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r
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o
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o
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t
sy
ste
m
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ra
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n
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e
r
d
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e
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n
t
c
rit
ica
l
c
o
n
d
it
i
o
n
s
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ter
n
a
l
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istu
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n
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e
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e
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DFIG
p
a
ra
m
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v
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ra
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p
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n
a
l
In
teg
ra
l
(F
OP
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c
o
n
tro
ll
e
r
is
p
r
o
p
o
se
d
.
F
i
n
a
ll
y
,
th
e
s
y
ste
m
’s
p
e
r
fo
rm
a
n
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e
i
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a
n
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o
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ss
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n
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ti
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n
a
n
d
n
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ise
m
in
im
iz
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ti
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n
.
K
ey
w
o
r
d
:
DFI
G
FOP
I
Fra
ctio
n
al
o
r
d
er
co
n
tr
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l
MP
PT
Vec
to
r
co
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tr
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p
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©
201
8
In
s
t
it
u
te o
f
A
d
v
a
n
c
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d
E
n
g
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n
e
e
rin
g
a
n
d
S
c
ien
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e
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
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ing
A
uth
o
r
:
A
b
d
elaz
iz
A
zz
a
,
L
A
S
A
L
ab
o
r
ato
r
y
,
Dep
ar
t
m
en
t o
f
E
lectr
o
n
ics,
B
ad
j
i M
o
k
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tar
-
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1
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f
r
1.
I
NT
RO
D
UCT
I
O
N
No
w
ad
a
y
s
,
a
m
aj
o
r
ity
o
f
t
h
e
w
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n
d
en
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g
y
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io
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s
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te
m
s
u
til
ize
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o
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b
l
y
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ed
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n
d
u
ctio
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e
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er
ato
r
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ec
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s
e
o
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its
h
i
g
h
e
f
f
icien
c
y
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d
lo
w
co
s
t
o
w
in
g
to
its
co
n
f
i
g
u
r
atio
n
[
1
]
,
[
2
]
.
DFI
G
h
av
e
w
i
n
d
in
g
s
o
n
b
o
t
h
s
tato
r
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d
r
o
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r
p
ar
ts
,
w
h
er
e
b
o
th
o
f
t
h
e
m
tr
an
s
f
er
co
n
s
id
er
ab
le
p
o
w
er
b
et
w
ee
n
g
e
n
e
r
ato
r
an
d
g
r
id
.
I
n
DFI
G,
th
e
co
n
v
er
ter
s
p
r
o
ce
s
s
o
n
l
y
ab
o
u
t
2
0
-
3
0
%
o
f
to
tal
g
en
er
ated
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o
w
er
,
a
n
d
th
e
r
est
is
f
ed
to
th
e
g
r
id
d
ir
ec
tl
y
f
r
o
m
t
h
e
s
ta
to
r
[
3
]
-
[
5
]
.
Usu
al
l
y
,
DFI
G
is
co
n
tr
o
lled
u
s
in
g
v
ec
to
r
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n
tr
o
l
s
tr
ate
g
y
,
w
h
ic
h
i
s
eit
h
er
s
tato
r
v
o
l
ta
g
e
o
r
ien
ted
,
o
r
s
tato
r
f
l
u
x
o
r
ie
n
ted
.
T
h
is
s
ch
e
m
e
d
ec
o
u
p
les
n
o
n
li
n
ea
r
Mu
ltip
le
I
n
p
u
t
M
u
ltip
le
O
u
tp
u
t
(
MI
MO
)
s
y
s
te
m
o
f
DFI
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in
to
t
w
o
lin
ea
r
S
in
g
le
I
n
p
u
t
Si
n
g
le
Ou
tp
u
t
(
SISO)
s
u
b
s
y
s
te
m
s
r
ep
r
esen
t
in
g
d
ir
ec
t
an
d
q
u
ad
r
ate
r
o
to
r
cu
r
r
en
ts
s
ep
ar
atel
y
[
6
]
-
[
8
]
.
T
h
e
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
co
n
tr
o
l
o
f
DFI
G
is
atta
in
ed
b
y
co
n
tr
o
lli
n
g
t
h
ese
t
w
o
lin
ea
r
f
ir
s
t o
r
d
er
SISO
s
u
b
s
y
s
te
m
s
w
i
th
t
w
o
P
I
co
n
tr
o
ll
er
s
.
T
h
e
d
r
a
w
b
ac
k
o
f
th
e
v
ec
t
o
r
co
n
tr
o
l stra
teg
y
is
th
at
t
h
e
s
y
s
te
m
p
er
f
o
r
m
an
ce
d
ep
en
d
s
o
n
t
h
e
D
FIG
p
ar
a
m
e
ter
s
,
esp
ec
iall
y
t
h
e
r
o
to
r
r
esis
t
an
ce
[
6
]
,
[
7
]
.
T
h
u
s
,
th
e
p
er
f
o
r
m
an
ce
d
e
g
r
ad
es
w
h
en
t
h
e
p
ar
a
m
eter
s
o
f
DFI
G
u
s
ed
in
t
h
e
co
n
tr
o
l
s
y
s
te
m
d
es
ig
n
ar
e
alter
ed
d
u
e
to
te
m
p
er
atu
r
e
v
ar
iat
io
n
,
s
at
u
r
ati
o
n
,
etc.
T
o
s
o
lv
e
th
is
p
r
o
b
le
m
,
w
e
h
av
e
r
ep
lace
d
th
e
co
n
v
e
n
tio
n
a
l
p
r
o
p
o
r
tio
n
al
in
te
g
r
al
co
n
tr
o
ller
w
i
th
a
f
r
ac
tio
n
al
o
r
d
er
p
r
o
p
o
r
tio
n
al
in
te
g
r
al
o
n
e
w
h
ich
i
s
a
g
e
n
er
aliza
tio
n
o
f
t
h
e
f
o
r
m
er
[
9
]
,
[
1
0
]
.
T
h
e
f
r
ac
tio
n
al
o
r
d
er
PI
co
n
t
r
o
ller
h
as
a
p
o
te
n
tial
to
i
n
cr
ea
s
e
s
y
s
te
m
r
o
b
u
s
tn
es
s
a
n
d
i
m
p
r
o
v
e
t
h
e
s
y
s
te
m
p
er
f
o
r
m
a
n
ce
w
it
h
th
e
ad
d
itio
n
al
p
ar
a
m
eter
λ
,
w
h
ich
is
t
h
e
f
r
ac
t
io
n
al
o
r
d
er
o
f
th
e
in
teg
r
at
io
n
ac
tio
n
[
1
1
]
,
[
1
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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P
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w
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&
Dr
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R
o
b
u
s
t Co
n
tr
o
l o
f D
o
u
b
ly
F
ed
I
n
d
u
ctio
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Gen
era
to
r
Usi
n
g
F
r
a
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n
a
l O
r
d
er C
o
n
tr
o
l (
A
b
d
ela
z
iz
A
z
z
a
)
1073
I
n
th
is
w
o
r
k
,
o
u
r
co
n
tr
ib
u
tio
n
to
DFI
G
r
o
b
u
s
t
co
n
tr
o
l
is
th
e
u
s
e
o
f
a
s
i
m
p
le
an
d
p
r
ac
tical
f
r
ac
tio
n
al
o
r
d
er
PI
co
n
tr
o
ller
,
w
h
ic
h
lea
d
s
to
g
o
o
d
d
y
n
a
m
ic
p
er
f
o
r
m
a
n
ce
a
n
d
r
o
b
u
s
t
n
es
s
o
f
DFI
G
i
n
b
o
th
h
ea
l
th
y
a
n
d
cr
itical
co
n
d
itio
n
s
.
I
n
s
ec
tio
n
2
,
w
e
i
n
tr
o
d
u
ce
a
b
r
ief
d
escr
ip
tio
n
o
f
th
e
w
i
n
d
en
er
g
y
co
n
v
er
s
io
n
s
y
s
te
m
to
b
e
s
tu
d
ied
.
T
h
en
,
th
e
co
n
s
tr
u
ctio
n
o
f
a
m
ath
e
m
atica
l
m
o
d
el
f
o
r
ea
ch
c
o
m
p
o
n
en
t
(
DFI
G
a
n
d
w
in
d
t
u
r
b
in
e)
o
f
th
e
w
i
n
d
s
y
s
te
m
i
s
p
r
esen
ted
i
n
s
ec
tio
n
3
.
Nex
t,
th
e
co
n
tr
o
l
s
tr
ate
g
y
i
s
d
ev
elo
p
ed
in
s
ec
tio
n
4
.
T
h
e
d
esig
n
o
f
f
r
ac
tio
n
al
o
r
d
er
P
I
c
o
n
tr
o
ller
is
estab
lis
h
ed
in
s
ec
tio
n
5
f
o
llo
w
ed
b
y
th
e
s
i
m
u
latio
n
r
es
u
lts
a
n
d
d
is
cu
s
s
io
n
i
n
Sec
tio
n
6
.
Fin
all
y
,
w
e
co
m
p
lete
t
h
i
s
w
o
r
k
w
it
h
a
co
n
clu
s
io
n
.
2.
SYST
E
M
DE
SCRI
P
T
I
O
N
T
h
e
W
E
C
S
to
b
e
s
tu
d
ied
is
p
r
esen
ted
in
Fig
u
r
e
1
.
T
h
is
s
y
s
te
m
co
n
s
is
t
s
o
f
a
w
i
n
d
tu
r
b
i
n
e
d
r
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in
g
a
DFI
G
t
h
r
o
u
g
h
a
g
ea
r
b
o
x
.
T
h
e
r
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to
r
is
co
n
n
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ted
th
r
o
u
g
h
t
w
o
co
n
v
er
ter
s
,
an
d
t
h
e
s
tat
o
r
o
f
th
e
DFI
G
i
s
d
ir
ec
tl
y
co
n
n
ec
ted
to
th
e
g
r
id
.
Fig
u
r
e
1
.
DFI
G
-
b
ased
W
E
C
S
s
tr
u
ct
u
r
e
3.
M
O
DE
L
I
N
G
O
F
T
H
E
SYS
T
E
M
3
.
1
.
Wind
t
urbin
e
m
o
del
I
n
W
E
C
S,
d
u
e
to
t
h
e
d
i
f
f
er
e
n
t
lo
s
s
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t
h
e
e
x
tr
ac
ted
p
o
w
er
a
v
ailab
le
o
n
t
h
e
r
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to
r
o
f
th
e
w
i
n
d
tu
r
b
in
e
ca
n
b
e
ex
p
r
ess
ed
as
[
1
3
]
,
[
1
4
]
:
=
1
2
(
,
)
3
(
1
)
w
h
er
e
is
t
h
e
t
u
r
b
in
e
p
o
w
er
,
is
th
e
p
o
w
er
co
ef
f
icie
n
t,
is
t
h
e
air
d
en
s
it
y
,
S
is
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e
s
w
ep
t
t
u
r
b
in
e
ar
ea
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n
d
is
th
e
w
i
n
d
s
p
ee
d
.
T
h
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p
o
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er
co
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f
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is
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n
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l
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d
b
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itch
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n
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d
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tip
-
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p
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atio
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TSR
=
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w
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u
r
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r
ad
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d
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r
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.
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h
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w
in
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e
m
o
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el
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s
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o
w
n
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Fi
g
u
r
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2
,
w
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er
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is
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e
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p
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ain
o
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th
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th
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ae
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y
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m
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q
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e,
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th
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tp
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tial
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v
is
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u
s
f
r
ict
io
n
co
ef
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icien
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o
f
th
e
r
o
to
r
,
an
d
Ω
is
th
e
r
o
to
r
s
p
ee
d
.
3.
2
.
DF
I
G
m
o
de
l
T
h
e
s
tato
r
an
d
r
o
to
r
eq
u
atio
n
s
o
f
th
e
DFI
G
m
ac
h
i
n
e
ar
e
d
er
iv
ed
f
r
o
m
P
ar
k
r
ef
er
en
ce
f
r
a
m
e
r
o
tatin
g
at
s
y
n
ch
r
o
n
o
u
s
s
p
ee
d
[
1
5
]
,
[
1
6
]
,
an
d
ca
n
b
e
d
escr
ib
ed
b
y
:
T
h
e
s
tato
r
an
d
r
o
to
r
v
o
ltag
e
e
q
u
atio
n
s
:
=
+
−
(
2
)
=
+
+
(
3
)
=
+
−
(
−
)
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
0
7
2
–
1
0
8
0
1074
=
+
+
(
−
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(
5
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w
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d
ar
e
th
e
d
ir
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t
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ad
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ir
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m
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e
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ir
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ad
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t
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A
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,
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d
ar
e
th
e
s
tato
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d
r
o
to
r
r
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ce
s
(
Ω
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d
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d
ar
e
th
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s
tato
r
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d
r
o
to
r
p
u
ls
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s
(
r
ad
/s
)
.
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h
e
s
tato
r
an
d
r
o
to
r
f
lu
x
eq
u
at
io
n
s
:
=
+
(
6
)
=
+
(
7
)
=
+
(
8
)
=
+
(
9
)
w
h
er
e
an
d
ar
e
th
e
d
ir
ec
t
an
d
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u
ad
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ate
co
m
p
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e
n
ts
o
f
s
tato
r
f
lu
x
(
w
b
)
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d
ar
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th
e
d
ir
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n
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ad
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o
m
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e
n
t
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o
f
r
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to
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f
l
u
x
(
w
b
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,
is
th
e
m
u
t
u
al
i
n
d
u
ctan
ce
(
H)
an
d
an
d
ar
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th
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s
tato
r
an
d
r
o
to
r
in
d
u
ctan
ce
s
(
H)
.
T
h
e
elec
tr
o
m
a
g
n
et
ic
to
r
q
u
e
eq
u
atio
n
i
s
g
i
v
e
n
b
y
:
=
(
−
)
(
1
0
)
w
h
er
e
is
t
h
e
n
u
m
b
er
o
f
p
o
le
p
air
s
.
4.
CO
NT
RO
L
ST
R
AT
E
G
Y
4
.
1
.
Wind
t
urbin
e
co
ntr
o
l
I
n
o
r
d
er
to
ex
tr
ac
t
m
a
x
i
m
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m
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m
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w
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d
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w
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ap
p
l
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h
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Ma
x
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m
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m
P
o
w
er
P
o
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t
T
r
ac
k
in
g
b
ased
o
n
th
e
r
o
to
r
s
p
ee
d
co
n
tr
o
l.
T
h
e
tip
-
s
p
ee
d
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atio
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t
u
n
e
d
to
o
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er
d
if
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er
en
t
w
i
n
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s
p
ee
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s
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b
y
ad
ap
tin
g
t
h
e
r
o
to
r
s
p
ee
d
to
_
=
(
_
)
/
[
1
7
]
.
T
h
e
MPPT
s
ch
e
m
e
is
s
h
o
wn
in
Fig
u
r
e
2
.
Fig
u
r
e
2
. M
P
PT
b
ased
o
n
r
o
to
r
s
p
ee
d
co
n
tr
o
l
4
.
2
.
DF
I
G
co
ntr
o
l
W
e
ap
p
ly
v
ec
to
r
co
n
tr
o
l
s
tr
ateg
y
to
t
h
e
DFI
G,
w
h
ic
h
d
ec
o
u
p
les
th
e
DFI
G
m
o
d
el
in
to
t
wo
in
d
ep
en
d
en
t
s
u
b
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y
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te
m
s
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f
f
l
u
x
a
n
d
to
r
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u
e,
in
o
r
d
er
to
g
et
th
e
p
er
f
o
r
m
an
ce
s
i
m
i
lar
to
DC
m
o
to
r
s
p
ee
d
co
n
tr
o
l
[
1
8
]
.
T
h
u
s
,
t
h
e
s
tato
r
f
lu
x
is
ch
o
s
en
to
b
e
o
r
ien
ted
to
d
ir
ec
t a
x
is
i
n
th
e
p
ar
k
r
e
f
er
en
c
e
f
r
a
m
e
(
=
an
d
=
0
)
,
an
d
b
y
n
eg
lec
tin
g
s
ta
to
r
r
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tan
ce
,
an
d
b
ec
o
m
e:
=
0
an
d
=
=
.
C
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n
s
e
q
u
en
tl
y
,
th
e
elec
tr
o
m
a
g
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to
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q
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(
_
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an
d
th
e
ac
ti
v
e
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d
r
ea
ctiv
e
s
tato
r
p
o
w
er
s
(
,
)
b
ec
o
m
e:
=
−
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
R
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b
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s
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n
tr
o
l o
f D
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b
ly
F
ed
I
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d
u
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Gen
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Usi
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A
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1075
=
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=
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1
3
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A
l
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r
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r
v
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ltag
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a
n
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e
ex
p
r
ess
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as:
=
+
(
−
2
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−
(
−
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(
1
4
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=
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(
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1
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w
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er
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t
h
e
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f
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T
h
e
p
r
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p
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ed
c
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tr
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l p
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f
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ased
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n
t
w
o
FOP
I
co
n
t
r
o
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s
h
o
w
n
in
Fig
u
r
e
3
.
Fig
u
r
e
3
.
T
h
e
co
n
tr
o
l sch
e
m
e
o
f
DFI
G
w
it
h
FOP
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co
n
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s
5.
F
RACTI
O
N
AL
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R
P
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CO
NT
RO
L
L
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R
T
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NIN
G
P
RO
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DUR
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I
n
th
e
p
r
ev
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s
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tio
n
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e
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e
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f
o
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m
o
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a
n
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er
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n
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tio
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t
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p
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w
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s
:
(
)
=
+
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(
1
6
)
w
h
er
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T
an
d
K
ar
e
co
n
s
tan
ts
.
I
n
t
h
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t
w
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e
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t
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p
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ed
:
th
e
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teg
er
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r
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er
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d
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Fra
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Or
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tr
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s
f
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e
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as f
o
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s
:
(
)
=
(
1
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1
7
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(
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=
(
1
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1
8
)
w
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e
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an
d
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∈
[
0
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.
5
.
1
.
Desig
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n
[
1
9
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[
2
0
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,
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ch
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eq
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a
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r
th
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n
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ain
ts
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e
co
n
s
id
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ed
:
[
1
9
]
,
[
2
0
]
a)
P
h
ase
m
ar
g
in
co
n
s
tr
ai
n
t:
[
(
)
]
=
[
(
)
(
)
]
=
∠
(
)
+
∠
(
)
=
−
+
(
1
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
0
7
2
–
1
0
8
0
1076
w
h
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e
G(
j
ω
)
is
th
e
o
p
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lo
o
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tr
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s
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Gain
c
r
o
s
s
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o
v
er
f
r
eq
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en
c
y
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n
s
tr
ai
n
t:
|
(
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|
=
|
(
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(
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=
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(
2
0
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c)
R
o
b
u
s
t
n
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s
to
lo
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,
w
h
ich
d
e
m
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d
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th
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B
o
d
e
p
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t
to
b
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f
lat
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t
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g
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n
cr
o
s
s
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v
er
f
r
eq
u
e
n
c
y
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,
i.e
.
,
th
e
d
er
iv
ativ
e
o
f
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h
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o
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p
p
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ase,
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t
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ased
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Or
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FOP
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n
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o
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h
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n
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ller
ca
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ex
p
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2
3
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p
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o
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f
r
eq
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n
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y
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,
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d
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ir
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t d
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n
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n
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ce
,
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r
elatio
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s
h
ip
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et
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en
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d
ca
n
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e
estab
lis
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ed
as,
=
−
[
(
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(
2
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2
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[
(
)
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An
d
th
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o
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cr
o
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r
eq
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en
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ai
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r
d
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g
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th
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t
h
ir
d
co
n
s
tr
ai
n
t (
c)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
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8
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694
R
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o
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ar
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il
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if
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er
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ap
p
r
o
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h
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r
tu
n
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n
g
th
e
FOP
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co
n
tr
o
ller
an
d
class
ical
P
I
co
n
tr
o
ller
f
o
r
th
e
r
o
to
r
cu
r
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en
t
co
n
tr
o
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lo
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p
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s
a
m
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-
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er
f
r
eq
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p
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r
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ase
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ar
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6.
RE
SU
L
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S AN
D
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to
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t
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s
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m
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h
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f
ir
s
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et
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r
ied
o
u
t
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n
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is
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lated
DFI
G
cu
r
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n
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ess
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ased
W
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to
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ted
in
T
ab
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1
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ab
le
1
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d
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s
e
1
:
T
h
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is
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lated
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(
w
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t W
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C
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cu
r
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t c
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tr
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l lo
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p
T
h
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w
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t
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c
lass
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co
n
tr
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o
f
th
e
D
FIG
cu
r
r
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n
t
co
n
tr
o
l
lo
o
p
.
Un
d
er
f
o
u
r
d
if
f
er
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t
s
p
ec
if
ica
tio
n
s
,
i.e
.
th
e
s
et
-
p
o
in
t
r
e
f
er
en
ce
,
th
e
r
o
b
u
s
t
n
es
s
,
th
e
d
is
t
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r
b
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ce
r
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tio
n
an
d
th
e
n
o
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e
m
in
i
m
izatio
n
.
Fig
u
r
e
4
s
h
o
w
s
t
h
e
u
n
it
s
tep
r
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n
s
es
o
f
t
h
e
D
FIG
c
u
r
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en
t
co
n
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o
l
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p
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it
h
t
h
e
F
OP
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co
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tr
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ller
as
s
h
o
w
n
i
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Fi
g
u
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4
(a
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,
an
d
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lass
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I
co
n
tr
o
ller
as
s
h
o
w
n
in
F
ig
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r
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4
(b
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.
T
h
e
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it
s
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r
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ar
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w
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ai
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(
)
:
1
,
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1
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d
0
.
5
1
.
I
t
is
clea
r
t
h
at
t
h
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F
OP
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n
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o
ller
ex
h
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it
s
a
g
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o
d
r
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ce
tr
a
ck
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g
a
n
d
,
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n
co
n
tr
ar
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to
t
h
e
class
ica
l
P
I
co
n
tr
o
ller
,
its
o
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er
s
h
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o
ts
w
er
e
n
o
t
af
f
ec
ted
b
y
th
e
d
i
f
f
er
e
n
t
g
ain
s
.
T
h
er
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o
r
e,
th
e
co
n
tr
o
lled
s
y
s
te
m
u
s
i
n
g
th
e
f
r
ac
tio
n
al
co
n
tr
o
ller
r
em
ai
n
s
r
o
b
u
s
t
o
v
er
g
ain
c
h
a
n
g
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
0
7
2
–
1
0
8
0
1078
Fig
u
r
e
4
.
Step
cu
r
r
en
t r
esp
o
n
s
es: (
a)
w
it
h
FOP
I
co
n
tr
o
ller
,
(
b
)
w
ith
cla
s
s
ica
l P
I
co
n
tr
o
ller
T
h
e
u
n
it
s
tep
r
esp
o
n
s
e
s
o
f
D
FIG
cu
r
r
en
t
co
n
tr
o
l
lo
o
p
w
ith
th
e
FOP
I
co
n
tr
o
ller
an
d
th
e
class
ical
P
I
co
n
tr
o
ller
ar
e
d
ep
icted
in
F
ig
u
r
e
5
.
A
d
is
t
u
r
b
an
ce
o
f
0
.
5
is
ap
p
lied
o
n
th
e
o
u
tp
u
t
o
f
th
e
p
lan
t
f
r
o
m
=
0
.
2
o
n
,
an
d
a
m
ea
s
u
r
e
m
e
n
t
n
o
is
e
w
it
h
Gau
s
s
ia
n
d
i
s
tr
ib
u
ted
r
a
n
d
o
m
s
i
g
n
a
l
w
it
h
ze
r
o
m
ea
n
a
n
d
0
.
1
v
ar
ian
ce
v
al
u
e
is
ass
u
m
ed
in
t
h
e
o
u
tp
u
t
o
f
t
h
e
p
lan
t
f
r
o
m
=
0
.
4
o
n
.
B
y
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m
p
ar
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n
g
t
h
e
t
w
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tan
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u
p
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n
.
RE
F
E
R
E
NC
E
S
[1
]
Ya
n
g
B,
Yu
T
,
S
h
u
H,
e
t
a
l.
Ro
b
u
st
slid
in
g
-
m
o
d
e
c
o
n
tro
l
o
f
w
in
d
e
n
e
rg
y
c
o
n
v
e
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n
s
y
ste
m
s
f
o
r
o
p
ti
m
a
l
p
o
w
e
r
e
x
trac
ti
o
n
v
ia n
o
n
li
n
e
a
r
p
e
rt
u
rb
a
ti
o
n
o
b
se
rv
e
rs.
Ap
p
l
E
n
e
rg
y
2
0
1
8
;
2
1
0
:
7
1
1
-
7
2
3
.
[2
]
A
b
d
e
l
m
a
lk
i
F
,
Ou
a
a
li
n
e
N.
T
-
S
F
u
z
z
y
o
b
se
rv
e
r
a
n
d
c
o
n
tr
o
ll
e
r
o
f
Do
u
b
ly
-
F
e
d
In
d
u
c
ti
o
n
G
e
n
e
ra
to
r.
In
t
e
rn
a
ti
o
n
a
l
J
o
u
rn
a
l
P
o
we
r E
lec
tro
n
Dr
ive
S
y
st
em
(
IJ
PE
DS
)
2
0
1
6
;
7
:
6
1
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
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8
8
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8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
0
7
2
–
1
0
8
0
1080
[3
]
Ba
b
u
NR,
A
ru
lm
o
z
h
iv
a
r
m
a
n
P
.
W
in
d
e
n
e
rg
y
c
o
n
v
e
rsio
n
sy
ste
m
s
-
a
tec
h
n
ica
l
re
v
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w
.
J
En
g
S
c
i
T
e
c
h
n
o
l
2
0
1
3
;
8
:
493
-
5
0
7
.
[4
]
L
ise
rre
M
,
Ca
rd
e
n
a
s
R,
M
o
li
n
a
s
M
,
e
t
a
l.
Ov
e
rv
ie
w
o
f
M
u
lt
i
-
M
W
W
in
d
T
u
rb
in
e
s
a
n
d
W
in
d
P
a
rk
s.
I
EE
E
T
ra
n
s
In
d
El
e
c
tro
n
2
0
1
1
;
5
8
:
1
0
8
1
-
1
0
9
5
.
[5
]
A
z
z
a
o
u
i
M
E,
M
a
h
m
o
u
d
i
H,
Bo
u
d
a
ra
ia
K.
Ba
c
k
ste
p
p
in
g
Co
n
tr
o
l
o
f
W
in
d
a
n
d
P
h
o
to
v
o
lt
a
ic
H
y
b
rid
Re
n
e
w
a
b
le
En
e
rg
y
S
y
ste
m
.
In
t
e
rn
a
ti
o
n
a
l
J
o
u
rn
a
l
P
o
we
r E
lec
tro
n
Dr
ive
S
y
st
em
(
IJ
PE
DS
)
2
0
1
6
;
7
:
6
7
7
-
6
8
7
.
[6
]
T
a
v
e
iro
s
F
EV
,
Ba
rro
s
L
S
,
Co
sta
F
B.
Ba
c
k
-
to
-
b
a
c
k
c
o
n
v
e
rter
sta
t
e
-
f
e
e
d
b
a
c
k
c
o
n
tro
l
o
f
DFI
G
(d
o
u
b
l
y
-
fe
d
in
d
u
c
ti
o
n
g
e
n
e
ra
to
r)
-
b
a
se
d
w
in
d
tu
r
b
in
e
s.
E
n
e
rg
y
2
0
1
5
;
8
9
:
8
9
6
-
9
0
6
.
[7
]
Zh
i
D,
Xu
L
,
M
o
rro
w
J.
Imp
ro
v
e
d
Dire
c
t
Po
we
r
Co
n
tro
l
o
f
Do
u
b
l
y
-
Fed
In
d
u
c
t
io
n
Ge
n
e
ra
to
r
Ba
se
d
W
in
d
E
n
e
rg
y
S
y
ste
m
.
In
:
2
0
0
7
I
EE
E
I
n
tern
a
ti
o
n
a
l
El
e
c
tri
c
M
a
c
h
i
n
e
s Driv
e
s Co
n
f
e
r
e
n
c
e
.
2
0
0
7
,
p
p
.
4
3
6
-
4
4
1
.
[8
]
P
e
n
a
R,
Clare
JC,
A
sh
e
r
G
M
.
Do
u
b
ly
f
e
d
in
d
u
c
ti
o
n
g
e
n
e
ra
to
r
u
sin
g
b
a
c
k
-
to
-
b
a
c
k
P
W
M
c
o
n
v
e
rters
a
n
d
it
s
a
p
p
li
c
a
ti
o
n
t
o
v
a
riab
le
-
sp
e
e
d
w
in
d
-
e
n
e
rg
y
g
e
n
e
ra
ti
o
n
.
IEE
Pr
o
c
-
El
e
c
tr P
o
we
r A
p
p
l
1
9
9
6
;
1
4
3
:
2
3
1
-
241
.
[9
]
Bo
u
d
jeh
e
m
B,
Bo
u
d
jeh
e
m
D.
P
a
ra
m
e
ter
T
u
n
in
g
o
f
a
F
ra
c
ti
o
n
a
l
-
Ord
e
r
P
I
C
o
n
tr
o
ll
e
r
Us
in
g
th
e
IT
A
E
Crit
e
ria.
In
:
Ba
lea
n
u
D,
M
a
c
h
a
d
o
JA
T
,
L
u
o
A
CJ
(e
d
s)
Fra
c
ti
o
n
a
l
Dy
n
a
mic
s
a
n
d
Co
n
tro
l
.
Ne
w
Yo
rk
,
NY
:
S
p
rin
g
e
r
Ne
w
Yo
rk
,
p
p
.
4
9
-
57
.
[1
0
]
P
o
d
l
u
b
n
y
I.
F
ra
c
ti
o
n
a
l
-
o
rd
e
r
sy
st
e
m
s a
n
d
P
I
λ
D
µ
-
c
o
n
tr
o
ll
e
rs.
IE
EE
T
ra
n
s A
u
to
m
Co
n
tro
l
1
9
9
9
;
4
4
:
2
0
8
-
2
1
4
.
[1
1
]
Jia
c
a
i
H,
Ho
n
g
sh
e
n
g
L
,
F
u
li
n
T
,
e
t
a
l.
F
ra
c
ti
o
n
a
l
o
rd
e
r
slid
i
n
g
m
o
d
e
c
o
n
tro
l
ler
f
o
r
th
e
sp
e
e
d
c
o
n
tro
l
o
f
a
p
e
r
m
a
n
e
n
t
m
a
g
n
e
t
s
y
n
c
h
ro
n
o
u
s
m
o
to
r.
In
:
Co
n
tro
l
a
n
d
De
c
isio
n
Co
n
fer
e
n
c
e
(
CCDC
),
2
0
1
2
2
4
t
h
Ch
i
n
e
se
.
IEE
E,
2
0
1
2
,
p
p
.
1
2
0
3
-
1
2
0
8
.
[1
2
]
Ou
sta
lo
u
p
A
,
S
a
b
a
ti
e
r
J,
L
a
n
u
ss
e
P
.
F
r
o
m
f
r
a
c
tal
ro
b
u
stn
e
ss
to
th
e
CRON
E
c
o
n
tro
l.
FCA
A
1
9
9
9
;
2
:
1
-
30
.
[1
3
]
He
ier
S
.
Gr
id
in
teg
ra
ti
o
n
o
f
win
d
e
n
e
rg
y
:
o
n
sh
o
re
a
n
d
o
ff
sh
o
re
c
o
n
v
e
rs
io
n
sy
ste
ms
.
T
h
ird
e
d
it
o
n
.
Ch
ich
e
ste
r,
W
e
st
S
u
ss
e
x
,
Un
it
e
d
Ki
n
g
d
o
m
:
W
il
e
y
,
2
0
1
4
.
[1
4
]
Zara
g
o
z
a
J,
P
o
u
J,
A
rias
A
,
e
t
a
l.
S
tu
d
y
a
n
d
e
x
p
e
ri
m
e
n
tal
v
e
ri
f
i
c
a
ti
o
n
o
f
c
o
n
tro
l
t
u
n
i
n
g
stra
teg
ie
s
in
a
v
a
ri
a
b
le
sp
e
e
d
w
in
d
e
n
e
rg
y
c
o
n
v
e
rsio
n
s
y
ste
m
.
Ren
e
w
En
e
rg
y
2
0
1
1
;
3
6
:
1
4
2
1
-
1
4
3
0
.
[1
5
]
A
lt
u
n
H,
S
ü
n
ter
S
.
M
o
d
e
li
n
g
,
si
m
u
latio
n
a
n
d
c
o
n
tro
l
o
f
w
in
d
tu
rb
in
e
d
riv
e
n
d
o
u
b
ly
-
f
e
d
in
d
u
c
ti
o
n
g
e
n
e
ra
to
r
w
it
h
m
a
tri
x
c
o
n
v
e
rt
e
r
o
n
th
e
r
o
t
o
r
sid
e
.
El
e
c
tr E
n
g
2
0
1
3
;
9
5
:
1
5
7
-
1
7
0
.
[1
6
]
Bh
a
rti
OP,
S
a
k
e
t
RK,
N
a
g
a
r
S
K.
Co
n
tro
ll
e
r
d
e
sig
n
f
o
r
d
o
u
b
ly
fe
d
in
d
u
c
ti
o
n
g
e
n
e
ra
to
r
u
sin
g
p
a
rti
c
le
s
w
a
r
m
o
p
ti
m
iza
ti
o
n
tec
h
n
iq
u
e
.
Ren
e
w
E
n
e
rg
y
2
0
1
7
;
1
1
4
:
1
3
9
4
-
1
4
0
6
.
[1
7
]
Bo
u
k
h
e
z
z
a
r
B,
S
ig
u
e
rd
id
jan
e
H.
No
n
li
n
e
a
r
c
o
n
tro
l
w
it
h
w
in
d
e
sti
m
a
ti
o
n
o
f
a
DFIG
v
a
riab
le
sp
e
e
d
w
in
d
tu
rb
in
e
f
o
r
p
o
w
e
r
c
a
p
tu
re
o
p
ti
m
iza
ti
o
n
.
En
e
r
g
y
Co
n
v
e
rs
M
a
n
a
g
2
0
0
9
;
5
0
:
8
8
5
-
8
9
2
.
[1
8
]
F
a
n
L
,
M
iao
Z.
M
o
d
e
li
n
g
a
n
d
a
n
a
lys
is
o
f
d
o
u
b
ly
fed
i
n
d
u
c
ti
o
n
g
e
n
e
ra
t
o
r
win
d
e
n
e
rg
y
sy
ste
ms
.
Ne
w
Yo
rk
:
A
c
a
d
e
m
ic P
re
ss
,
2
0
1
5
.
[1
9
]
L
u
o
Y,
Ch
e
n
YQ
,
W
a
n
g
CY,
e
t
a
l.
T
u
n
in
g
f
ra
c
ti
o
n
a
l
o
rd
e
r
p
ro
p
o
rti
o
n
a
l
i
n
teg
ra
l
c
o
n
tro
ll
e
rs
f
o
r
fra
c
ti
o
n
a
l
o
r
d
e
r
s
y
ste
m
s.
J
Pro
c
e
ss
Co
n
tro
l
2
0
1
0
;
2
0
:
8
2
3
-
8
3
1
.
[2
0
]
L
i
H,
L
u
o
Y,
Ch
e
n
Y.
A
f
r
a
c
ti
o
n
a
l
o
rd
e
r
p
ro
p
o
rt
io
n
a
l
a
n
d
d
e
riv
a
ti
v
e
(F
OP
D)
m
o
ti
o
n
c
o
n
tr
o
ll
e
r:
tu
n
i
n
g
ru
le
a
n
d
e
x
p
e
ri
m
e
n
ts.
IEE
E
T
ra
n
s Co
n
tro
l
S
y
st T
e
c
h
n
o
l
2
0
1
0
;
1
8
:
5
1
6
-
5
2
0
.
[2
1
]
A
tt
o
u
i
I,
Om
e
iri
A
.
M
o
d
e
li
n
g
,
c
o
n
tro
l
a
n
d
f
a
u
lt
d
iag
n
o
sis
o
f
a
n
is
o
late
d
w
in
d
e
n
e
rg
y
c
o
n
v
e
rsio
n
sy
s
tem
w
it
h
a
se
lf
-
e
x
c
it
e
d
in
d
u
c
ti
o
n
g
e
n
e
ra
to
r
su
b
jec
t
to
e
lec
tri
c
a
l
f
a
u
lt
s.
En
e
rg
y
Co
n
v
e
rs
M
a
n
a
g
2
0
1
4
;
8
2
:
1
1
-
26
.
[2
2
]
M
irec
k
i
A
,
Ro
b
o
a
m
X
,
Rich
a
rd
e
a
u
F
.
A
rc
h
it
e
c
tu
re
Co
m
p
lex
it
y
a
n
d
E
n
e
rg
y
E
ff
icie
n
c
y
o
f
S
m
a
ll
W
in
d
T
u
rb
in
e
s.
IEE
E
T
ra
n
s In
d
E
lec
tro
n
2
0
0
7
;
5
4
:
6
6
0
-
6
7
0
.
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