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2471
1.
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RO
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Ma
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Actu
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ce
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in
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in
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th
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ex
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On
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ch
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th
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id
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[
4
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[
6
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.
Ho
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in
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T
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th
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ates
with
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ly
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te
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is
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ec
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ar
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r
s
id
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[
7
]
.
T
h
at
is
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s
ay
th
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th
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ased
win
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tu
r
b
in
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Fu
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t
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r
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ax
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tr
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m
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k
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o
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ev
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al
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an
d
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o
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s
tn
ess
[
8
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,
[
9
]
.
Var
io
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s
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tech
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s
p
ee
d
v
ar
iatio
n
s
an
d
e
x
ter
n
al
d
is
tu
r
b
an
ce
s
,
a
n
d
to
ac
h
iev
e
th
e
h
ig
h
est
r
ate
o
f
ef
f
icien
cy
,
s
u
ch
as
f
iled
o
r
ien
ted
co
n
tr
o
l
(
FOC
)
b
ase
d
o
n
PI
c
o
n
tr
o
ller
,
h
o
wev
e
r
th
e
p
er
f
o
r
m
an
ce
ca
n
b
e
d
em
o
ted
if
th
e
s
y
s
tem
in
ter
n
al
g
ain
s
ar
e
ch
an
g
ed
[
1
0
]
,
[
1
1
]
.
T
o
o
v
er
co
m
e
th
e
d
r
awb
ac
k
s
o
f
FOC
,
s
ev
er
al
ad
v
an
ce
d
n
o
n
lin
ea
r
ap
p
r
o
ac
h
es
ca
n
b
e
u
s
ed
to
en
h
an
ce
W
E
C
S
r
o
b
u
s
tn
ess
.
R
ef
er
r
in
g
to
[
1
2
]
,
a
n
ad
a
p
tiv
e
co
n
tr
o
l
h
as
b
ee
n
im
p
lem
en
ted
,
an
d
th
e
r
o
b
u
s
tn
ess
was
h
ig
h
u
n
d
er
ab
r
u
p
t
s
p
ee
d
c
h
an
g
es.
N
o
n
eth
eles
s
,
v
ar
io
u
s
d
esig
n
p
ar
am
eter
s
r
ev
ea
l w
h
e
n
th
is
a
p
p
r
o
ac
h
is
ap
p
lied
.
T
h
u
s
,
th
e
y
af
f
ec
t th
e
co
n
tr
o
lled
s
y
s
tem
p
er
f
o
r
m
a
n
ce
.
R
o
b
u
s
t
co
n
tr
o
l
d
esig
n
u
s
in
g
N
eu
r
o
n
al
n
etwo
r
k
alg
o
r
ith
m
h
as
p
r
o
p
o
s
ed
in
[
1
3
]
.
T
h
e
Si
m
u
latio
n
s
s
h
o
w
an
ef
f
icien
t
p
er
f
o
r
m
an
ce
in
ter
m
o
f
o
v
er
s
h
o
o
t
an
d
r
esp
o
n
s
e
tim
e.
Yet,
th
is
ap
p
r
o
ac
h
n
ee
d
s
an
ab
u
n
d
an
t
p
ar
am
eter
a
d
ju
s
ted
an
d
a
m
a
s
s
iv
e
d
ata
in
th
e
tr
ain
in
g
p
h
ase.
T
h
e
a
u
th
o
r
s
i
n
[
1
4
]
d
esi
g
n
ed
a
f
u
zz
y
l
o
g
ic
co
n
tr
o
ller
in
o
r
d
er
to
co
n
tr
o
l
W
E
C
S.
T
h
e
co
n
tr
o
ller
d
eliv
er
s
an
ap
p
r
o
p
r
iate
r
esu
lt
with
f
lu
ctu
atio
n
s
in
g
en
er
ato
r
v
elo
city
d
u
e
to
th
e
s
ev
er
al
tu
n
in
g
p
a
r
am
eter
s
o
f
th
e
m
en
tio
n
ed
al
g
o
r
ith
m
.
Sli
d
in
g
Mo
d
e
C
o
n
tr
o
l
(
SMC
)
is
a
g
o
o
d
s
o
lu
tio
n
t
o
c
o
n
tr
o
l
th
e
DFI
G
d
u
e
to
its
r
o
b
u
s
tn
ess
,
b
u
t
ev
en
s
o
,
a
p
u
r
e
SMC
s
u
f
f
er
s
f
r
o
m
th
e
ch
atter
in
g
ef
f
ec
t.
Am
id
s
t
th
e
l
im
itatio
n
s
o
f
ab
o
v
e
-
m
en
tio
n
e
d
tech
n
o
lo
g
ies,
n
o
n
lin
ea
r
B
ac
k
s
tep
p
in
g
co
n
tr
o
l
is
p
r
o
p
o
s
ed
an
d
test
ed
o
n
a
h
ig
h
p
o
wer
DFI
G
b
ased
W
E
C
S
i
n
th
is
s
tu
d
y
,
f
o
r
its
m
an
y
ad
v
an
tag
es
in
ter
m
s
o
f
p
er
f
o
r
m
an
ce
s
im
p
r
o
v
em
en
t,
s
im
p
licity
o
f
im
p
lem
en
tatio
n
,
an
d
r
o
b
u
s
tn
ess
ag
ain
s
t
th
e
ex
ter
n
al
d
is
tu
r
b
an
ce
s
[
1
5
]
,
[
1
6
]
.
M
o
r
eo
v
e
r
,
th
e
s
y
s
tem
s
tab
ilit
y
ca
n
b
e
en
s
u
r
e
d
b
y
ap
p
l
y
in
g
L
y
ap
u
n
o
v
f
u
n
ctio
n
.
I
n
o
r
d
er
to
p
r
o
v
e
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
s
u
g
g
e
s
ted
co
n
tr
o
l,
a
co
m
p
ar
is
o
n
h
a
s
b
ee
n
co
n
d
u
cted
in
th
is
p
ap
e
r
with
an
im
p
r
o
v
ed
s
lid
in
g
m
o
d
e
a
p
p
r
o
ac
h
u
s
in
g
(
s
at)
f
u
n
ctio
n
as
a
r
ep
lace
m
en
t
o
f
th
e
r
eg
u
lar
(
s
ig
n
)
f
u
n
ctio
n
to
r
e
d
u
ce
th
e
ch
atter
in
g
p
r
o
b
lem
.
Mo
r
eo
v
er
,
an
o
v
e
r
all
co
m
p
a
r
is
o
n
o
f
th
e
co
llected
r
esu
lts
with
o
th
er
p
u
b
lis
h
ed
wo
r
k
s
h
as
b
ee
n
m
ad
e
r
eg
a
r
d
in
g
p
r
ec
is
io
n
,
ef
f
icac
y
,
q
u
ality
o
f
in
jecte
d
p
o
wer
,
s
et
-
p
o
in
t
tr
ac
k
in
g
,
r
esp
o
n
s
e
tim
e,
s
tatic
er
r
o
r
s
,
an
d
m
in
im
izin
g
th
e
to
t
al
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws:
af
ter
th
e
in
tr
o
d
u
ctio
n
th
at
is
b
r
in
g
in
g
a
g
en
er
al
r
ev
iew
in
liter
atu
r
e,
s
ec
tio
n
2
,
ca
m
e
to
p
r
esen
t
th
e
m
o
d
elin
g
o
f
th
e
win
d
en
er
g
y
s
y
s
tem
,
an
d
th
e
MPP
T
co
n
tr
o
l
s
tr
ateg
y
.
T
h
er
ea
f
ter
,
s
ec
tio
n
3
d
ea
ls
with
th
e
im
p
lem
e
n
tatio
n
o
f
v
ec
to
r
co
n
tr
o
l
o
n
th
e
DF
I
G.
T
h
e
n
,
s
ec
tio
n
4
ex
am
in
es
th
e
p
r
o
p
o
s
ed
Sli
d
in
g
M
o
d
e
Al
g
o
r
ith
m
,
w
h
ile
s
ec
tio
n
5
ex
p
la
in
s
th
e
s
u
g
g
ested
b
ac
k
s
tep
p
i
n
g
s
tr
ateg
y
o
f
DFI
G.
Su
b
s
eq
u
en
tly
,
s
ec
tio
n
6
i
n
tr
o
d
u
ce
s
th
e
m
o
d
ellin
g
o
f
th
e
r
o
to
r
s
id
e
co
n
v
er
ter
.
T
h
en
,
th
e
s
im
u
latio
n
r
esu
lts
ar
e
s
h
o
wn
in
s
ec
tio
n
7
.
Fin
ally
,
s
ec
tio
n
8
s
u
m
m
a
r
izes th
e
co
n
clu
s
io
n
.
2.
WI
ND
E
NE
RG
Y
CO
NVE
R
SI
O
N
SY
ST
E
M
M
O
DE
L
DFI
G
b
ased
win
d
en
er
g
y
s
y
s
tem
is
r
ep
r
esen
ted
b
y
th
e
s
i
m
p
lifie
d
s
ch
em
atic
d
iag
r
am
o
f
Fig
u
r
e
1
.
T
h
is
elec
tr
ical
m
ac
h
in
e
h
as
a
r
o
to
r
cir
cu
it
co
n
n
ec
ted
to
th
e
g
r
id
t
h
r
o
u
g
h
b
ac
k
-
to
-
b
ac
k
p
o
wer
elec
tr
o
n
ic
co
n
v
er
ter
s
,
wh
ile
th
e
s
tato
r
cir
cu
it is
d
ir
ec
tly
co
n
n
ec
te
d
to
th
e
p
o
wer
g
r
id
.
D
F
I
G
T
u
r
b
i
n
e
G
e
a
rb
ox
R
S
C
G
S
C
W
i
n
d
T
r
a
n
s
f
o
r
m
e
r
G
r
i
d
t
g
P
o
w
e
r
P
o
w
e
r
V
dc
Fig
u
r
e
1
.
W
in
d
e
n
er
g
y
co
n
v
er
s
io
n
s
y
s
tem
co
n
f
ig
u
r
atio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
4
70
–
24
82
2472
2
.
1
.
M
o
delin
g
o
f
t
he
wind
t
urbi
n
e
a
nd
M
P
P
T
co
ntr
o
l
s
t
ra
t
eg
y
T
h
e
m
ath
em
atica
l m
o
d
el
o
f
t
h
e
tu
r
b
in
e
is
ex
p
r
es
s
ed
b
y
th
e
f
o
llo
win
g
[
1
7
]
:
P
V
=
ρ
S
V
3
2
(
1
)
P
aer
=
C
p
P
V
=
1
2
ρπ
R
2
V
3
C
p
(
λ
,
β
)
(
2
)
T
h
e
ae
r
o
d
y
n
am
ic
p
o
wer
c
o
ef
f
icien
t
C
p
as a
f
u
n
ctio
n
o
f
th
e
tip
s
p
ee
d
r
atio
(
T
SR
)
λ
an
d
th
e
p
itc
h
an
g
le
β
is
g
iv
in
g
b
y
I.
Ya
sm
in
e
a
n
d
B.
Ba
d
re
[
1
8
]
:
{
Cp
(
,
)
=
0
.
5
(
116
−
0
.
4
−
5
)
(
−
21
)
+
0
.
0068
1
=
1
+
0
.
08
−
0
.
035
3
+
1
;
=
(
3
)
T
h
e
v
ar
iatio
n
o
f
th
e
p
o
wer
co
ef
f
icien
t (
C
p
)
as a
f
u
n
ctio
n
o
f
(
T
SR
)
is
illu
s
tr
ated
in
Fig
u
r
e
2
.
As it c
an
b
e
s
ee
n
,
th
e
m
a
x
im
u
m
v
alu
e
o
f
C
p
m
ax
=0
.
4
7
9
is
o
b
tain
ed
w
h
en
λ
o
p
t=8
.
1
an
d
β =
0
.
Fig
u
r
e
2
.
T
h
e
p
o
we
r
co
ef
f
icien
t
C
p
cu
r
v
e
v
er
s
u
s
th
e
s
p
ee
d
r
ati
o
T
SR
f
o
r
s
ev
er
al
b
la
d
e
an
g
le
s
T
h
e
elec
tr
o
m
ag
n
etic
an
d
m
ec
h
an
ical
to
r
q
u
es e
q
u
atio
n
s
ar
e
r
elate
d
b
y
:
=
=
−
−
(
4
)
w
h
er
e
=
2
+
,
=
.
co
ef
f
icien
t o
f
f
r
ac
t
io
n
ate
.
,
an
d
in
er
tia
o
f
th
e
tu
r
b
in
e,
g
en
er
ato
r
an
d
th
e
to
tal
in
er
tia.
,
,
ar
e
th
e
to
r
q
u
e
ap
p
lied
o
n
th
e
g
e
n
er
ato
r
,
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
an
d
t
h
e
to
r
q
u
e
r
esu
ltin
g
f
r
o
m
th
e
v
is
co
u
s
f
r
ic
tio
n
,
r
esp
ec
tiv
ely
.
T
o
ca
p
tu
r
e
th
e
m
ax
im
u
m
o
f
th
e
win
d
en
er
g
y
,
th
e
r
o
ta
tio
n
al
s
p
ee
d
o
f
th
e
tu
r
b
in
e
m
u
s
t
b
e
co
n
tin
u
o
u
s
ly
ad
ju
s
ted
ac
co
r
d
i
n
g
to
th
e
win
d
s
p
ee
d
v
ar
iatio
n
s
[
1
9
]
.
T
h
e
m
ain
g
o
al
o
f
t
h
is
co
m
m
an
d
is
to
ad
ju
s
t c
o
n
tin
u
o
u
s
ly
th
e
tu
r
b
in
e
r
o
tatio
n
al
s
p
ee
d
at
t
h
e
v
alu
e
th
at
g
u
ar
an
tees a
n
o
p
tim
al
s
p
e
ed
r
atio
(
λ
o
p
t
)
.
In
th
is
p
ap
er
,
T
h
e
MPPT
tec
h
n
iq
u
e
h
as
b
ee
n
r
ea
lized
with
m
ec
h
an
ical
s
p
ee
d
co
n
tr
o
l
a
s
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
is
co
n
t
r
o
l
s
tr
ateg
y
co
n
s
is
ts
o
f
ad
ju
s
tin
g
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
th
at
i
s
d
ev
elo
p
ed
b
y
th
e
elec
tr
ical
g
en
er
ato
r
in
o
r
d
er
t
o
f
ix
it
at
its
r
ef
e
r
en
ce
v
alu
e.
T
o
ac
h
iev
e
th
is
,
a
s
p
ee
d
c
o
n
tr
o
l
h
as
b
ee
n
u
s
ed
to
en
s
u
r
e
th
at
th
e
m
ec
h
an
ical
s
p
e
ed
is
eq
u
al
to
th
e
r
e
f
er
en
ce
s
p
ee
d
.
T
h
is
s
p
ee
d
r
eg
u
latio
n
h
as
b
ee
n
p
r
o
ce
s
s
ed
b
y
th
r
ee
ty
p
es o
f
co
n
tr
o
ller
s
with
a
v
iew
to
m
ak
e
a
s
y
n
th
esis
an
d
a
co
m
p
ar
is
o
n
b
etwe
en
th
o
s
e
th
r
ee
co
n
t
r
o
ller
s
.
2
.
3
.
1
.
P
I
co
ntr
o
ller
T
h
e
clo
s
ed
-
lo
o
p
tr
an
s
f
er
f
u
n
ctio
n
ca
n
b
e
wr
itten
as:
Ω
(
)
Ω
∗
(
)
=
2
.
.
+
2
2
+
2
.
.
+
2
=
+
.
2
+
.
.
+
(
5
)
T
h
e
p
ar
am
eter
s
K
p
an
d
K
i
o
f
th
e
PI
co
n
tr
o
ller
a
r
e
g
iv
e
n
b
y
:
{
K
p
=
2ξ
.
ω
n
.
J
−
f
V
K
i
=
J
.
ω
n
2
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
P
erfo
r
ma
n
ce
imp
r
o
ve
men
t o
f th
e
va
r
ia
b
le
s
p
ee
d
w
in
d
t
u
r
b
in
e
d
r
ivin
g
a
d
o
u
b
l
y
fe
d
…
(
C
h
o
ja
a
Ha
mid
)
2473
t
R
Ω
V
v
1
J
s
+
F
1
G
23
p
t
1
C
ρ
π
R
V
2
Ω
1
G
G
+
_
PI
B
S
C
S
M
C
+
_
g
t
β
V
C
t
C
g
g
~
C
g
opt
λV
R
C
p
λ
T
u
r
b
i
n
e
G
e
a
r
b
o
x
A
x
i
s
o
f
D
F
I
G
C
o
n
t
r
o
l
s
p
e
e
d
Fig
u
r
e
3
.
B
lo
ck
d
iag
r
am
o
f
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t tr
ac
k
in
g
tech
n
iq
u
e
u
s
in
g
s
p
ee
d
co
n
tr
o
l
2
.
3
.
2
.
B
a
ck
s
t
eppin
g
co
ntr
o
ller
T
o
d
esig
n
a
b
ac
k
s
tep
p
in
g
c
o
n
t
r
o
l
o
f
th
e
m
e
ch
an
ical
s
p
ee
d
.
W
e
s
tar
t
b
y
d
ef
in
in
g
th
e
tr
ac
k
in
g
er
r
o
r
o
f
th
e
s
et
p
o
in
t a
s
[
2
0
]
:
e
(
Ω
g
)
=
Ω
g
∗
−
Ω
g
(
7
)
W
e
co
n
s
id
er
th
e
f
o
llo
win
g
L
y
ap
u
n
o
v
f
u
n
ctio
n
:
v
(
e
)
=
1
2
e
(
Ω
g
)
2
(
8
)
B
y
d
er
iv
in
g
(
9
)
a
n
d
u
s
in
g
th
e
s
p
ee
d
d
y
n
a
m
ic
in
(
4
)
,
T
h
e
L
y
a
p
u
n
o
v
f
u
n
ctio
n
d
er
iv
ativ
e
ca
n
b
e
f
o
r
m
u
lated
as:
v
̇
(
e
)
=
e
(
Ω
g
)
.
e
̇
(
Ω
g
)
=
(
Ω
)
.
(
Ω
∗
̇
+
1
(
+
.
−
)
)
(
9
)
T
h
e
s
tab
ilizin
g
co
n
tr
o
l o
f
b
ac
k
s
tep
p
in
g
is
d
ef
in
ed
as f
o
llo
ws:
C
em
∗
=
−
.
Ω
∗
̇
−
.
+
−
1
.
(
Ω
)
(
1
0
)
W
ith
K
1
is
a
p
o
s
itiv
e
co
n
s
tan
t.
B
y
s
u
b
s
titu
tin
g
th
e
(
1
0
)
i
n
(
9
)
,
t
h
e
r
esu
lt c
an
b
e
g
iv
en
as:
̇
(
)
=
−
1
.
e
(
Ω
g
)
2
<
0
(
1
1
)
2
.
3
.
3
.
Sli
di
ng
m
o
de
co
ntr
o
ller
T
o
d
eter
m
in
e
th
e
co
m
m
an
d
m
ag
n
itu
d
e
C
em
∗
,
th
e
r
elativ
e
d
eg
r
ee
o
f
th
e
s
u
r
f
a
ce
is
eq
u
al
to
o
n
e.
T
h
e
s
lid
in
g
s
u
r
f
ac
e
is
d
ef
in
e
d
b
y
:
S
(
Ω
g
)
=
Ω
g
∗
−
Ω
g
(
1
2
)
W
e
co
n
s
id
er
th
e
f
o
llo
win
g
L
y
ap
u
n
o
v
f
u
n
ctio
n
:
V
(
S
(
Ω
g
)
)
=
1
2
S
(
Ω
g
)
2
(
1
3
)
T
h
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
d
er
iv
a
tiv
e
ca
n
b
e
e
x
p
r
ess
ed
as:
V
̇
(
S
(
Ω
g
)
)
=
(
Ω
)
.
̇
(
Ω
)
(
1
4
)
W
it
h
S
̇
(
Ω
)
=
Ω
∗
̇
−
Ω
̇
(
1
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
4
70
–
24
82
2474
B
y
r
e
p
l
ac
i
n
g
th
e
(
4
)
,
W
e
g
et:
S
̇
(
Ω
g
)
=
Ω
∗
̇
+
1
J
(
C
em
+
f
v
.
Ω
g
−
C
g
)
(
1
6
)
R
ep
l
ac
i
n
g
th
e
c
o
m
m
a
n
d
C
em
b
y
i
ts
e
q
u
i
v
al
en
t
co
m
p
o
n
en
ts
(
C
em
eq
+
C
em
n
)
in
(1
6
)
,
we
f
i
n
d
:
S
̇
(
Ω
g
)
=
Ω
g
∗
̇
+
1
J
(
(
C
em
eq
+
C
em
n
)
+
f
v
.
Ω
g
−
C
g
)
(
1
7
)
Du
r
in
g
t
h
e
s
lid
in
g
m
o
d
e
a
n
d
in
th
e
s
tead
y
s
tate
we
h
av
e:
S
(
Ω
g
)
=
0
;
S
̇
(
Ω
g
)
=
0
an
d
C
em
n
=
0
.
Fro
m
th
ese
s
tatem
en
ts
,
we
ca
n
ex
tr
ac
t th
e
e
x
p
r
ess
i
o
n
o
f
th
e
e
q
u
i
v
al
en
t
co
m
m
a
n
d
C
em
eq
as t
h
e
f
o
ll
o
wi
n
g
:
C
em
eq
=
−
J
.
Ω
g
∗
̇
−
f
v
.
Ω
g
+
C
g
(
1
8
)
R
ep
lacin
g
th
e
(
18
)
i
n
(
1
7
),
th
e
r
es
u
lt
b
e
ca
m
e
as
:
S
̇
(
Ω
g
)
=
1
J
C
em
n
(
1
9
)
T
o
en
s
u
r
e
th
e
co
n
v
er
g
e
n
ce
o
f
L
y
ap
u
n
o
v
'
s
f
u
n
ctio
n
,
we
s
et:
C
em
n
=
−
K
2
.
s
ign
(
S
(
Ω
g
)
)
(
2
0
)
Su
ch
as
K
2
is
a
p
o
s
itiv
e
co
n
s
tan
t.
2
.
2
.
M
o
delin
g
o
f
t
he
wind
t
urbi
n
e
a
nd
M
P
P
T
co
ntr
o
l st
ra
t
eg
y
T
h
e
g
e
n
e
r
a
l
m
ath
em
atica
l
e
q
u
ati
o
n
s
o
f
th
e
v
o
lt
ag
es,
f
lu
x
an
d
ac
t
iv
e/
r
e
ac
t
iv
e
p
o
we
r
s
o
f
t
h
e
d
o
u
b
l
y
f
e
d
in
d
u
cti
o
n
g
en
e
r
at
o
r
i
n
t
h
e
d
q
P
ar
k
r
ef
er
en
ce
a
r
e
g
i
v
e
n
b
y
t
h
e
f
o
ll
o
wi
n
g
ex
p
r
ess
i
o
n
s
[
21
]
,
[
22
]:
vol
ta
ge
e
q
ua
tion
s
∶
{
=
+
−
=
+
+
=
+
−
(
−
)
=
+
+
(
−
)
(
2
1
)
fl
ux
e
q
ua
tion
s
∶
{
=
+
=
+
=
+
=
+
(
2
2
)
pow
e
r
e
q
ua
tio
n
s
∶
{
=
3
2
{
⃗
×
∗
}
=
3
2
(
+
)
=
3
2
{
⃗
×
∗
}
=
3
2
(
−
)
(
2
3
)
w
h
er
e
ω
s
is
th
e
p
u
ls
atio
n
o
f
th
e
s
tato
r
v
ar
iab
les an
d
ω
r
is
th
e
p
u
ls
atio
n
o
f
th
e
r
o
to
r
o
n
es.
T
h
is
last
p
ar
am
eter
is
g
iv
en
b
y
:
=
−
.
(
2
4
)
T
h
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
is
ex
p
r
ess
ed
as:
=
3
2
{
⃗
⃗
⃗
⃗
⃗
×
∗
⃗
⃗
⃗
}
=
3
2
(
−
)
(
2
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
P
erfo
r
ma
n
ce
imp
r
o
ve
men
t o
f th
e
va
r
ia
b
le
s
p
ee
d
w
in
d
t
u
r
b
in
e
d
r
ivin
g
a
d
o
u
b
l
y
fe
d
…
(
C
h
o
ja
a
Ha
mid
)
2475
3.
AP
P
L
I
CA
T
I
O
N
O
F
T
H
E
V
E
CT
O
R
CO
N
T
RO
L
O
N
T
H
E
DF
I
G
T
h
e
asy
n
ch
r
o
n
o
u
s
m
ac
h
in
e
ca
n
ad
o
p
t
s
ev
er
al
ty
p
es
o
f
co
n
tr
o
l
s
u
ch
as
v
ec
to
r
co
n
tr
o
l,
wh
i
ch
en
s
u
r
es
d
ec
o
u
p
lin
g
b
etwe
en
its
v
a
r
iab
l
es
an
d
m
ak
es
it
s
im
ila
r
t
o
a
D
C
g
en
er
ato
r
[
2
3
]
-
[
2
5
]
.
T
o
d
ec
o
u
p
le
t
h
e
c
o
n
tr
o
l
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
,
we
ad
o
p
t
in
th
is
wo
r
k
th
e
tech
n
iq
u
e
o
f
s
tato
r
f
ield
o
r
ien
tatio
n
.
B
y
s
ettin
g
th
e
s
tato
r
f
ield
v
ec
to
r
alig
n
ed
with
d
-
ax
i
s
,
we
o
b
tain
:
{
∅
=
0
∅
=
(
2
6
)
{
=
0
=
=
(
27
)
Acc
o
r
d
in
g
t
o
th
is
s
tatem
en
t,
th
e
(
2
2
)
ca
n
b
e
s
im
p
lifie
d
:
{
=
−
=
−
(
2
8
)
T
h
e
ex
p
r
ess
io
n
o
f
th
e
r
o
to
r
f
lu
x
b
ec
o
m
es:
{
∅
=
+
∅
=
(
29
)
W
ith
=
1
−
2
is
th
e
d
is
p
er
s
io
n
co
ef
f
icien
t o
f
B
lo
n
d
el.
Fro
m
(
2
1
)
,
we
d
e
d
u
ce
th
e
ex
p
r
ess
io
n
s
o
f
th
e
co
n
tr
o
l v
ar
ia
b
les
an
d
:
{
=
+
−
=
+
+
+
(
3
0
)
R
ep
lacin
g
th
e
ex
p
r
ess
io
n
s
o
f
,
an
d
∅
in
th
e
ex
p
r
ess
io
n
o
f
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
an
d
th
e
s
tato
r
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
in
(
2
3
)
an
d
(
2
5
)
,
we
ca
n
ex
p
r
ess
C
em
,
P
s
an
d
Q
s
b
y
(
3
1
)
a
n
d
(
3
2
)
r
esp
ec
tiv
ely
:
=
−
3
2
=
−
3
2
(
3
1
)
{
=
−
3
2
=
3
2
(
−
)
(
32
)
4.
AP
P
L
I
CA
T
I
O
N
O
F
T
H
E
S
L
I
D
I
NG
M
O
D
E
CO
NT
RO
L
O
F
DF
I
G
T
h
e
s
lid
in
g
m
o
d
e
k
n
ew
a
b
ig
s
u
cc
ess
d
u
r
in
g
last
y
ea
r
s
.
I
t
is
d
u
e
to
its
im
p
lem
en
tatio
n
s
im
p
licity
an
d
th
e
r
o
b
u
s
tn
ess
with
r
eg
ar
d
to
th
e
s
y
s
tem
u
n
ce
r
tain
ties
an
d
th
e
ex
ter
n
al
d
is
tu
r
b
an
ce
s
.
T
h
e
SMC
co
n
s
i
s
ts
to
r
etu
r
n
th
e
s
tate
tr
ajec
to
r
y
t
o
war
d
s
th
e
s
lid
in
g
s
u
r
f
ac
e
an
d
t
o
d
e
v
elo
p
it
ab
o
v
e,
with
a
ce
r
tain
d
y
n
am
ic
u
p
t
o
th
e
eq
u
ilib
r
iu
m
[
2
6
]
.
T
h
e
s
lid
in
g
m
o
d
e
co
n
tr
o
l g
o
es th
r
o
u
g
h
th
r
ee
s
tag
es:
-
C
h
o
ice
th
e
s
witch
in
g
s
u
r
f
ac
e
-
C
o
n
v
er
g
en
ce
co
n
d
itio
n
-
C
alcu
latio
n
o
f
th
e
co
n
tr
o
l la
w
s
T
h
e
s
tato
r
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
co
n
tr
o
l su
r
f
ac
es h
av
e
th
e
f
o
r
m
:
{
S
(
)
=
−
(
)
=
−
(
33
)
T
h
e
d
e
r
i
v
ati
v
es
o
f
t
h
e
s
u
r
f
a
ce
s
a
r
e
o
b
t
ai
n
e
d
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
4
70
–
24
82
2476
{
̇
(
)
=
(
̇
−
̇
)
̇
(
)
=
(
̇
−
̇
)
(
34
)
W
e
r
ep
lace
th
e
ex
p
r
ess
io
n
s
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
(
3
2
)
in
th
e
last
o
n
e:
{
̇
(
)
=
(
̇
+
3
2
.
.
.
̇
)
̇
(
)
=
̇
−
(
−
3
2
.
.
.
̇
)
(
3
5
)
T
h
e
n
e
x
t
s
t
ep
is
t
o
d
r
a
w
t
h
e
ex
p
r
ess
i
o
n
s
o
f
t
h
e
cu
r
r
e
n
ts
d
er
iv
ati
v
es
I
̇
r
d
q
f
r
o
m
(
30
)
a
n
d
s
u
b
s
ti
tu
t
e
i
t i
n
th
e
(
3
6
)
:
{
̇
(
)
=
̇
+
3
2
.
.
.
.
(
−
.
−
.
.
.
.
+
.
.
.
)
̇
(
)
=
(
̇
+
3
2
.
.
.
.
.
(
−
+
.
.
.
.
)
(
3
6
)
R
ep
l
ac
i
n
g
V
r
d
q
b
y
(
V
r
d
q
eq
+
V
r
d
q
n
)
,
th
e
c
o
n
tr
o
ls
p
r
i
n
ci
p
als
a
p
p
ea
r
s
cle
a
r
l
y
i
n
(
3
7
)
:
{
̇
(
)
=
̇
+
3
2
.
.
.
.
.
(
(
+
)
−
.
−
.
.
.
.
+
.
.
.
)
̇
(
)
=
(
̇
+
3
2
.
.
.
.
.
(
(
+
)
−
+
.
.
.
.
)
(
3
7
)
Du
r
in
g
th
e
s
lid
in
g
m
o
d
e
an
d
in
th
e
s
tead
y
s
tate,
we
h
av
e:
{
(
)
=
0
,
̇
(
)
=
0
,
=
0
(
)
=
0
,
̇
(
)
=
0
,
=
0
(
3
8
)
T
h
e
eq
u
iv
ale
n
ts
co
n
tr
o
l c
o
m
p
o
n
en
ts
V
r
d
q
eq
ca
n
d
ed
u
ce
d
as:
{
=
−
2
3
.
.
.
.
.
̇
+
.
+
.
.
.
.
−
.
.
.
=
−
2
3
.
.
.
.
.
̇
+
−
.
.
.
.
(
3
9
)
Du
r
in
g
th
e
c
o
n
v
e
r
g
en
ce
m
o
d
e
,
s
o
th
at
th
e
co
n
d
itio
n
s
(
)
.
̇
(
)
≤
0
an
d
S
(
Q
)
.
S
̇
(
Q
)
≤
0
ar
e
s
atis
f
ied
,
we
ass
u
m
e:
{
̇
(
)
=
3
2
.
.
.
.
.
̇
(
)
=
3
2
.
.
.
.
.
(
4
0
)
T
h
er
ef
o
r
e,
th
e
s
witch
in
g
ter
m
s
g
iv
en
b
y
:
{
=
−
.
(
(
)
)
=
−
.
(
(
)
)
(
4
1
)
T
o
ch
ec
k
th
e
s
tab
ilit
y
co
n
d
iti
o
n
o
f
th
e
s
y
s
tem
,
th
e
p
ar
a
m
e
ter
s
K
Vd
an
d
K
Vq
m
u
s
t
b
e
p
o
s
itiv
e.
I
n
o
r
d
er
to
r
e
d
u
ce
an
y
p
o
s
s
ib
le
o
v
er
s
h
o
o
tin
g
o
f
th
e
v
o
ltag
es
co
m
p
o
n
e
n
ts
V
r
d
q
,
it
is
o
f
ten
u
s
ef
u
l
to
ad
d
v
o
ltag
e
s
lim
iter
s
,
wh
ich
ex
p
r
ess
ed
b
y
:
{
=
.
(
)
=
.
(
)
(
4
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
P
erfo
r
ma
n
ce
imp
r
o
ve
men
t o
f th
e
va
r
ia
b
le
s
p
ee
d
w
in
d
t
u
r
b
in
e
d
r
ivin
g
a
d
o
u
b
l
y
fe
d
…
(
C
h
o
ja
a
Ha
mid
)
2477
5.
B
ACK
S
T
E
P
P
I
NG
CO
NT
R
O
L
O
F
T
H
E
DF
I
G
T
h
e
b
ac
k
s
tep
p
in
g
ap
p
r
o
ac
h
is
a
r
ec
u
r
s
iv
e
tech
n
iq
u
e
d
esig
n
f
o
r
s
tab
ilizin
g
h
ig
h
l
y
n
o
n
lin
ea
r
d
y
n
am
ical
s
y
s
tem
[
2
7
]
.
T
h
e
p
r
in
cip
le
o
f
th
e
b
a
ck
s
tep
p
i
n
g
co
n
t
r
o
ller
is
th
e
u
s
e
o
f
a
v
ir
tu
al
co
n
t
r
o
l
to
d
ec
o
m
p
o
s
e
a
c
o
m
p
lex
n
o
n
li
n
ea
r
s
y
s
tem
p
r
o
b
lem
in
to
v
ar
io
u
s
s
im
p
ler
d
esig
n
s
tep
s
.
T
h
e
s
tab
ilit
y
an
d
p
er
f
o
r
m
an
ce
o
f
th
e
s
y
s
tem
is
ac
h
iev
ed
b
y
u
s
in
g
a
L
y
a
p
u
n
o
v
f
u
n
ctio
n
th
at
is
u
s
ed
to
d
r
iv
e
th
e
v
ir
tu
al
c
o
n
tr
o
l
[
2
8
]
,
[
2
9
]
.
T
h
e
er
r
o
r
s
b
etwe
en
th
e
r
ef
er
en
ce
an
d
th
e
m
ea
s
u
r
e
d
s
ig
n
als
o
f
s
tato
r
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
ar
e
d
ef
in
ed
as [
3
0
]
.
{
1
=
−
2
=
−
(
4
3
)
T
h
eir
d
er
iv
ates a
r
e
g
iv
en
as:
{
̇
1
=
̇
+
.
.
.
(
−
.
−
.
.
.
+
.
.
.
)
̇
2
=
̇
+
.
.
.
(
−
.
+
.
.
.
)
(
4
4
)
T
h
e
ch
o
o
s
ed
L
y
ap
u
n
o
v
f
u
n
cti
o
n
is
f
o
r
m
u
lated
as:
{
(
1
)
=
1
2
1
2
(
1
,
2
)
=
1
2
1
2
+
1
2
2
2
(
4
5
)
T
h
e
d
er
iv
ativ
e
o
f
ea
c
h
er
r
o
r
L
y
ap
u
n
o
v
f
u
n
ctio
n
is
wr
itten
as f
o
llo
w:
{
̇
(
1
)
=
1
.
̇
1
=
1
.
(
̇
+
.
.
.
(
−
.
−
.
.
.
+
.
.
.
)
)
̇
(
2
)
=
1
.
̇
1
+
2
.
̇
2
=
−
1
.
1
2
+
2
(
̇
+
.
.
.
(
−
.
+
.
.
)
)
(
4
6
)
T
h
e
co
n
tr
o
l v
o
ltag
es selecte
d
as f
o
llo
ws:
{
V
rq
r
ef
=
−
σ
.
L
s
.
L
r
V
s
.
L
m
.
P
̇
s
r
ef
+
R
r
i
rd
+
ω
r
.
σ
.
L
r
.
i
rd
−
g
.
L
m
.
V
s
ω
s
.
L
s
−
σ
.
L
s
.
L
r
V
s
.
Lm
.
K
3
.
e
1
V
rd
r
ef
=
−
σ
.
L
s
.
L
r
V
s
.
L
m
.
Q
̇
s
r
ef
+
R
r
i
rd
−
ω
r
.
σ
.
L
r
.
i
rq
−
σ
.
L
s
.
L
r
V
s
.
Lm
.
K
4
.
e
2
(
4
7
)
W
h
er
e:
K
3
an
d
K
4
ar
e
p
o
s
itiv
es c
o
n
s
tan
ts
.
6.
G
RID SI
D
E
CO
NV
E
R
T
E
R
T
h
e
d
-
q
ax
is
co
m
p
o
n
en
ts
o
f
th
e
g
r
id
s
id
e
co
n
v
er
ter
ar
e
f
o
r
m
u
lated
as:
{
=
.
+
.
−
.
.
=
.
+
.
+
.
.
.
(
4
8
)
th
e
v
o
ltag
e
o
f
th
e
DC
lin
k
[
21
]
.
{
=
−
=
=
.
=
.
(
4
9
)
w
h
er
e
a
n
d
r
ep
r
esen
ts
th
e
o
u
tp
u
ts
cu
r
r
en
ts
o
f
r
o
to
r
s
id
e
co
n
v
er
ter
an
d
g
r
id
s
id
e
co
n
v
er
ter
,
r
esp
ec
tiv
ely
.
T
h
e
ac
tiv
e
an
d
r
e
ac
tiv
e
p
o
w
er
ex
p
r
ess
ed
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
4
70
–
24
82
2478
{
=
.
=
.
(
5
0
)
T
o
illu
s
tr
ate
th
e
s
ch
em
at
ic
d
ia
g
r
am
o
f
th
e
g
l
o
b
al
co
n
tr
o
l stra
teg
y
f
o
r
DFI
G,
a
b
lo
c
k
d
iag
r
a
m
o
f
th
e
w
h
o
le
s
y
s
tem
is
p
r
o
p
o
s
ed
i
n
Fig
u
r
e
4
.
D
F
I
G
Lf
P
M
W
P
M
W
A
B
C
dq
A
B
C
dq
Wi
n
d
T
u
r
b
i
n
e
G
e
a
r
b
o
x
R
S
C
G
S
C
Rf
V
Fo
c
-
PI
B
SC
SM
C
T
r
a
n
s
f
o
r
m
e
r
G
r
i
d
F
i
l
t
e
r
P
_
Q
r
e
f
=
0
V
d
c_
m
es
PI
P
o
w
e
r
f
a
c
tor
c
o
n
tr
o
l
V
dq
V
dc
*
+
Q
r
e
f
=
0
V
dq
t
g
M
P
P
T
P
s
*
β
β
V
g
Fig
u
r
e
4
.
Sch
em
atic
d
iag
r
am
o
f
th
e
g
l
o
b
al
co
n
tr
o
l stra
teg
y
f
o
r
DFI
G
7.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
I
n
o
r
d
e
r
to
ev
alu
ate
th
e
p
e
r
f
o
r
m
an
ce
o
f
th
e
win
d
e
n
er
g
y
c
o
n
v
er
s
io
n
ch
ain
,
eq
u
ip
p
e
d
with
th
e
MPPT
co
n
tr
o
l
s
tr
ateg
y
with
m
ec
h
a
n
ical
s
p
ee
d
c
o
n
tr
o
l
an
d
two
p
o
wer
co
n
v
er
ter
s
c
o
n
n
ec
ted
to
t
h
e
r
o
to
r
an
d
to
th
e
g
r
id
(
R
SC
an
d
GSC
)
a
s
s
h
o
w
n
in
Fig
u
r
e
1
.
W
e
p
er
f
o
r
m
ed
a
s
er
ies
o
f
s
im
u
latio
n
s
in
th
e
MA
T
L
AB
/S
im
u
lin
k
en
v
ir
o
n
m
en
t,
u
n
d
e
r
an
in
s
tan
tan
eo
u
s
win
d
s
p
ee
d
p
r
o
f
ile,
v
ar
y
in
g
b
etwe
en
8
m
/s
an
d
1
2
m
/s
as
Fig
u
r
e
5
(
a)
d
em
o
n
s
tr
ates
.
T
h
e
s
tu
d
ied
g
lo
b
al
s
y
s
tem
p
ar
am
eter
s
ar
e
lis
ted
in
T
ab
le
1
.
T
ab
le
1
.
Par
am
eter
s
o
f
MA
T
L
AB
/
Simu
lin
k
P
a
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r
ed
r
eg
ar
d
less
o
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th
e
r
ef
er
en
ce
v
ar
iatio
n
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d
with
d
if
f
er
en
t
r
esp
o
n
s
e
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e,
o
v
er
s
h
o
o
t
an
d
o
s
cillatio
n
s
f
o
r
th
e
th
r
ee
c
o
n
tr
o
l
s
tr
ateg
ies.
No
te
th
at
th
e
b
est
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alu
es
o
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th
e
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er
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o
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ce
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ar
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e
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e
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es
o
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ly
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o
l
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y
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e
b
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ck
s
tep
p
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g
tech
n
i
q
u
e.
Fig
u
r
e
6
(
d
)
s
h
o
ws
th
e
s
im
u
latio
n
r
esu
lt
o
f
th
e
DC
b
u
s
v
o
ltag
e.
I
t
is
clea
r
th
at
i
ts
cu
r
v
e
f
o
llo
ws
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e
r
ef
er
en
ce
with
a
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ast
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an
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ien
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r
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e
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lo
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o
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cillatio
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s
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o
r
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e
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ee
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n
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o
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ateg
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lied
.
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u
r
e
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ity
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at
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e
s
tato
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s
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e,
we
m
ain
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ain
ed
th
e
s
tato
r
r
ea
ctiv
e
p
o
wer
r
ef
er
en
c
e
at
ze
r
o
(
Qs*
=
0
VAR).
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o
o
p
tim
ize
th
e
q
u
ality
o
f
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e
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er
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e
r
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e
f
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k
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f
ac
to
r
o
p
tim
al
as
s
h
o
wn
in
Fig
u
r
e
6
(
e)
.
B
ased
o
n
f
in
d
in
g
s
f
r
o
m
th
e
s
im
u
latio
n
,
th
e
u
n
ity
p
o
wer
f
ac
to
r
(
c
o
s
ϕ
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is
p
er
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ec
tly
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h
iev
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b
y
th
e
r
ea
ctiv
e
p
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we
r
co
n
tr
o
l
f
o
r
th
e
th
r
ee
co
n
tr
o
l
tech
n
iq
u
es
in
v
a
r
iab
le
s
p
ee
d
o
p
er
atio
n
.
Ho
wev
e
r
,
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