In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
3, S
ep 2019,
pp.
1
1
8
7
~1
1
9
6
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1187-1196
1187
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Broke
n
rotor bar fault di
agnosti
c for DTC fed i
nductio
n motor
usi
n
g st
ator instantane
ous
com
p
lex apparent power envelope
signat
ur
e analysi
s
Lach
tar
Salah
1
, G
h
o
g
gal
Ad
e
l
2
,
K
o
us
s
a
K
ha
l
e
d
3
, Bou
raiou Ahmed
4
, A
t
t
oui
I
ssam
5
1,
2
LG
EB- lab
o
rat
o
ry, Dep
artm
en
t
o
f
E
l
e
ct
rical Engi
neerin
g, Uni
ve
rs
it
y
of
B
is
kra,
A
lg
eria
1,
3,
4
U
n
i
t
é d
e
recherche
en E
nergi
e
Reno
u
v
e
labl
es en
mil
i
eu
sah
arien
,
Cent
r
e de D
é
v
el
opp
em
ent
des En
ergies
Reno
uvel
a
bl
es,
A
lg
eria
3
D
e
p
a
rtm
e
n
t
o
f El
ectrical
En
g
i
n
eer
i
ng,
U
niv
e
rs
ity
o
f
B
echar,
Al
g
eria
5
Rese
arch
Cent
e
r
in Ind
ust
r
ial
Tech
no
log
i
es
CRTI,
A
lg
eria
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Dec
9
, 2
0
18
Re
vise
d F
e
b 12,
201
9
Ac
ce
p
t
ed
M
ar 2
0
,
2
019
Th
e bro
k
en
rot
or b
ar is an
un
e
xp
ec
t
e
d fau
l
t
and
a
co
m
m
on cause
o
f
i
nd
uction
m
o
t
o
r
f
a
ilu
r
es
t
h
a
t
threat
en
t
h
e
s
t
r
uc
t
u
ral
integrit
y
o
f
e
l
ectr
i
c
m
achi
n
es
.
In
th
is
p
ap
er,
a
n
e
w
app
r
oach
t
o
a
bro
k
en
r
ot
or
b
ar
d
i
a
gn
osi
s
,
wit
ho
ut
s
lip
est
i
m
a
tion
,
b
ase
d
o
n
t
h
e
en
vel
ope
o
f
t
h
e
stator
i
nstan
t
an
eous
c
om
ple
x
app
a
rent
pow
er
(
S
I
CAP
)
i
s
pro
p
o
s
ed
.
Th
e
en
v
e
lop
e
i
s
ob
tai
n
ed
f
r
om
t
he
SICAP
mo
du
la
t
i
on
a
nd
t
he
n
tra
n
sfe
rre
d
to
a
c
ompu
te
r
for
m
o
n
i
tor
ing
the
c
h
a
r
a
c
t
e
r
i
s
t
i
c
f
r
e
q
u
e
n
c
y
a
n
d
i
t
s
a
m
p
l
i
t
u
d
e
u
s
i
n
g
t
h
e
F
a
s
t
F
o
u
r
i
er
T
rans
for
m
(F
F
T
).
F
or
t
h
i
s
purp
o
s
e
,
t
h
e
wind
in
g
f
unc
t
i
o
n
a
pp
roach
(
W
F
A)
i
s
u
s
e
d
t
o
sim
u
l
a
te
t
he
b
roken
rot
o
r
bar
o
ccurren
c
e
in
a
s
qu
irrel
cage
in
d
ucti
on
motor
(S
CIM
)
f
ed
o
n
d
i
rect
t
orq
u
e
contro
l
(DTC).
T
he
o
b
t
ain
e
d
sim
u
lat
i
o
n
re
su
lts
con
f
irm
t
h
e
interest
a
n
d
e
ffi
cien
cy
o
f
t
h
e
p
r
op
os
ed
t
echn
i
q
u
e.
Eve
n
w
hen
th
e
induct
i
on
motor
is
o
pe
rating
at
t
he
n
o-
load
l
e
v
el
c
ondition
,
t
h
e
p
r
op
osed
m
e
th
od
is
a
ls
o
e
ffi
cient
t
o
d
etect
t
h
e
b
ro
ken
roto
r b
a
r
f
a
ult
a
t
l
o
w
s
l
ip
K
eyw
ord
s
:
B
r
ok
e
n
rot
o
r
ba
r
DTC
Fau
l
t
di
a
g
no
si
s
SCIM
SI
C
A
P
E
S
i
gna
t
u
re
ana
l
y
sis
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Lacht
a
r S
a
lah,
LG
EB- la
bor
at
ory,
D
epa
r
tment
o
f
E
l
e
c
t
rica
l
Eng
i
ne
eri
n
g,
University of
Biskra,
BP
145
RP
Biskr
a 07
00
0,
A
lg
eria
.
Em
ail:
l
a
chr
t
ar
sala
hba
@gm
a
i
l
.c
om
1.
I
N
TR
OD
U
C
TI
O
N
I
nduc
t
i
on
m
o
t
o
rs
a
r
e
w
ide
l
y
use
d
i
n
au
t
o
ma
ted
pro
duc
tio
n
sys
t
em
s.
M
o
s
t
o
f
t
hese
s
yst
e
m
s
r
e
qui
r
e
hi
gh
per
f
orm
a
nce
s
c
o
n
t
ro
l
t
o
m
a
i
n
t
a
i
n
a
sta
b
le
v
e
l
oc
i
t
y
in
de
pe
n
de
nt
o
f
a
ny
loa
d
d
isturba
n
ce
s
or
m
ode
l
unce
r
tai
n
t
i
e
s
.
The
S
C
I
M
h
as pro
ven
i
t
se
lf
t
h
r
ou
gh
the
suc
c
ess
t
ha
t
preva
i
l
s
i
n
t
h
e
fiel
d
o
f
s
pee
d
v
a
r
iat
i
o
n
a
n
d
thr
o
u
g
h
a
n
i
n
flu
x
o
f
re
se
arc
h
w
ork
w
h
i
c
h
is
e
xc
e
p
t
i
ona
lly
i
nte
n
de
d
[1,
2].
T
h
e
partic
ular
r
easo
n
s
for
th
is
ac
quir
e
d
co
nfi
d
enc
e
i
n
t
he
S
CI
M
a
r
e
ba
se
d
on
i
t
s
in
trin
sic
q
u
al
itie
s
s
u
ch
a
s
i
t
s
s
i
m
p
lic
i
t
y
o
f
c
o
nstr
uct
i
on,
its
me
cha
n
ic
al rob
us
tness a
nd l
o
w
purc
h
ase
an
d m
a
nufac
t
u
ri
n
g
c
os
t
s
.
Ho
we
v
e
r,
a
sy
nc
h
r
on
ou
s
ma
c
h
i
n
es
a
re
o
ft
en
s
u
b
j
ect
ed
d
u
r
i
n
g
th
ei
r
ope
rat
i
o
n
t
o
se
vera
l
stresse
s
of
di
ffe
re
nt
n
a
t
ur
es
(
exc
e
ssive
h
e
a
t
i
n
g,
m
agne
tic
w
e
a
ri
n
e
ss
ca
use
d
b
y
the
e
l
ectr
o
m
a
gne
tic
f
or
ces
a
n
d
env
i
ro
nm
en
tal
stre
sse
s
t
ha
t
the
r
o
t
o
r
m
u
st
u
n
d
er
go
d
u
r
in
g
i
t
s
u
s
u
al
u
se
).
T
he
a
c
c
u
mula
t
i
on
of
t
he
se
con
s
trai
n
t
s
ca
u
s
e
s
d
e
f
ec
ts
i
n
t
h
e
differ
e
n
t
pa
r
t
s
of
t
he
m
a
c
h
i
n
e
such
a
s
s
t
ator
s
hort-cir
cu
it
s
[3
],
e
cc
en
t
r
i
c
i
t
y
[4],
b
ro
ke
n
ro
tor
bar
[5],
w
hic
h
g
e
n
era
t
es
u
ltim
ate
l
y
s
t
o
p
s,
l
e
a
d
i
n
g
to
p
ro
du
ct
io
n
losse
s.
T
o
avo
i
d
th
e
s
e
uns
che
d
ule
d
s
hu
t
dow
ns,
t
h
e
re
se
arc
h
ers
ha
ve
s
bee
n
w
or
ki
ng
for
s
e
v
era
l
y
e
a
rs
t
o
de
ve
lo
p
ma
int
e
na
nce
te
c
h
n
i
que
s.
I
t
i
s
w
e
l
l
k
now
n
tha
t
t
he
w
i
d
es
pre
a
d
m
e
t
h
od
t
o
de
tec
t
b
roke
n
r
o
t
o
r
b
a
rs
i
s
mot
o
r
cu
rre
n
t
si
gn
at
u
r
e
ana
l
ys
is
(
M
C
S
A
),
w
hi
c
h
i
s
ba
se
d
o
n
s
i
g
n
a
l
pr
oce
s
s
i
n
g
t
o
o
l
s
s
u
ch
a
s
F
a
st
F
ourier
T
r
ansfor
ms
(
FFT).
I
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
118
7
– 1
196
1
188
depe
n
d
s
on
d
e
t
ect
i
n
g
t
h
e
s
i
d
e
ban
d
s
(
1
±2k
s
)f
(
s
is
t
he
r
ot
or
s
l
i
p,
f
i
s
the
fu
n
d
am
ent
a
l
f
r
eque
ncy
a
nd
k
=
1,
2
,
3…
)
,
in
duc
i
n
g
i
n
t
he
s
ta
t
o
r
c
u
rre
nt
s
pec
t
ru
m
pr
odu
ci
n
g
b
y
ge
om
e
t
r
i
c
a
nd
m
a
g
n
e
tic
u
nba
la
nce
s
c
a
u
se
d
b
y
bro
k
en ro
t
or b
a
r
s. There
fore
, t
h
e
s
e
si
de
ba
nd
fre
que
nc
ie
s ap
pea
r
in
g
aroun
d
t
h
e
fund
a
m
e
n
ta
l
fre
qu
e
n
c
y
a
n
d
th
e
eva
l
ua
tio
n
o
f
t
heir
a
m
p
lit
ude
s
c
a
n
be
i
den
t
ify
a
nd
use
d
a
s
a
re
l
i
a
b
l
e
a
nd
acc
urate
a
ppro
a
c
h
t
o
d
i
a
g
nos
e
roto
r
bar
fa
ults.
H
o
w
e
ver,
t
he
M
CS
A
has
so
m
e
d
raw
b
acks,
w
he
re
t
he
r
el
i
a
bi
lit
y
a
n
d
t
h
e
a
cc
u
r
ac
y
a
r
e
aff
e
c
t
ed
b
y
th
e
dia
g
no
si
s
o
f
r
o
t
or
a
s
y
mm
etrie
s
a
t
ve
ry
l
ow
s
l
i
p.
T
he
refore
,
the
s
ide
b
a
n
d
fre
que
nc
ie
s
be
com
e
q
uite
c
lo
se
t
o
the
fun
d
a
m
e
n
ta
l
fre
que
ncy
[6-
8
].
I
n
add
i
tion,
i
n
the
c
l
os
ed-
l
oo
p
drive
s
,
the
c
o
nt
r
o
l
l
er
l
oo
p
compe
n
sa
tes
the
fa
ul
t
effect
i
.
e
.
m
a
sk
t
he
f
a
u
l
t
e
ffe
c
t
[
9,
1
0].
Ther
efor
e,
u
s
i
ng
s
t
a
t
or
c
urre
nt
a
na
l
y
si
s
ca
use
s
a
d
iffic
u
lt
y
i
n
fa
ul
t de
tec
t
io
n, w
hi
c
h
m
otiv
at
e
d
re
s
e
a
rc
hers attem
p
t
e
d t
o
us
e
o
ther
quanti
t
ies for fault ana
l
ysis [11-
1
6
]
.
To
h
a
n
d
l
e
t
h
e
s
e
pro
b
lem
s
,
o
t
her
me
tho
d
s
ba
se
d
o
n
t
he
a
m
p
lit
ud
e
m
o
du
la
tio
n
of
t
h
e
t
h
r
ee
-p
has
e
st
a
t
or
c
urr
e
nt
i
nd
uc
e
d
by
a
br
oke
n
ro
tor
bar
is
u
se
d
i
n
a
i
d
o
f
d
i
ag
n
o
s
t
ic
.
In
f
ac
t,
t
he
r
o
t
o
r
f
au
lt
e
ffect
c
a
n
b
e
loca
l
i
ze
d
in t
he
s
ta
tor
curr
ent e
nve
l
ope s
pe
ct
rum
at freque
n
c
ie
s e
x
pressed
by t
h
e
com
p
on
ent
s
2ks
f [1
7
-
2
0
].
Thi
s
p
ap
e
r
a
d
d
r
e
sse
s
t
h
es
e
di
ff
i
c
ul
ti
e
s
w
i
t
h
an
i
nnov
a
t
iv
e
met
h
o
d
b
ased
o
n
the
a
m
p
l
i
t
ud
e
modu
la
ti
o
n
o
f
t
h
e
S
I
CA
P
is
t
he
s
o-
cal
le
d
en
ve
lo
pe
(
S
I
CA
P
E
)
t
o
d
et
ec
t
t
h
e
b
r
o
k
e
n
r
o
t
o
r
b
ars
f
a
ult
i
n
a
D
TC
-
fe
d
i
n
d
u
c
t
i
o
n
m
o
tor.
A
s
e
c
o
nd-
orde
r
l
o
w
-
pass
fil
t
e
r
i
s
use
d
t
o
el
i
m
i
n
at
e
t
h
e
hi
gh
f
req
u
en
c
y
g
en
era
t
ed
b
y
th
e
D
T
C
i
n
v
e
rter
.
The
F
a
st
F
ouri
e
r
Transfo
r
m
(F
F
T
)
is
a
pp
lie
d
t
o
t
h
e
fi
ltere
d
en
ve
l
o
pe
c
o
m
pone
n
t
i
n
or
der
to
extra
c
t
t
he
f
a
u
lt
inde
xes
u
s
i
n
g
the
n
o
rm
alize
d
b
a
n
d
a
m
p
l
itu
de
o
f
t
h
e
s
p
ect
rum
com
p
o
n
e
n
t
s
.
The
sim
u
l
a
tio
n
is
perform
ed
u
s
i
n
g
M
a
tla
b/S
i
m
u
l
i
nk.
T
he
o
b
t
aine
d
res
u
l
t
s
s
how
t
hat
t
h
e
p
r
o
p
o
s
e
d
m
e
t
h
o
d
i
s
a
b
l
e
t
o
d
e
t
e
c
t
t
h
e
bro
k
en
r
ot
or b
a
r
s fa
ul
t
at a
ny
load
l
e
ve
l co
n
d
i
t
ion
i
n
t
he S
CIM
drives
as well
as at ve
ry
l
o
w
slip
c
o
ndi
ti
on
.
2.
M
A
T
E
RI
AL
A
N
D
M
E
T
H
O
D
S
The
br
ok
e
n
b
a
r
f
aul
t
i
n
the
S
C
IM
i
s
m
o
dele
d
base
d
on
the
w
i
n
d
i
n
g
f
u
n
c
t
i
on
a
p
proa
c
h
W
F
A
.
A
l
l
the
space
h
arm
o
n
i
c
s
i
n
the
ma
ch
i
n
e
ar
e
take
n
i
n
t
o
a
cc
ou
n
t
.
Th
e
WF
A
approa
ch
p
red
i
c
t
s
t
h
e
perfo
r
m
a
n
ces
o
f
the
di
ffe
re
nt
ia
l
eq
ua
ti
on
s
m
ode
l.
T
his
m
o
del
re
fer
s
t
o
th
e
c
o
u
p
le
d
ma
gne
t
i
c
appr
oa
ch
by
tr
eati
n
g
t
h
e
c
u
rrent
i
n
ea
ch
r
o
t
or
b
a
r
a
s
a
n
i
n
d
e
p
e
n
d
e
nt
v
aria
ble
[2
1].
The
i
n
duc
t
i
on
m
o
t
or
m
od
el
i
s
c
onsi
d
e
r
ed
w
i
t
h
t
h
e
fo
l
l
o
w
i
n
g
si
m
p
li
fy
ing
ass
u
mpt
i
on
s [2
2].
The m
a
gne
t
i
c
circ
u
i
ts
a
re
uns
atura
t
e
d
,
The i
n
ter
-
bar
curr
ent is ne
g
le
cted,
The sk
in e
ffe
c
t
s ar
e
ne
glec
te
d
,
Th
e
ef
f
ect
of slo
t
s i
s
n
e
g
l
e
ct
ed
,
The d
i
str
i
b
u
t
i
o
n of t
he
m
a
g
n
e
tomo
t
i
ve f
orce
in t
h
e
air-ga
p
i
s s
in
uso
i
da
l.
The
rot
o
r
squir
r
e
l-ca
ge
m
odel
i
ng
is
b
ased
o
n
the
eq
ui
va
le
nt
d
ia
gra
m
o
f
(
N
r+1)
m
e
s
hes
as
s
how
n
in
Fi
g
u
r
e
1
.
E
a
c
h
mes
h
i
s
su
bs
tit
ut
e
d
b
y
a
n
e
qu
iv
al
e
n
t
ci
rc
ui
t
rep
r
e
sente
d
b
y
a
r
o
t
o
r
bar
a
nd
a
se
gme
n
t
of
e
n
d
-
rin
g
,
respec
tiv
e
l
y
u
n
d
er
r
esistive
an
d
ind
u
c
t
i
v
e
nat
u
re
(Rb,
R
e
, Lb
,
Le)
.
R
b
a
n
d
L
b,
e
p
r
ese
n
t
t
h
e
ro
t
o
r
bar
r
e
sista
n
c
e
a
nd
i
s
i
n
duc
t
a
nce
.
R
e
a
n
d
L
e
a
r
e
t
h
e
e
n
d
-
r
i
n
g
s
e
g
m
e
n
t
resista
n
ce
a
nd
its
i
n
d
u
c
t
a
n
ce.
The
rot
or
v
o
l
ta
ge
e
qua
t
i
o
n
s
of
t
he
N
r loops c
an
b
e e
xpresse
d
as foll
o
w
2
.
.
.
0
(
1
)
Whe
r
e,
ϕr,
k is the
ro
t
or
f
l
u
x
cr
ossi
ng
the
rot
o
r lo
op k.
The
d
ynam
i
c
m
a
them
at
ical
m
ode
l
o
f
t
he
i
n
duc
t
i
o
n
m
ot
or
can
b
e
w
r
it
te
n in vec
t
o
r m
a
trix a
s
V
R
.
I
(
2
)
W
h
ere
t
h
e v
o
lt
ag
e
v
e
c
t
o
r
mat
ri
x
V
is gi
ven
b
y
V
↔
…
0
(
3
)
Whe
r
e
Nr
i
s
th
e
num
ber
of r
ot
or
bar
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Broke
n
ro
to
r
b
a
r
f
a
u
lt di
a
g
n
o
s
tic
for D
T
C
f
e
d in
d
u
ct
ion
m
o
to
r
usin
g
stat
o
r
… (L
ach
t
ar S
a
l
a
h)
1
189
F
i
gure
1.
T
he
e
qu
i
v
ale
n
t c
i
r
c
u
i
t
o
f
t
he
rot
or
s
quirr
el-c
age
The
curr
ent vector m
atrix [I] is
c
om
posed
I
↔
…
(
4
)
The
g
l
o
b
a
l
r
esista
nce
m
a
trix[
R
]
i
s
give
n as
f
o
l
l
o
w
0
,
0
,
(
5
)
Whe
r
e,
[
R
s
]
is
t
he dia
g
ona
l
ma
tri
x
of
the
sta
t
o
r
resist
a
nces
p
hases o
f
(
m, m
) dim
e
ns
io
ns.
00
0
0
00
(
6
)
R
s1
,
R
s2
a
nd
R
s3
a
re the
i
de
n
t
ic
al re
s
i
s
ta
nc
es o
f stat
or pha
se
s w
i
n
d
i
ng.
The
resistance
[
R
r
] is
a
symmetric
m
a
t
r
i
x
(
Nr
+1
, N
r
+1
)
give
n a
s
⎣
⎢
⎢
⎢
⎢
⎢
⎡
00
,
,
⋮0
0
R
⋮⋮
⋮0
⋱
⋮
,
⋮0
R
,
⋮
,
,
⎦
⎥
⎥
⎥
⎥
⎥
⎤
(
7
)
Whe
r
e,
2
,
is
t
he
rot
or
b
ar resist
a
nce
and
i
s t
h
e en
d
ri
ng
resi
s
t
a
n
c
e
.
The
g
l
o
b
a
l
i
nd
uc
t
a
nce
m
a
trix
is as
f
ollow
,
,
,
(
8
)
Whe
r
e
the
in
d
u
cta
n
ce
m
atrix
is gi
ve
n by
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
118
7
– 1
196
1
190
0
(
9
)
Whe
r
e,
,
and
are
t
he ide
n
t
ica
l
p
ro
per
ind
u
c
t
a
n
ce
s of
t
he
sta
t
o
r c
o
i
l
a
nd
i
s t
h
e mu
t
u
al
ind
uc
t
a
n
c
e
of
t
he
sta
tor p
h
a
se
s.
T
he ind
u
c
tanc
e
ma
t
r
ix
i
s
a
sym
m
e
tric ma
t
rix
1
,
1
given by
⎣
⎢
⎢
⎢
⎢
⎢
⎡
…
,
⋮
⋮
⋮
⋱
⋮
⋮
,
⋮
,
,
⎦
⎥
⎥
⎥
⎥
⎥
⎤
(
10)
Whe
r
e,
2
,
i
s
th
e
ma
gnet
i
z
i
ng
ind
u
c
t
a
n
ce
o
f
eac
h
rotor
l
o
o
p
.
i
s
the
rotor
bar
leaka
g
e
in
d
u
ct
a
n
c
e
,
i
s
the
r
o
t
o
r
en
d
r
i
n
g
l
e
a
ka
ge
i
nd
uc
ta
nc
e
an
d
i
s
t
h
e
mu
t
u
al
i
nd
uc
t
a
n
c
e
b
e
t
w
ee
n
two rotor
l
o
ops
.
The
m
u
tua
l
i
nd
uc
ta
n
c
e
m
a
t
r
ix
,
betw
e
e
n
t
h
e
stat
or
w
i
n
di
n
g
s
and
r
o
tor
l
o
o
p
s
of
3
,
1
di
m
e
n
s
i
o
ns,
w
h
ic
h
si
gn
i
f
i
e
d
t
h
at
t
he
v
e
c
t
o
r
of
t
he
r
otor
c
u
r
ren
ts
c
o
m
prise
1
e
l
e
m
e
n
t
s
corr
espo
n
d
in
g
t
o
t
he n
um
ber
of
r
ot
or c
age
b
a
rs
, plus t
h
e
end-r
i
ng
l
oop
1
.
..
..
..
(
11)
The
me
chan
ica
l
rot
or
e
quat
i
o
ns
o
f
ve
l
o
ci
ty
Ω
a
n
d
po
si
t
i
on
a
r
e
r
epresented as f
o
llows
.Ω
Ω
(
12)
Whe
r
e,
i
s
t
h
e
m
o
m
e
n
t
o
f
i
n
e
r
t
i
a
,
i
s
t
he
l
o
a
d
torq
ue
a
nd
t
he
e
lectrom
a
g
n
e
tic
t
or
que
p
rod
u
c
e
d
by
th
e
mac
h
i
n
e
i
s
o
bt
ai
n
e
d
by
0
,
5
.
(
13)
I
n
o
r
d
e
r
t
o
s
i
m
u
l
a
t
e
t
h
e
b
r
o
k
e
n
rotor
bar
s
f
ailure
u
s
i
ng
M
ATLAB
s
oft
w
ar
e,
t
he
b
ro
k
e
n
bar
r
e
sista
n
ce
i
s
st
r
o
ng
ly
i
ncre
ased
by
an
a
dd
i
tio
na
l
r
e
sista
n
c
e
c
a
l
l
e
d
the
de
fec
t
r
esista
nce,
e
xpre
s
se
d
by
the
fo
l
l
o
w
in
g
m
a
tr
ix
.
⎣
⎢
⎢
⎢
⎢
⎡
00
0
…
…0
00
0
0
…0
00
0⋮
⋮0
0⋮
⋮⋮
0
0
⋮
⋮
⋮⋮
⋮
⋮
⋮
⋮
⎦
⎥
⎥
⎥
⎥
⎤
(
14)
The
re
si
s
t
an
c
e
m
a
trix
o
f
th
e
rotor
sq
u
i
r
r
el
c
a
g
e
is
c
ha
n
g
ed
t
ak
i
ng
i
n
to
a
cco
un
t
t
h
e
a
d
dit
i
on
al
d
e
f
ec
t
resistance m
atrix
,
the
n
e
w
r
e
sista
n
ce
ma
trix
is defi
n
e
d a
s
f
ol
low
(
15)
3.
DIAGNO
S
I
S
O
F
R
OT
OR FA
I
LURE IN DT
C
FED IN
DUCTION MO
TO
R
DTC
i
s
a
n
AC
d
riv
e
t
e
c
hn
olog
y
t
h
a
t
d
i
r
ec
tly
con
t
rol
s
t
h
e
t
o
r
qu
e
a
n
d
m
agn
e
ti
zi
ng
f
l
u
x
of
t
h
e
m
ot
o
r
(F
i
gur
e
2)
.
Th
is
m
eth
od
es
tim
a
t
es
t
he
m
ag
ne
tic
f
l
ux
a
nd the
mot
or
t
or
q
u
e b
y
m
easuri
n
g
the
s
u
p
p
lie
d
v
o
l
t
age
s
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Broke
n
ro
to
r
b
a
r
f
a
u
lt di
a
g
n
o
s
tic
for D
T
C
f
e
d in
d
u
ct
ion
m
o
to
r
usin
g
stat
o
r
… (L
ach
t
ar S
a
l
a
h)
1
191
and
c
u
rre
nts.
I
f
t
h
e
t
o
r
qu
e
or
f
l
u
x
f
a
ll
s
o
u
t
s
i
d
e
a
p
r
e
d
efi
n
ed
t
o
l
eran
ce
r
an
g
e
,
t
h
e
i
n
v
e
r
t
e
r
t
r
a
n
s
i
s
t
o
r
s
a
r
e
sw
it
c
h
e
d
to
the
next s
tate
so
t
h
at t
he
y
re
t
u
r
n
t
o t
h
e
range
a
s
f
a
st as possible
[
23].
3.1.
Stat
o
r f
l
u
x
b
eh
av
ior
In
t
h
e
(
α
,
β
) re
f
e
r
e
nce
,
t
he
stat
o
r
flu
x
ca
n
be
ob
ta
ine
d
b
y
th
e
fol
l
o
w
i
ng e
qu
at
io
n
̅
̅
(
16)
Whe
r
e,
i
s
t
h
e
sta
t
or
f
l
u
x vec
t
or
,
is the
in
it
ia
l sta
t
or
f
l
u
x ve
c
t
or of
a
nd,
is the
st
a
t
or resi
s
tance.
If
the v
o
lta
ge
d
ro
p due
t
o t
h
e
st
a
t
or
re
s
i
s
ta
nc
e n
e
glec
te
d,
c
an
b
e
wri
t
t
e
n
as
f
o
llo
w
̅
(
17)
F
i
gure
2.
D
TC
b
l
o
c
k
dia
gra
m
for
in
d
u
ct
ion
motor
dri
v
e.
The
e
s
tim
ated
f
l
u
x
i
s
car
ried
o
u
t
b
y
t
h
e
i
n
t
e
grat
io
n
of
t
he
s
ta
tor
vo
l
t
a
g
e.
T
he
s
e
l
ec
t
i
o
n
o
f
t
h
e
vo
l
t
age
vect
or
depe
n
d
s
o
n
the
pos
it
ion
o
f
sta
tor
fl
u
x
.
(
18)
3.2.
Tor
q
u
e
b
eh
avior
The
e
l
ec
t
r
oma
gne
t
i
c
tor
que
c
om
po
ne
nt
i
s
p
r
op
ort
i
ona
l
t
o
t
he
v
ec
t
o
r
p
r
odu
c
t
b
e
t
ween
t
he
s
t
a
to
r
and
rotor flux
an
d
. The
ele
ctrom
a
gne
t
i
c tor
que
e
q
u
a
tio
n
i
s
g
ivi
ng b
y
̅
(
19)
3.3.
S
witc
h
i
ng
s
trate
gy d
e
v
e
lop
m
en
t
Base
d
o
n
t
he
h
ys
tere
sis state
of the t
or
que
, the
f
l
u
x
an
d
the
s
w
itc
hi
n
g
s
ec
tor
of
t
he sta
tor
fl
ux, w
hic
h
is
d
e
s
i
gna
te
d
b
y
(
20)
,
the
D
T
C
a
l
go
r
i
t
h
m
(Fig
ure
2)
s
e
l
ect
s
t
h
e
su
i
t
ab
le
i
n
v
ert
e
r
v
o
ltage
v
ect
or
t
o
a
p
p
l
y
to
the
ind
u
c
t
i
o
n
motor
from
t
h
e
T
abl
e
1
.
The
ou
tpu
t
s
of
t
he
s
w
itc
h
in
g
ve
ct
ors
in
t
he
d
i
ffe
r
e
nt
s
ta
tor
flu
x
sector
s
are
pa
ra
m
e
ter
s
for
the
i
n
v
e
r
ter
sw
i
t
ch
i
ng de
v
i
c
e
s.
Where,
∠
(
20)
The
act
ive
swit
chi
n
g ve
ct
ors a
r
e
→
,
and
t
h
e zero
s
witching ve
c
tors are
,
as shown in the Table
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
118
7
– 1
196
1
192
Tab
l
e
1.
S
w
itc
hi
n
g
seq
uenc
es
of in
verte
r
vo
l
tage
v
ec
t
o
rs
Se
ct
o
r
(
S)
1
2
3
4
5
6
k
=1
k
T=
1
k
T=
0
k
T
=
-1
110
111
101
010
000
100
011
111
110
001
000
010
101
111
011
100
000
001
k
=0
k
T=
1
k
T=
0
k
T=
-
1
010
000
001
011
111
101
001
000
100
101
111
110
100
000
010
110
111
011
3.4.
D
escr
i
p
tion
o
f S
I
C
A
P
for
b
oth
h
e
alth
y
an
d
fau
l
ty cases
I
n
t
h
i
s
s
e
c
t
i
o
n
,
a
t
h
e
o
r
e
t
i
c
a
l
s
t
u
d
y
f
r
o
m
w
h
i
c
h
e
x
p
l
a
i
n
t
h
e
e
f
f
e
c
t
o
f
b
r
o
k
e
n
r
o
t
o
r
b
a
r
s
i
n
t
h
e
D
T
C
f
e
d
S
C
IM.
I
n
t
he
h
ea
lt
hy
ca
se
,
the
S
I
CA
P
E
d
e
t
erm
i
ne
d
fro
m
t
he
rms
v
a
l
ues
o
f
c
urre
n
t
a
nd
vol
ta
ge
m
ust
b
e
c
o
nst
a
nt
a
nd
c
o
n
t
a
i
n
ed
on
l
y
th
e
d
c
c
o
m
pon
e
n
t
.
T
h
e
s
e
rms
val
ues o
f
c
ur
rent
an
d
vo
l
ta
ge pro
vi
de
d by t
h
e
D
T
C
fe
d i
n
duc
t
i
o
n
m
otor
c
o
n
side
r
e
d
bala
nc
e
d
a
n
d
si
nuso
i
da
l
[2
4].
Th
e SICAPE resu
l
ting is given by
‖
̅
‖
(
21)
wher
e,
̅
√
3
.
̅
.
̅
∗
(
22)
̅
(
23)
and
̅
(
24)
Ho
we
v
e
r,
w
h
e
n
a
b
r
ok
e
n
r
otor
b
a
r
f
a
u
lt
a
pp
ears,
a
n
a
ddi
ti
on
al
r
i
p
p
l
e
com
p
o
n
e
n
t
prod
uc
es
m
ani
f
e
s
t
i
n
g
on
t
h
e
cyc
lica
l
l
y
r
e
p
e
a
ti
n
g
e
nve
l
o
pe
(
F
i
gure
5)
a
t
a
r
a
te
e
qua
l
t
o
t
w
i
c
e
t
he
s
l
i
p
freque
nc
y
2
.
The
appa
ren
t
pow
er
̅
becom
es
̅
̅
∑
̅
.c
o
s
2
π
.
(
25)
Whe
r
e,
̅
i
s
the
c
o
mpone
nt
i
n
t
h
e
hea
lth
y
c
a
se,
a
n
d
the
sec
o
n
d
t
erm
in
(
2
5
)
is
c
alled
̅
,
repr
esen
ts
t
he
add
i
tio
na
l
ri
pp
l
e
c
om
po
ne
nt
b
e
s
ide
s
t
he
d
c
com
p
one
n
t
,
w
h
ic
h
pre
se
n
t
s
the
broke
n
r
o
t
o
r
ba
r
fa
u
lt
at
t
he
di
st
urba
nce
fre
que
nc
y
[
25]
.
̅
∑
̅
.c
o
s
2π
.
0
1
̅
∑
̅
.c
o
s
2π
.
0
1
(
26)
4.
RESULT
S
A
N
D
DISCU
SSIO
N
Th
e
p
r
o
c
ed
u
r
es
f
o
r
obt
a
i
ni
ng
t
h
e
SICAPE
d
ev
ot
e
d
t
o
si
gna
t
u
re
s
a
nal
y
sis
re
veal
in
g
t
h
e
bro
k
en
r
o
t
or
bars
can
b
e
su
m
m
a
riz
e
d a
s
fol
l
o
ws:
I
n
t
he
f
ir
st
s
te
p,
a
m
odu
lat
i
o
n
o
f
t
he
s
ta
tor
appar
e
n
t
p
ow
er
i
s
n
ece
ssary
t
o
o
b
t
ai
n
t
h
e
so-
cal
le
d
enve
l
ope
(F
i
gu
r
e
3
(
a
) and
3(
b
)
).
T
his
e
n
ve
l
o
pe resu
l
t
i
n
g
fro
m
t
he m
od
u
l
at
i
o
n
o
f
t
he sta
tor
ap
pa
ren
t
pow
e
r
for
a
D
T
C
fe
d
IM
i
n
t
h
e
hea
l
t
hy
a
n
d
fa
u
lty
c
ases
w
it
h
on
e,
t
w
o
a
n
d
t
h
r
e
e
bro
k
en
b
ar
s
unde
r
d
i
ffe
r
ent
l
o
ad
con
d
i
t
i
on
s
is
s
how
n
in
t
he
o
bta
i
ne
d
resu
l
t
s
prese
n
te
d
i
n
F
igure
5
.
Th
e
se
con
d
st
e
p
,
t
h
e
id
e
n
t
i
f
i
cati
on
of
t
he
enve
l
ope
co
n
s
i
st
s
of e
x
t
r
act
i
n
g on
l
y
the
p
osi
t
i
v
e pe
a
k
of t
h
e s
ta
t
o
r
a
p
pa
rent
p
ow
e
r
(F
i
gu
re
4(a
) a
nd 4(b
)
). The
th
i
r
d
s
t
ep,
a
Low
-
Pa
ss
F
i
lter
f
o
r
the
D
T
C
fed
IM.
T
h
e
st
ator
a
p
pa
ren
t
pow
er
,
w
h
ic
h
com
p
ris
e
s
the
three-
pha
se
s
ta
t
o
r
c
u
rr
ents
(
2
2
),
w
hich
c
om
prises
a
h
igh-
fre
q
u
e
n
c
y
c
o
mp
one
nt
d
u
e
t
o
t
h
e
freq
ue
nc
y
o
f
t
he
s
pac
e
vec
t
or
m
od
u
l
a
tio
n
(S
V
M
)
of
t
he
D
TC
i
nver
t
er
.
A
s
a
g
e
n
e
r
al
r
ule,
t
he
f
u
ndam
e
n
t
a
l
f
re
q
u
enc
y
o
f
the
s
t
at
or
curr
ent
v
a
r
i
e
s
f
r
o
m
0
t
o
5
0
H
z
a
nd
t
h
e
sa
m
p
li
n
g
f
r
e
q
u
e
n
c
y
i
n
o
u
r
c
a
se
w
ent
u
p
t
o
4
kH
z,
a
c
c
ordin
g
t
o
t
h
e
hys
t
e
res
i
s
ba
n
d
s
of
f
l
u
x
a
n
d
t
o
r
q
ue
.
Th
is
S
V
M
c
om
p
o
n
en
t
is
r
e
m
o
ve
d
fr
om
t
he
s
ta
t
o
r
a
ppare
nt
p
ow
er
s
i
gna
l
by
a
s
e
c
o
nd-or
de
r
low
-
pass
fil
t
er.
A
s
a
r
e
s
ult,
t
he
e
n
v
e
l
o
p
e
is
i
s
o
l
a
te
d
from
t
he
a
ppa
rent
p
ow
er
w
i
t
hou
t
a
sign
ifica
n
t
S
V
M
c
o
mpo
n
e
n
t
.
T
here
fore,
the
fi
lte
red
e
nve
l
o
pe
o
f
the
s
t
a
t
or
a
ppa
re
nt
p
ow
er
i
s
usefu
l
a
s
an
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Broke
n
ro
to
r
b
a
r
f
a
u
lt di
a
g
n
o
s
tic
for D
T
C
f
e
d in
d
u
ct
ion
m
o
to
r
usin
g
stat
o
r
… (L
ach
t
ar S
a
l
a
h)
1
193
indicator
to
d
e
t
ect
b
roken
rotor
ba
rs
f
au
lt.
A
f
a
s
t
F
ourier
tra
nsform
(
FF
T)
i
s
a
p
p
lie
d
o
n
t
he
f
il
tere
d
e
nve
l
ope
to
d
etec
t
an
e
ven
t
ual
br
o
k
e
n
r
ot
or
b
ars
faul
t
fr
om
w
hic
h
t
he
s
l
i
p
freque
nc
i
e
s
ap
pe
ar
a
t
2
a
s
show
n
in Fig
ure
6.
(a)
(b)
F
i
gure
3.
S
I
C
A
P
a
nd its
e
n
v
el
ope
f
or
h
ea
lth
y
c
a
se (a) a
nd
f
a
u
lt
y c
a
se
(
b), unde
r d
i
ffe
r
ent
loa
d
co
n
d
i
t
i
ons
(a)
(b)
Figure
4.
S
ICA
P
E
and
i
t
s
filte
r
e
d spe
c
trum
for
hea
lth
y
case
(a)
a
nd fa
ult
y
case
(
b
),
under
d
i
f
f
e
r
ent l
o
ad
c
o
n
d
iti
o
n
s
F
i
gure
5
show
s
t
h
e
en
ve
l
o
pe
a
nd
i
t
s
fi
ltere
d
spe
c
trum
i
n
bo
t
h
h
e
a
l
t
h
y
and
fa
ult
y
c
as
es
d
iv
i
d
ed
ac
cord
in
g
t
o
t
h
e
l
oad
l
e
ve
l
c
o
nd
i
t
i
o
ns.
The
s
i
mula
t
i
on
s
h
o
w
s
cl
ear
ly
i
n
t
h
e
hea
l
t
h
y
cas
e
,
t
he
f
i
l
ter
e
d
e
nve
l
ope
is
p
r
e
sen
t
e
d
o
nl
y
the
c
o
n
t
i
n
uo
us
c
om
p
o
n
e
n
t
un
de
r
n
o
l
oa
d
a
n
d
m
e
di
u
m
l
oa
d
c
o
n
d
i
t
i
ons
(
F
i
g
u
re
5
(
a
)
and
5(d))
.
O
n
t
h
e
o
t
he
r
ha
n
d
,
in
t
he
f
au
l
t
y
ca
s
e
,
the
a
m
pl
i
t
u
d
e
m
o
d
ul
a
t
i
o
n
i
ndu
c
e
d
b
y
bro
k
e
n
ro
to
r
b
a
rs
f
aul
t
appe
ars
c
l
ea
rly
at
n
o
l
o
a
d
c
o
n
d
i
tio
n
(F
ig
ure
5(
b)
a
n
d
5
(c
))
and
the
a
mpl
i
t
ude
m
o
d
u
la
t
i
on
i
n
cre
a
sed
ca
use
d
b
y
me
dium
l
o
a
d c
o
n
d
i
t
i
on
(F
i
g
ure
5(e
)
a
nd 5(
f)).
F
i
gure
6
present
s
t
he
s
pe
c
t
ru
m
of
t
he
f
i
l
ter
e
d
S
I
CA
P
E
.
In
t
he
h
e
a
l
th
y
c
a
se,
F
i
gure
6
(
a
)
a
nd
6(
d)
show
t
ha
t
the
r
e
is
n
o
cha
r
ac
te
ristic
freq
u
e
n
cy
f
o
r
b
o
t
h
n
o
l
o
a
d
a
n
d
m
e
d
i
u
m
l
o
a
d
c
o
n
d
i
t
i
o
n
s
.
I
n
c
o
n
t
r
a
s
t
,
F
i
gure
6(b)
s
how
s
the
en
v
e
l
o
pe
F
F
T
i
s
re
vealed
c
lea
r
ly
t
he
c
har
a
c
t
eris
ti
c
fr
eque
nc
y
w
ith
a
s
l
i
g
h
t
am
plit
ud
e ind
i
ca
tin
g the
pr
esence
o
f
a broken rotor b
a
r f
a
ult
i
n sp
i
t
e of n
o-l
o
a
d
co
n
d
i
t
io
n (ver
y low
sl
i
p
). The
a
mpli
t
u
de
i
s
inc
r
ea
sed
ei
t
h
er
by
t
h
e
bro
k
e
n
r
otor
b
ar
s
nu
mbe
r
as
s
how
n
in
F
igure
6(
b)
a
nd
6(
c),
by
t
he
loa
d
r
atio
a
s sh
ow
n
in
F
igure
6(b)
and
6(e)
, or
by t
h
e
bo
t
h
t
og
e
t
her
as sho
w
n
i
n
F
i
g
u
re
6
(b)
and
6
(
f).
The
i
nves
t
iga
t
ion o
n
t
he l
ow
-
f
re
que
nc
y com
p
o
n
e
n
t
s
at
2
m
a
k
e
s
it p
o
ss
ible
t
ha
t t
h
e sam
p
li
ng r
a
te
of
t
he
f
i
l
t
e
r
ed
S
ICA
P
E
ca
n
be
d
ecim
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There
f
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ed
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.
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nste
ad
o
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e
class
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l
M
C
SA
m
e
t
ho
d
t
h
at
h
a
s
d
em
o
n
stra
ted
i
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s
ina
b
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it
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to
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e
tec
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b
r
o
ken
ro
t
o
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ba
rs
a
t
ve
ry
l
ow
s
lip,
a
n
d
fa
ils i
n de
te
ct
i
ng fa
u
l
ts o
f cl
o
s
ed
l
oo
p
ap
pl
i
c
ati
o
ns
[
6,
10].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
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e
p
2
0
1
9
:
118
7
– 1
196
1
194
(a)
(d)
(b)
(e)
(c)
(f
)
F
i
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5.
S
ICA
P
E a
nd its fil
te
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um.
N
o
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d con
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i
t
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o
n
:
a
)
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hy
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se,
b)
1
BR
B,
c
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BR
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Me
dium
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con
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on
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h
e
a
l
t
h
y c
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e
)
1
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, f) 3
BR
B
F
i
gur
e 6.
FFT of S
I
CA
PE
f
ilte
red
spectrum
. N
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d
i
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:
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alt
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ca
se,
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B
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dium
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: d)
h
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)
1
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B
, f) 3
BR
B
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Broke
n
ro
to
r
b
a
r
f
a
u
lt di
a
g
n
o
s
tic
for D
T
C
f
e
d in
d
u
ct
ion
m
o
to
r
usin
g
stat
o
r
… (L
ach
t
ar S
a
l
a
h)
1
195
5.
CONCL
U
S
ION
I
n
t
h
e
s
c
o
p
e
o
f
t
h
i
s
w
o
r
k
,
a
n
e
w
a
p
p
r
o
a
c
h
w
a
s
p
r
o
p
o
s
e
d
t
o
d
i
a
g
n
o
s
i
s
t
he
b
r
oke
n
ro
tor
b
a
rs
f
a
u
l
t
i
n
a
D
T
C-fe
d
in
du
c
tio
n
mot
o
r
usi
ng
t
h
e
s
i
g
n
a
t
ur
e
a
n
a
l
ysis
o
f
t
h
e
S
I
C
A
P
e
nve
l
o
pe
(
S
I
CA
P
E
).
T
he
p
rop
o
se
d
me
tho
d
w
as
p
erfor
m
e
d
t
o
de
te
ct
t
he
b
ro
ke
n
r
o
tor
bar
s
f
a
u
lt
f
o
r
d
i
ffe
ren
t
l
oa
d
le
ve
ls
i
n
t
h
e
S
C
IM
d
r
i
ve
s
as
w
e
ll
as
f
or
n
o-l
o
ad
c
on
d
i
t
i
o
n.
T
he
s
ys
t
e
m
m
odel
w
a
s
deve
lo
pe
d
a
n
d
i
m
p
lem
e
n
t
e
d
i
n
Ma
t
l
ab
/Sim
ul
ink
env
i
ro
nm
en
t.
T
he
s
im
ula
t
io
n
w
a
s
carried
o
ut
i
n
order
t
o
e
st
i
m
at
e
t
h
e
S
C
I
M
p
er
form
anc
e
s
unde
r
t
h
e
effect
o
f
the
bro
k
e
n
r
ot
or
b
a
r
.
Based
o
n
t
he
o
b
t
a
i
n
e
d
resul
t
s,
t
he
f
oll
o
w
i
ng
c
o
ncl
u
s
i
ons
can
b
e
dra
w
n;
f
irs
t
,
the
c
l
ose
d
-
lo
op
has
n
o
i
nflue
n
c
e
o
n
t
h
e
faul
t
in
duc
t
o
r,
d
e
s
pite the
e
lim
in
ati
o
n
of
r
i
pple
s
o
n
th
e
ou
t
put
q
u
a
nt
i
t
i
e
s
e
n
su
re
d
by
t
h
e
e
ffe
c
t
o
f
t
h
e
D
T
C
con
t
ro
l.
S
econd
,
the
pr
o
p
o
s
e
d
m
etho
d
a
l
l
ow
s
ge
nera
ti
ng
b
r
oke
n
rot
o
r
ba
rs
f
a
u
lt
signa
tur
e
s
usi
n
g
F
F
T,
a
voi
din
g
t
he
d
igi
t
a
l
me
t
h
o
d
s,
w
hic
h
r
eq
u
i
re
a
n
e
xpe
ns
ive
t
echn
o
l
o
g
y
.
Th
ird,
t
he
ana
l
yz
e
d
c
om
po
ne
nt
s
h
o
w
s
o
n
l
y
t
h
e
si
g
n
a
t
ure
s
o
f
a
bro
k
e
n
r
o
t
or
ba
r,
w
hich
m
ake
s
i
t
possi
b
l
e
t
o
a
vo
id
inc
o
rre
ct
ly
a
t
t
rib
u
te
d
to
t
he
o
t
h
e
r
s
e
l
ec
tr
ical
o
r
m
e
c
h
an
ica
l
d
e
f
e
c
t
s
(sta
t
o
r
or
e
cce
n
t
r
i
ci
ty
f
au
l
t
s)
.
F
ourth,
the
pro
pose
d
m
e
t
hod
is
a
b
l
e
to
d
e
t
e
c
t
t
he
b
r
oke
n
ro
tor
bar
at
t
he
n
o-l
o
a
d
c
o
n
d
i
tio
n
a
nd
t
h
e
char
act
er
ist
i
c
fre
que
nc
y
is
c
l
ear
l
y
v
i
s
ib
le
w
it
h
a
l
o
w
am
p
l
i
t
u
d
e.
L
a
s
tl
y,
a
f
a
u
l
t
se
v
e
rit
y
r
ati
o
i
s
defi
ned
by
t
h
e
am
p
l
i
t
u
d
e
o
f
the
c
h
ara
c
teris
tic
fre
que
nc
y
com
p
o
n
e
n
t,
w
hic
h
c
o
n
side
re
d
a
s
a
g
oo
d
i
n
d
i
c
a
t
or
o
f
t
h
e
state
o
f
t
he
S
CIM
rela
t
e
d to t
he
n
umbe
r of bro
k
e
n
rot
o
r ba
rs and l
o
a
d
l
e
v
e
l
c
ond
i
t
i
on.
REFE
RENCES
[1]
M.
Z
air
and
A.
H
azz
ab
,
“
M
RAS
S
p
eed
S
ens
o
r
l
es
s
Vect
or
C
on
tro
l
o
f
I
nd
uct
i
on
M
o
t
o
r
Dri
v
es
U
sin
g
P
redi
ctive
Adap
tat
i
o
n
M
echan
is
m
,
”
Int
e
rn
a
t
i
o
n
a
l
Jour
nal o
f
P
o
wer
Elect
r
o
ni
cs
Drive
S
y
stems
,
v
o
l
.
9,
n
o
.
4
,
pp
.
15
23
-1
53
3
,
201
8.
[2]
M.
E
s-s
aadi,
M
.
K
h
af
all
a
h,
H
.
Ch
aik
hy,
a
n
d
H
.
Ch
aikh
y,
“
Usi
ng
t
he
F
iv
e
-
Le
v
e
l
NP
C
Inv
e
rte
r
t
o
I
m
pro
v
e
th
e
FOC
Cont
rol
o
f
t
he
Asy
nch
r
on
ous
M
achi
n
e,
”
In
terna
t
i
onal
J
o
ur
nal o
f
Power
El
ectr
o
n
i
cs Dri
ve Sys
t
em
s
,
vo
l
.
9
,
no.
4
,
pp.
1
4
5
7
–14
66
, 2
01
8.
[3]
M.
D
rif
an
d
A
.
J
.
M
.
C
ardo
so,
“Stat
o
r
f
a
u
l
t
d
i
agnos
ti
cs
i
n
sq
ui
rre
l
cag
e
th
ree-p
h
a
s
e
i
nd
ucti
on
m
o
t
o
r
d
ri
ves
usin
g
t
h
e
instan
tan
e
ous
a
cti
v
e
an
d
react
iv
e
po
wer
si
gn
a
t
u
r
e
anal
yses
,”
IEEE Tr
ans
.
In
d.
In
f
o
r
m
a
tics
,
v
o
l
.
1
0
,
n
o
.
2
,
pp.
1
3
4
8
–13
60
, 2
01
4.
[
4
]
M
.
A
k
a
r
,
“
D
e
t
e
c
t
i
o
n
o
f
a
s
t
a
t
i
c
e
c
c
e
n
t
r
i
c
i
t
y
f
a
u
l
t
i
n
a
c
l
o
se
d
lo
op
d
riv
e
n
in
d
u
c
t
io
n
mo
tor
by
u
sing
t
he
a
ng
ula
r
dom
ai
n
o
r
der t
r
a
c
ki
ng
analy
s
i
s
met
ho
d,
”
Me
c
h
. S
y
st.
Sign
a
l
Proc
e
s
s
.
,
vol.
3
4
,
n
o.
1–2
,
p
p.
1
73
–1
82
,
20
13
.
[5]
R.
J
.
Ro
m
e
ro-Troncoso,
A
.
Gar
c
i
a
-Perez
,
D
.
M
orinigo-
Sot
e
lo,
O
.
Duq
u
e-Per
e
z,
R
.
A
.
O
sorn
i
o
-Rios
,
a
nd
M
.
A.
Ibarra-M
an
zano
,
“
Rotor
u
n
b
a
lance
and
brok
en
r
o
t
o
r
b
ar
d
etectio
n
i
n
inv
e
rte
r
-
f
e
d
i
nd
uc
t
i
o
n
m
o
t
o
r
s
a
t
s
ta
rt-up
a
nd
stead
y-s
t
ate
regimes
by h
i
gh
-res
o
lutio
n
spect
ral an
aly
s
is,”
Elect
r
.
P
o
wer
Syst.
Re
s.
,
vol.
1
3
3
,
pp.
14
2
–
1
4
8
,
2
01
6.
[6]
R.
P
u
c
he-P
an
a
d
ero,
M
.
Pi
ned
a
-S
an
chez,
M
.
Riera-G
u
as
p,
J
.
Ro
ger-F
o
l
ch,
E
.
H
u
r
tad
o
-P
erez,
a
nd
J
.
P
e
rez-Cru
z
,
“Im
p
rov
e
d
res
o
lu
ti
on
o
f
t
h
e
MCS
A
m
eth
od
v
i
a
Hilbert
t
r
an
s
f
o
r
m
,
enab
li
ng
th
e
di
agno
sis
of
r
o
t
or
a
sym
m
e
t
r
ies
a
t
very
l
ow
s
lip,
”
I
E
E
E
Tran
s. Ene
r
gy
Co
nv
e
r
s
.
,
vol.
2
4
,
n
o.
1
,
p
p
.
5
2
–59
,
2
00
9.
[
7
]
B
.
X
u
,
L
.
S
u
n
,
L
.
X
u
,
a
n
d
G
.
X
u
,
“
I
m
p
r
o
v
e
m
e
n
t
o
f
t
h
e
H
i
l
b
e
r
t
method
v
ia
e
spri
t
f
o
r
detecti
n
g
ro
tor
f
a
u
l
t
in
induction
motors
at
low
sli
p
,”
I
E
EE T
r
an
s.
En
e
r
gy
Co
nv
e
r
s
.
,
v
ol.
28
,
n
o.
1
,
p
p
.
225–
233
,
2
01
3.
[8]
A.
N
aha, A. K
.
Sam
an
ta, A
.
R
out
r
ay, and A. K.
Deb,
“
A
m
e
t
h
o
d
f
o
r
de
t
ecti
n
g
half
-broken
rotor
bar
in
l
i
ghtl
y
l
oaded
induction
motor
s
us
i
ng
current
,”
I
EEE Tr
ans. Instrum.
Meas
.
,
v
o
l
.
6
5
,
no
.
7,
p
p
.
1
6
1
4–1
62
5,
201
6.
[9]
T.
A
m
e
i
d
,
A.
M
en
ac
er,
H.
T
a
l
hao
u
i
,
a
n
d
I
.
Harzel
li
,
“
B
ro
ken
r
oto
r
b
ar
f
ault
di
ag
no
si
s
usin
g
f
a
st
F
ouri
e
r
transf
orm
appl
ied
t
o
f
ie
l
d
-o
rien
ted
co
ntro
l
in
du
cti
on
m
ach
i
n
e:
s
imulation
a
nd
ex
p
e
rim
e
n
t
al
s
tu
dy,
”
In
t.
J. Ad
v. M
a
n
u
f
.
Te
c
h
n
o
l.
, v
ol
.
9
2
, n
o.
1–
4
, p
p.
91
7
–
9
2
8
,
2
01
7
.
[10
]
G
.
S
i
n
gh,
C
.
A
n
i
l
K
umar,
an
d
V.
N
.
A.
N
ai
kan,
“
Effectiv
ene
s
s
o
f
Curren
t
E
nv
elo
p
e
anal
ysi
s
t
o
detect
b
rok
e
n
rot
o
r
bar
and
i
n
t
e
r
t
u
rn
f
au
lt
s
in
a
n
invert
er
f
ed
i
nd
uction
moto
r
dr
iv
e,”
Pr
oc.
20
15
IEEE
In
t.
Co
nf.
Po
wer Ad
v.
Co
n
t
ro
l
Eng.
ICPAC
E
2
0
15
,
pp
.
19
1–
194,
201
5.
[
1
1
]
T
.
W
a
n
g
,
H
.
L
i
u
,
L
.
Z
h
a
o
,
J
.
H
u
a
n
g
,
a
n
d
Z
.
H
o
u
,
“
Q
u
a
n
t
i
t
a
t
ive
bro
k
en
r
ot
or
b
ar
f
au
lt
d
e
t
ecti
on
f
o
r
closed-loo
p
cont
rolled
in
ductio
n
m
oto
r
s,
”
IET Electr
.
P
o
wer Ap
pl
.
,
vol.
1
0
,
n
o. 5
,
p
p.
403
–4
10
, 2
016
.
[12
]
Y
.
Mao
u
ch
e,
M
.
E.
K
.
Ou
maam
ar,
M.
B
o
u
cherm
a
,
and
A
.
K
hezz
a
r,
“
Instan
tan
e
ous
p
ower
s
pectrum
analy
s
i
s
f
o
r
broken
b
ar
f
ault
detect
ion
in
i
nvert
er-fed
s
i
x-p
h
ase
squirrel
c
ag
e
in
du
cti
on
m
o
t
o
r,”
Int.
J.
E
l
e
c
t
r
. Power E
n
ergy
Syst
.
,
v
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l
.
62
,
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p
. 1
10
–1
17
,
20
14
.
[1
3]
T
.
Gok
t
a
s
,
“D
isc
e
rn
in
g
br
ok
e
n
r
o
t
or
b
a
r
f
a
i
lu
re
fro
m
lo
w-
f
re
q
u
en
cy
l
o
a
d
torq
ue
o
s
c
i
l
l
a
ti
on
i
n
DTC
in
du
ctio
n
m
o
tor
driv
es,
”
201
6
.
[1
4]
Z
.
Ho
u
,
J
.
Hu
ang
,
H
.
Li
u
,
M
.
Ye,
Z.
Liu,
and
J.
Y
ang
,
“
D
i
a
g
n
o
s
is
o
f
b
r
oken
ro
to
r
bar
f
a
ul
t
i
n
o
p
e
n-
a
n
d
c
los
e
d-l
oop
cont
rolled
wy
e-c
o
nn
ected
in
duct
i
o
n
m
oto
r
s u
s
i
n
g
zero-seq
u
en
ce v
o
ltag
e
,
”
v
o
l
.
1
1
, p
p.
121
4–
12
23
, 20
1
7
.
[15]
Y
.
Grit
l
i
,
A.
O
.
Di
T
o
mmaso
,
R
.
M
iceli,
F
.
Fi
lippet
t
i,
a
nd
C
.
Ro
s
s
i,
“
Clos
ed-l
oop
ban
d
wi
d
t
h
imp
act
o
n
M
V
S
A
f
or
roto
r
b
r
ok
en
b
ar
d
iag
n
o
s
is
i
n
IRF
O
C
do
ub
le
s
qui
rrel
cag
e
i
n
d
u
ct
io
n
mo
tor
dr
iv
e
s
,”
4t
h
Int.
Conf
.
Cl
ean
Electr.
Power Renew. En
erg
y
Res
o
u
r
. Im
pa
ct,
ICCEP 201
3
,
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5
2
9
–
534,
2
01
3.
[16
]
M
.
A
k
ar
a
nd
H
.
S
.
G
ercekci
og
lu,
“
I
n
s
t
a
ntan
eou
s
p
o
w
er
f
acto
r
s
i
gn
atu
r
e
an
aly
s
is
f
or
e
fficien
t
faul
t
di
agn
o
sis
in
in
ve
rte
r
f
e
d
t
hre
e
p
h
a
s
e
d
ind
uc
ti
on
m
o
t
ors
,
”
In
t.
J.
H
y
dro
g
en
En
erg
y
, v
o
l
. 4
2,
no
.
1
2
,
p
p.
8
33
8–
83
45
, 20
1
7
.
[1
7]
A
.
M. d
a
Silva,
R
.
J.
P
ov
i
n
el
li,
a
n
d
N
. A. O
.
Demerd
ash,
“
In
duct
i
o
n
m
ach
in
e bro
k
en bar an
d
s
tat
o
r s
h
o
r
t
-
circu
i
t
f
a
ul
t
diag
no
stics
based
on
t
h
r
ee-ph
a
s
e
st
ato
r
c
urren
t
e
nv
elo
p
es
,
”
IEEE Trans. Ind.
Electr
o
n
.,
v
o
l
.
5
5
,
no
.
3,
pp.
1
3
1
0
–13
18
, 2
00
8.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
118
7
– 1
196
1
196
[18
]
I
.
O
u
ach
tou
k
,
S.
El,
S
.
Gued
ira
,
K
.
D
a
hi,
an
d
H.
M
edi
o
u
n
i
,
“
Bro
k
en
R
o
t
or
B
ar
f
au
lt
d
etect
io
n
based
o
n
S
t
at
or
Current
E
n
v
e
l
ope
s
An
aly
s
i
s
i
n
Squi
rrel
Cag
e
I
nduct
i
on
M
achi
n
e,”
pp.
2
–
7
,
201
7
.
[19
]
P
.
T
a
y
l
or,
H
.
A
rabaci
,
and
O
.
B
ilg
in,
“
A
S
im
plifi
e
d
Al
go
ri
t
h
m
to
D
etect
R
o
t
o
r
B
ar
F
aul
t
s
b
y
Usin
g
S
tat
o
r
Current
E
n
v
e
l
o
p
e
A
S
i
m
p
l
i
f
i
e
d
A
l
g
o
r
i
t
h
m
t
o
D
e
t
e
c
t
R
o
t
o
r
B
a
r
F
a
u
l
t
s
b
y
U
s
i
n
g
S
t
a
to
r
Curren
t
E
nvel
o
p
e
,”
n
o.
D
ecem
ber,
p
p
.
3
7–
41
,
20
14
.
[20
]
M
.
A
b
d
-
el-M
alek
,
A.
K
.
Abd
e
lsalam
,
and
O.
E
.
H
a
ss
an,
“
I
nd
u
ction
m
o
to
r
brok
en
r
o
t
or
b
ar
f
au
lt
l
ocat
ion
detect
ion
through
envelope
a
n
a
lysis
o
f
s
ta
rt
-up
current
u
s
i
ng
H
i
l
ber
t
t
ra
ns
f
o
rm
,
”
Me
c
h
. Sy
st. Sign
a
l
P
r
o
c
e
s
s
.,
v
o
l
.
9
3
,
p
p
.
3
32
–3
5
0
,
20
17
.
[21
]
P
.
S
h
i,
Z
.
Chen,
Y.
V
ag
apo
v
,
and
Z.
Z
o
u
ao
ui
,
“
A
n
ew
d
iag
n
o
sis
of
b
ro
ken
ro
tor
bar
f
a
u
l
t
ex
te
nt
i
n
th
re
e
ph
ase
squ
i
rrel
cage
i
nduct
i
on
m
o
t
or,
”
Me
c
h
.
S
y
st.
S
i
gn
al
Proc
e
s
s
.
,
v
ol.
42
,
n
o.
1–2
,
p
p
.
38
8–4
03
,
2
014
.
[2
2]
C
.
Kral,
F
.
P
i
r
k
e
r,
G
.
Pascol
i
,
a
nd
H
.
Kapell
e
r
,
“Ro
b
u
s
t
r
ot
or
f
au
lt
det
ectio
n
by
mean
s
o
f
t
h
e
V
ienn
a
M
oni
to
rin
g
Met
h
o
d
an
d
a
p
a
r
am
eter t
rackin
g
techn
i
q
u
e,”
I
E
EE
Trans.
Ind. Elect
ron
.,
v
o
l
. 55
, n
o. 1
2,
pp
.
4
2
2
9
–
4
2
3
7
, 2
00
8.
[23
]
A
.
Am
mar,
A
.
Bo
urek,
and
A
.
B
enak
ch
a,
“
N
onl
in
ear
S
VM
-D
T
C
f
or
i
n
d
u
c
ti
o
n
m
o
t
o
r
d
ri
ve
u
sin
g
i
np
ut-o
u
t
put
feed
back
l
i
n
eariz
at
io
n
an
d
hig
h
o
rder
s
li
di
ng m
o
d
e
c
on
trol
,
”
ISA
Tr
ans
.,
v
ol
. 67
,
p
p. 4
28
–4
42
,
2
0
17
.
[
2
4
]
L
.
C
r
i
s
t
a
l
d
i
,
A
.
M
o
n
t
i
,
a
n
d
F
.
P
o
n
c
i
,
“
T
h
r
e
e
-
p
h
a
s
e
L
o
a
d
S
i
g
n
at
ure :
a
w
a
v
e
let
-
based
app
r
o
ach
t
o
p
o
w
e
r
an
aly
s
is,”
Sixt
h Int.
W
o
r
k. Power
De
f
i
n.
Mea
s
.
un
der
No
n-S
i
n
u
s
o
id
al Con
d
.,
2
00
3
.
[25]
S
.
M
.
A
.
Cruz,
A.
S
te
f
a
ni,
F.
F
i
l
ippe
tti,
a
nd
A
.
J.
M
.
Car
dos
o,
“
A
new
m
o
d
e
l-b
a
sed
t
echn
i
qu
e
f
o
r
th
e
diag
no
sis
o
f
rotor
f
a
ults in R
F
OC ind
uction
motor
drives
,
”
IEEE
T
r
an
s
.
In
d.
Elect
ro
n
.
,
vol.
5
5
,
no
.
1
2
,
p
p
.
4218
–42
28
,
2
008
.
B
I
OGRAPHIES
O
F AUTHO
RS
L
achtar
S
a
lah
rec
e
i
v
ed
t
he
E
n
g
i
n
eer’s
d
egree
and
t
h
e
M
a
gi
st
e
r
d
egree
in
E
lect
ri
c
con
t
rol
re
sp
e
c
t
iv
e
l
y
in
2
00
3
a
n
d
20
07
fro
m
An
na
ba
U
n
i
v
e
rsity
o
f
Alg
e
ria
.
In
2
01
6
,
h
e
prepared
his
P
h
.D
.
T
h
esis
i
n
con
t
rol
and
anal
ysi
s
e
l
ectri
c
sy
stem
s
f
a
il
ure
a
t
B
i
skra
U
niversi
t
y,
A
lgeria.
H
e
j
o
i
n
ed
t
he
R
es
earch
U
ni
t
o
n
R
e
n
ewabl
e
E
n
e
rgy
in
M
id
d
l
e-S
a
h
a
ran
A
d
rar
i
n
2013.
H
i
s
c
urrent
res
earch
in
t
eres
ts
in
c
lu
de co
n
tr
ol and
a
nalysis e
l
ectric
syste
m
s
perf
o
r
m
a
nce and
f
a
il
ure,
A
d
el
G
ho
gg
al
receiv
e
d
th
e
E
n
gin
eer,
M
a
gi
ster
d
ip
lo
m
a
a
n
d
t
he
P
hD
d
eg
ree
in
e
l
ectrical
e
n
g
i
ne
e
r
ing
fro
m
t
he
U
n
i
ve
rsit
y
o
f
B
iskra
,
i
n
1
9
9
6
,
2
00
5
a
n
d
20
10
r
es
pecti
v
el
y.
H
e
is
a
n
as
sistan
t
p
r
o
f
es
so
r
wit
h
t
he
U
nivers
it
y
of
B
is
kra
s
i
n
c
e
20
05
an
d
he
i
s
a
m
e
m
b
er
i
n
th
e
LGE
B
L
a
borat
ory
.
H
is
r
esearch
i
nteres
ts
a
re
f
ocu
s
ed
o
n
elect
rical
m
a
ch
ines
d
es
ign
and
fau
lt
diag
nos
i
s
i
n
p
ow
er electroni
cs s
y
s
tem
s
and
m
achin
es.
K
ous
sa
K
hal
e
d
receiv
e
d
t
h
e
En
gi
n
eer
d
eg
ree
i
n
Elect
ronic
co
ntro
l
s
y
stem
s
i
n
2
01
0
an
d
th
e
M
a
gi
s
t
er
d
eg
ree
in
E
l
ectro
nic
c
ont
rol
sy
s
t
ems
in
2
01
3
f
r
o
m
E
co
l
e
N
a
ti
ona
l
e
P
ol
y
t
echn
i
qu
e
O
r
an,
A
l
g
e
ria.
I
n
2
018
,
h
e
p
rep
a
red
h
is
P
h.
D.
T
hes
i
s
in
c
on
tro
l
an
d
a
n
aly
s
i
s
e
lectric
sy
stem
s
f
a
ilure
a
t
Bechar
U
ni
versit
y
,
A
lgeri
a
.
H
e
jo
ine
d
t
he
R
esearch
Un
it
o
n
Renewab
l
e
En
erg
y
i
n
M
i
dd
l
e
-S
aharan
A
d
r
ar
i
n
20
14.
H
i
s
c
urrent
r
es
earch
i
n
t
erest
s
i
n
c
l
u
d
e
con
t
rol
and
anal
ysis
el
ectric
sy
s
t
ems
perf
o
r
man
ce and
f
a
il
ure,
A
h
m
e
d
Bou
r
ai
o
u
r
ecei
ved
th
e
En
gi
neer’s
d
eg
ree
in
A
ut
o
m
atic
a
n
d
the
M
a
gi
ster
d
eg
ree
in
E
l
ectri
c
cont
rol
respect
iv
ely
i
n
2
0
0
7
and
2
0
1
1
f
rom
An
nab
a
U
niv
ersi
ty
o
f
A
l
geria,
P
h
D
d
egree
f
r
om
t
he
D
epartm
en
t
of
E
l
e
c
t
ric
a
l
En
g
i
n
eerin
g,
N
ati
onal
P
o
l
y
t
e
c
hni
c
S
c
ho
ol
o
f
Oran
i
n
March
2
0
1
8
.
He
i
s
a
Research
er,
i
n
R
esearch
U
nit
on
Renew
a
bl
e
E
n
ergy
i
n
M
idd
l
e-Sa
haran
Adrar,
A
l
geri
a
(E
lectroni
c
S
y
stems
Team
,
Ph
o
t
ov
o
l
ta
ic
C
on
versi
o
n
Di
vis
i
o
n
)
.
His
current
r
es
earch
i
n
t
e
res
t
s
in
clu
d
e
an
aly
s
i
s
of
ph
o
t
ov
ol
ta
ic systems perf
o
rm
ance
an
d f
a
i
l
ure, renew
able energy
and
el
ectrical
syst
e
ms co
n
t
r
ol.
Is
sam
Atto
u
i
w
as
born
in
A
nnaba,
Alg
e
ria,
i
n
1
9
8
5
.
He
r
eceiv
e
d
th
e
eng
i
n
eer’s
d
eg
re
e,
m
a
gi
s
t
er’s
d
egree,
a
n
d
P
h
.
D.
i
n
electri
cal
e
n
g
in
eerin
g
f
r
o
m
B
ad
ji
M
ok
ht
a
r-A
nn
a
b
a
U
n
iv
ersi
ty,
A
l
geri
a
i
n
2
0
07,
200
9,
a
n
d
2
0
1
5
resp
ecti
v
ely
.
I
n
20
11,
h
e
joi
n
e
d
th
e
Res
earch
C
enter
in
In
dus
tri
a
l
Techn
o
l
o
-g
ies
/
Research
U
n
i
t
i
n
A
dv
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ced
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