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
5
9
2
~1
6
0
2
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1592-1602
1592
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
Fuzzy sliding m
o
de contr
ol of
doubly-
f
ed induction generator
dr
i
v
e
n
b
y w
i
n
d
t
ur
bi
ne
M. Ben
mezi
an
e
1
,
S.
Z
e
birate
1,2
,
A. C
h
a
k
e
r
1
,
Z.
B
o
u
d
j
e
m
a
3
1
S
C
A
M
RE
Laborat
ory
,
M
auri
ce
Au
din
Natio
nal P
o
l
y
t
echni
c
S
c
h
o
ol
o
f
O
ran
, ENP
O,
Oran
,
Algeria
2
IM
S
I
,
U
n
i
vers
ity
of
O
ran
2 M
oham
e
d
BE
NA
HM
ED,
O
r
an,
A
lgeria
3
D
e
p
a
rt
men
t
o
f E
l
ectri
cal E
ng
ine
e
ri
ng
,
U
niv
e
rsity
of
S
i
d
i
Bel-A
b
bes, Algeria
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Jan
2
2, 201
9
Re
vise
d Mar
1,
201
9
A
c
c
e
pte
d
A
pr 8,
201
9
Th
is
p
a
p
er
p
resent
a
h
y
b
rid
n
onlinear
c
o
n
t
r
ol
b
ased
o
n
f
u
zzy
s
l
idin
g
m
ode
t
o
con
t
ro
l
wi
nd
e
n
e
rgy
c
o
nv
ersi
on
s
y
s
t
em
u
s
i
ng
a
dou
bl
y
f
e
d
i
n
d
u
ct
io
n
g
e
ne
ra
to
r
(DFIG).
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s
i
t
in
g
o
f
c
ou
pl
in
g
fu
z
z
y
l
o
g
ic
c
on
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l
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s
l
i
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i
ng
m
o
d
e
c
o
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l
t
h
i
s
t
echni
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e
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ntrod
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o
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ant
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ge
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v
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s
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yste
ms,
na
me
ly
t
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c
ha
tte
r
in
g
ph
e
n
o
m
e
n
on
.
E
ff
ect
iv
e
n
ess
and
f
e
a
s
ib
il
it
y
o
f
t
he
p
ro
po
sed
co
nt
rol
strat
e
gy
a
re
v
erif
ied
b
y
s
i
m
u
lati
on
results
i
n
Matlab S
i
mul
i
nk.
K
eyw
ord
s
:
D
o
u
b
l
y
f
e
d
in
d
u
ct
ion
ge
ner
a
t
o
r
Fu
zz
y
l
ogi
c
Nonlinear
controll
er
Po
wer
co
ntro
l
S
lid
ing
mode
c
ontro
l
l
er
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:
Meriem
B
e
n
m
e
z
i
ane,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
Eng
i
ne
eri
ng,
N
a
ti
ona
l P
o
ly
t
e
c
h
n
i
c
S
c
ho
o
l
of
O
r
a
n
,
Ma
urice
A
u
d
i
n
, A
lgeria.
Em
ail:
m.
benm
ezia
n
e
@
ya
h
oo.fr
1.
I
N
TR
OD
U
C
TI
O
N
Win
d
p
ower
h
a
s
b
ec
ome
i
n
c
r
ea
si
ng
l
y
p
op
u
l
ar
b
ec
a
u
s
e
o
f
t
h
e
i
n
c
r
e
asi
n
g
di
ff
i
c
ul
ty
o
f
th
e
e
n
vi
ron
m
e
n
t
a
l
po
ll
ut
ion
an
d
th
e
g
r
e
e
nho
use
e
ffe
c
t
.
H
u
ge
e
ff
o
r
ts
h
a
v
e
b
e
e
n
m
ad
e
i
n
p
ro
moti
ng
the
w
i
nd
ene
r
g
y
c
onv
e
r
sio
n
s
ys
t
e
m,
to r
e
duce
c
o
sts, i
ncre
ase relia
b
i
l
i
t
y
a
nd r
o
bus
tn
ess [1]. V
ar
i
a
b
l
e spe
e
d
ope
ra
t
i
o
n
o
f
w
i
n
d
t
urb
i
ne
i
s
usua
l
l
y
use
d
t
o
pr
ovi
de
e
ne
rgy
w
i
t
h
b
es
t
e
ffic
i
e
n
c
y
.
Th
ose
base
d
on
do
u
b
l
y
f
e
d
i
nd
uc
ti
on
gene
ra
tors
a
re
w
i
d
e
l
y
use
d
e
s
p
ec
ia
l
l
y
i
n
h
i
g
h
p
o
w
e
r
fie
l
ds,
tha
n
k
s
to
d
i
ffe
rent
a
dva
n
t
age
s
it
pr
esen
ts
n
a
m
e
l
y
:
re
d
u
c
i
n
g
th
e
si
ze
o
f
th
e
c
onv
ert
e
r,
o
p
e
rat
i
n
g
in
a
l
arge
g
ame
o
f
s
p
ee
d,
a
nd
t
h
e
pos
s
i
b
ili
t
y
o
f
co
n
t
rol
l
i
n
g
in
de
pen
d
e
n
t
l
y
the
g
e
n
er
ate
d
acti
v
e
an
d r
eac
t
i
ve
power
s
[2].
A
D
oubl
y
F
e
d
Ind
u
c
t
i
on
G
e
n
e
rator
(
D
FI
G
)
i
s
a
n
e
le
c
t
rica
l
a
s
y
n
c
h
rono
us
t
h
r
e
e
-
ph
ase
ma
ch
i
n
e
w
i
th
ope
n
rot
o
r
w
i
n
d
i
n
gs
w
hic
h
c
a
n
b
e
fe
d
by
e
x
t
e
r
n
al
v
ol
ta
ges.
T
he
t
y
p
i
ca
l
co
nnec
tio
n
sc
h
e
m
e
o
f
t
h
is
m
a
c
hi
ne
i
s
repor
t
e
d
in
F
i
g
ure
1.
T
he
s
t
a
tor
w
i
n
d
i
n
g
s
a
r
e
d
i
rec
tly
c
o
n
n
e
cte
d
t
o
t
he
l
i
n
e
gri
d
,
w
h
ile
t
he
r
o
t
or
w
i
n
di
ngs
a
r
e
con
t
ro
l
l
ed b
y
me
ans of an
inve
rter
[
3].
M
a
n
y
c
o
nt
ro
l
t
e
c
hni
qu
e
s
a
re
u
s
e
d
t
o
c
ont
ro
l
do
u
b
ly
f
ed
i
ndu
c
t
i
o
n
ge
ne
rator.
Z
erz
ouri
e
t
a
l
.
h
a
v
e
trie
d
to
i
mpr
o
v
e
t
he
p
erf
o
rma
n
ce
o
f
a
D
F
IG
w
in
d
e
n
e
r
g
y
c
on
ve
rsi
o
n
s
ys
t
e
m
;
t
he
y
have
p
ro
pose
d
t
he
v
e
c
tor
con
t
ro
l
w
i
t
h
t
h
e
P
I
con
t
rol
l
e
r
t
o
dec
o
uple
t
h
e
ac
tive
a
nd
re
act
iv
e
po
we
r
of
t
h
e
s
t
a
t
o
r.
T
he
y
h
a
v
e
u
se
d
a
s
i
n
g
l
e
P
I
i
n
ea
ch
c
o
n
tr
ol
l
o
o
p
,
bu
t
t
h
is
c
o
n
t
r
o
l
has
osc
i
l
l
a
t
i
o
n
s
,
exc
ee
d
a
nce
s
,
a
nd
the
de
c
o
u
p
lin
g
is
n
ot
f
u
l
ly
ma
int
a
ine
d
[
4].
P
o
i
t
ier
s
e
t
a
l
.
have
u
se
d the R
S
T
p
o
l
y
nom
i
a
l
co
n
t
ro
ll
e
r
,
t
h
ey h
a
v
e
fo
un
d
tha
t
the RS
T
c
ontro
l
is
m
ore
robust
than
t
he
P
I
contro
l
c
o
mpa
r
ed
t
o
t
h
e
r
o
tor
resist
a
n
c
e
v
aria
ti
o
n
,
b
u
t
t
h
e
osc
i
l
l
at
ion
s
rem
a
in
a
ppar
e
nt [5]
.
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
Fuzzy
sli
d
i
n
g m
ode
co
nt
ro
l o
f
do
u
b
ly-
f
ed
in
duc
tio
n ge
ner
a
to
r
dri
v
e
n
by
w
i
nd
t
u
rbi
n
e
(M. Be
nm
ezia
ne)
1
593
The
s
l
i
d
i
ng
m
ode
c
o
n
t
rol
(S
M
C
)
ac
h
i
e
v
e
s
r
ob
ust
c
o
n
t
r
o
l
by
ad
d
i
n
g
a
dis
c
on
t
i
n
uou
s
c
o
n
t
ro
l
s
i
gn
a
l
across
the
sliding
su
rface
,
sa
t
i
sfyi
ng
t
he
s
l
i
d
i
ng
c
o
n
d
i
tio
n [6
].
I
n
[7],
a
d
y
n
a
mica
l
s
l
i
d
i
n
g
m
ode pow
er
c
ontro
l
st
r
u
c
t
ure
is
s
u
g
g
es
ted
for
D
F
IG
.
I
n
[
8
]
,
the
SM
C
tec
h
n
i
q
u
e
is
u
se
d
t
o
c
o
n
t
r
ol
t
he
r
ota
t
i
o
n
a
l
spe
e
d
i
n
t
he
r
ot
or
side
a
s
w
e
l
l
a
s
t
h
e
dc-l
in
k
v
o
l
t
a
ge
i
n
t
h
e
gr
id
s
ide
of
a
w
i
n
d
ene
r
gy
c
on
ve
rsi
on
s
y
ste
m
;
a
m
ode
l
pred
ict
i
v
e
con
t
ro
l
bas
e
d
S
M
C
i
s
p
ro
po
sed
t
o
c
o
n
t
r
o
l
a
thre
e-p
h
a
s
e
gri
d
-c
on
nec
t
e
d
c
on
ver
t
e
r
a
n
d
t
he
g
rid
c
u
rre
nt
t
o
t
a
l
harm
on
ic
d
i
s
t
o
rtion
an
d
the
sw
itc
hi
ng
lo
sse
s
a
re lar
gel
y
m
itiga
te
d
in [9]
.
DFI
G
T
GB
–
G
ear
b
ox
I
G
–
I
n
d
u
c
ti
o
n
G
en
er
ato
r
RS
C
–
Roto
r
-
S
id
e C
o
n
v
er
ter
G
S
C –
G
r
id S
ide Conv
erte
r
T
–
Tr
a
n
s
f
o
r
m
e
r
RS
C
GS
C
GB
F
i
gure
1.
C
o
n
f
i
gur
a
tio
n
of D
F
I
G
-
Win
d T
u
r
b
i
n
e
Th
e
S
M
C
h
a
s
a
ma
j
o
r
in
c
onve
n
i
en
ce
w
hi
c
h
t
h
e
c
h
a
t
t
eri
n
g
e
f
f
e
c
t
i
s
c
r
ea
t
e
d
b
y
t
he
d
isco
n
t
i
n
uous part
o
f
c
on
t
r
o
l
.
C
h
at
t
e
ri
n
g
c
a
u
s
es
s
ev
e
r
al
d
a
m
ag
e
s
t
o
t
h
e
me
ch
a
n
i
c
a
l
c
omp
o
n
e
n
ts.
T
o
t
rea
t
t
he
se
d
iffic
u
lt
ies
a
n
d
impro
v
e
t
h
e
p
e
r
f
orm
a
nce
s
,
d
i
ffere
nt
m
et
ho
ds
w
er
e
pro
p
o
s
ed
s
uc
h
as
b
y
re
p
l
a
c
i
n
g
th
e
si
gn
func
t
i
o
n
w
it
h
sat
u
rati
o
n
[
1
0
]
or
u
s
i
ng
Q
u
a
s
i-S
M
C
a
n
d
fuz
z
y
m
a
t
h
em
atic
s
[1
1].
I
n
[
12]
a
n
o
p
tim
ized
s
lid
in
g
mo
de
c
o
n
t
r
ol
s
(S
M
C
)
stra
t
e
g
y
t
o
ma
x
i
m
i
z
e
exi
s
te
nce
regi
o
n
f
or
s
ing
l
e-
phase
d
y
na
mic
v
o
l
t
ag
e
rest
ore
r
s.
I
t
i
s
s
how
n
a
n
al
yt
ic
a
lly
t
ha
t
t
h
ere
e
x
ist
s
a
n
op
ti
mu
m
sli
d
ing
co
ef
fi
ci
e
n
t
w
hic
h
en
l
ar
g
e
s
the e
x
is
te
nc
e
re
gion o
f
the
sl
i
d
i
ng
mode
t
o
i
t
s
m
a
x
i
m
u
m.
A
lso,
i
t
is
p
oin
t
ed
o
u
t
t
ha
t
t
h
e
o
p
t
i
mum
s
li
di
n
g
c
oe
ffic
i
e
n
t
im
prove
s
the
d
ynam
i
c
respo
n
se.
In
[
1
3
]
t
h
e
a
u
thor
p
r
opose
s
a
S
M
C
c
o
n
t
ro
l
stra
te
gy
w
h
ic
h
c
o
mbine
s
a
s
w
i
t
c
hed
p
o
l
i
c
y
w
i
t
h
a
t
i
me
-
base
d
ada
p
ta
t
i
on
of
t
h
e
c
ontr
o
l
ga
in,
t
h
er
eb
y
a
l
l
o
w
i
ng
to
e
ffe
c
tive
l
y
dea
l
i
n
g
w
i
th
a
v
ery
co
nserva
t
i
ve
p
rior
kn
ow
le
d
g
e
of
t
he
u
p
p
e
r
b
ou
nds
o
n
t
h
e
u
n
c
e
r
tai
n
t
i
e
s
,
w
h
i
c
h
usua
l
l
y
l
e
a
d
s
t
o
a
l
a
r
g
e
c
o
n
t
r
o
l
a
u
t
h
o
r
i
t
y
,
a
n
d
rela
t
e
d per
f
or
m
a
nc
e de
grada
t
i
o
n in
[
1
4
].
The
fuzz
y
l
o
gi
c
con
t
ro
l
l
er
i
s
a
pow
erf
u
l
t
o
o
l
f
or
c
o
n
tr
ol
lin
g
c
o
m
p
l
e
x
p
r
o
c
e
s
s
e
s
,
w
i
t
h
o
u
t
t
h
e
n
e
e
d
o
f
a
deta
i
l
ed
m
a
t
he
ma
tic
al
m
o
d
e
l
o
f
t
he
s
ys
te
m
.
I
n
fac
t
,
th
i
s
t
ec
h
ni
qu
e
of
c
o
n
t
r
ol
h
a
s
b
ee
n
u
s
e
d
t
o
sol
v
e
t
h
e
un
k
now
n
par
a
m
e
ter
s
v
ar
i
a
t
i
o
n
s
or
t
o
rem
ove
t
he
e
ffe
c
t
o
f
no
n
lin
ea
rity
;
it
h
as
b
e
e
n
suc
c
e
ssfu
l
l
y
a
p
p
li
e
d
t
o
elec
tr
oma
gne
t
i
c
m
o
tors con
trol
a
n
d
t
he
f
uzz
y
m
odel o
f
a
p
la
nt i
s ver
y
ea
s
y to a
pp
ly
[
1
5
].
I
n
t
his
pa
per
t
h
e
slid
i
ng
m
ode
c
on
tro
l
ler
is
c
ombi
ne
d
w
i
th
F
uz
z
y
L
o
g
i
c
(
F
L)
t
o
form
a
f
uzz
y
s
l
i
d
in
g
mode
c
o
n
t
r
o
l
l
e
r
(
F
S
M
C)
t
o
re
duce
t
h
e
c
h
a
tter
i
n
g
p
hen
o
m
enon
a
nd
im
pro
v
e
ti
m
e
o
f
repo
nse
[1
6]
.
D
e
sig
n
,
i
m
p
l
e
m
en
t
a
ti
on
,
an
a
l
y
s
i
s
a
nd
c
o
mp
a
r
i
s
o
n
bet
w
ee
n
t
h
e
cl
assi
c
a
l
s
l
i
d
in
g
mode
c
o
n
t
rol
(
S
M
C
)
an
d
t
h
e
hy
br
id
fuz
z
y
sl
i
di
ng
mode
c
on
tro
l
(
F
S
M
C)
i
s
presente
d w
i
t
h
sim
ula
t
io
n
in Matlab
Simulink.
2.
RESEARCH
M
ETH
O
D
2.1.
D
FIG
mod
e
l
The
D
o
u
b
l
y F
e
d I
n
d
u
ct
ion
G
e
ne
rat
o
r
DF
IG
m
odel u
s
i
n
g P
a
rk
t
r
a
nsf
orm
a
tio
n is a
s
(1)
[17]:
ds
s
d
s
d
s
s
qs
qs
s
q
s
q
s
s
ds
dr
r
d
r
d
r
r
qr
qr
r
q
r
q
r
r
dr
d
VR
I
ω
dt
d
VR
I
ω
dt
d
VR
I
ω
dt
d
VR
I
ω
dt
The
fl
u
x
ca
n
b
e
expre
ssed a
s
(2):
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
. 3
,
S
e
p
2
019
:
1
5
9
2
–
1
602
1
594
qs
qr
r
qr
ds
dr
r
dr
qr
qs
s
qs
dr
ds
s
ds
MI
I
L
MI
I
L
MI
I
L
MI
I
L
The
sta
t
or
a
n
d
r
ot
or
a
ngu
lar
v
e
loc
i
t
i
es
a
r
e
l
in
ke
d
b
y
t
he
f
o
l
lo
w
i
ng
rela
ti
o
n
:
ω
s
=
ω
+
ω
r
.
The
m
e
c
h
a
n
ica
l
e
qua
t
i
o
n
i
s
g
i
ven
b
y
(
3)
:
f
dt
d
J
C
C
r
em
(3
)
Where
t
h
e
elec
trom
ag
ne
tic
t
orque
C
em
c
an
b
e
wr
i
t
ten
as
a
f
unc
t
i
on
o
f
s
ta
t
o
r
fl
uxes
and
r
o
tor
cur
r
ent
s (
4
):
()
em
qs
dr
ds
qr
s
M
Cp
I
I
L
(4
)
2.
2.
Act
i
v
e
an
d
reac
t
ive
powe
r c
o
ntr
o
l
To
eas
i
l
y
c
o
n
t
r
o
l
t
h
e
pr
o
duc
t
i
o
n
of
e
lectr
i
c
i
t
y
f
r
o
m
w
i
nd,
w
e
w
il
l
a
c
h
i
e
v
e
an
i
n
d
e
p
e
nde
nt
c
on
tr
ol
o
f
a
c
ti
ve
a
n
d
r
e
acti
v
e
p
o
w
e
r
by
t
h
e
st
a
t
or
f
l
u
x
o
r
i
e
n
t
at
ion
as
s
h
o
w
n
o
n
F
i
gur
e
2
[1
8]
.
F
i
gur
e
2.
P
ow
e
r
c
ontr
o
l
betw
e
e
n
t
he
s
tat
o
r
an
d
netw
or
k
To
r
ea
l
i
z
e
a
s
ta
tor
ac
t
i
ve
a
n
d
r
eac
ti
ve
p
owe
r
v
ec
t
o
r
co
ntro
l,
w
e
c
hoose
a
d-
q
r
e
fer
e
nce
-
fr
am
e
sync
h
r
o
n
i
z
e
d
w
i
t
h
t
he
s
t
a
t
o
r
f
l
u
x
[
1
9
]
.
B
y
sett
ing
n
u
ll
t
h
e
qua
dr
at
i
c
c
ompo
n
e
n
t
o
f
t
he
s
t
a
t
o
r
f
l
ux,
w
e
have
(
5)
:
and
0
ds
s
q
s
(
5
)
a
nd t
h
e
elec
tro
m
agne
tic
t
orq
u
e
can
b
e
expre
s
se
d (6)
:
em
q
r
d
s
s
M
Cp
I
L
(6
)
B
y
s
ubs
t
itu
t
i
ng
(
6)
i
n
(
3
)
,
t
he
f
o
l
low
i
n
g
r
ot
or
f
l
u
x
eq
uat
i
ons
ar
e
obt
a
i
ne
d
:
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
Fuzzy
sli
d
i
n
g m
ode
co
nt
ro
l o
f
do
u
b
ly-
f
ed
in
duc
tio
n ge
ner
a
to
r
dri
v
e
n
by
w
i
nd
t
u
rbi
n
e
(M. Be
nm
ezia
ne)
1
595
0
s
sd
s
d
r
s
qs
q
r
L
IM
I
L
IM
I
(7
)
More
ove
r,
t
he
sta
tor
vol
ta
ge
equa
tio
ns a
re
r
e
duc
e
d
t
(
8)o:
0
ds
qs
s
s
V
V
(8
)
By
s
up
po
si
ng
t
h
a
t
t
h
e
el
e
c
t
ri
cal
s
up
ply
n
e
t
w
o
r
k
i
s
s
t
a
bl
e
,
h
a
vi
n
g
f
or sim
ple
vo
lta
ge
V
s
tha
t
led t
o
a
st
a
t
or
f
lux
s
c
o
n
s
t
a
n
t
.
Th
i
s
c
on
si
dera
ti
on
a
ssoc
i
a
te
d
w
i
t
h
(
7)
s
h
o
w
s
t
h
a
t
t
h
e
e
l
ectr
o
m
a
gne
tic
t
or
q
u
e
on
l
y
d
e
p
e
nds
o
n
the
q
-
a
xis ro
tor
curre
nt
c
om
po
nen
t
.
U
s
in
g (
8
),
a
relati
o
n be
t
w
ee
n
the
sta
t
or a
nd rot
o
r
curr
ents ca
n
be
esta
bl
is
he
d (9)
[
2
0
]:
s
ds
d
r
s
s
qs
q
r
s
M
II
LL
M
II
L
(
9)
The
sta
t
or
ac
t
ive
and
rea
c
t
i
ve
pow
e
r
s a
r
e
writ
te
n(1
0
):
qs
ds
ds
qs
s
qs
qs
ds
ds
s
I
V
I
V
Q
I
V
I
V
P
(
10)
B
y
u
s
i
n
g
(
1
)
,
(
2
)
,
(
4
)
a
n
d
(
1
0
)
,
t
he
s
t
a
t
o
r
i
c
a
c
t
i
v
e
a
n
d
re
act
ive
p
o
w
e
r,
t
he
r
otor
i
c
f
l
u
xes
and
v
o
lta
ges
c
a
n
b
e
w
r
itte
n ve
rsus
r
ot
oric
c
urre
nts
as:
2
ss
sq
r
s
s
ss
s
sd
r
ss
ω
M
PI
L
ω
M
ω
QI
LL
2
2
()
()
s
dr
r
d
r
ss
qr
r
q
r
s
M
M
L-
I
LL
M
L-
I
L
22
dr
dr
r
d
r
r
s
r
qr
ss
22
qr
s
qr
r
q
r
r
s
r
d
r
s
ss
s
dI
MM
VR
I
L
-
g
ω
L
-
I
Ld
t
L
dI
M
MM
VR
I
L
-
g
ω
L
-
I
g
ω
Ld
t
L
L
()
()
()
()
In stea
d
y sta
t
e,
the
s
eco
nd
der
i
va
t
i
ve
t
e
r
ms
o
f the
tw
o e
qua
t
i
o
ns i
n
(14)
a
re nil. We
can
t
h
u
s
w
r
ite:
2
2
()
()
dr
r
d
r
s
r
q
r
s
s
qr
r
q
r
s
r
d
r
s
ss
M
VR
I
g
ω
L-
I
L
M
M
VR
Ig
ω
L-
I
g
ω
LL
The
th
i
r
d
ter
m
,
w
h
ic
h
c
o
nst
i
tute
s
cr
oss-
co
u
p
li
ng
t
e
rm
s,
can
b
e
ne
g
l
ec
te
d
b
e
ca
use
o
f
t
heir
s
m
a
l
l
i
n
f
l
u
ence
.
These
term
s c
a
n be
c
ompe
n
s
a
t
e
d
b
y an a
de
q
u
ate
sy
n
t
he
sis of t
he
regu
la
t
o
rs i
n
the c
o
nt
r
o
l lo
op
s [20]. F
igure
3
show
s t
h
e
P
o
w
e
r
Con
t
r
o
l
of D
F
I
G
.
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
. 3
,
S
e
p
2
019
:
1
5
9
2
–
1
602
1
596
F
i
gur
e
3.
P
ow
e
r
c
ontr
o
l
of
D
F
I
G
2.
3.
S
lid
in
g
mod
e
c
on
t
r
ol
The
s
l
idi
n
g
m
ode
t
ec
hni
q
u
e
is
d
eve
l
op
e
d
f
r
o
m
var
i
a
b
le
s
tr
uc
t
u
r
e
c
o
n
t
r
ol
t
o
sol
v
e
t
h
e
di
sadv
a
n
t
a
g
e
s
of
o
t
h
er
d
e
s
ig
ns
o
f
no
n
line
a
r
c
o
n
t
r
o
l
sys
t
em
s.
T
he
s
l
i
d
i
n
g
mode
i
s
a
t
echn
i
q
u
e
t
o
adj
u
st
f
e
e
db
ac
k
by
pr
ev
io
u
s
ly
d
efin
i
ng
a
s
u
rfa
c
e
.
The
syst
e
m
w
hich
i
s
co
n
t
ro
ll
e
d
w
ill
be
f
or
ced
t
o
t
h
a
t
s
urface
,
t
h
en
t
h
e
be
ha
v
i
o
u
r
o
f
t
he
s
yst
e
m
sl
ide
s
t
o
t
h
e
des
i
r
e
d
e
q
u
i
l
i
br
i
u
m
po
i
n
t
.
Th
e
ma
i
n
f
e
a
t
u
re
o
f
th
is
c
ont
rol
is
t
h
a
t
we
on
l
y
n
ee
d
t
o
d
r
i
ve
t
he
e
r
r
o
r
to
a
“
sw
it
c
h
ing
sur
f
ace
”.
W
he
n
t
h
e
s
y
s
te
m
is
i
n
“
s
lid
i
ng
m
ode
”,
t
he
s
ys
tem
be
ha
v
i
o
u
r
is
n
ot
a
ffe
c
t
e
d
b
y
any
mo
de
ll
i
n
g
u
n
ce
r
t
a
i
n
tie
s
and
/
or
d
i
s
t
u
r
b
anc
e
s
.
The
d
e
si
gn
of
t
he
c
on
tr
o
l
sys
t
em
will be
d
em
on
st
r
a
te
d f
o
r
a
non
li
near
sys
t
e
m
prese
n
te
d in
t
he
c
a
n
o
n
ic
al
f
or
m(
15)
[
21
]
:
x
= f
(
x,t
)
+B
(
x,t
)
U
(
x,t
)
, x
R
n
, U
R
m
, r
a
n
(
B
(
x,t
))
= m
(
15)
Wit
h
c
on
tr
o
l
i
n
t
h
e
s
lid
i
ng
m
ode
,
t
h
e
g
o
al
i
s
t
o
k
ee
p
the
s
y
s
t
e
m
moti
o
n
on
the
ma
n
i
f
o
ld
S
,
wh
ich
is
d
e
f
i
n
e
d
as:
S
= {
x
:
e
(
x
,
t
)
=
0
}
(1
6
)
e
=
x
d
-
x
(
1
7
)
Here
e
i
s
the
tr
acki
n
g
error
ve
ct
or,
x
d
i
s
the
d
e
si
r
e
d
s
t
at
e
,
x
i
s
t
h
e
sta
t
e
ve
ct
or
.
The
c
o
ntr
o
l
i
n
pu
t
U
h
a
s
t
o
gua
r
a
ntee
t
ha
t
the
mo
ti
o
n
o
f
t
h
e
sys
t
em
d
e
s
c
r
ibe
d
i
n
(
17)
i
s
r
e
str
i
c
t
e
d
t
o
b
e
lo
n
g
t
o
t
h
e
ma
nif
o
ld
S
i
n
th
e
state
spac
e.
T
he
s
l
i
d
i
ng
m
ode
c
o
n
tr
ol
s
ho
u
l
d
b
e
c
hose
n
s
uc
h
tha
t
t
he
ca
ndi
d
a
t
e
L
y
a
pun
ov
f
un
cti
o
n
sa
ti
sfi
e
s
the
L
y
ap
u
n
o
v
sta
bi
l
i
t
y
c
riteri
a
[22]
:
2
)
(
2
1
x
S
(
18)
)
(
)
(
x
S
x
S
(
19)
This can
b
e as
su
r
e
d
fo
r
:
x
S
(
20)
Here
η
i
s
s
t
r
i
c
tly
p
os
iti
ve
.
Essen
t
i
a
l
l
y,
e
q
u
at
i
o
n
(1
8)
s
t
a
tes
th
at
t
he
s
qua
r
e
d
“
d
ista
nc
e”
t
o
t
h
e
s
u
r
f
ace
,
m
e
a
s
ur
ed
by
e
(
x
)
2
,
dec
r
ea
se
s
a
l
o
n
g
a
l
l
s
y
s
te
m
t
r
ajec
tori
e
s
.
The
r
efore
(
19),
(20)
s
at
i
s
f
y
t
h
e
L
y
a
p
unov
c
o
n
d
it
i
on.
W
it
h
se
le
c
t
ed
L
y
a
pu
n
o
v
f
unc
t
i
on
t
he
s
ta
bi
li
ty
o
f
the
w
h
o
l
e
c
o
nt
r
o
l
sy
s
t
e
m
i
s
gua
r
a
n
t
ee
d.
The
co
ntro
l
fu
nct
i
o
n
wi
ll
s
a
tisfy re
ach
in
g c
o
nd
iti
o
n
s i
n
the
f
o
l
l
ow
in
g
for
m
[
23]
:
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
Fuzzy
sli
d
i
n
g m
ode
co
nt
ro
l o
f
do
u
b
ly-
f
ed
in
duc
tio
n ge
ner
a
to
r
dri
v
e
n
by
w
i
nd
t
u
rbi
n
e
(M. Be
nm
ezia
ne)
1
597
U
co
m
= U
eq
+
U
n
(
21)
Her
e
U
com
i
s
th
e
con
t
r
o
l
v
ecto
r
,
U
eq
i
s
the
e
qui
va
l
e
n
t
c
o
n
t
r
o
l
vec
t
or,
U
n
i
s
t
he
c
orre
cti
o
n
fa
ct
or
a
nd
mu
st
b
e
c
a
l
c
ul
a
t
ed
so
t
h
at
th
e
st
a
bi
li
ty
condi
tions f
or
the sel
ected
co
n
t
ro
l a
r
e
sa
ti
s
f
ie
d.
U
n
= K
sat
(
S
(
x
))
(
22
)
Whe
r
e
sa
t(
S
(
x
)
)
is the
prop
ose
d
s
a
t
urati
o
n fu
nc
ti
on,
K
is t
he
c
ont
r
o
lle
r ga
in
.
In th
i
s pa
per
w
e
p
r
o
p
o
se
the
S
lo
t
i
ne
m
et
ho
d [24]
:
e
ξ
X
S
n
1
dt
d
(
23)
Her
e
,
e
i
s
the tra
c
ki
n
g
e
rror
ve
c
t
or
,
ξ
is a
positi
ve
c
oe
ffic
i
en
t
a
nd
n
i
s
t
h
e
r
e
la
ti
v
e
d
e
g
r
e
e
.
2.4.
Ap
p
licati
o
n
of S
MC
to th
e D
F
IG
In
o
ur
s
t
u
dy,
w
e
cho
o
se
t
he
e
r
r
or
b
etw
e
en
t
he
m
ea
sur
e
d
an
d
re
f
e
re
n
ces
s
t
a
t
o
r
po
we
rs
a
s
sl
idi
ng
mode
surface
s, so
w
e
can
w
rite
t
he
fo
l
low
i
ng
e
xpre
s
si
o
n
:
S
ref
S
q
S
ref
S
d
Q
Q
S
P
P
S
(
24)
The
firs
t orde
r de
ri
va
te
o
f (24)
,
g
i
ves:
S
ref
S
q
S
ref
S
d
Q
Q
S
P
P
S
(
25)
Re
plac
i
ng t
h
e
pow
ers
in (2
5
) by
t
h
e
i
r
expre
ssi
ons g
i
v
en
i
n
(11)
,
one
o
bt
a
i
n
s
:
s
2
s
s
dr
s
s
s
ref
S
2
qr
s
s
s
ref
S
1
L
ψ
ω
I
L
M
ψ
ω
Q
S
I
L
M
ψ
ω
P
S
(
26)
V
dr
a
n
d
V
qr
w
i
ll
b
e
the
tw
o
c
o
m
p
o
n
e
n
t
s
o
f
the
c
o
n
t
ro
l
ve
ctor
u
se
d
t
o
c
ons
t
r
a
i
nt
t
h
e
s
y
s
t
e
m
t
o
c
on
ve
rg
e
t
o
S
dq
=
0
.
The
c
o
nt
r
o
l
vec
t
or
V
dq
e
q
i
s
obta
i
ne
d
by
im
p
o
si
n
g
0
dq
S
s
o
t
h
e
e
q
u
i
va
len
t
c
on
tro
l
c
o
m
pone
n
t
s
a
r
e
gi
ve
n by
the
fo
ll
ow
i
ng
rela
tio
n:
s
s
s
dr
s
s
2
r
qr
r
*
s
s
s
s
s
s
2
r
qr
s
s
2
r
dr
r
*
s
s
s
s
2
r
s
eqdq
L
M
ψ
g
ω
I
g
ω
L
M
L
I
R
P
M
ψ
ω
L
M
ψ
L
M
L
I
g
ω
L
M
L
I
R
Q
M
ψ
ω
L
M
L
L
V
(
27)
To
o
bt
ai
n
go
od
p
e
r
fo
rman
c
e
s,
d
yn
a
m
i
c
a
nd
c
o
m
mu
ta
tion
s
a
rou
n
d
t
h
e
s
u
r
f
a
c
e
s
,
t
h
e
c
o
n
t
r
o
l
v
e
c
t
o
r
i
s
impo
sed
as fo
l
l
o
w
s
:
)
(
K
dq
eqdq
dq
S
sat
V
V
(28)
The
SM w
ill e
x
i
s
t o
n
l
y i
f
t
he
fol
low
i
n
g
co
n
d
i
t
i
on
i
s
m
e
t
:
0
S
S
(29)
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
:
1592
– 1
602
1
598
2.5.
Fu
zzy
s
l
i
d
i
n
g
mod
e
control of
th
e
D
FIG
Th
e
di
sa
dv
a
n
tag
e
o
f
s
lid
in
g
mo
d
e
c
on
t
r
o
l
l
e
rs
i
s
t
h
at
t
he
d
i
s
co
n
ti
nuo
us
c
ont
ro
l
si
gna
l
p
r
od
u
c
es
cha
tter
i
n
g
.
In
o
rder
t
o
e
l
im
i
n
ate
the
c
h
a
t
t
e
ring
p
h
en
om
eno
n
,
we
p
ro
po
se
t
o
u
s
e
t
h
e
f
u
z
z
y
sli
d
in
g
mo
de
con
t
ro
l.
T
he
f
uzzy
s
l
i
d
i
n
g
mode
c
o
n
t
rol
l
er
(
F
S
M
C)
i
s
a
modi
fica
ti
on
o
f
t
h
e
s
l
id
ing
mode
c
o
n
t
rol
l
er,
w
h
e
r
e
t
h
e
swit
ch
ing
co
n
t
roll
e
r
t
e
r
m s
a
t
(
S
(
x
)
)
,
has be
en
r
eplac
e
d
b
y
a
fuzz
y
co
n
t
rol i
n
pu
t as
g
ive
n
bel
ow
[
25
].
U
co
m
= U
eq
+
U
Fu
z
z
y
(
30)
The
pr
op
ose
d
fuz
zy
s
l
i
d
i
n
g
mode
c
o
n
t
r
ol,
w
h
ic
h is de
s
i
g
ne
d to c
on
tro
l
t
he
ac
t
i
v
e a
nd rea
c
ti
ve pow
er
o
f
t
h
e
D
F
I
G
i
s
s
h
o
w
n
i
n
F
i
g
u
r
e
4
.
T
o
s
y
n
t
h
e
s
i
s
t
h
e
f
u
z
z
y
c
o
n
t
r
o
l
l
e
r
o
f
t
h
e
two
varia
b
les
(a
cti
v
e
a
n
d
re
acti
v
e
pow
er
s)
f
uz
z
y
c
on
tro
l
u
se
s
a
set
o
f
r
ule
s
t
o
r
e
pre
s
e
n
t
h
o
w
to
c
o
n
tr
ol
t
he
s
ys
tem
;
t
he
se
a
re
t
he
s
te
ps
o
f
fuz
z
i
fica
t
i
o
n
a
nd
de
fuzz
ifica
t
i
o
n
a
s
s
h
o
w
n
i
n
Ta
b
l
e
1.
T
he
m
e
m
b
e
r
shi
p
f
u
n
c
t
i
ons
f
or
i
np
ut
a
n
d
o
u
t
put
varia
b
l
e
s ar
e gi
ven
b
y
F
i
g
ur
e 5.
Figure 4.
B
l
oc
d
i
a
gram
of the D
F
IG
c
ont
ro
l w
i
th FSMC
Ta
b
l
e 1.
Matri
x
o
f
Infere
n
ce
ΔE
E
NB
N
M
NS
E
Z
P
S
P
M
PB
NB
N
B
NB
N
B
NB
N
M
NS
E
Z
NM
N
B
NB
N
B
NM
N
S
EZ
P
S
NS
N
B
N
B
N
M
NS
E
Z
PS
P
M
EZ
N
B
NM
N
S
EZ
P
S
PM
P
B
PS
N
M
N
S
E
Z
PS
P
M
PB
P
B
PM
N
S
EZ
P
S
P
M
P
B
PB
P
B
PB
E
Z
P
S
P
M
PB
P
B
P
B
P
B
- NB
:
Neg
a
tiv
e
B
i
g
,
- NM:
Neg
a
t
i
ve
M
i
d
dl
e,
- N
S
: N
e
gat
i
ve
Sm
a
ll,
-
EZ:
E
qual Zero,
- PS
:
Posit
i
ve
S
m
a
ll,
- PM: P
o
si
ti
ve M
id
d
l
e
,
- PB:
Po
sitiv
e Bi
g
.
F
i
gure
5
. Fu
zzy s
ets
and it
s
me
mb
ersh
ip f
unctio
n
s
-1
-0
.
8
-0
.
6
-0
.
4
-0.2
0
0.2
0.4
0.
6
0.8
1
x
1
0
4
0
0.
5
1
"mem
ber
s
h
i
p
chan
g
e
r
ate
of
e
r
r
o
r
s
"
De
lt
a
ed(
k
)
,
D
e
l
t
a
eq(
k
)
sN
G
sN
M
sN
P
sE
Z
sP
P
sP
M
sP
G
-1
-0.
8
-0.
6
-0.
4
-0.
2
0
0.2
0.4
0.6
0.8
1
x
1
0
4
0
0.5
1
"
m
e
m
b
e
r
s
h
i
p
c
o
n
tro
l s
ig
n
a
ls"
u
d(
k
)
,u
q(
k
)
sNG
sN
M
sNP
sE
Z
sP
P
sP
M
sP
G
-1
-0.8
-0
.6
-0
.
4
-0
.
2
0
0.
2
0.4
0.
6
0.8
1
x
1
0
4
0
0.
5
1
"
m
e
m
be
r
s
hi
p
e
r
r
o
r
s
"
e
d(k)
, e
q(
k)
sNG
sNM
sNP
sE
Z
sP
P
sP
M
sP
G
K
P
S
-mes
F
L
V
q
r
n
S
(
P
)
V
qr
-r
e
f
P
S
-re
f
-
+
+
+
K
Q
S
-m
es
F
L
V
dr
n
S
(
Q
)
V
dr
-r
e
f
Q
S
-re
f
-
+
+
+
V
qr
eq
V
dr
eq
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
Fuzzy
sli
d
i
n
g m
ode
co
nt
ro
l o
f
do
u
b
ly-
f
ed
in
duc
tio
n ge
ner
a
to
r
dri
v
e
n
by
w
i
nd
t
u
rbi
n
e
(M. Be
nm
ezia
ne)
1
599
3.
RESULT
S
A
N
D
ANALY
S
IS
The
s
e
s
i
mula
t
i
ons
r
epre
se
nt
a
c
om
par
i
s
on
betw
e
e
n
t
he
c
on
ve
nti
o
n
a
l
s
l
i
d
i
ng
m
o
de
c
on
tro
l
a
n
d
t
h
e
f
u
z
z
y
s
l
i
d
i
n
g
m
o
d
e
c
o
n
t
r
o
l
.
I
n
t
h
e
a
i
m
t
o
e
v
a
l
u
a
t
e
t
h
e
p
e
r
f
o
rman
c
e
s
o
f
th
e
s
e
t
w
o
co
nt
rol
l
ers,
t
h
re
e
cat
eg
o
r
i
e
s
of
t
est
s
h
a
v
e
b
e
e
n
r
ea
li
z
e
d
b
y
t
h
e
si
mu
l
a
ti
on
in
M
a
tla
b/S
i
m
u
lin
k.
T
he
p
a
r
am
eter
s
ut
i
l
iz
e
d
a
r
e
liste
d
in
T
ab
les
2
and
3.
Table
2. DFI
G par
a
m
e
ters
P
N
=
1.
5MW
V
s
=
398/690
V
f=
50
Hz
J
=
1000
Kg.m
2
P
=
2
R
s
=
0
.
012
Ω
R
r
=
0
.
021Ω
f
v=
0.
0024
Nm
/
s
M=
0.
0135
H
L
s
=
0
.
0137
H
L
r=
0.
0136
H
Tab
l
e
3. Tur
bine
par
am
eters
Diam
e
t
e
r
=
35.
25 m
Ge
a
r
box
G=
90
N
u
m
be
r
of
b
l
a
de=3
3.1.
Pu
rsu
i
t test
S
i
mulat
i
o
n
resul
t
s
a
r
e
pre
s
ente
d
in
F
ig
ures
6
a
nd
7.
As
i
t’s
sh
own
by
Figure
6,
f
o
r
t
h
e
t
wo
controlle
r
s,
t
h
e
s
ta
to
r
a
c
tive
a
nd
r
e
activ
e
po
we
rs
t
ra
ck
a
lmost
p
e
r
f
e
c
t
l
y
t
h
e
i
r
r
e
f
e
r
e
n
c
e
s
a
n
d
e
n
s
u
r
e
a
p
e
r
f
e
c
t
dec
o
upling
b
e
tween
t
he
t
w
o
a
xe
s.
B
oth
c
o
n
t
ro
ll
e
r
s
p
r
ove
d
very
g
oo
d
perfo
r
manc
e
f
o
r
t
h
is
t
est.
O
n
th
e
other
hand,
F
igure
7
shows
the
h
a
rmonic
spectru
m
o
f
one
p
h
a
se
s
tato
r
c
u
rre
n
t
of
t
h
e
D
F
I
G
obta
i
ned
u
s
ing
F
a
st
F
our
i
e
r
Tran
sfor
m
(FF
T
)
.
It
is
observ
e
d that
t
he F
SMC is e
ffe
c
t
ive in
e
liminating
chatterin
g
phe
nomen
on.
3.2.
S
e
n
sitivit
y
t
o
th
e
sp
e
e
d
var
i
a
ti
on
T
h
e
a
i
m
o
f
t
h
i
s
t
e
s
t
i
s
t
o
a
n
a
l
y
z
e
t
h
e
i
n
f
l
u
e
n
c
e
o
f
a
s
p
e
e
d
v
a
r
ia
ti
on
o
f
the
D
F
IG
on
a
c
ti
ve
a
n
d
rea
c
ti
ve
pow
er
s
for
t
h
e
t
w
o
c
o
n
t
ro
l
l
ers.
F
or
t
h
i
s
o
b
je
ct
ive
a
n
d
a
t
time
=
0.
04s,
the
s
p
ee
d
w
a
s
va
rie
d
f
ro
m
15
0
ra
d
/
s
to
1
7
0
r
ad
/s
.
Th
e
si
mu
l
a
ti
on
re
sul
t
s
a
r
e
sho
w
n
in
F
i
g
u
re
8
.
A
s
i
t
is
s
h
o
w
n
i
n
F
i
gure
8,
t
h
e
s
pe
e
d
varia
t
i
o
n
pro
d
u
ced
a
s
li
gh
t
e
f
fe
ct
o
n
t
h
e
po
w
e
rs
c
urves
of the
sys
t
em
w
i
t
h
SM
C
co
n
t
rol
l
er,
w
h
ile t
he
e
ffec
t is
alm
o
st
n
e
g
li
g
i
ble
fo
r
t
h
e
s
y
s
t
em
w
it
h
FS
MC
o
n
e
.
It
ca
n
b
e
n
o
t
ic
e
d
t
ha
t
th
is
l
a
s
t
has
a
nea
r
ly
p
er
fec
t
s
pe
ed
di
st
urba
nce
re
j
ecti
o
n,
i
n
d
eed
;
o
n
ly
v
er
y
sm
all
p
o
wer
var
i
a
t
i
o
ns
c
an
b
e
observ
e
d
(fe
we
r
th
a
n
2
%
)
.
Th
i
s
r
esu
l
t
is
a
ttra
c
t
i
v
e
fo
r
w
i
nd
ener
gy
a
pplica
t
i
ons
t
o
e
n
s
u
r
e
s
t
a
bil
i
t
y
a
n
d
q
u
a
lit
y
of
t
he
g
e
n
era
t
e
d
pow
er
w
h
e
n
t
h
e
spee
d
is
v
ary
i
n
g
.
3.3.
R
ob
u
s
n
e
ss
I
n
o
rder
t
o
te
st
t
he
r
obus
t
n
ess
of
t
he
u
se
d
co
ntr
o
l
l
e
r
s,
t
he
m
a
chine
par
a
m
e
ters
h
a
v
e
be
e
n
m
od
ifie
d
:
the
va
lue
s
o
f
t
h
e
sta
t
or
a
nd
t
he
r
o
t
or
r
e
s
i
s
ta
nc
es
R
s
a
n
d
R
r
a
re
d
o
uble
d
a
nd
t
he
v
a
l
ues
of
i
nd
uc
t
a
nces
L
s
,
L
r
and
M
a
r
e
d
i
v
i
d
e
d
b
y
2
.
The
ma
ch
i
n
e
is
r
u
nni
n
g
a
t
i
t
s
n
o
m
i
n
al
s
p
e
e
d
.
Th
e
re
sul
t
s
p
res
e
n
ted
in
F
ig
ure
10
show
s
tha
t
t
he
p
ara
m
e
t
ers
va
riat
i
o
ns
o
f
the
D
F
I
G
i
ncre
ase
sli
g
h
tly
t
he
t
i
m
e-r
e
spo
n
se
o
f
the
t
w
o
co
n
t
rolle
rs.
O
n
t
h
e
o
t
h
e
r
h
a
n
d
t
h
i
s
r
e
s
u
l
t
s
s
h
o
w
t
h
a
t
p
a
r
a
m
e
t
e
r
v
a
r
i
a
t
i
o
n
s
o
f
t
h
e
DFIG
p
re
se
nts
a
clea
r
effe
c
t
o
n
the
pow
er
s
cur
v
e
s
(
the
i
r
er
rors
c
urves)
a
nd
t
h
a
t
t
h
e
e
ffec
t
a
p
p
ea
rs
m
or
e
si
gn
ifi
c
a
n
t
for
S
M
C
co
ntr
o
l
l
e
r
t
ha
n
tha
t
w
i
t
h
F
S
M
C
one
.
Thu
s
i
t
c
a
n
be
c
o
n
c
l
ud
ed
t
hat
t
h
is
l
a
s
t
is
m
o
re
r
obus
t
tha
n
t
he
c
lass
i
cal
S
MC
c
on
t
r
oller
.
W
e
c
an
t
h
e
refore
s
ay
t
hat
f
o
r
th
e
F
S
MC,
the
respo
n
se
t
i
m
e
is
s
i
g
n
if
i
c
a
n
t
l
y
reduc
e
d
a
nd
t
h
e
osc
i
l
l
a
t
i
ons
a
re
li
m
i
te
d
a
n
d
da
m
p
ed
m
ore
ra
pid
l
y
c
o
mpa
r
e
d
t
o
S
M
C
co
ntr
o
l
l
e
r
.
S
i
m
ula
tio
ns
w
it
h
th
i
s
t
ype
o
f
c
o
n
t
rol
l
er
prese
n
t
e
d
ve
ry
i
n
t
er
est
i
n
g
p
er
form
ance
s
i
n
t
erm
s
o
f
r
e
fe
re
nc
e
t
rac
k
ing
(t
i
m
e
r
e
spo
n
se,
over
s
hoo
t),
se
nsi
t
i
v
it
y
to per
t
u
r
b
a
t
ion
.
F
i
gur
e 6.
Refe
r
enc
e
s tra
c
k
i
ng
tes
t
0
0.
0
2
0.
04
0.
0
6
0.
08
0.
1
-10
-8
-6
-4
-2
0
x
10
5
Ti
m
e
(
s
)
A
c
t
i
v
e
p
o
w
er
P
s
(
W
)
P
s-
re
f
P
s
(S
M
C
)
P
s
(F
S
M
C
)
0
0.
0
2
0.
0
4
0.
06
0.
08
0.
1
-4
-3
-2
-1
0
1
x
1
0
5
Ti
m
e
(
s
)
React
i
v
e
p
o
w
e
r
Q
s
(
V
a
r
)
Q
s-
re
f
Q
s
(S
M
C
)
Q
s
(F
S
M
C
)
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
. 3
,
S
e
p
2
019
:
1
5
9
2
–
1
602
1
600
F
i
gure
7.
S
pectrum h
a
rmonic of
one
p
h
a
se
s
tato
r cu
rren
t
fo
r
S
MC
a
nd
FSMC
controllers
F
i
gur
e
8.
S
e
n
siti
v
ity
t
o
the
s
p
e
e
d
va
r
i
at
i
o
n
F
i
gur
e
1
0
.
Rob
u
stness
t
e
s
t
4
.
CONCLUSION
Th
is pap
e
r
p
r
e
sen
t
s
H
ybr
id
F
uz
zy
S
l
i
d
i
ng
Mode
C
o
n
tr
ol
o
f
ac
ti
ve
a
n
d
r
e
a
c
t
i
v
e
p
o
w
e
r
i
n
a
D
F
I
G
a
n
d
pe
r
f
or
m
a
nc
e
e
v
a
l
ua
t
i
o
n
s.
A
f
te
r
pr
ese
n
t
i
n
g
a
d
escr
ip
t
i
o
n
o
f
a
dou
bl
y
f
e
d
i
n
d
u
c
t
i
on
gene
r
a
t
o
r
,
a
d
e
c
o
u
p
l
i
n
g
c
o
n
t
r
o
l
m
e
t
h
o
d
o
f
a
c
t
i
v
e
a
n
d
r
eac
ti
ve
p
o
w
ers
for
DFIG
h
as
b
ee
n
de
vel
o
ped.
A
f
t
er
m
ode
lin
g
t
h
e
sys
t
em
,
the
de
scr
i
p
tio
n
of
t
he
c
la
ssic
a
l
s
l
i
di
n
g
m
ode
c
on
tr
o
ller
(
S
M
C
)
i
s
p
r
e
s
e
n
t
e
d
i
n
d
e
t
a
i
l
,
t
h
i
s
c
o
n
t
r
o
l
l
e
r
h
a
s
b
e
e
n
a
p
p
lied
d
u
e
t
o
its
e
xce
lle
n
t
p
r
o
pe
r
t
i
e
s,
s
uc
h
as
i
nse
n
s
i
t
i
v
i
t
y
to
c
er
ta
i
n
e
xter
na
l
d
i
st
ur
banc
e
s
,
how
ev
e
r
i
n
sta
nda
r
d
s
lid
i
n
g
mode
t
her
e
i
s
lar
g
er
c
ha
tter
i
n
g
.
A
hy
br
id
f
uzz
y
sl
id
i
n
g
m
ode
a
ppr
oac
h
u
s
i
n
g
v
e
c
t
or
c
on
tr
o
l
str
a
t
e
gy
w
a
s
e
s
t
a
b
lis
hed
a
n
d
p
r
e
s
e
n
te
d.
Res
p
onse
s
o
f
o
u
r
sy
stem
w
it
h
t
h
is
t
y
p
e
of
c
on
t
r
o
ller
ha
ve
s
h
o
w
n
t
h
a
t
the
las
t
g
ive
s
v
er
y
i
n
t
e
r
e
s
t
i
n
g
per
f
or
m
a
nc
es
t
ow
ar
d
r
e
fer
e
nce
t
r
a
c
k
ing,
s
e
n
s
i
t
i
vi
t
y
t
o
pe
r
t
ur
bat
i
on
an
d
r
obustness under para
m
e
ters var
iation.
0
500
1000
1500
2000
0
500
1000
1500
2000
Fr
e
q
uenc
y
(
Hz
)
S
t
at
o
r
c
ur
r
e
nt
(
S
M
C
C
o
nt
ro
l
l
e
r
)
,
T
H
D
=
3.
05%
Ma
g
0
500
1000
150
0
200
0
0
50
0
100
0
150
0
200
0
Fr
e
q
uen
c
y
(
Hz
)
S
t
a
t
o
r
c
u
r
r
e
n
t
(
F
S
M
C
C
o
n
t
r
o
l
l
e
r
)
,
T
H
D
=
2
.8
5
%
Ma
g
0
0.
02
0.
04
0.
06
0.
08
0.
1
-60
-40
-20
0
20
40
60
80
Ti
m
e
(
s
)
A
c
t
i
v
e
pow
e
r
E
rror
(%
)
SM
C
FS
M
C
0
0.
0
2
0.
04
0.
0
6
0.
08
0.
1
-1
5
0
-1
0
0
-50
0
50
10
0
15
0
20
0
Ti
m
e
(
s
)
R
e
a
c
t
i
v
e
p
o
w
e
r
E
rro
r
(
%
)
SM
C
FSM
C
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
Fuzzy
sli
d
i
n
g m
ode
co
nt
ro
l o
f
do
u
b
ly-
f
ed
in
duc
tio
n ge
ner
a
to
r
dri
v
e
n
by
w
i
nd
t
u
rbi
n
e
(M. Be
nm
ezia
ne)
1
601
NOMENCL
ATURE
D
F
I
G
D
oub
ly
F
e
d
Induc
t
i
o
n
G
e
n
era
t
or
Vs,
f,
w
s,
w
st
a
t
o
r
v
ol
ta
ge
, freque
nc
y gr
id
a
nd
elec
tric
a
l
sp
e
e
d
, r
espec
t
iv
el
y
Vds, Vqs
,Vdr,
Vqr
st
a
t
or
and
r
otor vo
lta
ge
s
in d-
q
r
efe
r
enc
e
f
ra
me,
respec
tive
l
y
id
s
,
iqs ,
idr
,
iq
r
stator a
nd ro
tor
curr
ents i
n d-q
refere
nce
fra
m
e, respe
cti
v
e
l
y
Φ
ds
,
Φ
qs
,
Φ
dr
,
Φ
qr
stator
a
n
d
r
otor
flu
x
lin
kage
s
in
d
-
q
reference-
f
r
ame,
respective
l
y
Rs ,
R
r
stator
a
nd
ro
tor re
si
st
o
r
s of m
ac
hi
ne
per
phase
, r
espec
t
i
v
e
l
y
Ls, L
r
c
y
clic i
nd
uc
tanc
e
s
of sta
t
or
a
nd r
o
tor
w
i
nd
i
n
gs,
re
spe
c
ti
ve
l
y
M
the
m
a
g
n
e
t
i
z
i
n
g
i
nd
uc
t
a
nc
e
Te,
T
r
el
e
c
t
r
o
ma
g
n
e
t
i
c
a
nd
r
e
s
i
s
t
a
nt
to
r
qu
e
Ps, Qs
s
t
at
o
r
a
ct
iv
e a
n
d
re
ac
t
i
v
e
p
o
w
ers, re
s
p
e
c
t
i
v
e
l
y
S
M
C,
F
LC
slidi
n
g M
ode C
o
n
tr
ol an
d
F
uz
zy Lo
g
ic
r
espe
c
tive
l
y
PN, J
,
fv
a
nd
P
N
om
i
n
a
l
P
ow
er, inerti
a
,
visc
ous fr
i
ct
ion
an
d the
n
u
mbe
r
o
f po
l
e
pa
irs, re
s
pe
c
tive
l
y
REFE
RENCES
[1]
A.
R
ahab
,
F
.
S
e
n
an
i,
H
.
Benalla,
"
D
irect
P
ow
er
C
o
n
tro
l
o
f
Brush
les
s
D
ou
bl
y-Fed
In
duct
i
o
n
G
enerat
or
U
sed
i
n
Wi
nd En
ergy
Conv
ersi
on
S
ystem,
"
Int
e
rn
ation
a
l
Jo
urn
a
l
of
Po
we
r
Electro
nics
a
n
d
Dr
ive S
y
stem
,
Vo
l
.
8
,
No.
1
,
p
p
.
41
7-4
33,
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arch 2
01
7.
[2]
K.
B
o
u
lâam
a
nd
A.
B
ou
kh
elif
a
,
"
F
u
zz
y
sl
idi
n
g
mo
de
c
on
tro
l
o
f
D
F
IG
pow
er
f
or
a
w
in
d
con
v
er
s
i
on
s
yste
m
,
"
16
th
Int
e
rna
t
i
o
n
a
l
Power Electr
onics
an
d M
o
tio
n Co
n
t
ro
l
Confer
ence a
n
d
Exp
o
si
ti
on,
A
n
talya
,
p
p
.
353-35
8,
201
4.
[3]
Kh
eira
B
elgace
m
,
A
b
d
el
kad
e
r
M
ezou
a
r,
N
aji
b
E
s
s
o
unb
ouli
,
"
Desi
gn
a
nd
A
nal
y
s
i
s
of
A
dap
t
iv
e
S
l
id
in
g
M
o
d
e
w
it
h
Ex
po
nential
Re
ach
ing
Law
Co
n
t
ro
l
f
o
r
Dou
b
le-F
ed
I
nd
ucti
on
G
e
ner
ato
r
B
as
ed
W
i
n
d
Tu
rb
ine,"
Internation
a
l
Jou
r
n
a
l
o
f
Po
we
r Electr
onics
and D
r
i
ve Sys
t
em
,
Vo
l.
9
,
N
o
.
4
,
pp.
1
5
3
4
-
154
4,
D
e
cem
ber
201
8.
[4]
N.
Z
erzo
uri
an
d
H.
L
ab
ar,
"
A
ctive
and
Rea
c
ti
ve
P
ower
C
on
tro
l
o
f
a
D
ou
bl
y
F
e
d
Indu
cti
o
n
,
"
Int
e
rn
at
io
na
l
Jour
na
l
of
Po
wer Elect
r
o
n
i
cs
an
d
D
r
i
ve Sys
t
em
,
vo
l.
5
,
p
p
.
2
4
4
-2
51
,
Oct
o
b
e
r
20
14
.
[5]
Arama
Fat
i
ma
Z
ohra,
B
ousserhane
Ismail
Khalil,
L
ari
b
i
S
lima
n
e,
S
a
h
l
i
Y
o
u
cef,
Mazari
Ben
y
o
u
n
e
s
,
"
Artif
i
ci
a
l
Int
e
ll
igen
ce
Co
ntro
l
Appli
e
d
in
W
i
n
d
En
ergy
C
o
nvers
io
n
S
y
st
em,
"
I
n
te
r
n
a
t
io
na
l
J
o
u
r
na
l of
Po
w
e
r E
l
e
c
t
ro
ni
c
s
a
n
d
Dr
ive S
y
s
t
e
m
,
Vol
.
9
,
No
.
2
,
p
p. 5
71
-
5
7
8
,
J
un
e
2
0
18
[6]
Benk
ahla
M
.
,
Ta
l
e
b
R.
,
Boudjema
Z,
"
A
new
rob
u
s
t
c
on
tro
l
u
si
ng
ad
apt
i
ve
f
uzzy
s
li
din
g
m
od
e
co
ntro
l
f
o
r
a
D
F
IG
su
pp
lied
by
a
19
-lev
el
i
n
v
erter
w
i
th
l
ess
n
u
m
b
er
o
f
switch
e
s,"
Elect
ri
cal en
gin
eeri
n
g
&
e
l
ect
ro
m
echa
n
i
c
s jo
urn
a
l
,
no
.
4
,
pp.
1
1
-
19,
2
01
8.
[7]
B.
H
aman
e,
M
.
L.
D
oum
bi
a,
M
.
Bou
h
am
id
a,
M
.
Ben
g
h
a
n
e
m
,
“
Co
nt
rol
o
f
W
ind
T
u
rb
in
e
Based
on
D
F
I
G
Us
in
g
F
u
zzy
-PI
an
d
S
l
idin
g
Mo
de
C
o
n
trol
le
rs,”
IEEE Pro
ceedin
gs
Nin
t
h Inter
nati
o
n
a
l
Con
f
eren
ce
on
Ecol
ogica
l
Veh
i
cles a
nd Renewa
bl
e En
erg
i
es (EVE
R),
Mo
nte-Carlo
(Mo
n
aco
),
F
rench
,
p
p
.
440
-44
8
,
2
01
4.
[8]
Z.
B
ou
d
j
em
a,
A
.
M
e
rouf
el
a
nd
Y
.
D
j
eri
r
i,
"
No
nl
in
ear
C
o
n
trol
o
f
a
Do
ubly
F
e
d
In
du
ctio
n
Gen
e
rato
r
f
o
r
W
i
n
d
En
ergyCo
n
v
e
rsion,
"
Ca
rp
at
h
i
a
n
Jour
na
l of Elect
ro
nic
an
d
Co
mp
u
t
er
En
gi
neeri
n
g
, Vo
l
.
6
, N°1
,
p
p
. 2
8 -
35
,
2
0
1
3
.
[9]
K.
B
el
gacem
,
“S
li
di
ng
M
o
de
C
o
n
tro
l
o
f
a
Dou
b
l
y
-f
ed
I
n
d
u
c
t
i
o
n
G
e
nerator
for
Wi
nd
E
n
er
gy
C
onvers
ion,
”
In
te
rn
at
io
na
l J
o
urna
l o
f
Ene
r
g
y
Eng
i
ne
e
r
in
g
,
vol/
i
s
s
u
e
:
3
0
(01
)
,
pp
3
0
-3
6,
201
3
.
[10]
O.
B
ou
gh
azi,
“S
li
di
ng
M
o
d
e
B
ack
st
eppi
ng
C
o
n
t
r
ol
o
f
Ind
u
c
t
io
n
M
o
to
r
,
”
I
n
te
r
n
at
io
na
l J
o
u
r
na
l o
f
P
o
w
e
r
El
ectro
n
i
cs
a
n
d
Dr
ive S
y
s
t
em
,
vo
l
/
i
s
s
u
e:
4
(4
),
pp.
4
81
-488
,
2
01
4.
[11]
M
e
rabet
A.
,
et
a
l.
,
“
I
m
p
l
e
m
e
nta
t
io
n
of
s
li
di
ng
m
od
e
co
ntro
l
sys
tem
f
o
r
generat
o
r
an
d
gri
d
s
id
e
con
t
ro
l
of
w
in
d
e
n
e
r
gy
c
on
ve
rsion
sy
ste
m
,”
IEEE
T
r
a
n
s
Su
st
ain E
n
erg
y
,
v
o
l
/is
sue:
7
(3),
p
p
.
1
3
27–3
5,
2
01
6.
[12]
Li
ao
K
.,
e
t
al.,
“
A
s
l
idin
g
mo
d
e
b
as
ed
d
am
pi
n
g
c
on
tro
l
o
f
DFIG
f
o
r
i
n
t
e
rarea
power
os
cill
a
tions,”
IEEE Tr
a
n
s
S
u
sta
i
n En
e
r
gy
,
vo
l/
issue
:
8(1
),
p
p. 2
58
–6
7,
2
01
7.
[13]
H.
A
s
c
hem
a
nn
a
nd
D
.
S
c
h
i
nd
ele,
“
S
l
i
d
in
g-m
o
d
e
c
o
n
t
r
ol
o
f
a
h
i
gh
s
pe
e
d
l
ine
a
r
a
x
is
d
rive
n
by
p
ne
u
m
a
t
ic
m
u
s
c
l
e
actu
a
tors
,”
I
E
E
E
Tra
n
s
. On In
du
strial E
l
ectr
onics
,
vo
l/is
su
e
:
5
5(11),
p
p.
385
5-3
8
6
4
,
200
8.
[14]
B.
B
el
kacem
,
“Hy
b
rid
F
u
zzy
S
lid
in
g
M
ode
C
ontro
l
o
f
a
D
F
I
G
In
teg
r
a
t
e
d
into
t
he
N
etwork,”
International J
o
urn
a
l
of
Po
wer Elect
r
o
n
i
cs
an
d
D
r
i
ve Sys
t
em
,
v
o
l
/issu
e: 3(4
),
pp
. 3
51
-
3
6
4
,
2
01
3.
[15]
S.
B
i
r
ici
k
,
“Op
timi
zed
S
liding
mo
de
c
on
trol
t
o
max
i
mi
ze
exi
s
t
e
n
ce
reg
i
o
n
f
o
r
s
in
gle-p
h
as
e
d
ynam
i
c
vo
lt
a
g
e
rest
orers,
”
I
EEE Tr
ans
actions
on Indus
t
r
i
a
l
In
f
o
rmat
i
c
s
,
v
o
l/i
s
s
u
e
:
12(4
)
,
p
p
.
148
6
-
1
4
9
7
,
2
01
6.
[16]
Oua
ssila
B
e
l
ou
nis,
H
o
c
in
e
La
ba
r,
"
Fu
z
z
y
S
liding
M
o
d
e
C
o
n
trol
le
r
o
f
D
F
IG
f
or
W
in
d
Energy
C
o
n
v
e
rsio
n,
"
Int
e
rnat
i
o
na
l
Jo
urnal of Int
e
lligent Engineer
ing
a
n
d Systems
,
V
ol.1
0,
N
o
.
2,
2
01
7,
p
p
.
16
3-17
4,
2
0
1
7
.
[17]
T
.
M
es
bahi,
T
.
G
h
e
nn
am,
E.M
.
B
erk
o
u
k
,
“A
d
o
ubl
y
f
e
d
in
du
c
t
io
n
g
enerato
r
f
or
w
ind
stand
¬
alo
n
e
po
w
e
r
appli
c
at
ion
s
(
si
mula
ti
on
a
nd
e
xperiment
a
l
validat
i
on),
”
IEEE X
X
th
In
ter
nationa
l Con
f
er
ence on E
l
ectr
i
ca
l
M
a
chin
es
(ICEM)
,
M
a
rsei
lle, F
ra
nce, pp
. 20
2
8
-
20
33
, 20
1
2
.
[18]
T.
G
hen
n
am
,
E.
M.
B
erk
o
u
k
,
B.
F
ranço
i
s
,
“
M
ode
l
i
n
g
a
nd
c
on
trol
o
f
d
ou
b
l
y
fe
d
in
d
u
c
tion
ge
ne
ra
to
r
(
D
FIG)
b
a
s
e
d
wi
nd
c
onv
ersi
on
sy
ste
m
,
”
IEEE, S
econd
Int
e
rn
ati
o
n
a
l
Conferen
ce on
Po
wer
En
g
i
neeri
n
g
,
En
erg
y
an
d E
l
ectrica
l
Dr
ives (
P
ower
en
g
)
,
L
isbo
n,
Po
r
tu
ga
l,
p
p
. 5
07
-51
2
,
2
00
9.
[19]
Smai
l
Mansouri
,
A
l
i
Benatill
a
h
,
“Indirect
C
o
n
trol
o
f
a
Dou
b
ly-F
ed
I
n
d
u
c
tion
M
achi
n
e
f
o
r
W
i
n
d
E
nerg
y
Conversi
on,
”
In
ter
nat
io
nal
Jour
n
a
l
of
Po
wer Elec
t
r
o
n
i
c
s a
n
d
D
r
iv
e
Sys
t
em
,
Vo
l.
4
,
No
.
3,
pp.
4
0
0
-4
05
,
S
e
p
t
em
ber
20
14
.
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