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
.
50
2
~
51
1
I
S
SN
: 208
8-8
6
9
4
5
02
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
Power Control of
Wind Turbine
B
a
s
e
d on Fuzzy Sl
iding-Mode
Control
T
a
hi
r K
h
al
f
a
l
l
ah*
,
B
e
l
f
ed
al
Chei
kh
*,
Al
l
a
oui
T
aye
b*
,
Gerard Cham
penois
**
*Laboratoire de
Génie
Energ
itiq
ue et Gén
i
e Infor
m
ati
que
LGEGI, Universit
é
Ibn
Khaldoun de T
i
aret, Algér
i
e
**Universit
y
of
Poitiers, Labo
rat
o
ire d’Info
rm
ati
que et
d’Autom
a
tique pour l
e
s S
y
stèm
es, Bât
i
m
e
n
t
B25, 2, rue
Pierre Brousse,
86022 Poitiers,
France
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 1, 2014
Rev
i
sed
D
ec 14
, 20
14
Accepte
d Ja
n
5, 2015
This paper pr
esents the stud
y
o
f
a
variable speed wind energ
y
conversio
n
s
y
stem (WECS)
using a Wound
Field
S
y
nchrono
us Generator
(WFSG) based
on a Fuzzy
sliding mode control (FSMC)
applied
to a
c
hiev
e con
t
r
o
l of a
c
tiv
e
and reactive po
wers exchang
e
d
between
the stator of the WFSG
and the gr
id
to ens
u
re
a
M
a
xim
u
m
P
o
wer P
o
int Tr
acking
(M
P
P
T
) of a w
i
nd en
erg
y
conversion s
y
stem. However the principa
l drawb
ack of the
slidin
g mode, is
the chat
ter
i
ng ef
fect which ch
ara
c
ter
i
zed b
y
torq
ue ripple
,
this
phenom
ena is
undesirable and
harmful for th
e
machin
es,
it g
e
n
e
rates noises an
d additional
forces
of tors
ion on the m
achi
n
e s
h
aft. A dire
ct fuzz
y
logic c
ontrolle
r is
designed and th
e sliding mode controller
is
add
e
d to com
p
ens
a
t
e
the f
u
z
z
y
approxim
a
tion
errors. Th
e
sim
u
lation r
e
sults cl
earl
y
indic
a
te
th
e
effectiven
ess an
d validity
of th
e propos
ed method, in terms of convergence,
time and
precision.
Keyword:
Fuzzy
sl
i
d
i
n
g
m
ode cont
rol
M
a
xi
m
u
m
pow
er
poi
nt
t
r
ac
ki
n
g
W
i
nd
en
e
r
g
y
co
nv
er
s
i
on
s
y
s
t
e
m
W
oun
d f
i
eld syn
c
hr
ono
u
s
gene
rat
o
r
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
:
Tahir K
h
alfallah,
Depa
rtem
ent of Electrical a
nd Co
m
p
u
t
er
Engin
eer
ing
,
Uni
v
ersity
I
b
n
Khal
du
n Tiaret
,
Al
geria,
Em
a
il: tah
i
r.comman
d
e
@g
m
a
il.co
m
1.
INTRODUCTION
W
i
n
d
e
n
er
gy
i
s
bec
o
m
i
ng
on
e o
f
t
h
e m
o
st
i
m
port
a
nt
re
ne
wabl
e
ene
r
gy
s
o
u
r
ces
[
1
]
.
R
e
c
e
nt
l
y
, p
o
w
er
con
v
e
r
t
e
r c
ont
r
o
l
ha
s m
o
st
l
y
been st
udi
e
d
a
n
d
devel
ope
d
f
o
r
WEC
S
i
n
t
e
gr
at
i
on i
n
t
h
e
el
ect
ri
cal
gri
d
.
In
rece
nt years, va
riable s
p
eed
WECSs
have
bec
o
m
e
t
h
e i
n
dust
r
y
st
anda
rd
beca
u
s
e of t
h
ei
r
ad
v
a
n
t
ag
es
o
v
er fi
x
e
d
sp
eed
o
n
e
s su
ch as im
p
r
o
v
e
d
en
ergy cap
ture, b
e
tt
er
p
o
wer
q
u
a
lity. Th
ey
are cap
a
b
l
e of
ext
r
act
i
n
g o
p
t
i
m
al
energy
ca
pt
u
r
e i
n
a
ddi
t
i
on t
o
ha
vi
ng
reduce
d
m
echanical stress and aerodynam
ic
noise
.
[2]
.
In t
e
rm
s of t
h
e
gene
rat
o
rs f
o
r
WEC
S
, se
ver
a
l
t
y
pes of el
ect
ri
c gene
rat
o
r
s
are use
d
suc
h
as Sq
ui
re
d
-
C
a
ge I
n
duct
i
o
n
Gene
rat
o
r
(
S
C
I
G
)
,
Sy
nc
h
r
o
n
ous
Ge
ne
r
a
t
o
r
wi
t
h
e
x
t
e
rnal
fi
el
d e
x
c
i
t
a
t
i
on, D
o
ubl
y
Fed
In
d
u
ct
i
on
Gen
e
rat
o
r
(D
FI
G)
and
Perm
anent
M
a
gnet
Sy
nc
hr
o
n
o
u
s G
e
ne
r
a
t
o
r (
P
M
S
G
)
wi
t
h
p
o
w
er el
e
c
t
r
o
n
i
c
con
v
e
r
t
e
r sy
st
em
[3]
.
Theref
o
r
e, t
h
e st
udy
o
f
sy
nch
r
o
n
o
u
s
gene
rat
o
r has r
e
gai
n
e
d
im
port
a
nce. Th
e pri
m
ary
adva
nt
age
s
o
f
W
o
u
nd Fi
el
d
Sy
nch
r
o
n
o
u
s
Gene
rat
o
r are:
The ef
fi
ci
enc
y
of t
h
i
s
m
a
chi
n
e i
s
us
ual
l
y
hi
gh
,
because it e
m
ploys the whole stator
curre
nt
for the electromagnetic torque
production.
The m
a
in bene
fit of
t
h
e em
pl
oym
ent
o
f
w
o
un
d fi
el
d sy
nc
hr
on
o
u
s g
e
ne
rat
o
r w
i
t
h
sal
i
e
nt
pol
e
i
s
t
h
at
i
t
al
l
o
ws t
h
e di
rect
c
o
nt
r
o
l
o
f
the powe
r fa
ctor
of the
machine, c
ons
eque
ntly th
e
stator curre
nt
m
a
y be
m
i
nim
i
zed any operation
circum
stances [4].
Th
e
Slid
ing
M
o
d
e
Con
t
ro
ller
(SMC) is a p
a
rticu
l
ar typ
e
o
f
v
a
riab
le stru
ctu
r
e con
t
ro
l syste
m
s th
at is
d
e
sign
ed
as a
r
obu
st con
t
ro
l to
dr
iv
e an
d then
con
s
t
r
ain
the syste
m
to
lie
with
in
o
f
th
e
switch
i
ng
fun
c
tio
n.
Ho
we
ver i
n
t
h
e prese
n
ce of
l
a
rge u
n
cert
a
i
n
t
i
e
s or hi
g
h
er
swi
t
c
hi
n
g
gai
n
i
s
requi
re
d w
h
i
c
h p
r
o
d
u
ce hi
g
h
er
am
pl
i
t
ude of
c
h
at
t
e
ri
n
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Pow
e
r C
ont
r
o
l
of
Wi
nd
T
u
rbi
n
e B
a
se
d
on
F
u
zzy
Sl
i
d
i
n
g
-
M
ode
C
o
nt
rol
(
T
ahi
r
K
h
al
f
a
l
l
a
h)
50
3
Fuzzy
l
o
gi
c
ha
s em
erged as a
p
o
we
rf
ul
i
n
c
ont
rol
a
p
pl
i
cat
i
ons
. It
al
l
o
ws
one
t
o
desi
gn
a co
nt
r
o
l
l
e
r
u
s
ing
lingu
istic ru
les withou
t
k
nowing
th
e math
em
at
ical
m
o
d
e
l of t
h
e
p
l
an
t
.
In th
is
p
a
p
e
r ou
r obj
ectiv
e is to
app
l
y a fu
zzy co
n
t
ro
ller co
m
b
in
ed
with
slid
in
g m
o
d
e
t
o
o
v
e
rco
m
e
shat
t
e
ri
n
g
o
f
b
o
t
h
sl
i
d
i
n
g m
ode an
d f
u
zzy
l
ogi
c c
ont
r
o
l
l
e
r
s
and t
h
e
n
t
o
obt
ai
n a c
ont
r
o
l
sy
st
em
for a hi
gh
per
f
o
r
m
a
nce f
o
r
p
o
we
r sy
ste
m
[5]
.
Sim
u
lation
res
u
lts are
p
r
ov
id
ed
to sho
w
th
e effectiven
ess
o
f
th
e
pro
p
o
s
ed
ove
ral
l
WFS
G
cont
rol
sy
st
em
.
2.
WIND CONVERSION SYSTEM
MODE
L
Th
e
WECS d
e
scrib
e
d
in th
is article in
cludes th
e
w
i
nd
t
u
r
b
i
n
e,
g
earbo
x,
W
F
SG, a
n
d back-t
o-back
con
v
e
r
ters.
Th
e rot
o
r
win
d
in
g o
f
the
WFSG is connected to the
gri
d
by
DC/AC converter, whereas the stator
wind
ing
is fed b
y
b
a
ck-to-back
b
i
d
i
rection
a
l PW
M
-
VS
C. In
th
is syst
e
m
, th
e wi
n
d
en
erg
y
is transmitted
th
ro
ugh
th
e turb
i
n
e to
th
e t
h
ree-p
h
a
se
WFSG an
d
g
e
n
e
rated
in
electrical fo
rm
. Th
is en
erg
y
is transmitted
d
i
r
ectly th
r
ough
a b
r
i
d
g
e
r
ectif
ier
an
d
i
n
v
e
r
t
er
to
th
e electr
i
cal n
e
tw
o
r
k
(Fig
ur
e 1)
.
W
e
co
nsid
er
in
t
h
is stu
d
y
th
at th
e rectifi
e
r is p
e
rfect.
So
sem
i
co
n
ducto
rs are id
eal
[6
].
In th
is
p
a
p
e
r
o
u
r stud
y is li
m
ited
to
th
e
gene
rat
i
o
n of p
o
we
r
i
n
c
ont
i
n
uo
us f
o
rm
.
Fi
gu
re
1 s
h
ow
s t
h
e e
q
ui
val
e
nt
di
a
g
ram
of
t
h
e el
ect
ri
cal
po
rt
i
o
n
of
t
h
e
st
ri
ng
co
n
v
ersi
on
o
f
wi
n
d
energy.
Fi
gu
re 1.
WFS
G
base
d
wi
n
d
ener
gy
c
o
n
v
er
s
i
on sy
st
em
2.
1.
M
o
del
i
n
g
of
the
Wi
nd
T
u
rbi
n
e
and
G
e
arb
o
x
The t
u
r
b
i
n
e
p
o
w
er
an
d t
o
r
que
de
vel
o
ped
are
gi
ve
n
by
t
h
e
f
o
l
l
o
wi
n
g
rel
a
t
i
on
[7]
:
,
2
1
3
2
p
w
a
C
V
R
P
(1)
,
2
1
2
3
p
w
t
a
a
C
V
R
P
T
(2)
Whic
h
prese
n
t
s
the ratio between the turbi
n
e angula
r
sp
eed
and
th
e wind
sp
eed
.
Th
is ratio
called
th
e tip
sp
eed
ratio
n
an
d is
d
e
fi
n
e
d as:
w
t
V
R
(3)
Whe
r
e
is th
e air d
e
n
s
ity,
R
i
s
t
h
e bl
a
d
e l
e
ngt
h,
w
V
is the
wind s
p
eed,
p
C
is th
e
p
o
wer
coefficient,
t
is
th
e turb
i
n
e an
gu
lar sp
eed
.
The powe
r
coe
fficient
p
C
prese
n
t
s
the aerodyna
m
ic efficiency
of t
h
e t
u
rbi
n
e
and
de
pe
nds
o
n
t
h
e
specific s
p
ee
d
and
t
h
e a
n
gl
e
of t
h
e
bl
ades
. I
t
i
s
di
ffe
re
nt
f
r
o
m
a t
u
rbi
n
e t
o
a
not
her
,
a
nd
i
s
us
ual
l
y
pr
ov
i
d
ed
by
t
h
e m
a
nu
fa
ct
urer
an
d c
a
n
be
use
d
t
o
de
fi
ne a m
a
t
h
em
at
ical
app
r
oxi
m
a
ti
on.
Th
e wi
n
d
t
u
rbin
e sh
aft is co
n
n
ected
to
th
e
W
F
SG ro
tor th
rou
g
h
a g
e
arb
o
x
wh
ich
ad
ap
ts th
e slow
spee
d
of t
h
e t
u
rbi
n
e t
o
t
h
e
W
FSG
spee
d.
T
h
i
s
gear
b
o
x
i
s
m
odel
e
d
by
t
h
e
f
o
l
l
o
wi
ng
eq
uat
i
ons
[
8
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
50
2
–
51
1
50
4
G
m
t
;
G
T
T
a
m
(4)
Fro
m
th
e
d
y
n
a
mics fu
nd
am
en
tal relatio
n
,
t
h
e tu
rb
in
e sp
eed
i
s
d
e
term
in
ed
as fo
llo
ws:
m
em
m
m
f
T
T
dt
d
J
(5)
J
and
f
are th
e
to
tal
m
o
m
e
n
t
o
f
i
n
ertia an
d
th
e v
i
sc
ous fri
c
tion c
o
efficient appea
r
ing a
t
the
gene
rat
o
r si
de
,
m
T
i
s
t
h
e gea
r
bo
x t
o
rq
ue,
em
T
i
s
t
h
e ge
nerat
o
r t
o
r
que
, a
nd
m
is the m
echanical generat
o
r
spee
d.
Fi
gu
re 2 rep
r
es
ent
s
the
power
coefficient
p
C
as
a f
unct
i
o
n
of
and
.
Figure 3 shows the
m
echanical powe
r
as a function of
rot
o
r spee
d of the tur
b
ine for
different val
u
es
of
wi
nd
spee
d
[9]
.
Fi
gu
re
2.
P
o
we
r c
o
ef
fi
ci
ent
ve
rsus
t
i
p
s
p
ee
d
r
a
t
i
o
Fi
gu
re
3.
R
o
t
o
r
p
o
we
r
ver
s
us
r
o
t
a
t
i
onal
s
p
ee
d
o
f
gene
rat
o
r
2.
2. M
o
del
i
n
g
of
the
WF
SG
I
n
th
e sy
n
c
hron
ou
s
d-
q coor
din
a
tes, th
e vo
ltag
e
eq
u
a
ti
o
n
of
th
e
W
F
SG
is
ex
pr
essed
as follo
w
s
[
1
0
]
:
dt
di
m
dt
di
m
dt
di
L
i
m
i
L
i
r
v
D
sD
f
sf
ds
d
Q
sQ
e
qs
q
e
ds
s
ds
(6)
dt
di
m
dt
di
L
i
m
i
m
i
L
i
r
v
Q
sQ
qs
q
D
sD
e
f
sf
e
ds
d
e
qs
s
qs
(7)
qs
sQ
Q
Q
Q
ds
sD
f
fD
D
D
D
Q
Q
Q
D
D
D
i
m
i
L
i
m
i
m
i
L
dt
d
i
r
dt
d
i
r
.
0
0
(8)
Where:
D
L
,
Q
L
:
i
nduct
a
nces
of t
h
e
di
rect
and q
u
adrat
u
re d
a
m
p
er wi
ndi
ng
s.
f
L
:
i
nduct
a
nce of
t
h
e
m
a
i
n
fi
el
d
wi
ndi
n
g
.
d
L
,
q
L
:
i
nduct
a
nces
of t
h
e
d-axi
s
st
at
or wi
ndi
n
g
a
nd
q-axi
s
st
at
or
wi
ndi
n
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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S
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6
9
4
Pow
e
r C
ont
r
o
l
of
Wi
nd
T
u
rbi
n
e B
a
se
d
on
F
u
zzy
Sl
i
d
i
n
g
-
M
ode
C
o
nt
rol
(
T
ahi
r
K
h
al
f
a
l
l
a
h)
50
5
sf
m
:
m
u
t
u
al
i
nductance bet
w
een t
h
e fi
el
d wi
ndi
n
g
an
d t
h
e d
-
axi
s
st
at
or wi
ndi
n
g
.
sD
m
:
m
u
t
u
al
i
nductance bet
w
een t
h
e d-a
x
i
s
st
at
or wi
ndi
n
g
an
d t
h
e d-a
x
i
s
dam
p
er wi
ndi
n
g
.
sQ
m
:
m
u
t
u
al
i
nductance bet
w
een t
h
e q-a
x
i
s
st
at
or wi
ndi
n
g
an
d t
h
e q-a
x
i
s
dam
p
er wi
ndi
n
g
.
fD
m
:
m
u
t
u
al
i
nductance bet
w
een t
h
e fi
el
d wi
ndi
n
g
an
d t
h
e d
-
axi
s
dam
p
er wi
ndi
ng.
e
:
i
s
t
h
e el
ect
r
i
c
al
angul
ar spee
d,
m
e
p
The el
ect
r
o
m
a
gnet
i
c
t
o
r
que
i
s
ex
pre
ssed
by
:
ds
q
qs
d
em
i
i
p
T
.
(9)
3.
SLIDI
N
G M
O
DE CO
NTR
O
L
To achi
e
ve t
h
e
m
a
xim
u
m
po
wer at
bel
o
w r
a
t
e
d wi
n
d
spe
e
d, sl
i
d
i
n
g m
ode base
d t
o
r
q
u
e
cont
r
o
l
i
s
pr
o
pose
d
i
n
[1
1]
. T
h
e m
a
i
n
ob
ject
i
v
e
o
f
t
h
i
s
con
t
ro
ller is to
track th
e refere
nce rot
o
r spee
d
ref
m
_
fo
r
maxim
u
m
power extraction. In conve
n
tional sliding m
ode cont
rol, sliding surface
gene
ra
lly depends
on
error,
and
de
ri
vat
i
v
e
of
t
h
e e
r
r
o
r
si
g
n
al
i
s
gi
ve
n i
n
(1
0)
.
x
x
dt
d
x
ref
n
x
1
(10)
Whe
r
e
is th
e
po
sitiv
e co
n
s
tant an
d
n
is th
e
o
r
d
e
r of th
e un
con
t
ro
lled
system.
The s
p
ee
d e
r
r
o
r i
s
defi
ned
by
[1
2]
:
m
ref
m
m
e
_
.
(11)
For
1
n
, t
h
e
p
o
s
ition
co
n
t
ro
l m
a
n
i
fo
l
d
eq
u
a
tion
can
b
e
o
b
t
ained fro
m
Eq
u
a
tion
(10
)
as fo
llow:
m
ref
m
m
_
.
(12)
The deri
vative of
this
s
u
rface is
give
n by
the
expressi
on:
.
)
(
)
(
3
_
1
2
qs
D
sD
f
sf
ref
m
m
i
i
m
i
m
c
c
c
(13)
Du
ri
n
g
t
h
e sl
i
d
i
ng m
ode a
n
d i
n
perm
anent
r
e
gi
m
e
, we ha
ve:
0
,
0
)
(
,
0
)
(
n
qs
m
m
i
.
(14)
T
h
e
cu
rr
en
t c
o
n
t
ro
l
qs
i
i
s
defi
ne
d
by
:
n
qs
eq
qs
qs
i
i
i
.
(15)
Th
e con
t
ro
l
voltag
e
ref
qs
i
_
i
s
defi
ne
d by
:
))
(
(
)
(
3
_
1
2
_
m
D
sD
f
sf
ref
m
m
ref
qs
sat
k
i
m
i
m
c
c
c
i
m
.
(16)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
50
2
–
51
1
50
6
The stator currents
qs
i
and
ds
i
are
the im
ages, respectively, of the
s
P
and t
h
e
s
Q
, whic
h m
u
st
follo
w t
h
eir
ref
e
rences
.
3.
1.
Qu
adr
a
ti
c R
o
t
o
r
Cu
rre
nt
Contr
o
l with S
M
C
The sliding s
u
rface re
prese
n
ting the e
r
ror betwee
n the
m
easured and refe
re
nce quadratic rotor
cur
r
ent
i
s
gi
ve
n
by
:
qs
ref
qs
i
qs
i
i
e
i
qs
_
)
(
(17)
qs
ref
qs
qs
i
i
i
_
)
(
(18)
Sub
s
titu
tin
g
t
h
e exp
r
essi
o
n
of
qs
i
Equat
i
on
(
7
)
i
n
E
quat
i
o
n
(
1
8
)
,
Eq
uat
i
o
n
(1
9)
an
d E
q
uat
i
on
(2
0
)
can be obt
ai
ne
d.
qs
Q
sQ
D
f
ds
qs
s
q
ref
qs
qs
v
i
m
i
a
i
a
i
a
i
r
L
i
i
3
2
1
_
1
)
(
(19)
An
d,
n
qs
eq
qs
qs
v
v
v
.
(20)
Du
ri
n
g
t
h
e sl
i
d
i
ng m
ode a
n
d i
n
perm
anent
r
e
gi
m
e
, t
h
ere i
s
:
0
,
0
)
(
,
0
)
(
n
q
qs
qs
v
i
i
(21)
Whe
r
e t
h
e e
qui
val
e
nt
c
ont
rol
i
s
:
Q
sQ
D
f
ds
qs
s
ref
qs
q
eq
qs
i
m
i
a
i
a
i
a
i
r
i
L
v
3
2
1
_
(22)
There
f
ore, the
correctio
n
fact
or
i
s
gi
ven
by
:
)
(
qs
v
n
qs
i
sat
K
v
q
(23)
Whe
r
e
q
v
K
i
s
p
o
si
t
i
ve co
nst
a
nt
.
3.2.
Direc
t Rotor
Cu
rrent Control with SMC
The sliding surface re
prese
n
ting the
e
r
ror
be
tween the m
e
a
s
ure
d
and re
ference direct rot
o
r c
u
rrent is
gi
ve
n by
:
ds
ref
ds
i
ds
i
i
e
i
ds
_
)
(
(24)
ds
ref
ds
ds
i
i
i
_
)
(
(
2
5)
Sub
s
titu
tin
g the exp
r
ession
o
f
ds
i
Eq
u
a
tion
(6) i
n
Equ
a
tio
n (2
5), t
h
ere is:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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PED
S
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:
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8-8
6
9
4
Pow
e
r C
ont
r
o
l
of
Wi
nd
T
u
rbi
n
e B
a
se
d
on
F
u
zzy
Sl
i
d
i
n
g
-
M
ode
C
o
nt
rol
(
T
ahi
r
K
h
al
f
a
l
l
a
h)
50
7
ds
D
sD
f
sf
Q
qs
ds
s
d
ref
ds
ds
v
i
m
i
m
i
b
i
b
i
r
L
i
i
2
1
_
1
)
(
(
2
6)
An
d,
n
ds
eq
ds
ds
v
v
v
.
(27)
Du
ri
n
g
t
h
e sl
i
d
i
ng m
ode a
n
d i
n
perm
anent
r
e
gi
m
e
, Equat
i
o
n
(
2
8
)
ca
n
be
ob
t
a
i
n
ed.
0
,
0
)
(
,
0
)
(
n
ds
ds
ds
v
i
i
(28)
Whe
r
e t
h
e e
qui
val
e
nt
c
ont
rol
i
s
:
D
sD
f
sf
Q
qs
ds
s
ref
ds
d
eq
ds
i
m
i
m
i
b
i
b
i
r
i
L
v
2
1
_
(29)
There
f
ore, the
correctio
n
fact
or
i
s
gi
ven
by
:
)
(
ds
v
n
ds
i
sat
K
v
d
(30)
Whe
r
e
d
v
K
i
s
p
o
si
t
i
ve co
nst
a
nt
.
e
sf
m
a
2
;
e
sQ
m
b
2
;
J
f
c
2
;
J
p
c
3
;
e
d
L
a
1
;
e
q
L
b
1
;
e
sD
m
a
3
;
J
T
c
m
1
4.
FUZ
Z
Y
LOGIC
CONTROLLER
Fu
zzy-l
o
g
i
c co
n
t
ro
l
h
a
s th
e cap
ab
ility to
co
n
t
ro
l
n
o
n
linear,
u
n
c
ertain
an
d ad
ap
tiv
e syste
m
s with
p
a
ram
e
ter v
a
riatio
n
.
Fu
zzy co
n
t
ro
l do
es no
t
strictly
n
eed
an
y
m
a
th
e
m
atic
al
m
o
d
e
l o
f
th
e p
l
an
t. Its con
t
ro
l ru
le
can
b
e
qu
alitativ
ely ex
p
r
essed
on
th
e b
a
sis
o
f
log
i
c-langu
ag
e v
a
riatio
n
and
th
e fu
zzy
m
o
d
e
l o
f
a p
l
an
t is v
e
ry
easy
t
o
ap
pl
y
.
In
fact
,
fuzzy
cont
rol
i
s
go
o
d
a
d
apt
i
v
e
co
n
t
rol
am
ong t
h
e
t
echni
ques
di
s
c
usse
d s
o
fa
r.
In t
h
i
s
p
a
p
e
r,
fu
zzy-l
o
g
i
c con
t
ro
l is asso
ciated wit
h
slid
i
n
g-m
o
d
e
con
t
ro
l to
g
e
nerate th
e switch
i
ng
co
n
t
ro
ller term
)
(
dqs
i
Ksat
, which ensure
s the
precisi
on
and ro
bust
n
ess
o
f
t
h
e
co
nt
r
o
l
[1
2]
.
The ge
ne
ral
st
ruct
u
r
e of a f
u
z
z
y
-
co
nt
rol
sy
st
em
i
s
shown i
n
Fi
gu
re 4. T
h
er
e are t
w
o i
n
put
si
gnal
s
t
o
th
e fu
zzy co
n
t
ro
ller, th
e erro
r
E
and t
h
e cha
n
ge in error
CE
, wh
i
c
h
is related
to th
e d
e
ri
v
a
tiv
e
dt
DE
/
of
error. The clos
ed-l
oop error
E
and c
h
an
ge i
n
err
o
r
CE
signals are conve
rted to the respective
scale factors
,
GE
E
e
/
and
GC
CE
ce
/
. The
o
u
t
put
pl
ant
co
nt
r
o
l
si
g
n
al
DU
i
s
d
e
ri
ve
d
by
m
u
l
t
i
p
l
y
i
ng
by
t
h
e
scale factor
GU
, that is
GU
du
DU
*
, and t
h
en integrated t
o
ge
nerate t
h
e
U
si
gn
al
[1
3]
.
Th
e scale
fact
o
r
s can ch
ange th
e sen
s
itiv
ity o
f
t
h
e con
t
ro
ller
with
ou
t ch
ang
i
ng
its st
ru
cture. Th
e
fuzzy controller is com
posed
of thr
ee bloc
ks
: fuzzification, rule bases
,
and de
fuzzificati
o
n. The m
e
m
b
ershi
p
fu
nct
i
o
ns f
o
r i
n
p
u
t
s
out
put
v
a
ri
abl
e
s a
r
e s
h
ow
n i
n
Fi
g
u
r
e
5.
The
f
u
zzy
sub
s
et
s are
as
fol
l
o
ws:
GN
(
G
ra
n
d
n
e
g
a
tiv
e),
N (Neg
ativ
e), ZR
(Zero
)
, P (Po
s
i
tiv
e), and
GP
(Grand
po
sitiv
e). Th
ere are sev
e
n
fu
zzy su
b
s
ets fo
r
each varia
b
le, whic
h gives
5 ×
5
= 25 possi
ble
rules.
T
h
e
fuzzy
rules tha
t
produce
thes
e control actions a
r
e
rep
o
rte
d
in
Ta
ble 1
.
The Defuzzifi
cation of the
out
put c
ont
rol
is accom
p
lished usi
n
g the
m
e
thod
of ce
nter of
gravity.
Whe
n
t
h
e e
r
r
o
r i
s
bel
o
w
z
e
ro
, t
h
e
u
n
i
v
e
r
se
of t
h
e c
o
n
t
rol
val
u
e s
h
o
u
l
d
be e
x
pan
d
e
d
by
a c
ont
r
act
i
on-
expa
nsi
on fact
or
x
F
.
Whe
n
t
h
e e
r
r
o
r i
s
a
b
ove z
e
ro
, t
h
e
uni
ver
s
e sh
oul
d
be c
ont
ract
ed.
The
r
ef
ore
x
F
is
defi
ned
as
M
x
M
x
F
/
1
.
(M g
a
in
po
sitiv
e).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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94
I
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PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
50
2
–
51
1
50
8
Fi
gu
re 4.
St
r
u
c
t
ure of
t
h
e f
u
zz
y
cont
rol
l
e
r
Fi
gu
re
5.
M
e
m
b
ers
h
i
p
f
u
nct
i
o
ns
of
e
,
ce
and
DU
Tabl
e 1.
R
u
l
e
s base
G
N
N
ZR
P
GP
GN
GN
GN
GN
N
ZR
N
GN
N
N
ZR
P
ZR
N N
ZR
P
P
P
N ZR
P
P
GP
GP
ZR P GP
GP
GP
5.
SIM
U
LATI
O
N
RESULTS
AN
D DIS
C
US
SION
To dem
onst
r
at
e t
h
e pert
i
n
e
n
c
e
of t
h
e
pr
o
p
o
s
ed
WFSG Fuzzy-slid
in
g-con
t
ro
l approach (Figure
6),
sim
u
l
a
t
i
on has
been
per
f
o
r
m
e
d f
o
r
7.
5K
W
WFS
G
wi
nd
p
o
we
r sy
st
em
usi
ng M
a
t
l
a
b/
Si
m
u
li
nk™
. The
wi
nd
p
r
o
f
ile
u
s
ed
in
o
u
r sim
u
latio
ns is shown in
Fig
u
re
7
(
a).
In a
d
di
t
i
on, ae
ro
dy
nam
i
c po
wer i
s
opt
i
m
i
z
ed wi
t
h
M
P
PT
st
rat
e
gy
an
d
keep
s at
hi
s n
o
m
i
nal
val
u
e
whe
n
the wi
nd spee
d exceeds
the nom
i
nal value as
s
h
ows i
n
Figure 7(b),
and t
h
e
powe
r
coefficient
p
C
is t
h
e
max
i
m
u
m
ar
o
u
n
d
0.48
as sh
ow
n in
Figu
r
e
7(
c)
.
By applying t
h
e proposed c
ont
rol sc
hem
e
,
the op
tim
al s
p
eed c
o
mm
an
d is accuratel
y
tracked to
extract the m
a
xim
u
m
power from
the
wind energy at any m
o
m
e
nt. In
Fi
g
u
r
e 7
(
d)
t
h
e ge
nerat
e
d
t
o
r
q
u
e
referen
ce fo
llows
th
e op
ti
m
u
m
m
echanical torque
of th
e tu
rb
in
e
q
u
ite
well. Figu
re
7(e) sho
w
s t
h
e
sp
eed
track
ing
resu
lts of th
e
WFSG.
In term
s o
f
th
e act
u
a
l
wi
nd
sp
eed
, t
h
e
opt
i
m
al
W
F
S
G
s
p
ee
d c
o
m
m
a
nd i
s
obt
ai
ne
d
by
E
q
. (
3
)
.
The
decoupling effect of the betw
ee
n the
direct and
quadratic st
ator current
of t
h
e
W
F
SG is
illu
strated
in Fi
g
u
re
7
(
f).
The st
at
o
r
c
u
r
r
e
nt
an
d
vol
t
a
ge
wave
f
o
rm
s and t
h
ese z
o
om
of t
h
e
WFS
G
a
r
e pres
ent
e
d i
n
Fi
gi
re
7(
g)
.
As sh
own
in
this Fig
u
res, t
h
e
stato
r
curren
ts
are propo
rtional to
th
e wi
n
d
sp
ee
d. T
h
is is
due t
o
the
reas
on t
h
at
whe
n
t
h
e
wind s
p
ee
d inc
r
ea
ses (not larger than 9.1 m
/
s), t
h
e
r
e i
s
m
o
re
p
o
we
r
ge
nera
t
e
d, t
h
us
y
i
el
d m
o
re
currents
in t
h
e
stator
w
i
nd
ing
s
of
th
e
W
F
SG
.
Fi
gu
re 6.
Gl
ob
al
di
ag
ram
of
s
i
m
u
l
a
t
i
on
an
d cont
rol
of
WF
SG wi
t
h
Fuzzy
-SM
C
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6
9
4
Pow
e
r C
ont
r
o
l
of
Wi
nd
T
u
rbi
n
e B
a
se
d
on
F
u
zzy
Sl
i
d
i
n
g
-
M
ode
C
o
nt
rol
(
T
ahi
r
K
h
al
f
a
l
l
a
h)
50
9
Fi
gu
re 7.
Sy
st
em
perfo
rm
ance
u
nde
r wi
n
d
s
p
eed vari
at
i
o
n. (
a
) W
i
n
d
s
p
eed
[m
/
s
]
.
(b
) Aer
o
dy
nam
i
c
powe
r
[W
].
(
c
) Po
w
e
r co
ef
f
i
cien
t. (d)
Gen
e
r
a
ted
to
rq
u
e
[N
.
m
].
(e)
Gene
rato
r s
p
ee
d
[ra
d/s]
. (
f
)
Di
rect an
d
q
u
ad
r
a
tic
stato
r
cu
rr
en
t
[A
].
(g
) Stator
cu
rr
en
t and
v
o
l
tag
e
w
ith
zo
o
m
[
A
, V
]
6.
CO
NCL
USI
O
N
In th
is
p
a
p
e
r,
a fu
zzy slid
ing
m
o
d
e
co
n
t
roller is
app
lied to
co
n
t
ro
l t
h
e po
wer
g
e
n
e
rated
By th
e
WEC
S
base
d
on
w
o
u
n
d
fi
el
d sy
nc
hr
o
n
o
u
s
gene
rat
o
r an
d
t
o
real
i
ze n
onl
i
n
ear c
o
nt
rol
.
We ha
ve est
a
b
l
i
s
hed a
m
odel
of t
h
e w
i
nd co
n
v
ersi
o
n
chai
n, a
nd
des
i
gn a co
nt
r
o
l
st
rat
e
gy
base
d o
n
vect
o
r
co
nt
r
o
l
.
Thi
s
st
ruct
ur
e has
been
use
d
f
o
r
r
e
fere
nce t
r
ac
ki
ng
of act
i
v
e a
n
d react
i
v
e
po
w
e
rs exc
h
a
nge
d
bet
w
ee
n t
h
e st
at
or an
d t
h
e
gr
i
d
by
co
n
t
ro
lling
th
e stato
r
co
nv
erter. A
series
o
f
sim
u
lati
o
n
s
are perform
e
d
to
test th
e
effectiv
en
ess
o
f
t
h
is
co
n
t
ro
ller. Th
e si
m
u
latio
n
resu
lts show th
at
th
e propo
se
d
fu
zzy-SMC is
very go
od
i
n
d
e
alin
g
with
th
e
ti
m
e
-
vary
i
n
g,
no
nl
i
n
ear
nat
u
r
e
of
WEC
S
. T
h
e f
u
zzy
-SM
C
wa
s also proven m
o
re effec
tiv
e th
an
th
e FLC an
d
SM
cont
rol
l
e
r
re
ga
rdi
n
g
t
h
e c
o
nt
r
o
l
pe
rf
o
r
m
a
nce an
d
po
we
r ca
p
t
ure.
Evaluation Warning : The document was created with Spire.PDF for Python.
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94
I
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S
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l. 5
,
No
. 4
,
Ap
r
il 2
015
:
50
2
–
51
1
51
0
ACKNOWLE
DGE
M
ENTS
The a
u
thors
gratefully apprec
iate the supp
ort of Tiaret
Uni
v
ersity,
Alge
ria.
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5.
BIOGRAP
HI
ES OF
AUTH
ORS
Tahir Khalfallah
is PhD student in the Depa
rtm
e
nt of
Elec
tr
ica
l
Engine
ering
in at the Dr
M
oula
y
Tah
a
r Univers
i
t
y
of S
a
id
a, ALGERIA. H
e
rec
e
iv
ed a M
A
S
TER degre
e
in
Actuator
and
industrial contr
o
l from the U
D
MT of Saida. Hi
s research
activities
includ
e the R
e
newable
Energi
es
and the Control of Ele
c
tri
cal S
y
s
t
em
s
.
He is
a m
e
m
b
er in Energeti
c En
gineer
ing and
Computer Engin
eering
Laborator
y
(L2GEGI).
Belfed
al Ch
eik
h
received th
e
M
a
gis
t
er degre
e
in elec
tric
al en
gineer
ing from
Tiar
et Univers
i
t
y
,
Algeria, in 1996. Currently
he is with the
De
partment of Electrical Eng
i
neering
,
Tiar
et
Universit
y
. His fields of inter
e
st
are contro
l
of el
ectr
i
cal m
achines, power convert
ers, m
odelling
and contro
l of
wind turbin
es. He is a memb
er in
Energetic Engin
eer
ing
and Computer
Engineering Lab
o
rator
y
(
L
2GEG
I)
Allaoui Tayeb
received his eng
i
neer degr
ee in
elec
trical
engineering from the Ibn Khaldoun
University
of
Tiaret in 1996
and his master
degree from the University
of
Science and
Techno
log
y
of
Oran in 2002.His research interest
s includes intelligent
c
ontrol of
power sy
stems
and F
A
CTS
,
Act
i
ve f
ilt
er and
ren
e
wable
en
ergies
.
He is
a Director
of En
ergetic En
gineer
ing an
d
Computer Engin
eering
Laborator
y
(L2GEGI).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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S
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:
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6
9
4
Pow
e
r C
ont
r
o
l
of
Wi
nd
T
u
rbi
n
e B
a
se
d
on
F
u
zzy
Sl
i
d
i
n
g
-
M
ode
C
o
nt
rol
(
T
ahi
r
K
h
al
f
a
l
l
a
h)
51
1
Gera
rd
Ch
amp
e
n
o
is
(M’09)
was born in France in 1957
. He receiv
e
d
the Ph.D. and
“Habilitation” d
e
grees from
the
Institut Nat
i
onal
Po
l
y
t
echniqu
e de
Grenobl
e, Grenoble, France,
in 1984 and 1992, respectively
.
He is currently
a Professor
with the Automatic Control and
Industrial Dat
a
Processing Laborator
y
(
L
AII), Po
itiers Nation
a
l
School of Engineering (ESIP),
Universit
y
of P
o
itiers
, Poitiers,
France. His m
a
jor
fields of int
e
rest in resear
ch
are renewabl
e
energ
y
s
y
s
t
em
s
,
energ
y
s
t
or
age
s
y
s
t
em
s
,
e
l
e
c
tri
cal m
a
chines
as
s
o
ciat
ed with s
t
ati
c
conv
erter
,
control, modelin
g
, and
diagnosis.
Evaluation Warning : The document was created with Spire.PDF for Python.