TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 13, No. 2, Februa
ry 20
15, pp. 264 ~ 270
DOI: 10.115
9
1
/telkomni
ka.
v
13i2.691
0
264
Re
cei
v
ed O
c
t
ober 2
6
, 201
4; Revi
se
d Decem
b
e
r
8, 2014; Accepte
d
De
cem
ber
22, 2014
DTC Method for Vector Control of 3-Phase Induction
Motor under Open-Phase Fault
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,
Univers
i
ti T
e
knolo
g
i Mal
a
y
s
ia,
8131
0 Skud
ai,
Johor Bahr
u, MALAYSIA
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: jann
atim94
@
y
a
h
o
o
.com
A
b
st
r
a
ct
T
h
ree-p
hase I
nducti
on Motor
(IM) drives are w
i
dely
us
ed
in ind
u
stria
l
e
qui
p
m
ents. On
e of the
essenti
a
l
pro
b
l
e
ms
of
3-ph
as
e IM dr
ives is their hig
h
s
pee
d
a
nd
t
o
rqu
e
p
u
lsati
on in
the fault
co
nditi
ons
.
T
h
is pap
er sh
ow
s Direct T
o
rque C
ontrol (D
T
C
) strat
egy for vector control of
a 3-ph
as
e IM under op
en-
circuit fault. T
h
e obj
ective
is to i
m
pl
e
m
e
n
t a soluti
on fo
r ve
ctor control of
3-ph
ase IM dri
v
es w
h
ich ca
n
b
e
also
use
d
u
n
d
e
r op
en-
ph
ase
fault. MAT
L
A
B
si
mul
a
tio
n
s
w
e
re carrie
d
o
u
t an
d p
e
rfor
ma
nce
an
alysi
s is
prese
n
ted.
Ke
y
w
ords
: 3-p
hase IM, DT
C, ope
n-ph
ase fa
ult, simu
lati
on r
e
sults
Copy
right
©
2015 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
3-ph
ase Indu
ctiom Moto
r (IM), beca
u
se
of it
s simplicity of constru
c
tion, low
co
st, and
robu
stne
ss, is a go
od can
d
idate for in
d
u
strial
appl
i
c
ations [1]. Th
e IM can b
e
affected by m
any
different type
s of faults. T
hese faults in
clud
e the
followin
g
: 1) stat
or faults
(ope
n or short
circuit
faults); 2) rot
o
r elect
r
ical
f
aults (op
e
n
o
r
sho
r
t
ci
rcuit
faults fo
r
wou
nd
rotor IM a
nd b
r
o
k
en
ba
r(s)
or
cra
c
ked
end-rin
g
for squi
rrel-ca
g
e
IM);
3
)
rotor me
ch
an
ical fault
s
(beari
ng
dam
age,
eccentri
city, bent shaft, and misalignment)
[2-7].
In some critical
a
ppli
c
at
ions, a backup
approa
ch mu
st be implem
ented to
guarantee that the fault is han
dl
ed in su
ch
a way that there
will be n
o
da
mage. Fault
-
tolera
nt co
ntrol is pa
rt of this ba
ckup
a
ppro
a
ch. It aims at in
suri
n
g
a
degrade
d op
eration m
ode
in the pre
s
en
ce of faults.
The
b
a
si
c
v
e
ct
or co
nt
rol s
c
hem
s su
ch as
Fi
el
d-Orie
nted Control
(FOC
) o
r
Di
re
ct Tor
que
Control (DTC) whi
c
h are e
m
ploy
ed to control 3-pha
se IM under b
a
lan
c
ed cond
ition cann
ot be
use
d
dire
ctly for vector
co
ntrol of 3-p
h
a
s
e IM
und
er
unbal
an
ced
condition (fa
u
lt conditio
n
). If a
basi
c
ve
ctor
control meth
od is used to
cont
rol
u
nba
lanced IM, hi
gh o
scill
ation
s
in th
e ma
chine
torque a
nd speed
can be
observed. In these co
nditio
n
s, it is necessary a
ne
w control alg
o
rith
m
is appli
ed [8-23].
The m
a
in
co
ntribution
of t
h
is
re
sea
r
ch i
s
to
int
r
od
uce
a novel
an
d
simple
vecto
r
co
ntrol
techni
que
ba
sed
on
DT
C
for 3
-
ph
ase I
M
whi
c
h
can
be
also u
s
e
d
for 3-pha
se IM u
nde
r f
ault
con
d
ition (o
p
en-p
h
a
s
e faul
t). Differently from t
he previous te
chni
qu
es to co
ntrol I
M
unde
r ope
n-
pha
se fa
ult (e.g., [8-23]),
the rotational
tran
sfor
mati
on m
a
trices
are
not
nee
d
to
control fa
ulty
machi
ne. (th
e
previou
s
m
e
thod
s to co
ntrol IM
in [8-24] are b
a
sed on FO
C).
This re
sea
r
ch is
orga
nized as
follows: In section 2, d-q m
odel of f
aulty
3-ph
ase IM is pres
ented. After that, vector
control equ
ations fo
r faulty 3-ph
ase IM base
d
on DTC are presente
d
in se
ction 3
.
The MATLAB
simulatio
n
re
sults a
nd cop
m
ari
s
ion
s
are
sho
w
n in section 4 and se
ction 5 con
c
lu
des the p
ape
r.
2.
Fault
y
Machine Model
The
d-q
mo
del of
3-pha
se IM
un
de
r ope
n-circuit
fault
can
b
e
sho
w
n
as followi
ng
equatio
ns [9]:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
DTC M
e
thod
for Vecto
r
Co
ntrol of 3-Pha
s
e Indu
ction
Motor un
der
Open
-Pha
se
… (M. Jan
nat
i)
265
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
(1)
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
(2)
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
(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
st
at
or a
nd ro
t
o
r re
sist
a
n
c
e
s.
L
ls
, L
ms
a
nd
L
r
den
ote
the stator a
nd roto
r lea
k
age an
d mut
ual
indu
ct
an
ce
s.
r
is the ma
chine
sp
eed.
τ
e
,
τ
l
, J
an
d
F
are el
ectrom
agneti
c
to
rqu
e
, load
torqu
e
,
inertia an
d viscou
s friction
coefficie
n
t. The d-q m
odel
of 3-pha
se IM unde
r ope
n-ci
rcuit fault wa
s
obtaine
d usi
n
g an app
roa
c
h like that used to obt
ain the model fo
r a healthy 3-p
hase IM [9].
3.
DTC o
f
fa
ulty
3-phase IM
In this s
e
c
t
ion, DTC
s
t
rategy
is
adapted to a faulty
3-
phase IM
(in th
is paper
SVPWM
DTC i
s
use
d
). Due to the
fact that the
uneq
ual
para
m
eters in the model
of faulty 3-pha
se IM
there is an o
s
cillating term i
n
the electro
m
agneti
c
to
rq
ue of machin
e. It is possibl
e to remove the
oscillating term of elect
r
omagnetic torque
by using The transformation element. This
transfo
rmatio
n element is:
s
qs
s
qs
s
ds
s
ds
s
qs
s
qs
s
ds
s
ds
v
v
v
v
i
i
i
i
k
1
1
1
1
3
1
,
3
,
3
(5)
Usi
ng
(5), th
e faulty machine m
odel
(equat
io
ns (1
)-(4
)) ca
n
be
obtaine
d
a
s
followin
g
equatio
ns:
dt
d
i
r
v
dt
d
i
r
v
s
qs
s
qs
s
s
qs
s
ds
s
ds
s
s
ds
1
1
1
1
1
1
3
3
3
3
3
(6)
(7)
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 2, Februa
ry 2015 : 264 – 270
266
Equation
s
(6
) and (7
) ca
n be written a
s
:
dt
d
L
M
dt
di
L
i
r
v
dt
d
L
T
M
T
v
s
qr
r
s
qs
s
s
s
qs
s
s
qs
s
ds
r
s
r
s
dr
s
r
s
ds
s
ds
1
1
1
1
1
1
1
1
3
(8)
(9)
More
over, the electroma
g
netic torq
ue
o
f
faulty machine is given by
:
s
qs
s
ds
s
ds
s
qs
e
i
i
Pole
1
1
1
1
2
(10
)
Whe
r
e:
r
s
s
L
L
M
2
1
(11
)
Since, the st
ator flux vector is alig
ned
with d-axis t
hen Equatio
n
(8)-(1
0)
can
be re-
written a
s
(i
n these e
q
u
a
tions
sup
e
rscript “
sf
” in
dicate that the vari
abl
es are in the stator
referenc
e frame:
s
s
qs
e
e
sf
qs
r
s
r
sf
qs
s
s
sf
qs
s
sf
qs
e
sf
ds
sf
ds
s
r
s
r
r
s
r
s
s
r
s
sf
ds
i
Pole
i
L
L
r
dt
di
L
i
r
v
Mi
di
M
L
L
M
L
L
T
M
dt
d
T
v
sf
qs
sf
ds
1
1
1
1
1
1
1
1
2
1
1
(12
)
(13
)
(14
)
Based
o
n
(12
)
a
nd
(1
3), th
e ne
ce
ssa
r
y
voltages for faulty ma
chin
e (
v
ds1
sf
and
v
qs1
sf
) can
be pro
d
u
c
ed
by 2 PI controllers and
e
ds
1
sf
and
e
qs1
sf
.
Therefore, Fi
gure 1
can b
e
pre
s
ente
d
for
vector
control
base
d
DT
C of 3-pha
se IM
under o
pen
-pha
se fault.
Figure 1. DT
C blo
ck di
agram
of faulty 3-pha
se IM
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
DTC M
e
thod
for Vecto
r
Co
ntrol of 3-Pha
s
e Indu
ction
Motor un
der
Open
-Pha
se
… (M. Jan
nat
i)
267
In this Figure, [
T
s
sf
] perform
s sig
nal transfo
rmatio
n from stato
r
referen
c
e frame t
o
stationa
ry ref
e
ren
c
e fram
e
.
Moreove
r
, the blo
ck [
T
s
fa
ult
] is 2 to 2 tran
sform
a
tion
for the stato
r
curre
n
t variab
les an
d difine
d as follo
ws [
9
]:
1
1
1
1
2
2
fa
u
l
t
s
T
(15
)
In addition:
s
ds
s
qs
sf
s
qs
s
ds
s
1
1
1
2
1
2
1
tan
(16
)
Based
on
Fi
gure
1, Fig
u
re 2
can
be
p
r
opo
se
d for
vector
co
ntro
l of both
hea
l
thy and
faulty 3-pha
se IM. To swit
ch bet
wee
n
the two
con
d
itions
(bal
an
ce
d and u
nbala
n
ce
d co
nditio
n
s),
four switche
s
are u
s
e
d
wh
ereby the
swi
t
che
s
will
cha
n
ge p
o
sition
s from bal
an
ced condition t
o
unbal
an
ced
condition
after
fault dete
c
tio
n
. The
pa
ra
m
e
ters in th
e p
r
opo
se
d
sche
me that
req
u
i
r
e
to be cha
nge
d from bala
n
ced co
ndition t
o
unbal
an
ced
conditio
n
are
given in Tabl
e 1.
Figure 2. DT
C blo
ck di
agram of
healthy and faulty 3-pha
se IM
Table 1. Co
m
pari
s
on b
e
tween Two Vect
or Co
ntrol Te
chni
que
s
3 to 2 (2 to
2) tra
n
sformation matrix for
the stator variabl
es:
Transform
ation
matrix fo
r stator
q-axis variables:
Health
y
3
-
phase
IM
cs
bs
as
s
qs
s
ds
i
i
i
i
i
2
3
2
3
0
2
1
2
1
1
3
2
1
k
Fault
y
3
-
phase I
M
bs
as
s
qs
s
ds
i
i
i
i
1
1
1
1
2
2
3
k
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 2, Februa
ry 2015 : 264 – 270
268
4.
Simulation Results a
nd Comparisions
Some MATLAB simulations
were done to eval
uate
the prop
sed
vector
co
ntrol
strate
gy
perfo
rman
ce.
The 3
-
p
h
a
s
e IM is fe
d b
y
an ide
a
l 3-l
e
g voltage
source i
n
verte
r
. The
refe
re
nce
spe
ed i
s
give
n by: (100,
1
00, 30
0, 30
0)rpm
at (0
, 0.
5, 0.5, 1
)
s,
resp
ectively.
The
simul
a
te
d 3-
pha
se ma
chi
ne paramete
r
s are give
n a
s
follows:\
The simul
a
tio
n
results for the first test, whi
c
h co
nsi
s
t
s
in usin
g the basic
DTC a
p
pro
a
ch
is sho
w
n in
Fi
gure
3 (l
eft). In the second
test, the prop
ose
d
DTC
ap
proa
ch
ba
sed
on Fig
u
re
2 i
s
use
d
for
healt
h
y and faulty
3-ph
ase IM. In both te
sts, t
he 3
-
pha
s
e
m
a
chi
ne
starte
d in the
healt
h
y
con
d
ition an
d
then at t=0.3
s
a ph
ase cut
-
off fault is
occured. In Figu
re 3(a), the to
rque
wavefo
rm
is p
r
e
s
ent
ed.
Moreove
r
, Fi
gure
3
(
b)
sho
w
s the
refe
re
nce
an
d a
c
tu
al value
of th
e moto
r
spe
e
d
.
As
can
be
se
en from Fi
gure 3, i
n
the
he
althy
co
nditio
n
, both
conve
n
tional
and
p
r
opo
se
d ve
ct
or
control
sch
e
m
e show go
od pe
rform
a
n
c
e a
nd fa
st
resp
on
se
with
out any tra
n
sient and
stea
dy-
state e
r
ror.
Compa
r
ed
to t
he b
a
si
c
DT
C al
gorith
m
,
the IM
spe
e
d
and
torque
of the
pro
p
o
s
ed
scheme
co
ntains ve
ry lo
w speed
osil
lations.
Ba
se
d on Fig
u
re
3(a
)
, usin
g
prop
osed
DTC
scheme, the
electroma
gne
tic torqu
e
wa
veforms
co
ntain
low osill
ations ev
en aft
e
r fault condit
i
on.
It is sho
w
n th
at the p
r
op
osed
DTC sch
e
m
e for he
althy and fa
ulty 3-pha
se
IM ve
ctor
co
ntrol
h
a
s
adeq
uate vector cont
rol ch
ara
c
teri
stics.
(a)
(b)
Figure 3. Simulation re
sult
s of the com
p
aris
on bet
we
en co
nventio
nal DT
C (left) and pro
p
o
s
e
d
DTC
(rig
h
t) fo
r vector
cont
rol of healthy and faulty 3-p
hase IM; (a)
Torq
ue, (b
) Speed
5. Conclu
sion
In this p
ape
r,
two
cont
rol
strategie
s
fo
r
ve
ctrol
co
ntro
l of healthy
a
n
d faulty 3
-
p
hase IM
drive b
a
sed
on DTC
ha
s been
di
scussed
and
sim
u
la
ted
(the f
ault co
ndition
in this pap
e
r
is
limited to ope
n-ci
rcuit fault). In the first schem
e,
ba
sic DTC
algo
rith
em is u
s
e
d
for both
healt
h
y
and fa
ulty 3-pha
se IM.
Th
e
simulatio
n
results
of the basic
DTC
shown that, th
e conventio
n
a
l
DTC al
go
rith
em is una
ble
to control the faulty 3-pha
se IM prope
rly.
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TELKOM
NIKA
ISSN:
2302-4
046
DTC M
e
thod
for Vecto
r
Co
ntrol of 3-Pha
s
e Indu
ction
Motor un
der
Open
-Pha
se
… (M. Jan
nat
i)
269
The
second
v
e
ctor co
ntrol scheme (p
ro
posed
me
th
o
d
) is
derive
d
from the con
v
entional
DTC sch
e
me
by so
me m
odificatio
n
s
o
n
it. The p
r
o
posed m
e
tho
d
pa
rtially co
mpen
sated
the
ripple
s
that
occur o
n
th
e spee
d a
n
d
torque
respon
ce
s of
convention
a
l
DTC al
gorith
e
m.
Analyzing th
e
simul
a
tion re
sults, it i
s
po
ssi
ble to
im
pl
ement hig
h
p
e
rform
a
n
c
e v
a
ctor control
of
AC 3-p
h
a
s
e IM drives
with a faulty 3-pha
se IM.
Although thi
s
method
ha
s a
simpl
e
impl
e
m
entation
but
it has some
dra
w
ba
cks
such
as
torque di
sto
r
tions, lo
w-spe
ed ope
ration
probl
em
s.
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 2, Februa
ry 2015 : 264 – 270
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