Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 95
3
~
96
8
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p95
3-9
68
9
53
Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
Control of P
M
SG based variable
speed wi
nd energy conversion
system connected to the grid
with PI and ADRC approach
Yo
u
s
se
f
B
a
rr
ad
i
1
, K
h
al
id
a
Z
a
zi
2
, M
a
lika Zazi
3
, N
a
ou
fe
l
Kh
al
di
4
1,
2,
3
Dep
a
rte
m
ent
El
ectr
i
cal
En
gin
eering
Depar
t
me
nt in
Th
e
Hi
gh
er
S
c
ho
ol of
T
ech
nica
l Edu
c
a
t
ion
(EN
S
ET),
M
o
h
a
mmed
V
Un
iv
ersity,
M
o
rocco
4
De
p
a
rtme
n
t
o
f
El
ec
tric
a
l
E
n
g
i
n
e
e
r
i
ng,
Moh
a
mm
a
d
ia
Sc
h
o
o
l
o
f
En
gi
ne
e
r
in
g, Moha
m
e
d V Uni
v
e
r
sit
y
, Mo
rocc
o
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
Au
g 2
4
, 2
019
Re
vise
d
Oc
t 2
3
, 2
019
Acc
e
pt
e
d
Dec 15
, 20
19
T
h
i
s
pa
p
e
r p
r
e
s
e
n
t
s
th
e
m
o
de
lin
g a
n
d sim
u
l
a
ti
on
o
f
win
d
e
n
e
r
gy
Co
nv
e
r
sio
n
S
y
s
t
em us
in
g th
e Perman
ent
M
a
g
n
et S
y
nchr
o
n
o
u
s G
e
nerato
r (PM
S
G
)
.
Th
e
ob
je
ctiv
es
are: to
extra
c
t th
e
maxi
m
u
m
p
o
w
er of
th
e w
i
nd
sp
eed
by
c
o
nt
rol
l
i
n
g
th
e ele
c
t
r
om
a
gne
tic to
rqu
e
o
f
the P
M
SG,
to maint
a
i
n
constant
t
h
e
DC-li
n
k voltage de
spite
the wi
nd speed
vari
a
tio
ns
and to
attain t
h
e unit
y
power factor. In order t
o
ensure a
r
e
g
u
l
a
tion
wi
th
high
p
e
rform
ance
and
a
go
od
rob
u
stnes
s
ag
ains
t the
int
e
rn
al an
d
the
e
x
terna
l
dis
t
u
r
b
a
n
c
es
,
a new
cont
rol
str
a
tegy
called t
h
e Acti
v
e
Di
st
urban
c
e R
e
ject
ion Control (ADRC) i
s
us
ed. Th
erefor
e, the An
alys
is
an
d
s
i
mu
la
tion
o
f
th
e
A
D
RC
an
d P
I
con
t
ro
ll
e
r
s
a
r
e d
e
ve
lo
pe
d wit
h
MAT
L
AB/Sim
u
l
i
nk so
ft
wa
re.
T
h
e p
e
rfo
rm
a
n
c
e
of
t
h
e
s
e
con
t
ro
ll
ers
is
comp
ar
ed
in
t
e
rm o
f
re
fere
nces
tr
ack
ing
,
ro
bu
stness
and grid
f
a
u
l
ts.
Ke
yw
ords:
A
D
R
C
con
t
ro
ll
er
Lin
e
a
r
e
x
t
e
nde
d
st
at
e ob
serv
e
r
MPP
T
P
I
con
t
r
o
lle
r
PMS
G
W
i
nd
turb
in
e
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
Yo
us
s
e
f Ba
rra
di
,
Depa
rt
eme
n
t
E
l
ec
tric
al
Engi
n
e
e
r
i
n
g,
Depa
rt
me
nt i
n
The
Hi
g
h
er Sc
h
o
ol
o
f
Te
ch
ni
cal
Educ
at
i
o
n
(ENS
E
T
),
Mo
ha
mme
d
V
Uni
v
e
r
si
ty
,
B
P
6
207 Ra
bat
,
Mo
rocco
.
Emai
l:
barradi
y
o
usse
f.e
l
e
c
t
r
i
que
@
g
mai
l
.
co
m
1.
IN
TR
O
DUCTION
In
t
h
e rece
nt
yea
r
s
,
wi
n
d
en
ergy
be
came a
fam
ous cl
e
a
n
ener
g
y
s
o
u
r
c
e
.
The
wi
nd e
n
e
r
g
y
s
o
urc
e
sy
st
em
s are
qu
ic
k
l
y g
r
o
w
i
n
g
th
ank
s
to t
h
e i
n
nov
at
io
ns
a
n
d th
e
r
e
search
e
s
in
win
d
e
n
ergy
te
c
hno
lo
gy
f
o
r
el
ec
tric
al
pow
er
p
r
o
d
u
ct
i
o
n
.
Ori
g
i
n
al
l
y
,
a
win
d
p
o
w
e
r
s
o
urc
e
was use
d
in
st
anda
l
o
ne appl
ic
at
i
ons, ho
weve
r,
wi
n
d
syst
e
m
s
c
o
n
n
ect
e
d
di
re
ct
ly
t
o
t
h
e g
r
i
d
[
1
]. Th
ree t
ype
s o
f
ge
ne
ra
t
o
rs are
ma
i
n
l
y
usa
b
l
e
i
n
th
e
win
d
ene
r
g
y
co
n
v
e
r
sion
syst
em:
t
h
e
squi
rrel
c
a
g
e
in
d
u
ct
i
o
n
g
e
ne
rat
o
r
(S
CIG
)
,
d
oubl
y fe
d i
n
d
u
ct
i
o
n
ge
ne
rat
o
r
(DF
I
G) a
n
d
Pe
rma
n
ent
Mag
n
e
t Sync
h
r
o
n
o
u
s
Ge
ne
rat
o
r (P
M
S
G).F
or t
h
is
wo
rk
, t
h
e P
M
S
G
is use
d
si
nce
i
t
has
sma
l
l
si
ze, p
r
o
v
i
d
es
a sel
f
e
x
ci
ta
ti
on an
d a
hig
h
po
we
r de
nsi
t
y.
In a
ddi
t
i
on
, the
g
e
ne
ra
t
o
r
has
t
h
e
ca
p
a
ci
t
y
t
o
cont
rol
re
ac
ti
v
e
po
we
r, wo
rki
ng al
so wi
th
o
u
t
t
h
e ge
ar
box
due
t
o
t
h
e
hi
ghe
r n
u
m
b
er of p
o
l
e
s
fo
r lo
w
spee
d
ope
ra
t
i
o
n
[2,
3].
A
c
o
n
f
i
g
urat
i
on
of a
wi
n
d
po
we
r s
y
st
e
m
ba
se
d
on t
h
e P
M
SG
i
s
i
l
l
u
st
rat
e
d
i
n
F
i
g
u
re
1
.
The s
ync
hro
n
ous ge
nera
t
o
r i
s
c
o
n
n
ect
ed t
o
t
h
e g
r
i
d
t
h
rou
g
h
a bac
k
-t
o-
bac
k
co
nve
r
t
e
r
com
pose
d
of
t
h
e
gene
rat
o
r si
de
con
v
e
r
te
r a
n
d
t
h
e
gri
d
-si
d
e
c
o
nve
rt
er [4].
The
l
a
st
yea
r
s,
man
y
re
se
a
r
c
h
es h
a
ve
a
ppea
r
ed
d
o
cu
ment
in
g t
h
e c
o
ntr
o
l
o
f
no
nli
n
ea
r
sys
t
ems
rel
a
t
e
d
to
w
i
nd
e
n
er
gy. I
n
th
e
li
ter
a
tur
e
,
pr
opo
r
t
ion
a
l
in
t
e
gr
a
l
(
P
I) co
n
t
ro
l
l
e
r
s b
a
se
d
on
f
i
e
l
d
or
i
e
n
t
e
d
con
t
ro
l
(F
O
C
)
i
s
made
up, t
h
i
s
co
nve
nt
i
o
nal
te
chni
q
u
e
pre
s
e
n
ts s
o
me s
h
ort
c
omin
gs, suc
h
a
s
a
lo
w a
c
c
u
r
acy e
s
pe
ci
al
l
y
wit
h
t
h
e di
st
urba
nce
a
n
d
nonl
i
n
ea
ri
ti
es a
ccor
d
in
g
t
o
d
y
n
amic
c
h
arac
te
ri
sti
c
s o
f
syst
ems
[5].
In
order
to
o
v
e
r
come
t
h
e di
sad
v
a
n
t
a
ge
s o
f
the
c
o
n
v
e
n
ti
o
n
al
PI
cont
rol
l
er
whi
c
h su
ffe
r
s f
r
o
m
man
y
l
i
mit
a
t
i
ons, a
ne
w
c
o
n
t
rol
st
ra
te
g
y
c
a
lle
d
Lin
ear
A
c
tiv
e
D
i
sr
up
tio
n
Re
j
e
c
t
io
n
C
o
n
t
ro
l
(A
D
RC)
f
ound
e
d
b
y
H
a
n i
n
199
5
is
ado
p
t
e
d
t
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
9
5
3
–
968
95
4
re
move
dist
urbanc
e
s
a
f
fec
t
i
n
g
t
h
e
faci
l
i
ty
[
6
,7].
T
h
i
s
pa
per i
n
t
r
o
duce
d
an
a
dva
nced
me
tho
d
a
s
th
e
li
nea
r
ac
ti
ve di
st
urba
nc
e re
je
ct
i
on c
ont
rol (
A
DRC
)
ba
sed
o
n
vect
or c
ont
rol, i
n
o
r
de
r t
o
ac
hie
v
e
a ma
xim
u
m
pow
e
r
ext
r
a
c
t
i
o
n
, t
o
mai
n
ta
i
n
the
D
C
bus at
d
e
si
re
d v
o
l
t
a
g
e
va
lue
t
h
ro
ug
h t
h
e
DC
-l
i
n
k ci
rc
ui
t
,
and t
o
mee
t
pow
e
r
st
ab
l
e
of
th
e w
i
n
d
e
n
erg
y
c
onv
er
sio
n
sy
s
t
e
m
[8
]
.
In
d
e
ta
il,
t
h
e su
gg
e
s
ted
d
e
s
i
gn
te
chn
i
qu
es
pr
opo
se
a c
o
mpa
r
i
s
on
b
e
twe
e
n
P
I
a
n
d
AD
RC
te
c
h
n
i
que
w
h
ich
h
a
v
e
be
en
exp
l
or
ed
an
d
u
s
ed
r
e
c
e
n
t
ly
a
s
a n
e
w
te
c
h
no
logy
fo
r
e
s
ti
mat
i
ng
and
c
o
mp
e
n
s
a
ti
ng
unce
r
t
a
i
n
ti
es a
nd
d
i
st
u
r
ba
nc
e
s
, i
s
base
d
on
Ext
e
n
d
e
d
st
a
t
e
Obse
rve
r
(ES
O
) w
h
i
c
h i
s
the
mai
n
pa
rt
of
t
h
e c
o
m
m
an
d.
An
e
v
al
ua
ti
o
n
i
s
ens
u
red
t
o
c
ont
rol
t
h
e
gri
d
an
d
gene
rat
o
r si
de
c
o
nve
rt
er
i
n
order
t
o
re
gul
at
e
t
h
e el
ec
troma
gne
t
i
c
t
o
rq
ue
a
n
d
t
h
e st
at
or c
u
rrent
of
t
h
e P
M
S
G
. S
i
mul
a
t
i
on
i
s
ma
d
e
u
nde
r
M
A
TLA
B/
Simu
lin
k
en
v
i
ronme
n
t w
ith
a
c
o
mp
aris
on
b
e
twe
e
n
bo
th
c
o
mma
nd
s. Resu
l
t
s
prov
i
d
e
d
show
cle
a
r
ly
th
e
f
e
a
s
ib
ilit
y
an
d
th
e
eff
e
c
t
iv
e
n
ess of
th
e
pr
opo
se
d
t
w
o
tec
h
n
i
q
u
e
s. Th
ey
pr
e
s
e
n
t al
so
a
g
ood
c
h
a
r
a
c
t
e
r
i
st
ic,
e
x
ce
ll
en
t
o
u
t
pu
t
f
r
o
m
th
e
AD
RC
c
o
n
t
ro
l c
o
mp
ar
i
n
g
w
i
th PI
co
mma
nd
e
s
p
e
ci
all
y
i
n
ter
m
s of ro
bu
st
ne
ss an
d
r
e
f
e
re
n
c
e
tr
acki
n
g
.
Th
e
sequ
e
n
t
i
a
l
w
o
r
k
fl
ow
of
t
h
is p
a
p
e
r i
s
a
s
fo
l
l
ow
s:
In
se
ct
ion
2,
com
p
le
te
a
r
ch
it
ec
tu
r
e
o
f
t
h
e va
ri
a
b
le
sp
e
e
d
wi
n
d
t
u
r
b
ine
c
o
n
v
e
r
si
o
n
chai
n
base
d o
n
t
h
e P
M
S
G
ha
s bee
n
desc
ri
b
e
d a
n
d
the
mo
del
ha
s
bee
n
det
e
rmi
n
ed. Se
ct
io
n
3 c
ove
rs b
o
t
h
P
I
a
n
d
ADR
C
de
si
gn
, fol
l
o
w
e
d
by
a
c
ont
rol
o
f
g
r
i
d
si
de
c
o
n
v
ert
e
r
,
bus v
o
l
t
a
ge
a
n
d ge
nera
t
o
r si
d
e
c
o
n
v
e
r
t
e
r o
f
the
PM
SG
t
o
maxi
mi
z
e
t
h
e
pro
duct
i
on
of
t
h
e
w
i
nd e
n
e
r
g
y
usi
n
g
r
e
s
p
ec
tiv
e
l
y
bo
th
con
t
ro
lle
r
s
in
se
c
tion
4
an
d 5
.
S
i
mu
l
a
tio
n
r
e
su
lts a
nd d
i
s
c
u
s
s
i
on
are
mad
e
in se
c
t
io
n
6
.
La
stly
,
in s
e
c
tio
n
7,
a
con
c
lu
sio
n
h
a
s b
een
ad
d
e
d
to
f
i
n
a
liz
e
th
e w
o
rk
.
F
i
gu
re
1.
A
r
chi
t
e
c
t
u
re
of t
h
e
v
a
ria
b
le
s
p
ee
d wi
n
d
t
u
rbi
n
e c
o
n
v
e
r
si
o
n
c
h
ai
n ba
se
d on
the
P
M
S
G
2.
M
O
D
E
LING
OF THE
WI
ND EN
ERGY
C
O
N
V
E
RS
ION S
Y
S
TEM B
A
S
E
D ON
THE
PM
S
G
2.1.
Wind turbine
Th
e tu
rb
i
n
e
t
r
an
sfo
r
ms th
e
w
i
n
d
en
e
r
g
y
i
n
t
o
a
mec
h
an
ic
al
en
e
r
gy
a
v
a
i
l
a
bl
e on
a w
i
n
d
t
u
rb
in
e ro
tor
[9
,10]
. T
h
is
pow
er is ex
p
r
e
s
se
d by:
P
C
λ
,
β
ρπ
R
V
(1
)
Wh
er
e
is
t
h
e air
d
e
nsit
y
,
R
is t
h
e t
u
rb
in
e ra
d
i
o
s
a
n
d
V
is
th
e
w
i
n
d
v
e
lo
city
.
T
h
e
pow
er
c
o
eff
i
c
i
e
n
t
Cp i
s
gi
ve
n by
the
fol
l
o
wi
ng e
x
p
r
e
ssi
on
[11
,
12]:
C
λ
,
β
C
C
β
C
e
C
λ
(2
)
whe
r
e:
λ
.
.
(3
)
C
1
=0
.
517
6,
C
2
=11
6
, C
3
=0.
4
, C
4
=5
,
C
5
=21
,
C
6
=0
.
006
8
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
C
o
n
t
r
o
l
of
PM
SG
b
a
se
d v
a
ri
abl
e
spee
d wi
n
d
e
n
er
gy c
onve
r
si
on
sy
ste
m
c
o
n
n
e
c
t
e
d
…
(Y
ou
s
s
ef
B
a
rr
adi
)
9
55
The
ma
xi
mu
m
val
u
e
o
f
p
o
we
r c
o
ef
fi
ci
ent
C
p
is
C
0.4
8
, is
a
c
h
i
e
ve
d
for pi
t
c
h a
n
g
l
e
o
f
rot
o
r
bl
ades
β
is
se
t t
o
z
e
ro a
n
d
λ
=8
.
1
, t
h
i
s
po
in
t co
rre
sp
ond
s a
t
th
e
max
i
mum
p
o
w
e
r
po
in
t t
r
a
c
k
i
ng
(M
PP
T).
Thi
s
m
ode
l
i
s
t
r
ansl
at
ed
b
y
t
h
e
fol
l
owi
n
g
e
q
uat
i
on
[2
1]:
T
T
f
Ω
J
(4
)
Whe
r
e
Tg
a
n
d
Tem
are
res
p
ec
ti
vel
y
t
h
e
me
chani
c
a
l
a
n
d t
h
e el
ec
tr
oma
gne
t
i
c
t
o
rq
ue o
f
PMS
G
, J is
th
e
to
ta
l mo
me
n
t
of
i
n
e
r
tia
a
n
d fv
is t
h
e
f
r
i
c
tio
n co
eff
i
c
i
e
n
t
of
th
e
tur
b
in
e.
Th
e
e
l
e
c
t
r
o
magn
et
ic to
rque
r
e
f
e
re
n
c
e
is de
ter
m
i
n
e
d
by
th
e
fo
ll
o
w
in
g
e
qua
tio
n
:
T
C
ρπ
R
Ω
(5
)
The
F
i
g
u
re 2
represe
n
t
s
t
h
e
b
l
oc
k di
ag
ra
m o
f
the
t
u
rbi
n
e
m
odel
wit
h
MP
P
T
strat
e
g
y
:
Fi
gu
re
2. M
o
d
e
l
of t
h
e
t
u
rbi
n
e wi
th
MP
PT
s
t
rat
e
gy
2.2.
Mo
del
o
f
c
o
n
v
erters
The
ge
nerat
o
r si
de
c
o
n
v
e
r
t
e
r
a
n
d
gri
d
si
d
e
co
n
v
erte
r a
r
e c
o
ntrol
l
e
d
b
y
t
h
e
P
W
M
c
ont
rol
.
T
h
ese
c
o
nv
ert
e
r
s
a
r
e
r
e
pr
e
s
en
te
d
by
sim
p
le
li
n
e
vo
lt
ag
e
s
an
d
th
e
co
n
t
r
o
l
si
g
n
a
ls S
i
(6
)
[8
].
⎩
⎪
⎨
⎪
⎧
v
U
v
U
v
U
(6
)
2.3.
M
o
deling
of
the PM
S
G
The
e
l
e
c
t
r
i
c
a
l
volt
a
ge
s of t
h
e
P
M
S
G
a
r
e
gi
v
e
n by
t
h
e f
o
ll
o
w
i
n
g
e
qua
t
i
o
n
s
:
v
R
i
L
e
v
R
i
L
e
(7
)
Wh
er
e t
h
e
d
i
rec
t
a
n
d th
e
qu
adr
a
t
u
re e.
m.
f
com
p
o
n
e
n
t
s
ar
e ex
pre
ssed
a
s
fo
l
l
o
w
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
9
5
3
–
968
95
6
e
ω
L
i
e
ω
L
i
ω
ϕ
(8
)
Wh
er
e:
L
,
L
ar
e
d
an
d
q
a
x
i
s
i
n
du
ct
an
c
e
s
(
H
)
;
R
is the
st
at
o
r
res
i
sta
n
ce (
Ω
);
i
,
i
a
r
e
th
e
d
a
n
d
q
a
x
i
s
m
ach
in
e c
u
r
r
en
t
(A
);
ϕ
is the
flu
x
li
n
k
a
ge
est
a
bl
i
s
he
d
b
y
t
h
e
perma
n
e
n
t
ma
g
n
et
s
i
n
t
h
e
st
a
t
or
wi
ndi
ng
s (Wb);
ω
is
th
e
ang
u
l
ar
f
r
e
q
u
e
n
cy
o
f
the
st
at
o
r
vo
lt
ag
e (
r
a
d
/
s)
;
The
e
xpressi
on
o
f
the
el
e
c
t
r
o
m
ag
net
i
c
t
o
rq
u
e
i
s
a
l
so e
x
pres
sed as
a fu
nct
i
on
o
f
c
u
rre
n
ts
“(9
)
”:
T
p
ϕ
i
p
L
L
i
i
(9
)
p
:
P
a
ir
s of
po
le
s
The
s
e
e
q
uat
i
o
n
s
ha
ve
bee
n
grou
pe
d to
form a
si
mpl
i
fi
e
d
mode
l
o
f
P
M
S
G
as
de
pic
t
ed
i
n
F
i
gu
re
3.
Fi
gu
re
3.
Si
m
p
li
fie
d
Th
eo
ret
i
c
a
l
M
odel
of P
M
S
G
2.4.
M
o
de
li
ng
of RL
g
r
id f
i
lt
er
and
D
C
lin
k
The
el
ec
t
r
i
cal
vol
t
a
ges
of t
h
e gri
d
-si
d
e
are
gi
ve
n
i
n
t
h
e
(d,
q
)
re
fere
nc
e
frame
b
y
th
e
fo
l
l
ow
ing
e
q
u
a
ti
on
s:
v
R
i
L
e
v
R
i
L
e
(1
0)
Whe
r
e
t
h
e
dire
ct
and
t
h
e
q
u
a
d
ra
ture
e
.
m
.
f
co
mp
one
nt
s a
r
e
e
x
p
r
e
s
se
d as
fol
l
ow:
e
ω
L
i
i
e
ω
L
i
(1
1)
The
a
c
t
i
ve
a
nd
re
act
i
v
e
pow
e
r
su
ppl
i
e
d to
the
ne
tw
o
r
k ca
n
b
e
ex
pre
s
se
d
a
s
:
P
v
.i
v
.i
Q
v
.i
v
.i
(12)
The
gri
d
vol
t
a
ge
vect
or is o
r
i
e
nt
ed o
n
d-a
x
i
s
, t
h
e
n
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
C
o
n
t
r
o
l
of
PM
SG
b
a
se
d v
a
ri
abl
e
spee
d wi
n
d
e
n
er
gy c
onve
r
si
on
sy
ste
m
c
o
n
n
e
c
t
e
d
…
(Y
ou
s
s
ef
B
a
rr
adi
)
9
57
v
V
v
0
(1
3)
Thus:
P
v
.i
Q
v
.i
(1
4)
The
dc-li
n
k
c
a
pac
i
tor i
s
i
n
t
e
rfa
ce
bet
w
ee
n
gene
rat
o
r
si
de c
o
n
v
e
r
t
e
r
a
nd g
r
i
d
si
de
c
o
n
v
e
r
t
e
r; By
negl
ec
ti
n
g
t
h
e
con
v
e
r
te
rs l
o
ss
es,
t
h
e
st
at
e
eq
ua
ti
on
o
f
t
h
e
dc
-l
i
n
k
v
o
l
t
a
g
e
are
e
x
p
r
esse
d a
s
fol
l
ow:
V
i
dt
i
i
dt
(1
5)
w
h
ere
C
:
th
e
D
C
li
n
k
C
a
p
a
c
ito
r.
3.
S
YNTHESIS
O
F
PI AND AD
RC
C
O
N
T
R
O
LLER
S
3.1.
PI con
t
ro
ll
er
Th
e
p
r
op
or
ti
on
al
-In
te
gr
al
c
o
n
t
ro
lle
r
is a
co
mb
in
a
t
io
n
o
f
bo
th
a
c
t
i
on
s
p
r
op
or
ti
o
n
a
l
a
n
d
in
te
gr
al
in
order t
o
ca
nce
l
t
h
e sta
t
i
c
e
rror
.
The st
ruct
u
r
e o
f
a
pa
ral
l
e
l
PI c
o
ntroll
er
syst
em is re
p
r
esent
e
d i
n
Fi
gu
re 4
[1
0,
11
,
1
6
]
. T
h
e
de
ri
vat
i
v
e
a
c
t
i
on o
f
P
I
D
c
ont
rol
l
e
r
i
s
e
x
c
l
ude
d be
ca
use
i
t
i
s
c
h
ara
c
t
e
riz
e
d
b
y
a
m
pl
i
f
y
i
ng t
h
e
effec
t
of sy
st
em n
o
i
s
e.
F
i
gu
re 4.
S
t
r
u
c
t
ure
of P
I
c
ont
rol
l
e
r
syst
em fo
r
t
h
e
P
M
S
G
3.2.
L
i
n
e
ar
AD
RC
con
t
r
o
l
l
e
r
Th
e
m
a
t
h
e
m
at
ic
expr
e
ssion
of t
h
e
first
o
r
d
e
r
f
o
r
a
time
-v
a
r
yi
n
g
dyn
a
m
ic
sy
st
em w
ith si
ng
le
inpu
t
u
and
si
n
g
l
e
-out
put
y is
g
i
ve
n a
s
foll
ow
[1
3-1
6
].
f
y,
d,
t
b
u
(1
4)
whe
r
e:
f(y, d,
t
)
: t
h
e
e
ffe
ct
of i
n
te
rna
l
a
n
d
e
x
te
rnal
di
st
urba
nc
es,
b
0
: Re
pre
s
en
ts p
a
ra
me
te
r g
a
i
n
t
o
e
s
ti
ma
te
.
d :
The
e
x
te
rna
l
di
st
urba
nc
e.
The
mat
h
emat
i
c
a
l
syst
em a
s
f
o
ll
ow
d
e
scri
be
s the
proc
ess
[
19-
21
]:
x
x
b
u
x
f
y
x
(1
5)
x
x
β
y
x
b
u
x
β
y
x
(1
6)
Wh
er
e
t
h
e
v
e
c
t
o
r
of
th
e ob
serv
er
g
a
in
is
ex
pr
ess
e
d
b
y
:
β
β
2S
S
(1
7)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
9
5
3
–
968
95
8
The
pol
e
o
f
t
h
e
obse
r
ver S
E
S
O
i
s
det
e
rmi
n
e
d
by t
h
e
t
e
c
hni
que
o
f
pl
ac
em
ent
o
f
t
h
e
p
o
l
e
s. T
h
ere
f
o
r
e
,
t
h
e co
nt
rol
pl
ant
ca
n
be
e
n
sure
d
by
a
si
m
p
le
p
r
op
ort
i
o
n
a
l
K
(1
8). T
h
e
inp
u
t
si
g
n
al
re
fere
nce
den
o
t
e
d
r
[2
0,
2
1
]
.
u
K
r
y
K
r
x
(1
8)
whe
r
e:
Kp
=
S
C
L.
S
C
L i
s
t
h
e pol
e o
f
desire
d cl
o
s
e
d
l
o
o
p
.
SES
O
=
3~
7
S
C
L
Th
e
on
l
y
se
tt
ing
p
a
r
a
me
ter
is SC
L.
Fi
gure
5 re
p
r
es
ent
the
Str
u
ct
u
r
e
of ADRC
c
o
ntrol
l
e
r
an
d t
h
e
ESO
Fi
gu
re 5.
St
ruc
t
ure
of
A
D
R
C
cont
rol
l
e
r an
d
t
h
e
E
S
O
4.
C
O
N
T
ROL OF THE
WIND
SYS
T
EM B
Y
PI
CON
T
ROLLER
4.1.
C
o
nt
ro
l o
f
t
h
e g
e
ne
rat
o
r
side
c
o
nv
e
r
t
e
r
The
st
at
or c
u
rre
n
t
is
al
ig
ne
d
o
n
t
h
e
q-
axi
s
(i
s
d
=0
). C
o
ns
eque
nt
l
y
, t
h
e
el
ec
troma
gnet
i
c
t
o
rq
ue
is
cont
rol
l
e
d
b
y
t
h
e
q-a
x
is c
u
rre
nt
i
s
q: T
h
e
ex
p
r
essi
o
n
of t
h
e
e
l
ect
roma
gne
ti
c
t
o
rq
ue (9
) be
c
o
me:
T
p
ϕ
i
(19)
Thus:
i
T
(2
0)
The
o
p
en
l
oop
trans
f
e
r
f
unct
i
o
n
i
s
:
G
s
k
(2
1)
We
u
s
e
th
e me
th
od
o
f
po
l
e
s c
o
mp
e
n
sa
ti
on in
o
r
d
e
r to
elimi
n
at
e th
e
z
e
r
o
pr
e
s
en
t
on
th
e
tr
an
sf
e
r
fu
nct
i
o
n
[1
1, 1
2
]. We pose
:
(22)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
C
o
n
t
r
o
l
of
PM
SG
b
a
se
d v
a
ri
abl
e
spee
d wi
n
d
e
n
er
gy c
onve
r
si
on
sy
ste
m
c
o
n
n
e
c
t
e
d
…
(Y
ou
s
s
ef
B
a
rr
adi
)
9
59
Thus:
G
s
(2
3)
Wh
er
e
τ
r
is
r
e
sp
on
se ti
me
:
τ
(24)
In
cl
ose
d
lo
o
p
we wi
ll
ha
ve:
F
s
(2
5)
The
r
e
f
ore,
t
h
e
para
me
te
rs
k
p
and
ki
of P
I
c
o
ntr
o
ll
er a
r
e
gi
v
e
n
by:
k
L
k
R
(2
6)
We chose:
τ
r =
1
0
m
s
4.
2.
Co
n
t
r
o
l
of th
e
gri
d
sid
e
c
o
n
v
e
r
te
r
an
d
D
C
li
n
k
vol
tage
Th
e op
e
n
lo
o
p
t
r
a
n
sf
er
fu
n
c
ti
on
f
o
r
t
h
e
gr
id f
ilte
r
c
o
n
t
r
o
lled
b
y
P
I
is:
G
s
k
(2
7)
The
r
e
f
ore,
t
h
e
para
me
te
rs
of
P
I
c
o
ntroll
er
ar
e:
k
L
k
R
(2
8)
The
defe
re
nce
bet
w
ee
n
t
h
e a
c
t
i
ve
p
o
we
r gene
rat
e
d
b
y
t
h
e
wi
nd ge
nera
tor
P
m
a
nd
t
h
e del
i
v
e
re
d
p
o
w
e
r to
gr
id
P
g
i
s
stored i
n
t
h
e
D
C
-l
i
n
k c
a
pa
ci
t
o
r, t
h
e s
t
ruct
u
r
e
of DC
l
i
nk vol
t
a
ge
c
ont
rol i
s
sh
ow
n
i
n
Fi
gu
re
6. The
c
o
n
v
e
r
te
rs
l
o
sse
s
a
r
e
ne
gl
ec
te
d
,
t
h
e
r
efore
the
equa
ti
o
n
o
f
t
h
e
dc
-l
i
n
k
v
o
l
t
a
g
e is ex
pre
s
se
d
by:
P
P
P
(2
9)
F
i
gu
re
6.
S
t
r
u
c
t
ure
of D
C
li
nk
v
o
l
t
age
c
ont
ro
l
F
i
gure
7
s
h
ows
t
h
e P
I
c
o
nt
rol
st
ruc
t
u
r
e
a
p
pli
e
d t
o
t
h
e ge
nera
tor
a
nd
gri
d
si
de c
o
n
v
e
r
t
e
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
9
5
3
–
968
96
0
F
i
gure
7.
P
I
C
ont
rol
st
ruct
ure
o
f
t
h
e
w
i
nd
sy
st
em b
a
se
d o
n
PMS
G
5.
C
O
N
T
ROL OF THE
WIND
SYS
T
EM B
Y
AD
R
C
C
O
NTR
O
LLER
5.1.
C
o
n
t
ro
l
o
f
t
h
e g
e
n
erat
o
r
side
c
o
nv
e
r
te
r
Th
e c
u
rr
en
ts of th
e
s
t
at
or are
re
a
r
r
a
n
g
e
d
as
foll
o
w
:
I
ω
I
V
I
ω
I
ϕ
V
(3
0)
The
s
e e
x
pres
si
ons
ca
n
be
wri
t
t
e
n
i
n
t
h
e
fol
l
o
w
i
n
g
fo
rm:
f
I
,d
,
t
b
u
t
(3
1)
Wh
er
e:
f
I
,d
,
t
I
ω
I
u
t
V
and
b
(3
2)
Wh
er
e:
f
I
,d
,
t
b
u
t
(3
3)
In
the s
a
m
e
w
a
y:
f
I
,d
,
t
I
ω
I
ϕ
u
t
V
and
b
(3
4)
5.2.
C
o
n
t
ro
l
o
f
t
h
e g
r
id
side
c
o
nv
er
t
er and
DC
lin
k
vo
lta
g
e
5.2.
1.
T
h
e c
u
r
ren
ts
of th
e
gr
i
d
fi
l
t
er
Th
e c
u
rr
en
ts of th
e
g
r
i
d
f
i
lt
er
a
r
e r
ear
rang
ed
a
s
fo
l
l
o
w
:
V
I
ω
I
V
I
I
ω
I
V
(3
5)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
C
o
n
t
r
o
l
of
PM
SG
b
a
se
d v
a
ri
abl
e
spee
d wi
n
d
e
n
er
gy c
onve
r
si
on
sy
ste
m
c
o
n
n
e
c
t
e
d
…
(Y
ou
s
s
ef
B
a
rr
adi
)
9
61
The
s
e e
x
pres
si
ons
ca
n
be
wri
t
t
e
n
i
n
t
h
e
fol
l
o
w
i
n
g
fo
rm:
f
I
,d
,
t
b
u
t
(3
6)
Wh
er
e:
f
I
,d
,
t
V
I
ω
I
u
t
V
a
n
d
b
(3
7)
Wh
er
e:
f
I
,d
,
t
b
u
t
(3
8)
In
the s
a
m
e
w
a
y:
f
I
,d
,t
I
I
ω
I
u
t
V
a
n
d
b
(3
9)
5.2.
2.
D
C
b
u
s
vol
ta
ge
c
o
n
t
r
o
l
The
p
o
we
r on
the
DC
l
i
n
k
C
a
pac
i
t
o
r ca
n
be
give
n by:
P
CV
V
i
i
(4
0)
Wh
en
th
e lo
sse
s
i
n
th
e
RL filte
r
,
th
e c
a
p
a
c
i
to
r
and
i
n
t
h
e
tw
o po
we
r c
onv
e
r
t
e
rs
are
n
e
gl
ec
te
d
,
th
e
po
we
rs ac
ros
s
t
h
e
DC
b
u
s i
s
t
h
e
di
ffe
r
e
n
ce
b
e
t
w
ee
n
t
h
e
ge
n
e
ra
t
o
r
p
o
w
e
r
P
m
an
d
g
r
i
d
p
o
w
er
Pg:
P
P
P
(4
1)
Or
:
CV
V
i
V
i
(4
2)
i
i
(4
3)
Taking
A=Vdc²:
√
i
i
(4
4)
Thus:
f
A,
d,
t
√
i
u
t
i
a
n
d
b
(4
5)
F
i
gure
8
s
h
ows
t
h
e
ADR
C c
o
nt
rol st
ruct
ure
appl
i
e
d
t
o
t
h
e
gene
rat
o
r a
n
d
gri
d
side
c
o
n
v
e
r
t
e
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
I
n
t J
P
o
w
El
ec
&
D
r
i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
:
9
5
3
– 96
8
96
2
F
i
gu
r
e
8.
A
D
R
C
C
ont
r
o
l st
r
u
ct
ure
of
t
h
e
wi
nd
sy
st
em base
d on
P
M
S
G
6.
SIMU
LA
TI
ON
RESU
LTS A
N
D
D
I
SCUSS
I
ON
As sh
own
i
n
Figu
re
9, the
si
mula
ti
on
wa
s car
ri
ed
o
u
t
wi
t
h
M
A
TL
AB
/
SIM
UL
INK in
o
r
de
r
t
o
va
li
dat
e
t
h
e
c
o
ntr
o
l st
ra
te
g
y
st
udi
e
d
i
n
t
h
i
s
wo
rk
. T
h
e
sy
st
em co
nsi
s
ts of se
ve
ral
bl
o
c
ks,
f
o
r
ex
am
pl
e t
h
e
t
u
r
b
i
n
e m
o
del
wi
t
h
i
t
s wi
n
d
pr
of
il
,
t
h
e
mode
l i
nve
r
t
e
r
s
wi
t
h
it
s pa
r
a
m
e
t
e
rs,
a
nd c
o
n
t
r
o
ll
er
s
base
d
on t
h
e
AD
RC
i
n
F
i
g
u
re
1
0
a
nd P
I
a
p
pr
oac
h
.
Al
l pa
ra
me
te
rs a
r
e gi
ven i
n
A
ppe
n
d
i
x
.
A
ra
nd
om
w
i
n
d
pr
of
il
e i
s
sho
w
n i
n
F
i
gu
r
e
11
. To e
x
t
r
a
c
t
the
ma
xim
u
m
w
i
n
d
e
n
e
r
g
y
of th
e
wi
nd s
p
ee
d, a
n
MPP
T
str
a
t
e
gy i
s
a
d
o
p
te
d.
I
n
o
r
d
e
r t
o
ma
i
n
ta
in t
h
e
D
C
-
l
i
nk
v
o
l
t
a
ge
c
onsta
nt
, a
c
ont
r
o
l
o
f
t
h
e
gr
id
si
de
co
n
v
e
r
t
e
r i
s
nece
ssa
r
y.
This
te
ch
n
i
qu
e
is b
a
se
d
on
th
e co
n
t
r
o
l o
f
d
i
r
e
ct
and
q
u
a
dr
at
ic
gr
id
cu
rr
en
ts,
a
n
d
en
su
res
also
an
ex
ch
ang
e
o
f
ac
tiv
e
an
d r
e
ac
ti
v
e
po
w
e
rs
b
e
twe
e
n
th
e
s
t
a
t
o
r
o
f
th
e PM
SG a
n
d
t
h
e
g
r
id
.
To a
tta
in
th
e
un
ity
p
o
w
e
r f
a
c
t
or
,
i
t
’
s
ne
cessa
ry
t
o
re
gul
at
e t
h
e
g
r
i
d
re
act
i
v
e
p
o
we
r t
o
i
t
s
de
si
re
d
va
lue
.
In
Fi
g
u
r
e 1
2
, the
r
o
to
r spee
d
t
r
a
c
k
t
h
e
p
r
o
f
il
o
f
th
e
w
i
nd
which
allo
ws th
e
eff
i
cien
c
y
o
f
the
MPPT s
t
r
a
teg
y
.
F
i
gu
r
e
9.
The
wh
ol
e syst
em
si
mula
t
i
on
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