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J
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Vo
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Dec
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1731
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J
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C
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1.
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ca
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tr
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co
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ter
s
.
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n
th
is
w
o
r
k
,
t
h
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w
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n
d
tu
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b
in
e
w
i
ll
b
e
ex
p
lo
ited
at
th
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m
a
x
i
m
u
m
p
o
w
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p
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tin
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p
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in
t
(
MP
PT)
f
o
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v
ar
io
u
s
w
i
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d
s
p
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ed
s
b
y
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ti
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n
tr
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llin
g
t
h
e
s
p
ee
d
o
f
t
h
e
s
h
a
f
t
[
1
]
.
I
n
co
n
tr
ast,
r
eg
u
lat
in
g
th
e
r
o
to
r
f
lu
x
n
ee
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th
e
s
tate
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to
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tr
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lled
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f
th
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to
r
f
lu
x
is
a
n
ec
es
s
it
y
[
2
]
-
[
3
]
-
[
4
]
.
Hen
ce
;
t
h
e
u
s
e
o
f
a
p
h
y
s
ica
l
s
en
s
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tr
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ce
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lo
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f
p
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h
e
n
t
h
e
s
p
ee
d
is
esti
m
ated
f
r
o
m
f
lu
x
[
5
]
–
[
6
]
.
I
n
d
ee
d
;
d
if
f
er
e
n
t
m
o
d
els
h
a
v
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ex
a
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p
le
s
tatis
tical
m
o
d
els
(
e.
g
.
[
7
]
)
.
T
h
e
p
r
o
p
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ed
esti
m
a
to
r
s
g
en
er
all
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e,
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th
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Ob
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ased
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w
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th
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n
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alan
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k
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al
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D
FIG
w
h
e
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th
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s
tato
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is
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ir
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t
l
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ted
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th
e
g
r
id
as
i
n
o
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r
ca
s
e
s
t
u
d
y
[
8
]
.
I
n
t
h
is
s
en
s
e,
an
d
d
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e
to
th
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s
tr
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to
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tr
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m
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s
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as so
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m
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er
v
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et
w
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r
k
d
is
t
u
r
b
an
ce
s
[
9
]
-
[
1
0
]
-
[
1
1
]
.
W
ith
th
e
in
cr
e
asin
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s
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w
in
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p
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w
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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8
8
-
8
694
IJ
PEDS
Vo
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8
,
No
.
4
,
Dec
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b
er
2
0
1
7
:
1
7
2
3
–
1
7
3
1
1724
f
av
o
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s
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w
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w
in
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in
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id
[
9
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[
1
2
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-
[
1
3
]
.
I
n
[
1
4
]
-
[
1
5
]
th
e
P
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n
ch
r
o
n
o
u
s
r
ef
er
e
n
ce
f
r
a
m
e
ca
n
d
ir
ec
tl
y
r
eg
u
late
b
o
th
p
o
s
itiv
e
an
d
n
eg
ati
v
e
s
eq
u
en
ce
c
o
m
p
o
n
en
t
s
w
it
h
o
u
t
in
v
o
l
v
i
n
g
s
eq
u
e
n
tia
l
d
ec
o
m
p
o
s
itio
n
[
1
6
]
.
Mo
r
eo
v
er
,
s
o
m
e
s
tr
ateg
ies
s
u
c
h
as
DP
C
b
ased
o
n
p
o
w
er
d
ef
i
n
it
io
n
co
n
n
ec
ted
to
u
n
b
alan
ce
d
g
r
i
d
v
o
ltag
e
ar
e
p
r
o
p
o
s
ed
w
it
h
r
ed
u
ce
d
d
o
u
b
le
g
r
id
f
r
eq
u
e
n
c
y
o
s
cillat
io
n
s
o
f
elec
tr
o
m
ag
n
etic
to
r
q
u
e
[
1
7
]
-
[
1
8
]
,
b
u
t
d
esp
ite
th
e
s
i
m
p
licit
y
o
f
t
h
ese
co
n
tr
o
ller
s
,
t
h
e
y
ar
e
n
o
t
en
o
u
g
h
at
t
h
e
p
o
in
t o
f
p
r
ec
is
io
n
.
I
n
th
i
s
w
o
r
k
,
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
w
i
n
d
in
te
g
r
atio
n
u
n
d
er
u
n
b
ala
n
ce
d
g
r
id
h
as
b
ee
n
en
h
an
ce
d
b
y
th
e
eli
m
in
at
io
n
o
f
o
s
cillatio
n
s
in
d
u
ec
ed
b
y
t
h
e
as
y
m
m
e
tr
ic
v
o
ltag
e,
b
ased
o
n
r
o
to
r
f
lu
x
s
lid
i
n
g
m
o
d
e
o
b
s
er
v
er
.
T
h
e
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
t
h
e
w
in
d
t
u
r
b
in
e
m
o
d
elin
g
u
n
d
er
u
n
b
ala
n
ce
d
g
r
id
v
o
ltag
e
is
p
r
esen
ted
in
s
ec
tio
n
2
.
Sect
io
n
3
is
d
ev
o
ted
to
d
esi
g
n
o
f
t
h
e
r
o
to
r
f
lu
x
s
lid
i
n
g
m
o
d
e
o
b
s
er
v
er
an
d
co
n
tr
o
ller
s
’
la
w
s
.
T
h
e
co
n
tr
o
l
p
er
f
o
r
m
a
n
c
e
is
s
h
o
w
n
b
y
s
i
m
u
latio
n
i
n
S
ec
tio
n
4
,
a
co
n
cl
u
s
io
n
a
n
d
r
ef
er
en
ce
lis
t
en
d
th
e
p
ap
er
2.
WI
ND
T
URB
I
N
E
M
O
DE
L
UNDER U
NB
AL
ANC
E
D
G
RID
2
.
1
.
T
urbi
ne
m
o
del
T
h
e
tu
r
b
in
e
m
o
d
el
is
i
n
s
p
ir
ed
f
r
o
m
[
1
]
.
T
h
e
av
ailab
le
ae
r
o
d
y
n
a
m
ic
w
in
d
p
o
w
er
i
s
g
i
v
e
n
b
y
:
P
aero
=
1
2
ρ
π
R
2
C
P
(
λ
,
β
)
v
w
3
(
1
)
W
h
er
e
β
is
a
b
lad
e
p
itch
an
g
le,
in
t
h
is
p
ap
er
,
β
is
h
eld
co
n
s
ta
n
t (
C
P
(
λ
,
β
)
≝
C
P
(
λ
)
)
,
C
P
(
λ
)
is
th
e
co
ef
f
icie
n
t o
f
p
er
f
o
r
m
an
ce
,
v
w
is
the
w
in
d
v
elo
cit
y
,
ρ
is
the
a
ir
d
en
s
it
y
,
R
is
t
h
e
r
ad
iu
s
o
f
t
h
e
w
i
n
d
tu
r
b
in
e
r
o
to
r
an
d
th
e
tip
s
p
ee
d
r
atio
λ
is
g
iv
e
n
b
y
λ
=
R
ω
t
v
w
(
2
)
2
.
2
.
Dy
na
m
ic
DF
I
G
m
o
del w
it
h iro
n lo
s
s
es
T
h
e
eq
u
iv
alen
t c
ir
cu
it o
f
a
D
F
I
G
is
in
s
p
ir
ed
f
r
o
m
th
e
p
r
o
p
o
s
ed
m
o
d
el
in
[
1
9
]
-
[
2
0
]
.
W
h
en
th
e
ir
o
n
lo
s
s
r
esis
ta
n
ce
R
m
is
co
n
n
ec
ted
i
n
p
ar
allel
w
ith
t
h
e
s
tato
r
in
d
u
cta
n
ce
(
L
s
σ
an
d
M)
.
T
h
e
ch
o
ice
o
f
th
i
s
m
o
d
el
is
j
u
s
ti
f
ied
m
ai
n
l
y
b
y
t
h
e
s
i
m
p
licit
y
o
f
ca
lcu
lat
io
n
s
,
b
ec
au
s
e
w
e
w
i
ll h
a
v
e
a
s
i
m
ilar
cir
cu
i
t t
o
th
e
co
n
v
e
n
tio
n
al
m
o
d
el
(
w
ith
o
u
t i
r
o
n
lo
s
s
es)
u
s
i
n
g
t
h
e
v
en
i
n
’
s
t
h
eo
r
em
.
T
h
e
eq
u
iv
a
len
t c
ir
c
u
it
o
f
th
e
DFI
G
af
ter
ar
r
an
g
e
m
e
n
t is
s
h
o
w
n
in
Fig
u
r
e
1
.
I
n
ad
d
itio
n
,
th
e
R
m
r
esis
tan
ce
is
a
v
ar
iab
le
p
ar
am
eter
.
T
h
e
T
h
ev
en
i
n
’
s
eq
u
i
v
ale
n
ts
f
o
r
s
ta
to
r
r
esis
tan
ce
an
d
v
o
ltag
e
s
/c
u
r
r
en
ts
ar
e
ca
lcu
lated
i
n
th
e
s
tati
o
n
ar
y
,
α
-
β
r
ef
er
en
ce
f
r
a
m
e
as
f
o
l
lo
w
s
[
1
9
]
-
[
2
0
]
-
[
2
1
]
.
(
3
)
(
a)
(
b
)
Fig
u
r
e
1
.
DFI
G
eq
u
iv
ale
n
t c
ir
cu
it i
n
th
e
+
r
ef
er
en
ce
f
r
a
m
e:
(
a)
d
ir
ec
t a
x
is
,
(
b
)
q
u
ad
r
atu
r
e
a
x
is
[
1
9
]
+
-
+
+
+
+
+
L
r
σ
Lsσ
Rr
R
sT
+
+
(
−
)
+
M
+
-
+
-
+
-
+
-
-
+
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
Desig
n
o
f a
n
I
m
p
r
o
ve
d
MPP
T C
o
n
tr
o
l o
f D
F
I
G
W
in
d
Tu
r
b
i
n
e
u
n
d
er Un
b
a
la
n
ce
d
…
(
Yo
u
s
s
ef
Ma
jd
o
u
b
)
1725
T
h
e
m
o
d
el
co
n
s
id
er
ed
f
o
r
DFI
G
ca
n
b
e
w
r
itte
n
as
f
o
llo
w
s
:
̇
=
(
,
,
)
≝
[
1
(
,
,
)
2
(
,
,
)
…
5
(
,
,
)
]
w
it
h
=
[
+
+
+
+
]
=
ℎ
(
)
≝
[
ℎ
1
(
)
ℎ
2
(
)
ℎ
3
(
)
]
=
[
+
+
]
an
d
=
[
+
+
]
1
(
,
,
)
=
−
η
i
s
Td
+
+
ω
s
i
s
Tq
+
+
αβ
φ
rd
+
+
β
ω
φ
rq
+
+
1
σ
L
s
V
s
Td
+
−
β
V
rd
+
2
(
,
,
)
=
−
+
−
+
−
+
+
+
+
1
σ
L
s
V
s
Tq
+
−
+
3
(
,
,
)
=
+
−
+
+
+
+
+
(
4
)
4
(
,
,
)
=
+
−
+
−
+
+
+
5
(
,
,
)
=
(
+
+
−
+
+
)
–
+
W
h
er
e:
=
1
−
2
;
=
(
1
+
1
−
)
;
=
;
=
1
−
;
=
;
=
;
=
Ω
:
DFI
G
r
o
to
r
s
p
ee
d
;
J
:
to
tal
in
er
tia
co
n
s
ta
n
t;
f
:
v
is
co
u
s
f
r
ictio
n
co
ef
f
icien
t;
(
L
s
,
L
r
,
M
)
:
Stato
r
,
r
o
to
r
an
d
m
u
t
u
al
c
y
cl
ic
in
d
u
cta
n
ce
;
(
L
s
σ
,
L
r
σ
)
:
s
tato
r
,
r
o
to
r
cy
c
lic
leak
a
g
e
in
d
u
ctan
ce
;
(
R
s
,
R
r
)
:
s
tato
r
an
d
r
o
to
r
r
esis
tan
ce
s
;
(
φ
s
,
φ
r
)
:
s
tato
r
,
r
o
t
o
r
f
lu
x
co
m
p
o
n
en
ts
;
Su
p
er
s
cr
ip
ts
(
+,
-
)
:
p
o
s
itiv
e
,
n
eg
ati
v
e
r
ef
er
en
ce
f
r
a
m
e
; S
u
b
s
cr
ip
ts
(
+,
-
)
: p
o
s
itiv
e,
n
e
g
ati
v
e
s
eq
u
e
n
ce
co
m
p
o
n
e
n
t .
Fig
u
r
e
2
p
r
esen
t
s
t
h
e
s
p
atial
r
elatio
n
s
h
ip
s
b
et
w
ee
n
t
h
e
s
ta
t
io
n
ar
y
(
αβ
)
s
r
ef
er
en
ce
f
r
a
m
e,
th
e
r
o
to
r
(
αβ
)
r
r
o
tatin
g
at
th
e
s
p
ee
d
o
f
ω
r
,
a
n
d
th
e
dq
+
an
d
dq
−
r
ef
er
en
ce
f
r
a
m
es
r
o
tatin
g
at
t
h
e
a
n
g
u
lar
s
p
ee
d
o
f
ω
s
an
d
−
ω
s
,
r
esp
ec
tiv
el
y
.
+
=
(
)
s
−
;
−
=
(
)
s
;
+
=
(
)
r
−
+
;
−
=
(
)
r
−
−
W
h
er
e:
f
r
ep
r
esen
ts
t
h
e
v
o
lta
g
e
(
cu
r
r
en
t a
n
d
f
l
u
x
)
,
ω
s
l
i
p
+
=
ω
s
−
ω
an
d
ω
s
l
i
p
−
=
−
ω
s
−
ω
A
cc
o
r
d
in
g
to
(
4
)
,
th
e
s
tato
r
cu
r
r
en
t c
a
n
b
e
ca
lcu
lated
as:
i
s
T
d
q
+
=
φ
s
dq
+
−
M
i
r
dq
+
L
s
(
5
)
Fro
m
(
4
)
an
d
(
5
)
,
th
e
r
o
to
r
f
lu
x
ca
n
b
e
w
r
itte
n
φ
r
d
q
+
=
M
φ
s
dq
+
L
s
+
L
r
σ
i
r
d
q
+
(
6
)
Su
b
s
ti
tu
t
in
g
(
6
)
in
to
(
4
)
y
ield
s
th
e
r
o
to
r
v
o
ltag
e
in
t
h
e
dq
+
r
ef
er
en
ce
f
r
a
m
e
as
v
r
d
q
+
=
R
r
i
r
d
q
+
+
M
L
s
d
φ
s
dq
+
dt
+
L
r
σ
d
i
r
dq
+
dt
+
j
ω
s
l
i
p
+
(
M
φ
s
dq
+
L
s
+
L
r
σ
i
r
d
q
+
)
(
7
)
Fig
u
r
e
2
.
R
elatio
n
s
h
ip
s
b
et
w
e
en
s
tatio
n
ar
y
(
αβ
)
s
r
ef
er
en
ce
f
r
a
m
e,
th
e
r
o
to
r
(
αβ
)
r
r
ef
er
en
ce
f
r
am
e
+
−
−
+
ω
−
−
ω
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
2
0
1
7
:
1
7
2
3
–
1
7
3
1
1726
2
.
3
.
I
ns
t
a
nta
neo
us
a
ct
iv
e
a
nd
re
a
ct
iv
e
po
w
er
f
lo
w
un
der
un
ba
la
nced
g
rid
B
y
n
eg
lecti
n
g
t
h
e
s
tato
r
r
esis
t
an
ce
v
o
lta
g
e
d
r
o
p
an
d
co
n
s
id
er
in
g
(
4
)
,
th
e
s
tato
r
v
o
lta
g
e
ca
n
b
e
r
ep
r
esen
ted
in
th
e
p
o
s
iti
v
e
dq
+
r
ef
er
en
ce
f
r
a
m
e
as [
1
9
]
v
sT
d
q
+
≈
j
ω
s
(
φ
sdq
+
+
−
φ
sdq
−
−
e
−
j2
ω
s
t
)
(
8
)
A
cc
o
r
d
in
g
to
(
8
)
,
th
e
s
tato
r
f
lu
x
in
t
h
e
p
o
s
iti
v
e
dq
+
r
ef
er
en
ce
f
r
a
m
e
ca
n
b
e
ex
p
r
es
s
ed
ev
id
en
t
l
y
as:
φ
sdq
+
=
−
j
ω
s
(
v
sT
d
q
+
+
−
v
sT
d
q
−
−
e
−
j2
ω
s
t
(
9
)
Un
d
er
u
n
b
ala
n
ce
d
g
r
id
v
o
ltag
e
co
n
d
itio
n
s
,
th
e
i
n
s
ta
n
ta
n
eo
u
s
ac
tiv
e
an
d
r
ea
cti
v
e
p
o
w
er
o
u
tp
u
ts
f
r
o
m
DFI
G
s
tato
r
ca
n
b
e
ex
p
r
ess
ed
in
(
1
0
)
w
ith
i
̅
s
T
d
q
+
is
th
e
co
n
j
u
g
ate
co
m
p
le
x
o
f
i
s
T
d
q
+
:
P
s
+
j
Q
s
=
v
sT
d
q
+
×
i
̅
sT
d
q
+
(
1
0
)
Su
b
s
ti
tu
t
in
g
(
5
)
,
(
8
)
an
d
(
9
)
i
n
to
(
1
0
)
an
d
s
ep
ar
atin
g
t
h
e
in
s
tan
ta
n
eo
u
s
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
s
in
to
d
if
f
er
en
t p
u
ls
ati
n
g
co
m
p
o
n
en
t
s
y
ield
[
1
9
]
:
P
s
=
P
s0
+
P
s
−
sin
2
s
in
(
2
ω
s
t
)
+
P
s
−
c
o
s2
c
os
(
2
ω
s
t
)
(
1
1
.
a)
Q
s
=
Q
s0
+
Q
s
−
sin
2
s
in
(
2
ω
s
t
)
+
Q
s
−
c
o
s2
c
os
(
2
ω
s
t
)
(
1
1
.
b
)
W
h
er
e,
(1
2
)
3.
RO
T
O
R
F
L
UX
S
L
I
DIN
G
M
O
DE
O
B
SE
RVE
R
AND
M
P
P
T
CO
NT
RO
L
S
T
RA
T
E
G
Y
F
O
R
DF
I
G
T
h
e
ai
m
o
f
th
e
c
o
n
tr
o
l
i
s
t
o
o
p
tim
ize
t
h
e
ex
tr
ac
tio
n
o
f
ae
r
o
d
y
n
a
m
ic
p
o
w
er
(
MP
P
T
)
u
n
d
er
a
n
u
n
b
ala
n
ce
d
n
et
w
o
r
k
v
o
lta
g
e.
T
h
e
r
ef
er
en
ce
ac
tiv
e
p
o
w
er
is
d
eter
m
i
n
ed
as
a
f
u
n
ctio
n
o
f
t
h
e
w
in
d
s
p
ee
d
.
So
,
b
ased
o
n
th
e
cu
r
r
en
t
m
o
d
el
o
f
th
e
DFI
G,
a
s
lid
in
g
m
o
d
e
f
u
l
l
s
tate
o
b
s
er
v
er
i
s
p
r
esen
ted
t
o
esti
m
ate
t
h
e
r
o
to
r
f
l
u
x
[
2
2
]
-
[
2
3
]
.
3
.
1
.
Ro
t
o
r
f
lux
s
lid
ing
m
o
de
o
bs
er
v
er
I
n
th
is
s
ec
t
io
n
,
w
e
p
r
esen
t
th
e
r
o
to
r
f
lu
x
s
lid
i
n
g
m
o
d
e
o
b
s
er
v
er
f
o
r
th
e
MPPT
c
o
n
tr
o
l
w
ith
r
o
to
r
f
lu
x
r
eg
u
lat
io
n
.
T
h
e
s
i
m
p
lici
t
y
an
d
ea
s
e
o
f
i
m
p
le
m
e
n
tat
io
n
a
m
o
n
g
t
h
e
a
d
v
a
n
ta
g
es
o
f
th
i
s
o
b
s
er
v
er
.
Fi
g
u
r
e
3
s
h
o
w
s
th
e
s
tr
u
ctu
r
e
o
f
t
h
e
r
o
to
r
f
lu
x
o
b
s
er
v
er
.
Fig
u
r
e
3
.
R
o
to
r
f
lu
x
s
lid
i
n
g
m
o
d
e
o
b
s
er
v
er
s
tr
u
ctu
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
Desig
n
o
f a
n
I
m
p
r
o
ve
d
MPP
T C
o
n
tr
o
l o
f D
F
I
G
W
in
d
Tu
r
b
i
n
e
u
n
d
er Un
b
a
la
n
ce
d
…
(
Yo
u
s
s
ef
Ma
jd
o
u
b
)
1727
L
et
u
s
r
e
w
r
ite
th
e
D
FIG
m
o
d
e
l (
4
)
in
th
e
f
o
llo
w
i
n
g
f
o
r
m
:
I
̇
sT
+
=
1
I
sT
+
+
1
Ф
+
+
δ
−
β
(
1
3
)
Ф
̇
r
+
=
I
sT
+
+
2
Ф
+
+
W
ith
1
=
[
−
η
ω
s
−
−
]
;
1
=
β
[
α
ω
−
ω
α
]
;
2
=
[
−
α
−
−
α
]
;
δ
=
1
σ
L
s
;
I
sT
+
=
[
+
+
]
an
d
Ф
+
=
[
φ
rd
+
φ
rq
+
]
Hen
ce
,
th
e
s
tr
u
ct
u
r
e
o
f
t
h
e
o
b
s
er
v
er
ca
n
b
e
ex
p
r
ess
ed
b
y
[
2
2
]
-
[
2
3
]
:
I
̂
̇
sT
+
=
1
I
̂
sT
+
+
1
Ф
̂
+
+
δ
−
β
+
(
1
4
)
Ф
̂
̇
r
+
=
I
̂
sT
+
+
2
Ф
̂
+
+
+
Ф
T
h
e
d
y
n
a
m
ic
s
o
f
t
h
e
esti
m
atio
n
er
r
o
r
ar
e
ex
p
r
ess
ed
b
y
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
s
:
I
̃
̇
sT
+
=
1
I
̃
sT
+
+
1
Ф
̃
+
−
(
1
5
)
Ф
̃
̇
r
+
=
I
̃
sT
+
+
2
Ф
̃
+
−
Ф
W
ith
:
I
̃
sT
+
=
I
sT
+
−
I
̂
sT
+
;
Ф
̃
+
=
Ф
+
−
Ф
̂
+
;
=
[
(
1
)
(
2
)
]
;
=
[
1
2
]
=
I
̃
sT
+
is
th
e
s
l
id
in
g
m
o
d
e
s
u
r
f
ac
e
a
n
d
(
;
Ф
)
ar
e
th
e
m
atr
ix
e
s
(
2
x
2
)
th
a
t
w
e
w
il
l d
eter
m
i
n
e
later
.
C
o
n
s
id
er
th
e
L
y
ap
u
n
o
v
ca
n
d
i
d
ate
f
u
n
ctio
n
=
1
2
,
w
e
o
b
tain
:
̇
=
̇
=
I
̃
̇
sT
+
=
(
1
I
̃
sT
+
+
1
Ф
̃
+
)
−
(
1
6
)
in
o
r
d
er
to
s
atis
f
y
th
e
co
n
d
it
io
n
o
f
attr
ac
ti
v
en
e
s
s
(
̇
<
0
)
,
w
e
m
u
s
t
h
av
e
(
1
I
̃
sT
+
+
1
Ф
̃
+
)
<
(
1
7
)
I
f
w
e
p
u
t:
=
[
1
0
0
2
]
.
T
h
en
w
e
o
b
tai
n
t
h
e
co
n
d
itio
n
b
elo
w
μ
1
|
S
1
|
+
μ
2
|
S
2
|
>
S
T
(
A
1
I
̃
sT
+
+
B
1
Ф
̃
r
+
)
(
1
8
)
W
h
en
t
h
e
s
lid
i
n
g
m
o
d
e
is
r
ea
ch
ed
,
th
e
s
w
i
tch
i
n
g
s
u
r
f
ac
e
w
il
l
v
er
if
y
it:
I
̃
̇
sT
+
=
I
̃
sT
+
=
0
T
h
er
ef
o
r
e,
w
e
o
b
tain
:
=
−
1
1
Ф
̃
+
(
1
9
)
I
n
tr
o
d
u
cin
g
(
1
9
)
in
(
1
5
)
,
w
e
o
b
tain
Ф
̃
̇
r
+
=
(
2
−
Ф
−
1
1
)
Ф
̃
+
(
2
0
)
W
e
p
u
t :
−
2
+
Ф
−
1
1
=
P
(
2
1
)
E
q
u
atio
n
(
2
0
)
b
ec
o
m
es:
Ф
̃
̇
r
+
=
−
Ф
̃
+
I
n
o
r
d
er
to
h
av
e
ex
p
o
n
en
tia
l c
o
n
v
er
g
e
n
ce
,
w
e
ch
o
o
s
e
P
in
t
h
e
f
o
llo
w
in
g
f
o
r
m
:
=
[
1
0
0
2
]
W
h
er
e
1
an
d
2
ar
e
p
o
s
itiv
e
co
n
s
t
an
ts
.
Fin
all
y
,
(
2
1
)
ca
n
b
e
r
ew
r
it
ten
as f
o
llo
w
s
:
Ф
=
(
[
1
0
0
2
]
+
2
)
1
−
1
[
1
0
0
2
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
2
0
1
7
:
1
7
2
3
–
1
7
3
1
1728
T
o
co
m
p
lete
th
e
d
esig
n
o
f
t
h
i
s
o
b
s
er
v
er
,
w
e
m
u
s
t
ch
o
o
s
e
t
h
e
co
n
v
e
n
ab
le
o
b
s
er
v
er
p
ar
a
m
eter
s
.
W
e
n
o
te
th
at
t
h
e
(
1
;
2
)
p
ar
am
eter
s
d
eter
m
in
e
t
h
e
d
y
n
a
m
ics
o
f
o
b
s
er
v
er
co
n
v
er
g
en
ce
a
n
d
th
e
(
1
;
2
)
p
ar
am
eter
s
v
er
i
f
y
t
h
e
co
n
d
itio
n
s
o
f
attr
ac
t
iv
e
n
es
s
an
d
s
tab
ili
t
y
o
f
t
h
e
o
b
s
er
v
er
.
3
.
1
.
M
a
x
i
m
u
m
w
ind
po
w
er
ex
t
ra
ct
io
n
I
n
o
r
d
er
to
ca
p
tu
r
e
th
e
m
a
x
i
m
u
m
p
o
w
er
o
f
t
h
e
in
cid
e
n
t
w
i
n
d
,
w
e
m
u
s
t a
d
j
u
s
t t
h
e
r
o
tatio
n
a
l
s
p
ee
d
o
f
th
e
tu
r
b
in
e
p
er
m
a
n
en
tl
y
to
t
h
e
w
i
n
d
s
.
T
h
e
o
p
tim
u
m
o
p
er
atio
n
s
p
ee
d
o
f
th
e
g
en
er
ato
r
is
es
ti
m
a
ted
f
o
r
λ
o
p
t
=
8
,
2
b
y
:
ω
o
p
t
=
G
V
w
λ
o
p
t
R
(
2
2
)
W
h
er
e
G
is
Gea
r
b
o
x
r
atio
o
f
th
e
w
i
n
d
tu
r
b
in
e.
3
.
2
B
a
ck
s
t
epp
ing
co
ntr
o
l desig
n
un
der
un
ba
la
nced
g
ri
d v
o
lt
a
g
e
co
nd
it
io
ns
T
h
e
co
n
tr
o
l
o
b
j
ec
tiv
e
is
t
w
o
f
o
ld
:
th
e
o
b
j
ec
tiv
e
o
f
h
i
g
h
er
p
r
io
r
ity
is
tr
ac
k
in
g
t
h
e
r
ef
er
e
n
ce
s
tr
aj
ec
to
r
y
(
P
s
−
r
ef
,
Q
s
−
r
ef
)
w
h
er
e
P
s
−
r
ef
is
th
e
o
p
ti
m
al
s
tato
r
ac
tiv
e
p
o
w
er
r
ef
er
en
ce
ac
co
r
d
in
g
to
o
p
ti
m
al
s
p
ee
d
o
f
th
e
g
en
er
ato
r
an
d
t
h
e
s
ec
o
n
d
is
to
k
ee
p
th
e
r
o
to
r
f
lu
x
at
it
s
n
o
m
i
n
al
v
a
lu
e
b
y
co
n
tr
o
llin
g
t
h
e
s
t
ato
r
r
ea
ctiv
e
p
o
w
er
g
iv
e
n
v
ia
(
2
7
)
r
eg
ar
d
less
o
f
th
e
as
y
m
m
etr
ic
v
o
lta
g
e
.
Usi
n
g
s
tato
r
v
o
ltag
e
o
r
ien
ta
tio
n
ap
p
r
o
ac
h
,
i.e
.
V
s
T
d
+
+
=
0
,
th
e
r
o
to
r
cu
r
r
en
t
r
ef
er
en
ce
s
ca
n
b
e
co
n
s
id
er
ed
f
o
r
eli
m
i
n
ati
n
g
t
h
e
d
o
u
b
le
f
r
eq
u
en
c
y
p
u
l
s
ati
o
n
s
o
f
s
tato
r
o
u
tp
u
t
ac
tiv
e
p
o
w
er
(
P
s
−
s
i
n
2
=
P
s
−
co
s
2
=0
)
.
A
cc
o
r
d
in
g
to
(
1
1
-
a)
,
th
e
r
ef
er
en
ce
s
o
f
t
h
e
p
o
s
itiv
e
an
d
n
eg
at
iv
e
s
eq
u
en
ce
r
o
to
r
cu
r
r
en
ts
ar
e
ca
lcu
lated
as [
1
9
]
:
+
_
+
=
−
+
+
D
1
0
+
+
+
(
2
3
)
+
_
+
=
−
+
+
D
2
0
(
2
4
)
−
_
−
=
[
−
−
+
+
−
−
−
+
+
]
+
+
−
2
−
−
(
2
5
)
−
_
−
=
−
[
−
−
+
+
+
−
−
+
+
]
+
+
+
2
−
−
(
2
6
)
W
ith
:
1
=
+
+
2
+
−
−
2
+
−
−
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t
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rd
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-
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2
3
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2
4
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2
5
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d
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2
6
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e
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ig
n
al
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∅
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o
f
th
e
r
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f
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x
m
a
g
n
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√
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y
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2
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[
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−
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cted
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r
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45
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Usi
n
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7
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,
(
2
3
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,
(
2
4
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,
(
2
5
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an
d
(
2
6
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th
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r
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y
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m
ic
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v
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y
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1
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1
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0
−
1
[
+
+
−
+
+
+
+
+
+
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(
2
8
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2
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2
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−
1
[
+
+
−
+
+
−
+
+
+
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(
2
9
)
e
̇
3
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d
dt
(
v
s
T
q
−
−
i
rd
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v
s
T
d
−
−
i
rq
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M
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s
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r
[
v
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r
i
rd
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ip
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rq
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−
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(
3
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
Desig
n
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2
8
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2
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(
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d
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3
1
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atis
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y
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g
V
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[
1
9
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k
1
e
1
−
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D
1
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0
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+
+
+
−
+
+
+
(
3
3
)
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[
k
2
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2
−
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+
D
2
̇
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+
+
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(
3
4
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2
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2
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3
5
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k
4
e
4
−
(
−
−
+
+
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−
−
+
+
+
+
−
2
−
−
)
]
+
+
−
−
+
−
−
−
(
3
6
)
W
h
er
e
k
1
,
k
2
,
k
3
a
n
d
k
4
ar
e
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o
s
itiv
e
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n
s
tan
t
s
.
I
n
tr
o
d
u
cin
g
(
3
3
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,
(
3
4
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,
(
3
5
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an
d
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3
6
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in
(
3
2
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,
th
e
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e
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o
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th
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ate
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n
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ec
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m
es
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eg
at
iv
e
d
e
f
in
ite:
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=
−
1
e
1
2
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2
e
2
2
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3
e
3
2
−
4
e
4
2
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0
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T
h
is
ass
u
r
es
th
e
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lo
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p
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s
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o
f
t
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y
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te
m
.
B
ased
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n
t
h
e
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r
o
p
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s
ed
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tr
o
l la
w
d
escr
ib
ed
b
y
(
3
3
)
,
(
3
4
)
,
(
3
5
)
an
d
(
3
6
)
,
Fig
u
r
e
4
s
h
o
w
s
th
e
s
c
h
e
m
atic
d
iag
r
a
m
o
f
t
h
e
co
n
tr
o
l
s
y
s
te
m
f
o
r
a
DFI
G.
Fig
u
r
e
4
.
T
h
e
s
ch
e
m
atic
d
ia
g
r
a
m
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
4.
SI
M
UL
AT
I
O
N
S RE
SU
L
T
S
I
n
o
r
d
er
to
d
e
m
o
n
s
tr
ate
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
r
o
to
r
f
lu
x
s
lid
in
g
m
o
d
e
o
b
s
er
v
er
,
t
h
e
s
i
m
u
latio
n
p
r
o
ce
d
u
r
e
is
d
esig
n
ed
to
co
n
s
id
er
a
c
o
n
s
tan
t
r
o
to
r
f
lu
x
(
eq
u
al
to
its
n
o
m
in
al
v
al
u
e
:
∅
r
e
f
=
0
,
45
Wb
)
.
T
h
e
o
b
s
er
v
er
p
ar
am
eter
s
(
p
1
,
p
2
)
an
d
(
μ
1
,
μ
2
)
ar
e
ch
o
s
en
a
s
f
o
llo
w
s
:
p
1
=
200
,
p
2
=
60
,
μ
1
=
1000
a
n
d
μ
2
=
1000
.
Fig
u
r
e
5
s
h
o
w
s
th
e
s
ati
s
f
ac
t
o
r
y
p
er
f
o
r
m
an
c
e
s
o
f
t
h
e
r
o
to
r
f
l
u
x
esti
m
at
io
n
.
T
h
e
est
i
m
a
t
ed
r
o
to
r
f
lu
x
tr
ac
k
s
t
h
e
ac
tu
al
r
o
to
r
f
l
u
x
w
i
t
h
g
o
o
d
p
r
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is
io
n
an
d
th
e
e
s
ti
m
atio
n
er
r
o
r
o
b
tain
ed
is
p
r
ac
tica
ll
y
ze
r
o
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
2
0
1
7
:
1
7
2
3
–
1
7
3
1
1730
T
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I
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in
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I
: D
FIG
p
ar
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DFI
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4
k
W
Nu
m
b
er
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la
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es
T
u
r
b
i
n
e rad
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s
,
R
(
m
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Gear
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o
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r
atio
Po
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t
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in
win
d
s
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eed
R
ated
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s
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eed
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o
to
r
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tia
3
3
1
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.
5
5
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4
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2
5
m
/s
1
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5
m
/s
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0
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m
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Nu
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b
er
o
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p
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p
air
s
o
f
th
e D
F
I
G
Stato
r
r
esis
tan
ce
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leak
a
g
e in
d
u
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R
o
to
r
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tan
ce
R
o
to
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leak
ag
e in
d
u
cta
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ce
Mu
tu
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d
u
ctan
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Vis
co
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s
f
r
ictio
n
c
o
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f
icien
t
Gen
er
ato
r
in
er
tia
2
1
.
2
5
0
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0
0
0
9
6
H
0
.
1
7
0
.
0
0
1
8
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0
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0
7
7
2
H
0
.
0
0
1
m
/s
0
.
3
3
k
g
m
2
Fig
u
r
e
5
.
R
o
to
r
f
lu
x
esti
m
atio
n
r
esu
lts
.
Up
p
er
: A
ct
u
al
a
n
d
esti
m
ated
r
o
to
r
f
lu
x
; lo
w
er
: e
s
ti
m
atio
n
er
r
o
r
4
.
2
.
Co
ntr
o
llers per
f
o
r
m
a
nce
s
T
h
e
s
ti
m
u
la
tio
n
p
r
o
ce
d
u
r
e
i
s
d
esig
n
ed
i
n
s
u
c
h
a
w
a
y
:
d
u
r
i
n
g
(
0
s
-
2
s
)
,
t
h
e
co
n
v
e
n
tio
n
al
B
ac
k
s
tep
p
in
g
co
n
tr
o
l
w
as
e
s
tab
lis
h
ed
d
u
r
i
n
g
s
tead
y
s
tate
(
u
n
d
er
th
e
s
tab
le
g
r
id
)
.
T
h
en
at
2
s
,
w
e
s
tar
ted
a
n
as
y
m
m
etr
ic
f
a
u
lt
(
a
2
0
%
o
f
t
h
e
n
o
m
i
n
al
g
r
id
v
o
ltag
e
d
ip
o
f
V
sa
)
to
s
h
o
w
th
e
i
m
p
ac
t
o
f
t
h
e
a
s
y
m
m
etr
ic
f
a
u
lt
o
n
v
ar
io
u
s
s
ig
n
al
s
o
f
DFI
G
(
w
i
th
t
h
e
co
n
v
e
n
tio
n
al
co
n
tr
o
l)
.
A
t
t
h
e
en
d
,
f
o
r
(
4
s
-
7
s
)
w
e
s
h
o
w
t
h
e
f
ea
s
ib
ili
t
y
o
f
t
h
e
en
h
an
ce
d
B
ac
k
s
tep
p
in
g
co
n
tr
o
l
b
ased
o
n
t
h
e
co
n
tr
o
l
la
w
d
escr
ib
ed
b
y
(
3
3
)
,
(
3
4
)
,
(
3
5
)
an
d
(
3
6
)
.
T
h
e
co
n
tr
o
l
p
ar
am
e
ter
s
ar
e
ch
o
s
en
as
f
o
llo
w
s
:
k
1
=
30
,
k
2
=
120
,
k
3
=
115
a
n
d
k
4
=
500
.
T
h
e
s
atis
f
ac
to
r
y
p
er
f
o
r
m
a
n
ce
s
o
f
th
e
s
ta
to
r
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
tr
ac
k
i
n
g
ar
e
s
h
o
w
n
in
Fi
g
u
r
e
6
.
b
an
d
Fig
u
r
e
6
.
d
b
y
li
m
iti
n
g
t
h
e
m
ec
h
a
n
ical
s
tr
es
s
i
n
d
u
ce
d
b
y
as
y
m
m
etr
ical
f
a
u
lt.
A
l
s
o
,
n
o
te
th
at
f
o
r
i
m
p
o
s
in
g
a
co
n
s
ta
n
t
r
o
to
r
f
lu
x
,
th
e
s
tato
r
r
ea
ctiv
e
p
o
w
er
r
ef
er
en
ce
is
i
m
p
o
s
ed
ac
co
r
d
in
g
to
(
2
7
)
,
s
e
e
Fig
u
r
e
6
.
c.
W
e
s
ee
th
at
th
e
er
r
o
r
v
alu
es
r
e
m
ain
s
p
r
ac
ticall
y
ze
r
o
F
ig
u
r
e
6
.
Si
m
u
latio
n
r
esp
o
n
s
e
s
f
o
r
2
0
% o
f
d
ep
th
o
f
V
sa
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
Desig
n
o
f a
n
I
m
p
r
o
ve
d
MPP
T C
o
n
tr
o
l o
f D
F
I
G
W
in
d
Tu
r
b
i
n
e
u
n
d
er Un
b
a
la
n
ce
d
…
(
Yo
u
s
s
ef
Ma
jd
o
u
b
)
1731
5.
CO
NCLU
SI
O
N
I
n
th
is
ar
ticle,
an
i
m
p
r
o
v
ed
MPPT
co
n
tr
o
l
is
d
ev
elo
p
ed
u
s
in
g
b
ac
k
s
tep
p
i
n
g
tec
h
n
i
q
u
e
u
n
d
er
u
n
b
ala
n
ce
d
g
r
id
v
o
lta
g
e
ass
o
c
iated
w
it
h
a
r
o
to
r
f
lu
x
o
b
s
er
v
er
b
ased
o
n
th
e
s
lid
in
g
m
o
d
e
ap
p
r
o
ac
h
.
T
h
e
f
au
l
t
m
o
d
e
is
ac
ti
v
ated
w
h
e
n
an
as
y
m
m
etr
ic
f
a
u
lt
o
cc
u
r
s
i
n
th
e
g
r
i
d
v
o
ltag
e
in
o
r
d
er
to
elim
i
n
ate
th
e
o
s
cillatio
n
s
o
f
th
e
s
ig
n
als.
R
e
f
er
en
ce
r
o
to
r
cu
r
r
en
ts
ar
e
ca
lcu
la
ted
,
in
o
r
d
er
to
m
ai
n
tai
n
s
a
f
e
o
p
er
atio
n
,
a
s
to
d
a
y
'
s
g
r
id
co
d
es
r
eq
u
ir
e.
T
h
e
p
r
o
p
o
s
ed
r
o
to
r
f
lu
x
o
b
s
er
v
er
is
b
ased
o
n
m
ea
s
u
r
in
g
elec
tr
ical
s
ig
n
al
s
(
s
tato
r
cu
r
r
en
ts
,
r
o
to
r
an
d
s
tato
r
v
o
lta
g
es).
T
h
e
p
er
f
o
r
m
a
n
ce
a
n
d
s
tab
ilit
y
o
f
co
n
tr
o
l
la
w
s
an
d
o
b
s
er
v
er
h
a
v
e
b
ee
n
s
h
o
w
n
b
y
s
i
m
u
la
tio
n
s
tu
d
ie
s
in
Ma
tlab
/
Si
m
u
l
in
k
®
en
v
ir
o
n
m
e
n
t.
RE
F
E
R
E
NC
E
S
[1
]
Y.
M
a
jd
o
u
b
,
e
t
a
l.
,
“
V
a
ria
b
le
S
p
e
e
d
Co
n
tro
l
o
f
DFI
G
-
W
in
d
T
u
rb
in
e
w
it
h
W
in
d
Esti
m
a
ti
o
n
,
”
IEE
E
IRS
EC
c
o
n
f
.
,
In
ter
n
a
t
io
n
a
l
Ren
e
wa
b
le a
n
d
S
u
st
a
in
a
b
le E
n
e
rg
y
c
o
n
fer
e
n
c
e
,
Oc
to
b
e
r
2
0
1
4
,
p
p
.
2
6
8
–
2
7
4
.
[2
]
B.
P
u
rw
a
h
y
u
d
i,
e
t
a
l.
,
“
RNN
Ba
se
d
Ro
to
r
F
l
u
x
a
n
d
S
p
e
e
d
Esti
m
a
ti
o
n
o
f
In
d
u
c
ti
o
n
M
o
to
r,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m (
IJ
PE
DS
),
V
o
l
.
1
,
N
o
1
,
2
0
1
1
,
p
p
.
5
8
-
6
4
.
[3
]
A
.
Be
n
h
e
n
ich
e
,
e
t
a
l.
,
“
A
Hig
h
G
a
in
Ob
se
rv
e
r
Ba
se
d
S
e
n
so
rles
s
No
n
li
n
e
a
r
Co
n
tro
l
o
f
In
d
u
c
ti
o
n
M
a
c
h
in
e
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m (
IJ
PE
DS
),
V
o
l.
5
,
N
o
3
,
2
0
1
5
,
p
p
.
3
0
5
-
3
1
4
.
[4
]
H.
Ech
e
ik
h
,
e
t
a
l.
,
“
On
li
n
e
A
d
a
p
tatio
n
o
f
Ro
t
o
r
Re
sista
n
c
e
b
a
se
d
o
n
S
l
id
i
n
g
M
o
d
e
O
b
se
rv
e
r
w
it
h
Ba
c
k
ste
p
p
in
g
Co
n
tr
o
l
o
f
A
F
iv
e
-
P
h
a
se
In
d
u
c
ti
o
n
M
o
t
o
r
Driv
e
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
IJ
PE
DS
),
V
o
l
.
7
,
N
o
3
,
2
0
1
6
,
p
p
.
6
4
8
-
6
5
5
.
[5
]
Re
n
u
k
rish
n
a
B.
,
e
t
a
l.
,
“
S
e
n
s
o
rles
s
V
e
c
to
r
Co
n
tr
o
l
o
f
In
d
u
c
ti
o
n
M
o
to
r
Driv
e
s
u
sin
g
Ro
to
r
F
l
u
x
Ob
se
rv
e
r,
”
IEE
E
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
P
o
w
e
r E
lec
tro
n
ics
,
Dr
ive
s a
n
d
En
e
rg
y
S
y
ste
ms
,
De
c
e
m
b
e
r
2
0
1
2
.
[6
]
G
.
L
e
f
e
b
v
r
e
,
e
t
a
l.
,
“
El
e
c
tri
c
a
l
p
a
r
a
m
e
ter
o
b
se
rv
a
ti
o
n
f
o
r
in
d
u
c
ti
o
n
m
a
c
h
in
e
se
n
so
rles
s
d
riv
e
u
sin
g
a
se
n
siti
v
it
y
a
n
d
o
b
se
rv
a
b
il
it
y
b
a
se
d
EKF
,
”
IE
EE
In
ter
n
a
t
io
n
a
l
Po
we
r
E
lec
tro
n
ics
a
n
d
M
o
ti
o
n
Co
n
tro
l
Co
n
fer
e
n
c
e
(
PE
M
C)
,
2
0
1
6
,
p
p
.
8
0
6
-
8
1
1
.
[7
]
G
.
Rig
a
to
s,
“
A
d
e
riv
a
ti
v
e
-
f
re
e
Ka
l
m
a
n
F
il
terin
g
a
p
p
ro
a
c
h
f
o
r
se
n
so
rles
s
c
o
n
tr
o
l
o
f
n
o
n
li
n
e
a
r
s
y
ste
m
s
,
”
IEE
E
In
ter
n
a
t
io
n
a
l
S
y
mp
o
si
u
m o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
2
0
1
0
,
p
p
.
2
0
4
9
-
2
0
5
4
.
[8
]
Y.
Zh
o
u
,
e
t
a
l.
,
“
Op
e
ra
ti
o
n
o
f
G
rid
-
Co
n
n
e
c
ted
DFIG
Un
d
e
r
Un
b
a
lan
c
e
d
G
rid
V
o
lt
a
g
e
Co
n
d
it
i
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s ON
En
e
rg
y
C
o
n
v
e
rs
io
n
,
Vo
l.
2
4
,
No
.
1
,
M
a
rc
h
2
0
0
9
.
[9
]
M
.
F
a
rsh
a
d
n
ia,
e
t
a
l.
,
“
Cu
rre
n
t
-
b
a
se
d
d
irec
t
p
o
w
e
r
c
o
n
tro
l
o
f
a
DFIG
u
n
d
e
r
u
n
b
a
lan
c
e
d
g
rid
v
o
lt
a
g
e
,
”
El
e
c
trica
l
Po
we
r a
n
d
E
n
e
rg
y
S
y
ste
ms
,
v
o
l.
6
2
,
2
0
1
4
,
p
p
.
5
7
1
–
5
8
2
.
[1
0
]
J.
Hu
,
e
t
a
l.
,
“
DFIG
w
i
n
d
g
e
n
e
ra
ti
o
n
sy
ste
m
s
o
p
e
ra
ti
n
g
w
it
h
li
m
i
ted
c
o
n
v
e
rter
ra
ti
n
g
c
o
n
sid
e
re
d
u
n
d
e
r
u
n
b
a
lan
c
e
d
n
e
tw
o
rk
c
o
n
d
it
i
o
n
s
-
A
n
a
ly
sis a
n
d
c
o
n
tro
l
d
e
sig
n
”
,
Re
n
e
wa
b
le
En
e
r
g
y
,
v
o
l.
3
6
,
2
0
1
1
,
p
p
.
8
2
9
-
8
4
7
.
[1
1
]
N.
Am
u
th
a
n
,
e
t
a
l.
,
“
V
o
lt
a
g
e
sa
g
rid
e
th
ro
u
g
h
u
sin
g
Im
p
ro
v
e
d
Ad
a
p
ti
v
e
In
tern
a
l
M
o
d
e
l
Co
n
tr
o
ll
e
r
f
o
r
d
o
u
b
ly
f
e
d
in
d
u
c
ti
o
n
g
e
n
e
ra
to
r
w
in
d
f
a
rm
s”
,
Co
mp
u
ter
s
a
n
d
El
e
c
trica
l
E
n
g
in
e
e
rin
g
,
2
0
1
3
.
[1
2
]
J.
Hu
,
e
t
a
l.
,
“
En
h
a
n
c
e
d
c
o
n
tr
o
l
o
f
DFI
G
u
se
d
b
a
c
k
-
to
-
b
a
c
k
P
W
M
V
S
C
u
n
d
e
r
u
n
b
a
lan
c
e
d
g
rid
v
o
lt
a
g
e
c
o
n
d
it
io
n
s,”
J
Z
h
e
ji
a
n
g
Un
iv S
c
i
A,
v
o
l.
8
(
8
),
2
0
0
7
,
p
p
.
1
3
3
0
-
1
3
3
9
.
[1
3
]
B.
I.
Na
ss
,
e
t
a
l.
,
“
M
e
th
o
d
s
f
o
r
Re
d
u
c
ti
o
n
o
f
V
o
lt
a
g
e
Un
b
a
lan
c
e
in
W
e
a
k
G
rid
s
Co
n
n
e
c
ted
to
W
in
d
P
lan
ts”
.
IEE
E
W
o
rk
sh
o
p
o
n
W
i
n
d
P
o
we
r a
n
d
th
e
Imp
a
c
ts
o
n
P
o
we
r S
y
ste
ms
,
2
0
0
2
.
[1
4
]
L
.
X
u
,
“
Co
o
rd
in
a
ted
Co
n
tr
o
l
o
f
DFIG
’s
Ro
to
r
a
n
d
G
rid
S
id
e
Co
n
v
e
rters
Du
rin
g
Ne
tw
o
rk
Un
b
a
lan
c
e
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
i
c
s
,
v
o
l.
2
3
,
M
a
y
2
0
0
8
,
p
p
.
1
0
4
1
-
1
0
4
9
.
[1
5
]
L
.
F
a
n
,
e
t
a
l.
,
“
Ne
g
a
ti
v
e
S
e
q
u
e
n
c
e
Co
m
p
e
n
sa
ti
o
n
T
e
c
h
n
iq
u
e
s
o
f
DFI
G
-
b
a
se
d
W
in
d
En
e
rg
y
S
y
ste
m
s
u
n
d
e
r
Un
b
a
lan
c
e
d
G
rid
Co
n
d
i
ti
o
n
s,”
Po
we
r E
lec
tro
n
ics
a
n
d
M
a
c
h
in
e
s in
W
in
d
A
p
p
li
c
a
ti
o
n
s (
PE
M
W
A),
Ju
n
e
2
0
0
9
.
[1
6
]
J.
Hu
,
e
t
a
l.
,
“
Im
p
ro
v
e
d
Co
n
tro
l
o
f
DFI
G
S
y
ste
m
s
Du
rin
g
Ne
t
w
o
rk
Un
b
a
lan
c
e
Us
in
g
P
I
–
R
Cu
rre
n
t
Re
g
u
lato
rs,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stri
a
l
El
e
c
tro
n
ics
,
v
o
l.
5
6
,
n
o
.
2
,
F
e
b
r
u
a
ry
2
0
0
9
,
p
p
.
4
3
9
-
4
5
1
.
[1
7
]
P
.
P
u
ra
,
e
t
a
l.
,
“
Dire
c
t
P
o
w
e
r
Co
n
tr
o
l
o
f
DFI
G
Co
n
n
e
c
ted
to
Un
b
a
lan
c
e
d
P
o
w
e
r
G
rid
,
”
Ei
g
h
t
h
In
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
a
n
d
Ex
h
ib
i
ti
o
n
o
n
Ec
o
lo
g
ica
l
Veh
icle
s a
n
d
Ren
e
wa
b
le
En
e
rg
ies
,
2
0
1
3
.
[1
8
]
M
.
J.
Zan
d
z
a
d
e
h
,
e
t
a
l.
,
“
M
o
d
e
li
n
g
a
n
d
im
p
ro
v
e
m
e
n
t
o
f
d
irec
t
p
o
w
e
r
c
o
n
tro
l
o
f
DFIG
u
n
d
e
r
u
n
b
a
lan
c
e
d
g
ri
d
v
o
lt
a
g
e
c
o
n
d
it
i
o
n
,
”
El
e
c
trica
l
P
o
we
r a
n
d
En
e
rg
y
S
y
ste
ms
,
v
o
l.
5
9
,
2
0
1
4
,
p
p
.
5
8
–
6
5
.
[1
9
]
Y.
M
a
jd
o
u
b
,
A
.
A
b
b
o
u
,
M
.
A
k
h
e
rra
z
,
R.
El
a
k
h
rif
“
In
telli
g
e
n
t
Ba
c
k
ste
p
p
in
g
Co
n
tr
o
l
o
f
V
a
riab
l
e
S
p
e
e
d
DFIG
-
W
in
d
T
u
rb
in
e
u
n
d
e
r
u
n
b
a
la
n
c
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