Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
5, N
o
. 4
,
A
p
r
il
201
5, p
p
.
55
2
~
56
7
I
S
SN
: 208
8-8
6
9
4
5
52
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
ESPRIT Method Enhancement
f
o
r Real-ti
me Win
d
Turbine
Fault Recognition
Sa
ad
Ch
ak
ko
r, M
o
s
t
a
f
a B
a
gh
ouri
,
Ab
der
r
ahm
a
ne
H
a
jr
ao
ui
Univers
i
t
y
of
Ab
delm
alek
Es
s
aâd
i, F
a
cult
y
of S
c
i
e
nces
,
Depar
t
m
e
nt of P
h
ys
ics
,
Communication
and Detection S
y
stem
s Laborato
r
y
,
Tetou
a
n, Morocco
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 12, 2014
Rev
i
sed
Feb 3, 20
15
Accepted
Feb 20, 2015
Early
fault diag
nosis play
s
a v
e
r
y
im
portan
t
r
o
le in
th
e m
odern en
er
g
y
production
s
y
stems. The win
d
turbin
e machine r
e
quir
e
s
a regu
lar
maintenan
ce to
guarantee an
acceptab
le
lif
etime and to minimize production
loss. In order to im
plem
ent a fast, proact
ive con
d
ition m
onitorin
g
, ESPRIT-
TLS method seems the correct choice due to its robustness in improving the
frequency
and
amplitude de
tection. Never
t
heless, it has a very
complex
com
putation to
im
plem
ent
in real tim
e.
To avoid this problem, a Fast-
ESPRIT algori
t
h
m
that com
b
ine
d
the IIR b
a
nd-
pass filter
i
ng t
e
chnique
, th
e
decimation tech
nique and
the or
iginal
ESPRIT-
TLS method were emplo
y
ed
to enhanc
e extra
c
ting ac
cura
tel
y
fre
quencies and their magnitudes from the
wind stator
curr
ent. The proposed algorithm has
been
evalu
a
ted
b
y
computer
sim
u
lations with m
a
ny
fau
lt
scenar
ios. Stud
y results dem
onstrate th
e
performance of
Fast-ESPRIT allowing
fast and high resolution
harmonics
identif
ic
ation
wi
th m
i
nim
u
m
com
putation
tim
e
a
nd less m
e
m
o
r
y
cost.
Keyword:
Diagnosis
ESPRIT
Real Tim
e
Sp
ectral Esti
matio
n
W
i
nd
Tu
rb
ine
Fau
lts
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
:
Saad C
h
a
k
kor,
Uni
v
ersity of
Abdelm
alek Essaâdi,
Facu
lty of Scien
ces, Dep
a
rtmen
t
of
Ph
ysics,
Co
mm
u
n
i
catio
n
an
d Detection
System
s Labo
rat
o
ry,
Tet
oua
n,
M
o
ro
cco
Em
a
il: saad
ch
ak
kor@g
m
a
i
l
.co
m
1.
INTRODUCTION
W
i
n
d
ene
r
gy
has
becom
e
one o
f
t
h
e
p
o
p
u
l
a
r re
ne
wable
powe
rs all over t
h
e worl
d
in electricity
gene
ration capacity. W
i
nd t
u
rbi
n
es contain a com
p
lex el
ectrom
ecanical syste
m
whic
h is prone
to
defects.
Co
n
s
equ
e
n
tly, th
ere is an
i
n
crease
need t
o
im
ple
m
ent a
p
r
ed
ictiv
e mo
n
itoring
sch
e
me o
f
win
d
tu
rb
in
es,
allowing an e
a
rly detection
of elect
r
o
m
echani
cal
faul
t
s
, i
n
o
r
de
r t
o
av
o
i
d cat
ast
r
o
phi
c
dam
a
ge, t
o
reduce
main
ten
a
n
ce co
sts, to
en
su
r
e
co
n
tinu
ity o
f
p
r
od
u
c
tion
an
d to
min
i
m
i
ze d
o
wn
tim
e. I
t
mean
s th
at stoppin
g
a
wind
in
stallatio
n
fo
r
un
exp
e
cted
failures co
u
l
d
lead
t
o
e
xpe
nsi
v
e re
pai
r
. T
h
ese
faults
cause a m
o
dulation
im
pact
i
n
t
h
e
m
a
gnet
i
c
fi
el
d
of t
h
e wi
nd
ge
nerat
o
r,
w
h
ich
is characterize
d
by t
h
e appea
r
ance
of a significant
harm
onics (pe
a
ks) in the stator c
u
rrent spe
c
trum
. For th
is
reason, m
o
st
of the r
ecent researche
s
ha
ve
been
orie
nted t
h
eir i
n
terest towa
rd
electri
cal
m
o
n
ito
ring
, with
focu
s
on freque
ncy analysis of
stato
r
cu
rr
en
t (CSA
).
Thi
s
t
ech
ni
q
u
e
i
s
m
o
re p
r
act
i
cal
and l
e
ss c
o
st
l
y
[1]
-
[
4]
.
Furt
herm
ore,
wi
t
h
rece
nt
di
gi
t
a
l
si
gnal
pr
ocess
o
r
(DS
P
) t
ech
n
o
l
ogy
de
vel
o
pm
ent
s
, m
o
t
o
r and ge
nerat
o
r fa
ul
t
di
agn
o
si
s can n
o
w be
d
one i
n
real
-t
i
m
e [1]
.
ESPR
IT i
s
o
n
e
hi
g
h
re
sol
u
t
i
on
o
r
s
ubs
pac
e
m
e
t
hod
(
H
R
M
) w
h
i
c
h i
s
wi
del
y
ad
o
p
t
e
d i
n
el
ect
r
o
m
e
chani
c
a
l
machine dia
g
nosis. It ca
n be
use
d
for s
p
ectral estim
a
tion
[3
],
[5
]-
[6
].
Th
is alg
o
r
ith
m
al
l
o
w
s
v
e
r
y
h
i
gh
sp
ectr
a
l
det
ect
i
on acc
ur
acy
and a
hi
g
h
resi
st
ance t
o
n
o
i
s
e com
p
are
d
t
o
ot
he
rs m
e
t
hods
l
i
k
e M
U
S
I
C
and R
oot
-M
USIC
.
Co
n
t
rariwise, it requ
ire long
co
m
p
u
t
atio
n
time to
find
m
o
re frequ
e
n
c
y esti
m
a
tes wh
en th
e au
t
o
correl
a
tio
n
m
a
t
r
i
x
i
s
l
a
rge and t
h
e o
r
de
r o
f
sam
p
l
e
d dat
a
di
m
e
nsi
on
in
crease. Th
is fact
m
a
k
e
s its ap
p
licatio
n
in
real ti
m
e
det
ect
i
on
ve
ry
l
i
m
i
t
e
d des
p
i
t
e
i
t
s
hi
g
h
preci
s
i
on.
T
h
i
s
article p
r
esen
ts
an
amelio
rated
v
e
rsio
n
of ESPRIT-TLS
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
ESPR
IT
Method E
n
hance
m
ent for Re
al-time
Wind
Tu
rb
i
n
e
Fau
lt Recogn
itio
n
(
S
aad
Chakko
r)
55
3
m
e
thod for fa
s
t
wind turbine
faults
detection a
nd
diagnosis
based on a
band pass filtering techni
que. The
propose
d
im
provem
e
nt allows
m
a
ny
advant
ages: reduction of com
putati
on tim
e
, saving of m
e
m
o
ry space and
accuracy i
n
cre
a
se in a
specified fr
eque
ncy
bandwidth. T
h
e pa
per is
orga
nized a
s
follows: t
h
e
proble
m
is
fo
rm
ul
at
ed i
n
sect
i
on 2, t
h
e s
t
at
or cur
r
e
n
t
si
gnal
i
s
pr
ese
n
t
e
d i
n
sect
i
on 3
,
and t
h
e
n
sect
i
on 4 de
scri
bes
wi
nd
tu
rb
in
e fau
lt m
o
d
e
ls. W
h
ile
sectio
n5
fo
cuses
on
ESPRIT
m
e
th
o
d
th
eo
ry, sectio
n6
ex
p
l
ains
in
d
e
tails
th
e
pr
o
pose
d
a
p
pr
oach
t
o
en
ha
nc
e o
r
i
g
i
n
al
ESP
R
IT al
g
o
r
i
t
h
m
.
Si
m
u
l
a
t
i
on re
sul
t
s
are
p
r
ese
n
t
e
d
an
d
di
scu
ssed
i
n
Sectio
n
7
.
Fin
a
lly, co
n
c
lusions with fu
ture
wo
rk
are
d
r
awn
i
n
th
e last sectio
n.
2.
RELATED WORK
M
a
ny
researc
h
st
udi
es a
ppl
y
i
ng e
n
hance
d
a
nd a
d
vance
d
s
i
gnal
p
r
ocessi
ng t
e
c
hni
que
s
have
bee
n
u
s
ed
in th
e mo
tor an
d g
e
n
e
rato
r stat
o
r
curren
t t
o
m
oni
t
o
r a
n
d
t
o
di
a
g
n
o
se
pr
os
pective electrom
echanical
faul
t
s
. T
h
e cl
assi
cal
m
e
t
hods
l
i
k
e peri
o
d
o
g
r
am
and i
t
s
ext
e
nsi
o
ns w
h
i
c
h a
r
e eval
uat
e
d t
h
ro
u
gh a Fast
F
o
u
r
i
e
r
Transfo
r
m
(FFT) are no
t a con
s
isten
t
estim
a
t
o
r
o
f
th
e
PSD beca
use its
va
riance
does
not tend t
o
ze
ro
as the
d
a
ta len
g
t
h
tend
s to
in
fi
n
ity. Desp
ite th
is drawb
a
ck
, th
e
period
og
ram
h
a
s b
een
u
s
ed
exten
s
iv
ely for failu
re
d
e
tectio
n
in
resear
ch
wo
rk
s [
4
],
[6
].
Th
e (
FFT)
do
es
no
t g
i
v
e
an
y in
form
at
io
n
on
th
e ti
m
e
a
t
wh
ich
a
fre
que
ncy
c
o
m
ponent
occu
rs. T
h
er
ef
ore
,
t
h
e Sh
o
r
t
Ti
m
e
Fo
uri
e
r Tra
n
sf
orm
app
r
o
a
ch (
S
TFT
)
i
s
use
d
t
o
rem
ove t
h
i
s
s
h
o
r
t
c
om
i
ng.
A
di
sad
v
a
n
t
a
ge
of t
h
i
s
approach is the i
n
c
r
eased
sam
p
li
n
g
tim
e fo
r a g
ood
fre
que
ncy
res
o
l
u
t
i
on [
7
]
.
The
di
scri
m
i
nat
i
on of t
h
e f
r
e
q
u
e
ncy
com
pone
nt
s cont
ai
ned
wi
t
h
i
n
t
h
e si
g
n
al
, i
s
l
i
m
i
t
e
d by
t
h
e l
e
ngt
h
of t
h
e wi
n
d
o
w
rel
a
t
i
v
e t
o
t
h
e d
u
rat
i
on
of t
h
e si
g
n
a
l
[8]
.
To
ove
rc
om
e t
h
i
s
probl
em
, i
n
[9
] and
in [10
]
Discrete
Wav
e
let Tran
sfo
r
m
(DWT) is
u
s
ed
to
d
i
agn
o
s
e fai
l
u
r
es und
er tran
sien
t con
d
ition
s
for
w
i
nd
en
erg
y
co
nv
er
sion
syst
e
m
s b
y
an
alyzin
g fr
equ
e
n
c
ie
s
with
d
i
fferen
t reso
l
u
tio
ns
. This m
e
th
o
d
facil
itates
signal inte
rp
re
tation beca
use
it oper
a
tes w
ith all info
rm
ation c
ontaine
d in t
h
e sig
n
a
l
by
tim
e
-freq
u
enc
y
redi
st
ri
but
i
o
n.
One l
i
m
i
t
a
t
i
on of t
h
i
s
t
ech
ni
que t
h
at
i
t
gi
ves a
go
o
d
t
i
m
e resol
u
t
i
o
n
and
p
o
o
r
fre
que
nc
y
resol
u
t
i
on at
h
i
gh f
r
eq
ue
nci
e
s, and i
t
pr
ovi
des a go
o
d
fre
que
ncy
res
o
l
u
t
i
on an
d p
o
o
r
t
i
m
e resol
u
t
i
on
at
l
o
w
fre
que
ncies [4], [11]. Recently, high re
sol
u
tion m
e
thods (HRM) are applied to
detect m
o
re frequenci
es with
l
o
w S
N
R
.
I
n
fa
ct
, M
U
SIC
an
d
ESPR
IT t
ech
n
i
ques
wi
t
h
i
t
s
zoom
i
ng ext
e
ns
i
ons are c
o
nj
u
g
a
t
e
d t
o
im
pro
v
e
t
h
e
i
d
ent
i
f
i
cat
i
on
o
f
a l
a
rge
num
ber o
f
fre
q
u
enci
es i
n
a gi
ve
n ra
nge
[1
2]
, [
1
3]
. In
[1
4]
a com
p
arat
i
v
e pe
rf
or
m
a
nce
anal
y
s
i
s
o
f
(H
R
M
) i
s
m
a
de.
Thi
s
st
udy
has
dem
onst
r
at
e
d
t
h
at
ESPR
IT
m
e
t
hod
has
a
hi
g
h
acc
ura
c
y
whi
c
h
exceeds all other algorithm
s
even
w
ith the
existence
of a
n
annoying
noi
se. More
ove
r, these algorithm
s
are
base
d
on
an
ei
gena
nal
y
si
s
of
t
h
e a
u
t
o
c
o
rrel
a
t
i
on m
a
t
r
i
x
o
f
a si
g
n
al
c
o
r
r
u
pt
ed
by
n
o
i
s
e.
Thi
s
dec
o
m
posi
t
i
on
r
e
qu
ir
es a long co
m
p
u
t
atio
n ti
m
e
m
a
in
ly w
h
en
th
e size
o
f
th
e au
to
co
rr
elatio
n
m
a
tr
ix
and th
e
n
u
m
b
e
r
of d
a
ta
sam
p
les increase. In [15] a ra
nk
re
duc
ed
ESPRIT techn
i
que is p
r
o
p
o
s
ed
t
o
tran
sfo
r
m
it
in
to
sim
p
lified
lo
w-
co
m
p
lex
ity al
g
o
rith
m
.
Howev
e
r, th
is m
e
t
h
od
presen
t
s
per
f
o
r
m
a
nce
d
e
t
e
ri
ora
tion
m
a
in
ly with
t
h
e SNR
d
ecreasi
n
g
and
lowers
h
a
rm
o
n
i
c a
m
p
litu
d
e
s. M
o
reo
v
e
r, it h
a
s no
t fo
cused
o
n
t
h
e
m
i
n
i
mizatio
n
o
f
the
com
put
at
i
onal
t
i
m
e
execut
i
on
fo
r real
a
ppl
i
cat
i
o
ns. T
h
i
s
w
o
r
k
p
r
o
pos
es a sol
u
t
i
on t
o
o
v
erc
o
m
e
t
h
e
co
m
p
lex
ity co
st o
f
ESPR
IT-TLS in th
e
pu
rpo
s
e
o
f
its u
s
e in
a
real tim
e win
d
t
u
rb
in
e m
o
n
ito
ri
n
g
.
3.
STATO
R
CU
RRE
NT MO
DEL
Th
e
p
o
ssib
ility o
f
d
e
tectin
g fau
lts i
n
electrical in
du
ction
m
ach
in
es h
a
s b
e
en
ex
ten
s
i
v
ely stu
d
i
ed
u
s
ing
v
i
bratio
n
surv
eillan
ce. Howev
e
r,
th
e reliab
ility
o
f
the resu
lts of th
i
s
techn
i
qu
e is
stron
g
l
y
d
e
p
e
nd
ing
o
n
the accelerom
e
t
ers position
placed in thes
e
machines acc
ordi
ng to t
h
e
ve
rtical
, axial a
n
d
radial a
x
es.
This is
in
fact t
h
e m
a
i
n
d
r
awb
ack of
th
is techn
i
qu
e
o
f
v
i
b
r
ation
.
In add
itio
n, it may also
b
e
affected
b
y
th
e sp
eed
of
t
h
e m
achi
n
e,
especi
al
l
y
whe
n
t
h
e
m
echani
cal
com
pone
nt
s are
dam
a
ged
.
T
h
erea
ft
er,
t
h
ese
pr
oce
d
ur
es ar
e
expe
nsi
v
e bec
a
use t
h
ey
req
u
i
r
e ad
di
t
i
onal
t
r
ansd
uce
r
s.
Their use m
a
k
e
s sense only in the case of large
m
achi
n
es o
r
h
i
ghl
y
cri
t
i
cal
appl
i
cat
i
o
ns.
N
e
vert
hel
e
ss, m
oni
t
o
ri
n
g
of st
at
or c
u
r
r
ent
l
i
nes a
ppea
r
s t
o
be t
h
e
m
o
st interesting a
n
d m
o
st attractive m
ode t
o
support
fa
ult rec
o
ngnition
because the
st
ator c
u
rre
nt is ve
ry
accessible and
it can be
m
eas
ure
d
directly. In addition,
it can be use
d
to
diagnose
m
ech
anical and electrical
defects. T
h
is
offe
rs a cost effective and acc
eptable alte
rna
t
i
v
e based
o
n
t
h
e C
S
A t
e
c
hni
que
. I
n
fact
, t
o
bui
l
d
a
correct detection
of the wi
nd turbine
fault m
odulations a
nd signatures in th
e stator current, it is necessary to
construct a c
o
m
p
lex signal associated
with
the real one. T
h
is
anal
y
t
i
cal
si
gnal
m
odel
de
scri
bes
preci
se
l
y
t
h
e
beha
vi
o
r
an
d t
h
e ev
ol
ut
i
o
n o
f
t
h
e real
stator curre
n
t. It contains rele
vant
fau
lt in
fo
rm
at
io
n
.
For these
reasons
it is o
f
ten
u
s
ed
fo
r co
mman
d
pu
rpo
s
es. Th
e stud
ied
wi
nd
g
e
n
e
rat
o
r st
ato
r
curren
t
will b
e
d
e
n
o
t
ed
b
y
th
e
discrete signal
i
[
n
]. T
h
is signal is consi
d
ere
d
as a
sum
of
L
com
p
lex sinusoi
d
s a
n
d whi
t
e noise. It is
obtaine
d
by
sam
p
l
i
ng t
h
e cont
i
n
uo
us t
i
m
e current
eve
r
y
T
s
=1/F
s
sec
o
n
d
s. T
h
e i
n
du
ct
i
on ge
nerat
o
r
st
at
or cur
r
ent
i
[
n
] in
prese
n
ce
of m
e
chanical a
n
d/or electri
cal
faul
t
s
has
a
dat
a
m
odel
w
h
i
c
h
can
be e
x
p
r
esse
d a
s
f
o
l
l
o
ws
[
1
0]
:
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S
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:
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J
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S
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l. 5
,
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. 4
,
Ap
r
il 2
015
:
55
2
–
56
7
55
4
2.
.
1
k
k
s
f
L
jn
F
k
k
in
I
e
b
n
(1
)
Whe
r
e
i
[
n
]
cor
r
esp
o
nds t
o
t
h
e
nt
h st
at
or c
u
r
r
e
nt
sam
p
l
e
wi
th n=
0,
1, 2
...
N
s
-1
.
I
k
,
f
k
, a
nd
φ
k
are the am
plitude
,
the freque
ncy
and th
e
phase
of the
k
th
c
o
m
p
l
e
x si
nus
oi
d
(ha
r
m
oni
c c
o
m
pone
nt
s)
re
spect
i
v
el
y
,
b
[
n
] is a
gau
ssi
an whi
t
e
noi
se.
F
s
i
s
t
h
e sam
p
l
i
ng f
r
e
que
ncy
an
d
N
s
i
s
t
h
e num
ber
of
dat
a
sam
p
les.
L
re
prese
n
t
s
the
num
ber of
rese
arche
d
harm
on
i
c
s.
4.
WIND T
URB
INE FAULT
MODELS
The wi
nd m
achine is suscept
i
ble to dive
rse
electro
-m
echanical anom
alie
s that involve
m
o
stly five
com
pone
nts: the stator, the rotor, the bea
r
ings
, gea
r
box
and/
or the air gap (ecce
nt
ricity) [16]. These
defects
require a
pre
d
i
c
tive recognition t
o
ave
r
t any
side effect provoking a
brea
kd
own
or a fatal
spo
ilag
e
. Becau
s
e it
co
n
t
ains th
e t
o
tally relev
a
n
t
fau
lt info
rm
a
tio
n
,
t
h
e st
ator curre
nt s
p
ec
trum
is
examined to
withdraw the
si
deba
n
d
f
r
e
q
uency
c
o
m
p
o
n
ent
s
i
n
se
rt
ed
by
t
h
e
fa
ul
t
.
These
fa
ul
t
fre
que
nci
e
s a
r
e l
o
cat
ed
ar
o
u
n
d
t
h
e
fu
n
d
am
ent
a
l
line f
r
eq
ue
ncy
and a
r
e cal
l
e
d l
o
we
r si
de
ba
nd
and
u
ppe
r si
d
e
ban
d
c
o
m
pon
ent
s
. T
h
i
s
det
e
ct
i
o
n
tech
n
i
qu
e is
used
in co
llaboratio
n with
one b
it v
i
b
r
ation sen
s
o
r
s fo
r an
early id
en
tifyin
g
o
f
pro
s
pectiv
e
electro
m
ech
an
ical failu
res which
can
o
c
cu
rs in
an
y ti
m
e
.
A syn
o
p
s
is of
wind
tu
rb
in
e fau
lts an
d
th
ei
r related
fre
que
nci
e
s
fo
r
m
ul
as are pres
ent
e
d i
n
Ta
bl
e
1.
Tabl
e 1. W
i
nd
Tu
rbi
n
es Faul
t
s
Si
g
n
at
u
r
es
Failur
e
Har
m
onic
Fr
equencies
Par
a
m
e
ter
s
Br
oken r
o
tor
bar
s
(b
rb
)
0
1
br
b
s
f
fk
s
P
1
,
3
,
5
,
...
k
Bearing
dam
a
ge
(
bng)
0,
bn
g
i
o
f
fk
f
1
,
3
,
5
,
...
k
,
0.4
0.6
br
io
br
nf
f
nf
Misalign
m
ent
(
mi
s
)
0
mi
s
r
f
fk
f
1
,
3
,
5
,
...
k
Air
gap
eccentricit
y
(ecc)
0
1
1
ecc
s
ff
m
P
1
,
2,
3
,
...
m
Whe
r
e
f
0
is th
e electrical su
pply fre
quenc
y
,
s
is
th
e p
e
r-un
it slip
,
P
i
s
t
h
e num
ber o
f
pol
es
,
f
r
is
t
h
e ro
t
o
r
fre
que
ncy
,
n
b
is th
e b
e
aring
balls n
u
m
b
e
r,
f
i,o
i
s
t
h
e i
nne
r a
nd t
h
e o
u
t
e
r
fr
eque
nci
e
s
depe
ndi
ng
o
n
t
h
e
b
eari
n
g
characte
r
istics, and
m, k
∈
ar
e th
e h
a
r
m
o
n
i
c f
r
e
qu
en
cy ind
e
x [4
],
[
9
]-[
10
].
Slip
s
i
s
def
i
ned
a
s
:
s
r
s
s
(2
)
0
120
s
f
P
(3
)
ω
s
i
s
t
h
e
ge
ner
a
t
o
r sy
nch
r
on
o
u
s s
p
ee
d,
ω
r
is the
relative m
echanical
speed of t
h
e
generator,
These
ha
rm
onics are e
x
tensively used as
di
agnostic m
easures in t
h
e CSA
approach.
5.
ESPRIT MET
HOD
THEORY
High res
o
lution m
e
thods are
recen
tly use
d
for fa
ult diagnosis
. T
h
ey can detect a
nd i
d
entify the
faulty ele
m
ent
base
d on its fre
que
ncy. T
h
e most accurate
and efficie
n
t technique is ESPRIT whic
h bel
o
ngs to
the subspace
param
e
tric spectrum
estim
a
tion
m
e
thods. It
is base
d on eigenvector dec
o
m
position
whic
h aim
s
to separate the
obs
ervation s
p
ace in a signal subspace
, co
ntaining only
us
eful
inform
at
ion, and its orthogonal
com
p
le
m
e
nt, called noise s
u
bspace.
The
rotational inva
ria
n
ce betwee
n both subs
paces allows
e
x
tracti
n
g
of
t
h
e pa
ram
e
t
e
rs of
spect
ral
co
m
ponent
s
pre
s
ent
wi
t
h
i
n
t
h
e i
nve
st
i
g
at
ed
wa
vef
o
rm
[1
7]
,
[1
8]
, [
2
0]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
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8-8
6
9
4
ESPR
IT
Method E
n
hance
m
ent for Re
al-time
Wind
Tu
rb
i
n
e
Fau
lt Recogn
itio
n
(
S
aad
Chakko
r)
55
5
5.
1.
Autoc
o
rrelation Matri
x
Estimation
B
a
sed
on t
h
e
st
at
or c
u
r
r
ent
m
odel
defi
ne
d
by
t
h
e E
q
uat
i
on
(
1
),
t
h
e a
u
t
o
co
rrel
a
t
i
o
n m
a
t
r
i
x
can
be
th
en
esti
m
a
ted
as fo
llo
w [19
]
:
2
..
.
.
HH
is
b
b
RE
i
n
i
n
R
R
S
P
S
I
(4
)
It
i
s
com
posed
by
t
h
e s
u
m
of si
gnal
a
nd
noise autoc
o
rrelation m
a
trices. Whe
r
e
H
is th
e Herm
itian
tran
spo
s
e,
σ
b
²
is the variance of the
whit
e noise,
I
is th
e id
en
tity
matri
x
o
f
size (
N
s
x
N
s
) and
P
is th
e p
o
wer m
a
trix
o
f
th
e
harm
oni
cs:
22
2
12
L
Pd
i
a
g
I
I
I
(5
)
(6
)
S
i
s
t
h
e
Van
d
er
m
onde m
a
t
r
i
x
defi
ned
by
:
1
iL
Ss
s
s
(7
)
2.
4
.
2.
1
.
1
kk
k
s
ss
s
T
ff
f
jj
j
N
FF
F
k
Se
e
e
(8
)
The
fi
ni
t
e
dat
a
l
e
ngt
h
of
t
h
e
si
gnal
m
a
kes t
h
e c
o
m
put
at
i
on
of t
h
e a
u
t
o
c
o
r
r
el
at
i
on m
a
t
r
i
x
R
i
in
accurate.
For
real purpose, this m
a
trix is unknown a
nd it
m
u
st be singul
ar. F
o
r e
ffective detection, it is necessa
ry to
reduce
th
e statistical flu
c
tu
ation
s
presen
t in estimatin
g
t
h
e au
toco
rrelatio
n m
a
trix
b
y
th
e averag
i
n
g [7
],
[19
]
.
In
ad
d
ition
,
th
e accu
racy of ESPRIT d
e
p
e
n
d
s
o
n
th
e
d
i
m
e
n
s
i
o
n
(
M
≤
N
s
) o
f
R
i
. It is p
o
ssible to
esti
mate
i
t
fro
m
t
h
e acq
ui
re
d
da
t
a
sam
p
l
e
s by
t
h
e
fol
l
o
wi
n
g
re
l
a
t
i
onshi
p [
7
]
,
[1
9]
:
1
ˆ
.
1
H
i
s
R
DD
NM
(9
)
Whe
r
e
M
is th
e d
a
ta m
a
trix
ord
e
r and
D
is
a H
a
nk
el d
a
ta
matr
ix
d
e
f
i
ned
by:
0
11
s
s
ii
N
M
D
iM
i
N
(1
0)
The di
m
e
nsi
o
n
of
R
i
s
h
o
u
l
d
b
e
hi
g
h
e
n
ou
g
h
t
o
ha
ve m
o
re e
i
gen
v
al
ues
f
o
r
noi
se
space
an
d s
h
o
u
l
d
b
e
lo
w eno
ugh
to
min
i
mize th
e co
m
p
u
t
a
tion time cost.
Whe
n
t
h
e
value
of
M
decrease
s
below
N
s
/3, it can
be seen
the increa
se of the
fre
quenc
y
de
t
ect
i
on e
r
r
o
r
.
C
o
nt
ra
ri
wi
se, i
f
M
i
n
cre
a
ses bey
o
nd
N
s
/2
, calcu
lation ti
m
e
increases
. So,
there is a
tra
d
e-
of
f fo
r th
e
rig
h
t
ch
o
i
ce of
M
. Em
p
i
rically, th
e
v
a
lu
e
of
M
is
cho
s
en to
b
e
bo
u
nde
d a
s
s
h
ow
n i
n
(1
0)
t
o
gi
ve a
g
o
o
d
pe
rf
orm
a
nce:
32
s
s
NN
M
(1
1)
In th
is
p
a
p
e
r, th
e au
to
co
rrelatio
n
m
a
trix
d
i
men
s
ion
M
is taken
r
oun
d
e
d
dow
n as
f
o
llow
s
:
1
ˆ
2
s
N
M
R
ound
(1
2)
Evide
n
tly,
the num
ber of fre
quencies
L
i
s
n
o
t
a pri
o
ri
kn
o
w
n. T
h
e
fre
q
u
en
cy
si
gnal
di
m
e
nsi
o
n
or
der
(FS
D
O
)
L
m
u
st
t
o
be
est
i
m
ated
by
t
h
e
m
i
nim
i
zat
i
on of
a c
o
st
f
u
nct
i
o
n
MD
L
(
k
)
nam
e
d
m
i
nim
u
m
descri
pt
i
o
n
l
e
ngt
h
.
I
n
or
de
r t
o
obt
ai
n a
r
o
bust
est
i
m
at
e,
(M
DL
) cri
t
e
ri
o
n
i
s
use
d
as s
h
ow
n i
n
t
h
e f
o
l
l
o
wi
ng
f
o
rm
ul
a [1
8]
fo
r
k=
1,
2
,
…,
L
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
55
2
–
56
7
55
6
1
1
1
1
(
)
lo
g
2
lo
g
(
)
1
2
Lk
L
Lk
i
ik
L
i
ik
MD
L
k
k
L
k
Lk
(1
3)
2
s
NL
(1
4)
Whe
r
e
λ
i
are eig
e
nv
alu
e
s au
t
o
correlation
matrix
R
i
.
Analytically, the
estimate
of
L
can then be
expre
s
sed
in
th
e fo
rm
:
ˆ
arg
m
i
n
k
L
MDL
k
(1
5)
Ho
we
ver
,
ES
P
R
IT
per
f
o
r
m
a
nces are c
o
m
p
l
e
t
e
l
y
degra
d
e
d
by
ch
o
o
si
n
g
a
wr
on
g
FS
DO
v
a
l
u
e.
5.
2.
Eigendec
o
mposition
of autocorrelation m
a
tri
x
The ei
ge
ndec
o
m
posi
t
i
on of t
h
e aut
o
c
o
rrel
a
t
i
on m
a
t
r
i
x
R
i
i
s
gi
ve
n by
expl
oi
t
i
ng t
h
e
ei
gen
v
al
ues
{
λ
1
,
λ
2
,…,
λ
M
}
and their corre
sponding si
gna
l eigenvectors
{
v
1
, v
2
,…, v
M
} [17]:
1
..
.
.
s
sb
N
H
HH
ik
k
k
s
s
s
b
b
b
k
RR
Rv
v
U
E
U
U
E
U
(1
6)
Whe
r
e:
11
,
s
Ls
L
U
v
v
E
di
ag
(1
7)
2
1
,
ss
bL
N
b
b
N
L
Uv
v
E
I
(1
8)
U
s
re
prese
n
ts
the eige
nvectors m
a
trix
of t
h
e si
gnal
spac
e related to t
h
e
L
larg
est eig
e
nv
alu
e
s
arra
nge
d
i
n
de
scen
di
n
g
or
der
.
Whe
r
eas,
U
b
represen
ts
th
e eig
e
nv
ectors matrix
of
t
h
e
noi
se
space
rel
a
t
e
d t
o
th
e
N
s
-L
eige
nvectors that, ideally, have ei
ge
nvalue
s equal to the varia
n
ce noise
σ
b
²
. Diago
n
a
l m
a
tr
ices
E
S
and
E
b
c
ont
ai
n ei
gen
v
al
ues
λ
i
cor
r
es
po
n
d
i
n
g t
o
ei
ge
nve
ct
or
s
v
i
.
5.
3.
Frequenc
y Es
timation
ESPRIT
m
e
th
od is base
d
on the study
of t
h
e signal s
u
bs
pace
E
s
. It
u
s
es so
m
e
ro
tation
a
l inv
a
rian
ce
p
r
op
erties fo
und
ed
n
a
turally in
th
e case
of ex
pon
en
tial.
A
d
eco
m
p
o
s
ition o
f
t
h
e m
a
trix
S in
to
two
m
a
t
r
ices S
1
and S
2
is co
n
s
i
d
ered
as fo
llows:
12
12
2.
2.
2.
1
2
2.
1
.
2.
1
.
2.
1
.
11
1
L
ss
s
L
ss
s
ss
s
ff
f
jj
j
FF
F
ff
f
jN
jN
j
N
FF
F
ee
e
S
S
S
ee
e
(1
9)
S
1
re
pre
s
ents
the
first
N
s
-1
rows
o
f
th
e m
a
trix
S
S
2
rep
r
esen
ts th
e last
N
s
-1
rows
o
f
th
e m
a
trix
S
The
rotational
inva
riance
bet
w
een both s
u
bspaces lea
d
s t
o
the e
quati
on:
12
SS
(2
0)
Th
e m
a
trix
Φ
c
ont
ai
n
s
al
l
i
n
fo
rm
ati
ons a
b
out
L
c
o
m
pone
nt
s
fre
q
u
e
n
ci
es.
N
e
vert
hel
e
ss, t
h
e est
i
m
a
t
e
d
matrices
S
ca
n
contain errors
.
Therea
fter, the
ESPR
IT-T
LS
(t
o
t
al least-sq
uares) algo
rith
m
find
s t
h
e m
a
trix
Φ
by
m
i
nim
i
zat
i
o
n
of
m
a
t
r
i
x
err
o
r
gi
ven
by
[2
0
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
ESPR
IT
Method E
n
hance
m
ent for Re
al-time
Wind
Tu
rb
i
n
e
Fau
lt Recogn
itio
n
(
S
aad
Chakko
r)
55
7
1
2
2.
2.
2.
00
00
00
s
s
L
s
f
j
F
f
j
F
f
j
F
e
e
e
(2
1)
Th
e
d
e
term
in
atio
n
of th
is m
a
trix
can lead to
ob
tain
th
e freq
uen
c
y estim
a
t
es d
e
fi
n
e
d b
y
t
h
is fo
rm
u
l
a:
,
,1
,
2
,
.
.
.
,
2
kk
ks
Ar
g
f
Fk
L
(2
2)
5.
4.
Harm
onics Powers
Estimation
Once t
h
e sear
ched
fre
q
u
enci
es com
pone
nt
s
of t
h
e
si
g
n
al
are est
i
m
a
t
e
d by
ESPR
I
T
, t
h
e val
u
es
o
f
t
h
ei
r am
pl
i
t
udes and t
h
en t
h
ei
r po
we
rs can
be est
i
m
a
t
e
d. B
y
usi
ng t
h
e e
i
gen
d
ecom
posi
t
i
on o
f
t
h
e s
u
b
s
pac
e
si
gnal
[1
7]
, [1
9
]
:
2
1
..
.
.
L
H
H
s
kb
k
k
k
R
SP
S
v
v
(2
3)
It is ass
u
m
e
d that the ei
ge
nve
ctors
of the
signal s
ubs
pace a
r
e norm
alized as follows:
.1
H
kk
vv
(2
4)
Thus, for
k
=
1, 2,…
,
L
:
..
ik
k
k
R
vv
(2
5)
Mu
ltip
lyin
g
b
o
th
sid
e
s of t
h
is
eq
u
a
tion
b
y
v
k
H
:
..
.
.
HH
ki
k
k
k
k
vR
v
v
v
(2
6)
A
ccord
ing
to (4
),
(11
)
and
(
2
1
)
:
2
1
..
.
.
.
L
HH
H
ki
k
k
k
k
k
b
k
k
k
vR
v
v
P
s
s
I
v
(2
7)
Th
is eq
u
a
ti
o
n
can
b
e
sim
p
lified
as fo
llo
ws:
2
2
1
..
L
H
kk
k
k
b
k
Ps
v
(2
8)
Using
t
h
e fo
llowing
eq
u
a
tion
:
2
2
2
.
k
jf
H
kk
k
sv
Q
e
(2
9)
Equ
a
tio
n
(2
2) can
b
e
written
in
th
e fo
llo
wi
ng
ex
pressi
o
n
:
2
2
2
1
.
k
L
jf
kk
k
b
k
PQ
e
(3
0)
Th
is equ
a
tio
n
is a set
o
f
L
lin
ear equ
a
tion
s
with a
n
u
m
b
e
r
L
of
un
kno
wn
h
a
r
m
o
n
i
cs po
w
e
r
s
.
I
t
is
very
easy
t
o
e
x
t
r
act
t
h
e
harm
oni
cs
po
wer
s
ve
ct
or
P
fro
m
th
e equ
a
tio
n (25
)
b
y
sim
p
le reso
l
u
tio
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
55
2
–
56
7
55
8
6.
IMPROVED ESPRIT MET
HOD
Th
e
d
i
scr
i
m
i
n
a
tio
n
o
f
all small a
m
p
litu
d
e
fr
equ
e
n
c
y co
m
p
on
en
ts ar
ound
f
0
by
ES
PR
I
T
m
e
t
hod i
s
d
i
fficu
lt. Th
is
is
m
a
in
ly
d
u
e
to
th
e sig
n
i
fican
t co
m
p
u
t
atio
n ti
me elap
sed
b
y
th
is alg
o
rith
m
to
fin
d
h
a
rm
o
n
i
c
si
deba
n
d
com
p
o
n
e
n
t
s
cor
r
e
c
t
l
y
. Furt
herm
ore
,
ESPR
I
T
calculation cost increases
when the size
of the
au
to
co
rrelatio
n
m
a
trix
an
d
the n
u
m
b
e
r of data sa
m
p
les increase. It de
pe
nds
on the com
p
lexity of
N
s
3
. This
delay form
s a major
drawbac
k
that ca
n ca
us
e a catastro
p
h
i
c evo
l
u
tion
of
a wind
turb
in
e
fau
lt wh
ich m
a
y lead
t
o
g
r
eat
est
dam
a
ges.
In
o
r
de
r t
o
ap
pl
y
a p
r
oa
ct
i
v
e, r
o
b
u
st
a
nd
real
t
i
m
e wind t
u
r
b
i
n
e c
o
n
d
i
t
i
on m
oni
t
o
ri
ng
, an
i
m
p
r
ov
ed v
e
rsi
o
n of ESPRIT
alg
o
rith
m
en
tit
led
Fast-E
SPR
IT
was
u
s
ed
.
Th
e am
elio
rated
alg
o
rith
m
is b
a
sed
o
n
bo
th a
b
a
n
d
-p
ass IIR
filterin
g
and
d
ecimati
o
n
tech
n
i
q
u
e in
the fau
lt freq
u
e
n
c
y
b
a
ndwid
th [
f
l
,
f
h
],
wh
er
e
f
l
,
f
h
are th
e lo
w
cu
t-o
f
f and
h
i
gh
cu
t-off
freq
u
en
cy of th
e
b
a
n
d
-p
ass filter.
Th
is process prov
id
es a
rem
a
rk
ab
l
e
redu
ction
in
co
m
p
u
t
atio
n
time an
d
in
d
a
ta
m
e
m
o
ry siz
e
. Th
e
d
ecim
a
tio
n
fact
o
r
u
s
ed
in
th
is
research
i
s
co
m
p
u
t
ed
with resp
ect to
t
h
e
Nyqu
ist criteri
a as fo
llows
[21
]
:
00
00
95
24
95
500
61
2
Ny
qu
ist
s
h
N
y
qui
s
t
s
h
F
F
if
f
H
z
ff
F
F
if
H
z
f
H
z
ff
(3
1)
Fi
gu
re 1 s
h
ow
s t
h
e bl
oc
k
di
agram
schem
e
of
di
ffe
re
nt
st
ages t
h
at
Fast
-ESPR
IT al
g
o
r
i
t
h
m
m
u
st
ex
ecu
tes to
i
d
en
tify th
e
fau
lt
h
a
rm
o
n
i
c freq
uen
c
ies an
d th
ei
r
p
o
wers.
Fi
gu
re
1.
B
l
oc
k
di
ag
ram
schem
e
of t
h
e Fast
-
E
SPR
IT
alg
o
rith
m
Three Phase
Stator
Current
Sa
m
p
ling with
F
s
for
N
s
data points
Co
m
putation of the cur
r
e
nt space vector
i
d
by
(
31
)
i
1
(t)
i
2
(t)
i
3
(t)
i
1
[n]
i
2
[n]
i
3
[n]
i
d
[n]
E
s
tim
a
tion of
R
i
by (
8
)
and eigendeco
m
position to obtain
λ
i
and
v
i
Fr
equency
esti
m
a
tes
f
k
Powers
esti
m
a
tes
P
k
IIR Pass
-band filtering of bandwidt
h
f
BW
=[
f
l
,
f
h
]
Decim
a
tion of
i
df
[n
]
by
the factor
Г
i
d
f
[n]
Application of E
SPRI
T
on deci
m
a
ted
signal with
N
s
/
Г
d
a
ta sa
m
p
les
i
d
fr
[n]
E
s
tim
a
tion of
L
by (
14)
and calculation of
Г
by
(
30)
i
d
[n]
λ
i
i
d
[n]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
ESPR
IT
Method E
n
hance
m
ent for Re
al-time
Wind
Tu
rb
i
n
e
Fau
lt Recogn
itio
n
(
S
aad
Chakko
r)
55
9
Fi
gu
re 2 sh
o
w
s t
h
e vari
at
i
on
of
Г
accordi
n
g to
f
h
. The dec
i
m
a
ti
on fact
o
r
d
ecrease
s
with the increase
of
t
h
e m
a
xim
u
m
har
m
oni
cs f
r
e
que
ncy
det
ect
ed i
n
t
h
e
si
g
n
al
.
Fi
gu
re
2.
E
vol
ut
i
o
n
o
f
deci
m
a
t
i
on
fact
o
r
wi
t
h
faul
t
fre
que
ncy
In th
e
first time, th
e ac
quire
d
sequences
i
1,2,3
[
n
]
of the t
h
ree
phase stator c
u
rrent
sam
p
led at the
fre
que
ncy
F
s
, a
r
e
used to calc
u
late the stator
cu
rrent
space
vector as
follows [22]:
2
2
12
3
3
..
,
3
j
d
ia
i
a
i
ia
e
(3
2)
Whe
r
e
a
,
a
2
are the s
p
atial operat
ors
.
T
h
is
vector allows
a fa
ult diagnos
i
s on
all phase
stator curre
nt
instea
d
of e
x
am
i
n
i
ng faul
t
si
gn
at
ure
on eac
h o
n
es.
W
i
t
h
t
h
i
s
m
e
tho
d
com
put
at
i
on t
i
m
e wi
ll
be
m
i
nim
i
zed. I
n
t
h
e
secon
d
step
, an
estim
at
io
n
of th
e au
to
correlatio
n
m
a
trix
R
i
is realized
and the
r
efore
the eige
nvalues
λ
i
are
extracted t
o
estim
a
te the number
of re
searc
h
ed ha
rm
onics
L
in the stator
current
signal
with res
p
ect to
MDL
criterion seen
in (14).
T
h
e
n
,
the signal sequence
i
d
[
n
] is
filtered
v
i
a a recu
rsi
v
e In
fi
n
i
te Im
p
u
l
se Resp
on
se
(IIR)
d
i
g
ital b
a
n
d
-p
ass
filter based
o
n
a least
sq
uares
fit in
t
h
e freq
u
e
n
c
y ran
g
e
[
f
l
,
f
h
] cha
r
acterizing the
fault.
Th
is filter h
a
s a flat resp
on
se
in
th
e d
e
sired
b
a
ndwid
th
an
d
its u
s
e is j
u
stified
b
y
th
e fact th
at it wil
l
b
e
h
e
lp
fu
l
to
ex
tract j
u
st th
e in
form
atio
n
s
con
t
ain
e
d
in
th
e si
g
n
a
l wh
ich
are usefu
l
in
th
e fau
lt reco
gn
itio
n
wh
ich
can
occurs at a
n
y
tim
e
. In the
thir
d stage
,
the
receive
d se
quence
of
the st
ator c
u
rre
n
t s
p
ace
vector
i
df
[
n
] is
deci
m
a
t
e
d by
a fact
or
Г
sh
own
in
(30
)
. In
add
itio
n
,
t
h
e app
l
ied
d
ecim
a
tio
n
u
s
es low-p
a
ss
filter to
en
su
re
an
ti-
al
i
a
si
ng. T
h
e
m
o
ti
vat
i
on
fo
r
t
h
i
s
deci
m
a
t
i
on
i
s
t
o
red
u
c
e
t
h
e co
st
p
r
o
cessi
ng
an
d m
e
m
o
ry
re
qui
red
fo
r a
ch
eap
er im
p
l
e
m
en
tatio
n
.
Finally, th
e ESPRIT algo
rith
m
is
ap
p
lied
on
th
e d
ecim
a
ted
sign
al sequ
en
ce hav
i
ng
N
s
/
Г
dat
a
sam
p
l
e
s t
o
i
d
e
n
t
i
f
y
al
l
fre
que
ncy
com
pone
nt
s a
n
d t
h
ei
r
po
wer
s
cont
ai
ne
d i
n
t
h
e si
g
n
al
.
7.
SIM
U
LATI
O
N
RESULTS
AN
D A
NAL
Y
S
IS
The
de
vel
o
ped
ap
pr
oac
h
see
n
i
n
t
h
e
pre
v
i
o
u
s
sect
i
o
n
has
b
een a
p
pl
i
e
d a
n
d si
m
u
l
a
t
e
d u
n
d
er
di
ffe
rent
scenari
o
s of
wind
tu
rb
in
e
fau
l
t
t
y
pes sho
w
n i
n
Tabl
e
1. T
o
eval
uat
e
i
t
s
perf
orm
a
nce i
n
real
t
i
m
e
faul
t
d
e
tectio
n, Fast
-ESPR
IT algorith
m
h
a
s b
e
en in
teg
r
ated
with
a
fau
lt d
i
agn
o
s
is
con
t
ro
ller wh
ich coo
r
d
i
n
a
tes
wi
t
h
vi
brat
i
o
n
sens
ors l
o
cal
i
zed i
n
s
p
eci
fi
c wi
n
d
t
u
r
b
i
n
e
m
echani
cal
co
m
ponent
s t
o
m
oni
t
o
r vi
brat
i
o
n l
e
vel
s
.
The controller decides a
nd cl
assifies the existence of
a fa
u
l
t
depen
d
i
n
g o
n
vi
b
r
a
tion m
e
asurem
ents collected
by the sens
ors and t
h
e ha
rm
onic fre
quencies
with thei
r p
o
w
ers est
i
m
a
t
e
d by
t
h
e Fast
-ESP
R
I
T m
e
t
hod
. F
i
gu
re
2
illu
strates the ex
p
l
ai
n
e
d
tech
n
i
q
u
e
. Besides, th
e ap
p
lie
d d
i
agn
o
sis algo
rith
m
is b
a
sed
on
th
e
u
s
e
of a fau
l
t
fre
que
ncy
ba
n
d
swi
t
c
hi
n
g
w
h
i
c
h swee
ps a
n
y
pr
os
pect
i
v
e
faul
t
s
t
h
at
m
a
y
occur an
d
sub
s
eq
ue
nt
l
y
cl
assi
fy
them
by
type according to t
h
eir freq
ue
nci
e
s. Thus, t
h
e diagnosis is
made
by the int
e
rvals
of the s
p
ectrum
reflecting the signature of a possible
de
fa
ult [23], [25]. Thi
s
m
eans that
the Fast ESPRIT
m
e
thod will not be
ap
p
lied to th
e
en
tire sign
al
bu
t on
ly on
a
p
a
rt th
at co
n
t
ains th
e targ
et inform
at
io
n
to
be
e
x
tracted for analysis.
In case
of fa
ult detection, a
syste
m
alar
m is trigge
red
t
o
alert m
o
n
ito
ring
and
m
a
in
ten
a
n
ce staff
fo
r an
em
ergency
i
n
t
e
rve
n
t
i
o
n re
pai
r
. Thi
s
p
r
oce
d
ur
e pr
o
v
i
d
es
m
a
ny b
e
n
e
fits b
ecau
s
e it allo
ws h
i
g
h
reco
gn
izing and
cl
assi
fi
cat
i
on
o
f
fa
ul
t
s
wi
t
h
e
c
on
om
i
c
and r
eal
t
i
m
e
im
p
l
em
ent
a
t
i
on [
2
4]
. C
o
m
put
er si
m
u
l
a
t
i
ons are
r
eal
i
zed
in
Matlab
for a fau
lty wind
turb
i
n
e
g
e
n
e
rator u
s
i
n
g 2 p
a
ir po
les,
4kW
/
5
0Hz, 230
/40
0
V.
0
10
0
20
0
300
400
50
0
1.
5
2
2.
5
3
3.
5
4
4.
5
5
5.
5
H
i
gh c
u
t
-
of
f
f
r
eq
uenc
y
[
H
z
]
D
e
ci
m
a
t
i
o
n
F
a
ct
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
55
2
–
56
7
56
0
Fig
u
re
3
.
In
tellig
en
t wi
n
d
turb
in
e
fau
lts d
i
ag
no
sis
b
y
Fast-ES
P
RIT
The i
n
duct
i
o
n
gene
rat
o
r st
at
o
r
cur
r
e
n
t
,
i
s
si
m
u
l
a
t
e
d by
usi
ng t
h
e si
gnal
m
odel
descri
b
e
d i
n
(
1
) f
o
r
t
h
e di
ffe
rent
fa
i
l
u
re
ki
n
d
s
des
c
ri
be
d i
n
Ta
bl
e 1.
T
h
e
param
e
t
e
rs o
f
t
h
e si
m
u
l
a
t
i
ons
are i
l
l
ust
r
at
ed
i
n
Tab
l
e 2.
Tab
l
e
2
.
Parameters u
s
ed
in
th
e sim
u
latio
n
s
Para
m
e
ter
Value
s 0,
033
P 2
f
0
50 Hz
f
r
29,
01 Hz
n
b
12
N
s
1024
F
s
1000 Hz
Fundam
e
ntal Stato
r
Cur
r
e
nt
Am
plitude
10 A
Co
m
putation Pr
ocessor
I
n
tel Cor
e
2 Duo T6570
2,
1 GHz
To si
m
p
l
i
f
y
t
h
e sim
u
l
a
t
i
on,
a si
ngl
e
pha
se
of t
h
e ge
ne
ra
t
o
r st
at
o
r
cu
rr
ent
has
bee
n
s
t
udi
ed
. T
h
e
po
we
r
of eac
h
faul
t
i
s
cal
c
u
l
a
t
e
d
base
d
on
i
t
s
am
pl
it
ude as
f
o
l
l
o
w
s
:
10
10
lo
g
2
k
k
I
P
(3
3)
Before ex
am
in
in
g
th
e stat
o
r
cu
rren
t si
g
n
a
l, it
m
u
st b
e
filt
ered
t
o
ob
tain
in
th
e ou
tpu
t
a co
m
p
o
s
ite
sig
n
a
l
h
a
v
i
ng
a to
tally n
e
g
lig
i
b
le no
ise co
m
p
ared to
t
h
e fund
am
en
tal an
d
i
t
s h
a
rm
o
n
i
cs.
P
k
Gearbo
x
Sa
m
p
ling with
F
s
fo
r
N
s
da
ta
poin
t
s
C
o
m
puta
tion of
the
dire
c
t
c
o
m
pone
nt
I
d
i
1
(t)
i
2
(t)
i
3
(t)
i
1
[n]
i
2
[n]
i
3
[n]
V
i
b
r
a
ti
o
n
se
n
so
r
s
Cur
r
e
nt/Voltage sensor
s
i
d
[n]
Fast-ESPR
IT
with
r
e
duced co
m
putation
ti
m
e
Vibr
ation level
f
k
Fa
ul
ts
diagn
o
sis
contr
o
lle
r
No fault
Switching of fault
bandwidth
f
BW
i
=[
f
li
,
f
hi
]
+
Start Al
ar
m
s
y
ste
m
and
classif
y
detected f
a
ult
Fault detect
ed
Generator
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
ESPR
IT
Method E
n
hance
m
ent for Re
al-time
Wind
Tu
rb
i
n
e
Fau
lt Recogn
itio
n
(
S
aad
Chakko
r)
56
1
7.
1.
Air Gap Ecce
ntricity De
tection
Table 4 shows
the sim
u
lation results
for ide
n
tifying
wi
nd turbi
n
e ge
ne
rator ai
r ga
p ecce
nt
ricity fault
sig
n
a
t
u
re in
the g
o
a
l to
co
mp
are th
e
perform
a
nce of the origi
n
al ES
PRIT-TLS with th
e p
r
opo
sed Fast-
ESPR
IT
. T
h
e
h
a
rm
oni
cs cha
r
a
c
t
e
ri
zi
ng t
h
i
s
f
a
ul
t
are
gi
ve
n
by
Ta
bl
e 3
.
Table
3.
Air gap ecce
ntricity fault
param
e
ters
f
ecc
(Hz
)
I
ecc
(A
)
P
ecc
(d
B)
N
h
SNR (dB)
25.
825
74.
175
0.
4
0.
3
-
10.
97
-
13.
46
3
80
Thi
s
e
xpe
ri
m
e
nt
wa
s
do
ne
wi
t
h
a
hi
g
h
si
gnal
t
o
noi
se
rat
i
o
t
o
det
e
rm
i
n
e t
h
e com
put
i
n
g t
i
m
e and t
h
e
requ
ired
m
e
m
o
ry size in
bo
th
alg
o
rith
m
s
.
Tabl
e 4.
C
o
m
put
at
i
o
n per
f
o
r
m
ance
com
p
ari
s
on
M
e
thod
Data
sa
m
p
le
s
Har
m
onics
f
k
/
P
k
Signal M
e
m
o
r
y
size
(
KB
)
M T
i
m
e
(
s
)
Original
ESPRI
T
1024
50.
00Hz
/
16.
99
dB
25.
82 Hz/ -
10.
97d
B
74.
17Hz
/
-
13.
47d
B
16
511
4.
3471
Fast
ESPRI
T
205
49.
99Hz
/
16.
96
dB
25.
81Hz/ -
12.
10d
B
74.
17Hz
/
-
14.
12d
B
3.
2 102
0.
0304
6
It
i
s
very
cl
ear fr
om
t
a
bl
e 4 t
h
at
bot
h
ori
g
i
n
al
an
d fast
ESPR
IT al
g
o
r
i
t
h
m
s
provi
de
sat
i
s
fact
ory
accuracy, a
nd they co
rrectly identify the
L=3
h
a
rm
o
n
i
cs d
e
sp
ite with
sm
alles
t
p
o
wers case. The littl
e
per
f
o
r
m
a
nce di
ffe
rence
o
b
se
r
v
ed
i
n
t
h
e Fa
st
- ES
PR
IT i
s
j
u
st
i
f
i
e
d by
t
h
e a
t
t
e
nuat
i
o
ns ca
u
s
ed
by
t
h
e
I
I
R
ban
d
p
a
ss
filter u
s
ed. Fu
rth
e
rm
o
r
e,
th
e ob
tain
ed
resu
lts con
f
i
r
m
s
th
e im
p
o
r
tan
t
red
u
c
tion
of th
e co
m
p
u
t
atio
n
a
l
ti
m
e
with 1
4
2
.
7
tim
e
s, the m
e
m
o
ry
size require
d
fo
r p
r
oce
ssi
n
g
wi
t
h
5 t
i
m
es and c
o
m
p
l
e
xi
t
y
has been c
h
ange
d
fr
om
N
s
3
to
(
N
s
/
Г
)
3
. I
n
ad
d
i
t
i
on, a negl
i
g
i
b
l
e
perf
o
r
m
a
nce l
o
ss i
s
obs
erve
d i
n
t
h
e p
o
we
r an
d f
r
eq
uency
esti
m
a
t
i
o
n
caused
b
y
th
e
b
a
n
d
p
a
ss filter
atten
u
a
tion
s
. Fig
u
re 4
illu
strates th
e esti
matio
n
of th
e sig
n
a
l
sub
s
pace
di
m
e
nsi
o
n
by
m
eans o
f
t
h
e
R
i
ssan
e
n c
r
i
t
e
ri
a base
d
on
MDL
fu
nc
t
i
on c
o
st
s
h
o
w
n i
n
(
1
2) a
n
d
(
1
4
)
.
Fi
gu
re
4.
Est
i
m
a
t
i
on o
f
si
g
n
a
l
harm
oni
cs
n
u
m
b
er by
M
D
L cri
t
e
ri
o
n
Fig
u
re 5
sho
w
s th
e frequ
en
cy resp
on
se
g
a
i
n
of th
e Yu
le-Walk
IIR b
a
nd p
a
ss filter u
s
ed
in
th
e Fast
-
ESPR
IT
al
g
o
ri
t
h
m
havi
ng
a
n
or
der
h
=25
.
Ob
v
i
o
u
sly, th
e
filter h
a
s a flat
respo
n
s
e in
t
h
e
b
a
ndwid
th target.
0
5
10
15
20
25
30
35
-1
00
00
-80
0
0
-60
0
0
-40
0
0
-20
0
0
0
20
00
X:
3
Y
:
-
8881
Nh
M
D
L C
o
s
t
f
unc
t
i
on v
a
l
u
e
Evaluation Warning : The document was created with Spire.PDF for Python.