TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 9, September
2014, pp. 66
3
3
~ 664
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i9.630
9
6633
Re
cei
v
ed Ma
y 21, 201
4; Revi
sed
Jul
y
6, 2014; Accept
ed Jul
y
15, 2
014
Indirect Rotor Field-Oriented Control of Fault-Tolerant
Drive System for Three-Phase Induction Motor with
Rotor Resistan
ce Estimation Using EKF
M. Jannati*,
N. R. N. Idris, M. J. A. Az
iz
Univers
i
ti T
e
knolo
g
i Mal
a
ysia,
UT
M-PROTON Future Driv
e
Lab
orator
y, F
a
cult
y
of Electric
al Eng
i
ne
eri
ng,
813
10 Sku
dai,
Johor Ba
hru, MALAYSIA
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: Jannatim
94
@
y
ah
oo.com
A
b
st
r
a
ct
T
he p
e
rforma
nce
of an
Ind
i
rect Rotor
F
i
eld-
Orie
nted
C
ontrol (IRF
OC
) sche
m
e
for
Inductio
n
Motors (IMs) is strongly d
e
p
end
ent o
n
the
motor
par
a
m
eters esp
e
cia
l
l
y
, rotor resista
n
ce. As such,
to
ensur
e high performanc
e dr
ive system
, the var
i
ation
of the r
o
tor res
i
stance
due to the temper
atur
e
incre
a
se
nee
d
to be
esti
mate
d bas
ed
on
th
e ava
i
l
abl
e ter
m
i
nal
vari
ab
les
.
How
e
ver, the
alg
o
rith
m
use
d
t
o
estimate the ro
tor resistance f
o
r a bal
anc
ed
T
h
ree-
Ph
ase Inducti
on Motor
(T
PIM) cannot be use
d
for a
n
ope
n-ph
ase fa
ult IM; this is b
e
caus
e the
mo
del
of a fa
u
l
ty mac
h
i
ne is
different fro
m
the
bal
ance
d
3-
ph
a
s
e
mac
h
i
ne. In th
i
s
pa
per, a
n
IR
F
O
C of fault-to
lera
nt dr
iv
e sy
stem (w
ith stat
or op
en-
ph
ase
fault) for
a T
P
IM
w
i
th rotor resistance esti
mati
o
n
usin
g Extend
ed Kal
m
an F
ilt
er (EKF
) is propose
d
. T
he pe
rforma
nce of th
e
EKF
based rotor resistance
estimator is ev
alu
a
ted
un
der
different
op
era
t
ing c
o
n
d
itio
ns
usi
n
g
MAT
L
A
B
simulati
on p
a
c
k
age. T
he pr
op
osed a
l
g
o
rith
m for estimati
on
of rotor resista
n
ce in this p
a
p
e
r can be
app
li
ed
to either
ba
la
n
c
ed T
P
IM or F
aulty T
P
IM (F
T
P
IM).
T
he simulati
on res
u
lts
show
ed th
at the pro
pos
ed sy
ste
m
is abl
e to over
come the rotor
resistance v
a
r
i
atio
ns,
loa
d
di
sturbanc
e as
w
e
ll as
stator ope
n-ph
ase fa
ul
t
cond
ition, w
i
th goo
d trackin
g
capa
bil
i
ty.
Ke
y
w
ords
: TPIM, IRFOC, EK
F, rotor resistance estim
a
tion,
fault-tolerant
drive system
, sim
u
lation
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
In some
appli
c
ation
s
, su
ch
as in military
,
sp
a
c
e explo
r
ation a
nd el
ectri
c
vehi
cle,
Faulty
Thre
e-Ph
ase Inductio
n
Mot
o
r (F
TPIM) control i
s
ve
ry
signifi
cant an
d vital (in this pape
r, FTPIM
is refe
rre
d to
stator op
en-pha
se fault).
For safe
ty re
aso
n
s, the
s
e
application
s
requi
re a faul
t-
tolerant
control method
where
b
y the d
r
ive
system operation
ca
nnot
be sto
p
ped even u
n
der
faulty conditi
on. In these
situation
s
, the dr
ive sy
stem shoul
d kee
p
its min
i
mum ope
rati
ng
perfo
rman
ce
at least until
the fault is rectifi
ed. It is well kno
w
n that the most
widely ado
pted
control for el
ectri
c
al ma
ch
ines i
s
the Field-O
r
ie
nted
Control
(FO
C
) o
r
vector
control [1-4].
In
orde
r
to en
sure co
ntinuo
us
o
p
e
r
ation of
FOC
und
e
r
faulty co
ndi
tions, the
alg
o
rithm m
u
st
be
modified to cater for the u
nbala
n
ce faulty condi
tions.
If a
conventi
onal vecto
r
control techniq
ue
is a
pplie
d to
an
ope
n-p
h
a
se
faulty in
ductio
n
ma
ch
ine, severe
o
scill
ation
s
in
the torque,
a
n
d
hen
ce the
sp
eed m
a
y be
observed
[5, 6]. Several re
sea
r
che
s
h
a
ve bee
n
cond
u
c
ted to
study
on
the faulty IM
and hen
ce m
odificatio
n
s n
eede
d to
be applie
d to the conventio
n
a
l vector co
n
t
rol
scheme
un
de
r faulty co
ndit
i
ons. A fault
-
tolera
nt dr
iv
e
sy
stem fo
r In
dire
ct R
o
tor F
O
C
(IRF
OC
)
of
TPIM based
on rotation
al transfo
rmatio
ns was p
r
op
ose
d
in [5, 6]; it was sho
w
n that by using
some mi
nor
modificatio
n
to the convent
ional
IRFO
C for TPIM, the FOC of unb
al
anced or FTP
IM
is po
ssi
ble.
In IRFOC, a
n
accurate estimation of
rotor re
si
stance, rega
rd
less of whet
her the
machi
ne i
s
a
balan
ce
d TPIM or FTPIM, i
s
vital to en
sure hi
gh p
e
rf
orma
nce torq
ue control [7].
In
this pa
per, fo
cu
s is
given to the proble
m
of
paramet
er vari
ation (i
.e. rotor resi
stance,
r
r
) of the
indu
ction ma
chin
e und
er f
aulty conditio
n
s (one
pha
se cut-off). Inaccurate valu
e of rotor tim
e
con
s
tant (
T
r
=L
r
/
r
r
; where
L
r
is the stator induct
ance) used in F
O
C algori
thm
will result in
an
impro
per d
e
couple
d
between torq
ue
and flux co
mpone
nts [8]
.
In practice, the value of
r
r
increa
se
s wit
h
temperature afte
r operating the mo
tor over a certain pe
riod
of time.
It
wa
s
repo
rted that
the
r
r
can vary to as high
as 1
00% of its
nomi
nal val
ue [9-1
1]. Th
e variation
of
r
r
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ISSN: 23
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TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 66
33 – 664
3
6634
from its nomi
nal value
(he
n
ce
the va
riat
ion in
T
r
)
ca
n
sig
n
ifica
n
tly affect the
performan
ce
of t
h
e
IRFO
C e
s
pe
cially for TPIM und
er fa
ul
t con
d
ition. T
h
erefo
r
e
in o
r
de
r to m
a
int
a
in the
high
e
s
t
perfo
rman
ce
of IRFOC, e
s
timation of rot
o
r re
si
stan
ce
unde
r faulty condition i
s
mandato
ry.
One of th
e
most effe
ctive algo
rithm
s
use
d
in the
estimation
of
paramete
r
s,
su
ch
as
spe
ed and
re
sista
n
ce, for electri
c
al m
a
chin
es i
s
the Extended Kal
m
an Filter (E
KF) [12-1
4
]. EKF
is a type of o
b
se
rver th
at con
s
id
ers the
nonlin
ear
ity
of the ma
chin
e model
, filters the m
easured
noises a
nd system noi
se
s, and estimat
e
s the state
s
variable
s
[1
3]; this is the
rea
s
on
why the
EKF has
est
ablished
extensive a
ppli
c
a
t
ions in
co
ntrol syste
m
s. I
n
this
wo
rk,
a ro
bu
st IRF
O
C
method
fo
r a fault-tolerant driv
e system
based on
EK
F
is propo
se
d.
At the sam
e
time, an
oth
e
r
EKF
is also use
d
to estim
a
te
the roto
r resi
stan
ce
for IRFO
C
sche
me. In thi
s
p
aper,
sim
u
lati
on
results
obtai
ned fo
r a
fa
ult-tolerant d
r
ive sy
st
em based on
I
R
FOC, with
a
nd without rotor
resi
stan
ce
e
s
timation a
r
e
pre
s
ente
d
. T
he dyn
a
mi
cs
and th
e p
e
rfo
r
man
c
e
c
haracteri
stics of the
prop
osed met
hod are verifi
ed and eval
u
a
ted usi
ng M
A
TLAB software.
The
re
st of the p
ape
r i
s
o
r
gani
ze
d a
s
f
o
llows
: In
se
ction
2, the d
-
q m
odel
of
FTPIM is
pre
s
ente
d
. T
he IRF
O
C
eq
uation
s
for
a
fault-tolerant
driv
e
sy
st
em
as
well a
s
t
h
e st
r
u
ct
u
r
e of
t
h
e
prop
osed te
chniqu
e a
r
e
prese
n
ted i
n
section
3.
EK
F eq
uation
s f
o
r
roto
r resi
st
ance e
s
timati
on
for fault-tole
rant drive sy
stem ar
e give
n
in sectio
n 4. In sectio
n
5, the re
sults
are pre
s
ente
d
and
discu
s
sed an
d finally secti
on 6 co
ncl
u
d
e
s the pa
per.
2. d-q Model
of FTPIM
As mentioned earlier, the fault condition as
sum
e
d in this paper is a phase cut-off.
Specifically, it will be assu
med t
hat a phase cut-off fault occurre
d
in phase
“c” of a TPIM. With
this
faulty co
ndition,
the e
l
ectri
c
al equ
a
t
ions
with sy
mmetrical sta
t
or
wi
ndin
g
s in
a stationary
referen
c
e (su
perscript ‘‘
s
’’
) can b
e
de
scri
bed by Equati
on (1
)-(9) [5].
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Whe
r
e,
(9)
In (
1
)-
(9)
,
v
s
ds
,
v
s
qs
are th
e stato
r
d
-
q
axes voltag
e
s
i
s
ds
,
i
s
qs
are
the stato
r
d
-
q axe
s
cur
r
e
n
t
s
i
s
dr
,
i
s
qr
are the
rot
o
r d
-
q axe
s
currents
λ
s
ds
,
λ
s
qs
are the
st
ator d
-
q axe
s
fluxes an
d
λ
s
dr
and
λ
s
qr
are the roto
r d-q axes fluxes
i
n
the stator
referen
c
e fra
m
e.
r
s
and
r
r
are the
stator and
rotor re
sista
n
c
e
s
,
re
spe
c
tiv
e
ly
. L
ds
,
L
qs
,
L
r
,
M
d
and
M
q
denote the
st
ator, the roto
r self and m
u
tual
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Indire
ct Roto
r Field-O
r
iente
d
Control of Faul
t-Tolerant Driv
e Sys
t
em for… (M. J
annati)
6635
indu
ct
an
ce
s.
r
is the motor spee
d. Electrom
agn
etic
torque
and m
e
ch
ani
cal eq
uation
s
ca
n
be
written as
follows
:
(10
)
(11
)
In (10
)
a
nd (1
1),
e
an
d
l
are ele
c
trom
ag
netic to
rqu
e
a
n
d loa
d
torqu
e
and
P
,
J
and
F
ar
e
the nu
mbe
r
o
f
pole
s
, mom
ent of in
ertia
and vi
scou
s f
r
iction
coefficient respe
c
tively. As
can
b
e
see
n
from (1)-(11
)
, the equatio
ns of
FTPIM are
similar to t
h
e bala
n
ced
one. In fact, b
y
s
u
bs
tituting
M
d
=M
q
=M
=
3/
2
L
ms
and
L
ds
=L
qs
=L
s
=L
ls
+3/
2
L
ms
in the F
T
PIM equatio
ns, we
ca
n o
b
tain
the familiar e
quation
of T
P
IM. Becau
s
e of the
asy
mmetrical
structure of F
T
P
IM, convent
ional
vector co
ntro
l algo
rithm fo
r
symmetri
c
al
IM c
annot
b
e
directly u
s
ed for
control
ling the
FTPI
M
sin
c
e it will re
sult in a sig
n
ificant rip
p
le in
t
he torque a
nd sp
eed [5, 6]. To overco
me this probl
em,
simila
r metho
d
as introdu
ced in [5] will be used he
re
. In [5], two rotational tran
sform
a
tion
s for
variable
s
tra
n
sformation f
r
om u
nbal
an
ced
set
(e.g., FTPIM) to the bal
an
ced
set (e.g., TPIM)
have bee
n propo
sed. The
s
e rotational transfo
rmatio
n
s
are give
n b
y
(12) an
d (1
3).
(12
)
(13
)
Whe
r
e,
θ
e
i
s
the
angl
e b
e
twee
n the
stationary
refe
ren
c
e
fram
e
and th
e
roto
r
field-
oriente
d
refe
ren
c
e fra
m
e.
It can be sho
w
n t
hat
by applying
these tra
n
sformation
s, the
asymmet
r
ic
equatio
ns
of the FTPIM become
simi
l
a
r to the
structure of eq
uation
s
for t
h
e
balan
ce
d TPI
M
[5]. With
so
me min
o
r cha
nge
s in
the
T
P
IM paramet
e
rs,
it is p
o
ssi
b
le to
apply
the
conve
n
tional
IRFO
C meth
od to the FTPIM [5].
3. Fault-toler
a
nt Driv
e Sy
stem Based
on IRFO
C
Open
ci
rcuit fault is
one
of most famili
a
r
failures in t
he IMs stato
r
windi
ng
s [15
-
18]. In
the literature, different meth
ods h
a
ve bee
n prop
osed
to
detect stato
r
and roto
r faul
ts in elect
r
ical
machi
n
e
s
[1
5-18]. T
h
e
s
e
tech
niqu
es
provide
ap
proximately im
mediate
ope
n
stato
r
win
d
ing
detectio
n
and
will be assu
med in this p
aper.
The obje
c
tive
of FOC is to sepa
rate the
motor cu
rren
ts into flux and torqu
e
produ
cing
comp
one
nts.
The torq
ue i
s
prop
ortion
al to the
prod
uct of these two com
pon
ent
s
and th
ey can
be treated
separately. In RFO
C
metho
d
, the roto
r fl
ux vector is
aligne
d with
d-axis
(
λ
dr
e
=|
λ
r
|,
λ
qr
e
=0) [8]. With this a
ssumption an
d
by applying
(12) a
n
d (1
3) to the eq
uation
s of FTPIM
(equ
ation
s
(1)-(11)) a
nd by co
nsid
erin
g o
f
L
ds
/
L
qs
=(
M
d
/
M
q
)
2
, (in the FTP
IM:
M
d
=3/
2
L
ms
,
M
q
=
√
3/2
L
ms
,
L
ds
=
L
ls
+1/
2
L
ms
,
L
qs
=
L
ls
+1/2
L
ms
and
L
ms
˃˃
L
ls
), RFOC
equ
a
t
ions for F
T
PIM
are obtai
ned
as follo
wing e
quation
s
:
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TELKOM
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14: 66
33 – 664
3
6636
(14
)
(15
)
(16
)
Whe
r
e,
(17
)
(18
)
(19
)
(20
)
(21
)
(22
)
The su
pe
rscript “
e
” in
dicates the variable
s
are i
n
the rotatin
g
referen
c
e
frame.
More
over,
T
r
and
ω
e
are
rotor time
consta
nt (
T
r
=
L
r
/
r
r
) and th
e angul
ar velo
city of the RFO
referen
c
e fra
m
e re
sp
ectiv
e
ly. As sho
w
n by usi
ng t
hese rotatio
n
a
l tran
sform
a
tions (equ
ations
(12
)
and
(13
)
), IRFOC
equ
ations fo
r FT
PIM re
sem
b
l
e
the IRFO
C for balan
ce
d
TPIM equatio
ns.
Based o
n
(1
4)-(22
), it ca
n be se
en that t
he only differen
c
e b
e
twee
n these equatio
ns
and
balan
ce
d TPI
M
eq
uation
s
i
s
that
for
bala
n
ce
d TPIM,
we have
r
s
,
M
=
3/2L
ms
and
L
s
=
L
ls
+3/2
L
ms
[8
],
but for FTPIM
r
s
=(
r
s
M
q
2
+
r
s
M
d
2
)/2
M
d
2
,
M=M
q
=
√
3/2L
ms
,
L
s
=L
qs
=
L
ls
+1/
2
L
ms
and
v
ds
-e
,
v
qs
-e
as sho
w
n
in (14
)
-(22
). Therefore,
with some min
o
r chang
es
t
o
the para
m
e
t
ers of moto
r, it is possi
ble
to
apply the co
n
v
entional IRF
O
C meth
od to the FTPIM [5, 6].
4. EKF for Rotor Resis
t
a
n
ce Estimati
on in Fault-tolerant
Driv
e
Sy
stem
As mention
e
d
before, the performan
ce of
the IRF
O
C de
pen
ds mainly on the roto
r
resi
stan
ce
th
at increa
se
s
with temp
era
t
ure. In
I
R
FO
C,
any ch
an
ges
in roto
r resi
stan
ce gives
wro
ng valu
e
of rotor time
con
s
tant a
n
d
con
s
e
que
ntly prod
uce
s
e
rro
r in th
e e
s
timated rotor f
l
ux
positio
n. Sub
s
eq
uently, e
r
rors i
n
th
e
ro
tor flux
p
o
siti
on m
ean
that
the
de
cou
p
ling of
the to
rque
and flux
co
mpone
nts of
the
stator
curre
n
t is
co
mpromi
se
d a
nd the
in
sta
n
taneo
us torque
respon
se i
s
no lon
ger
est
ablished. Th
erefo
r
e, onl
i
n
e estimatio
n
of rotor
re
si
stance
ha
s to
be
inco
rpo
r
ate
d
in ord
e
r to im
prove the p
e
rforma
n
c
e of t
he drive
syst
em over a
wi
de sp
eed
ran
g
e
of operation
[7], [19-21]. Evidently, th
e co
nventio
n
a
l EKF for rotor resi
stan
ce e
s
timatio
n
in
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6637
TPIMs can
n
o
t
be directly e
m
ployed for
FTPIM beca
u
s
e of the different mo
del
s that are use
d
to
descri
be
a ba
lanced
TPIM and
a FTPIM.
This aspect of
the study i
s
an
exte
nsi
o
n of the auth
o
rs’
previou
s
re
se
arch pre
s
e
n
ted in Refs. [5, 6] and
[22-29]. In this paper, an EKF
is prop
osed to
estimate the rotor re
si
stan
ce for both TPIM and FTPIM
in associ
ated
with IRFO
C.
Figure 1 sho
w
s the st
ru
cture
of the propo
sed fault-tolera
nt drive
system ba
sed on
IRFO
C (d
etai
ls of the fault
-
tole
rant driv
e system i
n
Figure 1 is
g
i
ven in Appe
ndix A and fully
discu
s
sed in
[5]) with the propo
se
d EKF-ba
s
ed rotor re
sista
n
ce
estimator. T
he estimatio
n
is
perfo
rmed
by
the EKF
usi
ng me
asured
termin
al va
riable
s
,
i.e.
rotor spe
ed, sta
t
or curre
n
ts a
nd
voltages. T
h
e
estimate
d va
lue of
roto
r re
sista
n
ce i
s
th
en u
s
e
d
in th
e drive
sy
ste
m
. In this
pap
er
an EKF algori
t
hm with two
different pa
ra
meters for
estimation of rotor res
i
s
t
anc
e
in fault-tolerant
drive system
is propo
se
d. The
chan
ge
s of these p
a
ram
e
ters ar
e performed
after the fault is
detecte
d and
by a switch
as sh
own in Figur
e 1. In the prop
osed EKF and
under b
a
lan
c
e
d
condition,
M
d
=M
q
=
3/2
L
ms
and
L
ds
=L
qs
=L
ls
+3/
2
L
ms
are u
s
ed in the E
K
F algorithm.
When th
e fault
occ
u
rs
, the values
are s
u
bs
tituted with,
M
d
=
3/2
L
ms
,
M
q
=
√
3/2L
ms
,
L
ds
=L
ls
+3/2
L
ms
and
L
qs
=
L
ls
+1/2
L
ms
. In other
wo
rds, th
e p
r
op
ose
d
EKF b
a
s
ed
roto
r
re
si
stan
ce
estim
a
tion
can
be
use
d
for the balan
ced TPIM as well as for the
FTPIM.
Figure 1. Sch
e
me of Propo
sed Fa
ult-to
le
rant Drive System Based o
n
IRFO
C
For th
e pu
rp
o
s
e
of roto
r
re
sista
n
ce e
s
ti
mation, the
d
-
axis
(
i
dr
)
and
the q
-
axis (
i
qr
) of the
rotor current
s as
well
as th
e rotor re
si
stance
(
r
r
)
ar
e
c
h
os
en
as the
s
t
a
t
e va
r
i
a
b
le
s
.
U
s
in
g
the
s
e
state varia
b
le
s, it is po
ssibl
e
to expre
s
s the st
ate
sp
ace model
of the IM in the fo
rm of Equatio
n
(23
)
and (24
)
:
(23
)
(24
)
In these e
q
u
a
tions,
A
,
B
and
C
are th
e system, in
p
u
t and outp
u
t matrices
re
spectively.
x
,
y
a
nd
u
are the
syst
em state m
a
trix, system
output matrix
and syste
m
input mat
r
ix
respe
c
tively. In orde
r to im
plement a
nd
simulate th
e
EKF algorith
m
, continu
o
u
s
state
equati
ons
sho
u
ld
be t
r
a
n
sformed
int
o
di
screte
sta
t
e equ
atio
n
s
. The
r
efo
r
e, E
quation
(2
3)
and
(2
4)
ca
n
be
re-
w
ritten a
s
f
o
llow
s
:
(25
)
(26
)
Becau
s
e
of
IM model
a
c
curacy
and
measur
ement
errors,
sto
c
hasti
c
vari
abl
es
are
introdu
ce
d (
w
(
n
) i
s
the sy
stem noi
se an
d
v
(
n
) is the m
easure
m
ent
noise). The
matrices of
A
(
n
),
B
(
n
) an
d
C
(
n
) in equation
s
(25
)
and (2
6) are given in Appendix B. The matrice
s
x
(
n
),
y
(
n
)
an
d
u
(
n
) are give
n as follo
ws:
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33 – 664
3
6638
(27
)
(28
)
(29
)
The ste
p
s of the EKF algori
t
hm can be fo
rmulate
d
as [
14]:
1)
Estimation of the Erro
r Cov
a
rian
ce M
a
tri
x
:
(30
)
2)
Comp
utation
of Kalman Filter Gain:
(31
)
3)
Upd
a
te of the Error
Covari
ance Matrix:
(32
)
4) State
Estimation:
(33
)
In these e
q
u
a
tions,
Q
and
R
are the
covarian
ce
ma
trice
s
of
the
noises.
To
b
egin th
e
cal
c
ulatio
n, the initial valu
es of the
stat
e variabl
es
a
n
d erro
r
cova
rian
ce m
a
trices
(
P
,
Q
and
R
)
need to be id
entified. In this wo
rk, the ini
t
ial values of matrices
P
,
Q
and
R
for e
s
t
i
mation of rot
o
r
resi
stan
ce a
r
e obtaine
d fro
m
the trial an
d error p
r
o
c
e
ss.
5. Simulation Resul
t
s
In ord
e
r to
ve
rify the effecti
v
eness of th
e
pr
o
p
o
s
ed
structure of I
R
F
O
C fo
r fault-t
o
lera
nt
drive syste
m
and the EKF base
d
roto
r re
sista
n
ce
estimation, si
mulation is
condu
cted u
s
i
n
g
MATLAB sim
u
lation p
a
cka
ge. The
pa
ra
meters that
are
used fo
r the sim
u
lati
on a
r
e give
n
in
Appendix C. Thre
e differe
nt drive
syste
m
s are simul
a
ted: (1) IRF
O
C drive
with
out fault-tolerant
and without
rotor
re
si
stan
ce estimato
r,
(2
)
IRF
O
C drive with
fa
ult-tolerant
a
nd without rotor
resi
stan
ce e
s
timator, and (3) IRFO
C d
r
i
v
e with faul
t-tolera
nt and with rotor resi
st
ance estimat
o
r.
The th
ree
dri
v
e system
s
a
r
e te
sted u
n
d
e
r the
sa
me
operating
co
ndition
s
a
s
f
o
llows: a
pha
se
cut-off fault i
s
introdu
ced
at t=0.5s, th
e value
of th
e load i
s
in
creased fro
m
zero to
1N.m
at
t=1.5s
(see F
i
gure
2)
and t
he value
of the roto
r
re
sistance i
s
in
cre
a
se
d by 10
0
%
of its nomi
n
al
value at t=2s
(se
e
Figu
re 3
)
. In all case
s, the referen
c
e spe
e
d is
se
t to the 500rp
m
.
Figure 2. Vari
ation of Load
Figure
3. Vari
ation of Rotor Resi
stan
ce
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TELKOM
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046
Indire
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r
iente
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Control of Faul
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e Sys
t
em for… (M. J
annati)
6639
(a) Stator a
n
d
rotor current
s
(b) Spe
ed respon
se
(c) Torque
re
spo
n
se
Figure 4. IRF
O
C Drive wit
hout Fault-tol
e
rant
an
d wit
hout Roto
r Resi
stan
ce Est
i
mator
(a) Stator a
n
d
rotor c
u
r
r
ent
s
(b) Spe
e
d r
e
s
pon
se
(c) Torque
re
spo
n
se
Figure 5. IRF
O
C Drive wit
h
Fault-tole
ra
nt and witho
u
t
Rotor Resi
st
ance Estimat
o
r
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Vol. 12, No. 9, September 20
14: 66
33 – 664
3
6640
(a) Stator a
n
d
rotor c
u
r
r
ent
s
(b) Spe
e
d r
e
s
pon
se
(c) Torque
re
spo
n
se
Figure 6. IRF
O
C Drive wit
h
Fault-tole
ra
nt and with Rotor Re
si
stan
ce Estimato
r
Figure 7. Estimated Roto
r
Re
sista
n
ce Wavefo
rm
The respon
ses of
stator
a
nd
roto
r
cu
rrents, rotor
sp
eed a
nd el
ectromag
netic t
o
rqu
e
of
the IRF
O
C d
r
ive sy
stem
s
are
sh
own in
Figu
re
4,
Fi
gure
5
and
F
i
gure
6,
re
sp
ectively. With
out
the fault-tolerant drive (Fig
ure 4), severe oscill
ation i
n
the torque can be se
en at the moment the
pha
se
cut-off
fault is intro
duced at t=0.5s.
The re
sp
onses are ge
tting
worse a
s
the
lo
ad
to
que
and vari
ation
in rotor
re
si
stan
ce a
r
e in
trodu
ced
at t=1.5
s
and t
=
2s, re
sp
ectiv
e
ly. In Figure
5
,
whe
r
e the fa
ult-tolerant is inco
rpo
r
ated
to t
he drive
system, the
pha
s
e cut-o
ff faulty can be
overcome
as
soo
n
a
s
the f
ault-tole
rant
mech
ani
sm
i
s
activated (Note: the algo
ri
thm use
d
for
the
fault-tolerant system i
s
full
y discu
ssed i
n
[5]).
Ho
wev
e
r, as
a step
cha
n
ge in
rot
o
r resi
stan
ce
is
introdu
ce
d at
t=2s, th
e de
terioration in
the re
sp
on
se
, particularly
the torq
ue re
spo
n
se, ca
n
be
observed. Th
e rotor resi
st
ance estimat
o
r man
aged
to improve th
e respon
se b
y
restori
ng th
e
rotor resi
stan
ce value u
s
e
d
in the cont
rol algo
ri
thm to the actual
value (i.e. twice its nomi
n
al
value). Figu
re 6 sh
ows th
e perfo
rma
n
ce of the es
ti
mator in tra
c
king the va
ri
ation of the rotor
resi
stan
ce. T
he simul
a
tion
result
s dem
onstrated
the
robu
stne
ss
of the estimator to a faulty
con
d
ition the
load variatio
n
s
.
6. Conclusio
n
This pa
per p
r
esents the f
ault-tole
rant driv
e s
y
s
t
em for IRFOC
with EKF-bas
ed rotor
resi
stan
ce e
s
timator. The prop
osed rot
o
r re
si
stan
ce
estimator ca
n be use
d
u
n
der n
o
rm
al and
pha
se
cut-off co
ndition,
with minimal
modificatio
n
t
o
the p
a
ram
e
ters u
s
ed
i
n
the al
go
rithm.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
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ISSN:
2302-4
046
Indire
ct Roto
r Field-O
r
iente
d
Control of Faul
t-Tolerant Driv
e Sys
t
em for… (M. J
annati)
6641
Simulation re
sults
demo
n
strated the ex
cellen
c
e tr
a
c
ki
ng pe
rform
a
n
c
e of the
pro
posed e
s
tima
tor
as
well
a
s
it
s ro
bu
stne
ss
again
s
t lo
ad
variatio
n
and
faulty conditi
on. Sin
c
e
FT
PIM and
si
ng
e-
pha
se IM can be mod
e
lled as un
ba
lanced 3-pha
se IM, the prop
osed techniqu
e is al
so
appli
c
able
to singl
e-p
h
a
s
e IMs.
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ces
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H Amimeur, D
Aouze
lla
g, R Abdess
e
med, K
Ghedams
i
. Slid
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o
n
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nerg
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o
n
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ersio
n
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u
ctio
n
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D Jan
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ontro
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ase
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Appe
ndix A:
Fault-tole
rant
drive system
base
d
on IRFOC [5]
In the balan
ced mode
we
have:
r
s
,
M=3/2L
ms
and
L
s
=
L
ls
+3/
2
L
ms
In the faulty
mode we hav
e:
r
s
=(
r
s
M
q
2
+
r
s
M
d
2
)/2
M
d
2
,
M=M
q
=
√
3/2L
ms
and
L
s
=L
qs
=
L
ls
+1/
2
L
ms
More
over:
e
e
e
e
e
s
T
cos
sin
sin
co
s
Appe
ndix B:
Equation
(1
)-(8),
whi
c
h
a
r
e u
s
ed
to
m
odel th
e F
T
P
IM, can
be
written in
t
he fo
rm
followin
g
equ
ation:
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