Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l. 10
, No
. 1, Febru
a
r
y
2
020, pp
. 35
~
4
6
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v10
i1
.p
p35
-46
35
Jo
urn
a
l
h
o
me
pa
ge
: http://ijece.iaesc
o
re
.c
om/index
.
php/IJ
E
CE
Enhancement of the direct
power control applied to
DFIG-WECS
Ha
la Al
a
m
i
Aro
u
ssi
1
, El
M
o
st
af
a Z
i
a
n
i
2
, Manale
B
o
u
d
erbala
3
, Badre Bo
sso
u
fi
4
1,2
Laborator
y
of
Electrical and
M
a
inte
nance
Engineering
(LGEM)
, Mohamed Pr
e
m
ier Univers
i
t
y
,
Oujda, M
o
ro
cco
3,4
LIS
T
A
Laborator
y
,
Faculty
of
Sciences
Dh
ar
El Mahraz, Sidi
M
ohammed Ben Abdellah Univ
ersity
, Fez, Morocco
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 29, 2018
Rev
i
sed
Ju
l 20
,
20
19
Accepted Aug 29, 2019
This work is de
dica
ted to
the st
ud
y
of
an improved direct
contr
o
l of powers
of the doub
ly
fed induction gen
e
rator (DFIG) incorporated
in a wind ener
g
y
conversion s
y
s
t
em '
W
ECS'
.
The
control
method
adopts
dire
ct po
wer contro
l
'
D
PC' because
of its v
a
rious
advantag
es
lik
e
t
h
e e
a
s
e
of
im
pl
em
entat
i
on
which allows decoupled regu
lat
i
on for
active an
d react
ive power
s, as well as
a good performance at transien
t and stead
y
state without PI regulators and
rotating
coordin
a
te tr
ansform
a
ti
ons. To do this,
the m
odeling o
f
the turbin
e
and gener
a
tor
is performed. Th
erefore,
the
Maxi
m
u
m
Power Point Tra
c
king
(MPPT) technolog
y
is implemented to
extr
act optimal
pow
er at
var
i
ab
le
wind speed cond
itions. Subsequently
,
an
explanation of the said
command is
s
p
read out as
we
ll as
the pr
incip
l
e of adjus
ting
th
e ac
tive
and rea
c
tive power
accord
ing to the
desired speed.
Then,
th
e estim
ation m
e
thod of these two
control vari
abl
e
s will be presented as
well as the
adopted switchi
ng table o
f
the h
y
ste
r
esis c
ontrolle
r m
odel
used based on
t
h
e m
odel of
the
m
u
ltilev
e
l
invert
ers. Finall
y
,
the robustnes
s of the develop
e
d s
y
stem
will
be anal
y
z
ed
with valid
ation i
n
Matlab/Sim
u
li
nk environm
ent to illustra
te th
e perform
anc
e
of this
command.
K
eyw
ords
:
DFI
G
DPC
Hysteresis co
n
t
ro
llers
MPPT
WECS
Copyright ©
202
0 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
:
Hala Alam
i Ar
ous
si,
Laboratory of Electrical
and Ma
i
n
t
e
nance
E
ngi
neeri
n
g
(L
GEM
)
,
Ecol
e S
u
péri
e
u
r
de Tec
h
n
o
l
o
g
i
e, M
o
ham
e
d Prem
i
e
r Uni
v
e
r
s
i
t
y
,
B
P
4
7
3
C
o
m
p
l
e
xe
uni
versi
t
a
i
r
e
Al
Q
o
ds,
O
u
jda
6
0
0
0
0
O
u
j
d
a, M
o
r
o
cc
o.
Em
a
il : h
.
ala
m
i
a
rro
u
ssi@u
m
p
.ac.m
a
, ala
m
i.arous
si.hala
@
gmail.co
m
1.
INTRODUCTION
The
pr
od
uct
i
o
n o
f
el
ect
ri
cal
ener
gy
i
n
t
h
e
wo
rl
d
ge
nerat
e
s vari
ou
s p
o
l
l
u
t
i
ons. T
h
us, t
h
erm
a
l
powe
r
st
at
i
ons
(coal
,
oi
l
)
a
r
e
resp
onsi
b
l
e
f
o
r at
m
o
spheri
c em
i
ssi
ons l
i
nke
d
t
o
t
h
e
com
bust
i
o
n
of
f
o
ss
i
l
fuel
s
.
In
con
t
rast, nu
clear p
o
wer p
l
an
ts, wh
o
s
e
d
e
v
e
l
o
p
m
en
t will in
crease fo
llowing
the o
il crisis, hav
e
no
adve
rse
infl
ue
nce
on air quality although they
produce
ra
dioactive
waste that ca
us
es storage
problem
s
,
treat
m
e
n
t
o
r
tran
sp
ort.
Tod
a
y, th
e
fear of
b
e
ing
li
mited
to
eph
e
meral en
e
r
gies,
the awa
r
ene
ss
of t
h
e ne
gative im
pact of
these on the e
nvi
ronm
ent, the craze for re
newable e
n
ergi
e
s
and t
h
e ope
n
ing
of the m
a
rket of t
h
e production
of e
n
e
r
gy towards
other alte
rnatives
are
fa
ctors t
h
at
give
an im
portant
place to
the
s
e
energies (hydraulic,
wind
, so
lar,
b
i
o
m
ass, ...) in the produ
ctio
n of electricity [1
-3
].
Am
ong t
h
e m
o
st
covet
e
d re
ne
wabl
e ene
r
gi
es, we fi
n
d
t
h
e w
i
nd ene
r
gy
t
h
at
i
n
t
e
rest
s
m
o
re and m
o
re
countries
as it produces a
cl
ean a
n
d s
u
stainable e
n
e
r
gy.
We als
o
notic
e that a large
part
of wi
nd t
u
rbines
i
n
st
al
l
e
d t
oday
i
s
equi
ppe
d
wi
t
h
a d
o
ubl
y
fe
d
i
n
d
u
ct
i
o
n
g
e
nerato
r (DFIG).
Th
e latter allows th
e
produ
ctio
n
o
f
electricity under variable
spe
e
d, t
h
is m
a
kes it possi
ble
to
better exp
l
o
it turb
i
n
e resou
r
ces. These turb
i
n
es are
al
so eq
ui
p
p
e
d
wi
t
h
vari
a
b
l
e
bl
ade
pi
t
c
h
an
gl
e i
n
or
d
e
r t
o
be a
d
a
p
t
e
d t
o
di
ffe
r
e
nt
wi
nd
co
n
d
i
t
i
ons
.
Th
e turb
i
n
e is
co
n
t
ro
lled
so
as to
p
e
rm
an
en
tly
m
a
x
i
mize th
e p
o
wer produced
ind
e
p
e
nd
en
tly o
f
th
e
v
a
riatio
n
o
f
th
e wind
p
r
ofile
[4
].
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
E
36
a DF
I
is to
cont
r
o
th
e D
P
and s
i
2.
T
a the
o
th
e f
o
th
e s
p
of
t
h
e
N
um
e
expre
a fun
c
Wi
t
h
and :
th
e c
o
p
asse
s
desi
g
n
E
lec & C
o
m
p
The m
a
in
I
G in a
wind
e
ens
u
re the s
a
o
l
o
f
th
e activ
In th
is
p
e
PC co
n
t
ro
l la
w
i
m
u
latio
n
res
u
T
URBI
N
E
M
A t
h
eo
ret
i
o
retical powe
r
P
The aero
d
o
llowing
fo
rm
u
P
.
Th
e pow
e
p
ee
d ra
t
io
λ
a
n
e
blades
a
n
d t
h
λ
e
rical approx
i
ssi
ons
ha
ve
b
e
In the c
o
n
c
tion
o
f
the s
p
C
λ,
β
:
c1= 0.
58
7
.
Fi
gu
re 2
o
efficient
C
s
t
h
rou
gh a
m
n
ate by
λ
(
w
En
g, V
o
l
.
10
,
ob
j
e
ctiv
e of
t
e
n
e
rg
y conv
e
r
a
m
p
l
i
ng of
si
n
e and
reactiv
e
e
rspe
ctive, a
w
[5
-7
].
Th
e
w
u
lts are e
xpos
e
Fi
gu
re 1.
S
M
ODEL
i
cally
und
ist
u
r
of
t
h
e wi
nd
o
.
ρ.
A.
v
d
yn
amic p
o
w
u
la:
.
ρ.
A.
C
λ,
β
e
r c
o
e
fficien
t
C
n
d t
h
e pi
t
c
h a
n
h
e wind spee
d
i
m
a
ti
ons ha
v
e
e
en
p
r
op
os
ed
n
tex
t
o
f
th
is
p
ee
d
λ
and the
c
c
.
2
,
c2= 11
6, c
3
.
.
sh
ow
s
th
e
as
a
function
m
axim
u
m
(
C
_
w
he
re
λ
,
No
. 1, Feb
r
u
t
hi
s
w
o
r
k
i
s
t
o
r
si
on system
(
n
us
oi
dal
c
u
r
r
e
e
p
o
w
e
r
s
.
co
m
p
lete m
o
w
ho
le o
f
the
s
e
d a
n
d analy
z
e
S
ynop
sis o
f
t
h
e
u
rb
ed
w
i
nd
c
r
o
r
w
i
nd
pow
e
r
w
er a
p
peari
n
g
.v
C
λ,
β
repr
e
n
gl
e of
t
h
e bl
a
d
:
e
bee
n
devel
o
[4, 8]
.
wo
r
k
,
we wi
l
angl
e
β
as fo
l
c
.β
c
.
3
=
0.4, c4=
5
si
m
u
lat
i
on
of
th
e sp
ee
d
_
0
.
4
8
)
f
8
).
u
ar
y 20
20
:
3
5
o
st
udy
t
h
e di
r
(
WE
C
S
)
a
s
s
h
e
n
t
s wh
ile g
u
o
del
i
ng of
t
h
e
s
yste
m
is i
m
p
ed in order t
o
e
di
re
ct
po
we
r
r
ossing a
sur
f
r
co
rres
p
on
di
n
g
at the
rot
o
e
se
nts the aer
o
a
de
β
. The sp
e
o
pe
d i
n
t
h
e l
i
t
ll use
an ap
p
l
lo
ws:
e
c
.
λ
, c
5
=
21, c
6
=
resu
lts u
n
d
e
d
ratio
λ
for
a
f
or
β0
an
d
5
-
46
r
ect power c
o
h
ow
n i
n
Fi
gu
r
e
u
a
r
anteeing a
e
ar
ch
ite
c
t
u
r
e
p
lem
e
n
t
ed
un
d
prove the
ef
fi
r
c
ont
r
o
l
o
f
t
h
f
ace
A
wit
h
o
u
n
g
to th
e
fo
ll
o
o
r of th
e tu
r
b
o
dy
nam
i
c eff
i
e
ed
ratio
is d
e
t
erature t
o
m
o
p
rox
i
m
a
t
e
ex
p
λ
=
0
.
00
85
.
e
r M
A
TL
AB
/
few p
itch
a
n
d
a
pa
r
t
i
c
ul
ar
o
n
t
ro
l (activ
e
a
e
1. T
h
e com
m
un
i
t
powe
r
f
a
e
is pr
opose
d
d
er th
e Matla
b
i
ciency of t
h
e
e D
F
IG-W
E
C
u
t a
decreas
e
w
i
n
g
expr
ess
i
b
i
n
e is dete
r
i
ciency of th
e
e
fi
ned as the
r
o
del the coef
f
p
r
e
ssion
of
t
h
/
SIMULINK
gl
es
β
. We n
o
val
u
e o
f
t
h
e
s
ISS
N
:
2
a
nd reactive
)
m
o
n
go
al of
t
h
fa
ct
or with a
d
i
n
or
der
t
o
b
/Si
m
u
lin
k
en
co
ntr
o
l.
C
S
in
sp
eed
v
w
i
on:
(
r
m
i
ned ana
l
y
(
e
tu
rbi
n
e. It
d
r
atio
of th
e li
n
(
f
icien
t
C
an
d
h
e power c
o
e
f
(
of t
h
e e
v
o
o
te th
at t
h
is
c
s
p
e
ed
ratio
t
h
2
088
-87
08
ap
p
lied t
o
h
i
s
c
ont
rol
d
ecoup
led
ela
b
orate
v
iro
n
m
e
n
t
w
oul
d gi
v
e
(
1)
tical
ly b
y
(
2)
epe
n
ds on
n
ear spe
e
d
(
3)
d
different
f
ficient as
(
4)
o
lu
tion
of
c
o
e
fficien
t
at we will
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
E
3.
M
b
y e
x
th
e
m
Powe
r
It is
p
th
e c
o
adapt
s
Suc
h
th
e w
i
TSR
cont
r
o
to
m
a
4.
D
sum
m
4.
1.
E
4.
2.
F
E
lec & C
o
m
p
M
AX
IM
U
M
Wi
n
d
t
u
r
b
x
pl
oi
t
i
ng t
h
e
e
m
echanical or
e
r
Po
in
t Trac
k
p
os
si
bl
e t
o
c
h
a
o
nt
r
o
l
of
t
h
e
g
s
itself t
o
e
a
system
s
als
o
i
nd
bec
o
m
e
s
t
In t
h
is c
o
(Tip Spe
e
d
R
o
l beca
us
e
of
a
in
tain
λ
at an
D
OUBLY F
E
In
th
e lit
e
m
arized in fou
r
E
lectrical
eq
u
V
R
V
R
V
R
V
R
F
lux
equa
t
i
o
n
The stato
r
ψ
L
ψ
L
ψ
L
ψ
L
Eng
En
ha
nce
m
Fi
g
POWER P
O
b
ines
, used fo
r
e
nergy avai
la
b
e
lectrical part
k
i
ng (M
P
P
T
).
a
ng
e th
e
pitc
h
g
e
n
erator. T
h
e
a
ch
v
a
riatio
n
o
in
t
r
odu
ce s
a
t
oo st
ro
n
g
an
d
o
nt
e
x
t
,
seve
r
a
R
atio) c
ont
rol
,
its si
m
p
licity
o
p
tim
al v
a
lu
e
E
D
IN
DUC
T
I
e
ratur
e
, we fi
n
r
typ
e
s of eq
u
u
ati
o
ns
i
–
i
i
i
n
s
r
a
n
d rot
o
r flu
x
L
i
M
i
L
i
M
i
L
i
M
i
L
i
M
i
I
S
en
t o
f
th
e d
i
r
e
g
ur
e 2
.
Pow
e
r
c
O
INT TRAC
K
r
th
e pr
odu
cti
o
b
le in
th
e wi
n
,
are
devel
o
p
e
The
s
e syste
m
h
angle
of the
s
e
ar
ch
f
o
r
th
e
n
o
f
wi
nd t
o
a
fet
y
de
vi
c
e
s
d
ma
y
d
a
ma
g
e
l typ
e
s of
M
,
Pow
e
r
cont
r
and acc
ura
c
y
e
s
o
t
h
at the
po
I
ON
G
E
N
E
R
n
d
th
at th
e
D
a
tion
s
: electri
ω
ψ
ω
ψ
ω
ω
ψ
ω
ω
ψ
x
a
r
e c
o
nnect
e
SSN
:
208
8-8
7
e
ct power
co
n
c
o
efficient as
K
IN
G
S
T
RA
T
o
n of electric
i
n
d. Th
is is w
h
e
d t
o
m
a
xim
i
z
m
s use di
ffe
r
bl
a
d
es, o
r
t
h
e
e
ma
x
i
mu
m i
s
o
b
e
i
n
a
c
o
s
th
at allo
w
f
e
th
e wi
n
d
tur
b
M
PP
T al
gorit
h
r
o
l
and
Hill
C
y
. Th
is tech
n
i
q
o
we
r e
x
tracte
d
R
AT
OR MO
D
D
FI
G m
odel
i
i
cal, m
a
gnetic
e
d
to
cu
rre
nts
Ma
ximum
Powe
r
Point (MPP)
7
08
tro
l
app
lied
t
o
a fun
c
tio
n o
f
T
EGY
i
ty, m
u
st
allo
w
h
y
m
a
ny
wi
n
z
e the ene
r
gy
r
ent m
eans
to
e
spee
d of rot
a
s
do
ne perm
a
n
o
n
f
i
g
ur
atio
n
o
f
or e
x
am
ple
b
in
e.
h
m
s
ex
ist. T
h
C
li
m
b
in
g
[9
].
q
ue
re
gul
at
es
d
i
s
ma
x
i
ma
l
.
D
EL
i
n the re
f
e
re
n
, electrom
a
g
n
b
y
th
e
follo
w
o
DFIG
-WE
C
λ
and
β
w
the product
i
d
tu
rb
in
e co
n
co
nv
er
s
i
on
.
T
obt
ai
n t
h
i
s
m
a
t
i
on
of
t
h
e
p
r
n
en
tly an
d
th
e
o
f
ma
x
i
mu
m
t
o
limit th
e
ey can be
d
i
In t
h
is w
o
r
k
,
t
h
e ro
tation
a
l
c
e d
q
related
etic and
m
e
c
h
w
ing
relatio
n
s
:
C
S (
H
al
a
A
l
a
m
i
on m
a
xim
u
m
n
trol syste
m
s,
T
h
i
s is called
M
m
axi
m
um
po
w
r
op
eller o
r
ev
e
e
wind
tu
rb
in
e
m
e
x
traction
o
p
o
w
e
r
pr
od
u
i
vi
ded
i
n
t
h
r
e
,
we f
o
c
u
s o
n
l
s
p
eed of the
d
to
th
e ro
tati
h
ani
cal [10-1
4
(
(
m
i Ar
oussi)
37
m
of po
wer
acting on
M
axim
u
m
w
e
r
poi
nt
.
e
n pl
ay
o
n
e
th
e
r
ef
or
e
o
f p
o
we
r.
u
ced when
e
e gr
ou
ps:
n
th
e
T
S
R
ge
nerat
o
r
n
g fl
u
x
i
s
4
].
(
5)
(
6)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
n
t J Elec & C
o
m
p
Eng
,
Vo
l.
1
0
,
N
o
.
1
,
Febru
a
r
y
20
20
:
35 -
46
38
4.3.
Electrom
a
gnetic tor
que
The e
x
pres
si
o
n
of
t
h
e
el
ect
r
o
m
a
gnet
i
c
t
o
r
que
as
a f
u
nct
i
on
o
f
t
h
e st
at
or
fl
ux
an
d
r
o
t
o
r c
u
rre
nt
i
s
gi
ve
n
by
T
i
ψ
i
ψ
)
(7
)
4.
4.
Mec
h
a
n
i
c
al
equ
a
ti
on
The e
v
olution
of the
m
echanical spee
d
from the t
o
tal m
echanical torque
(
T
) is
d
e
term
in
ed b
y
t
h
e
f
und
am
en
tal
e
q
u
a
tion
of
d
yna
m
i
cs:
J
T
T
T
f
Ω
(8
)
5.
DIRE
CT P
O
WER
CO
NT
ROL
APPLIE
D TO
THE
D
F
IG
5.1.
Principle
of the
direct power of c
o
ntr
o
l
The basi
c
pri
n
ci
pl
e o
f
di
re
ct
powe
r
co
nt
rol
(
D
PC
)
wa
s pr
op
ose
d
by
No
guc
hi
[
15]
, i
t
i
s
based
in
itially
o
n
the d
i
rect con
t
ro
l o
f
torq
u
e
(DTC), in
tend
ed
fo
r th
e co
n
t
ro
l of th
e electric
m
o
to
rs [1
6-2
0
]
.
In t
h
e case
of
DPC, active a
n
d reactive
powers re
place to
rque electrom
a
gnetic a
nd t
h
e
a
m
plitude of the stator
fl
u
x
o
f
t
h
e
D
T
C
.
Thi
s
no
n
-
l
i
n
ear co
nt
r
o
l
st
rat
e
gy
i
s
de
f
i
ned as a t
e
c
h
ni
q
u
e o
f
di
rec
t
cont
r
o
l
beca
use i
t
chooses the a
p
propriate volta
ge vect
or
of
the co
nv
er
ter
w
ith
ou
t an
y m
odu
l
a
t
i
on t
echni
q
u
e
. The basi
c co
ncept
is to select t
h
e
appropriate switchi
ng
st
at
es f
r
om
a swi
t
c
h
t
a
bl
e
based
on
err
o
rs
,
whi
c
h a
r
e l
i
m
i
t
e
d by
a
ba
n
d
hysteresis,
pres
ent in t
h
e active and
reactive
powe
rs.
In
stan
t activ
e an
d reactiv
e
powers
are
calcul
a
ted from
the e
x
pressi
ons
bel
o
w:
P
ω
|
ψ
||
ψ
|
sinδ
(9
)
Q
3
2
ω
σL
|
ψ
|
L
L
|
ψ
|
co
sδ
|
ψ
|
with
:
δ
The
angle betwee
n t
h
e
stator’s
fl
ux
an
d t
h
e
r
o
t
o
r’s
fl
ux
vect
ors
.
σ
1
²
: Coefficient of dis
p
ersi
on.
The re
fere
nce
act
i
v
e po
we
r i
s
cal
cul
a
t
e
d f
r
o
m
t
h
e out
p
u
t
of t
h
e DC
bus
vol
t
a
ge
re
gul
at
or
U
DC
[2
1]
.
Th
e referen
c
e o
f
th
e reactiv
e po
wer is main
tain
ed
at
zero i
n
or
de
r t
o
ensu
re a
uni
t
po
wer
fact
or
.
The
n
, t
h
e
powers a
r
e c
o
m
p
ared a
n
d the e
r
rors
obt
ai
ne
d
a
r
e appl
i
e
d
t
o
re
gu
l
a
t
o
rs of
hy
st
er
esi
s
.
5.2.
Hystere
sis contr
o
ller
Th
e m
a
in
id
ea o
f
d
i
rect
power con
t
ro
l is to
m
a
in
tain
t
h
e in
stan
t activ
e an
d
reactive po
wers i
n
a desi
red
ba
nd
. Thi
s
co
nt
r
o
l
i
s
based o
n
t
w
o
hy
st
eresi
s
com
p
arat
ors
w
h
i
c
h u
s
e as i
n
put
t
h
e er
r
o
r s
i
gnal
s
betwee
n the
refere
nce
value
s
and estim
a
t
es of the
active
and reactive
powe
rs.
Th
e
s
e tw
o
con
t
ro
lle
r
s
a
r
e
resp
o
n
si
bl
e f
o
r
deci
di
n
g
ho
w
m
u
ch a ne
w
swi
t
c
h a
nd/
or
out
put
vol
t
a
ge
vect
o
r
o
f
t
h
e
i
nvert
e
r
i
s
ap
pl
i
e
d.
If the e
r
r
o
r
of
the po
we
r (
eP
s
or
eQ
s
) is increasing a
n
d reaches t
h
e hi
ghe
r level, the
hysteresis controlle
r
chan
ges
i
t
s
o
u
t
put
t
o
'
1
'
.
5.
3.
Vec
t
or se
l
ecti
o
n
The infl
uence
of each output vector on t
h
e activ
e and reactive powers is very de
pende
n
t on
t
h
e act
ual
posi
t
i
on
of t
h
e vec
t
or
of t
h
e s
o
u
r
ce v
o
l
t
a
ge T
h
u
s
, i
n
a
d
di
t
i
on t
o
t
h
e
si
g
n
al
s o
f
t
h
e t
w
o
hy
st
eresi
s
co
n
t
ro
llers, th
e switch
i
ng
tab
l
e o
p
e
rates acco
r
d
i
ng
to
th
e position of
the vector
of
th
e so
urce vo
ltag
e
, wh
ich
tu
rn
s to
th
e pu
lsatio
n
(
m
)
,
i
n
t
h
e com
p
lex pl
an
. H
o
w
e
ver
,
i
n
st
ead
of
i
n
t
r
o
duci
ng t
o
t
h
e swi
t
c
hi
n
g
t
a
bl
e
t
h
e exact
p
o
si
t
i
on o
f
t
h
e ve
ct
or o
f
t
h
e v
o
l
t
a
ge, t
h
e sect
or sel
ect
i
o
n bl
ock i
n
f
o
rm
s us i
n
whi
c
h d
o
m
ai
n
the c
u
rrent
ve
ctor
of the
s
o
urce voltage
is located [22,
2
3
]
.
There
f
ore,
we pr
o
pos
e t
o
use a
m
odi
fi
ed DP
C
whi
c
h, u
n
l
i
k
e t
h
e co
nv
ent
i
o
n
a
l
DPC
,
can
pr
od
uce t
w
e
n
t
y
seven
vol
t
a
ge v
ect
ors i
n
st
ea
d
of t
h
e ei
g
h
t
ve
ct
ors.
In ot
her
words, we
will
decom
pose twel
ve
sectors instea
d of six in orde
r
to increase
the
accuracy and
also t
o
avoi
d t
h
e
p
r
o
b
l
e
m
s
enco
u
n
t
e
r
e
d i
n
b
o
u
n
d
ari
e
s o
f
eac
h c
ont
rol
vect
o
r
.
Wi
t
h
t
h
i
s
i
n
m
i
nd,
we
used
a fi
ve-
s
t
a
ge
hysteresis c
o
rrector
for t
h
e re
active powe
r a
n
d
a three-le
ve
l corrector
for t
h
e active
powe
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
E
5.
4.
S
vecto
r
also
b
In t
h
i
opt
i
m
6.
A
gene
r
6.
1.
S
(su
b
-
s
in
du
c
t
th
e si
m
E
lec & C
o
m
p
S
wit
c
hin
g
ta
b
Th
e switc
h
r
o
f
t
h
e i
nve
r
b
ase
d
on
the
p
i
s wo
rk
, we
a
m
al minimizati
Sect
o
1
0
-1
=
[
=[
0
=[
A
PPLI
CAT
I
The Fi
gur
ato
r
fo
r
a wi
n
S
etpoint tr
a
c
The syst
e
s
yn
ch
rono
u
s
,
t
i
on gene
rat
o
m
ul
at
i
on are
s
Eng
En
ha
nce
m
b
le
h
ing
tab
l
e
is
t
r
ter in
ord
e
r t
o
p
ositio
n
of th
e
a
do
pt
ed
a
m
o
on i
n
er
ro
r
p
o
Tabl
e
o
r’s Nu
m
b
e
r
2
1
0
-1
-2
2
1
0
-1
-2
2
1
0
-1
-2
[
0,
0,
0]
;
=[1,
0,
0
0
,-1
,
-1
] ;
=[
0,0
,
1,
-
1
,
-
1]
;
=[
1,
=[
0
I
ON
S AND
R
e
3 s
h
ows t
h
e
n
d system
in
M
Fig
u
c
kin
g
test
e
m
is
analys
e
sy
nch
r
on
ou
s
o
r a
nd t
h
e
wi
s
ho
w
n
i
n
F
i
g
u
I
S
en
t o
f
th
e d
i
r
e
t
he par
a
m
o
u
n
o
orien
t
th
e
i
n
e
so
ur
ce
vo
lta
o
di
fi
ed swi
t
c
h
o
we
r
as
s
h
ow
n
e
1. Swi
t
c
hi
n
g
1 2 3
0
] ;
=[1,
1,
0]
;
-1
] ;
=[
-1
,0
,-1
1
,
-1] ;
=[
-1,1,
0
,1
,-1
]
;
=[
-1,
1
R
ESULTS
e
bl
ock
di
ag
ra
m
M
atlab
/
Si
m
u
li
n
u
re 3.
Direc
t
p
e
d d
u
r
i
ng st
e
s
a
n
d
s
upe
r
-
s
n
d
tu
rb
in
e
a
r
u
re 4.
SSN
:
208
8-8
7
e
ct power
co
n
n
t
p
a
rt in d
i
re
c
n
stantane
ous
a
ge vect
o
r
a
n
d
h
ing
tab
l
e
co
m
n
i
n
Tabl
e 1.
g
tab
l
e
fo
r 3-
l
e
4 5
=[0,
1,
0
]
;
=[
0
1
] ;
=[
-1
,0
,0
] ;
-1
] ;
=[
-1
,1
,1
]
1
,0] ;
=[
-1
,0
,1
]
a
m o
f
t
h
e
mo
d
n
k
en
vi
r
o
nm
e
p
ow
er
co
n
t
ro
l
e
ad
y
-state a
n
synchr
ono
us)
r
e gi
ve
n res
p
7
08
tro
l
app
lied
t
o
c
t
p
o
we
r c
ont
r
active and
re
a
d
th
e er
ro
rs
o
f
m
pared t
o
t
h
e
v
e
ls an
d 5-
l
e
6 7 8
0
,1
,1
] ;
=[0,
0,
1
]
=[-
1
,
-
1,
1]
;
]
;
=[-
1
,
-
1,
1]
;
]
;
=[
0
,
-1
,1
] ;
d
el use
d
for t
h
n
t
[2
5]
:
(D
PC) bl
ock
n
d
tran
sien
ts
. T
h
e
differ
e
ectiv
ely in
T
o
DFIG
-WE
C
r
ol. It
selects
a
ctiv
e p
o
wer
s
f
th
e activ
e a
n
a
t
devel
o
p
ed
v
els inverte
r
9 10
]
;
=[1,
0,
1]
;
=[
0
,
-1
,0
] ;
=
=[
1
,
-1
,1
] ;
=[
1
,
-1
,0
]
e control
of t
h
diag
r
a
m
con
d
ition
s
a
t
e
nt
param
e
t
e
r
abl
e
2 an
d
T
C
S (
H
al
a
A
l
a
m
the appropri
a
s
in
th
eir
d
e
s
i
n
d reactive po
by N
ogu
ch
i
11
12
=[1,
1,
1]
;
=
[-
1,
-
1
,
-
1]
;
=[1,
0,
-
1
]
;
h
e dou
b
l
y fe
d
t
vari
abl
e
w
i
e
rs o
f
t
h
e
d
o
T
able 3. The
m
i Ar
oussi)
39
a
te v
o
ltag
e
i
re
d
value
,
w
ers
[
24]
.
to
e
n
su
r
e
d
ind
u
ctio
n
i
nd
sp
eed
o
ubly f
e
d
results o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
E
40
E
lec & C
o
m
p
En
g, V
o
l
.
10
,
Table
2
R
N
R
G
M
V
Fi
gu
re 4.
(
a
,
No
. 1, Feb
r
u
2
. Param
e
ters
No
m
i
nal
P
Stator V
o
Stator Fr
e
Stator Re
Stator In
d
Rotor Re
s
Ro
to
r In
d
Mu
tu
al I
n
No
. o
f
P
a
Tabl
e 3. P
a
R
ated powe
r
N
u
m
ber
of blades
R
otor
Radius
G
ear
box r
a
tio
M
o
m
ent of inertia
V
iscous friction c
o
a
) C
u
r
v
es
o
f
:
t
u
ar
y 20
20
:
3
5
o
f
t
h
e
do
ubl
y
DFIG Para
m
e
t
Powe
r
o
ltage
e
quency
sistance
d
uctance
s
istance
d
uctance
n
ductance
a
ir of Pole
s
a
ram
e
ters o
f
t
h
Turbine Para
m
e
a
o
ef
f
i
cien
t
(a)
(b
)
t
he w
i
nd spe
e
5
-
46
y
fed
i
n
duct
i
o
n
t
er
s
Pn = 1.
5 KW
Vs = 220/380V
fs = 50 Hz
Rs = 1.
18
Ω
L
s
= 0.
4 H
Rr
= 1.
66
Ω
L
r
= 0.
18 H
M
= 0.
17 H
P =2
h
e wind
turbi
n
t
ers
1.
5 KW
3
R = 1
m
G = 2
J = 1000Kg.m
²
f
v
= 0.
007 N.m
.
s
-
e
d
,
(b
) th
e stat
n
ge
nerat
o
r
n
e
-
1
o
r activ
e po
w
ISS
N
:
2
w
e
r
2
088
-87
08
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Int J
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lec & C
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Eng
En
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en
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SSN
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208
8-8
7
e
ct power
co
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(e)
(d
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7
08
tro
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o
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DFIG
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or
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H
al
a
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f
th
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m
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oussi)
41
to
r
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
E
42
6.
2.
R
te
m
p
e
of t
h
e
th
e f
o
a.
R
e
b.
In
d
in
Fi
g
a.
T
h
to
b.
T
h
th
e tr
a
th
eir
r
E
lec & C
o
m
p
R
obus
tness
t
e
The pa
ra
m
e
rature in
crea
s
e
pa
ram
e
ter
v
o
llow
i
ng
co
nd
i
e
sistance
R
m
d
uct
a
nces
L
a
Fi
gu
re 5
s
h
g
ur
e
4
an
d Fi
g
h
e stator acti
v
h
y
s
t
e
r
es
is
co
n
h
e stator a
n
d
r
From
the
s
a
nsi
e
nt
re
gi
m
e
r
e
f
erence
val
u
En
g, V
o
l
.
10
,
Fi
gu
re 4.
(
e
st
m
eters of th
e
s
e, ski
n
effec
t
v
ariatio
n
s
. So
,
i
tio
ns:
m
u
ltip
lied
b
y
2
a
nd
L
m
u
lt
ip
h
ow
s th
e sim
u
g
u
r
e 5 w
e
ca
n
e and reactiv
e
n
t
r
o
ller bu
t
t
h
r
ot
or c
u
rre
nt
s
s
e resu
lts, w
e
, and few
e
r
d
u
es
. T
h
e
robu
s
,
No
. 1, Feb
r
u
f
) t
h
e vo
ltag
e
s
e
DFIG
are
t
, etc. In this
c
,
th
e
ro
b
u
s
t
n
e
2
l
i
e
d b
y
0.
5
.
u
latio
n
’
s resu
l
en
su
r
e
, e
v
en
b
e
po
wers
foll
o
e
val
u
e
s
of p
o
(respectively
e ca
n concl
u
d
isturb
an
ce o
s
s
tn
e
s
s
o
f
t
h
is
a
u
ar
y 20
20
:
3
5
(
f)
(g
)
s
of the stato
r
ex
po
s
e
d
to
c
ase, the pro
p
e
ss
of t
h
e c
o
m
l
t
s
obt
ai
ned
.
C
b
y ch
ang
i
ng
t
h
o
w
their refe
r
e
o
wers
q
u
ickl
y
voltag
e
s) in t
h
u
de t
h
a
t
t
he
s
cillatio
n
s
in
t
h
a
pp
ro
ach
r
e
m
a
5
-
46
, (g
) th
e vo
lta
v
a
riatio
ns c
a
p
ose
d
DPC
m
u
m
m
a
nd use
d
C
om
pari
n
g
t
h
e
h
e in
itial v
a
l
u
e
n
c
es with
fe
w
reg
a
in
th
eir
r
h
e fra
m
e
(
a
,
b
t
echni
q
u
e
of
h
e curve
s
of
t
a
in
s g
ood
for
g
es
of the
rot
o
a
use
d
by
va
r
u
st
guara
nt
ee
(
DPC) has b
e
e
resu
lts of th
e
u
es of
D
F
IG
, t
h
w
er oscillatio
n
efe
r
ences
.
, c
)
have a
si
n
DPC h
a
s a
h
e various c
u
r
th
e
w
i
n
d
en
e
r
ISS
N
:
2
or
r
io
u
s
ch
an
ge
s
go
od re
sul
t
s
e
e
n
tested ac
c
e
sim
u
latio
n
s
t
hat:
n
s and
di
st
ur
b
n
usoi
da
l
sha
p
e
lo
w resp
on
s
u
r
v
e
s
t
h
at
qui
c
r
gy co
nv
er
sio
n
2
088
-87
08
s
suc
h
as
rega
rdle
s
s
c
or
di
n
g
t
o
illu
strated
b
a
n
ces due
e
.
s
e ti
m
e
in
c
kl
y
regai
n
n
sys
t
e
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
E
Figur
e
E
lec & C
o
m
p
e
5.
C
u
rv
es o
f
Eng
En
ha
nce
m
f
: (a
) the
st
ato
I
S
en
t o
f
th
e d
i
r
e
r activ
e powe
SSN
:
208
8-8
7
e
ct power
co
n
(a)
(b)
(c)
e
r,
(b)
th
e stat
o
7
08
tro
l
app
lied
t
o
o
r reactive po
w
o
DFIG
-WE
C
w
e
r
, (c
) t
h
e c
u
C
S (
H
al
a
A
l
a
m
u
rren
ts of
th
e
m
i Ar
oussi)
43
stato
r
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
E
44
Fig
u
E
lec & C
o
m
p
u
re 5.
Cu
rv
es
En
g, V
o
l
.
10
,
of
: (d
) th
e c
u
,
No
. 1, Feb
r
u
u
rren
ts of th
e
r
u
ar
y 20
20
:
3
5
(d)
(e)
(f)
r
ot
o
r
, (e)
the
v
5
-
46
v
oltag
e
s of th
e
e
st
ato
r
,
(
f) t
h
e
ISS
N
:
2
e
vol
t
a
ges of
t
2
088
-87
08
t
he rot
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.