Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 2
,
A
p
r
il
201
6, p
p
.
54
9
~
55
9
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
2.7
858
5
49
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
/
IJECE
Wind Energy Conversion Systems Based On a DFIG Controlled
By Indirect Vector Using PWM and SVM
Na
im Cherfia, Dja
llel Kerdoun
Department o
f
Electrical Engin
e
eri
ng,
LGEC-Res
earch
Laborator
y
,
Alger
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 19, 2015
Rev
i
sed
No
v
16
, 20
15
Accepted Dec 10, 2015
This work presents consider
atio
n and
use of th
e as
y
n
chronous g
e
nerator in
the production o
f
wind energ
y
.
To do this
,
a model of th
e wind
turbine h
a
s
been established, the
mathematical model of
the doubly
f
e
d induction
genera
tor (DFIG) variabl
e
speed is pr
esented and
the control qua
ntiti
es used
when integr
at
ed
with a wind s
y
s
t
em
. A modeling in a diphasic ref
e
rence
m
a
rk rela
ted
to
the
stator
fi
eld
and
a str
a
teg
y
vec
t
or
control
ac
tive
an
d
reac
tive power
are offer
e
d with
a P
W
M and SVM technique f
o
r inverter
control is
considered
in our
work
.
Keyword:
DFI
G
PW
M
SVM
Turbine
Wi
n
d
Copyright ©
201
6 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
:
Naim
Ch
erfia,
Dj
allel Kerd
oun
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
LGEC-Resea
rc
h La
b
o
rato
ry
,
C
onst
a
nt
i
n
e 1 Uni
v
ersi
t
y
, 25
00
0
C
o
nst
a
nt
i
n
e,
Al
geri
a.
Pho
n
e
: +21
3780
102
155
Em
ail: m
s
n822009@live.fr
, kerdjallel@yahoo.fr
1.
INTRODUCTION
Thi
s
pa
per i
s
t
o
st
udy
t
h
e i
n
d
i
rect
cont
r
o
l
po
wer
of
dou
b
l
y f
e
d
indu
ctio
n
gen
e
r
a
t
o
r
(D
FIG
)
op
er
atio
n
gene
rato
r fo
r
t
h
is, o
u
r w
o
r
k
i
s
o
r
ga
nized
as follo
ws:
-
Th
e
f
i
r
s
t
p
a
r
t
is d
e
d
i
cated
t
o
th
e descr
i
p
tio
n and
m
o
d
e
ling
o
f
w
i
n
d
tur
b
i
n
es b
a
sed on
physical eq
u
a
tions
r
e
spon
siv
e
op
er
atio
n.
-
Th
e secon
d
p
a
rt, we presen
t
a m
a
th
e
m
atica
l
m
o
d
e
l of t
h
e (DFIG) will si
m
u
late th
e mo
d
e
l i
n
g
e
n
e
rat
o
r
m
ode.
-
Th
e th
ird
is d
e
v
o
t
ed
to
th
e st
u
d
y
o
f
th
e techn
i
qu
e of ind
i
rect co
n
t
ro
l po
wer to
realize the co
nv
ersion
DC-
AC
i
nve
rt
er us
i
ng t
w
o v
o
l
t
a
g
e
l
e
vel
s
wi
t
h
t
e
chni
cal
usi
ng t
h
e P
W
M
co
nt
r
o
l
l
e
r (P
ul
se
W
i
dt
h M
o
dul
at
i
o
n
)
and SVM (s
pa
ce vector m
o
dulation)
2.
MODEL OF
THE TURBINE
A wi
nd t
u
r
b
i
n
e, com
m
onl
y
cal
l
e
d wi
n
d
i
s
a
devi
ce
whi
c
h
t
r
ans
f
o
r
m
s
a part
of t
h
e ki
net
i
c ener
gy
of
wind int
o
m
echanical e
n
ergy
availabl
e
on a
shaft a
n
d the
n
i
n
to electrical
e
n
ergy via
a generator
(DFIG) [1].
Mechanical
power available
on the
s
h
af
t
o
f
a wind
t
u
rb
in
e is exp
r
essed as:
.
(1
)
Wi
t
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
54
9 – 5
5
9
55
0
λ
(2
)
Ω
1
: Ro
tatio
n
sp
eed b
e
fo
re m
u
ltip
lier.
R
:
rot
o
r radi
us 35
.2
5
m
.
ρ
: air de
nsity,1.225 kg.m
-3
.
,
e
x
p
(3
)
Wi
t
h
:
1
λ
1
λ
0
.
O
8
β
0
.
035
β
1
C
1
=0.5
1
76;
C
2
=116; C
3
=0.4; C
4
=5; C
5
=21;
C
6
=0
.
006
8 [1
], [2
].
Characteristics
of C
p
in
term
s
o
f
λ
for d
i
ffere
nt
val
u
es
of t
h
e pi
t
c
h angl
e are sh
o
w
n i
n
Fi
g
u
r
e 1. Th
e
m
a
xim
u
m
val
u
e of C
p
(C
pm
ax
=
0
.4
353
)
is r
each
e
d
of
β
=2
°
and
λ
=
1
0
.
0
1
.
Thi
s
part
i
c
ul
a
r
val
u
e o
f
λ
i
s
defi
n
e
d as
th
e no
m
i
n
a
l v
a
lu
e [1
],
[3
].
Fi
gu
re
1.
The
po
we
r fact
or
f
o
r
di
f
f
ere
n
t
a
n
gl
es
of
st
al
l
s
3.
MO
DEL OF
THE DO
UBL
Y
FE
D I
N
D
U
C
TIO
N
GE
N
E
RATO
R
A c
o
m
m
onl
y
use
d
m
odel
f
o
r t
h
e
do
u
b
l
y
f
e
d i
n
d
u
ct
i
o
n
g
e
nerat
o
r
(
D
F
I
G)
i
s
t
h
e
Pa
rk
m
odel
.
T
h
e
electrical equat
i
ons
of the
DFIG in the
Park
re
fere
nce
fram
e
are
give
n as
follows
[4], [5]:
v
R
i
φ
ω
φ
v
R
i
φ
ω
φ
(4
)
v
R
i
φ
ω
φ
v
R
i
φ
ω
φ
(5
)
The stato
r
a
n
d
rot
o
r
flu
x
a
r
e
g
i
ven a
s
:
φ
L
i
L
i
φ
L
i
L
i
(6
)
φ
L
i
L
i
φ
L
i
L
i
(7
)
In t
h
ese e
quat
i
ons
, R
s
,R
r
,L
s
an
d L
r
are
res
p
e
c
tively the resi
stances a
nd t
h
e inductance
s
of t
h
e stator
and the
rotor windings
,
L
m
is the m
u
tual inductance.
0
5
10
15
20
25
-0
.
1
0
0.
1
0.
2
0.
3
0.
4
X
:
1
0
.0
1
Y
:
0.4353
r
epor
t
of
t
h
e
t
i
p
sp
eed l
a
m
bda
P
o
we
r
c
o
e
f
f
i
c
i
e
n
t
Cp
B=
2
°
B=
5
°
B
=
10°
B
=
15°
B=
20°
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Wi
nd
Ene
r
gy
C
onver
si
o
n
Sy
st
ems B
a
se
d
O
n
a
DFI
G
C
o
nt
rol
l
e
d By
I
n
di
rect
Vect
or
Usi
n
g
…
(
N
ai
m
C
h
erf
i
a
)
55
1
V
sd
,V
sq
,V
rd
,V
rq
,i
sd
,i
sq
,i
rd
,i
rq
,
φ
sd
,
φ
sq
,
φ
rd
,
φ
rq
are
t
h
e d an
d q co
m
ponent
s o
f
t
h
e st
at
or and r
o
t
o
r v
o
l
t
a
ges
,
cu
rre
nt
s
and fl
ux,
whe
r
eas
ω
r
is t
h
e
rotor s
p
ee
d in ele
c
trical degree.
The electrom
a
gnetic torque
is expre
ssed as:
.
.
(8
)
St
at
or a
n
d r
o
t
o
r
vari
abl
e
s
are
bot
h
refe
rre
d t
o
t
h
e
st
at
or
re
f
e
rence
Par
k
fra
m
e
.
W
i
t
h
t
h
e f
o
l
l
o
wi
ng
o
r
i
e
nt
at
i
on,
t
h
e d
com
p
o
n
e
n
t
o
f
t
h
e st
at
o
r
fl
u
x
i
s
e
qual
t
o
t
h
e t
o
t
a
l
fl
u
x
whe
r
eas t
h
e
q
com
pone
nt
o
f
t
h
e st
at
o
r
fl
u
x
i
s
n
u
l
l
Fi
gu
re 2.
[
6
]
.
Fi
gu
re
2.
Det
e
r
m
i
n
at
i
on o
f
t
h
e
el
ect
ri
cal
angl
es
in Park refe
rence fram
e
φ
φ
,
φ
0
(9
)
B
y
repl
aci
n
g
(
9
)
i
n
(6
) a
n
d (
8
), t
h
e el
ect
r
o
m
a
gnet
i
c
t
o
r
que
can
be
gi
ve
n as
f
o
l
l
o
ws:
C
p
i
φ
(1
0)
Ass
u
m
i
ng that the resistance
of the stator winding R
s
is neglected, and referring to the chose
n
refe
rence
f
r
am
e, t
h
e
v
o
l
t
a
ge e
quat
i
o
ns
an
d t
h
e fl
u
x
e
quat
i
o
n
s
o
f
t
h
e
st
at
or
wi
n
d
i
n
g ca
n
be
sim
p
l
i
f
i
e
d i
n
s
t
eady
state as follows:
v
0
v
v
ω
φ
(1
1)
φ
L
i
L
i
0L
i
L
i
(1
2)
From
(1
2
)
, t
h
e
equat
i
o
ns
l
i
nki
ng
t
h
e
st
at
or
cu
rre
nt
s t
o
t
h
e
rot
o
r
cu
rre
nt
s a
r
e
ded
u
ce
d
bel
o
w
:
i
φ
i
i
i
(1
3)
The active
and
reactive
powe
rs at the stat
or s
i
de are
de
fine
d as:
P
v
i
v
i
Q
v
i
v
i
(1
4)
Tak
i
ng
i
n
to con
s
id
eratio
n th
e cho
s
en
referen
ce
fram
e
, th
e
ab
ov
e power eq
u
a
tion
s
can
be written
as
fo
llows:
P
v
i
Q
v
i
(1
5)
0
d,q
frame
Stator axis
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
54
9 – 5
5
9
55
2
R
e
pl
aci
ng
t
h
e
st
at
or c
u
r
r
ent
s
by
t
h
ei
r
ex
pre
s
si
ons
gi
ven
i
n
(
1
5
)
,
t
h
e e
q
uat
i
ons
b
e
l
o
w are
obt
ai
ne
d:
P
v
i
Q
φ
i
(1
6)
The bl
ock
di
ag
ram
of t
h
e DF
IG m
odel
i
n
P
a
rk
refe
rence
f
r
am
e
i
s
depi
ct
ed i
n
Fi
g
u
r
e 3,
assum
i
ng a
con
s
t
a
nt
st
at
o
r
vol
t
a
ge
(
v
s
) [7
].
Fi
gu
re
3.
B
l
oc
k
di
ag
ram
of t
h
e DF
IG
m
odel
4.
REGUL
A
TION WIT
H
BUCKLE OF POWER
to
im
p
r
o
v
e
t
h
e con
t
ro
l system
th
e DFIG,
we
will in
trodu
ce an
add
ition
a
l loo
p
con
t
ro
l of activ
e and
react
i
v
e p
o
w
er
i
n
t
h
e bl
ock
d
i
agram
of t
h
e
cont
rol
l
o
o
p
w
i
t
hout
po
we
r s
o
t
h
at
eac
h axi
s
co
nt
rol
l
e
r c
o
nt
ai
ns
two
PI
con
t
ro
l, on
e to con
t
rol
the power and
the ot
her ro
to
r cur
r
ent (fi
gu
re 4)
[
8
]
.
Fi
gu
re
4.
Sc
he
m
a
bl
ock
i
n
di
r
ect
reg
u
l
a
t
i
o
n
wi
t
h
l
o
o
p
po
w
e
r
5.
MODELLING OF VOLTAGE
INVERTERS TWO
LEVELS
The t
h
ree
-
p
h
as
e v
o
l
t
a
ge i
nve
r
t
er at
t
w
o l
e
ve
l
s
, i
s
com
pose
d
of
t
h
ree
i
n
de
pen
d
e
n
t
arm
s
, com
p
ri
si
n
g
t
w
o s
w
i
t
c
hes e
ach. eac
h s
w
i
t
c
h c
o
m
p
ri
ses an I
G
B
T
or
GT
O th
yrist
o
rs and
a
d
i
od
e co
nnected
in
an
tip
arallel.
can be re
place
d group each tran
sistor-diode switches by kj
with (j = 1, 2,
3, 4, 5,
6), we
obtain t
h
e simplified
diagram
for ea
ch inve
rter as
sh
own
in Figur
e 5
.
[9
].
DFI
G
σ
PI
PI
σ
PI
PI
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Wi
nd
Ene
r
gy
C
onver
si
o
n
Sy
st
ems B
a
se
d
O
n
a
DFI
G
C
o
nt
rol
l
e
d By
I
n
di
rect
Vect
or
Usi
n
g
…
(
N
ai
m
C
h
erf
i
a
)
55
3
Fi
gu
re
5.
Si
m
p
l
i
f
i
e
d di
a
g
ram
of
t
h
e t
h
ree
-
p
h
a
se i
n
vert
er
Th
e equ
a
tio
ns
o
f
sim
p
le v
o
ltag
e
ap
p
lied to th
e three
ph
ases are:
V
V
V
V
V
V
V
V
V
(1
7)
Knowing that t
h
e system
is symme
trical stator phase
voltages:
so:
0
(1
8)
The
v
o
l
t
a
ge c
o
nve
rt
er ca
n
be
m
odel
e
d by
a
m
a
t
r
i
x
[T]
p
r
o
v
i
d
i
n
g
passa
ge
DC
t
o
AC
.
V
T
.
V
(1
9)
suc
h
that:
V
V
V
V
V
V
V
V
V
E
S
S
S
(2
0)
So,
for eac
h arm
there are
two inde
pendent states
, the
s
e states can be considere
d
as Boolea
n
vari
a
b
l
e
s. S
u
p
pos
ed
i
d
eal
s
w
i
t
c
hi
ng:
S
i
=(1o
u 0)
{i=1
,2
,3
}.
Th
e tran
sfer matrix
is:
T
2
1
1
12
1
1
1
2
(2
1)
In
o
u
r
w
o
r
k
, t
h
e s
w
i
t
c
hes
of
t
h
e i
n
vert
e
r
a
r
e m
a
de by
u
s
i
ng t
h
e P
W
M
cont
rol
l
e
r
(
P
ul
se
W
i
dt
h
Mo
du
latio
n)
an
d SV
M (
s
p
a
ce v
ector
m
o
du
latio
n
)
.
6.
PULSE WIDTH
MODU
LA
TION
(PWM
)
The m
o
st
wi
del
y
used
m
e
t
h
o
d
of
pul
se wi
dt
h m
odul
at
i
on i
s
based car
ri
er.
t
h
i
s
m
e
t
hod i
s
al
so kn
ow
n
as the sinusoi
d
al (SP
W
M),
triangul
ation,
subha
r
m
onic, or m
e
thod s
u
bos
cillation [10], [
11]. Si
nusoidal
m
odul
at
i
on i
s
base
d o
n
a
t
r
i
a
ng
ul
ar
car
ri
er s
i
gnal
as
sh
o
w
n
i
n
Fi
gu
re
6.
In
t
h
i
s
m
e
t
hod, t
h
ree
re
fere
nce
si
gnal
s
U
AC
, U
BC
, U
CC
com
p
ari
ng
wi
t
h
t
r
i
a
n
gul
ar c
a
rri
er si
gnal
U
t
wh
ich
is co
mm
o
n
to
all th
ree p
h
a
ses. In
th
i
s
way,
t
h
e l
o
gi
c si
g
n
al
s Sa,
Sb
, Sc
ar
e ge
nerat
e
d,
w
h
i
c
h
de
fi
ne t
h
e
swi
t
c
hi
ng
t
i
m
e
s o
f
t
h
e
p
o
w
er
t
r
ansi
st
ors
.
i
N
B
A
C
K
1
K
2
K
3
K
4
K
5
K
6
O
E/2
E/2
V
A
V
B
V
C
U
AB
U
CA
U
BC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
54
9 – 5
5
9
55
4
Fi
gu
re
6.
B
l
oc
k sc
hem
e
of ca
rri
er
base
d
si
n
u
soi
d
al
P
W
M
7.
THE SIMUL
A
TION
RESULTS OF TH
E IN
DIRE
CT
CO
NTR
O
L
WITH P
W
M
The si
m
u
l
a
t
i
on i
s
perf
orm
e
d by
im
posi
n
g t
h
e act
i
v
e and
re
act
i
v
e po
wer
r
e
fere
nce (P
re
f
, Q
ref
), wh
ile
t
h
e DF
I
G
i
s
d
r
i
v
e
n
at
va
ri
abl
e
spee
d
Pre
f
vari
es
bet
w
e
e
n
–3
0
0
0
0
0
a
nd
-
1
0
0
0
0
0
0
w
a
t
t
s
and
Qre
f
vari
e
s
b
e
tw
een
-
100
00
0
and
-4
000
00
1
000
00
VA
R
and
d
e
I
s
ab
c
var
i
es
b
e
t
w
een 1
000
A
and
25
00
A
Figure
7. Electrical activ
e pow
er pr
odu
ced
w
ith
PW
M
Figure
8. Electrical reactiv
e p
o
we
r pr
o
duce
d
wi
t
h
P
W
M
0
0.
5
1
1.
5
2
-1
4
-1
2
-1
0
-8
-6
-4
-2
0
x 1
0
5
tim
e
(s
)
act
i
ve pow
er
[
W
]
Pm
e
s
Pr
e
f
0
0.
5
1
1.
5
2
-5
-4
-3
-2
-1
0
1
2
x 1
0
5
tim
e
(s
)
r
e
a
c
tiv
e
p
o
w
e
r
[W
]
Qm
e
s
Qr
e
f
D
F
I
G
U
dc
Carrier
U
Bc
U
Ac
U
Cc
U
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Wi
nd
Ene
r
gy
C
onver
si
o
n
Sy
st
ems B
a
se
d
O
n
a
DFI
G
C
o
nt
rol
l
e
d By
I
n
di
rect
Vect
or
Usi
n
g
…
(
N
ai
m
C
h
erf
i
a
)
55
5
Fi
gu
re
9.
St
at
o
r
phase
cu
rre
nt
s wi
t
h
P
W
M
Fi
gu
re 1
0
.
T
H
D of cu
rre
nt
I
s
a
wi
t
h
P
W
M
8.
SPAC
E V
E
CTOR
M
O
DULA
T
ION
(SVM
)
M
o
d
u
l
a
t
i
o
n
t
echni
que
s
di
ffe
re
nt
s
p
at
i
a
l
vect
o
r
s
of
t
h
e
carrier o
n
th
e b
a
sis o
f
th
is
m
a
n
n
e
r,
th
ere
is no
separate m
odul
ators used
for each of the three phases
.
Inst
ead of them
, the refere
nce
vol
tages are supplied by
the voltage
vec
t
or
of the
space
and
the
output
voltages
of the
inve
rter
a
r
e c
o
nside
r
ed s
p
ace
vectors
[12]:
V
0i
0
,7
U
e
i
1.
.6
(2
2)
There
i
s
a p
o
s
s
i
b
l
e
ei
ght
vec
t
ors
out
put
v
o
l
t
a
ge, si
x
act
i
v
e vect
o
r
s
V
1
– V
6
, a
n
d two
zero
vectors
V
0
,V
7
figure
10
. Th
e
reference vo
ltag
e
v
e
cto
r
is
p
e
rfo
rmed
b
y
sequ
en
tially switch
i
n
g
th
e activ
e and
zero
vectors.
In Fi
gu
re 1
0
s
h
o
w
s
vol
t
a
ge
vect
o
r
refe
re
nc
e vol
t
a
ge
V
c
a
nd ei
ght
vect
or
s, w
h
i
c
h c
o
r
r
es
po
n
d
s t
o
t
h
e
pos
si
bl
e st
at
es of t
h
e i
n
vert
e
r
.
The si
x act
i
v
e vect
ors
di
vi
de
a plane for the six sectors 1- 6. In the sector
of
each of
the
vol
t
age
re
fere
nce
vector V
c
i
s
o
b
t
ai
ned by
s
w
i
t
c
hi
n
g
o
n
, fo
r
a
s
u
i
t
a
bl
e
t
i
m
e,
two
ad
jace
nt
ve
ct
ors.
Sh
ow
n i
n
Fi
g
u
r
e 1
0
refe
rence
vect
o
r
V
c
can
be i
m
pl
em
ent
e
d by
s
w
i
t
c
hi
n
g
vect
o
r
s
V
1
, V
2
and zero
vectors V
0
,
V
7
[13
]
,
[14
]
.
0
0.
5
1
1.
5
2
-4
0
0
0
-3
0
0
0
-2
0
0
0
-1
0
0
0
0
10
00
20
00
30
00
40
00
ti
m
e
(s
)
S
t
a
t
or
ph
ase cur
r
e
n
t
s
[
A
]
Is
a
Is
b
Is
c
0
20
40
60
0
50
0
10
00
15
00
TH
D
(
I
sa
)
=
0.
22
46
%
O
r
d
e
r o
f
H
a
rm
o
n
i
c
A
m
pl
.
H
a
r
m
oni
c
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
54
9 – 5
5
9
55
6
Fi
gure
10
.
Pr
incip
l
e of
th
e sp
ace v
ector
m
o
du
latio
n
The refe
re
nce voltage
vector V
c
i
s
sam
p
l
e
d
wi
t
h
t
h
e fi
xe
d
cl
ock
f
r
eq
ue
nc
y
f
s
=1/T
s
,a
nd
n
e
xt
a sam
p
l
e
d
val
u
e
V
c
(T
s
) is u
s
ed
for calcu
lation o
f
tim
es t
1
, t
2
, t
0
and t
7
. The
signal fl
ow i
n
space
vector m
o
dulator is shown i
n
F
i
g
u
r
e
11
.
Figure
11. Block schem
e
of
the space vector
m
odulator
9.
THE SIMUL
A
TION
RESULTS OF THE
IN
DIRE
CT
CO
NTR
O
L
WITH
SV
M
The r
o
t
o
r
of t
h
e D
F
I
G
i
s
p
o
we
re
d by
a t
h
ree
-
p
h
ase
bal
a
nced
sy
st
em
, and
by
a
vol
t
a
ge t
o
S
V
M
i
nve
rt
ers.
To
sim
u
l
a
t
e
t
h
e b
e
havi
or
o
f
t
h
e
DF
IG
, we
op
ted
for th
e
MATLAB /
Si
m
u
lin
k
software, the
si
m
u
latio
n
results are g
i
v
e
n
b
y
th
e
fo
llowing
figu
res
-0
.
6
-0
.
4
-0
.
2
0
0.
2
0.
4
0.
6
-0
.
5
-0
.
4
-0
.
3
-0
.
2
-0
.
1
0
0.
1
0.
2
0.
3
0.
4
0.
5
V7
(
1
1
1
)
V
0
(0
00)
q
Vb
Va
Se
c
t
o
r
3
Se
ct
o
r
1
V
3
(
010
)
V
2
(1
10)
V
6
(
101)
V
5
(0
01)
Vc
V
4
(0
11)
V
1
(
100)
d
S
e
c
t
or
4
S
ec
t
o
r
6
Se
c
t
o
r
2
Se
c
t
o
r
5
DFI
G
Sector
Selectio
n
Calcu
l
atio
n
U
dc
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Wi
nd
Ene
r
gy
C
onver
si
o
n
Sy
st
ems B
a
se
d
O
n
a
DFI
G
C
o
nt
rol
l
e
d By
I
n
di
rect
Vect
or
Usi
n
g
…
(
N
ai
m
C
h
erf
i
a
)
55
7
Figure
12. Elec
trical ac
tive
power p
r
o
duced
wi
t
h
SVM
Figure
13. Elec
trical reac
tiv
e power
pr
od
uced
wi
t
h
SVM
Fi
gure 14. St
ator phase
cu
rren
t
s
wi
t
h
SVM
0
0.
5
1
1.
5
2
-1
2
-1
0
-8
-6
-4
-2
0
x 1
0
5
tim
e
(s
)
ac
t
i
v
e
pow
er
[
W
]
Pm
e
s
Pr
e
f
0
0.
5
1
1.
5
2
-5
-4
-3
-2
-1
0
1
2
x 1
0
5
tim
e
(s
)
r
eac
t
i
v
e
pow
er
[
V
A
R
]
Qm
e
s
Qr
e
f
0
0.
5
1
1.
5
2
-3
0
0
0
-2
0
0
0
-1
0
0
0
0
10
00
20
00
30
00
ti
m
e
(s
)
S
t
at
or
ph
ase
cur
r
ent
s
[
A
]
Is
a
Is
b
Is
c
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
54
9 – 5
5
9
55
8
Fi
gure
11. T
H
D of
cur
r
ent
Is
a wi
t
h
SVM
10
.
CO
NCL
USI
O
N
In
ou
r
work
,
we h
a
v
e
estab
lish
e
d
th
e m
o
d
e
l th
e
m
ach
in
e with
its e
l
ec
tric
eq
u
a
tio
n
s
in
axis lin
k
e
d
to
t
h
e d-q sy
nchr
on
ous sy
st
em
.
W
e
have al
so devel
ope
d t
h
e m
e
t
hod of vect
or cont
r
o
l
po
w
e
r of t
h
e
m
achi
n
e t
o
kn
ow t
h
e
orde
r and
dedi
cat
e
d t
o
t
h
e st
udy
of t
h
e art
o
f
t
h
e powe
r
o
f
i
n
d
i
rect
cont
rol
t
o
achi
e
ve t
h
e D
C
-AC
conve
rsi
on usi
ng t
w
o v
o
l
t
a
ge l
e
vel
s
wit
h
t
echni
cal
PW
M
cont
rol
l
e
r Pul
s
e W
i
dt
h
M
odul
at
i
on an
d SVM
Modulation Ve
ctor Space. Indeed
we have se
en that the control indirect
ly
allows us, toge
ther with the closure
p
o
w
ers, to
h
a
v
e
an
efficien
t syste
m
an
d
ro
bu
st. It is certain
ly
m
o
re c
o
m
p
lex
to
work
,
b
u
t
will h
a
v
e
an
operat
i
on o
p
t
i
m
al sy
st
em
of
el
ect
ric generati
on
m
i
nim
i
zi
ng pot
ent
i
a
l prob
l
e
m
s
rel
a
t
e
d t
o
changes i
n
m
a
chi
n
e
param
e
t
e
rs and t
h
e wi
nd sy
st
em
.
APPE
NDI
X
A
Nom
i
nal Po
we
r =
1
.
5
(M
w
)
Stator Per Pha
s
e
Resistance
=
0
.012 (
Ω
)
Rotor Pe
r Phas
e Re
sistan
ce=0.02
1 (
Ω
)
S
t
a
t
o
r
L
e
ak
ag
e In
du
ctance=
2.0372.10
-004
(H)
Ro
to
r L
e
ak
a
g
e In
du
ctance=
1.7507.10
-004
(H)
M
a
gnet
i
z
i
n
g In
duct
a
nce= 0.
0
1
3
5
(
H
)
Num
b
er
Of
P
o
les Pairs=
2
Mo
m
e
n
t
O
f
I
n
er
tia= 10
00
(
K
g
.
M
2
)
Frictio
n Co
effi
cien
t =0
.00
24
REFERE
NC
ES
[1]
Z.
Lubosn
y
, “Wind Turbin
e Oper
ation
in
Electr
i
c
Po
wer S
y
stems“, Ber
lin
, German
y
:
Springer
,
200
3.
[2]
S. Heier
,
“Gid In
tegration of
Win
d
Energ
y
Conve
rsion S
y
stems“.
England:
John
Wiley
& Sons, 1
998.
[3]
J.
Usa
o
la,
P.
Le
de
sma
,
J.
M.
R
odriguez, J.L. Fernadez, D.
B
e
ato, R
.
Iturbe, J.R. Wi
he
l
m
i,
“Tra
nsi
e
nt st
a
b
il
ity
studies in grids
with great wind
power penetration. M
odeling
is
sues and operation re
quiremen
t
s”, Proceedings o
f
the I
EEE PES Tr
ansmission and
Distribution
Conference
and Exp
o
sition,
Septemb
e
r
7-12
, 2003
, D
a
llas (USA).
[4]
S.El Aimani, “Modélisation D
e
Différe
n
t
es Technolog
ies D’éolienn
es Intégr
ées Dans Un Ré
seau De Mo
y
e
n
n
e
Tension“.
[5]
F. Poiti
ers, “Etu
de E
t
Com
m
a
nde De Génér
a
tri
c
es Asy
n
chrones P
our L’ut
ilisation
De
L’én
ergi
e
Eo
lienn
e“, 2003.
[6]
A. Bo
y
e
tte, “Contrôle-
c
ommande d’un gén
é
rateu
r
as
y
n
chr
one
a d
ouble alimentation avec
s
y
stème de stock
a
ge pou
r
la produ
ction
éo
lienne”, thèse 20
06.
[7]
T. Ghennam,
E.M. Berkouk, B
.
Fran
cois, “Modeling and Control
of a Doubl
y
Fed
Induction Gen
e
r
a
tor Based Wind
Conversion S
y
stem”, Internation
a
l
conf
eren
ce o
n
power eng
i
neering, ener
g
y
an
d electr
i
cal
dr
iv
es (POWERENG
2009), Lisbon, P
o
rtugal, 18-20
Mach 2009
.
[8]
A. Mehdar
y
, ‘’
Étude d’une
chaine de conv
ersio
n
d’éner
gie éolienne à b
a
se d’u
n
e aéro
t
urbine"
,
6 émes
Journée
s
des doctor
a
nts, Labor
atoir
e
d
e
s scienc
es de
l’information
et des s
y
stèm
es
LSIS, université de St Jérôme,
Marseille,2009
.
0
20
40
60
0
50
0
10
00
15
00
O
r
d
e
r o
f
H
a
rm
o
n
i
c
A
m
pl
.
H
a
r
m
oni
c
T
H
D
(I
s
a
)=
1
.
1
0
7
7
%
Evaluation Warning : The document was created with Spire.PDF for Python.