a m
u
lti-phas
e
induct
i
on m
a
chine with struct
ural unbal
a
nce",
IEEE Transactio
ns on Energ
y
Co
nversion
, vo
l. 11
, pp
. 570-577
, 1
996.
[5]
Z. Yif
a
n
and T.A. Lipo
, "An
ap
proach
to modeling and
fi
eld-oriented
contro
l of
a thr
e
e phase
in
duction
machine
with s
t
ruc
t
ural
i
m
b
alance"
,
In
Pr
oc.
APEC, San Jose, TX
, pp
. 380
-386, 1996
.
[6]
M.
Ja
nna
ti
, et
al.
, "Stator Field-
Orientation Speed Control for
3-Phase Induction
Motor under Open-Phase Fault",
TELKOMNIKA (Telecommunica
tion Computing
Electronics and
Control)
, vol. 13
, pp
. 432-441
, 2
015.
[7]
M.
Ja
nna
ti
, et
a
l
.
, "A simple v
e
ctor contro
l technique for 3-ph
ase
induction
motor
under open-ph
ase fau
lt b
a
sed on
GA for
tuning of speed PI controller",
In 2014 IEEE Conferen
ce
on
Energy Conversion (
C
ENC
O
N)
, pp. 213-21
8,
2014.
[8]
B. Karan
a
y
i
l
, et
al.
,
"Online
s
t
ato
r
and ro
tor r
e
s
i
s
t
ance
es
tim
at
ion
s
c
he
me using ar
tificial neur
al n
e
tworks for vecto
r
controlled speed
sensorless induction motor driv
e",
IEEE Transactions on I
ndustrial Electronics
, vol. 54
, pp. 167
-
176, 2007
.
[9]
M.
Ba
rut
, et
a
l
.
,
"Switching EKF technique for ro
tor and
stator
res
i
stanc
e
est
i
m
a
tio
n in spe
e
d senso
r
less contro
l of
IMs",
Energy C
onversion and
M
anagement
, vol.
48, pp
. 3120-31
34, 2007
.
[10]
E
.
S.
De Sa
nta
n
a
, et al.
, "A pred
ictiv
e
algorithm for controlling
speed and
rotor
flux of indu
ctio
n motor",
IE
EE
Transactions on
Indus
trial Electronics
, vo
l. 55, p
p
. 4398-4407
, 2
008.
[11]
C. Patel
, et al.
, "
A
rotor flux es
tim
ation during z
e
ro and ac
tive v
ector per
i
ods
us
ing current error
s
p
ace vec
t
or fro
m
a h
y
s
t
eres
is
co
ntrolle
r for a
s
e
ns
or
less vector control of
IM drive",
IEEE Transaction
s
on Industrial
Electronics
, vol. 58, pp. 2334-23
44, 2011
.
[12]
M.
Ba
rut
, et
al.
, "Real-time
impl
ementation of
bi input-
e
xtend
e
d
Kalman fi
lter-b
ased estimator
for
speed-sensorless
control of
induction motors",
IEEE Transactions
on Industrial
Electronics
, vol. 59
, pp. 4197-4206,
2012.
[13]
F
.
R. S
a
lm
as
i and T.A. Najaf
a
ba
di, "An adaptiv
e obs
erver with
online rotor an
d s
t
ator res
i
s
t
an
ce es
tim
at
ion for
induction
motors with one ph
ase curren
t
sensor",
IEEE Transactions on Energy
Conversion
,
vo
l. 26, pp
. 959-966
,
2011.
[14]
T. Orlowska-Kowalska and M. D
y
bkowski, "
S
tator-curr
e
nt-b
ased MRAS est
i
mator for a wide range speed
-
sensorless induction-motor drive"
,
IEEE Transactions on
Industria
l Electronics
, vo
l. 57
, pp
. 1296-1
308, 2010
.
[15]
P. Vas, "Ve
c
tor
Control of
AC
Machines",
Oxfo
rd scienc
e pub
li
cation
, 1990
.
Evaluation Warning : The document was created with Spire.PDF for Python.