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.
4, D
e
c
e
m
ber
201
9,
pp.
2101~
21
17
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp2101-2117
2101
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
Ro
bust power control method
s
f
o
r wind turbines using
DFIG-generator
Iman
e El K
ar
aou
i
1
,
M
o
h
a
mme
d
Maarou
fi
2
,
B
a
d
r
e Bos
s
ou
fi
3
1
Dep
a
rt
m
e
nt of Elect
rical En
g
ineer
in
g,
M
o
h
amm
a
di
a
S
c
ho
o
l
o
f
Eng
i
n
eer
s
(E
MI
),
M
oh
am
m
e
d
V Uni
v
ersit
y
, Mor
o
cco
2
LIS
T
A
L
a
b
o
ratory
, F
aculty
o
f Sci
e
nces
Dh
a
r
El M
ahraz, S
i
d
i
M
o
h
a
med
Ben
Abdell
ah
U
n
i
versi
t
y,
F
ez,
M
o
r
occo
3
Labo
rato
ry o
f
El
ectrical
En
g
i
n
eerin
g
and
Mai
n
t
e
nan
c
e
,
Hi
g
h
e
r S
c
h
o
o
l
o
f
Te
c
hn
olog
y,
E
ST-
O
uj
d
a
,
Un
ive
r
si
ty
o
f
Mo
hamme
d I
, M
o
r
o
cco.
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Jan
1
5, 201
9
Re
vise
d Mar
1,
201
9
A
c
c
e
pte
d
J
u
n
1
,
2019
T
h
e
p
u
r
p
o
s
e
o
f
t
h
i
s
w
o
r
k
i
s
t
o
p
r
e
s
e
n
t
t
h
e
a
d
v
a
n
t
a
g
e
s
o
f
t
h
e
p
o
w
e
r
cont
rol
(acti
v
e
a
n
d
react
iv
e)
o
f
a
win
d
e
nerg
y
sys
t
em
i
n
o
r
d
e
r
t
o
i
m
p
ro
ve
t
h
e
q
uali
ty
of
t
h
e
e
n
e
rgy
p
r
odu
ced
t
o
t
h
e
gri
d
by
p
r
es
ent
i
n
g
t
wo
c
ont
ro
l
st
rat
e
gies
app
l
i
e
d
t
o
t
he
c
onv
ersi
on
sy
stem
o
f
w
i
n
d
e
n
e
rgy
equ
i
pp
ed
w
it
h
a
n
asy
n
ch
rono
us
g
e
n
erato
r
w
it
h
dua
l
p
o
w
e
r
s
upp
ly.
Bo
th
t
echn
i
qu
es
are
s
t
u
d
ied
and
d
e
velo
ped
and
co
nsi
s
t
of
a
f
i
e
ld
c
on
trol
(
F
O
C)
a
nd
a
s
li
di
n
g
mo
de
c
o
ntrol.
T
he
y
fi
nd
t
he
ir
s
tro
n
g
e
s
t
ju
st
ific
a
tio
ns
f
o
r
t
he
p
ro
bl
e
m
o
f
usin
g
a
nonl
ine
a
r
control
law
t
h
a
t
i
s
ro
bust
t
o
the
uncert
a
inties
of
t
h
e
mo
de
l.
T
he
go
al
i
s
t
o
a
pp
ly
t
h
e
se
t
w
o
c
om
mand
s
to
i
nd
e
p
end
e
nt
ly
c
on
tro
l
t
h
e
a
c
t
i
ve
a
nd
reacti
v
e
p
o
wers
g
en
erat
ed
b
y
t
h
e
d
e
co
up
led
asyn
chro
no
us
m
ach
in
e
b
y
fl
ow
ori
e
nt
at
ion.
T
hus,
a
study
of
t
he
se
c
ommands
will
be
d
etai
led
a
nd
v
a
li
dated
in
t
he
M
at
lab
/
Si
m
u
lin
k
en
vi
ron
m
en
t
wit
h
the
s
im
ult
a
neo
u
s
us
e
of
t
he
"
P
i
tc
h
Con
t
ro
l"
a
nd
"
M
axi
m
u
m
P
ower
P
o
i
n
t
T
ra
ck
in
g
(M
P
P
T)"
tec
h
niq
u
es
.
The
resu
lts
o
f
num
erical
s
im
ulati
o
n
s
o
b
t
ai
ned
s
h
o
w
t
h
e
i
ncreas
in
g
i
nteres
t
of
t
h
e
tw
o
con
t
rols
i
n
th
e
el
ectri
ca
l
sy
stem
s
.
T
hey
also
a
ttest
t
h
a
t
t
he
q
u
a
li
ty
o
f
t
h
e
acti
v
e
and
re
activ
e
po
wers
a
n
d
v
olt
a
ges
of
t
h
e
w
in
d
s
y
s
t
e
m
i
s
con
s
i
d
erabl
y
i
mpro
ved.
K
eyw
ord
s
:
DF
I
G
FOC
MPP
T
S
lid
ing
mode
c
ontr
o
l,
M
a
t
l
a
b/
Si
mu
lin
k
Wi
n
d
tur
bi
ne
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Im
ane
El Kara
o
u
i
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
Eng
i
ne
eri
ng,
M
o
h
a
m
ma
di
a
S
c
hoo
l of
E
n
g
i
neers
(EMI),
Mo
ham
m
e
d
V
U
nive
rsi
t
y,
Ra
b
at,
MO
RO
CC
O
Em
ail:
elkara
o
u
i
.
ima
n
e
@
gma
i
l
.
com
1.
I
N
TR
OD
U
C
TI
O
N
To
da
y,
D
ou
b
l
y
F
e
d
Induc
t
i
o
n
G
e
ner
a
tor
(D
F
I
G
)
i
s
w
i
del
y
u
se
d
for
p
o
w
e
r
g
e
n
e
r
a
t
i
o
n
i
n
w
i
n
d
f
a
r
m
s
because
of
i
ts
h
igh
ef
ficiency
,
en
ergy
quality
a
nd
t
he
a
bility
to
c
o
n
tro
l
p
ow
er
s
up
pl
ie
d
to
t
he
n
e
t
w
o
rk
[
1-3]
.
H
o
w
e
ve
r,
D
F
I
G
-
based
w
i
n
d
t
u
r
b
i
n
e
s
h
a
v
e
a
numbe
r
of
d
isa
d
v
a
n
t
a
g
e
s
such
a
s
their
se
n
s
iti
vit
y
t
o
l
o
ad
di
st
urba
nces,
turb
ine’s
rota
t
i
o
n
a
l
s
peed
v
ari
a
ti
o
n
,
and in
ter
n
a
l and
ex
terna
l
par
am
eters
of t
he
s
yste
m.
S
i
milarl
y,
t
he
s
ys
t
e
m
i
s
m
u
l
t
i
-
v
aria
bl
e,
d
y
n
a
m
i
c,
h
igh
l
y
c
oup
le
d
an
d
n
o
n
-l
inear
,
m
a
ki
ng
c
o
n
tro
l
very
d
if
fic
u
lt
[4].
O
n
t
h
e
ot
her
ha
n
d
,
t
h
e
need
f
or
d
eve
l
opm
en
t
o
f
w
i
nd
f
arm
s
f
or
t
he
u
se
o
f
rene
w
a
bl
e
source
s,
p
us
he
d
t
h
e
e
v
ol
u
tio
n
o
f
r
ese
a
rc
h
i
n
t
he
f
ie
ld
t
o
im
pro
ve
t
he
e
ffic
i
e
nc
y
of
t
he
e
le
ctrom
e
c
h
an
ica
l
con
v
er
sio
n
a
n
d
t
he
qua
l
i
t
y
of
t
he
e
le
ctr
i
ca
l
e
n
ergy
su
p
p
l
i
e
d
b
y
d
i
ffe
re
nt
c
on
trol
s.
[
5].
The
m
a
in
i
dea
of
t
h
i
s
appr
oa
ch
i
s
t
o
a
nal
y
ze
t
he
s
ta
bil
i
t
y
o
f
the
no
nli
n
ea
r
s
y
stem
w
i
t
h
ou
t
so
lvi
n
g
th
e
di
ffe
re
nt
i
a
l
e
q
uat
i
ons
o
f
t
h
i
s
syste
m
.
It
i
s
a
ve
ry
p
ow
er
fu
l
t
o
o
l
t
o
tes
t
a
n
d
find
s
u
ffi
c
i
e
n
t
c
o
nd
it
io
n
s
f
o
r
t
h
e
s
t
a
bi
l
ity
o
f
di
ff
ere
n
t
dy
na
mi
c
systems.
T
he
s
tudy
p
r
e
sented
i
n
t
h
i
s
p
a
p
er
a
im
s
to
o
p
t
i
m
i
ze
t
h
e
e
ne
rg
y
performa
n
ce
o
f
a
w
i
nd
t
urb
i
ne
i
n
order
to m
ax
i
m
i
z
e t
h
e
w
i
nd e
n
erg
y
ca
p
t
u
r
e
d w
h
i
l
e reduc
ing s
t
r
u
c
tura
l pr
ob
l
e
ms ci
t
ed p
r
e
vi
ousl
y
an
d
i
m
p
rove
c
o
nt
rol
p
e
rfo
rma
n
ce
b
y
re
duc
i
n
g
t
i
m
e
of
c
al
c
u
l
a
ti
on
.
This
o
pti
m
iza
t
i
o
n
is
c
apa
b
le
t
o
minim
i
z
e
t
he
c
os
ts
o
f
elec
tr
ici
t
y
pro
d
u
ct
i
on.
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.
10,
N
o.
4
, Dec
201
9 :
2
1
0
1
– 2
117
2
102
I
n
t
h
i
s
pa
per,
w
e
w
ill
s
t
a
r
t
by
e
xpos
i
n
g
a
w
i
nd
tur
b
i
n
e
m
o
d
e
l
i
n
g.
T
he
n,
a
s
tu
dy
of
t
he
oper
a
t
i
n
g
po
int
trac
k
i
n
g
t
ec
h
n
i
q
u
e
a
n
d
ma
x
i
m
u
m
p
o
w
e
r
w
ill
be
p
r
e
s
e
nte
d
.
S
u
b
s
eque
n
tly
,
we
p
re
se
n
t
a
D
FIG
mo
d
e
l
in
the
"
d
q"
f
r
a
m
e
a
nd
t
h
e
g
e
ner
a
l
pr
in
c
i
pl
e
o
f
c
on
tro
l
lin
g
b
o
t
h
p
o
w
e
r
co
nve
rte
r
s
w
h
ic
h
is
b
ase
d
o
n
the
c
ontro
l
st
r
a
te
gy
(F
O
C
,
and
S
lid
ing
Mode
).
I
n
t
h
i
s
w
o
r
k
,
w
e
d
e
v
e
l
o
p
t
w
o
c
o
n
t
r
o
l
s
t
r
a
t
e
g
i
e
s
e
n
t
i
t
l
e
d
:
F
i
e
l
d
O
rien
te
d
C
o
n
t
r
o
l
(
F
O
C
),
a
nd
Slid
ing
Mo
de
C
on
tro
l
.
A
stu
dy
of
t
h
e
se
c
omm
a
nds
i
s
de
ta
ile
d
a
n
d
de
ve
lo
p
e
d
i
n
Mat
l
a
b
/
S
im
uli
nk
e
n
vi
r
o
ne
m
e
nt.
Fi
n
a
lly
,
th
e
r
e
sul
t
s
a
r
e
an
al
y
z
ed
t
o
co
mp
a
r
e
th
e
eff
ect
iv
en
ess
of
t
h
e
c
o
n
t
r
oll
e
d
sy
st
em
o
f
th
e
t
w
o
control strat
e
gy
.
2.
WIND TURBI
N
E
MODE
LLI
N
G
2.1.
E
n
er
g
y
con
ve
rsi
o
n
ch
ai
n
Th
e
ov
e
r
al
l
dia
g
ram
o
f
a
w
i
n
d
e
n
e
r
gy
c
onv
ersi
o
n
c
h
a
i
n
co
nn
e
c
t
e
d
t
o
t
h
e
p
o
w
e
r
gr
i
d
i
s
de
pic
t
e
d
in Fig
ure
1.
F
i
gure
1.
D
i
a
gram
of a
n
ene
rgy c
o
n
v
ersi
o
n
cha
i
n
2.2.
Mod
e
llin
g of
t
he
win
d turbine
Powe
r
I
n
t
h
i
s par
t
,
w
e
d
e
f
i
n
e the
m
a
t
h
em
ati
c
a
l
m
ode
l
use
d
in
m
o
d
e
lin
g
t
he
w
in
d syste
m
.
The
e
xpr
essio
n
of
the m
e
c
h
a
n
ica
l
pow
er
c
a
p
tur
e
d by
the
w
i
n
d
t
urb
i
ne
a
n
d
tra
n
s
mit
t
e
d
t
o t
h
e
rot
o
r (
R
o
t
or)
is expr
esse
d b
y
[
3]:
.
,
.
,
(
1
)
With
,
i
s
t
h
e
p
o
w
e
r
c
o
e
f
f
i
c
i
e
n
t
,
i
s
th
e
w
i
nd
spee
d
(m
/s),
i
s
t
h
e
air
densi
t
y
and
i
s
t
h
e
swept a
r
ea
(
)
Be
tz
p
r
ove
d
tha
t
t
he
m
ax
im
um
e
x
t
rac
t
ab
le
pow
e
r
f
or
a
g
i
v
e
n
w
in
d
s
p
eed
b
y
i
d
eal
t
ur
bine
a
n
d
c
o
ndi
ti
o
n
s
i
s
,
0
.5
93
,
th
is
l
im
it
is
k
now
n
a
s
t
he
B
etz
l
i
mit.
F
or
t
he
D
F
I
G,
it
i
s
p
o
ss
ibl
e
t
o
mode
l
the
pow
e
r
c
oe
ffi
cie
n
t
(
,
)
w
ith
a
s
i
n
g
l
e
e
qua
t
i
o
n
t
ha
t
d
e
pe
nds
o
n
t
h
e
tip
s
pee
d
r
at
io
(
λ
)
and
the
pi
t
c
h ang
l
e
(β) of
t
he
b
lade
s.
Th
i
s c
a
n be
w
ri
t
t
e
n
a
s:
,
.
.
.
.
.
(
2
)
With
1
.5
872
1
1
6
0
.
4
5
2
1
0
.
0
0
8
5
.
.
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Ro
bus
t p
o
wer c
ontr
o
l m
e
t
h
od
s
f
o
r
wi
nd t
u
r
b
i
n
e
s
usi
ng
D
F
IG
-
g
enera
t
or (
I
m
ane
El
Kar
a
o
u
i)
2
103
Ω
.
(3
)
The
w
i
n
d
t
ur
b
i
ne
i
s
cha
r
ac
t
e
r
i
ze
d
b
y
t
he
c
ur
ves
o
f
t
he
c
oe
f
f
i
c
i
e
n
t
p
o
w
e
r
,
w
hic
h
c
or
r
e
sp
on
ds
t
o
t
h
e
a
e
r
o
d
yna
mic
tor
q
ue
(
)
,
s
how
n
in
f
oll
o
w
i
n
g
e
qua
tio
n.
Ω
.
,
.
Ω
(
4
)
I
t
i
s
ne
cessar
y
t
o
c
o
nn
ec
t
t
h
e
w
i
n
d
t
ur
b
i
ne
a
nd
the
D
F
I
G
t
o
t
h
e
G
ea
r
b
ox
i
n
or
de
r
to
a
da
pt
t
he
s
pe
ed
of
t
he
t
ur
bi
ne
t
o
tha
t
o
f
the
ge
ner
a
t
o
r
.
I
t
is
m
ode
le
d
by
t
h
e
t
w
o
f
ol
lo
wi
ng
e
q
u
a
ti
on
s:
Ω
.
Ω
.
(
5
)
The
e
v
olu
t
io
n
of
t
he
g
ene
r
a
t
o
r
s
pee
d
(
Ω
)
d
e
p
e
n
d
s
o
n
th
e
fund
a
m
e
n
t
a
l
eq
u
a
ti
on
o
f
th
e
dyna
mi
c
t
h
at
c
h
ara
c
teriz
e
s
t
h
e
m
echa
n
ica
l
b
eha
v
i
o
r
of
t
h
e
t
urbi
ne
a
n
d
g
e
n
era
t
o
r
f
r
o
m
t
h
e
t
ot
al
m
ec
ha
n
i
cal
t
o
r
qu
e
ap
pli
e
d
to
t
he
r
ot
or
.
I
t
i
s
give
n
b
y
t
he
f
o
l
low
i
n
g
f
or
m
u
la
(
F
i
g
u
r
e
2
)
:
Ω
.
Ω
(
6
)
Figure
2.
Wi
n
d
-
turb
ine
mod
e
l
2.
3.
Me
c
h
a
n
i
c
a
l
r
eg
ul
a
t
i
o
n
o
f
t
h
e
p
o
w
er
o
f
a
w
i
nd
t
ur
b
i
ne
-
p
i
t
c
h
c
o
n
t
ro
l
A
w
i
n
d
t
ur
bi
n
e
i
s
s
i
ze
d
to
d
evel
o
p
o
n
its
s
ha
f
t
a
p
ow
er
c
a
l
l
e
d
P
n
n
omi
n
al
p
o
w
er
o
bt
a
i
ne
d
fr
om
a
w
i
n
d
s
pee
d
vn,
c
al
l
e
d
nom
i
n
a
l
s
pe
e
d
.
W
h
en
t
he
w
ind
s
p
eed
i
s
gr
e
at
er
t
h
a
n
vn
,
t
h
e
w
i
nd
t
u
r
bi
n
e
m
u
s
t
mo
dif
y
it
s
p
a
r
a
me
ter
s
i
n
or
de
r
t
o
a
vo
i
d
m
ec
ha
ni
cal
d
e
s
t
r
uct
i
on
,
so
t
ha
t
i
t
s
r
o
t
a
t
i
o
n
sp
eed
r
emai
n
s
p
ra
ct
ic
a
l
ly
c
o
n
s
ta
nt.
[6-
10]
.
B
e
s
i
de
t
he
n
o
m
inal
s
pe
ed
,
we also
s
p
ecify
:
a.
The
star
t
i
ng
sp
ee
d
,
f
r
o
m
w
h
ich
t
h
e
w
i
nd
t
u
r
b
i
n
e
st
a
r
t
s
t
o
s
u
p
p
l
y
ene
r
gy
b.
The
m
a
xim
u
m
w
i
nd
sp
e
e
d
,
fo
r
w
h
i
c
h
th
e
tu
r
b
in
e
no
l
o
n
g
e
r
co
nv
erts
w
ind
en
ergy
,
for
rea
sons
o
f
ope
ra
ti
o
n
al saf
ety.
The
spee
d
s
,
a
nd
d
efi
n
e
fo
ur
z
ones
on
the
d
i
agr
a
m
of
t
he
u
sef
u
l
pow
er
a
s
a
f
unc
tio
n
of
t
he
wi
nd
sp
eed
:
a.
Zon
e
I, wh
e
re
0
,
the tur
b
i
n
e
d
o
e
s no
t wor
k
.
b.
Zo
ne
I
I
,
i
n
w
h
ich
the
p
o
w
e
r
sup
p
l
ie
d
o
n
t
h
e
t
r
e
e
depe
nds
o
n
the
w
i
nd
s
p
e
e
d
.
c.
Zon
e
III,
w
h
e
re th
e
sp
e
ed
o
f
ro
tati
on
i
s
k
e
pt co
n
s
t
a
n
t
an
d
the
pow
er
s
up
pli
e
d
r
e
m
a
ins
equ
a
l
to
.
d.
Zo
ne
I
V,
i
n
w
h
i
c
h
t
h
e
o
p
er
a
t
i
ng
sa
fe
t
y
s
ys
te
m
stops
t
he
t
r
a
nsfe
r
of
e
ne
r
g
y
[
6
-
10]
.
S
o
,
the
co
ntr
o
l
of
t
he
w
e
d
ge
a
ng
le
i
s
i
n
z
on
e
I
I
I
in
o
r
d
e
r
t
o
m
ain
t
a
i
n,
u
s
i
ng
the
or
ie
nta
tio
n
of
t
h
e
bla
d
e
s
o
f
t
h
e
tu
r
b
i
n
e,
t
he
pow
er
e
xtr
a
c
t
ed
a
t
a
value
ca
lle
d
no
mi
na
l
va
lue
We
p
r
e
sen
t
b
e
l
ow
t
he
i
nf
lue
n
ce
o
f
t
h
e
v
a
r
i
a
ti
on
o
f
t
he
a
n
g
l
e
o
f
c
a
l
age
on
the
val
u
e
o
f
t
he
pow
e
r
c
o
ef
f
i
c
i
e
n
t,
w
hic
h
r
e
p
r
e
se
nts
t
h
e
ene
r
g
y
e
ff
ic
ie
nc
y
o
f
t
he
t
ur
b
i
n
e
(
F
i
gur
e
3
and
F
i
g
u
r
e
4
)
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 El
ec &
D
ri S
y
s
t
Vo
l. 1
0
,
No
. 4
,
D
e
c
2
0
19
:
2
101
–
2
117
2
104
F
i
gure
3. D
i
a
gram
m
e
d
e
la
pui
ssa
n
ce
u
tile
s
ur
l’a
rbre
e
n
f
o
n
c
t
i
o
n
de
l
a
vi
t
e
sse
d
u
v
e
n
t
F
i
gur
e
4.
I
nfl
u
enc
e
o
f
t
h
e
an
g
l
e
β
on
the
po
w
e
r
coef
fic
i
ent
It c
an be
se
en t
hat
as t
he
w
edge
ang
le
i
ncre
ases,
the
effi
c
i
e
n
c
y
of
t
he
t
ur
b
i
ne
d
ec
r
e
ases.
The
c
o
ntr
o
l
o
f
t
he
w
e
dge
a
n
g
le
β
f
or
t
he
o
r
i
e
n
ta
t
i
o
n
o
f
t
he
b
la
de
s
of
t
he
t
ur
bi
ne
c
a
n
b
e
a
c
h
ie
ve
d
a
t
a
si
ng
le
l
oo
p
c
o
n
t
r
o
l
or
t
w
o
(
F
i
gur
e
5
and
6)
:
F
i
gur
e.
5.
C
o
n
tr
ol
o
f
the
ang
l
e
β
usi
ng
a
lo
o
p
c
ontr
o
l
F
i
gur
e.
6.
C
o
n
tr
ol
o
f
t
h
e
a
n
g
l
e
β
using
d
oub
le
-
l
oop
co
n
t
r
o
l
The
c
o
n
t
r
o
l
pe
r
f
or
m
e
d
by
a
sin
g
l
e
loo
p
c
on
t
r
ol
i
s
u
s
e
d
t
o
c
ontr
o
l
t
he
n
om
i
n
a
l
p
ow
e
r
.
The
ou
t
p
u
t
o
f
t
h
e
r
e
gul
at
o
r
o
f
t
h
e
no
mi
n
a
l
po
we
r
t
h
e
n
c
o
rresp
on
d
s
t
o
t
h
e
ref
e
r
e
nc
e
val
u
e
o
f
t
he
a
ng
le
β
,
an
d
it
i
s
tr
a
n
smi
tte
d
t
o
t
he
s
yste
m
of
o
r
i
e
n
ta
t
i
o
n
o
f
t
h
e
blade
s
by
an
o
p
e
n
-
l
oop
co
n
t
ro
l
.
W
h
e
n
t
h
e
c
o
n
t
r
o
l
i
s
c
a
r
r
i
e
d
o
u
t
w
i
t
h
d
o
u
b
l
e
-
l
o
o
p
c
o
n
t
r
o
l
,
t
h
e
f
ir
st
c
or
r
e
sp
on
ds
t
o
the
co
ntr
o
l
of
t
he
nom
i
n
a
l
pow
e
r
,
and
the
sec
o
n
d
t
o
t
h
e
c
o
n
t
r
o
l
of
t
he
c
al
ibr
a
t
i
on
a
ngl
e
.
The
sec
o
n
d
c
ontr
o
l
m
ode
i
s
m
o
r
e
c
om
ple
x
t
o
im
p
l
e
m
e
n
t
i
n
t
e
r
m
s
o
f
th
e
sy
nth
e
si
s
o
f
r
eg
ul
a
t
o
r
s,
a
nd
it
i
s
m
or
e
expe
nsive
si
nce
i
t
r
equ
i
r
e
s
the
use
of
t
w
o
r
e
g
u
l
a
t
or
s for
its
c
o
n
t
rol.
2.
4.
P
r
i
n
c
i
pl
e
o
f
p
o
w
er
c
o
n
tr
o
l
Ther
e
are
two
pri
n
ci
p
l
es
o
f
a
e
r
o
d
ynam
i
c
c
o
nt
r
o
l
t
o
lim
it
t
h
e
p
o
wer
e
x
tr
acted
f
r
o
m
t
h
e
t
u
rb
ine
to
t
he
r
a
ted
p
o
w
e
r
of
t
he
g
e
n
e
r
at
or
:
[
2
-
6
]
a.
"pi
t
c
h
"
or
"
v
a
r
i
a
b
le
p
itc
h"
s
y
s
tem
tha
t
a
d
j
u
s
ts
t
he
lift
o
f
t
he
b
lade
s
to
t
h
e
w
in
d
spe
e
d
t
o
m
a
i
n
ta
in
a
sub
s
ta
n
t
i
a
l
l
y
cons
ta
n
t
pow
er
i
n
t
h
e
spee
d
zo
ne
I
I
I
b.
"sta
ll" or
"a
ero
d
y
n
am
ic sta
ll" sys
tem
,
the mo
s
t
r
o
b
u
st
beca
u
s
e
it
i
s t
h
e
sh
ape
o
f
t
h
e
b
lad
e
s
t
h
at
l
ead
s
t
o
a
lo
ss
o
f
lift
be
yo
n
d
a
c
e
r
ta
in
w
in
d
s
p
ee
d,
b
u
t
t
he
p
o
w
e
r
c
u
r
ve
d
ro
p
s
f
as
t
e
r:
it
is
t
h
e
refo
re
a
pa
ss
ive
s
o
lu
ti
o
n
.
The
fi
r
s
t
pr
i
n
c
i
p
l
e
i
s
a
ssoc
ia
ted
a
bl
a
d
e
orie
nta
tio
n
m
e
cha
n
ism
,
a
l
l
o
wi
ng
t
h
e
v
aria
t
i
on
o
f
the
w
e
dg
i
n
g
a
ngl
e
d
u
r
i
ng
t
he
o
pe
r
a
t
i
on
o
f
t
h
e
w
i
n
d
t
ur
b
i
ne
t
o
allow
i
t
t
o
a
da
pt
t
o
d
i
f
f
e
r
en
t
w
i
n
d
c
on
dit
i
o
n
s
.
The
in
ter
e
st
o
f
th
is
c
on
tr
o
l
a
p
p
ea
r
s
by
obse
r
vi
n
g
t
he
c
har
acte
r
ist
i
cs
o
f
F
i
gu
r
e
7
t
ha
t
present
t
h
e
p
o
we
r
of
t
h
e
tur
b
i
n
e
as
a
f
u
n
c
t
ion
o
f
t
he
s
peed
o
f
r
o
ta
t
i
o
n
f
or
d
if
fer
e
nt
w
i
nd
sp
eed
s.
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
Ro
bust po
wer con
t
ro
l m
e
th
od
s for wi
nd tur
b
ine
s
usi
n
g
D
F
IG
-gene
r
at
or
(
I
m
ane El
K
a
ra
o
u
i)
2
105
F
i
g
u
r
e
7
.
P
o
w
e
r
of
a
turbi
ne
ac
c
ord
i
n
g
t
o it
s spee
d of
r
ota
t
i
o
n
, S
et in
wi
nd
speed.
2.5.
MPPT strategy
We
h
a
v
e
se
en
a
b
o
ve
t
hat
t
h
e
ex
trac
ti
on
o
f
w
i
n
d
powe
r
d
epe
nds
o
n
t
he
v
a
l
ue
o
f
the
pow
er
coe
f
fic
i
e
n
t.
T
he
f
i
g
ure,
b
e
l
ow
,
r
e
pre
s
e
n
t
s
t
he
p
ow
e
r
a
cc
ord
i
ng
t
o
t
he
r
o
t
at
iona
l
spee
d
o
f
a
g
i
v
e
n
tur
b
ine
(
F
igure
8):
I
t
c
a
n
b
e
s
e
e
n
t
h
a
t
,
f
o
r
e
a
c
h
v
a
l
u
e
o
f
w
i
n
d
s
p
e
e
d
V
,
t
h
e
c
h
a
r
a
c
t
e
ris
t
i
c
s
pow
e
r
-
r
ot
ati
o
nal
spee
d
grap
h
g
o
es
t
hrou
g
h
a
m
a
x
i
m
um
c
orre
spo
n
d
i
n
g
t
o
a
m
a
xim
u
m
pow
er
r
ea
ched
by
a
n
o
p
t
i
m
al
r
otat
iona
l
spee
d.
H
o
w
e
ve
r,
t
he m
axim
um
pow
er
i
s obt
a
i
ne
d f
o
r a
m
a
xim
u
m pow
er
c
oe
f
fic
i
ent (
F
ig
ure
9):
F
i
gure
8.
MP
P
T
-P
ow
e
r
o
f w
i
nd
tur
b
i
n
e
Figure
9.
M
PPT-
Powe
r c
o
eff
i
c
i
en
t cp
Th
is
m
ax
im
u
m
v
al
ue
o
f
the
pow
e
r
c
oe
ff
i
c
i
e
n
t
c
orr
e
spo
n
d
s
to
a
n
o
p
t
i
m
a
l
s
p
e
ci
fi
c
sp
eed
λ
opt
.
Thi
s
spec
ific
spee
d
i
s o
b
ta
i
n
ed f
or a
n op
t
i
m
a
l
rota
tio
na
l s
p
eed
:
Ω
.
(
7
)
Th
is
o
p
tim
al
v
al
ue
o
f
t
h
e
rota
ti
o
n
al
s
pe
ed
i
s
se
n
t
a
s
a
re
fere
n
ce
f
or
t
he
s
pee
d
c
ontr
o
l
o
f
elec
tr
ical m
ac
h
i
ne
s.
Th
e
sp
ee
d
co
nt
rol
of
t
h
e
e
l
ect
ri
cal
m
ac
h
i
ne
s
ca
n
b
e
a
c
h
iev
e
d
ei
t
h
er
i
n
sc
al
ar
c
on
t
r
ol
o
r
i
n
v
ect
o
r
con
t
ro
l
(a
lso
c
a
lle
d
Fiel
d
O
r
ie
nt
e
d
C
ontr
o
l)
.
The
sca
l
a
r
c
o
m
m
a
n
d
is
u
se
d
for
the
s
t
ea
d
y
-sta
te
c
o
n
tro
l
w
hi
le
the
vec
t
or
c
on
tro
l
i
s
use
d
i
n
t
r
ans
i
e
n
t
m
o
d
e
.
A
s
p
ar
t
of
t
hi
s
t
hes
i
s,
w
e
op
te
d
for
ve
c
t
or
c
on
tro
l
,
si
n
ce
the
mode
l
s
use
d a
r
e deve
l
o
pe
d u
n
d
er trans
ien
t
c
on
d
i
t
i
on
s.
The
c
on
t
r
ol is
mor
e
p
r
ecise and f
aster
, and
m
o
reover it
all
o
w
s
a
c
on
tro
l
of t
h
e m
a
gn
it
ude
s in
a
m
p
li
t
ude a
n
d
p
hase
.
Al
so
,
t
h
e
c
ont
ro
l
of
t
h
e
s
t
a
t
i
c
c
on
ve
rt
e
r
i
n
th
e
ma
chi
n
e
si
de
m
a
k
es
p
ossi
ble
to
c
o
n
t
ro
l
the
tor
que
o
f
the
ge
ne
rat
o
r
i
n
o
rde
r
t
o
ob
t
a
i
n
t
he
d
es
i
r
ed
r
ota
t
i
o
nal
s
p
ee
d
t
o
e
x
t
r
ac
t
t
h
e
m
a
xim
u
m
po
w
e
r.
T
hi
s
c
ons
is
ts
i
n
c
o
nt
roll
i
n
g
t
h
e e
l
ec
t
r
i
c
al
mac
hi
n
e
b
y
a
g
e
n
e
ral
ca
sc
ad
e st
ru
ctu
re
usi
ng ne
ste
d
l
oo
ps.
T
o
r
q
u
e
a
n
d
f
l
u
x
,
t
h
e
r
e
f
o
r
e
,
w
i
l
l
b
e
c
o
n
t
r
o
l
l
e
d
b
y
v
e
r
y
f
a
s
t
i
n
t
erna
l
curr
en
t
loo
p
s.
T
hese
c
omm
a
nds
are
ca
rried
o
u
t
i
n
a
r
o
t
a
t
i
ng
fr
am
e
(vec
tor
c
o
n
t
ro
l
with
f
l
u
x
o
rie
n
ted).
Th
e
torq
ue
s
e
t
p
o
i
nt
i
s
o
b
t
a
i
ne
d
from
a
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.
10,
N
o.
4
, Dec
201
9 :
2
1
0
1
– 2
117
2
106
slow
e
r
e
x
t
e
r
na
l
s
p
ee
d
c
o
n
t
r
o
l
lo
o
p
.
A
s
f
o
r
t
he
s
pee
d
r
efe
r
enc
e
,
i
t
i
s
c
a
l
c
u
l
a
t
e
d
f
r
o
m
a
M
P
P
T
s
t
r
a
t
e
g
y
a
s
prese
n
t
e
d a
b
o
v
e
.
3.
MODELLIN
G
O
F
THE DFIG
The
g
e
nera
t
o
r
cho
s
en
f
or
t
he
c
on
ver
s
ion
of
w
ind
ki
ne
tic
e
n
e
rg
y
is
t
he
d
o
u
b
le-fe
e
d
a
s
ync
hr
on
ous
gene
ra
tor
[1
1-12].
The
m
o
del
i
ng of the
D
F
I
G
is
d
esc
r
i
b
ed i
n th
e
P
a
rk refere
n
ce
s
ys
t
e
m.
T
he
f
oll
o
w
i
ng
e
q
u
a
t
i
o
n
s
ystem
descr
i
be
s
t
h
e
g
l
o
b
a
l
m
o
d
e
lin
g
o
f
t
he
g
e
n
era
t
or
t
ha
t
c
onne
c
t
s
th
e
v
o
lta
ge
s
t
o
t
he
c
ur
ren
t
s,
t
he
s
pee
d
,
the
fl
ow
of
t
he
m
achi
n
e
,
a
nd also t
he
m
echa
n
ic
al e
q
u
at
ion.
3.1.
Ele
c
tr
i
c
al
e
q
u
ati
o
n
s
S
t
ator a
n
d
roto
r
voltage
(
8
)
S
t
ator a
n
d
roto
r
c
urr
e
nts
1
.
.
.
.
1
.
.
.
.
.
1
.
.
.
.
.
.
.
.
.
(
9
)
S
t
ators and
rotor
f
l
ux
Ω
Ω
(
1
0
)
S
t
ator a
n
d
roto
r
pow
ers
The
c
o
n
t
r
o
l
of
t
he
D
F
I
G
m
u
st
a
l
l
ow
a
n
in
de
pe
n
d
e
n
t
c
o
n
t
r
o
l
of
t
h
e
act
i
v
e
and
rea
c
ti
ve
p
owe
r
s
by
t
h
e
rot
o
r vol
ta
ge
s
gene
ra
ted
b
y
an
inve
rter.
I
n
t
h
e
t
w
o
-
p
h
a
s
e
r
e
f
e
r
e
n
c
e
s
y
s
t
e
m
,
t
h
e
a
c
t
i
v
e
a
n
d
r
e
a
c
t
i
v
e
s
t
a
t
or
a
nd
rotor
powers
o
f
an
a
s
yn
c
h
ro
no
us g
en
e
r
a
t
o
r
are
wri
t
t
e
n
:
3
2
.
.
3
2
.
.
3
2
.
.
.
.
(
1
1
)
3.2.
Me
ch
an
ical e
q
u
at
i
o
n
s
Th
e el
ect
ro
me
c
h
ani
cal
to
r
q
u
e
c
an
b
e
d
e
t
e
rmi
n
e
d
by
th
e
f
o
ll
o
w
in
g
e
q
u
a
t
i
ons
(
F
i
gure
10):
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
Ro
bust po
wer con
t
ro
l m
e
th
od
s for wi
nd tur
b
ine
s
usi
n
g
D
F
IG
-gene
r
at
or
(
I
m
ane El
K
a
ra
o
u
i)
2
107
F
i
gure
1
0
.
DF
IG
m
odel
.
.
(
1
1
)
F
o
r
o
b
v
i
o
u
s
r
e
a
s
o
n
s
o
f
s
i
m
p
l
i
f
i
c
a
t
i
o
n
,
a
d
-
q
r
e
f
e
r
e
n
c
e
l
i
n
k
e
d
t
o
t
h
e
s
t
a
t
or
r
ota
t
i
n
g
fie
l
d
and
a
s
t
at
or
fl
u
x
a
li
g
n
e
d
w
ith
t
he
d
a
x
i
s
h
a
ve
b
ee
n
a
d
o
p
t
e
d
[1
1].
I
n
a
dd
iti
o
n
,
t
h
e
s
t
a
t
o
r
re
si
st
an
ce
can
b
e
n
e
gl
e
c
t
e
d
si
n
ce
th
i
s
i
s
a
r
eal
is
tic
a
ss
um
p
t
i
o
n
for
gene
ra
tors
u
se
d
i
n
w
i
n
d
pow
e
r.
O
n
t
h
e
bas
i
s
of
t
hese
c
o
n
s
i
dera
t
i
on
s,
t
h
e
tor
que
b
ec
om
es
.
(
1
2
)
4.
FIELD ORIENT
E
D
PO
WER CONTRO
L
4.1.
Principe
o
f po
w
e
r co
ntro
l
The
pri
n
ci
p
l
e
o
f
stat
o
r
fl
ux or
i
e
nta
t
io
n c
o
ntr
o
l
i
s
b
ase
d
on [1
3]:
=
a
nd
= 0.
F
o
r
lar
g
e
w
i
n
d
turb
i
n
es,
t
h
e
s
t
a
t
o
r
r
e
s
is
tors
a
r
e
n
e
g
l
i
g
i
b
l
e
,
a
nd
a
l
s
o
t
he
f
l
ux
be
c
o
me
s
co
ns
tan
t
.
F
o
r
th
i
s
,
the
flu
x
h
as a
n e
xpressi
o
n
:
0
.
.
(
1
3
)
F
r
om stator
an
d r
o
t
o
r
equa
ti
o
n
s,
w
e
o
b
ta
in
:
.
(
1
4
)
The
e
xpr
ession
o
f the
ele
c
t
ro
ma
gnet
i
c t
o
rq
u
e
[14]
:
.
(
1
5
)
Base
d
on the
assumptions
:
0
.
(1
6
)
Th
e ac
ti
v
e
powe
r
a
nd
t
h
e
re
acti
v
e
p
o
wer
o
f
t
h
e
w
i
n
d
s
y
s
t
em
c
an
b
e
w
r
i
t
t
en
[
14
]
.
.
.
.
(
1
7
)
F
r
om the
p
revi
ous e
q
u
a
tio
n,
w
e
obta
i
n [1
4]
:
.
.
.
.
(
1
8
)
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 El
ec &
D
ri S
y
s
t
Vo
l. 1
0
,
No
. 4
,
D
e
c
2
0
19
:
2
101
–
2
117
2
108
Th
e
ro
to
r fl
ux
i
s
g
i
v
e
n
by:
.
.
(
19)
S
ubseq
ue
n
t
l
y
,
the
co
n
t
r
o
l
vec
t
or
s
a
nd
c
an
b
e
de
t
e
r
m
i
n
e
d
b
y
the
eq
ua
tio
ns
:
.
.
.
.
.
.
.
.
.
.
.
.
(
20)
The
f
o
l
l
o
w
i
n
g
fi
gur
e
sh
ow
s
the
dia
g
r
a
m
bl
oc
k
us
i
n
g
S
i
m
u
l
i
n
k
t
h
a
t
m
o
de
ls
t
he
e
qua
tio
ns
de
f
i
ned
pr
ev
i
o
usly
:
The
F
i
gur
e
6
sh
ow
s
t
h
e
m
ode
l
i
n
g
o
f
D
F
IG
e
qua
ti
o
n
s
us
i
n
g
fir
s
t-
o
r
d
er
t
r
a
ns
f
e
r
f
unc
t
i
ons
f
or
vo
l
t
age
s
.
The
ve
ct
or
c
on
t
r
o
l
w
i
l
l
be
easi
l
y
i
mplem
e
n
t
e
d
l
a
t
er,
consi
d
er
i
n
g
t
h
at
t
he
s
li
p
val
u
e
g
is
n
e
g
l
i
g
i
bl
e
a
nd
t
h
e
inf
l
ue
n
ce
of
t
he
c
o
u
p
l
i
n
g
i
s
w
e
ak.
4.
2.
FOC
techn
i
que
I
n
t
h
i
s w
o
r
k
,
w
e
use
tw
o
ty
pe
s
of
v
ec
tor
co
n
t
r
o
l.
T
he f
ir
st
i
s
base
d
o
n
c
on
t
r
oll
i
ng
t
h
e
r
o
t
o
r
vo
l
t
a
g
e
o
f
the
D
F
I
G
t
o
c
o
ntr
o
l
t
h
e
p
o
w
e
r
of
t
he
s
y
s
te
m
(
F
igur
e
11)
.
F
i
gur
e
1
1
.
D
i
r
e
c
t
v
ect
or
c
on
tr
ol
The
seco
n
d
t
y
p
e
(
i
ndir
e
c
t
c
o
n
tr
ol)
is
b
as
ed on
c
o
n
t
r
o
ll
i
n
g
the
roto
r
cu
rr
en
t
to
c
ontrol
the
p
o
w
er
.
Th
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c
o
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t
r
o
l
vec
t
or
i
s
gene
r
a
te
d
fr
o
m
E
qua
tio
ns
1
9
and
2
1
(
F
i
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r
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1
2
).
4.
3.
Si
m
u
l
a
t
i
o
n
r
e
s
ul
t
s
I
n
t
h
i
s pa
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t
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w
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th
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i
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on
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s
of
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p
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d
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ode
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dir
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c
t
a
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d
i
n
d
ir
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c
t c
o
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r
o
l
of
f
l
u
x
(
F
O
C
)
(
Fi
g
u
r
e
1
2
).
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I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
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S
S
N
:
2088-
86
94
Ro
bus
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r
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u
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D
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-
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or (
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m
ane
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2
109
F
i
gur
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1
2
:
F
O
C
co
ntr
o
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Fi
g
u
re
1
3
.
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i
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c
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I
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The
F
i
g
u
r
e
14
pr
e
s
en
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the
s
i
m
u
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on
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lts
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or
t
he
p
r
o
p
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se
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c
on
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r
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s
:
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 El
ec &
D
ri S
y
s
t
Vo
l. 1
0
,
No
. 4
,
D
e
c
2
0
19
:
2
101
–
2
117
2
110
F
i
gur
e
1
4
.
R
e
sul
t
s
o
f
s
imu
l
at
i
on
o
f
a
w
i
nd
s
y
ste
m
b
ased
o
n
the
DFIG
v
ari
a
b
l
e
spee
d
5.
S
L
IDING MO
D
E
P
O
W
ER CONTROL
5.
1
S
lid
in
g
mod
e
p
owe
r
c
on
t
r
ol
s
t
r
at
egy
The
pr
i
n
ci
p
l
e
of
t
hi
s
t
e
c
h
ni
q
u
e
c
ons
is
t
s
i
n
br
i
n
g
i
ng
t
h
e
s
t
ates
t
ra
j
e
c
t
or
y
of
a
s
y
s
tem
tow
a
rds
the
sl
id
ing
s
u
r
f
ac
e
a
nd
to
s
witc
h
s
i
t
b
y
m
ea
ns
o
f
a
p
propr
iate
s
witc
hi
ng
l
ogic
aro
u
n
d
it
t
o
t
h
e
s
equi
lib
rium
p
o
i
nt
(
F
igur
e
15)
;
he
n
c
e,
t
he
phe
n
o
m
e
non
o
f
s
lip
[
15-
16]
.
F
i
gur
e
1
5
.
The
tr
aje
c
t
o
r
y
i
n
th
e
phase
p
lane
Evaluation Warning : The document was created with Spire.PDF for Python.