In
te
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rn
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o
f Po
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Elec
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D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
2, June
2
01
9, pp.
961~
9
7
0
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
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.
i
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961
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yn
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ac
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i
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osi
s
d
e
fects using stator and r
ot
or currents lissajou
s
curves
F. El Hammou
chi
1
, L.
E
l
M
en
zh
i
2
,
A.
S
aad
3
, Y.
I
h
e
d
rane
4
,
B
.
B
o
s
so
u
f
i
5
1,
3
N
atio
nal
Hi
gher S
c
ho
ol
o
f Electri
cit
y
an
d
M
ech
ani
c
,
Has
s
an 2 U
ni
versity,
M
o
rocco
2
Natio
nal S
c
hoo
l
o
f
A
pplied
S
c
ie
n
ces,
Abd
e
lm
alekEs
saad
i U
n
i
v
ers
ity,
Morocco
4
L
ISTA Lab
orato
r
y,
F
acu
lt
y of Sci
en
ces D
har E
l
M
ah
raz, S
idi M
o
h
am
m
e
d
Ben
Abdel
l
ah
U
niv
e
rsity,
M
o
rocco
5
Lab
orato
r
y of El
ectri
cal E
ng
in
eeri
n
g
and
M
a
intenan
ce, M
oh
amm
e
d
I
U
n
i
v
e
rsity
, Moro
cco
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Oct
1
0
,
2
018
Re
vise
d N
ov
1
9
,
201
8
Ac
ce
p
t
ed
J
an
30
,
2
0
19
In
t
he
c
urrent
p
ap
er,
a
m
e
t
h
o
d
i
s
d
e
vel
oped
t
o
d
iagn
os
e
po
ten
t
i
al
e
l
ectrical
def
ect
s
att
ackin
g
d
o
u
b
l
y
f
ed
i
n
ducti
on
g
enerat
or
i
n
M
o
roccan
w
i
n
d
t
urbi
nes
firms
.
T
he
p
roposed
m
e
thod
i
s
ba
se
d
on
s
ta
tor
a
n
d
rotor
current
s
Li
ss
a
j
ou
s
curv
es
a
nal
y
s
i
s
.
F
irstly
,
we
f
ocus
o
n
m
o
deli
n
g
o
f
a
no
n-defect
e
d
wi
nd
con
v
ers
i
on
s
y
s
te
m
s
b
as
e
d
o
n
mat
h
em
atic
m
od
el
c
reated
i
n
M
a
t
l
ab
S
i
m
u
li
nk
w
h
i
c
h
i
s
a
b
l
e
t
o
r
e
f
l
e
c
t
t
h
e
b
e
h
a
v
i
o
u
r
o
f
t
h
e
w
i
n
d
t
u
r
b
i
n
e
d
u
r
i
ng
asy
n
ch
rono
us
g
e
n
erato
r
d
ef
ects
-fr
ee
o
p
er
ati
on.
A
ft
er
t
hat,
a
n
i
nd
i
r
ect
s
tator
fiel
d
vect
or
o
ri
ent
e
d
con
t
rol
is
a
pp
li
ed
t
o
ob
tain
t
h
e
w
in
d
s
y
s
te
m
perf
o
r
man
ce.
F
inal
ly
,
st
ator
a
nd
r
oto
r
c
u
rrent
s
Liss
a
j
ou
s
curv
e
s
are
an
aly
zed
in
c
a
s
e
of
a
non-d
e
fe
c
t
e
d
g
e
n
era
t
or
t
h
a
t
re
p
r
e
s
e
n
ts
t
h
e
s
ys
te
m
ref
e
rence
c
u
r
v
e
s
f
o
r
d
i
a
g
n
o
s
i
n
g
d
e
f
e
c
t
s
.
T
h
e
s
i
m
u
l
a
t
i
o
n
s
h
a
d
b
e
e
n
r
e
a
l
i
z
e
d
b
y
M
a
tla
b
S
i
m
u
li
nk
.
Th
eir res
u
l
t
s
showed
the
e
ff
ecti
v
en
ess
of
t
he
p
ropo
se
d m
e
th
od
.
K
eyw
ord
s
:
A
s
ync
hro
n
o
u
s ge
nera
t
o
r
D
i
ag
no
sis
de
fe
ct
In
di
re
ct
f
i
e
ld
o
ri
ent
e
d
con
t
ro
l
Lissa
j
ous
c
ur
v
e
s
Wi
n
d
tur
bi
ne
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:
F
a
ti
m
a
E
l
H
a
m
m
o
u
c
h
i
,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
S
y
st
em
,
H
a
ssan
2 U
n
i
v
er
sit
y
,
N
a
ti
ona
l H
i
g
h
e
r
S
choo
l of
E
l
e
ctric
i
t
y
a
nd
Me
cha
n
i
c
,
Ca
sab
l
anca
8
118
, M
o
ro
c
c
o
.
Em
ail:
elham
m
ouc
h
i
.
f
at
im
a@
gm
a
il.c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
It
w
as
e
xtremel
y
p
ressing,
both
for
e
nviro
n
m
ental
a
n
d
e
c
o
nomic
asp
ect
s,
t
o
l
o
ok
fo
r
alt
e
rn
a
t
i
v
e
an
d
c
l
e
a
n
en
ergi
es
i
n
o
r
d
e
r
t
o
s
at
isfy
g
ro
w
i
ng
el
ec
t
r
i
c
ity
n
eed
s
,
a
nd
r
e
duc
e
the
CO
2
em
iss
i
o
n
[
1].
F
o
r
thes
e
rea
s
ons,
ma
n
y
c
o
un
t
r
i
e
s
s
t
ar
t
e
xpl
ori
n
g
t
h
eir
na
t
u
ral
a
n
d
s
u
s
t
a
i
n
a
b
le
r
esourc
e
s
s
u
c
h
a
s
w
i
nd.
A
ct
ual
l
y
,
con
s
i
d
era
b
l
e
w
in
d
p
o
t
e
n
t
ia
l
is
l
oca
t
e
d
i
n
l
o
t
of
p
arts
o
f
t
h
e
w
orl
d
.
This
p
o
t
e
n
t
i
a
l
i
s
c
o
mp
le
te
ly
free
,
ine
x
hau
s
t
i
ble
a
nd
re
new
a
b
l
e
.
H
ow
e
v
er,
the
w
i
n
d
e
ne
r
gy
c
o
s
t
r
e
m
a
i
n
s
hi
gh
d
u
e
t
o
t
he
e
xpe
ns
ive
o
p
era
tio
n
a
l
and
ma
in
te
na
n
ce
cos
t
s
(O&M)
o
f
w
i
n
d
t
u
rbi
n
es.
Indee
d
,
th
ese
b
i
g
s
t
r
u
c
tures
are
usua
ll
y
s
itua
t
e
d
i
n
re
mot
e
l
o
c
a
t
i
o
n
s
t
h
a
t
a
r
e
h
a
r
d
t
o
a
c
c
e
s
s
.
S
o
,
t
h
e
m
a
i
n
t
e
n
a
n
c
e
c
o
s
t
s
c
a
n
r
eac
h
from
10%
t
o
3
0
%
o
f
t
he
w
in
d
tur
b
ine
s
to
t
a
l
i
n
c
o
m
e
[
2].
The
s
e
cost
s
cou
l
d
be
r
e
d
u
ced
b
y
m
o
n
ito
rin
g
c
o
n
tin
uous
ly
t
h
e
s
y
s
t
e
m
h
e
a
lth
[
3
]
,
e
s
p
e
ci
all
y
the
gener
a
tor.
T
h
i
s
c
r
ucia
l
pa
rt
o
f
w
i
nd
t
u
rb
ine
i
s
r
e
s
po
ns
i
b
le
o
f
e
l
ec
tric
i
t
y
p
ro
duc
t
i
o
n
a
nd
it
s
transm
issi
on
t
o
the gr
i
d
.
In
f
a
c
t
,
t
h
e
D
ou
bl
y
Fe
d
Induc
t
i
on
G
en
e
r
at
or
(
D
F
I
G
)
i
s
t
h
e
m
o
s
t
u
s
ed
i
n
th
e
wind
t
u
r
bi
n
e
v
ari
a
bl
e
spee
d
in
d
u
s
t
r
y
[
4].
I
t
o
ffers
e
xc
el
le
n
t
ope
ra
t
i
o
n
a
l
a
n
d
c
on
tr
ol
f
ea
tur
e
s
t
h
a
t
m
ake
t
h
e
i
r
in
t
e
gra
t
i
o
n
w
i
t
h
pow
e
r
g
r
id
s
ea
sy
a
nd
e
f
fe
ct
iv
e
[
5
].
M
u
c
h
research
d
eals
w
ith
differen
t
m
e
t
h
od
s
to
i
mpr
ove
t
h
e
e
lectr
i
ca
l
e
n
ergy
perform
ance
a
nd
pro
d
u
ct
i
o
n
from
w
in
d
[6].
M
ost
o
f
i
t
de
v
e
l
o
ps
c
on
tr
ol
l
ows
for
D
F
IG
t
o
ext
r
act
m
axim
u
m
elec
tr
ical
p
ow
e
r
f
r
o
m
w
i
nd
t
u
rb
ine
[7,
8]
.
B
u
t,
d
uri
ng
t
h
eir
o
p
e
r
at
io
n,
t
he
D
FIG
can
b
e
exp
o
se
d
t
o
d
iffi
c
u
lt
con
d
i
t
i
on
s
or
m
anufa
c
t
uri
ng
defe
c
t
s
[9,
1
0
],
w
hic
h
c
a
n
i
mm
ediat
el
y
par
a
lyze
e
lec
t
ric
i
ty
p
ro
duc
t
i
o
n
an
d
l
e
a
d
to a
l
o
s
s
of str
u
c
ture
[11]
.
Thus,
the
defe
ct
s m
u
st
b
e
pred
ic
te
d
o
n
t
ime
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
9
6
1
–
9
70
96
2
A
lo
t
of
w
or
ks
h
a
v
e
be
e
n
d
o
n
e
t
o
i
ns
pec
t
D
F
I
G
f
a
ul
ts.
S
o
m
e
r
ese
arc
h
i
s
u
s
i
n
g
a
v
ail
a
bl
e
t
e
c
hni
qu
e
s
lik
e
S
up
er
v
i
sory
C
ont
r
o
l
And
D
a
ta
A
cqu
i
si
tio
n
S
C
ADA
[12
]
.
Oth
e
r
s
u
s
e
data
d
er
i
v
e
d
f
r
o
m
co
nd
i
tion
a
n
d
S
t
r
u
ct
ur
al
H
e
a
l
th
M
o
n
i
t
o
r
i
ng
(
SH
M)
t
o
dete
c
t
w
in
d
tur
b
i
n
e
fa
ult
s
by
u
sin
g
d
e
c
i
s
io
n
t
r
ee
l
e
a
r
nin
g
a
lgori
t
h
m
s
with
b
ig
d
a
t
a [
1
3
]
.
H
e
nce
,
t
he
g
e
n
er
at
or
d
ia
gno
sis
de
fec
t
s
pr
o
v
ide
s
e
a
r
l
y
d
e
t
e
c
tio
n
o
f
im
minen
t
f
a
u
lts,
a
n
d
m
i
n
i
m
i
ze
s
w
i
n
d
t
ur
bi
ne
d
ow
n
t
i
m
e
[
1
4]
.
A
l
so,
it
a
n
t
i
c
i
p
ates
s
er
io
us
d
a
m
age
a
ffe
ct
i
ng
w
i
n
d
e
ne
r
g
y
s
y
ste
m
b
y
pr
e
d
ic
ti
n
g
a
n
y
de
fe
ct
s,
s
t
o
p
p
i
n
g
t
he
ir
p
r
opa
g
a
t
i
on
a
n
d
sa
vi
n
g
time
an
d
m
o
n
e
y
.
In
o
r
d
er
t
o
de
te
ct
d
e
f
ec
t
s
a
n
d
t
he
ir
c
a
uses,
the
dia
g
n
o
s
tic
s
yste
m
has
t
o
u
se
d
a
t
a
fr
om
n
or
m
a
l
o
p
er
a
t
i
on
a
n
d
c
o
m
p
ar
e
it
w
i
t
h
d
e
f
ects
c
h
ar
a
c
ter
i
s
t
ics.
S
o,
a
n
ew
m
eth
o
d
i
s
pr
op
os
ed
f
or
h
av
i
ng
r
e
li
a
b
l
e
r
e
f
e
r
enc
e
s
ys
tem
i
n
c
ase
o
f
non-
de
fe
ct
e
d
D
F
I
G
s
o
as
t
o
pr
ed
ic
t
the
pr
ospe
c
tive
de
f
e
c
t
s.
I
n
t
he
f
i
r
st
p
a
r
t
of
t
h
i
s
r
e
sea
r
c
h
,
a
desc
r
i
pti
on
o
f
t
he
e
sse
n
t
i
a
l
w
i
n
d
e
ne
r
g
y
c
o
n
v
e
r
si
on
s
y
ste
m
s
c
o
mpo
n
e
n
t
s
i
s
pr
esen
ted.
I
n
t
h
e
seco
nd
par
t
,
w
i
nd
tur
b
i
n
e
be
ha
v
ior
d
u
r
i
n
g
d
efe
c
t
s-
fr
e
e
oper
a
ti
on
of
D
F
I
G
is
tr
e
a
te
d
usi
ng
ma
t
h
e
m
a
t
i
c
al
e
qua
t
i
ons
t
o
c
r
eate
m
ode
l
i
n
M
a
t
l
a
b
S
i
m
u
l
i
n
k.
I
n
t
h
e
las
t
p
ar
t,
s
ta
tor
an
d
rot
o
r
c
u
r
r
e
nt
s
L
i
ssa
j
ous
c
ur
ves
a
r
e
de
ve
l
ope
d
as
a
m
e
t
ho
d
f
o
r
D
F
I
G
d
i
agn
o
s
i
s
d
e
f
ec
t
s
.
Th
e
simula
t
i
o
n
r
esu
lts,
ob
ta
ine
d
b
y
M
a
tla
b
S
i
mul
i
nk,
s
how
t
he
e
f
f
ic
i
e
nc
y
o
f
t
he
p
r
o
p
o
se
d
a
p
pr
oa
ch.
2.
WIND
CO
NV
E
R
SION SYS
T
E
M
MODELI
NG
The
s
t
ud
y
w
i
l
l
b
e
a
b
o
u
t
t
w
o
M
or
occa
n
w
i
n
d
t
ur
b
i
n
e
f
ir
m
s
t
hat
co
nt
a
i
n
ho
r
i
z
o
nt
a
l
-
a
xi
s
HA
W
T
u
sin
g
DFIG.
I
n
f
act,
the
DF
IG
i
s
an
a
sy
nc
hr
o
n
o
u
s
m
achi
n
e
fe
d
from
t
h
e
s
t
a
t
o
r
a
n
d
r
o
t
o
r
.
T
h
e
r
o
t
o
r
o
f
D
F
I
G
i
s
co
nn
e
c
t
e
d
t
o
t
h
e
g
rid
t
h
rough
t
h
e
t
ran
s
fo
r
m
er
a
n
d
t
h
e
vo
lt
a
g
e
s
o
u
r
ce
con
v
er
t
e
rs
“
ba
c
k
-
t
o-
back”
:
t
h
e
R
o
t
or
S
i
d
e
C
onve
r
t
er
(
R
S
C
)
a
nd
th
e
G
r
id
S
ide
C
o
n
v
er
te
r
(
G
S
C
)
.
A
c
apac
it
or
i
s
p
l
ac
e
d
b
e
t
w
e
en
t
w
o
c
onve
r
t
er
s
to
r
e
duce
the vo
lt
a
g
e
r
i
p
p
le
s.
T
he
R
S
C
c
on
tr
o
l
s
fe
at
ur
e
s
o
f
t
h
e
a
c
ti
ve
a
nd
r
e
a
c
tive
pow
e
r
s,
t
he
d
e
v
e
l
o
p
e
d
t
or
q
u
e
a
nd
t
h
e
r
o
ta
t
i
o
n
s
pee
d
.
S
o
,
the
GS
C
con
t
r
o
l
s
t
he
D
C
bus
v
o
l
ta
ge
and
th
e
g
rid
f
a
cto
r
.
2
.
1
.
Wind
t
ur
b
i
ne
m
o
d
eling
The
w
i
nd
s
p
e
e
d
used
i
n
t
h
e
mode
l
is
a
s
u
m
o
f
s
i
n
u
s
o
id
a
l
s
ig
na
ls
w
it
h
di
ffe
ren
t
fre
qu
en
ci
e
s
a
nd
a
m
pli
t
u
d
e
s
as
s
how
n
in
t
he
F
igur
e
1
be
l
o
w
.
F
i
gur
e
1.
W
ind
spe
e
d
mode
l
B
y
a
p
p
l
y
in
g
t
h
e
the
o
r
y
o
f
mom
e
ntum
a
n
d
Ber
n
o
u
l
l
i
’
s
t
he
or
em
,
inc
i
d
e
n
t
t
h
e
o
r
e
t
i
ca
l
pow
er
d
ue
t
o
wind
win
d
P
i
s
e
xpr
e
sse
d
b
y
t
he
e
q
u
a
t
i
o
n
b
e
l
ow
:
3
.
.
2
v
A
P
win
d
(
1
)
wi
nd
P
:
Win
d
pow
er
;
:
Air D
e
nsity
; A
:
S
we
ep are
a swe
p
t b
y
t
he
b
la
de;
v
:
Wi
nd
spe
e
d
.
The P
o
wer ca
pt
ured
by
the
b
l
ade
tu
rb
P
is
d
ete
r
mi
ne
d
b
y
t
he
e
q
u
a
t
io
n
be
l
o
w
:
3
).
,
(
.
.
2
v
C
A
P
p
turb
(
2
)
With
.
k
e
.
k
.
k
K
.
k
.
k
)
,
(
C
K
k
p
6
4
3
2
1
5
(
3
)
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
Wi
n
d
tu
rb
in
e
do
ub
l
y
-f
ed
a
s
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ro
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1
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k
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(
4
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v
R
.
W
turb
(5
)
)
,
(
C
p
: C
o
effic
i
e
n
t
o
f
pe
r
for
m
a
n
ce
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spee
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rati
o
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t
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h
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gl
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=
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o
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ax
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um
p
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turb
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gul
ar s
p
eed
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f th
e
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=
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k6
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00
8
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k7
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0
8,
k
8
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035
[1
5]
.
The
ae
rod
ynam
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c
t
o
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ue
o
n
t
h
e
ma
in
s
haf
t
(
s
l
o
w
a
x
i
s
)
turb
T
c
an
b
e
expre
sse
d
by
t
h
e
equa
t
i
o
n
:
turb
p
turb
turb
turb
W
v
C
A
W
P
T
1
.
).
,
(
.
.
2
3
(
6
)
g
turb
J
G
J
J
2
(
7
)
T
turb
: Bla
d
e
t
o
rque
J:
In
e
rt
i
a
of
th
e
sy
st
e
m
b
ro
ught
b
ac
k
on
t
h
e
tu
r
bi
n
e
f
a
s
t
axi
s
J
tu
r
b
:
Tu
rb
in
e in
e
r
ti
a
G
:
G
e
a
rbox
ratio
Jg:
Generator
inertia
The
fun
d
am
enta
l
eq
ua
tio
n
of
d
yn
am
ics
is
a
p
p
lie
d
to
d
e
t
e
r
m
i
ne
t
h
e
ev
ol
u
t
i
o
n
of
t
he
D
F
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G
mec
h
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c
a
l
sp
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wh
i
ch
i
s p
r
e
s
ent
e
d
in
equ
ati
o
n
b
e
l
o
w:
mec
em
g
mec
W
.
f
T
T
dt
dW
J
(
8
)
W
me
c
: DF
IG me
c
han
i
ca
l
spee
d
T
g
: A
e
rody
na
m
i
c torq
ue
on t
h
e
the t
u
rb
i
n
e
fa
st
a
x
i
s
T
em
:
Electrom
a
gne
tic
tor
que
f
:
F
r
i
c
ti
o
n
c
o
e
f
f
i
c
i
e
n
t
The
e
q
uat
i
o
n
s
p
re
se
n
t
e
d
a
bo
v
e
,
are
used
t
o
cre
a
te
t
he
w
in
d
t
u
r
b
i
n
e
Ma
t
l
ab-S
i
m
ul
i
n
k.
W
e
s
u
pp
ose
t
h
at
th
e
f
ri
ct
ion
s
a
re
n
eg
l
ect
ed
. Th
e
sy
st
em p
e
rfo
rma
n
c
e
i
s sh
o
w
e
d
in
F
ig
ure
s
3
,
4,
5
and
6
.
2.2.
M
d
e
lin
g of
d
ou
b
l
y-f
e
d
ind
u
c
t
ion
mach
i
n
e
The
a
s
y
n
c
h
r
o
n
ous
m
ach
ine
e
qua
t
i
o
n
s for
th
e stat
or
U
s a
n
d
the r
o
tor
U
r
vol
t
a
ges i
n
P
ark re
fer
e
nce
f
r
ame
(d
, q
) a
r
e
[
1
6
]
:
)
(
i
.
R
dt
d
U
)
(
i
.
R
dt
d
U
i
.
R
dt
d
U
i
.
R
dt
d
U
r
s
dr
qr
r
qr
qr
r
s
qr
dr
r
dr
dr
s
ds
qs
s
qs
qs
s
qs
ds
s
ds
ds
(9
)
W
ith
:
w
.
P
s
r
(1
0
)
s
U
(d,
q
),
Ur
(d,q)
:
S
ta
t
o
r
an
d
rotor v
o
l
t
a
g
e
P
a
rk c
ompone
n
t
s r
e
sp
ec
t
i
ve
l
y
;
s
(d,
q),
r
(
d,
q
): S
tat
o
r a
nd rot
o
r
fl
u
x
P
ark
compo
n
e
n
ts
r
espe
ctive
l
y;
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.
2
, June
20
1
9
:
961
–
9
70
96
4
s
i
(d,
q),
r
i
(
d,q): S
t
ator
a
n
d
r
o
t
or
c
ur
rent
s i
n
P
ark com
p
o
n
e
n
t
s
resp
e
c
t
i
v
e
ly
;
Rs,
Rr: S
t
ator a
nd ro
tor
resista
n
ce
s
respe
c
t
i
v
e
ly. The
flu
x
equ
ati
o
n
s
c
an
be
wri
t
t
en
as
f
o
ll
o
w
s:
r
r
r
s
s
s
qs
qr
r
qr
ds
dr
r
dr
qr
qs
s
qs
dr
ds
s
ds
M
l
L
,
M
l
L
i
.
M
i
.
L
i
.
M
i
.
L
i
.
M
i
.
L
i
.
M
i
.
L
(1
1
)
Ls,
Lr
:
Sta
t
o
r
an
d
rot
o
r c
y
cl
ic in
d
u
c
t
anc
e
s
r
espec
t
i
v
el
y
;
ls,
lr
:
Sta
t
o
r
an
d
rot
o
r le
aka
g
e
in
d
u
cta
n
ce
s re
spe
c
ti
ve
ly
;
Ms, Mr
: M
u
tua
l
in
d
u
c
t
ance
s betw
e
e
n
stat
o
r
phases a
nd ro
tor
pha
ses
r
e
spect
i
vely;
M
:
M
a
x
i
mu
m m
u
tu
al
i
ndu
ct
an
c
e
b
e
t
we
en
st
a
to
r an
d
ro
to
r s
t
ag
e
s
;
p
re
presents the
D
F
I
G pole
pair
s num
ber
. The
e
l
e
ctr
o
m
a
gne
t
i
c
t
or
q
ue e
xpres
si
on is
:
)
i
.
i
.
(
p
T
ds
qs
qs
ds
em
(1
2
)
2.3.
Fie
l
d
orien
t
ed
c
on
tr
ol
The
pur
pose
o
f
o
r
i
en
t
i
n
g
t
he
s
t
a
t
o
r
fie
l
d
is
t
o
perf
orm
th
e
D
F
I
G
ac
tive
an
d
re
ac
tive
p
o
w
e
rs
by
con
t
ro
l
lin
g
dy
nam
i
c
a
l
l
y
a
nd
sepa
rate
ly
t
he
f
lu
x
a
n
d
the
t
o
rq
ue
.
T
ha
t
m
e
a
n
s
or
i
e
n
t
i
n
g
sta
t
or
f
l
u
x
a
l
o
n
g
th
e
direc
t
a
xis
in o
rde
r
to
ob
t
a
in
:
0
qs
and
sd
s
.
F
r
om (11)
a
nd
(12)
w
e g
e
t:
qr
s
qs
s
em
qr
qs
dr
s
ds
i
.
Ls
M
p
i
.
p
T
i
.
Ls
M
i
)
i
.
M
(
Ls
i
1
(
1
3
)
In
g
en
e
r
al
,
t
h
e
st
ato
r
r
e
s
i
s
t
a
n
c
e
i
s
n
egl
e
ct
e
d
f
o
r
l
a
r
g
e
p
o
w
er
e
q
u
i
pm
ent
use
d
i
n
w
i
nd
t
urb
i
ne.
It
i
s
sup
pose
d
tha
t t
h
e
gri
d
is sta
b
l
e
a
nd the
fie
l
d
is c
o
n
st
a
n
t
.
The
stat
o
r vol
ta
ge
p
ark
com
p
o
n
e
n
t
s
(9)
b
ec
ome
:
s
s
qs
ds
U
U
0
(
1
4
)
The
D
F
IG
ac
t
i
v
e
a
n
d
re
act
ive
pow
ers c
a
n
be w
ritten
as fo
l
l
o
w
s
:
qs
ds
ds
qs
s
qs
qs
ds
ds
s
i
.
U
i
.
U
Q
i
.
U
i
.
U
P
(
1
5
)
By
u
sin
g
(
14),
the
act
i
v
e
an
d reac
tive
p
o
wer
s
e
xpre
ssio
n
s be
com
e:
dr
s
s
s
s
s
qr
s
s
i
.
Ls
M
U
L
.
U
Q
i
.
Ls
M
U
P
2
(
1
6
)
S
o
t
he
a
c
t
ive
pow
er
i
s
in
de
p
e
nde
n
t
o
f
th
e
re
a
c
ti
ve
p
ow
er.
It
i
s
c
on
tro
lle
d
by
t
h
e
q
u
a
d
ra
tur
e
r
ot
or
c
urr
e
nt
i
qr
.
The
rea
c
ti
ve p
ow
e
r
is c
ontr
o
lle
d b
y
d
ire
c
t ro
tor
curr
ent i
d
r.
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
Wi
n
d
tu
rb
in
e
do
ub
l
y
-f
ed
a
s
ync
h
ro
no
u
s
ma
c
h
i
n
e
di
a
gno
si
s
de
f
e
ct
s u
s
ing
stat
or
…
(F.
El
H
a
mmo
u
c
hi
)
96
5
s
qr
r
s
qr
r
r
qr
qr
r
s
dr
r
r
dr
U
Ls
M
g
i
Ls
M
L
g
i
Ls
M
L
S
R
U
i
Ls
M
L
g
i
Ls
M
L
S
R
U
.
).
(
)).
(
(
).
(
)).
(
(
2
2
2
2
(
1
7
)
There
ar
e
tw
o
a
p
p
r
oac
h
e
s
o
f
the
ve
ct
or
c
on
tro
l
:
direc
t
a
nd
i
n
d
i
r
ect.
The
d
i
re
ct
o
ne
i
s
s
i
mple
t
o
implem
e
n
t
[1
7
]
b
u
t
n
o
t
t
he
m
ost
e
fficie
n
t
[1
8,
19]
b
eca
u
s
e
it
i
g
nores
t
he
t
erm
s
o
f
co
up
l
i
n
g
.
The
i
n
di
r
e
c
t
me
tho
d
i
s
be
in
g
m
o
r
e
c
om
mon
l
y
use
d
[
20]
b
eca
use
i
t
a
l
l
o
w
s
oper
a
t
i
ng
m
o
re
easily
t
hr
ou
g
h
o
u
t
a
l
l
t
he
s
pe
ed
range
[21]
.
I
n
o
r
d
e
r
t
o
h
a
v
e
p
e
r
f
o
r
m
i
n
g
s
y
s
t
e
m
,
t
h
e
w
i
n
d
t
u
r
b
i
n
e
m
o
d
e
l
i
s
i
m
p
le
me
n
t
e
d
i
n
Mat
l
a
b
S
i
m
ulin
k
b
y
u
s
i
n
g
t
h
e
i
n
d
i
r
e
c
t
m
e
t
h
o
d
(
I
F
O
C
)
.
T
h
e
o
r
i
e
n
t
a
t
i
o
n
o
f
t
h
e
D
F
I
G
s
t
a
tor
fl
ux
is
c
h
o
se
n
a
c
c
o
rd
i
n
g
to
t
h
e
d
i
r
ect
axi
s
.
The ove
rall pa
tte
rn o
f
the
w
i
nd
sys
t
em
m
odel
is
p
resente
d
i
n F
i
gure
s
7,
8,
9
and
10.
3.
DIAGNO
S
I
S
O
F
N
ON DEFECTED WIND
CO
NVE
RSIO
N
SYSTE
M
U
n
for
t
u
n
a
t
el
y,
w
in
d
t
u
rb
ine
fau
l
t
s
o
cc
ur
once
it
star
ts
w
or
king
.
In
de
ed
,
Wi
nd
e
ne
rg
y
h
a
s
it
s
c
o
ng
en
it
al
d
e
f
e
c
t
s
d
u
e
f
o
r
e
xa
mp
l
e
t
o
th
e
ha
rs
h
op
erat
in
g
e
n
vi
r
o
n
m
e
n
t
a
nd
t
he
h
i
g
h
l
y
t
u
rb
ule
n
t
w
i
nd
s
pee
d
[2
2].
But
,
u
nd
er
w
h
a
tever
op
era
t
i
on
c
ond
it
i
o
n
s
,
t
h
e
sta
b
ili
ty
a
nd
r
e
l
i
ab
i
l
i
t
y
of
w
i
nd
tur
b
i
n
e
a
r
e
r
e
quis
i
te
d
to
the
gr
id.
H
e
nc
e,
t
he
d
ia
g
n
o
si
s
of
w
i
n
d
t
u
rb
ine
sh
o
u
l
d
b
e
re
aliz
e
d
.
In
t
h
i
s
pa
rt,
w
e
d
ia
g
nos
e
a
no
n-de
fe
cted
syste
m
t
o
have
a
reliab
l
e
refere
nce
.
3.1.
R
e
vie
w
of
d
i
agn
osi
s
d
efe
c
ts essen
t
i
a
l
met
h
od
s
F
o
r
m
i
nim
i
z
i
ng
dow
nt
ime
,
p
re
d
i
c
t
ing
i
n
t
im
e
imm
i
ne
n
t
f
a
i
l
u
res
a
nd
i
m
p
ro
v
i
ng
m
a
inte
na
nc
e
sche
du
le,
seve
r
a
l
tec
h
n
i
que
s
a
r
e
a
p
p
l
i
e
d
for
m
o
n
itor
i
n
g
c
ont
in
u
ou
sly
t
h
e
w
i
nd
e
nerg
y
c
o
n
v
ersi
on
s
y
s
tem
h
e
al
th
[
23
].
I
n
d
ee
d
,
o
nli
n
e
di
ag
no
si
s
d
e
f
ect
s
al
l
o
ws
a
n
e
a
rly
d
e
t
e
c
t
i
o
n
of
t
he
s
t
r
uc
ture
h
e
a
l
t
h
d
e
g
ra
da
tio
n
a
n
d
preve
n
t
s
i
nc
ip
ie
nt
f
a
u
l
t
s
in
t
h
e
w
ind
e
n
e
r
g
y
c
o
nvers
io
n
sy
stem
w
h
ic
h
le
a
d
s
t
o
s
a
v
e
bo
t
h
m
o
n
e
y
a
n
d
time
.
Mu
lt
it
ude
o
f
inte
r
n
al
a
n
d
e
xter
nal
de
fe
ct
s
a
tta
ck
s
fre
q
ue
nt
ly
w
i
n
d
t
u
r
b
ine
s
o
nc
e
its
s
tart
w
ork
i
n
g
[2
4]
espec
i
al
ly
t
he
g
ene
r
at
or.
Inde
ed,
D
F
I
G
unde
r
goes
s
o
m
e
c
omm
on
de
f
e
ct
s
su
ch
a
s
g
e
n
e
ra
to
r
exc
e
ssiv
e
vi
brat
i
on, ge
n
e
r
a
t
or
over
h
ea
t
i
ng,
b
ear
ing
o
v
e
r
hea
t
i
n
g,
abn
or
ma
l
n
o
i
se
s and
ins
u
lat
i
on d
a
m
a
ge
,
etc
[25
]
.
Mu
ch
r
e
s
ear
ch
o
n
ge
nera
t
o
r
faul
ts
d
e
a
ls
w
ith
m
e
t
hod
s
of
p
roc
e
ss
s
im
u
l
a
t
i
on
a
n
d
al
g
o
rit
h
m
con
s
truc
t
i
o
n
w
hic
h
a
re
u
se
d
i
n
c
o
n
d
i
t
i
o
n
m
on
i
t
or
ing
t
o
d
e
t
ec
t
a
n
d
a
nt
ic
i
p
ate
de
fe
ct
s
[2
6].
Other
tech
ni
q
u
es
use
tim
e-frequency
a
nalys
i
s
tool
s,
s
uch
as
w
avel
e
t
s,
t
o
derive
a
fa
ul
t
de
tec
t
i
o
n
si
g
n
al
[
2
7
]
.
S
o
m
e
m
etho
ds
a
re
als
o
e
x
p
l
ori
n
g
da
ta
p
ro
vi
de
d
b
y
t
he
s
u
p
e
r
vis
o
ry
s
yste
m
and
a
p
pl
y
i
n
g
ma
ny
da
ta-m
in
ing
a
l
gor
i
t
h
m
s
to
deve
l
op mo
de
l
s
for pred
i
c
t
in
g occ
u
rre
nce
of pos
si
b
l
e
de
fec
t
s [2
8].
These
d
i
ffe
r
en
t t
e
c
h
ni
que
s a
r
e w
i
de
l
y
use
d
in co
n
t
ro
l sys
t
e
m
for
re
duci
n
g
the
w
i
nd
tur
b
ine
dow
nt
ime
a
n
d
m
i
n
i
m
i
z
i
ng
opera
t
i
o
n
al
a
n
d
m
ainte
n
a
n
c
e
c
os
ts.
3.2.
Me
t
h
o
d
d
e
ve
lop
e
d
for
D
F
IG d
i
agn
os
i
s
d
ef
ect
s u
s
in
g L
i
ssaj
o
u
s
curves
The
L
i
ssa
jo
us
c
urve
s
a
r
e
st
u
d
i
ed
f
irst
by
t
h
e
A
m
er
i
c
an
m
athem
a
t
i
c
ia
n
N
a
t
h
an
ie
l
Bow
d
itc
h
i
n
1
8
1
5
.
The
c
u
r
v
e
s
,
i
n
1
8
57-1
8
58,
w
e
r
e
inves
t
i
g
a
t
ed
i
nde
p
e
nde
nt
ly
b
y
th
e
F
r
e
n
ch
m
a
t
he
ma
ti
c
i
a
n
J
ules-A
nt
o
i
ne
Lissa
j
ous.
The
Fr
ench
m
a
t
he
m
a
tic
ian
u
s
e
d
a
n
arr
o
w
stre
am
o
f
san
d
po
u
r
in
g
from
t
he
b
ase
o
f
a
c
ompo
u
n
d
pen
d
u
l
u
m
to pr
o
d
u
ce
t
he
c
urv
e
s
[29,
30].
Lissa
j
o
u
fig
u
re
s
ar
e
cr
eate
d
b
y
the
c
o
mb
i
n
at
io
n
of
t
w
o
s
i
n
e
wa
v
es:
the
x
s
i
g
n
a
l
i
s
de
scri
bed
b
y
o
ne
sine
w
a
v
e,
a
nd
t
h
e
y
s
i
g
n
a
l
i
s
desc
ri
be
d
by
a
n
o
t
her
sin
e
w
ave
.
S
o
by
ex
pre
s
si
n
g
y
a
s
a
fu
nct
i
o
n
o
f
x,
i
n
t
e
r
e
s
t
i
n
g
p
a
t
t
e
r
n
s
a
r
e
c
r
e
a
t
e
d
.
R
e
c
e
n
t
d
e
v
e
l
o
p
m
e
n
t
s
i
n
t
h
e
f
i
e
l
d
of
L
issa
jo
us
c
urves
ar
e
rea
l
i
z
e
d
i
n
d
i
ffe
r
ent
doma
i
n
s
s
uc
h a
s
the r
ot
a
t
i
n
g
ma
chiner
y
fie
l
d [3
1
]
,
and fau
lts
d
i
a
g
nosis [
3
2
].
Lissa
j
ous
c
ur
v
e
s
are de
sc
ribe
d
b
y
t
he pa
r
am
etric
eq
ua
ti
on
s be
lo
w
[
3
3
]
:
s
i
n
s
inbt
(
18)
If
t
h
e
t
wo
w
av
es
h
a
v
e
ex
a
c
tl
y
t
h
e
sa
me
f
re
qu
e
n
cy
(
a
=
b
)
,
t
h
e
sa
m
e
am
pl
itu
de
(
A=
B),
with
a
n
an
g
l
e
α
=
π/
2,
t
h
e
para
me
tric a
s show
n in
18
bec
o
m
e
:
c
o
s
at
(
1
9
)
(
2
0
)
The
n
t
he
r
esul
ta
nt
o
u
t
pu
t
w
i
ll
be
a
c
i
r
cle.
I
n
th
is
v
iew
,
L
iss
a
jo
us
c
ur
ves
are
a
p
p
l
ie
d
i
n
t
h
i
s
pa
per
t
o
t
h
e
D
F
I
G
st
a
t
or
a
n
d
r
oto
r
t
hree
-phase
c
u
r
rents.
F
or
t
h
i
s
p
u
rp
ose,
i
t
is
nece
ssary
t
o
use
t
h
e
Co
nc
ord
i
a
tra
n
sf
orma
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
9
6
1
–
9
70
96
6
[
3
4
]
i
n
or
de
r
t
o
o
b
t
a
i
n
the
s
t
ator
a
n
d
r
o
t
or
c
ur
r
e
nts
C
o
nc
o
r
d
i
a
c
om
po
ne
nt
s
(
i
sα,
ir
α)
a
nd
(
i
s
β,
i
r
β
)
fr
om
t
he
t
h
ree
-
ph
as
e st
at
o
r
b
a
s
i
c
cu
rren
t
s i
s
abc
a
nd
t
h
e
thr
e
e
-
phase
r
ot
or
b
a
s
i
c
s
uch
as:
√
1
1
/
2
1
/
2
0
√
√
∗
(
21)
Ma
tla
b
S
i
mul
i
nk
s
o
f
t
w
a
r
e
i
s
use
d
f
or
s
i
m
u
l
atin
g
a
no
n-
de
f
ecte
d
syste
m
.
The
r
e
sul
t
s
a
r
e
pr
esente
d
in
F
igur
e
13
a
n
d
F
i
g
u
r
e
14.
T
h
e
se
c
ur
v
e
s
ar
e
c
onsi
d
e
r
ed
a
s
a
r
e
fe
r
e
nc
e
t
o
w
h
i
c
h
t
he
d
e
f
e
c
t
ed
s
ystem
curve
s
w
ill
be
c
o
mpa
r
ed
i
n
fu
tur
e
w
or
ks.
4.
RESU
L
T
S
A
ND ANALY
S
IS
The
r
e
sul
t
s
bel
o
w
r
e
pr
esent
the
sim
u
la
tio
n
of
t
he
w
i
nd
tur
b
i
n
e
m
ode
l
i
n
M
a
tla
b
S
i
mul
i
nk
a
t
t
he
f
i
r
st
th
ir
t
y
s
ec
o
n
d
s
.
The
r
e
sults
a
r
e
o
b
t
a
i
ne
d
b
y
c
h
oos
i
ng
the
f
o
ll
ow
i
ng
va
lue
s
o
n
Ta
b
l
e
1.
Tab
l
e
1.
M
o
d
e
l
par
am
eters
Turbine
pa
r
a
me
te
rs
Coeff
i
cients f
or
m
a
ximu
m Cp
M
achi
n
e
Parameters
=
1
.2
25
kg
/
m
3
k1
=
0.
587
2
Rs
=
0
.
0
12
Ω
A
=
39
03.
62
5
m
2
k
2
=
11
6
Rr =
0.0
21
Ω
R
=
35
.
25
m
k3
=0.
4
L
s
=
0
.
01
37
H
G
=
90;
k
4
=
5
L
r
=
0
.
0
1
36
H
j=
10
00
;
k
5
=
2
1
M
= 0
.01
3
5
H
f
=
0.
00
24
;
k
6
=
0
.
008
5
g
=
0
.
0
0
3
β
=
0 °
k7
=
0
.0
8
k
8=0
.
03
5
The
w
i
nd
sys
t
em
i
s
e
x
pose
d
t
o
var
i
a
b
le
w
in
d
spe
e
d
f
r
o
m
8
(
m
/
s
)
t
o
1
4
(
m
/s)
as
s
how
n
in
F
i
g
ur
e
2.
F
r
om
(
1)
w
e
obta
i
n
F
i
g
u
r
e
3
w
hich
r
epr
e
se
nt
s
t
h
e
w
i
n
d
p
ow
e
r
P
wi
n
d
.
Then,
by
u
s
i
n
g
(
2
)
w
e
g
e
t
t
he
pow
e
r
c
a
pt
ur
ed
b
y
th
e
b
l
ade
P
t
ur
b
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
4
.
The
F
i
g
u
r
e
s
5
,
6
a
n
d
7
sh
ow
t
he
s
ys
t
e
m
per
f
o
r
m
a
n
c
e
s
.
I
n
d
e
e
d
,
w
e
c
a
n
s
e
e
t
h
a
t
t
h
e
t
i
p
s
p
e
e
d
r
a
t
i
o
i
s
a
l
m
o
s
t
c
o
n
s
t
a
n
t
a
s
i
l
l
u
s
t
r
a
t
e
d
i
n
F
ig
ur
e
5
.
T
he
c
oef
f
i
c
i
e
n
t
of
pe
r
f
or
m
a
nc
e
r
e
a
c
hes
its
m
a
x
i
m
um
v
alue
w
hich
i
s
0.
57.
F
i
gur
e
2.
W
ind
speed
(
m
/
s)
F
i
gur
e
3.
P
w
ind
F
i
gur
e
4.
P
tur
b
pow
e
r
captur
e
d
by
t
h
e
b
l
ad
e
F
i
gur
e
5.
T
i
p
-
s
pe
ed
r
at
io
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Wi
nd t
u
r
b
ine
d
o
u
b
l
y-
fe
d asyn
chr
o
n
o
u
s m
a
c
h
i
n
e
d
i
ag
n
o
sis
de
fect
s usi
n
g st
a
t
or
… (
F
.
El H
a
m
m
ouc
h
i
)
96
7
F
i
gur
e
6.
C
oe
ff
icie
nt
o
f
pe
r
f
o
r
m
anc
e
F
i
gur
e
7.
M
ec
ha
nica
l
spe
e
d
o
f
DF
IG
The
sta
t
or
f
lu
x
of
D
F
I
G
is
o
r
i
e
n
t
e
d
a
c
c
or
di
n
g
t
o
the
di
r
e
ct
a
x
i
s
th
at
i
s
wh
y
th
e
mac
h
in
e
st
ato
r
i
n
d
i
r
e
c
t
f
l
u
x
,
i
n
F
i
g
u
r
e
8
,
r
e
a
c
h
e
s
z
e
r
o
a
n
d
t
h
e
s
t
a
t
o
r
d
i
r
e
c
t
flu
x
i
s
c
o
n
s
t
a
nt
a
s
s
how
n
in
F
igur
e
9.
I
n
a
ddit
i
o
n
,
t
h
e
i
n
d
i
r
e
c
t
f
ie
ld
o
r
i
e
n
te
d
c
o
n
t
r
o
l
i
s
u
s
e
d
t
o
c
o
n
tr
o
l
a
c
t
i
v
e
a
nd
r
e
ac
ti
ve
p
ow
er
s.
A
r
ef
ere
n
ce
f
or
a
c
t
i
v
e
pow
e
r
P
s
ref
is
c
h
o
se
n
to
h
av
e
a
f
o
rm o
f
s
t
ep
s
(3
s
t
e
p
s
)
. Th
e
F
ig
u
r
e 1
0 s
how
s a
c
o
mpa
r
ison
be
t
w
ee
n pow
e
r
r
efe
r
enc
e
an
d
re
al
a
cti
v
e
p
o
w
er.
It
i
s
cl
e
a
r
t
h
at
t
h
e
r
e
a
l
a
c
t
i
v
e
p
o
w
er
f
ol
l
o
w
s
t
he
pow
e
r
r
ef
er
e
n
ce.
T
he
s
ys
t
e
m
r
e
al
r
eac
t
i
ve
pow
er
i
s
a
l
s
o
a
r
o
u
n
d
t
he
r
e
act
ive
p
o
w
e
r
r
e
fer
e
nce
w
h
ic
h
i
s
z
e
r
o
F
i
gur
e
11.
S
tat
o
r
t
h
r
e
e
pha
se
c
u
r
r
e
nt
s
a
r
e
pr
esen
ted
i
n
F
i
g
ur
e
1
2
f
r
o
m
w
h
ic
h
s
how
s
t
h
at
D
F
I
G
three
-
phase
s
ta
tor
curre
nts
is
abc
h
a
v
e
a
p
e
rf
ect
s
i
nu
s
o
id
al
s
h
a
p
e
.
By
u
sing
(
15
),
t
h
e
s
tato
r
c
u
rren
t
s
ar
e
inf
l
ue
nce
d
b
y
P
s
r
e
f.
F
or
t
h
i
s
r
easo
n
,
t
h
r
e
e
va
r
i
a
t
i
on
z
one
s
of
s
ta
t
o
r
c
u
r
r
e
nt
s
ar
e
obse
r
ve
d.
T
hese
f
ig
ur
e
s
show
t
h
a
t
t
h
e
w
i
nd
s
y
ste
m
m
odel
im
p
l
em
ente
d
in
t
he
M
a
t
lab
S
i
mul
i
nk
r
e
ac
t
r
a
pi
d
l
y
a
nd
has
a
sa
t
i
s
f
a
c
t
o
r
y
d
yn
ami
c
.
F
i
gur
e
8.
I
ndir
e
c
t
s
ta
tor
f
i
e
l
d
of
D
F
I
G
F
i
gur
e
9.
D
ir
e
c
t
sta
t
or
f
ie
l
d
o
f
DF
IG
F
i
gur
e
1
0
.
C
om
par
i
s
on
be
t
w
e
e
n
P
sr
ef
a
nd
P
s
Fig
u
r
e 11
.
Co
mp
ar
is
on
b
etw
e
en
Qsref
an
d
Qs
F
i
gur
e
1
2
.
S
t
a
t
or
c
ur
r
e
nts
p
h
a
s
es
a
,
b
and
c
Th
e
F
i
g
u
r
e
s
1
3
a
n
d
14
e
xpose
Li
ssajou
s
c
u
r
v
e
s
o
f
a
D
F
I
G
sa
t
o
r
a
n
d
r
ot
or
c
ur
r
e
n
t
s
dur
ing
f
r
e
e
-
de
fec
t
s
op
er
ati
on.
E
ac
h
cur
v
e
,
h
as
t
hree
c
i
r
c
u
l
a
r
sha
p
es
p
a
s
s
i
n
g
fr
om
t
he
s
ma
l
l
c
i
r
c
l
e
to
t
he
b
ig
ge
st
one
.
T
h
ese
s
t
h
r
e
e
ci
rc
l
e
s
a
r
e
ob
t
a
i
n
e
d
b
ec
a
u
se
t
h
e
P
sre
f
i
s
cho
s
en
a
s
a
sig
n
a
l
wi
t
h
t
hre
e
s
tep
s
.
In
d
ee
d,
a
t
the
sim
u
la
ti
on
s
t
ar
t
i
n
g
t
im
e
a
n
d
aft
e
r
a
p
p
lica
t
io
n
of
t
he
a
c
t
ive
po
we
r
r
ef
e
r
e
n
c
e
s
i
g
n
a
l
fi
rst
st
ep
P
sref
,
t
h
e
f
i
rst
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
9
6
1
–
9
70
96
8
c
i
r
c
le
i
s
ob
ta
in
ed.
A
t
0
.
3
s
econ
d
,
a
not
he
r
step
i
s
a
d
d
e
d
t
o
t
he
f
irs
t
s
te
p
.
T
hus,
the
se
c
o
n
d
c
irc
l
e
is
d
r
o
w
n
.
F
i
n
a
l
l
y,
a
t
one
s
e
c
o
nd,
w
e
apply
t
h
e
t
h
ir
d
ste
p
t
ha
t
l
e
a
d
u
s
to
g
e
t
t
h
e
th
i
rd
c
i
r
cl
e
.
The
r
o
t
o
r
cur
r
e
nt
s
L
i
ssa
j
ous
c
ur
ve
s
a
r
e
s
h
ow
ed
i
n
F
i
g
u
r
e
1
3.
I
t
h
a
s
a
6
p
e
t
a
l
s
f
l
o
w
e
r
s
h
a
p
e
.
T
h
i
s
sha
p
e
i
s
d
ue
t
o
t
h
e
D
F
I
G
r
ot
o
r
s
up
ply
b
y
t
h
e
i
nve
r
t
er
w
i
t
h
6
sw
itc
he
s.
T
he
D
F
I
G
cur
r
e
n
t
s
L
issa
j
o
us
c
ur
ves
w
i
l
l
g
ive
a
n
i
d
e
a,
i
n fur
e
w
or
ks,
a
bo
ut
t
he
k
ind
of t
he
de
f
ec
ts
a
t
t
a
c
k
i
n
g w
i
nd c
o
n
v
er
si
o
n
sys
tem
.
S
o,
w
he
n
t
h
e
de
fec
t
s
occ
u
r
,
t
he
L
issa
j
ous
c
ur
ve
s
w
i
l
l
h
a
v
e
other
sha
p
es.
F
i
gur
e
1
3
.
Rot
o
r
Lissaj
o
us
c
u
r
ves
F
i
gure
1
4
. S
tator L
i
ssaj
o
u
s c
u
rves
5.
CONCLUSION
I
n
t
h
e
f
i
r
s
t
p
a
r
t
o
f
t
h
i
s
p
a
p
e
r
,
t
h
e
w
i
n
d
c
o
n
v
e
r
s
i
o
n
s
y
s
t
e
m
s
m
o
d
e
ll
in
g
ba
se
d
o
n
m
a
t
h
e
ma
ti
c
a
l
e
qua
t
i
o
n
s
is
p
resente
d
.
Then
,
a
n
i
n
d
ire
c
t
vec
t
or
c
o
n
tro
l
s
tat
o
r
f
ie
ld
o
r
i
e
n
te
d
is
a
p
p
l
i
e
d
t
o
i
n
c
r
e
a
s
e
t
h
e
pe
r
f
or
m
a
nc
e
o
f
t
he
w
i
n
d
c
o
n
v
er
si
on
c
h
ai
n.
T
he
s
y
s
t
e
m
is
s
imu
l
at
e
d
by
Ma
t
l
a
b
S
imul
i
nk
dur
ing
de
fe
c
t
s-
fr
e
e
ope
r
a
ti
o
n
.
I
n
t
he
s
ec
o
nd
par
t
,
a
me
t
h
o
d
w
a
s
d
e
v
e
l
ope
d
to
p
r
e
dic
t
t
h
e
po
t
e
nt
i
a
l
el
ect
ric
a
l
d
e
f
e
c
t
s
atta
ck
ing
w
i
n
d
t
ur
bi
ne
u
sing
Li
ssa
j
o
u
s
cur
v
e
s
o
f
the
D
F
IG
s
tator
and
r
o
t
o
r cu
rren
t
s.
The
o
b
t
a
i
n
e
d
r
esu
l
t
s
a
r
e
c
on
s
i
der
e
d
as
a
r
e
l
i
a
bl
e
r
e
fe
r
e
nc
e
sys
tem
for
DFI
G
d
iagn
os
is
o
f
M
o
roc
a
n
w
i
n
d
t
ur
b
i
ne
s par
k
s.
T
o
th
is
r
e
f
er
ence
s
yste
m
,
t
he
w
i
n
d
co
nver
s
i
o
n
e
n
er
g
y
b
e
h
a
v
i
our
w
ill
be
c
ompa
red
i
n
t
he
c
a
se
o
f
the
de
f
e
c
t
s.
T
he
n
e
x
t
w
o
r
k
w
il
l
be
d
ev
o
t
ed
t
o
m
ode
lli
n
g
a
n
d
s
im
ula
t
ion
of
d
e
f
ec
t
e
d
w
i
nd
e
n
er
g
y
c
o
n
v
er
si
o
n
s
ys
t
e
m.
L
issaj
o
us
c
ur
ve
s
a
n
d
f
r
eque
nc
y
s
p
ec
t
r
um
w
i
l
l
b
e
use
d
i
n
or
der
t
o
a
nal
y
se
a
n
d
d
ia
gn
ose
di
ff
er
e
n
t
de
fe
c
t
s
attac
k
in
g
the
tw
o
Mor
o
cca
n
w
i
n
d
t
ur
bi
nes
par
k
s.
REFERE
NC
E
S
[1]
U
n
ited
Nati
on
s
Cl
im
at
e
Chan
ge Co
n
f
e
rence
(CO
P
22
),
in
M
a
rrakech
,
Nov
e
m
be
r 2
0
1
6
.
[2]
Z
.
L
.
Y
i
n,
e
t
al
.,
"
S
t
art
u
p
S
p
eed
w
ith
D
ead
B
and
in
W
i
n
d
F
a
rms
wit
h
L
ow-M
ed
iu
m
Wind
S
p
e
e
d
P
r
ofil
e—Case
S
t
ud
y
of
H
o
ng Ko
ng
"
,
Ener
gy and
Po
wer E
ngineeri
n
g
,
vol.
9,
pp.
5
6
2
-5
72,
A
p
r
il
2
0
17.
[3]
Y.
A
mirat
a
,
et
a
l.
,
"
A
B
r
i
ef
S
tatus
on
C
ondi
ti
on
M
oni
t
ori
n
g
and
F
aul
t
D
i
a
gnos
is
i
n
Wi
nd
E
n
e
rg
y
Con
v
ers
i
o
n
Syst
e
m
s"
,
Ren
e
wab
l
e
a
nd
Sustain
ab
le E
n
er
gy Reviews
,
vo
l.
1
3
,
is
s
u
e
9
,
p
p
.
2
629–2
63
6,
200
9.
[4]
R.
M
.
R.
M
ut
hu,
"
D
oub
ly
F
ed
I
n
d
u
ct
io
n
Generat
o
r
fo
r
W
i
n
d
E
nerg
y
C
on
versi
o
n
S
y
s
t
e
m
-
a
S
urvey
"
,
Internat
ion
a
l
Co
nf
e
r
ence o
n
Ener
gy E
f
fici
e
nt Techn
o
lo
gi
es
f
o
r
Su
st
a
i
nab
ilit
y
,
pp.
6
17
-62
8
,
2013.
[5]
M
.
A
.
El-S
h
a
rkawi
,
"
W
i
nd En
ergy
A
n
In
t
r
od
ucti
o
n
"
,
U
n
i
v
e
rsit
y
o
f
W
a
s
h
i
n
g
ton
, S
eat
t
l
e, US
A
, pp
.
2
19
, 20
1
6
.
[6]
K
.
B
el
gacem
,
A
.
M
ezo
uar
and
N.
E
sso
un
bo
u
l
i,
"
Desi
gn
a
n
d
A
nal
y
s
is
o
f
A
d
aptiv
e
S
l
i
ding
M
o
d
e
with
E
xpo
nen
t
ial
Reach
ing
L
a
w
Con
t
rol
fo
r
D
o
u
b
le-F
ed
I
ndu
cti
o
n
G
e
nerato
r
Bas
e
d
W
ind
Turbi
n
e",
In
te
rn
at
io
na
l J
o
urna
l
o
f
Powe
r
E
l
ectr
onics an
d Dri
ve System
(
I
JPEDS
)
, vo
l
.
9
, no.
4,
pp
. 15
34
-1
5
4
4
, Decem
b
e
r 20
18.
[7]
D
.
C
.
P
h
a
n
a
n
d
T
.
H
.
T
r
i
n
h
,
"
M
a
x
i
m
u
m
P
o
w
e
r
E
x
t
r
a
c
t
i
o
n
M
e
t
h
o
d
f
o
r
Dou
b
l
y-fe
d
In
du
c
t
io
n
Ge
ne
ra
to
r
Wind
Tu
r
b
i
n
e
"
,
Inter
n
a
t
i
o
n
a
l
Jou
r
n
a
l
o
f
E
l
ect
ri
cal and Comp
ut
er Engin
eeri
n
g
(
I
JECE)
,
v
o
l
.
8
,
n
o
.
2
,
p
p
.
7
1
1
–
7
2
2
,
Ap
ril 20
18
.
[8]
A
.
A
.
Be
n
s
ab
er,
et
a
l
.,
"
N
on
li
near
A
dap
t
i
v
e
Co
ntrol
f
o
r
Wi
nd
T
u
rb
in
e
un
der
W
i
nd
S
peed
V
ariati
on
"
,
In
tern
at
io
nal
Jo
ur
nal
of
R
o
b
o
tics
and A
u
to
mation
(
I
J
RA)
, v
o
l
. 7
,
n
o
. 2
, p
p.
87
-
9
5
, Ju
n
e 2
0
1
8
.
[9]
S
.
M
arten
s
e
t
al
.,
"
S
im
u
l
atio
n
o
f
E
lectri
c
Fa
u
lts
i
n
Dou
b
l
y
-F
ed
I
nd
uc
tio
n
Ge
n
e
ra
tors
E
mp
lo
ying
A
dv
a
n
c
e
d
M
a
t
h
em
ati
cal
M
o
d
el
li
ng
"
,
Proceed
in
gs of
2
4
t
h
No
rd
ic Ins
u
la
ti
on
S
y
mpo
s
i
u
m
o
n
M
a
t
e
ri
a
l
s, Com
pon
ent
s
a
n
d
D
i
a
gno
stic
,
pp.
9
8
-10
4
,
2
01
5.
[10]
A
.
Josh
uv
a
and
V.
S
u
gumaran
,
"
F
aul
t
D
iag
nosti
c
M
e
th
od
s
f
o
r
Wi
nd
T
urbin
e
:
A
Revi
ew",
Jo
ur
n
a
l
of
En
g
i
neer
ing
an
d App
l
ie
d
S
c
ie
nc
e
s
(AR
P
N
)
,
vol.
1
1
,
n
o
7,
p
p
.
465
4-4
6
6
8
,
2
01
6.
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
Wi
n
d
tu
rb
in
e
do
ub
l
y
-f
ed
a
s
ync
h
ro
no
u
s
ma
c
h
i
n
e
di
a
gno
si
s
de
f
e
ct
s u
s
ing
stat
or
…
(F.
El
H
a
mmo
u
c
hi
)
96
9
[11]
F.
E
l
Ha
mmo
uc
h
i
,
L.
E
l
Me
nz
h
i
a
nd
A
.
Sa
a
d
,
"
W
in
d
Tu
rb
ine
Do
ub
ly
-Fed
Asynchr
onous
Mac
h
ine
Di
a
g
nosis
Def
ects
-
Stat
e
o
f
t
h
e
A
rt
"
,
DE
St
ech T
r
an
sactio
ns
on E
n
vi
ron
m
ent Ener
gy
and
E
a
rt
h
Sci
e
nces
,
pp
.
3
0
0
-
30
6,
O
cto
b
er
20
17
.
[12]
S.
S
harma
and
D.
M
ahto,
"Conditio
n
Monitor
i
ng
of
W
ind
Turbi
n
es:
A
R
e
v
i
e
w
"
,
International Jo
urnal o
f
Scientifi
c
&
En
gi
neeri
n
g
Res
e
ar
ch,
vo
l
.
4,
issue 8,
p
p.
35
-
49
, 20
1
3
.
[13]
Ab
dall
ah,
e
t
a
l
.
,
"F
aul
t
D
i
a
gn
osi
s
o
f
W
i
nd
T
u
r
bine
S
truct
u
res
U
sing
D
ecis
i
on
T
ree
Learni
ng
A
lg
o
r
i
t
hms
with
B
i
g
Dat
a
"
,
Pro
ceeding
s
of S
a
f
e
ty a
n
d
Reliabilit
y
Co
n
f
er
ence
,
p
p.
3053-3
0
6
1
,
n
o.
3
,
Ju
ne
2
018
.
[14]
N.
T
azi,
E.
C
hatelet
,
Y
.
Bouzidi,
e
t
a
l
.
,
"
W
i
n
d
F
a
r
m
T
o
p
o
l
o
g
y
-
F
indi
ng
A
lgo
r
it
hm
C
o
n
s
i
d
e
ring
P
erf
o
rm
an
ce,
C
o
s
ts,
and
E
n
v
i
ronm
en
t
a
l
Im
pact
s",
En
vi
ro
nm
ental Sc
i
e
nce an
d Po
ll
u
t
ion Res
e
a
r
ch
,
vo
l.
2
5,
i
ssu
e
2
5
,
p
p
.
2
452
6–
24
534
,
S
e
pt
emb
e
r
20
18
.
[15]
B.
B
osso
u
f
i,
e
t
a
l
.,
"
O
bse
r
ve
r
Ba
c
k
ste
p
ping
C
o
n
t
ro
l
o
f
D
FI
G-Ge
n
erat
ors
f
o
r
Win
d
T
urbin
e
s
Variab
le-S
peed
:
F
P
GA-Bas
e
d Imp
l
em
ent
a
ti
on
"
,
Ren
e
wa
bl
e En
ergy
,
vo
l.
81,
pp.
9
0
3
-917
,
2
01
5.
[16]
B.
B
os
soufi
,
et
a
l
.,
"Backst
epp
i
n
g
C
on
tro
l
o
f
DFIG
G
enerat
ors
f
o
r
Wid
e
-Range
V
ariabl
e-S
p
eed
W
in
d
Tu
rb
i
n
es",
Int
e
rnat
i
o
na
l
Jo
urnal of
Automati
on
and Con
t
ro
l
(
I
J
A
C
)
,
vo
l.
8
,
no.
2
,
p
p
.
122
–1
40,
2
0
1
4
.
[17]
Y
.
I
h
e
d
r
a
n
e
,
C
.
E
l
B
e
k
k
a
l
i
,
a
n
d
B
.
B
o
s
s
o
u
f
i
,
"
P
o
w
e
r
C
o
n
t
r
o
l
o
f
D
FIG-G
e
nerators
f
or
W
i
n
d
Turbines
V
ariable
-
S
p
eed
"
,
Inter
n
a
t
i
o
n
a
l
Jour
na
l of Power
El
ectr
o
n
i
cs
and
Drive
Syst
em
(
I
JPED
S
)
,
vol
.
8
,
n
o
.
1
,
p
p
.
444
-45
3
,
201
7.
[18]
M
.
A
llam
,
e
t
a
l
.,
"
Et
ud
e
Comparat
iv
e
Ent
r
e
la
C
om
m
a
n
d
e
Vect
ori
e
lle
D
ire
c
t
e
e
t
Ind
i
recte
d
e
l
a
M
achi
n
e
As
yn
chron
e
à
D
oub
le
A
l
i
m
e
n
t
a
t
ion
(M
ADA
)
D
é
di
ée
à
un
e
App
l
i
cati
o
n
E
o
lienn
e",
Jo
ur
nal
of
A
d
v
a
nced R
e
sear
ch
in S
c
ie
n
c
e
an
d
T
e
c
h
no
log
y
(J
AR
ST)
, v
o
l
.
1
,
i
ssue
2, p
p.
88
-
10
0
, 2
01
4.
[19]
B
.
B
o
s
s
o
u
f
i
,
M
.
K
a
r
i
m
,
A
.
L
a
g
r
i
o
u
i
a
n
d
M
.
T
a
o
u
s
s
i
,
"
F
P
G
A
-
B
a
s
e
d
Im
p
l
ement
a
ti
on
N
o
n
linear
B
ackstepping
C
o
n
t
r
o
l
o
f
a
P
M
S
M
D
r
i
v
e
"
,
Int
e
rna
t
i
o
n
a
l
Jou
r
n
a
l
of
P
o
wer
El
ectro
ni
cs
and
D
r
i
v
e
Sys
t
em (
I
JPEDS)
,
vol.
4
,
i
s
s
ue1,
pp
.
1
2-23
,
2
0
1
4
.
[20]
K.
S
e
jir,
"
C
om
ma
n
d
e
Ve
c
t
orie
lle
d
’u
ne
M
ac
hine
A
syn
c
h
r
on
e
Dou
b
le
m
e
n
t
Al
ime
n
té
e
(
M
A
D
A
)
"
,
T
hè
s
e
d
e
Doctorat
,
de
l
’Institut
Nat
i
onal
P
olytechnique de
T
oul
ouse, F
ra
nce, 20
0
6
.
[21]
Gan
D
o
n
g
,
"
S
en
so
rless
a
n
d
Effi
cien
cy
O
p
t
imi
zed
I
nd
ucti
on
M
ach
in
e
Control
with
Associ
a
t
ed
C
onverter
P
W
M
Mo
du
la
tion
Sc
he
me
s"
, the
F
a
c
u
lty o
f
t
h
e
Gra
d
u
a
t
e
Sc
ho
ol,
Te
n
n
e
s
see
Techn
o
l
ogical
U
ni
versit
y,
200
5.
[22]
K.
M
a,
e
t
al
.,
"
Act
i
v
e
P
ow
er
D
i
s
pa
t
c
h
St
rateg
y
o
f
Wi
nd
Farm
s
un
der
G
e
nerator
Faults
"
,
Pr
oceedi
n
g
s
o
f
the
Eu
ro
pean
Saf
ety
a
nd R
e
lia
bili
ty
Con
f
eren
ce: Saf
e Soci
e
ti
es in
a Cha
ngi
ng
W
o
r
l
d
,
1s
t
ed.
,
p
p.
2
1
4
7-21
52
L
on
do
n,
UK
:
CRC
Pres
s
,
2018.
[23]
F
.
E
l
Hamm
o
u
chi
,
L
.
El
M
enzhi
,
A
.
S
aad,
Y
.
I
hed
r
ane,
B
.
Bo
ss
ou
f
i
,
"Wi
n
d
Tu
rbin
e
Do
ub
ly-Fed
A
s
y
n
c
hron
ou
s
M
achi
n
e
D
i
agn
o
s
i
s
Def
ects-part
t
w
o
",
Co
ng
ress
CIS
T
18
Conference O
M
CS
,
I
E
E
E
XPLOR
E
,
ca
tal
ogu
e
n
u
m
b
er
CFP1
8
6
7
R
-AR
T
, pp
. 4
86
-4
54
, 2
01
8.
[24]
F
.
E
l
H
a
m
m
o
u
c
h
i,
L
.
El
M
enzh
i,
A
.
S
aad,
"
W
ind
Tu
rb
i
n
e
Do
uble-f
e
d
As
yn
chronou
s
M
achi
n
e
Diagn
o
si
s
Def
ect
s-
Part
O
ne",
Int
e
rn
ati
o
n
a
l
Co
ng
r
e
ss
o
f
Ind
u
strial
E
ngi
neerin
g
an
d Syst
ems
M
a
n
a
g
em
ent CIGIM
S
,
M
e
knes
,
M
o
ro
cc
o
,
p
p.
3
8
0
-38
3
,
Ma
i
2
017.
[25]
A.
J
osh
u
v
a
a
n
d
V
.
S
u
g
u
m
a
ran,
"
F
a
ul
t
Di
agno
stic
M
etho
ds
F
o
r
W
in
d
T
urb
i
ne
:
A
Re
v
i
e
w
"
,
J
o
u
r
n
a
l
of
E
n
gi
n
e
e
r
i
n
g
an
d A
ppli
e
d S
c
iences
(
A
RPN)
,
v
o
l
.
1
1,
no.
7
,
p
p
.
4654
-46
6
8
,
2
0
1
6
.
[26]
S
.
M.
T
ab
a
t
abaei
po
ur,
et
a
l.,
"F
aul
t
D
et
e
c
tio
n
o
f
W
i
n
d
T
u
rb
i
n
es
w
i
t
h
U
n
certain
P
aram
et
e
r
s
:
A
S
et-M
em
bers
h
i
p
Ap
pro
a
ch
",
E
n
e
rgi
e
s
,
v
ol.
5
,
issue
7,
pp.
2
224
-2248
,
2
012
.
[27]
W.Ya
n
g
,
P
.
J
.
T
a
v
n
e
r,
C
.
J.
C
r
a
b
tr
e
e
a
n
d
M.
W
ilk
i
nson
.
"
C
ost-
E
f
fe
cti
v
e
Con
d
iti
on
M
o
nit
o
ri
ng
f
o
r
W
i
n
d
T
u
r
b
i
n
e
s",
IEEE Transac
t
i
ons
on Indu
st
ria
l
E
l
ectronics
, v
o
l
. 5
7, n
o
.
1,
p
p.
26
3
-2
71
, 20
1
0
.
[28]
A.
K
us
ia
k
a
n
d
W.
L
i,
"
The
Pre
d
ic
t
i
o
n
a
nd
D
ia
gn
osis
o
f
Wind
T
u
r
b
ine
Faul
ts"
,
R
e
ne
wa
ble
En
e
r
g
y
,
vo
l.
3
6
,
i
ss
ue
1
,
pp
.
1
6-23
,
2
0
1
1
.
[29]
H.
C
undy,
a
nd
A
.
Ro
llett,
"
L
i
ss
aj
ous
's
F
i
g
u
r
es
i
n
M
a
th
em
a
tical
M
o
dels
",
3
rd
e
d.
S
tradb
r
oke,
E
n
g
land:
Tarqui
n
Pu
b. 1
98
9
.
[30]
A.
G
ray,
"
Modern
D
i
fferent
i
a
l
Ge
om
et
ry
o
f
C
u
rves
a
nd
S
urf
a
ces
w
i
t
h
M
a
th
e
m
atica",
2n
d
ed.
Boca
Rat
o
n
,
F
L:
CRC Press, 199
7.
[31]
H.
A
.
H
.
A
l-K
h
a
zal
i
and
M.
R
.
Ask
ari,
"
Geo
m
etrical
a
n
d
G
raph
ica
l
R
e
pr
e
s
e
n
ta
t
i
o
ns
A
n
a
ly
si
s
o
f
L
i
s
s
a
j
o
u
s
F
ig
ur
e
s
in Ro
t
o
r
D
y
n
ami
c
Sys
tem",
Jo
urna
l
of E
ngineer
in
g (
I
O
S
R),
vol.
2,
i
s
s
ue
5
,
p
p
.
971-9
78,
2
0
1
2
.
[32]
L.
E
l
Me
n
z
hi,
a
n
d
A.
S
a
a
d
,
"
L
is
sa
jo
us
C
u
r
ve
o
f
a
n
A
ux
il
ia
r
y
W
in
di
ng
V
o
l
tag
e
P
ark
Co
m
p
o
n
ent
s
f
or
D
oubly
-
F
e
d
Ind
u
ct
ion
M
achine
El
ectrical
F
aul
t
s
Diag
nos
is
"
,
T
h
e Jou
r
n
a
l of
A
d
van
ced M
a
t
e
ri
a
l
s
Resea
r
ch
,
v
o
l
.
86
0-86
3
,
p
p
.
22
23
-223
1,
2
0
1
4
.
[33]
H.
G
.
Yiyang,
"
D
emonstrat
i
ng
L
is
sajou
s
F
igure
s
w
i
t
h
Matl
ab
a
nd
T
h
eir
A
p
p
l
i
catio
ns
"
,
Jour
na
l o
f
Ch
in
a Sci
e
nce
an
d T
ech
nol
og
y
Inf
o
r
m
atio
n,
El
e
c
tr
oni
c
&
Ind
u
str
i
al Coll
ege
,
Y
iyang
Hu
nan
41
305
4,
2
,
Ch
in
a,
2
0
0
8.
[34]
B
.
B
o
s
s
o
u
f
i
,
M
.
K
a
r
i
m
,
S
.
I
o
n
i
ł
ă
a
n
d
A
.
L
a
g
r
i
o
u
i
,
"
P
e
r
f
o
r
m
a
n
c
e
An
aly
s
is
o
f
t
h
e
D
i
rect
T
o
r
que
C
on
tro
l
a
n
d
t
h
e
S
p
ace
Vecto
r
M
o
d
u
l
ation
fo
r
Perm
an
ent
M
a
gn
et
S
yn
chro
nou
s
M
o
t
o
r
Dr
i
v
e
"
,
Uni
versi
t
y
of
Pitesti Sci
e
n
t
i
fic
Bul
l
e
tin :
Electronics
An
d Computer
s
Sc
ien
c
e
, vo
l
.
1
0
,
i
ssue 2
, p
p
2
3
-3
4, 2
01
0.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
9
6
1
–
9
70
97
0
BIOGRAPHI
E
S
OF
AUT
HORS
F
a
tima
El
H
amm
o
uch
i
w
as
born
in
M
o
r
occo
o
n
O
c
to
ber
16
th
,
19
85.
I
n
2
0
0
8
,
S
h
e
r
e
c
e
i
v
e
d
t
h
e
En
gin
eer
d
egree
in
E
l
ectri
cal
E
ng
in
eerin
g
and
P
o
w
e
r
E
l
ectro
n
i
cs
(
EEP)
f
rom
the
National
Hi
gher
S
c
hoo
l
of
E
lectri
c
i
t
y
a
n
d
M
ech
ani
c
s
(
E
NSEM
)
H
a
ss
an
2
U
n
i
v
e
rsi
t
y
of
M
o
r
occo
i
n
Casabl
anca.
S
he
i
s
P
h
D
stu
d
en
t
i
n
e
l
ectrical
e
ng
in
eerin
g
at
E
l
e
ctrical
S
y
s
tems
T
eam
(
E
S
T)
o
f
EN
S
E
M
si
nce
201
5.
S
h
e
is
i
n
t
eres
te
d
i
n
e
l
ectri
c
a
l
m
achi
n
es
m
o
d
elli
ng,
c
ontrol,
o
n
li
ne
d
iagnos
is
d
ef
ect
s
i
n
w
i
nd
turbines
,
and
the
i
r
i
n
t
e
grat
i
o
n
in
g
rid.
Lamiaa
El
M
enzh
i
is
a
p
ro
f
e
s
s
o
r
i
n
A
b
d
e
lam
a
lek
E
ssaad
i
Univ
e
r
s
i
t
y
i
n
M
o
ro
cco
s
ince
2
0
1
0
.
O
n
20
02,
S
h
e
g
o
t
h
er
H
i
g
h
D
eepen
ed
S
tud
i
es
D
iplom
a
i
n
el
e
c
tri
cal
m
ach
in
es
i
n
e
l
ectrical
eng
i
neeri
n
g
f
r
o
m
t
h
e
H
i
g
h
Na
t
i
o
n
al
S
ch
oo
l
of
E
l
ectricity
a
nd
M
e
chani
c
s
E
N
SE
M
in
H
ass
a
n
2
Un
iversit
y
i
n
Cas
a
bl
anca.
F
ro
m
20
02
u
n
t
i
l
2
004,
s
he
w
as
a
r
es
ea
rch
s
t
u
d
en
t
i
n
o
ne
o
f
th
e
un
ivers
i
ties
in
j
apan
.
O
n
2
00
9,
s
h
e
o
b
t
ai
ned
h
e
r
Doct
or
d
egr
e
e,
t
h
e
n
her
H
a
bilit
a
ti
on
a
s
a
pro
f
es
so
r
res
earch
er
o
n
201
6
f
r
o
m
H
ass
a
n
2
U
n
ivers
ity
i
n
Casabl
anca
(ES
E
M
)
.
She
is
i
n
t
e
r
es
ted
in
e
lect
rical
m
achi
n
es
c
on
trol
a
n
d
o
n-l
i
n
e
d
i
a
gn
o
s
is
e
it
her
u
s
e
d
a
s
a
m
oto
r
o
r
a
gene
ra
to
r
in
w
in
d
tu
rbin
es.
L
ami
a
a
El
M
enzh
i
i
s
a
m
em
b
e
r
an
d
ad
vis
o
r
of
t
he
M
oro
ccan
C
ent
e
r
o
f
P
o
l
ytech
nical
Research
a
nd
In
no
vat
i
o
n
s
in
ce
2
0
15.
Ab
dall
ah S
aad
w
as
b
orn
in
M
oro
cco i
n S
e
p
t
em
be
r
19
56.
He
rece
i
v
e
d
th
e En
g
i
neer an
d
D
oct
o
r of
En
gin
eerin
g
deg
r
ees
f
rom
National
P
o
ly
t
echn
i
c
Ins
t
i
t
ute
of
G
ren
ob
le
–
F
rance
–
res
p
ecti
v
el
y
in
19
80
an
d
19
82.
F
ro
m
1
982
t
o
198
6,
h
e
was
Research
er
a
t
F
r
enc
h
N
at
io
na
l
Cen
t
er
f
or
S
cien
t
i
fi
c
Research
(
CNR
S
)
-
Elect
ros
t
a
tics
and
Dielectric
Mat
e
ria
l
s
Labo
r
ato
r
y
–
G
r
enob
le.
Aft
e
r
receivi
ng
t
he
D
octo
r
of
P
hy
sical
S
ci
ences
d
eg
ree
in
198
6,
h
e
j
o
i
n
ed
H
ass
a
n
2
Un
iv
ersity
o
f
M
o
rocco
.
P
r
o
f
e
s
so
r
o
f
e
lectri
cal
e
n
g
i
n
eerin
g,
h
e
h
a
s
s
e
veral
sc
i
e
ntific
a
nd
e
du
catio
nal
responsibili
t
i
es.
Hi
s
main
f
ie
l
d
s
of
i
nterest
are
H
i
g
h
V
ol
tag
e
and
E
l
ectri
cal
I
nsu
l
atio
ns,
m
o
d
e
li
n
g
and
con
t
rol
,
ren
ewabl
e
energ
y i
n
tegrat
io
n.
Yas
m
i
n
e
Ih
edrane
b
orn
D
ecemb
e
r
26
,
199
1
at
F
E
S
,
M
o
ro
cco,
she
ob
tain
ed
h
er
m
as
ter'
s
deg
r
ee
in
E
ngi
n
eeri
ng
of
I
ndu
s
tr
ial
Au
t
o
ma
ted
Sys
t
em
s
at
t
he
F
acult
y
o
f
S
c
i
e
nces
D
har
el
M
ahrez
-
F
E
S
-
w
h
e
re
h
e
curren
tly
w
o
r
ks
,
P
h
D
.
g
radu
ate
s
t
ud
ent
in
t
h
e
s
am
e
un
ivers
i
t
y
a
nd
i
s
a
m
e
m
b
er
lab
o
rato
ry L
IS
TA
. H
er interest
s
in
m
achin
e con
t
ro
l.
Badre
Bo
ss
oufi
w
a
s
b
o
rn
i
n
F
ez
ci
ty
,
M
o
ro
cco, o
n
M
ay 21
,
1
9
85.
H
e
r
eceiv
e
d the P
h
D deg
r
ee
in
Ele
c
tr
ic
a
l
E
ng
in
e
e
r
ing
fro
m
U
n
i
v
e
rsi
t
y
S
i
di
M
oh
a
mme
d
Be
n
Ab
de
ll
ah,
F
acu
lty
of
S
c
i
ences,
M
o
r
o
c
c
o
a
n
d
P
h
D
d
e
g
r
e
e
f
r
o
m
U
n
i
v
e
r
s
i
t
y
o
f
P
i
t
e
s
t
i
,
F
a
c
u
l
t
y
o
f
E
l
e
c
t
ronics
a
nd
C
om
p
u
ter,
Rom
a
ni
e
and
M
o
ntefi
o
re
I
ns
ti
tute
o
f
el
ectrical
e
ngi
neeri
ng,
L
u
i
k
,
B
el
gi
u
m
,
in
2013
.
He
w
as
a
n
As
sistan
t
P
r
o
f
esso
r
of
E
l
ectrical
E
ngin
eerin
g,
a
t
t
h
e
H
i
gh
er
S
c
hoo
l
of
t
echn
o
l
ogi
e,
O
u
j
da
M
o
rocco
.
His
research
i
n
t
erest
s
i
n
c
lu
de
s
t
a
tic
co
nv
ert
e
rs,
elec
t
r
ical
m
o
t
or
d
ri
ves
,
p
ow
er
electro
ni
cs,
sm
art
grid
, ren
e
wabl
e energ
y
an
d
art
i
f
i
c
ial intell
ig
e
n
t.
Evaluation Warning : The document was created with Spire.PDF for Python.