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
)
Vol.
11, No.
1, Mar
ch 2020,
pp.
45~55
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
5
9
1
/ij
ped
s
.
v11
.
i
1.pp
4
5
-5
5
45
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
A wind t
urbine sensorless aut
o
ma
tic control sys
tems, analysis,
modelling and de
v
elopment of IDA
-
PBC m
e
thod
Hamiani Hich
em
1
,
M
a
nso
u
ri Abdella
h
2
, Ta
d
j
e
ddine
A
li Abderra
zak
3
,
B
e
laid
i
A
b
del
k
ade
r
4
,
Salim
R
amzi
5
1
,
2,
4.
5
D
e
p
a
rtm
e
n
t
o
f El
ectri
c
a
l
E
n
gi
neeri
n
g
,
Lab
orat
ory
o
f
L
AA
S
,
Eco
le
N
a
t
i
onal
e
P
ol
y
t
echn
i
qu
e
d’O
r
an
M
au
rice
Audi
n,
Alg
e
r
i
a
3
Dep
a
rtm
e
nt of Elect
rical
En
g
i
n
eer
in
g,
L
abo
r
atory
o
f
S
CAM
R
E,
Eco
le
N
a
tio
nal
e
P
ol
y
t
echni
qu
e
d’O
r
an
M
au
rice
Audi
n,
Alg
e
r
i
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
May
7
, 2019
R
e
v
i
s
e
d
Jul
8
,
2
019
A
c
c
e
pte
d
J
u
l
31,
201
9
Several
non-
l
i
near
c
on
t
r
ols
a
r
e
developed
f
o
r
controlling
a
win
d
energy
con
v
ers
i
on
s
ystem
eq
ui
pped
w
i
t
h
a
D
F
I
G
do
ub
le
f
eed
a
sy
nch
r
on
ous
gen
e
rator.
E
xp
lo
it
a
tio
n
of
t
he
aerod
yn
am
ic
p
o
w
er
capt
u
red
b
y
th
e
tur
b
ine
gi
ves
a
n
e
w
i
n
stru
c
t
io
n
to
t
h
e
c
on
tro
l
l
e
r
bas
e
d
o
n
p
ass
i
vit
y
b
y
k
eepi
n
g
th
e
hy
pers
ynch
r
on
o
u
s
regi
me
o
f
t
h
e
D
F
IG
.
An
a
d
a
pt
iv
e
obs
erver
M
R
AS
was
dev
e
lo
ped
f
o
r
th
e
co
ns
idered
a
s
a
st
ructu
r
e
i
n
w
h
i
ch
t
h
e
r
o
t
or
sp
e
e
d
i
s
est
i
m
a
ted
f
r
o
m
t
he
m
easu
r
em
ent
of
s
t
a
to
r
and
roto
r
curren
t
s.
O
u
r
goal
i
s
to
m
a
xim
i
ze
act
iv
e
po
wer,
m
inim
iz
e
con
s
t
r
ucti
on
c
o
s
ts
i
n
ord
e
r
to
co
nt
rol
wi
nd
tu
rbi
n
e
s
y
stem
s
usi
ng
ou
r
passi
v
ity
a
nd
observ
a
tio
n
met
h
o
d
.
Bes
t
resu
l
t
s
were
o
bt
ain
e
d
u
s
in
g
sens
orl
e
ss MPPT and IDA-PBC m
e
thods.
K
eyw
ord
s
:
DF
I
G
,
IDA
-
PBC
control,
MPP
T
,
MR
AS,
S
e
nsor
l
e
ss co
n
t
ro
l,
Wi
n
d
tur
bi
ne
c
on
tro
l
Th
is
is a
n
o
p
en acces
s a
r
ti
cle u
n
d
e
r t
h
e
CC
B
Y
-S
A
li
cens
e
.
Corres
pon
d
i
n
g
Au
th
or:
Hami
an
i
Hi
ch
e
m
,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
Eng
i
ne
eri
ng,
L
abor
a
t
or
y of
L
A
A
S
,
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
,
Maurice Audin, Oran
, A
l
g
eria.
Em
ail:
hi
c
h
em
ham
i
a
n
i@
g
m
a
il.c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
The
pro
b
lem
e
v
ery
day
an
d a
r
ou
nd t
h
e w
o
rl
d is to m
e
e
t
t
he
ener
g
y
dem
a
n
d
t
ha
t
is
g
row
i
ng
m
ore an
d
mor
e
.
The
ac
cele
r
ate
d
i
ncr
e
a
s
e
in
i
n
d
u
s
t
r
ia
l
ac
ti
v
i
t
y
i
n
c
o
u
n
t
r
ies
a
n
d
b
u
s
i
ness
i
n
v
e
s
t
m
ent
tha
t
p
ro
vi
des
a
low
e
r
cos
t
o
f
pro
duc
t
i
o
n
h
as
i
ncre
ase
d
r
api
d
l
y
t
he
g
lo
ba
l
dem
a
n
d
for
e
n
ergy.
F
ace
d
w
ith
t
his
dem
a
n
d
,
t
he
in
dus
trial
i
ze
d
cou
n
t
ries
h
ave
m
a
ssi
ve
l
y
u
se
d
t
h
e
pr
od
uc
ti
on
of
de
ce
ntra
li
z
e
d
e
nerg
ies
w
h
e
t
he
r
re
new
a
bl
e
or
no
n-re
new
a
b
l
e
so
urce
s
[1,
2
]
.
Wi
n
d
e
ner
g
y
w
a
s
the
fi
r
s
t
of
t
he
en
ergy
s
ou
rc
es
e
x
p
lo
it
ed
b
y
man
.
T
hi
s
ine
x
hau
s
t
i
ble
s
ource
of
ene
r
g
y
has
d
e
v
el
o
p
e
d
s
i
g
n
i
fica
ntl
y
in
r
ec
en
t dec
a
d
e
s
[2,
3].
H
o
w
e
ver,
t
he
l
ar
ge
p
rop
o
rt
i
o
n
o
f
w
in
d
t
u
rb
ine
s
u
ses
D
F
IG
(
async
h
r
onou
s
dou
bl
e
-fe
ed
g
en
e
r
at
o
r
s
)
.
Thi
s
g
e
n
e
r
at
o
r
a
l
l
o
w
s
v
a
ri
ab
le
s
p
eed
e
l
ect
ric
i
t
y
g
ene
r
at
i
on
[
4
]
.
It
g
ive
s
t
he
o
p
por
tu
n
ity
,
to
b
e
t
t
e
r
c
o
n
t
rol
the
wi
nd
r
es
ou
rc
e
s
f
o
r
d
i
f
f
e
re
nt
w
i
n
d
c
o
ndi
tio
ns
[
5
]
.
In
t
h
e
f
ie
l
d
o
f
v
aria
ble
spee
d,
t
he
a
s
y
nchr
on
o
u
s
gen
e
rator
and
t
h
an
ks
t
o
the
de
ve
lo
pme
n
t
o
f
e
le
c
t
ro
n
i
c
i
n
ve
rters,
c
urre
ntl
y
ens
u
res,
i
n
add
i
tio
n,
a
v
e
r
y
imp
o
rta
n
t
ma
rket
share
.
I
n
the
l
a
st
y
e
a
rs,
a
n
a
pprec
iab
l
e
i
n
c
r
ea
se
i
n
t
h
e
or
de
r
of
g
e
n
er
at
ors
w
ith
d
ou
b
l
e
fee
d
i
n
g
ha
ve
b
e
e
n
gi
ve
n,
w
here
we
c
a
n give
t
he
v
e
c
t
o
r c
o
n
t
r
o
l
,
the
d
i
r
ect
c
o
n
t
rol
of
t
h
e co
up
le a
n
d
t
h
e ada
p
ti
v
e
c
ont
rol
.
S
i
m
i
l
a
rl
y
,
m
ul
ti
-scie
n
t
i
f
ic
w
or
ks
o
n
t
h
e
DF
IG
h
a
v
e
c
ont
ri
but
ed
t
o
t
h
e
c
o
n
tr
ol
s
of
w
i
n
d
s
y
stem
s
(back
st
ep
p
i
n
g
c
o
n
t
r
ol,
Sl
idi
n
g
m
o
de
c
on
t
r
ol,
M
P
P
T
c
on
t
r
ol,
PC
HD
M
o
d
el
c
ontrol,
D-F
O
C
control
etc.
[
1
,
2
,
6-10].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
45
– 55
46
Th
e
m
a
jor
disa
dvanta
ge
o
f
the
s
e
c
o
m
m
a
nd
s
i
s
a
ssem
b
led
on
a
r
ig
o
rous
m
ath
e
matical
a
s
p
ect
f
or
s
yn
t
h
e
s
i
z
e
d
.
I
n
co
n
t
rast, th
e
re a
re o
t
h
er
c
o
mma
nd
s
that ha
v
e
a
ph
y
s
ical mea
n
i
ng
s
uc
h
as
p
assi
ve
c
ont
r
o
l
[1
1-
14]
.
P
a
ssi
v
i
t
y
-
base
d
co
ntr
o
l
is
a
w
ell
-
est
a
bli
s
he
d
t
echni
q
u
e
t
h
at
h
a
s
bee
n
v
er
y
p
o
w
e
r
f
u
l
i
n
d
esi
g
ni
ng
r
o
bus
t
con
t
r
o
ls
f
or
p
h
y
si
cal
s
y
s
tem
s
.
In
heri
te
d
fr
om
w
ell
-
kn
ow
n
ph
y
s
i
c
al
phe
n
o
m
e
na,
not
i
o
n
s
o
f
passivi
t
y
a
re
a
dapted
t
o
sev
e
ral
sci
e
nti
f
i
c
d
o
m
ains
a
n
d
a
re
e
ffe
cti
v
e
for
t
h
e
re
gu
l
a
t
i
o
n
o
f
electrical,
mechanica
l
a
nd
e
lectromechanica
l
sy
s
t
e
m
s
prese
n
t
i
n
s
ev
e
r
al
f
ie
ld
s
of
e
n
g
i
n
eeri
n
g,
s
u
c
h
a
s
r
obot
i
c
s, p
o
w
er electron
i
cs etc.
[6
,
1
5
, 1
6
]
.
P
a
ssiv
i
t
y
-ba
s
e
d
c
on
tro
l
p
ro
v
i
de
s
r
o
b
u
st
c
on
tro
llers
t
hat
ha
ve
a
c
lea
r
p
h
y
sic
a
l
i
n
ter
p
reta
t
i
o
n
in
t
er
ms
of
t
he
s
yst
e
m
'
s
i
n
ter
c
o
n
n
ec
ti
o
n
s w
i
t
h
i
ts e
n
v
i
r
onm
en
t. In p
a
rti
c
u
lar,
t
he t
ot
a
l
e
ner
g
y
o
f
t
he
c
lose
d-
loo
p
s
yste
m
is
t
he
d
i
f
fer
e
nc
e
betwee
n
the
ene
r
g
y
o
f
the
sys
t
em
a
nd
t
h
e
ener
gy
su
p
p
l
i
e
d
b
y
t
h
e
c
o
n
t
r
o
ller
[7].
M
ore
ove
r,
sinc
e
the
E
u
ler-L
agrange
s
tru
c
ture
i
s
prese
r
ved
in
a
c
lose
d
loo
p,
t
he
p
a
s
si
vi
t
y
c
on
tro
l
h
as
a
r
o
bust
s
t
abi
l
i
t
y
w
ith
r
espe
c
t
t
o
t
h
e
n
on-
mode
lle
d
d
i
ss
i
p
at
ive
e
ffe
c
t
s
a
n
d
ex
h
i
b
i
ts
r
ob
us
t
pe
rform
anc
e
s
due
t
o
i
t
s
i
n
ve
rs
e
op
tim
al
ity
[
8,
9
].
M
o
d
e
l
i
ng
i
n
P
CH
(
Por
t
C
on
t
r
olle
d
H
a
milto
ni
an
)
f
o
r
m
a
n
d
i
t
s
u
s
e
f
o
r
n
o
n
-
l
i
n
e
a
r
s
y
s
t
e
m
con
t
ro
l
has
alr
e
ady
bee
n
s
uc
c
e
ssful
l
y
a
pp
li
e
d
i
n
m
a
n
y
a
r
eas
o
f
ph
ys
ics
to
d
e
s
cri
b
e
t
h
es
e
sys
t
em
s
in
t
e
r
m
s
o
f
exc
h
a
n
ge
o
f
e
n
e
r
g
y
[
17].
Th
i
s
b
y
ge
ner
a
l
i
z
i
n
g
t
he
n
o
t
io
n
o
f
D
ir
ac
s
truc
tur
e
i
n
t
o
a
n
i
n
t
erc
o
n
n
ect
i
on
st
ruc
t
u
r
e
tha
t
m
akes
i
t
p
o
ss
ib
le
t
o
clea
rly w
r
ite
t
he
i
nt
era
c
ti
o
n
o
f
the
sys
t
e
m
w
ith
i
t
s
e
nvir
onm
en
t [18,
19].
The
s
t
ruc
t
ure
t
h
a
t
i
nc
l
ude
s
pow
er
c
o
n
v
e
r
t
e
r
s
on
t
h
e
rotor
par
t
p
r
ov
id
e
s
a
h
ig
h
de
gree
o
f
c
o
nt
roll
a
b
il
ity
,
a
n
d
all
o
ws
f
o
r
m
ax
i
m
u
m
e
f
f
i
c
i
e
n
c
y
a
t
a
l
l
w
in
d
spe
e
d
s
.
To
e
nsur
e
th
e
c
ontr
o
l
o
f
M
P
P
T
(Max
im
um
P
o
w
e
r
P
oint
T
rac
k
in
g)
w
e
used the
dia
gra
m
p
rese
nte
d
i
n
F
i
g
ure
1
[20,
21].
F
i
gure
1.
B
l
o
c
k
d
i
a
gram
w
i
t
h
spe
e
d c
o
nt
r
o
l
The
c
ontr
o
l sc
hem
e
of the
D
F
IG
require
s
t
h
at
t
he ro
t
or sp
e
ed in
op
tim
al o
p
e
rat
i
o
n
, t
h
ere
f
ore,
t
he
use
of
s
pee
d
s
ens
o
r
t
o
e
ns
ure
th
i
s
m
agn
i
tu
de
i
m
p
li
e
s
t
he
i
nc
re
ase
i
n
i
n
s
t
a
l
l
a
t
i
o
n
c
o
m
p
l
e
x
i
t
y
a
n
d
c
o
s
t
.
F
o
r
t
h
i
s
pur
pose,
t
he
M
o
d
e
l
R
efere
n
ce
A
d
a
p
ti
ve
S
ystem
(
M
RA
S
)
obse
r
ver
w
a
s
use
d
t
o
e
s
ti
m
a
te
t
he
r
o
t
o
r
p
o
s
i
t
i
o
n
from
t
w
o
r
o
t
o
r
f
lu
x
m
o
de
ls
(re
fer
e
nce
mode
l
,
a
d
j
us
tab
l
e
m
odel)
to
o
b
t
a
i
n
t
h
e
ro
tor
s
p
eed
[
21].
F
i
gur
e
2
p
r
e
s
ent
s
t
h
e
sc
h
emat
i
c
d
i
a
g
r
am o
f
an
M
R
A
S o
b
s
erv
e
r.
F
i
gure
2.
P
rinc
i
p
le
d
i
a
gram
o
f a
n
MRA
S
obs
er
ver
Nevert
heless,
t
h
e
o
b
j
ecti
v
e
of
t
hi
s wor
k
s
h
o
w
s
t
he
r
e
s
ol
u
t
i
o
n
o
f
the
three
p
r
oble
ms
g
enerall
y
e
ncoun
tered
in t
he
c
o
n
t
r
o
l
of
the
DFI
G
,
t
h
e
n
the
f
i
r
st
p
robl
e
m
i
s
t
h
e
c
o
m
p
l
e
x
it
y
o
f
t
he
m
athematical
e
q
u
ations
wh
i
ch
c
lassically
m
o
d
e
l
s
t
h
e
s
y
s
t
e
m
t
o
s
t
u
d
y
,
t
h
e
second
p
rob
l
em
i
s
the
min
i
mizat
ion
of
t
he
c
o
s
t
s
o
f
con
s
tr
u
c
t
i
on
b
y
t
he
e
li
m
i
nat
i
o
n
of
m
echanical
s
e
n
s
o
rs
,
and
finally
w
e
m
o
de
l
and
c
o
n
t
rol
t
h
e
pro
duct
i
o
n
chai
n
i
n
c
l
o
sed
l
o
op.
T
heref
o
r
e
,
the
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
A
wi
nd t
u
r
b
ine
se
nsor
less a
u
t
om
a
tic c
o
n
t
r
o
l
system
s,
an
aly
s
is, m
odel
lin
g an
d
… (H
am
ia
ni H
i
c
h
e
m
)
47
pr
op
ose
d
s
ol
u
t
i
ons
p
rese
nt
e
q
u
a
t
i
o
n
s
t
hat
ha
ve
a
p
h
y
sic
a
l
a
s
p
e
c
t
(e
nergetic)
and
a
no
n
linear
c
o
n
t
r
ol
I
DA
-PBC
(Inte
rc
on
nect
io
n
a
nd
Dam
p
i
ng
A
ssi
g
n
m
e
nt
-
P
assi
v
i
t
y
B
ased
C
o
n
t
r
o
l
)
without
a
me
c
h
an
ical
s
pee
d
s
ensor
ass
o
ciated
w
ith
a
w
ind
tu
rbi
n
e
inte
g
r
a
t
e
d
i
n
t
o
the
electrical
n
e
t
w
o
r
k
(
F
i
g
u
r
e
3
s
h
o
w
s
t
h
e
o
v
e
r
a
l
l
s
y
s
t
e
m
s
t
u
d
i
e
d
)
.
Th
e
str
u
ct
ure
of
t
hi
s
c
o
n
t
ri
b
u
t
i
o
n
i
s
b
ase
d
on
t
h
e
m
o
d
e
li
ng
a
nd
c
on
t
r
ol
o
f
t
h
e
s
y
st
em
,
result
s
an
d
di
scu
s
si
on
fi
na
l
l
y
a
concl
u
sion
a
nd
p
erspecti
v
e.
V
ar
iants
and
s
c
en
a
r
ios
are
p
e
rfo
r
m
e
d
under
t
h
e
M
a
t
l
a
b
/
Sim
u
li
nk
en
vi
r
onm
ent
t
o
ev
al
u
a
te th
e
reliab
i
li
t
y
and
rob
ust
n
ess
o
f
se
n
so
rl
e
s
s p
a
ss
i
v
e c
ont
r
o
l.
F
i
gure
3.
S
truc
t
u
r
e
of se
nsor
l
e
ss c
o
n
t
r
o
l
w
ith
I
D
A
-
P
BC
m
e
t
ho
d
f
or
t
he
D
F
I
G
2.
MODELING OF TH
E
WIND
S
YSTE
M
2.1.
Mod
e
l
in
g
of th
e
win
d
tu
r
b
in
e
The
w
i
n
d
p
ow
e
r
e
quat
i
on
is d
efine
d
fr
o
m
t
h
e
fol
l
o
w
i
ng
w
ay
[
3]:
.
.
(
0
1
)
:
is the dens
i
ty of the
air.
:
i
s
the c
i
rcu
l
a
r
surfa
ce
swept by
the t
u
rb
i
n
e.
: is the
wind speed (m
/ s).
The
aer
od
yn
a
m
ic
power
of
the tur
b
i
n
e
is
t
he
n wr
i
tte
n
:
.
,
.
.
(
0
2
)
W
ith
w
hich r
epre
se
n
t
s
the
sp
ec
ific spe
e
d
The
p
o
w
e
r
coefficie
n
t C
p
r
epre
se
nt t
he a
erody
na
mic
y
i
e
l
d
of
t
he
w
in
d t
u
rbi
n
e,
it is de
t
e
r
m
i
ne
d as
f
o
l
lo
w
i
n
g
:
,
(
0
3
)
K
now
i
n
g tha
t
:
.
.
(
0
4
)
The
tor
que o
f t
h
e w
i
n
d
t
ur
bin
e
is gi
ven
by
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
45
– 55
48
.
.
,
(
0
5
)
The fu
n
d
am
ent
a
l e
qua
t
i
o
n
o
f dy
nam
i
c
s
a
l
l
o
w
s
de
te
rm
i
n
e
t
h
e e
v
o
l
u
t
i
on
o
f
t
h
e m
echa
n
ic
a
l
s
pe
e
d
f
r
o
m t
h
e tota
l
me
cha
n
ic
al t
orque
Tm
ec
app
l
ied t
o
t
he
r
ot
or:
(
0
6
)
: is
t
h
e
t
o
ta
l i
n
ertia
t
ha
t ap
pe
a
r
s on
the r
o
tor
of
t
he
ge
n
e
r
a
tor.
(
0
7
)
Th
is
m
e
c
ha
n
i
c
a
l
t
or
que
T
me
c
ta
ke
s
i
n
to
a
cc
ou
n
t
,
t
h
e
e
l
ectrom
a
g
n
e
tic
t
or
que
T
e
m
p
r
o
d
u
ce
d
by
t
he
gene
ra
tor,
the
T
orq
u
e of v
isc
ous fr
i
ct
ion
Tv
i
s
,
a
n
d
t
h
e torq
ue
fr
om
t
he
ge
a
rbo
x
.
(
0
8
)
2.2.
Mod
e
l
in
g
of th
e
D
FIG
The
m
ode
l of t
he do
u
b
le-
f
ee
d
gene
rat
o
r
i
n
t
h
e
d-
q
re
f
er
ence
ca
n
be
w
r
itten
a
s
below
[
8]:
⎩
⎪
⎪
⎨
⎪
⎪
⎧
Ф
Ф
Ф
Ф
Ф
Ф
Ф
Ф
(
0
9
)
W
ith
:
(
1
0
)
⎩
⎨
⎧
Ф
Ф
Ф
Ф
(
1
1
)
The
e
xpress
i
o
n
o
f
the
e
l
ec
t
r
o
m
agne
tic
t
or
qu
e
o
f
t
he
D
F
I
G
depe
n
d
i
n
g
on
f
low
a
nd
s
t
at
or
c
urre
n
t
s
c
a
n
be
w
r
itte
n a
s
f
o
l
l
o
w
s
:
Ф
Ф
(
1
2
)
Wi
t
h
p :
num
b
e
r
of
pole pa
i
r
s
of
t
he
D
F
I
G.
The
act
ive
an
d r
eac
tive
power
s
stat
or a
nd rot
o
r
of the
DFI
G a
r
e
w
ritte
n a
s
fo
l
low
s
[15]:
⎩
⎨
⎧
(
1
3
)
2.3.
I
D
A
-
PBC
con
t
r
o
l
l
er
a
p
p
lied
to
D
FIG
gen
e
rator
F
r
om
(
09),
it
is
c
lea
r
t
ha
t
t
h
e
dy
nam
i
c
mo
de
l
o
f
t
he
D
F
I
G
i
s
n
o
n-l
i
ne
ar
d
u
e
t
o
the
c
o
up
l
i
ng
be
t
w
e
e
n
the
s
p
ee
d
an
d
the
e
l
ec
tr
ic
c
u
r
r
e
nts.
A
cc
ording
to
t
he
v
e
c
t
o
r
co
n
t
ro
l
pri
n
cip
l
e
,
t
he
d
ire
c
t
a
xis
curr
en
t
I
d
i
s
alw
a
ys
f
or
ced
t
o
eq
ua
l
z
e
ro
i
n
order
t
o
o
rie
n
t
al
l
t
h
e
l
i
n
k
a
g
e
fl
u
x
i
n
t
h
e
d
a
x
i
s
a
nd
a
c
h
ie
ve
m
ax
imum
t
or
que
per
am
pere.
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
A
wi
nd t
u
r
b
ine
se
nsor
less a
u
t
om
a
tic c
o
n
t
r
o
l
system
s,
an
aly
s
is, m
odel
lin
g an
d
… (H
am
ia
ni H
i
c
h
e
m
)
49
⎩
⎪
⎪
⎨
⎪
⎪
⎧
Ф
Ф
Ф
Ф
(
1
7
)
S
o
t
he
m
ec
han
i
cal
e
q
u
a
t
io
n o
f
t
he
rota
t
i
ng p
a
rt of
the ge
ner
a
t
o
r
is g
ive
n
b
y:
(
1
8
)
Where ;
0
1
10
,
,
Th
e
s
t
a
t
e v
a
ri
ab
l
e
s are
:
Ф
Ф
W
ith
:
Ф
Ф
:
a
r
e
t
h
e
e
l
e
ct
ri
c
s
t
at
e
v
a
r
i
ab
l
e
s
.
: m
e
c
h
an
ica
l
v
ariab
l
e
.
Th
e
e
n
e
r
gy
f
unc
t
i
on
wri
t
t
e
n
by
:
(
1
9
)
W
ith
:
,
10
01
The
part
ia
l de
riva
t
i
ve
s of
e
ne
r
gy w
i
t
h
re
s
pe
ct to
the
sta
t
e
va
r
iab
l
es
a
re
:
⟹
(
2
0
)
F
i
nal
l
y
,
t
h
e
m
a
trice
s
o
f
inte
rc
on
nec
t
i
o
n,
dam
pin
g
an
d
t
h
e
m
atri
x of t
he
c
om
ma
n
d
a
r
e
:
0
0
0
,
0
0
0
0
0
0
(
2
1
)
0
0
0
0
0
0
1
,
(
2
2
)
W
ith
:
0
00
00
,
0
0
0
,
0
00
,
,
,
0
(
2
3)
Wi
t
h
the
se
m
a
t
rices
t
he
m
ode
l
P
C
H
is
w
ritte
n by
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
45
– 55
50
0
0
0
0
0
0
0
0
0
∇
0
0
0
0
0
0
1
(2
4
)
0
0
0
0
0
0
1
∇
(
2
5
)
2.4.
C
al
c
u
lat
i
on
o
f c
o
nt
rol vo
lta
g
es
V
d
r
, V
q
r
:
To
c
a
l
c
u
l
a
t
e
t
h
e
c
ontr
o
l v
o
lta
ges
one
ha
s
t
o
deter
m
i
n
e
a
nd
Fo
r t
h
a
t
we mu
st
d
et
e
r
mi
n
e
,
the c
o
n
t
r
o
ller
.
T
he c
lose
d-
loo
p
s
yste
m
i
s
w
ri
tt
e
n
b
y:
(
2
6
)
Whe
r
e
:
W
ith
:
:
T
he
e
ner
gy func
tio
n o
f
the
c
lo
se
d-l
o
op s
y
st
e
m
,
:
The
c
ontr
o
l
l
er
e
ner
g
y
func
tio
n.
: The
in
t
erc
o
n
n
ect
i
on m
a
tri
x
of t
h
e c
l
ose
d
-
l
oo
p
sys
t
e
m
,
: The
c
o
n
tro
lle
r in
terc
o
n
n
ect
i
o
n m
a
trix.
: The
da
m
pi
ng
m
atrix of t
he
c
lo
sed-l
o
op s
y
ste
m
,
:
T
he
c
on
t
r
ol
l
e
r da
mpi
n
g
m
a
trix
It is poss
i
bl
e
t
o
wr
i
te
(26)
a
s
fol
l
ow
s:
(
2
7
)
The
prev
io
us e
qua
tio
n is
e
q
u
i
va
le
n
t
to
:
(
2
8
)
So
t
h
e
t
ot
al
ene
rg
y
d
e
si
re
d:
∗
∗
∗
(
2
9
)
So
:
∗
∗
∗
∗
(
3
0
)
W
ith
:
∗
∗
, where
U
s
ing
t
h
i
s
r
ela
t
io
ns
hip,
(28)
b
ec
ome
s
:
∗
∗
(
3
1
)
The
com
m
a
nd V
r
i
s
fou
n
d
i
n
line
3 a
nd
4 o
f
t
he m
atrix
in
(
31).
So
:
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
A
wi
nd t
u
r
b
ine
se
nsor
less a
u
t
om
a
tic c
o
n
t
r
o
l
system
s,
an
aly
s
is, m
odel
lin
g an
d
… (H
am
ia
ni H
i
c
h
e
m
)
51
0
0
0
0
0
0
0
,
0
0
0
0
0
0
0
0
(
3
2
)
Whe
r
e
:
∈
t
o
be
d
eterm
i
n
e
d.
r
:
It is a
n
add
it
io
na
l re
si
sta
n
c
e
for c
urre
n
t
s
to
d
am
pen tra
n
s
ie
n
t
o
sc
i
l
la
tio
n
s
.
W
e
repl
a
ce the m
atrices
,
an
d us
in
g (30)
, w
e fin
d
:
∗
|
∗
|
∗
∗
(
3
3
)
So
:
∗
∗
∗
∗
∗
∗
(
3
4
)
Un
fo
rt
un
at
e
l
y
,
t
h
e
o
rd
e
r
i
s
si
ngu
l
a
r
i
n
p
oin
t
o
f
e
q
ui
li
b
r
iu
m.
I
t's
d
one
p
os
si
b
l
e
to
g
e
t
r
i
d
o
f
th
is
sing
u
l
ar
i
t
y
b
y
a
dd
ing
a
de
pr
e
c
iat
i
on
varia
b
le
.
N
o
w
w
e
k
e
e
p
a
nd
a
s
befor
e
,
and
w
e
c
ha
nge
t
he
ma
trix t
o ha
ve
t
he
f
orm
:
0
0
0
0
0
0
0
ξ
(
3
5
)
W
ith
:
ξ
∗
∗
(
3
6
)
and
:
∗
∗
(
3
7
)
Whe
n
r
eplace
d
in
t
he
c
l
o
se
d-lo
o
p
H
am
il
t
o
n
i
an
e
q
u
a
t
i
o
n
,
ξ
i
s
m
ul
ti
p
l
i
e
d
b
y
∗
,
the
r
efore
elimi
n
a
t
io
n
o
f
s
in
g
u
l
a
ri
ty.
Sinc
e
th
e
m
echa
n
ica
l
p
ar
t
of
(
27)
i
s
t
h
e
o
n
l
y
o
ne
t
ha
t
has
be
e
n
m
od
i
f
i
e
d,
the
n
t
he
e
xpre
s
si
on
o
f
V
r
i
n
t
er
ms
o
f
rest the
sam
e
.
U
s
ing
t
h
e e
q
u
i
l
i
br
ium
equa
t
i
o
n
s,
w
e
o
b
ta
in
:
(
3
8
)
The
cl
osed-
l
o
o
p
dy
n
am
ic
s
ys
t
e
m
is a
lw
ays of the
f
orm
(24)
w
ith
:
0
0
0
;
0
0
0
0
0
0
ξ
(
3
9
)
F
i
nal
l
y
,
t
h
e
rot
o
r
vo
l
t
a
g
es o
f
t
h
e or
der
are
w
r
i
t
te
n
b
y
:
∗
∗
∗
∗
∗
∗
(
4
0
)
W
ith
:
∗
∗
∗
∗
(
4
1
)
2.5.
Ap
p
l
i
catio
n
of
th
e
M
R
AS
The
eq
uat
i
o
n
s
o
f
the
ch
ose
n
re
f
er
ence
m
ode
l
and
ada
p
tiv
e
mode
l
ar
e gi
ve
n
by
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
45
– 55
52
R
e
fer
e
n
c
e m
odel
:
Ф
(
4
2
)
Ф
(
4
3
)
A
d
ap
tiv
e
mo
d
e
l:
Ф
Ф
Ф
(
4
4
)
Ф
Ф
Ф
(
4
5
)
Th
e
erro
r
bet
w
e
e
n
the
two
m
o
d
e
ls,
fun
c
t
i
on
t
o
b
e
m
i
nim
i
zed,
i
s
gi
ve
n
b
y
:
Ф
Ф
(4
6)
The
la
w
o
f
a
d
a
pta
t
ion
present
s
a
n
in
tegr
a
tion
i
n
o
pe
n
lo
op
(pro
b
l
em
o
f
of
fse
t
).
F
or
t
he
i
mpr
o
v
e
me
n
t
o
f
th
e
est
i
ma
t
i
o
n
r
espons
e a
low
pa
ss
f
il
ter
has be
e
n
pr
opose
d
b
y m
a
ny
a
ut
h
o
rs [10]
:
Ф
Ф
Ф
Ф
(
4
7
)
Wit
h:
,
p
o
si
ti
ve
c
on
st
ant
s
.
3.
RESULT
S
A
N
D
DISCU
SSIO
N
U
s
in
g
Ma
tl
a
b
/S
imuli
n
k,
t
he
r
esu
lts
o
b
t
ai
ne
d
for
t
h
e
se
ns
orl
e
ss
IDA
-
PBC
c
o
mm
and
ar
e
prese
n
t
e
d
in
F
i
gure
4,
F
igure
5,
F
igure
6,
a
nd
F
i
g
u
re
7 sh
o
w
s
t
he
re
f
er
ence
of
t
he d
yna
mic
w
i
nd spee
d
.
F
i
gure
4.
R
e
s
u
l
ts of
the
a
c
t
i
ve
pow
e
r
w
it
h its
e
r
r
or, w
itho
u
t
s
ens
o
r.
F
i
gure
5.
R
e
s
ul
ts of
t
h
e r
eac
tiv
e
pow
er
w
it
h it
s er
ror,
w
ith
out
s
en
s
o
r
.
02
468
1
0
1
2
time (s)
-10
-8
-6
-4
-2
0
2
10
4
P
re
f
P*
Err
o
r (W)
02468
1
0
1
2
ti
me (s
)
-1
0
1
2
3
4
5
6
7
10
4
Qs
me
s
Qs
re
f
Erro
r (
V
AR)
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
A
wi
nd t
u
r
b
ine
se
nsor
less a
u
t
om
a
tic c
o
n
t
r
o
l
system
s,
an
aly
s
is, m
odel
lin
g an
d
… (H
am
ia
ni H
i
c
h
e
m
)
53
Figure
6.
Resu
lts
o
f t
h
e
me
cha
n
ic
a
l
spee
d
w
it
h its
e
rr
or, w
itho
ut
sen
so
r.
F
i
gure
7.
T
he refe
r
enc
e
o
f t
h
e
dynam
i
c
w
i
nd
spe
ed.
4.
DISC
USSION
U
s
in
g
a
n
M
RA
S
o
b
se
rver
w
it
h
a
dy
nam
i
c
(r
andom
)
w
i
nd
spe
e
d,
t
he
r
e
su
lt
s
ob
t
a
i
n
e
d
f
or
F
igure
5
show
t
he
e
v
o
l
u
t
i
on
o
f
t
h
e
ac
ti
ve
p
ow
e
r
p
ro
vi
de
d
by
t
he
D
F
I
G
w
i
t
h
i
t
s
e
r
ro
r
as
a
f
un
ct
io
n
of
t
i
m
e.
N
o
t
e
t
h
at
t
h
e
c
u
r
v
e
o
f
t
h
e
acti
v
e
po
we
r
P*
(
i
n
b
l
a
ck
)
fo
ll
o
w
e
d
b
y
t
h
e
o
t
h
er
o
f
the
reference
(
i
n
blue)
Pref
w
ith
a
trans
i
en
t
regim
e
o
f
0.25
s
ec
o
nds.
T
h
e
m
a
xi
mum
peak
a
t
7
2
K
W
f
o
r
a
w
in
d
sp
ee
d
of
12.2
m/
s.
I
t
i
s
s
ee
n
th
a
t
the
c
u
rve
of
t
he
a
c
t
i
v
e
p
o
w
e
r
P
*
a
nd
i
t
s
e
rror
have
s
ma
ll
f
l
u
c
t
u
a
t
i
ons
b
eca
u
s
e
o
f
t
he
p
ro
pert
ies
of
t
he
obs
erve
r MRA
S
due to
t
h
e
se
ns
iti
vi
t
y
to t
h
e
dy
nam
i
c
var
i
a
t
i
o
ns
o
f
the
t
ur
b
i
ne
.
U
nde
r
the
sam
e
c
ond
i
t
i
ons
d
esc
r
ibe
d
a
bo
ve
,
F
i
gure
6
s
h
o
w
s
th
e
e
vo
l
u
t
i
on
o
f
t
h
e
r
eac
tive
pow
er
su
pp
li
e
d
t
o
th
e
mi
ni
mu
m
v
a
l
u
es
b
y
t
h
e
DFIG
w
i
t
h
it
s
e
r
ror
a
s
a
fu
nc
ti
o
n
o
f
t
i
m
e
.
It
i
s
n
o
te
d
t
h
a
t
t
he
c
urve
o
f
the
rea
c
t
i
v
e
po
w
e
r
Q
s
m
e
s
(in
blue
)
fo
ll
ow
e
d
t
he
o
t
h
e
r
o
f
the
re
fere
nce
(i
n
re
d)
Q
sref
w
i
t
h
a
trans
i
e
n
t
r
e
gim
e
of
0
.2
5
se
c
o
n
d
s
.
The
ma
ximum
va
lue
ge
nera
t
e
d
fr
om
t
he
r
e
acti
v
e
power
is
1
.
3
K
var
for
a
wi
nd
s
p
eed
o
f
12.2
m/s.
T
hi
s
m
i
n
i
mum
val
u
e
o
f
t
he
r
e
act
ive
pow
e
r
p
ro
du
c
e
d
is
t
he
c
o
n
se
que
nce
of
t
he
c
o
u
p
l
in
g
of
t
he
ma
them
at
i
c
al
m
ode
l
of
t
he
D
F
I
G
use.
T
he
s
m
a
ll
fl
uc
tu
ati
o
n
s
o
n
t
he
Q
sme
s
c
urve
i
s
t
h
e
c
a
use
o
f
t
h
e
pro
p
er
t
i
e
s
o
f t
h
e
MRA
S
obser
ver.
I
n
t
he
s
a
m
e
con
d
i
t
i
on
s
des
c
ribe
d
prev
i
o
u
s
ly,
F
i
gur
e
7
prese
n
ts
the
dy
nam
i
c
va
ria
tio
n
o
f
t
h
e
m
e
c
h
a
n
i
c
a
l
s
p
e
e
d
w
i
t
h
i
t
s
e
r
r
o
r
a
s
a
f
u
n
c
t
i
o
n
o
f
t
i
m
e
.
N
o
t
e
t
h
a
t
t
h
e
obse
r
ved
s
p
e
e
d
c
ur
ve
Ω
M
R
A
S
(
i
n
b
l
u
e
)
fo
l
l
ow
e
d
t
he
m
e
a
sured
s
p
ee
d
Ω
M
P
P
T
c
u
r
v
e
(in
red)
w
i
t
h
a
t
r
ans
i
e
n
t
p
e
r
i
o
d
o
f
0
.
25
se
co
nds.
In
t
h
i
s
ca
se
,
the
trans
i
en
t
re
gim
e
i
s
di
vide
d
in
t
o
t
w
o
p
arts,
th
e
first
pa
r
t
w
her
e
the
start
i
n
g
t
i
m
e
o
f
the
sy
stem
f
r
o
m
0
to
0
.2
5
se
c
o
n
d
s
a
s
wel
l
a
s
t
h
e
s
ec
ond
p
art
i
s
t
h
e
d
el
ay
ed
t
i
m
e
of
t
h
e
o
bser
ve
d
spee
d
Ω
M
RA
S
w
ith
r
es
pec
t
t
o
t
h
e
spee
d
m
easur
ed
Ω
MP
P
T
b
e
t
w
een
0
.25
a
nd
1.5
sec
o
nds.
Thi
s
d
el
ay
i
s
t
h
e
ca
use
of
a
d
a
p
t
ati
o
n
m
e
c
h
an
is
m
(PI
re
g
u
l
a
t
o
r)
o
f
th
e
ob
se
rv
er
i
n
wh
i
c
h
it
w
as
f
avo
r
e
d
t
h
e
a
ccu
ra
cy
o
f
ob
se
r
v
at
i
o
n
w
i
t
h
r
e
s
pec
t
t
o
s
p
ee
d.
T
he
ma
ximum
va
lue
of
t
he obser
v
e
d
s
p
ee
d
is
1
8
6
r
ad /
s
for
a
w
ind
s
pee
d
o
f 12.2
m /
s.
T
he
s
m
a
ll
fl
uc
tua
t
i
ons
o
n
the s
p
e
e
d c
u
rv
e
ΩMRA
S
is the
ca
u
se of t
h
e
p
r
opert
ies of o
ur
obs
erver
.
I
t
can be seen that th
e reference curves f
or
the active
p
o
w
e
r,
wh
i
c
h
re
ac
tiv
a
t
es
t
h
e
me
c
h
an
i
cal
s
p
e
e
d
,
has
bee
n
p
erfe
ctl
y
f
oll
o
w
e
d
t
h
a
nks
t
o
the
ID
A
-
P
B
C
c
o
mm
and
a
n
d
t
he
M
P
P
T
com
m
a
nd
f
or
t
he
d
yn
am
ic
varia
t
i
o
ns
o
f
t
h
e
win
d
.
T
h
e
er
ror
curve
s
o
f
t
h
e
ac
tive
a
nd
r
e
ac
t
i
ve
p
ow
er
s
ta
ke
i
m
p
ortan
t
v
a
l
ue
s
a
t
s
tart
up
f
or
the tra
n
si
e
n
t
regim
e
a
nd r
e
m
a
in i
n t
h
e
ave
r
age
of
zer
o for
t
h
e
pe
rm
anen
t
regim
e
.
02
468
1
0
1
2
time
(
s)
-100
-50
0
50
100
E
rror
(r
ad/s)
02
468
1
0
1
2
time (s)
9
9.5
10
10.5
11
1
1.5
12
12.5
W
i
nd
Speed
(
m
/
s)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
45
– 55
54
5.
CONCL
U
S
ION
I
n
t
h
i
s
c
o
n
t
ri
b
u
ti
on,
t
he
M
R
A
S
obser
ver
a
n
d
a
n
I
D
A
-
P
B
C
c
o
ntro
l
l
er
a
re
d
e
v
e
l
ope
d
u
s
in
g
a
d
va
nce
d
t
o
o
l
s
o
f
nonl
in
e
a
r
c
ont
rol
fo
r
win
d
s
yst
e
ms
t
o
a
DFIG
d
u
a
l
f
e
e
d
a
sy
nchr
on
o
u
s
gen
e
rator.
B
y
us
i
n
g
b
o
t
h
MPP
T
a
nd
I
DA-P
B
C
c
o
m
m
a
n
d
s
t
ha
t
g
u
ara
n
t
e
e
t
h
e
ma
x
i
m
i
zat
io
n
of
t
h
e
tra
c
ke
d
p
o
w
e
r
and
the
ro
bust
n
e
s
s
of
t
r
a
c
ki
ng
t
h
e
d
yn
ami
c
v
a
r
i
a
ti
on
s
o
f
t
h
e
w
ind.
M
ini
m
i
zat
i
on
of
t
r
ac
k
i
n
g
e
rrors
f
or
a
ct
ive
and
r
eac
ti
ve
p
o
w
ers
are
importa
nt
t
o
e
n
sure
r
el
ia
b
ili
ty
o
f
pow
er
g
e
n
era
t
i
o
n
un
d
e
r
n
or
ma
l
c
ondi
t
i
o
n
s.
T
he
r
e
s
ults
o
b
t
a
i
ne
d
for
the
g
e
n
e
rat
e
d
act
i
v
e
po
we
r
an
d
t
h
e
mec
h
an
i
c
a
l
s
p
eed
o
f
th
e
t
u
rbi
n
e
i
n
t
h
e
d
y
n
a
m
i
c
c
o
n
d
i
t
i
o
n
s
g
u
a
r
a
n
t
e
e
t
h
e
rob
u
st
n
e
ss of
o
ur c
on
t
r
o
l
an
d
t
he
val
i
d
ity o
f the
m
o
de
l pro
p
o
se
d,
ther
e
fore
, th
e
pr
ecis
i
on and
th
e
op
t
i
mi
za
tio
n
to trac
k
the
v
ar
iations of
t
h
e ae
ro
dy
n
a
mi
c
po
we
rs.
APPENDIX
The
para
me
t
e
rs use
d
i
n
the
m
ode
l
o
f
the
D
F
I
G
a
nd w
i
nd t
u
r
b
i
n
e
a
re shown in Table 1:
Ta
ble
1.
P
aramete
r
s used
i
n
sim
u
lat
i
on m
ode
l.
DF
I
G
P
a
ra
m
e
te
r
V
a
l
u
e
U
n
i
t
Pn
1
0
0
k
W
Rs
0
.4
5
5
Rr
0
.
1
9
Ls
0
.0
7
H
Lr
0
.
021
3
H
Lm
0
.
0
34
H
JDF
I
G
0,
5
3
K
g.m
²
f
0,
002
4
N
.
m
.
s/ra
d
p
2
/
W
i
nd
Turbine
R
35.25
m
S
π.
r2
m
2
ρ
1.
2
2
K
g/m
3
G
90
/
Jtur
bi
ne
100
0
Kg/m
2
REFE
RENCES
[1]
B.
B
ossou
f
i
,
M
.
Kari
m
,
et al.,
"
Ob
serv
er
b
ack
step
pi
ng
c
on
tro
l
o
f
DFIG
-gen
erat
ors
f
o
r
w
i
n
d
t
u
r
b
i
nes
variable-
sp
eed:
F
P
G
A
b
a
s
ed
i
m
p
lem
e
n
t
ation
,
"
Ren
e
wa
bl
e Ener
gy
Jo
urn
a
l
(
E
L
S
IV
ER)
,
vo
l.
81,
p
p.
9
03
-917,
S
e
pt
emb
e
r
20
15
.
[2]
H.
W
a
i
(
Alan
)
Li
o,
"
Bl
ade-p
itch
con
t
ro
l f
o
r
wi
nd
tu
r
bi
ne l
oad
r
ed
uctions,"
Book,
Fs
t
Edi
tion springer
, 2
01
8.
[3]
R. Ha
m
i
d
K
.,
"
St
ru
ctural
con
t
r
o
l
a
nd f
ault de
tection of
w
ind tu
rbine syst
e
m
s
,
"
B
o
ok,
Fs
t E
d
iti
on IET
, 20
1
8
.
[4]
R.
C
ardenas
,
R
.
P
e
na,
et
a
l
.,
"
O
v
erv
i
ew
o
f
co
nt
rol
s
y
stem
s
f
o
r
t
h
e
o
p
erati
o
n
of
D
F
I
Gs
i
n
w
i
n
d
energ
y
app
l
i
c
at
io
n
s
,"
IEE
E
Tr
ans
actio
ns on
Ind
u
stria
l
Electr
o
n
i
cs
,
v
o
l
.
6
0
,
N
o.
7
,
p
p
.
2
776-2
7
9
8
,
2
01
3.
[5]
A. Gh
a
ni A.
, A.
Tah
o
u
r
,
"
W
in
d
tu
rb
i
n
es d
esign
,
c
o
n
t
ro
l an
d ap
pl
i
cations,"
Book,
F
s
t
Edi
t
ion
Ex
L
i
4
E
v
A
, 2
01
6.
[6]
I.
M
in
ka
,
A.
E
ssa
d
k
i,
S
.
Me
nsou
,
T.
N
a
s
se
r,
"
Prima
r
y
fre
q
u
e
nc
y
co
nt
rol
app
l
i
e
d
to
t
h
e
w
in
d
turbin
e
b
a
sed
on
t
he
DF
IG
c
ontrolled
by
t
he ADRC,
"
Int
e
rn
atio
na
l
Jo
urn
a
l
o
f
P
o
wer Elect
ro
n
i
cs a
nd
Dr
ive S
y
st
em
(
I
J
P
EDS)
,
vo
l.
1
0,
No
.
2
,
pp.
1
04
9-10
58
,
2
019
.
[7]
M
.
N
a
d
o
u
r
,
A
.
E
s
s
a
d
k
i
,
T
.
N
a
s
s
e
r
,
M
.
F
d
a
i
l
i
,
"
R
o
b
u
s
t
c
o
o
r
d
i
n
a
t
e
d
co
ntro
l
usin
g
b
a
cks
t
ep
pin
g
o
f
flyw
heel
e
nerg
y
st
orage
sy
stem
a
nd
DF
IG
f
o
r
p
ower
s
m
oothing
i
n
win
d
p
o
w
e
r
p
l
a
n
t
s,"
I
n
te
r
n
a
t
io
na
l J
o
ur
na
l
o
f
P
o
w
e
r
El
ectro
n
i
cs a
n
d
Dr
ive S
y
s
t
em
(
I
JPEDS)
,
v
o
l.
10,
N
o.
2
,
p
p
.
1
1
10-1
1
2
2
,
201
9.
[8]
J.
W
an
g,
H
.
Yin
,
"
P
a
s
s
i
v
it
y
ba
s
e
d
con
t
ro
ll
e
r
d
e
s
ig
n
bas
e
d
on
E
L
a
nd
P
CHD
mo
del
,
"
E
l
s
e
v
ie
r
L
t
d
,
P
r
oc
e
d
ia
En
gi
neeri
ng,
v
o
l.
1
5
,
p
p.
33-3
7
,
20
11.
[9]
A.
M
ah
rou
s
,
K
.
M
etw
a
ly
,
I.
N
ag
y,
"
P
e
rf
orm
a
nce
inv
e
stig
atio
n
o
f
m
u
lti
-
l
evel
i
nverter
for
D
F
I
G
d
ur
i
ng
gri
d
aut
o
reclo
s
u
r
e
o
p
erati
o
n
,
"
Int
e
rnati
o
n
a
l
Jou
r
n
a
l
o
f
P
o
wer
El
ectr
onics
an
d
Dri
ve S
y
st
e
m
(
I
JPEDS)
,
Vol
.
1
0,
no.
1
,
pp
.
4
54-4
6
2
,
2
0
1
9.
[10]
M
.
Z
ai
r,
A
.
H
azz
ab,
"M
RAS
s
p
eed
s
ens
o
rle
s
s
v
ecto
r
c
o
n
t
r
ol
o
f
in
du
cti
on
moto
r
dri
v
es
u
si
ng
predi
c
ti
ve
adap
tati
on
m
echan
ism,
"
In
ter
natio
na
l Jo
ur
nal
of P
o
wer
Elect
ro
n
i
cs a
nd
Dri
ve Sys
t
em
(
I
JPED
S
)
,
v
o
l.
9
,
no
.
4
,
pp
.
1
523
-15
3
3
, 2
018
.
[11]
H.
M
ahm
o
udi,
"Backst
epp
i
n
g
a
dap
tiv
e
con
t
rol
o
f
D
F
I
G
f
o
r
w
i
n
d
t
u
rbi
n
es
v
ariab
l
e-sp
eed,"
JAT
I
T
Jour
na
l
,
20
th.
v
o
l.
8
1
, n
o.
2,
20
1
5
.
[12]
N.
L
uo,
Y
.
Vid
a
l
and
L.
A
ch
o,
"
Adv
a
nces
i
n
in
d
u
stri
al
c
ontro
l,
win
d
t
u
r
b
i
ne
c
on
tr
ol
a
n
d
m
on
ito
ring
,"
Book,
F
s
t
Edi
tion springer
,
20
14.
[13]
S
.
E
brahim
kh
ani,
"
Ro
bu
st
f
rac
t
io
nal
ord
e
r
slidi
n
g
m
o
d
e
c
on
trol
o
f
dou
b
l
y-f
e
d
indu
ctio
n
g
e
nerat
o
r
-bas
ed
w
in
d
turbi
n
es
,
"
ISA
Transaction
s
,
20
16
.
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