TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 11, Novembe
r
2014, pp. 75
4
9
~ 755
7
DOI: 10.115
9
1
/telkomni
ka.
v
12i11.60
02
7549
Re
cei
v
ed Ma
rch 2
2
, 2014;
Re
vised July
30, 2014; Accepted Augu
st
15, 2014
Fuzzy Sliding Mode Control for DFIG-based Wind
Energy Conversion Optimization
Han Yao
z
he
n*
1,2
, Liu Xiangjie
1
1
School of Co
n
t
rol and C
o
mp
uter Engi
ne
erin
g, North
Chi
na
Electric Po
w
e
r Univers
i
t
y
, Be
ij
ing, Ch
ina
2
School of Infor
m
ation Sci
enc
e and El
ectrica
l
Engi
neer
in
g, Shan
do
ng Jia
o
t
ong Un
iversit
y
, Jinan, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: h
y
z
125
@16
3
.
com
A
b
st
r
a
ct
T
h
is
study pro
poses a
fu
zz
y
slid
ing
mod
e
contro
l
stra
te
gy to
re
al
i
z
e win
d
en
e
r
g
y
conve
r
si
on
opti
m
i
z
at
ion
ba
sed on dou
bly-
fed
i
nducti
on g
ener
ator
(DF
IG)
. Its operati
o
n
a
l p
o
i
n
ts in
part
i
al
loa
d
z
o
ne
c
a
n
be electronically controlled.
Chatte
ring in wind
energy
conv
ersion sliding mode cont
rol system is
greatly
allev
i
ate
d
b
a
se
d on fu
zz
y
sw
i
t
ching
gai
n a
d
j
u
stme
n
t. T
he
purp
o
ses i
n
clu
d
in
g the
max
i
mu
m
pow
er p
o
int
tracking, d
e
co
upli
ng c
ontro
l
of active
an
d r
eactive
pow
er
of fed i
n
d
u
ctio
n ge
ner
at
ion
s
ystem
are fu
lfil
led.
F
i
tful an
d r
and
om w
i
nd
sp
ee
ds ar
e
mat
h
e
m
atical
mod
e
l
ed.
Si
mulati
on
re
sults ver
i
fied
effectiveness
a
n
d
feasib
ility
of t
h
e pr
op
osed
co
ntrol st
rate
gy
und
er th
e tw
o t
y
pes
of w
i
nd
s
pee
d
and
i
ndic
a
te th
at the
w
hol
e
control syste
m
has better ro
bu
stness aga
inst
uncer
ta
inties
a
nd can g
uar
ant
ee the p
o
w
e
r quality.
Ke
y
w
ords
: DIF
G,
w
i
nd ener
gy convers
i
on
opti
m
i
z
at
ion,
sl
idin
g
mod
e
, fu
z
z
y
g
a
in a
d
j
u
stme
nt
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
The i
n
crea
si
ng e
n
e
r
gy
deman
d, tog
e
ther wi
th the harmful
effec
t
of foss
il fuel
exploitation
o
n
the
clim
ate
and
e
n
viron
m
ent, ar
e
a
m
ong
the
m
a
in fa
ctors th
at have
bo
osted
worl
dwi
de int
e
re
st in
ren
e
w
abl
e en
ergi
es. Amon
g a
variety of
rene
wa
ble-en
ergy
re
sou
r
ces,
wind po
we
r is drawin
g the most attention
from a
ll over the wo
rld. Un
der a
n
advanced wi
nd
energy gro
w
th proje
c
tion,
cou
p
led with
ambiti
ou
s en
ergy savin
g
, wind po
we
r could be suppl
ying
29.1% of the
wo
rld ele
c
tri
c
ity by 2030
[1]. On
account of the
distin
ct
advan
tages, in
clu
d
i
ng
flexible powe
r
co
ntrol, co
mpetitive durabilit
y, and low conve
r
ter volume, DF
IGs have b
e
e
n
widely ap
plie
d in the wi
nd
-turbi
ne ge
ne
ration
syst
em
s, com
p
a
r
ed
with othe
r sol
u
tions
su
ch a
s
fixed-sp
eed i
ndu
ction ge
n
e
rato
rs o
r
the
ones
with fully rated conve
r
ters [2].
No
w the mo
st hot conte
n
ts abo
ut wi
nd
ene
rgy conversion
system (WECS
)
unde
r
resea
r
ch are
[3] the innovation on the ge
nerato
r
,
drive
train and p
o
w
er el
ect
r
oni
cs, the research
for ne
w mate
rials
and d
e
signs fo
r the
wind tu
rbin
es
, the use of
sign
al ob
se
rvation theo
ry to
estimate pa
rameters o
r
variabl
es of int
e
re
st, and th
e developm
e
n
t and de
sig
n
of novel co
ntrol
strategi
es.
The m
a
in
co
ntrol
obje
c
tive of va
riable
spe
ed
WE
CS is
po
we
r ext
r
actio
n
m
a
ximization.
For reali
z
ing t
h
is go
al, the
so-call
ed turb
ine ti
p sp
eed
ratio shoul
d b
e
maintain
ed
at its optimum
value in
de
spite of
win
d
variation
s
.
Neverthele
s
s,
control i
s
not
always aime
d at
ca
pturin
g a
s
much
en
ergy
as
po
ssi
ble.
In fact, in p
r
e
v
ious
ly
rated wind sp
eed,
t
he
captu
r
ed power nee
ds to
be limited. A
l
though
there
are
both
m
e
ch
ani
cal a
n
d
ele
c
tri
c
al
constraints, th
e mo
re
seve
re
probl
em
s are
commonly o
n
the generator and the co
nv
erter. The
r
efore, re
gulat
ion of the power
prod
uced by
the gene
rat
o
r is u
s
u
a
lly con
s
ide
r
ed.
Sliding mo
de co
ntrolle
r with intere
sting
cha
r
a
c
teri
stics make it attractive to de
al with
these
kinds of sy
stem, which rely on a ran
dom
sou
r
ce a
s
th
e win
d
, have
nonlin
ear b
ehavior and
operate u
nde
r extern
al di
sturb
a
n
c
e
s
a
nd
uncertaintie
s
in the model
para
m
eters [4-5]. High
er o
r
de
r slidin
g m
ode alg
o
rithm
s
are eve
n
used
whi
c
h have
a
c
hieve
d
outst
andin
g
co
ntro
l effects [6
-7]. However, in
stard
a
rd slidi
ng mod
e
there
are l
a
rg
er
chattering
and
for hig
her
orde
r
slidin
g
mode m
a
ss com
p
licate
d
paramete
r
s are
need
ed calcu
l
ated offline.
A fuzzy sli
d
in
g mo
de
co
ntroller for a
win
d
po
we
r syst
em with
a
twofol
d o
b
je
ctives,
stator
rea
c
tive po
wer
regul
ation
to co
mpe
n
sate the g
r
id
power fa
ctor,
and
maximi
ze th
e extra
c
ted
power by tra
cki
ng
a to
rqu
e
refere
nce t
o
control
the
point
s
of op
eration
within
the
partial
lo
ad
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 11, Novem
ber 20
14: 75
49 – 755
7
7550
zon
e
i
s
de
sig
ned i
n
this p
aper.
The
propo
sed
c
ontrol
sch
e
me provide
a suita
b
le comp
romi
se
betwe
en sim
p
licity and ro
bustn
ess, dri
v
e train me
ch
anical stre
sse
s
and
conve
r
sion effici
en
cy.
2. WECS Model
2.1. Analy
s
is
of Wind Tur
bine Char
ac
teristic
This pap
er concentrate
o
n
g
r
id-co
nne
cted
WE
CS with slip po
wer
r
e
c
o
v
e
ry
wh
os
e
config
uratio
n can
op
erate
at
different sp
eed
s
b
u
t
gen
erate
s
el
ect
r
i
c
ity at the
co
nstant f
r
equ
e
n
cy
and voltage fixed by the grid and, adeq
u
a
tely cont
roll
ed, allows po
wer
conve
r
si
on maximizat
i
on
and me
cha
n
i
c
al st
re
ss all
e
viation. Spe
c
ially a si
m
p
l
e
topology h
a
s be
en sele
cted a
s
a ca
se of
study. A sch
e
m
atic diag
ra
m of this c
onf
iguratio
n is shown in Figu
re 1.
As it ca
n be
o
b
se
rved, both
stat
or
and
ro
tor ci
rcuits p
r
ovide po
we
r to the g
r
id, del
ivering
thus mo
re p
o
w
er th
an the
rated a
nd in
crea
sing th
e e
fficiency. The
powe
r is di
rectly delivered
from the stat
or si
de an
d throu
gh a bi
di
rectio
nal
con
v
erter fro
m
the roto
r si
de
. The co
nverter
con
s
i
s
ts of an
unco
n
troll
ed
bridg
e
re
ctifie
r, a
smo
o
thin
g rea
c
tor, a
n
d
a line-co
m
m
utated inverter,
who
s
e firin
g
angle
can be
modified to contro
l the g
enerator torq
ue and, hen
ce, the syste
m
operation spe
ed and the o
p
e
ration p
o
int.
Figure 1. WE
CS-DFIG Co
nfiguratio
n
In fact, the mech
ani
cal po
wer th
at a wi
nd turbi
ne
ca
n ca
pture i
s
l
e
ss than the
available
power in the
wind a
nd it ca
n be written a
s
:
23
0.5
(
,
)
tl
p
p
PB
C
v
(1)
Whe
r
e
is the
air de
nsity,
v
re
pre
s
ent
s
the wind spe
e
d,
l
B
is the bla
de l
e
ngth, and
p
C
is the
power
coeffi
cient of the
turbine, whi
c
h de
pen
ds
on the shap
e and the g
eometry of the
blade
s.Thi
s
coefficient i
s
a
nonli
nea
r fu
nc
tion
of the
pitch
an
gle
of the bl
ade
s
p
, and th
e tip
spe
ed ratio,
rm
l
g
b
Bk
v
, where
rm
is the
mech
ani
cal rotation sp
ee
d of the gen
e
rato
r roto
r
and
gb
k
the ge
a
r
b
o
x rel
a
tion. Wh
en
the pit
c
h
angl
e i
s
maintain
ed
fixed, th
e
3
12
()
(
1
)
c
p
Cc
c
e
has a uni
que
maximum, for
opt
as it can be
see
n
in Figu
re 2.
Figure 2. Power
Coeffici
e
n
t
()
p
C
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Fuzzy Sliding
Mode Co
ntro
l for DFIG-ba
s
ed
Wind En
erg
y
Co
nversion… (Han Y
aozhen
)
7551
As is indi
cat
ed in Figu
re
3, with re
spec
t to po
wer ge
neratio
n, two regi
o
n
s can b
e
disting
u
ished
in the useful
operat
ion ra
nge of the tu
rbine.
Within
the partial l
o
ad zone, that
is
betwe
en
cu
t
i
n
v
(m
inimum win
d
speed at which the turb
ine start
s
ge
neratin
g) an
d
the rated
spe
ed
ra
te
d
v
, it is
desi
r
abl
e to maximize the
extracti
on of
the energy a
v
ailable in the wind. The
control in thi
s
zone i
s
usually perfo
rm
ed ele
c
tr
o
n
ically, maintain
ing the pitch angle fixed.
The
other u
s
eful region, kn
own
as t
he full load zon
e
, is defined betwe
en
ra
te
d
v
and
cu
t
o
u
t
v
(limit wind
spe
ed, up fro
m
whi
c
h the t
u
rbin
e shoul
d
be turn
ed of
f
to prevent d
a
mage
s). Wit
h
in this
zon
e
th
e
extraction
of power i
s
limited to the rate
d val
ue, whi
c
h can
be a
c
complished by
controlling ei
ther
the pitch angl
e of the blades or the ele
c
tri
c
al va
riabl
es of the DFIG[8]. The study in this pape
r
con
c
e
n
trate
s
on the partial
load zone.
Figure 3. Win
d
Turbi
ne Op
eration Z
one
2.2. Reduc
e
d
D
y
namic
Model
The DFIG m
odel i
s
a mul
t
ivariable
，
n
o
n
linea
r an
d strong
cou
p
lin
g syste
m
un
der th
ree
pha
se statio
nary co
ordi
n
a
te frame
w
o
r
k. In
ord
e
r to adjust active and
rea
c
tive power
indep
ende
ntly, the generat
or mod
e
l und
er the tw
o ph
ase rotating coordi
nate is d
edu
ced [9].
Voltage math
ematical e
q
u
a
tion is:
()
()
ds
s
d
s
d
s
s
qs
qs
s
q
s
q
s
s
ds
dr
r
d
r
d
r
s
r
m
qr
qr
r
q
r
q
r
s
r
m
dr
uR
i
uR
i
uR
i
p
uR
i
p
(2)
Flux linkage is:
ds
s
d
s
m
dr
qs
s
q
s
m
qr
dr
r
d
r
m
ds
qr
r
q
r
m
qs
Li
L
i
Li
L
i
Li
L
i
Li
L
i
(3)
Whe
r
e the va
riable
s
u
i
R
repre
s
ent voltage,
curre
n
t, elect
r
ic
resi
stan
ce
and flux. Subscript
s
s
r
d
q
re
pre
s
e
n
t th
e stato
r
and
rotor
com
pon
ent, qua
dratu
r
e
com
pon
en
ts, Mo
reove
r
,
s
is the
freque
ncy of
the
g
r
id (in ra
d/s),
p
is the
nu
mber
of pol
e
pairs,
s
L
and
r
L
are the
self-in
d
u
ctan
ce
s
of the windin
g
s, and
m
L
is the mutual indu
ctan
ce bet
we
en win
d
ing
s
.
The la
st eq
ua
tion acco
unts for the m
e
ch
anical
dynami
cs
of the rotating pa
rts,
whi
c
h
can
be den
oted b
y
:
1
()
rm
t
e
TT
J
(4)
Whe
r
e
J rep
r
ese
n
ts the i
n
ertia of the
whole
rotating
parts,
e
T
is
the electri
c
al re
si
stant
torque of
the DFIG, an
d
t
T
is the torq
ue pro
d
u
c
ed
by the wind o
n
the blade
s
(refe
rred to the high
spe
e
d
shaft with the
help of the gear box relati
on co
nsta
nt). these to
rque
s can be in
dicated as:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 11, Novem
ber 20
14: 75
49 – 755
7
7552
1.5
(
)
e
m
qs
dr
ds
qr
Tp
L
i
i
i
i
(5)
32
()
2
lt
t
gb
BC
v
T
k
(6)
Whe
r
e
()
t
C
is the torqu
e
co
effici
ent of the turbine, define
d
as
()
p
C
.
The WECS descri
bed previously
can
be si
mplifie
d by ma
king
som
e
ele
c
trical a
n
d
geomet
rical consi
deration
s
, regarding the relati
ve al
ignment bet
ween the rotati
ng frame
s
an
d
the spatial flu
x
es, an
d
negl
ecting
the
sta
t
or re
si
stan
ce
, A 3-ord
e
r m
odel
whi
c
h
is ade
quate
fo
r
th
e
co
n
t
ro
l de
s
i
gn
pr
oc
ess
c
a
n b
e
de
du
c
e
d
[1
0
].
T
h
is d
e
scription
co
nsi
s
ts of t
h
ree
different
ial
equatio
ns a
c
cou
n
ting for
electri
c
al dyn
a
mics of
the rotor a
nd the
dynamics of
the mech
ani
cal
rotational spe
ed.
1
1
3
1
(,
)
2
ms
r
s
s
qr
s
d
r
r
m
s
qr
qr
ee
e
rs
s
dr
s
q
r
r
m
s
dr
dr
ee
ms
rm
t
r
m
q
r
ss
LU
R
L
L
ii
p
i
u
LL
L
RL
L
ii
p
i
u
LL
pL
U
Tv
i
JL
(7)
Whe
r
e
s
U
is the
grid lin
e voltage an
d
2
es
r
m
LL
L
L
. The stator
cu
rrents
can b
e
algeb
rai
c
ally
cal
c
ulate
d
kn
owin
g the rot
o
r cu
rrents.
m
qs
qr
s
sm
ds
d
r
ss
s
L
ii
L
UL
ii
LL
(8)
Whe
n
the
ge
nerato
r
i
s
o
p
e
r
ating
on the
point
s
wh
ere
the po
we
r extractio
n
i
s
ma
ximum (
max
pp
CC
,
opt
), the co
rrespondi
ng torq
ue can b
e
ex
pre
s
sed
as
a
function
of the squa
red
rotational spe
ed.
5
ma
x
22
0
33
()
2
lp
o
p
t
rm
r
m
rm
gb
opt
BC
Tk
k
(9)
Eventually, th
e stator rea
c
tive powe
r
ca
n
be expre
s
se
d as:
2
33
22
sm
s
s
dr
ss
s
UL
U
Qi
LL
(10)
A propo
sal
control
strateg
y
is desi
gne
d
to accomp
lish two
sim
u
ltaneo
us o
b
j
ectives
simply, robu
stly, and avoid
i
ng u
nne
ce
ssary me
ch
ani
ca
l chatter. O
ne of th
e aim
s
contri
bute
s
to
comp
en
sate
the re
active
power
nee
ds of the g
r
id,
by re
gulatin
g the
stator
rea
c
tive po
wer
following
an external reference.
The ot
her involves t
he extracti
on of
power cont
rolling
the poi
nts
of operatio
n so that
eo
p
t
TT
for all wind
spe
e
d
s
in the zon
e
.
3. Design of
Fuzz
y
Slidin
g Mode Co
ntroller for WE
CS
3.1. Design
of Sliding Mode Con
t
roll
er
In ord
e
r to
achi
eve the
desi
r
ed
control obje
c
tives,
the comp
o
nents of the
slidin
g
variable
s
a
r
e
cho
s
e
n
as foll
ows:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Fuzzy Sliding
Mode Co
ntro
l for DFIG-ba
s
ed
Wind En
erg
y
Co
nversion… (Han Y
aozhen
)
7553
1
3
()
2
ms
ref
e
ref
r
m
q
r
ss
pL
U
s
TT
T
i
L
(11)
2
3
()
(
)
2
ms
s
re
f
s
r
e
f
d
r
ss
m
LU
U
sQ
Q
Q
t
i
LL
(12)
11
1
(,
,
,
)
(
,
,
,
)
qr
dr
rm
qr
dr
r
m
qr
s
f
t
ii
g
t
ii
u
(13)
22
2
(
,,,
)
(
,
,
,
)
qr
d
r
rm
qr
dr
rm
dr
s
f
t
ii
g
t
ii
u
(14)
Whe
r
e
0
1
32
(.
)
(
(
)
)
(
)
2
ms
ms
r
s
m
s
r
m
qr
s
r
m
r
m
t
e
ss
r
r
s
r
pL
U
L
U
R
L
p
L
U
k
f
ip
T
T
LL
L
L
J
1
3
(.
)
2
s
m
s
r
p
UL
g
L
,
2
3
(.)
2
s
m
r
p
UL
g
L
,
2
3
(.)
2
ms
r
s
ref
s
rm
d
r
sr
pL
U
R
L
f
Qp
i
LL
.
The
slidin
g
mode
cont
rolle
r i
s
co
mpos
ed
by equival
ent
co
ntrol
an
d switching
c
o
mponent.
Effec
t
of the former is
to
m
a
ke
the
state
s
m
o
ve o
n
th
e sli
dng
ma
ni
fold an
d th
e l
a
tter
is to kee
p
sta
t
es not esca
p
e
from slid
ng
mani
fold whe
n
the system
encounte
r
s u
n
ce
rtaintie
s.
eq
s
qr
qr
qr
eq
s
dr
dr
dr
uu
u
uu
u
(15)
Take
no a
c
co
unt of uncert
a
inties of
1
f
2
f
1
g
2
g
, th
e equivale
nt control comp
onet ca
n be
get easily fro
m
12
0
ss
1
11
1
22
(
,
,,
)
(
,,
,
)
(
,
,
,
)
(
,,,
)
eq
qr
q
r
dr
rm
qr
dr
r
m
eq
dr
q
r
dr
rm
qr
dr
r
m
ug
t
i
i
f
t
i
i
ug
t
i
i
f
t
i
i
(16)
Whe
n
syste
m
uncertainti
es exist, swt
i
chin
g co
ntro
l must be e
m
ployed to
drive the
escap
ed stat
es to the slidi
ng manifold.
The
switchi
n
g
controll
er i
s
desi
gne
d as (17).
1
11
1
22
(,
,
,
)
(
)
(,
,
,
)
(
)
s
qr
qr
dr
rm
q
r
s
dr
qr
dr
rm
d
r
ug
t
i
i
K
s
i
g
n
s
ug
t
i
i
K
s
i
g
n
s
(17)
Whe
r
e
qr
qr
qr
K
,
dr
dr
dr
K
,
0
qr
,
0
dr
,
qr
dr
are
the
uncert
a
inties com
pone
nts
su
ch a
s
u
n
-modele
d
dyn
a
mic, pa
ram
e
ters va
riatio
n and
external di
sturb
a
n
c
e
whi
c
h a
r
e
decompo
se
s
in (13
)
, (14
)
.
Stability analysis.Th
e
lyapunov functio
n
is cho
s
e
n
as:
2
1
0.5
Vs
(18)
Then,
1
11
1
1
1
((
(
)
)
)
(
(
)
)
0
qr
qr
qr
qr
qr
Vs
s
s
f
g
g
f
K
s
i
g
n
s
s
K
s
i
g
n
s
s
The Stability proof is the
same for
2
s
.
3.2. Fuz
z
y
S
w
i
t
ching Gain Adjustment
The chatterin
g
in (17
)
whi
c
h is u
s
e
d
to comp
ensate
unce
r
taintie
s
qr
dr
to guara
n
tee
sliding
mode existenc conditions
is
mai
n
ly ca
su
se
d
by swtchi
ng
gain
s
qr
K
dr
K
. The
chatterin
g
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 11, Novem
ber 20
14: 75
49 – 755
7
7554
can be red
u
ced
by cha
ngi
ng
qr
K
,
dr
K
re
al-timel
y according t
o
qr
,
dr
variation.T
he fuzzy the
o
r
y
can b
e
ado
pted to reali
z
e
variation of
qr
K
,
dr
K
in the light of the experie
nces of expert
s
.
Take
qr
K
for exa
m
ple and it is similar to
dr
K
. T
here a
r
e two fuzzy rule:
If
0
qr
qr
ss
, then
qr
K
s
h
ould be increas
e
d
(19)
If
0
qr
qr
ss
, then
qr
K
s
h
ould be dec
r
eased
(20)
Fuzzy sy
ste
m
abo
ut the
relation b
e
twe
en
qr
qr
s
s
and
qr
K
can
b
e
de
sign
ed
with re
spe
c
t to
(19
)
, (20
)
. Th
e fuzzy set is defined a
s
:
qr
qr
s
s
=
{
NB NM ZO
PM PB}
qr
K
=
{
NB NM ZO
PM PB}
Whe
r
e
NB is negative big
,
NM is ne
ga
tive middle, ZO is
zero, PM is po
sitive middle, PB is
positive big.
The fuzzy rul
e
s are de
scri
bed a
s
:
R1
：
IF
qr
qr
s
s
is
PB THEN
qr
K
is
PB.
R2
：
IF
qr
qr
s
s
is
PM THEN
qr
K
is
PM.
R3
：
IF
qr
qr
s
s
is ZO THEN
qr
K
is ZO.
R4
：
IF
qr
qr
s
s
is NM
THEN
qr
K
is NM.
R5
：
IF
qr
qr
s
s
is NB THEN
qr
K
is NB.
The integ
r
al o
f
qr
K
is em
ployed
to estimate u
pper b
oun
d o
f
qr
K
.
1
0
ˆ
t
qr
qr
K
GK
d
t
(21)
Whe
r
e
1
G
is prop
ortionality co
efficient whi
c
h is
determin
ed acco
rdin
g to experien
c
e
.
Then the la
st fuzzy sli
d
ing
mode control law is a
s
form
ula (23
)
.
1
11
1
1
22
2
ˆ
(,
,
,
)
(
,
,
,
)
(
)
ˆ
(,
,
,
)
(
,
,
,
)
(
)
qr
q
r
dr
r
m
qr
dr
rm
qr
dr
q
r
dr
r
m
q
r
dr
r
m
dr
u
g
ti
i
f
ti
i
K
s
i
g
n
s
u
g
ti
i
f
ti
i
K
s
i
g
n
s
(22)
4. Simulation Resul
t
s
To a
s
se
ss th
e de
sig
ned
controlle
rs u
n
d
e
r
r
eali
s
tic co
ndition
s, T
w
o
tests
were
condu
cted
usin
g a full-order m
odel
of the WE
CS in
cludi
ng b
o
th the me
cha
n
ical and th
e el
ectri
c
dyna
mi
cs,
together with
uncertaintie
s
and
distu
r
ba
n
c
e
s
. The
fifth-orde
r
set
of d
i
fferential e
q
u
a
tions u
s
ed i
n
these
sim
u
lati
ons to
mod
e
l
the WE
CS is
detailed
as f
o
llow.
380
Us
V
,
26
0
s
ra
d/s,
r
P5
0
H
P
,
2
p
,
0.
082
s
R
,
0.
228
r
R
,
0.
0355
s
LH
,
0.
0355
r
LH
,
0.
03
57
m
LH
,
3
1.
22
4
/
kg
m
,
2
3.
66
2
J
kgm
,
7.3
l
Bm
,
25
gb
k
,
max
0.4
p
C
,
7.5
opt
,
1
9.5
446
c
,
2
12
c
,
3
20
c
.
In addition, e
x
ternal di
sturban
ce
s and
para
m
eter
s v
a
riation
su
ch
as variatio
n
s
in the
electri
c
resi
st
ances a
nd in
the electrom
agneti
c
indu
ctance
s
was t
a
ke
n into co
n
s
ide
r
ation u
p
to
8% of their ra
ted value
s
, a
nd in the
grid
vo
ltage and
freque
ncy u
p
to 8% and 2
%
of their rat
ed
values
respec
tively.
The valu
es o
f
the pa
ram
e
ters for the
co
ntrolle
rs is fin
e
ly adju
s
ted
with the
aid
of dee
p
analysi
s
of
th
e
sy
stem and
re
altime sim
u
lati
on
s, an
d
the final
choi
ce
s a
r
e
the
followin
g
:
5
qr
2
dr
G
1
=16
25,G
1
=382.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Fuzzy Sliding
Mode Co
ntro
l for DFIG-ba
s
ed
Wind En
erg
y
Co
nversion… (Han Y
aozhen
)
7555
Mathemati
c
al
formul
as a
r
e
utilize
d
to
de
scri
be
the
variation of th
e
wind
spee
d [
11], and
built two different win
d
sp
e
ed model
s.
4.1. Fitful Wi
nd
The math
em
atical formula
to build the
model of the
fitful wind is
descri
bed
as
equatio
n
(23
)
. In this
work, th
e ba
se
wind
sp
eed i
s
5m/s. Th
e st
art-u
p
time a
nd variatio
n
cycle a
r
e 3
s
a
nd
5s, respe
c
tively. The inte
nsity of the fit
f
ul wind
is
5
m
/s. The
sp
e
ed vari
ation
of the fitful wi
nd is
s
h
ow
n
in
F
i
gu
r
e
4
.
1
21
2
1
1
2
12
,
2.5
1
cos
2
,
b
b
b
tt
t
vt
t
t
t
t
t
t
t
t
tt
t
t
(23)
Figure 4. Speed Variatio
n of Filful Wind
Figure 5. Electri
c
al To
rque
and Torque
R
e
fe
re
nc
e
The el
ect
r
ica
l
re
sista
n
t to
rque
of the
gene
rato
r
e
T
and the to
rqu
e
refe
ren
c
e
b
e
ing
tracked,
op
t
T
are depi
cted i
n
Figu
re 5.
The ove
r
la
pping
of bo
th cu
rves in
dicate
s the
accompli
sh
m
ent of the first slidin
g obj
ective. Fi
gure
6 pre
s
ent
s the tempo
r
al
variation
s
of the
stator rea
c
tive power, Q,
and of the re
active po
we
r referen
c
e, Qref. One cu
rve is exa
c
tly over
the othe
r, sh
owin
g the
su
ccessf
ul
achi
evement of t
he
se
con
d
o
b
jective. Fig
u
r
e 7
p
r
e
s
ent
s the
control inp
u
ts, the rotor voltages
uqr(u
p
per
box),
an
d
udr(lo
w
er bo
x), It is important to highlig
ht
the smooth
n
e
ss of the cont
rol sig
nal
s.
Figure 6. Rea
c
tive Stator Powe
r and its
R
e
fe
re
nc
e
Figure 7. Con
t
rol Voltage
s uqr an
d ud
r
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 11, Novem
ber 20
14: 75
49 – 755
7
7556
4.2. Random
Wind
The m
a
them
atical fo
rmul
a to b
u
ild th
e mod
e
l of t
he rand
om
wind
is
de
scribed
a
s
equatio
n (24
)
. The base
wind velo
city is 10m/s.
The intensity of random
wi
nd is 3m/s. The
spe
ed variati
on of the fitful wind is
sho
w
n in Figure 8.
(0
.
5
,
0
.
5
)
c
o
s
(
)
s
b
vv
u
n
i
f
r
n
d
w
t
v
(24)
Whe
r
e
s
v
is i
n
tensity of
ran
dom
wind
(m/
s
),
(0
.
5
,
0
.
5
)
un
i
f
rn
d
is rand
o
m
sa
mpling
value(ran
ge
betwe
en -0.5
to 0.5) .
Figure 9
indi
cate
s
rea
c
tive po
we
r tracking
curve
is goo
d
whe
n
wind
spee
d
cha
nge
s
rand
omly. The electri
c
al t
o
rqu
e
optimi
z
ation
curv
e
is de
scribe
d in Figure
10. After the initial
respon
se
tim
e
it can t
r
a
c
k the o
p
timal t
o
rqu
e
whi
c
k i
s
d
e
termi
ned
by wi
nd
sp
e
ed. The
control
voltage comp
onent
s uq
r, u
d
r a
r
e
depi
ct
ed in
Figu
re
11 an
d its pa
rtial enla
r
ge
d i
s
Fig
u
re
12
from
whi
c
h we ca
n
see the chattering i
s
sm
all enou
gh for sa
tisfying releva
nt electri
c
al code
s.
Figure 8. Speed Variatio
n of Filful Wind
Fi
gure 9. Rea
c
tive Powe
r a
nd its Refe
re
nce
Figure 10. Electri
c
al To
rqu
e
and To
rqu
e
R
e
fe
re
nc
e
Figure 11. Co
ntrol Voltage
s uqr and u
d
r
Figure 12. Partial Enlarg
ed
of Control Vo
ltages u
q
r an
d udr
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Fuzzy Sliding
Mode Co
ntro
l for DFIG-ba
s
ed
Wind En
erg
y
Co
nversion… (Han Y
aozhen
)
7557
5. Conclusio
n
Two mai
n
o
b
jective
s
of a grid
-conn
e
c
ted
varia
b
le
-sp
eed WECS
were com
p
leted
by
slidin
g mode
control strate
gy with fuzzy
swit
chin
g gai
n adju
s
tment. Two win
d
sp
eed mod
e
ls a
r
e
use
d
acco
rdi
ng to the ch
ara
c
teri
stics
of wind
that
wind tu
rbine
may meet wi
th. The re
sul
t
ing
controlle
r wa
s teste
d
afterward thro
ugh
extensive
si
m
u
lation
s usi
n
g
a reali
s
tic a
n
d
distu
r
be
d full-
orde
r mod
e
l. It was sho
w
n that the control obje
c
tives were
su
cce
ssfully atta
ined, perfo
rm
ing
robu
stly de
sp
ite the co
nsi
d
ered
distu
r
b
a
n
ce
s a
nd u
n
certaintie
s, an
d the in
cre
a
se in the o
r
de
r of
the system. In order to satisfy latest electri
c
al
codes, next we
will study fuzzy sliding m
ode
control for WECS unde
r h
a
rmo
n
ics gri
d
voltage and l
i
ttle imbalances conditio
n
s
Ackn
o
w
l
e
dg
ements
This
wo
rk i
s
partially supp
orted by
Nati
onal
Natural Scien
c
e F
o
u
ndation of
Ch
ina und
er
Grant
609
74
051, G
r
ant
6
1273
144, a
n
d
in p
a
rt by
the
Natural
Scien
c
e Fou
ndation of
B
e
ijing
unde
r Grant 4122
071 to Xiangjie Liu
and A Proje
c
t of Shandon
g Province Higher Ed
ucati
onal
Scien
c
e
and
Technol
ogy
Prog
ram
un
der
Grant J1
2LN29 a
nd
Shando
ng P
r
ovincial
Natu
ral
Scien
c
e F
o
u
ndation
und
e
r
Grant Z
R
20
13EEL01
4,
ZR20
13ZEM0
06 to Yao
z
h
en Han, Hairong
Xiao and S
hand
ong Province T
r
a
n
s
po
rtation In
novation Pro
g
ram
(No. 2012
-33
)
to
Hu
guan
sh
an.
Referen
ces
[1]
GW
EC. Global
w
i
nd
ene
rg
y
outl
ook.
Globa
l W
i
nd En
erg
y
Cou
n
cil
Rep
o
rt. Availa
ble
:
http://
w
w
w
.
g
w
e
c
.net/
[2]
Beltran, Br
ice,
T
a
rek Ahmed
-
Ali, Moh
a
me
d
Ben
bouz
id. H
i
gh-or
der s
lid
in
g-mod
e
co
ntrol
of vari
ab
le-
spee
d w
i
n
d
tur
b
in
es.
Industria
l Electron
ics, IEEE Transacti
ons on
. 20
09; 56(9): 33
14-
33
21.
[3]
H Simpso
n, Du
mb Rob
o
ts, 3rd ed.,
Sprin
g
fie
l
d: UOS Press, 2004, p
p
.6-9.
[4]
De Battista, H
e
rnn, R
i
card
o
J Mantz. D
y
na
mical v
a
ria
b
le
structure contr
o
ller
for po
w
e
r
regu
latio
n
o
f
w
i
nd
ener
g
y
c
o
nversi
on s
y
ste
m
s.
Energy Conversion,
IEEE Transactions
on
. 200
4; 19(4)
: 756-76
3.
[5]
Z
hang
Xia
n
y
o
n
g
, W
u
Jie, Y
a
n
g
Ju
nji
an, et
al.
Deco
up
led
p
o
w
e
r
co
ntrol
w
i
t
h
sli
d
in
g m
ode
for brussl
ess
dou
bl
y-fed ma
chin
e.
Ac T
ae Ner Giae So
lar
i
s Sinic
a
. 200
7; 128(1): 68-
73.
(In Chines
e)
[6]
Hu J,
Nia
n
H,
Hu B,
He
Y, Zhu ZQ. Dir
ect
active
an
d re
a
c
tive p
o
w
e
r
re
gul
ation
of
DF
IG usin
g sl
id
ing
-
mode co
ntrol a
ppro
a
ch
. Ener
gy Conv
ersion, IEEE Transactions on.
201
0; 25(4): 10
28-
10
39.
[7]
Vale
ncia
ga F
,
CA Evan
gel
ista. 2-slid
in
g acti
ve an
d
reactiv
e
po
w
e
r c
ontro
l of a
w
i
n
d
e
ner
g
y
c
onv
ersio
n
sy
s
t
e
m
.
Co
ntro
l T
heory & App
licatio
ns, IET
.
201
0: 4(11): 24
79-2
490.
[8]
C Evang
elista,
P Puleston, F
Valenc
iag
a
, LM F
r
idman. L
y
apu
nov-D
esi
g
n
ed Sup
e
r-T
w
i
s
t
ing Sli
d
in
g
Mode
Co
ntrol
for W
i
nd
En
erg
y
Co
nversi
on
Optimizatio
n
.
IEEE
Transactions on industrial electronic
s
.
201
3; 60(2): 53
8-54
5.
[9]
Abdu
lla
h MA, Yatim AHM, T
an CW
, et al.
A revie
w
of maximum p
o
w
e
r
point tracki
ng
alg
o
rithms fo
r
w
i
nd ener
g
y
s
ystems.
Renew
abl
e an
d Susta
i
na
ble En
ergy
Review
s.
201
2
;
16(5): 322
0-3
227.
[10]
Che
n
SZ
, Ch
e
ung
NC, W
o
n
g
KC, et
al. I
n
tegr
a
l
sl
idi
ng-
mode
dir
e
ct to
rque c
ontro
l o
f
dou
bl
y-fed
ind
u
ction
ge
ne
rators un
der
un
bal
ance
d
gr
id v
o
ltag
e.
Ener
gy
Conv
ersion, IEEE Transactions on.
20
10
;
25(2): 35
6-3
6
8
.
[11]
Beltran
B, El
H
a
chem
i Be
nb
o
u
zid
M, Ahme
d
-
Ali T
.
Second-
order
sli
d
in
g m
ode
contr
o
l
of
a d
oub
l
y
fe
d
ind
u
ction
ge
ne
rator drive
n
w
i
nd turb
ine.
E
n
ergy Convers
i
on, IEEE Transactions
on.
2
0
12; 27(
2): 26
1-
269.
[12]
Che
n
H
C
, Ch
e
n
PH. Activ
e
a
nd
Reactiv
e
P
o
w
e
r C
ontro
l of
a D
oub
l
y
F
e
d I
nducti
on G
ene
rator.
App
lie
d
Mathe
m
atics &
Informati
on Sc
ienc
es
. 201
4; 8(1L): 117-
12
4.
Evaluation Warning : The document was created with Spire.PDF for Python.