Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol.
6, No. 4, Decem
ber
2015, pp. 831~
841
I
S
SN
: 208
8-8
6
9
4
8
31
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
Novel
M
e
thod of FOC to Speed
Control in Three-Phase IM
under Normal and Faulty Conditions
Mohammad Jann
ati
1
, To
le
Sutikno
2
,
Nik
Rumz
i Nik I
d
ris
3
, Mo
hd Juna
idi
Abdul Azi
z
4
1,3,4
UTM-PROT
ON Future Driv
e Laborator
y
,
Fa
culty
of Electrical Engineering
,
Un
iversiti Tekno
logi
Malay
s
ia, J
ohor
Bahru, MALAYSIA
2
Department of Electrical
Eng
i
n
eering
,
Un
iv
ersitas Ahmad Dahlan, Yog
y
ak
arta, I
ndonesia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 20, 2015
R
e
vi
sed Oct
7,
2
0
1
5
Accepted Oct 20, 2015
This paper pro
poses a novel method for speed control of three-phase
induction
motor
(IM) which can
be used
for bo
th
health
y
thr
ee-ph
ase IM and
three-ph
ase IM
under open-ph
ase fau
lt.
Th
e pro
posed fault-toler
a
nt
contro
l
s
y
stem is der
i
ved from conventional fi
eld-or
iented contro
l (FOC) algorithm
with minor changes on it. The p
r
esented driv
e sy
stem is based on using an
appropria
te tr
an
sform
a
tion m
a
trix for
the s
t
at
or current var
i
ables
.
The
presented
metho
d
in
this pap
e
r
can be also
used
for speed
contro
l of sing
le-
phase IMs with
two windings.
The feasib
ility
of the proposed
strateg
y
is
verified b
y
s
i
mulation
results.
Keyword:
Fi
el
d-
Ori
e
nt
e
d
C
ont
r
o
l
Ope
n
-p
hase fa
ult
Single
-
phase i
n
duction m
o
tor
Three
-
phase
i
n
duct
i
o
n m
o
t
o
r
Transfo
r
m
a
tio
n
m
a
trix
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
Recently, the safety and
reliability of electri
c m
o
tor dr
ive
syste
m
s, especially
in critical applications,
have
dra
w
n t
h
e at
t
e
nt
i
on of
m
a
ny
research
ers. Fa
ul
t
-
t
o
l
e
r
a
nt
cont
rol
st
r
a
t
e
gi
es, w
h
i
c
h aim
t
o
keep a sy
st
em
ru
n
n
i
n
g co
nt
i
n
u
o
u
sl
y
aft
e
r
faul
t
s
ha
ve
ha
ppe
ne
d,
have
becom
e
a ver
y
act
i
v
e resea
r
ch
fi
el
d.
A l
o
t
o
f
researc
h
es ha
v
e
bee
n
pu
bl
i
s
h
e
d on
t
h
e fa
ul
t
-
t
o
l
e
rant
c
o
nt
r
o
l
t
echni
que
s of el
ect
ri
cal
m
achi
n
es
[
1
]
-
[
2
0
]
.
Gen
e
rally, th
ere are three types of fau
lts in
th
ree-
p
h
ase In
ductio
n
M
o
to
r (IM
) d
r
ive
sy
st
em
s:
m
o
tor
faul
t
s
(s
uch as
ope
n-
pha
se f
a
ul
t
i
n
st
at
or wi
n
d
i
n
gs, s
h
o
r
t
-
ci
rcui
t
faul
t
i
n
st
at
or wi
n
d
i
ngs
, br
o
k
en
b
a
r(s
),
cr
ack
ed
en
d-
r
i
n
g
and
etc)
[2
]
,
[6
],
[8
],
[1
1
]-[
20
],
in
ver
t
er
f
a
ults (
s
u
c
h
as open
-
cir
c
u
it and
sh
or
t-
cir
c
u
it)
[1
] and
sens
or fa
ults (mechanical and elect
ri
cal
) [3]
.
Ope
n
-p
has
e
faul
t
i
s
one of t
h
e m
o
st
com
m
on pro
b
l
e
m
s
i
n
i
n
d
u
st
ri
al
appl
i
cat
i
ons. C
o
nv
ent
i
onal
co
nt
r
o
l
m
e
t
hods s
u
ch as Fi
el
d-
O
r
i
e
nt
ed C
o
nt
r
o
l
(FOC
) an
d
Di
rect
Tor
q
ue C
ont
ro
l
(DTC
) w
h
i
c
h
have bee
n
des
i
gne
d base
d
on healthy
m
achine m
odel canno
t b
e
d
i
rectly u
s
ed
to
co
n
t
ro
l fau
lty
mach
in
e. If con
v
e
n
tion
a
l co
ntro
ller tech
n
i
ques are applied to the fa
u
lty
m
ach
in
e,
sig
n
ifican
t
o
s
cillatio
n
s
in
th
e
m
ach
in
e torqu
e
and
sp
eed can
b
e
ob
se
rved
[1
1
]
,[12
],[15
]
-[20
]. In
case o
f
op
en
-p
h
a
se fau
l
t
for th
ree-ph
ase IM, th
e
m
o
st
co
mm
o
n
tech
n
i
q
u
e
is to
u
tilize cu
rren
t
con
t
ro
ller [6
],[11
]
,[12
],[20
]
. Howev
e
r,
u
s
ing
cu
rren
t
co
n
t
ro
ller
h
a
s
p
r
ob
lem
in
lig
h
t
lo
ad
co
nd
itio
n. Fro
m
[15
]
-[1
8
]
, it can
be seen
t
h
at b
a
sed
on
vol
t
a
ge c
ont
rol
l
er, t
w
o di
ffe
re
nt
t
r
ansf
o
r
m
a
tion m
a
t
r
i
ces
ar
e neede
d
. The
dra
w
back of
these strateg
i
es is th
at
usi
n
g t
w
o
di
ff
erent
t
r
a
n
s
f
o
r
m
a
t
i
on m
a
t
r
i
ces fo
r st
at
o
r
v
a
ri
abl
e
s i
s
not
go
o
d
f
o
r hi
g
h
pe
rf
o
r
m
a
nce cont
rol
appl
i
cat
i
o
ns as i
n
t
h
i
s
condi
t
i
on t
h
e d
r
i
v
e s
y
st
em
i
s
sensi
t
i
v
e t
o
vari
at
i
o
ns o
f
m
o
t
o
r param
e
t
e
rs. Fro
m
t
h
e
researc
h
analy
zed above
, it can be see
n
tha
t
the fault-
t
o
l
e
rant
co
nt
r
o
l
ap
pr
oac
h
es i
n
t
h
ree-
pha
se IM
dri
v
es
still re
m
a
in
s a ch
allen
g
i
ng
task
for
research
ers.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-86
94
I
J
PED
S
Vo
l.
6
,
No
.
4
,
D
ecem
b
er
2
015
:
83
1 – 841
83
2
Thi
s
pa
pe
r f
o
c
u
ses
on a
n
o
v
e
l
m
e
t
hod f
o
r
spee
d co
nt
r
o
l
of st
a
r-c
on
nect
ed t
h
ree-
pha
se
IM
u
nde
r
ope
n
-
p
h
ase
fa
ul
t
base
d
v
o
l
t
a
ge c
ont
rol
l
e
r
.
In
t
h
e
p
r
o
p
o
se
d
faul
t
-
t
o
l
e
rant
co
nt
r
o
l
sy
st
em
whi
c
h i
s
ba
sed
o
n
i
ndi
rect
r
o
t
o
r
FOC
,
a
new
t
r
ansf
o
r
m
a
ti
on
m
a
t
r
i
x
f
o
r
st
at
or
cu
rre
nt
vari
abl
e
s i
s
i
n
t
r
od
uced
a
n
d
ap
pl
i
e
d.
Th
e
con
f
i
g
urat
i
o
n
of t
h
e
use
d
Vo
l
t
a
ge So
u
r
ce I
nve
rt
er
(
V
SI
)
f
e
d t
h
ree-
p
h
ase
IM
dri
v
e
sy
st
em
du
ri
n
g
ope
n-
p
h
as
e
faul
t
i
s
sho
w
n
i
n
Fi
gu
re 1
.
D
u
ri
ng
ope
n
-
p
h
a
s
e faul
t
co
ndi
t
i
on as i
t
can be
seen fr
om
Fi
gure
1, t
h
e m
i
d-poi
nt
of
DC
-l
i
n
k
vo
l
t
a
ge sh
oul
d b
e
con
n
ect
e
d
t
o
t
h
e
neut
ral
poi
nt
o
f
t
h
e
m
achi
n
e. T
h
e
rest
o
f
t
h
i
s
pa
per i
s
or
ga
ni
zed as
f
o
l
l
o
w
s
. I
n
sect
i
on
2,
the m
a
them
atical
m
odel of three-ph
a
s
e IM
u
nde
r st
at
or wi
n
d
i
n
g o
p
en
-
pha
se faul
t
i
s
prese
n
t
e
d
.
The
pro
p
o
se
d fa
ul
t
-
t
o
l
e
ra
nt
co
nt
r
o
l
m
e
t
hod ba
s
e
d FOC
al
g
o
ri
t
h
m
for a t
h
ree
-
p
h
ase
IM is sh
own
i
n
section
3
.
In ord
e
r to v
a
li
date th
eo
ry and to
inv
e
stig
ate th
e
p
e
rform
a
nce of
the propos
ed
m
e
t
hod,
si
m
u
lat
i
on
resul
t
s
a
r
e p
r
ese
n
t
e
d
i
n
sect
i
o
n
4.
C
oncl
u
si
o
n
s a
n
d
rem
a
rkabl
e
p
o
i
n
t
s
a
r
e l
i
s
t
e
d
i
n
sect
i
on 5.
Figure
1. Fa
ulty three-phase
IM dri
v
e
2.
THREE-PHASE IM MODEL UN
DER OPEN-PHASE
FAULT
The m
odel
of
t
h
ree-
p
h
ase I
M
un
der st
at
o
r
wi
n
d
i
n
g o
p
e
n
-
p
hase fa
ul
t
can be
descri
bed
by
t
h
e
fol
l
o
wi
n
g
e
q
ua
t
i
ons
[1
8]
:
St
at
o
r
v
o
l
t
age
equ
a
t
i
o
ns:
s
rq
s
rd
sq
sd
s
sq
s
sd
sq
s
sd
s
s
sq
s
sd
i
i
dt
d
M
dt
d
M
i
i
dt
d
L
r
dt
d
L
r
v
v
0
0
0
0
(
1
)
Ro
to
r vo
ltag
e
eq
ua
tion
s
:
s
rq
s
rd
r
r
r
r
r
r
r
r
s
sq
s
sd
sq
sd
r
sq
r
sd
s
rq
s
rd
i
i
dt
d
L
r
L
L
dt
d
L
r
i
i
dt
d
M
M
M
dt
d
M
v
v
0
0
(2
)
Tor
que
e
q
u
a
t
i
o
ns:
r
r
l
e
s
rq
s
sd
sd
s
rd
s
sq
sq
e
B
dt
d
J
pole
T
T
i
i
M
i
i
M
pole
T
2
2
(3)
whe
r
e:
2
3
,
2
1
,
2
3
,
2
3
,
2
3
rm
rl
r
sm
sl
sq
sm
sl
sd
sm
sq
sm
sd
L
L
L
L
L
L
L
L
L
L
M
L
M
(4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Novel Method
of F
O
C to
Spe
e
d C
ontr
o
l in
T
h
ree
P
h
ase
IM
under
Nor
m
al
.
... (
M
ohamm
ad Jannati)
83
3
I
n
(1
)-
(4)
,
v
s
sd
,
v
s
sq
are the sta
t
or d-q a
x
es voltages,
v
s
rd
,
v
s
rq
are the rotor d-q a
x
es voltages,
i
s
sd
,
i
s
sq
are the
stator
d-q a
x
es
curre
nts,
i
s
rd
,
i
s
rq
ar
e the
rot
o
r
d
-
q a
x
es c
u
rre
nts in t
h
e statio
nary
refe
re
nce
fram
e
(su
p
e
r
scri
pt “
s
”).
r
s
an
d
r
r
are
the stator and
rotor re
sistance
s
. L
sd
,
L
sq
,
L
r
,
L
sl
,
L
sm
,
L
rl
,
L
rm
,
M
sd
and
M
sq
indicate
t
h
e st
at
or an
d r
o
t
o
r d-
q axe
s
sel
f
, m
u
tual and leakage induc
t
ances.
r
is the
m
o
tor electrical speed.
T
e
a
nd
T
l
sho
w
el
ect
rom
a
gnet
i
c
t
o
r
que
an
d l
o
ad
t
o
r
que
.
J
and
B
are t
h
e m
o
ment
of i
n
ertia
and visc
ous
friction
coefficient re
s
p
ectively.
3.
PROP
OSE
D
FOC
METH
OD
FO
R
TH
REE-PH
ASE
IM UN
DE
R OPEN
-PH
A
S
E
FA
ULT
Am
ong t
h
e v
a
r
i
ous
vect
or
bas
e
d co
nt
r
o
l
m
e
tho
d
s, F
O
C
t
echni
que i
s
m
o
re con
v
eni
e
nt
. H
o
we
ve
r, d
u
e
to the unsymmetrical structure
of
t
h
r
e
e-
ph
ase I
M
m
o
del u
n
d
e
r
o
p
e
n-
ph
ase f
a
u
lt, th
e conv
en
tional FO
C
m
e
thod ca
nnot be em
ployed for faulty
m
achine.
T
h
is
asym
m
e
try
causes
oscillations i
n
the
m
o
tor
el
ect
rom
a
gnet
i
c
t
o
rq
ue. It
i
s
pos
si
bl
e t
o
re
m
ove t
h
e asy
mmetrical
ter
m
i
n
th
e fau
lty th
ree-ph
ase IM by u
s
in
g
a su
itab
l
e t
r
an
sform
a
t
i
o
n
m
a
trix
fo
r th
e
stator curre
nt va
riabl
e
s as
follows:
cos
sin
sin
cos
e
sd
sq
e
e
sd
sq
e
e
si
M
M
M
M
T
(5)
whe
r
e,
θ
e
i
s
t
h
e an
gl
e bet
w
ee
n t
h
e
st
at
i
ona
r
y
refere
nce
fra
m
e
and t
h
e r
o
t
a
t
i
ng re
fer
e
nce
fram
e
. Usi
n
g
(5
), t
h
e
n
e
w m
a
th
e
m
at
i
cal
m
o
d
e
l for t
h
ree-ph
ase IM
u
n
d
e
r
o
p
e
n
-
phase fau
lt can be written
as
(6)-(9
):
St
at
o
r
v
o
l
t
age
equ
a
t
i
o
ns:
s
rq
s
rd
e
s
e
s
sq
sd
e
s
s
sq
s
sd
e
si
e
si
sq
s
sd
s
e
s
s
sq
s
sd
e
s
i
i
T
T
dt
d
M
dt
d
M
T
i
i
T
T
dt
d
L
r
dt
d
L
r
T
v
v
T
0
0
0
0
1
1
(6
)
Ro
to
r vo
ltag
e
eq
ua
tion
s
:
s
rq
s
rd
e
s
e
s
r
r
r
r
r
r
r
r
e
s
s
sq
s
sd
e
si
e
si
sq
sq
r
sq
r
sd
e
s
i
i
T
T
dt
d
L
r
L
L
dt
d
L
r
T
i
i
T
T
dt
d
M
M
M
dt
d
M
T
0
0
1
1
(7
)
Tor
que
e
q
u
a
t
i
o
n:
s
sq
s
sd
e
si
e
si
sd
sq
T
e
s
T
e
s
s
rq
s
rd
s
sq
s
sd
sd
sq
s
rq
s
rd
s
rq
s
sd
sd
s
rd
s
sq
sq
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
(
8
)
whe
r
e,
e
e
e
e
e
s
T
cos
sin
sin
cos
(
9
)
(6)-(8) gives,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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-86
94
I
J
PED
S
Vo
l.
6
,
No
.
4
,
D
ecem
b
er
2
015
:
83
1 – 841
83
4
St
at
o
r
v
o
l
t
age
equ
a
t
i
o
ns:
e
rq
e
rd
sq
sq
sd
sq
sq
sd
e
sq
sq
sd
e
sq
sq
sd
e
sq
e
sd
sq
sd
sq
sd
e
sq
sd
e
sq
sd
e
rq
e
rd
sq
sq
sd
sq
sq
sd
e
sq
sq
sd
e
sq
sq
sd
e
sq
e
sd
sq
sd
s
sq
sd
e
sq
sd
e
sq
sd
s
e
sq
e
sd
i
i
dt
d
M
M
M
M
M
M
M
M
M
dt
d
M
M
M
i
i
dt
d
L
L
L
L
L
L
dt
d
L
L
i
i
dt
d
M
M
M
M
M
M
M
M
M
dt
d
M
M
M
i
i
dt
d
L
L
r
L
L
L
L
dt
d
L
L
r
v
v
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
2
2
2
2
2
2
(1
0)
Ro
to
r vo
ltag
e
eq
ua
tion
s
:
e
rq
e
rd
r
r
r
r
e
r
r
e
r
r
e
sq
e
sd
sd
sd
r
e
sd
r
e
sd
i
i
dt
d
L
r
L
L
dt
d
L
r
i
i
dt
d
M
M
M
dt
d
M
0
0
(1
1)
Tor
que
e
q
u
a
t
i
o
n:
)
(
2
e
rq
e
sd
sd
e
rd
e
sq
sd
e
i
i
M
i
i
M
pole
T
(
1
2)
whe
r
e,
cos
sin
sin
cos
s
sq
s
sd
e
sd
sq
e
e
sd
sq
e
e
sq
e
sd
i
i
M
M
M
M
i
i
(13a)
s
rq
s
rd
e
sd
sq
e
e
sd
sq
e
e
rq
e
rd
i
i
M
M
M
M
i
i
cos
sin
sin
cos
(
1
3b)
In t
h
ese equati
ons
,
ω
e
is th
e an
gu
lar
v
e
lo
city o
f
t
h
e ro
tor fi
eld
-
o
r
ien
t
ed
referen
ce fram
e. Fro
m
(10
)
-
(12
)
, it can
b
e
seen
th
at t
h
e st
ato
r
v
o
ltag
e
s,
ro
tor vo
lta
g
e
s an
d th
e torq
u
e
eq
u
a
tion
s
are si
milar to
th
e h
e
alth
y
t
h
ree-
p
h
ase
IM
eq
uat
i
ons
.
Ho
weve
r, t
h
e st
at
or
v
o
l
t
a
ge e
q
u
a
t
i
on (
e
q
u
at
i
o
n
(1
0
))
has a
n
e
x
t
r
a t
e
rm
(su
p
e
r
scri
pt
“e”). Conse
q
uently, it is
pos
sible to cont
rol three-phas
e
IM by the some
m
odifica
tions in the conve
n
tional
cont
roller.
In s
u
m
m
e
ry
t
h
e com
p
ari
s
on
bet
w
ee
n heal
t
h
y
t
h
ree-p
h
ase
IM
equat
i
o
ns
and e
quat
i
o
ns
(1
0)
-(
1
2
) i
s
listed
in
Tab
l
e
1
.
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I
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PED
S
I
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:
208
8-8
6
9
4
Novel Method
of F
O
C to
Spe
e
d C
ontr
o
l in
T
h
ree
P
h
ase
IM
under
Nor
m
al
.
... (
M
ohamm
ad Jannati)
83
5
Tabl
e
1. T
h
e
C
o
m
p
ari
s
on
bet
w
een
T
h
ree
-
P
h
ase IM
E
q
uat
i
o
ns a
n
d E
quat
i
o
ns
(1
0)
-(
1
2
)
Three
-
phase IM
Equations (10)
-(
12)
Stator
voltage
equations
e
rq
e
rd
sd
sd
e
sd
e
sd
e
sq
e
sd
sd
s
sd
e
sd
e
sd
s
e
sq
e
sd
i
i
dt
d
M
M
M
dt
d
M
i
i
dt
d
L
r
L
L
dt
d
L
r
v
v
e
rq
e
rd
sq
sq
sd
sq
sq
sd
e
sq
sq
sd
e
sq
sq
sd
e
sq
e
sd
sq
sd
sq
sd
e
sq
sd
e
sq
sd
e
rq
e
rd
sq
sq
sd
sq
sq
sd
e
sq
sq
sd
e
sq
sq
sd
e
sq
e
sd
sq
sd
s
sq
sd
e
sq
sd
e
sq
sd
s
e
sq
e
sd
i
i
dt
d
M
M
M
M
M
M
M
M
M
dt
d
M
M
M
i
i
dt
d
L
L
L
L
L
L
dt
d
L
L
i
i
dt
d
M
M
M
M
M
M
M
M
M
dt
d
M
M
M
i
i
dt
d
L
L
r
L
L
L
L
dt
d
L
L
r
v
v
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
2
2
2
2
2
2
Rotor
voltage
equations
e
rq
e
rd
r
r
r
r
e
r
r
e
r
r
e
sq
e
sd
sd
sd
r
e
sd
r
e
sd
i
i
dt
d
L
r
L
L
dt
d
L
r
i
i
dt
d
M
M
M
dt
d
M
0
0
e
rq
e
rd
r
r
r
r
e
r
r
e
r
r
e
sq
e
sd
sd
sd
r
e
sd
r
e
sd
i
i
dt
d
L
r
L
L
dt
d
L
r
i
i
dt
d
M
M
M
dt
d
M
0
0
Torque
equation
)
(
2
e
rq
e
sd
sd
e
rd
e
sq
sd
e
i
i
M
i
i
M
pole
T
)
(
2
e
rq
e
sd
sd
e
rd
e
sq
sd
e
i
i
M
i
i
M
pole
T
Based
o
n
eq
u
a
tio
n
s
(10)-(12
), th
e ro
tor FOC equ
a
tio
n
s
o
f
th
ree-ph
ase IM can
b
e
written
as
(1
4)-
(15g
)
(to ob
tain
th
ese eq
u
a
tion
s
t
h
e assu
m
p
tio
n
λ
rd
e
=|
λ
r
| and
λ
rq
e
=
0
has be
en
c
o
n
s
i
d
ere
d
):
,
,
2
,
1
e
sq
d
sq
ref
sq
e
sq
e
sd
d
sd
ref
sd
e
sd
r
r
r
e
sq
sd
r
e
e
sq
r
r
sd
e
r
r
e
sd
sd
r
v
v
v
v
v
v
v
v
r
L
i
M
i
L
M
pole
T
dt
d
r
L
i
M
(14)
whe
r
e,
e
sd
r
sq
sq
sd
sq
sd
e
sd
s
ref
sd
i
dt
d
L
M
M
M
L
L
i
r
v
2
2
2
2
2
(15a)
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I
S
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:
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94
I
J
PED
S
Vo
l.
6
,
No
.
4
,
D
ecem
b
er
2
015
:
83
1 – 841
83
6
r
r
r
e
sd
sq
sq
sd
r
sq
sq
sd
e
sq
r
sq
sq
sd
sq
sd
e
d
sd
r
L
i
M
M
M
L
M
M
M
i
L
M
M
M
L
L
v
2
2
2
2
2
2
2
2
2
2
2
(15b)
e
rq
sq
sq
sd
e
e
rd
sq
sq
sd
e
sq
sq
sd
e
e
sd
sq
sd
e
sd
i
M
M
M
i
dt
d
M
M
M
i
L
L
i
dt
d
L
L
v
2
2
2
2
2
2
2
2
(15c)
e
sq
r
sq
sq
sd
sq
sd
e
sq
s
ref
sq
i
dt
d
L
M
M
M
L
L
i
r
v
2
2
2
2
2
(15d)
r
r
sq
sq
sd
e
e
sd
r
sq
sq
sd
sq
sd
e
d
sq
L
M
M
M
i
L
M
M
M
L
L
v
2
2
2
2
2
2
2
2
(15e)
e
rq
sq
sq
sd
e
rd
sq
sq
sd
e
e
sq
sq
sd
e
sd
sq
sd
e
e
sq
i
dt
d
M
M
M
i
M
M
M
i
dt
d
L
L
i
L
L
v
2
2
2
2
2
2
2
2
(15f)
e
sq
r
sd
e
sd
r
sd
r
r
e
e
e
e
e
rd
rq
e
e
rd
rq
e
e
rq
e
rd
i
L
M
i
L
M
L
M
M
M
M
i
i
1
cos
sin
sin
cos
cos
sin
sin
cos
(15g)
From
t
h
e equat
i
ons (
1
4)
-(
15
g
)
, i
t
i
s
possi
bl
e
t
o
ado
p
t
t
h
e i
n
di
rect
rot
o
r F
O
C
schem
e
for t
h
ree
-
p
h
ase
IM
u
n
d
er
o
p
en
-p
hase
faul
t
as
sh
ow
n i
n
Fi
g
u
re
2.
It
ca
n
b
e
n
o
t
e
d t
h
at
Fi
gu
re
2 ca
n
be
use
d
f
o
r
b
o
t
h
heal
t
h
y
and
fa
ul
t
y
t
h
re
e-p
h
ase
IM
. T
h
e
necessa
ry
b
l
ocks i
n
Fi
gu
re
2
w
h
i
c
h s
h
oul
d
be c
h
an
ge
d f
r
om
heal
t
h
y
m
ode
t
o
faul
t
y
m
ode are s
h
o
w
n i
n
r
e
d. T
h
ese
cha
nge
s are
gi
ve
n i
n
Tabl
e
2.
M
o
re
o
v
er,
t
h
e bl
oc
k
di
ag
r
a
m
of
Deco
u
p
l
i
n
g
C
i
rcui
t
i
n
Fi
g
u
r
e
2 i
s
s
h
ow
n i
n
F
i
gu
re
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
Novel Method
of F
O
C to
Spe
e
d C
ontr
o
l in
T
h
ree
P
h
ase
IM
under
Nor
m
al
.
... (
M
ohamm
ad Jannati)
83
7
Fi
gu
re
2.
B
l
oc
k
di
ag
ram
of i
n
di
rect
r
o
t
o
r
FO
C
of
heal
t
h
y
an
d
faul
t
y
t
h
re
e-
pha
se IM
Tabl
e
2. T
h
e
N
ecessary
C
h
a
n
ges i
n
Fi
gu
re
2
fr
om
Heal
t
h
y
M
ode
t
o
Faul
t
y
M
ode
Normal condition
F
ault
y
condition
3 to 2 transfo
rma
t
ion for the stator
currents [21]
2
3
2
3
0
2
1
2
1
1
3
2
s
T
2 to 2 transfo
rma
t
ion for the stator
currents [18]
1
1
1
1
2
2
s
T
Transform
ation
matrix fo
r the sta
t
or curre
nts [21]
e
e
e
e
e
si
T
cos
sin
sin
cos
Transform
ation
matrix fo
r the sta
t
or curre
nts
cos
sin
sin
cos
e
sd
sq
e
e
sd
sq
e
e
si
M
M
M
M
T
Stator self and
mutual inductances used in
Decoupling Circuit block [21]
sm
sm
sl
s
L
M
L
L
L
2
3
,
2
3
Stator self and
mutual i
nductances used in Decoupling
Circuit block
sq
sq
sd
sq
sd
s
M
M
M
M
L
L
L
2
,
2
2
2
Extra te
rms in th
e stator voltage e
quations
---
---
--
---
--
---
--
--
Extra te
rms in th
e stator voltage e
quations
e
rq
sq
sq
sd
e
e
rd
sq
sq
sd
e
sq
sq
sd
e
e
sd
sq
sd
e
sd
i
M
M
M
i
dt
d
M
M
M
i
L
L
i
dt
d
L
L
v
2
2
2
2
2
2
2
2
e
rq
sq
sq
sd
e
rd
sq
sq
sd
e
e
sq
sq
sd
e
sd
sq
sd
e
e
sq
i
dt
d
M
M
M
i
M
M
M
i
dt
d
L
L
i
L
L
v
2
2
2
2
2
2
2
2
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
.
4
,
D
ecem
b
er
2
015
:
83
1 – 841
83
8
Fi
gu
re
3.
B
l
oc
k
di
ag
ram
of D
ecou
p
l
i
n
g C
i
rc
ui
t
4.
SIMULATION RESULTS
To ve
ri
fy
t
h
e effect
i
v
e
n
ess o
f
t
h
e pr
o
pose
d
f
a
ul
t
-
t
o
l
e
ra
nt
co
nt
r
o
l
st
rat
e
gy
, di
ffe
re
nt
sim
u
l
a
t
i
ons usi
n
g
M
A
TLAB
(M
-
F
ile) so
ftwa
re
are ca
rried
o
u
t
.
A
star
-co
n
n
e
c
ted th
ree-
p
h
as
e IM
is
fe
d
fr
o
m
a SP
W
M
V
S
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-
pha
se fa
ul
t
de
tectio
n
.
Th
e rati
n
g
s
an
d p
a
rameters of t
h
e si
m
u
la
ted
IM are as
fo
llows:
Fi
gu
re 4 s
h
ow
s sim
u
l
a
t
i
on re
sul
t
s
of t
h
e p
r
o
pos
ed t
ech
ni
q
u
e
fo
r spee
d co
nt
r
o
l
of
heal
t
h
y
and fa
ul
t
y
three-
p
h
ase IM
in diffe
rent va
lues of re
fe
re
nce sp
eed
(i
n
th
is test fro
m
t=0
s
to
t=2
s
,
ω
ref
=5
00
RPM. Fr
om t=2
s
to
t=4
s
,
ω
re
f
=
6
00R
PM
. F
r
om
t
=
4s t
o
t
=
5s,
ω
ref
=
3
0
0
R
P
M
)
.
I
n
Fi
gu
re
4,
t
h
e t
h
re
e-ph
ase IM is
starting in
t
h
e
b
a
lan
c
ed
(h
eal
th
y) co
nd
itio
n
th
en
a ph
ase cu
t-o
f
f fau
lt o
c
cu
rred at t=1
s
. Mo
reov
er, th
e v
a
lu
e of t
h
e l
o
ad is
0.
5N
.m
(l
oad i
s
ap
pl
i
e
d f
r
om
st
art
i
n
g
)
.
It
i
s
evi
d
e
n
t
f
r
om
Fi
gu
re
4 t
h
at
usi
n
g
pr
op
ose
d
F
O
C
m
e
t
hod, t
h
e
th
ree-ph
ase IM
un
d
e
r v
a
ri
ou
s
con
d
ition
s
an
d
op
en
-ph
a
se fau
lt can
fo
llo
w t
h
e
referen
ce sp
eed
with
ou
t an
y
ove
rs
ho
ot
a
n
d
st
eady
-
st
at
e e
r
r
o
rs
. Al
s
o
,
us
i
ng
pr
o
pos
ed t
echni
que
t
h
e
m
o
t
o
r cur
r
ent
s
i
n
b
o
t
h
heal
t
h
y
an
d
fau
lty con
d
ition
s
are
sinu
so
i
d
al. It can
b
e
seen
fro
m
th
e p
r
esen
ted
sim
u
la
tio
n
resu
l
t
s th
at th
e d
y
n
a
m
i
c
perform
a
nce of the
propose
d
fault-tolera
nt c
o
ntrol drive
syste
m
is acceptable.
Fi
gu
re
5 s
h
o
w
sim
u
l
a
t
i
on res
u
l
t
s
of
t
h
e
pr
o
pos
ed
di
ve
sy
st
em
for i
n
di
rec
t
rot
o
r F
O
C
of
heal
t
h
y
a
n
d
faulty
three
-
p
h
a
se IM
in hig
h
refere
nce s
p
ee
d (
ω
re
f
=1
500
R
P
M)
. In
Fi
g
u
r
e
5
,
a ph
as
e cu
t-off
fau
lt is o
c
cu
rred
at th
e start (t=
0
s). Furth
e
rm
o
r
e, in
th
is figu
re th
e v
a
lu
e o
f
t
h
e lo
ad
is ch
ang
e
d
fro
m
0
N
.m to
0
.
5
N
.m a
t
t=2
s
.
Based
on
Figure 5, sim
u
latio
n
resu
lts
of th
e p
r
op
o
s
ed
con
t
ro
ller con
f
irm
th
at th
e in
trodu
ced
con
t
ro
ller is ab
le
to
con
t
ro
l th
e fau
lty IM correctly. Th
e
d
i
fferen
c
e b
e
t
w
een
the real a
n
d re
fere
nce s
p
ee
ds
rem
a
ins very
sm
a
ll
even
d
u
ri
n
g
o
p
en
-
phase
faul
t
.
As can
be s
een f
r
om
Fi
gu
re 5, t
h
e p
r
o
p
o
se
d m
e
t
hod
p
r
o
d
u
ces a reas
ona
bl
e
ripp
le in
th
e sp
eed
an
d
torq
ue respo
n
s
es. It
is seen
t
h
at
from
Fi
gure 5 t
h
at
t
h
e dy
nam
i
c perf
o
r
m
a
nce of t
h
e
pr
o
pose
d
st
rat
e
gy
f
o
r
vect
or
c
ont
rol
of
b
o
t
h
heal
t
h
y
an
d
fa
ul
t
y
m
achi
n
es i
s
sat
i
s
fact
o
r
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Novel Method
of F
O
C to
Spe
e
d C
ontr
o
l in
T
h
ree
P
h
ase
IM
under
Nor
m
al
.
... (
M
ohamm
ad Jannati)
83
9
Fi
gu
re
4.
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 i
n
t
h
e
di
ffe
re
nt
val
u
e
s
o
f
r
e
fe
rence
s
p
eed
,
fr
om
t
op
t
o
bottom
:
Rotor
a-axis c
u
rre
nt,
Stator a
-
ax
is cu
rren
t, Electromag
n
e
tic to
rque, Sp
eed
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
.
4
,
D
ecem
b
er
2
015
:
83
1 – 841
84
0
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 i
n
t
h
e
hi
g
h
s
p
ee
d re
fe
rence
,
f
r
o
m
t
op t
o
bot
t
o
m
:
St
at
or a
-
axi
s
c
u
r
r
ent
,
El
ect
rom
a
gnet
i
c
t
o
r
que
, S
p
ee
d,
Zo
om
of s
p
eed
5.
CO
NCL
USI
O
N
Thi
s
pape
r
pr
o
pos
es a t
ech
ni
que
f
o
r
r
o
t
o
r
fi
el
d-
ori
e
nt
e
d
c
o
nt
r
o
l
o
f
t
h
ree-
pha
se IM
dri
v
e w
h
i
c
h ca
n
b
e
u
s
ed
fo
r
bo
th
health
y
th
r
e
e-
ph
ase I
M
and
th
r
ee-ph
ase I
M
u
n
d
e
r
o
p
e
n
-
phase
f
a
u
lt.
Th
e d
e
sign
o
f
pr
opo
sed
fau
lt-to
leran
t
co
n
t
ro
l system was d
i
scu
s
sed
in
d
e
tail. It was sh
own
th
at with
so
m
e
ch
an
g
e
s o
n
th
e
con
v
e
n
t
i
onal
fi
el
d-
ori
e
nt
e
d
co
nt
r
o
l
al
go
ri
t
h
m
i
t
i
s
possi
bl
e t
o
co
nt
r
o
l
t
h
ree
-
p
h
ase IM
un
d
e
r o
p
en
-
phase
faul
t
.
Si
m
u
latio
n
resu
lts in
d
i
cate th
at th
e p
e
rfo
r
m
a
n
ce of th
e prop
o
s
ed
fau
lt-to
l
e
ran
t
con
t
ro
l syste
m
is satisf
acto
r
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.