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%
o
f
th
e
co
u
n
tr
y
'
s
to
tal
el
ec
tr
icity
g
en
er
atio
n
ca
p
ac
ity
,
u
n
d
e
r
s
co
r
es
Mo
r
o
cc
o
'
s
co
m
m
itm
en
t
to
ac
h
iev
in
g
its
r
en
ewa
b
le
en
er
g
y
tar
g
ets
an
d
alig
n
s
with
its
p
lan
s
to
f
u
r
t
h
er
ex
p
an
d
its
win
d
p
o
wer
ca
p
ab
ilit
ies
[
4
]
.
E
n
s
u
r
in
g
o
p
tim
al
p
er
f
o
r
m
a
n
ce
an
d
s
tab
ilit
y
o
f
s
u
ch
g
e
n
er
ato
r
s
r
eq
u
ir
es
s
o
p
h
is
ticated
co
n
tr
o
l
s
tr
ateg
ies
f
o
r
b
o
th
th
e
m
ac
h
i
n
e
-
s
id
e
co
n
v
er
ter
(
MSC
)
an
d
th
e
g
r
id
-
s
id
e
co
n
v
er
ter
(
G
SC
)
.
T
h
is
r
esear
ch
f
o
cu
s
es
o
n
a
d
v
an
ci
n
g
th
e
u
n
d
er
s
tan
d
in
g
o
f
cu
r
r
en
t
c
o
n
tr
o
l
t
ec
h
n
iq
u
es
in
th
e
co
n
tex
t
o
f
D
D
-
PMSG
s
y
s
tem
s
,
em
p
lo
y
in
g
f
iled
an
d
v
o
ltag
e
-
o
r
ien
ted
co
n
tr
o
ls
[
5
]
.
T
h
e
ac
ad
em
ic
liter
atu
r
e
r
ev
ea
ls
a
p
r
o
g
r
ess
iv
e
ev
o
lu
tio
n
in
co
n
tr
o
l
tech
n
i
q
u
es
f
o
r
p
er
m
an
en
t
m
ag
n
et
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
(
PMSG
)
s
y
s
tem
s
.
E
ar
ly
s
tu
d
ies
p
r
ed
o
m
i
n
an
tly
f
o
cu
s
ed
o
n
v
e
cto
r
co
n
tr
o
l
m
eth
o
d
s
,
in
clu
d
i
n
g
f
ield
-
o
r
ie
n
ted
c
o
n
tr
o
l
(
FOC
)
an
d
d
ir
ec
t
to
r
q
u
e
co
n
tr
o
l
(
DT
C
)
.
T
h
ese
ap
p
r
o
ac
h
es
p
r
o
v
id
ed
f
o
u
n
d
atio
n
al
in
s
i
g
h
ts
in
to
co
n
tr
o
llin
g
to
r
q
u
e
a
n
d
f
lu
x
e
f
f
ec
tiv
ely
,
wh
ich
ar
e
cr
itical
f
o
r
th
e
ef
f
i
cien
t
o
p
er
atio
n
o
f
PMSGs
.
F
o
r
ex
am
p
le,
FOC
an
d
DT
C
estab
lis
h
ed
co
n
tr
o
l
m
ec
h
an
is
m
s
th
at
im
p
r
o
v
ed
th
e
ac
cu
r
ac
y
an
d
ef
f
icie
n
cy
o
f
PMSG
s
y
s
tem
s
,
th
o
u
g
h
th
ey
en
co
u
n
ter
e
d
ch
allen
g
es
s
u
ch
as
to
r
q
u
e
r
ip
p
les
an
d
v
a
r
iab
le
s
witch
in
g
f
r
eq
u
en
cies
[
6
]
.
W
ith
th
e
g
r
o
win
g
in
teg
r
atio
n
o
f
PMSGs
in
to
g
r
id
-
co
n
n
ec
ted
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
r
esea
r
ch
p
r
io
r
ities
s
h
if
ted
to
war
d
g
r
id
s
y
n
ch
r
o
n
izatio
n
an
d
p
o
wer
q
u
ality
en
h
a
n
ce
m
e
n
t.
T
h
is
tr
a
n
s
itio
n
em
p
h
asized
th
e
r
o
le
o
f
r
ea
ctiv
e
p
o
wer
co
n
tr
o
l
in
m
ain
tain
i
n
g
g
r
id
s
tab
ilit
y
an
d
m
itig
atin
g
d
is
tu
r
b
an
ce
s
.
Pro
p
o
r
tio
n
al
-
i
n
t
eg
r
al
(
PI)
co
n
t
r
o
ller
s
h
av
e
b
e
en
wid
ely
a
d
o
p
te
d
d
u
e
to
th
eir
s
im
p
licity
an
d
s
tead
y
-
s
tate
p
er
f
o
r
m
an
ce
; h
o
wev
er
,
th
eir
lim
itatio
n
s
u
n
d
e
r
d
y
n
am
ic
co
n
d
itio
n
s
an
d
p
ar
am
eter
v
a
r
iatio
n
s
ar
e
well
-
d
o
cu
m
e
n
ted
[
7
]
,
[
8
]
.
Ad
v
a
n
c
e
d
co
n
t
r
o
l
m
et
h
o
d
o
l
o
g
ies,
l
ik
e
s
li
d
i
n
g
m
o
d
e
c
o
n
tr
o
l
(
S
MC)
a
n
d
b
ac
k
s
t
e
p
p
in
g
c
o
n
tr
o
l
,
h
a
v
e
b
e
en
i
n
v
esti
g
ate
d
t
o
o
v
e
r
c
o
m
e
th
e
co
n
s
t
r
ai
n
ts
o
f
t
r
a
d
i
ti
o
n
al
co
n
t
r
o
ll
er
s
.
S
MC
is
r
ec
o
g
n
ize
d
f
o
r
its
r
o
b
u
s
t
n
ess
ag
ai
n
s
t
s
y
s
te
m
u
n
c
er
tai
n
t
ies
a
n
d
e
x
te
r
n
al
d
is
tu
r
b
a
n
c
es
b
u
t
s
u
f
f
e
r
s
f
r
o
m
c
h
atte
r
i
n
g
e
f
f
ec
ts
,
p
o
te
n
ti
all
y
im
p
ac
ti
n
g
g
e
n
e
r
a
to
r
s
ta
b
il
it
y
[
7
]
–
[
1
2
]
.
B
ac
k
s
t
ep
p
i
n
g
c
o
n
tr
o
l
,
w
h
il
e
o
f
f
er
in
g
s
ta
b
i
lit
y
g
u
a
r
a
n
t
ee
s
,
b
e
co
m
es
co
m
p
u
tati
o
n
a
ll
y
c
o
m
p
l
e
x
as
s
y
s
te
m
o
r
d
er
s
i
n
cr
ea
s
e
.
Si
m
il
a
r
ly
,
a
r
ti
f
ic
ial
in
tel
li
g
e
n
c
e
(
AI
)
b
as
ed
m
e
th
o
d
s
s
u
c
h
as
f
u
z
z
y
l
o
g
ic
an
d
n
e
u
r
a
l
n
et
wo
r
k
s
h
av
e
b
e
en
em
p
l
o
y
e
d
to
cr
ea
t
e
a
d
a
p
t
iv
e
c
o
n
t
r
o
l
l
aws
,
b
u
t
t
h
e
ir
r
e
lia
n
ce
o
n
ex
t
e
n
s
i
v
e
t
r
a
in
in
g
d
a
ta
an
d
c
o
m
p
u
t
ati
o
n
al
r
eso
u
r
c
es
m
ak
es
t
h
e
m
less
s
u
i
te
d
f
o
r
r
e
al
-
ti
m
e
c
o
n
tr
o
l
a
p
p
lic
ati
o
n
s
[
1
3
]
.
AI
-
d
r
iv
en
co
n
tr
o
l
m
eth
o
d
o
lo
g
ies,
in
clu
d
in
g
f
u
zz
y
lo
g
ic
s
y
s
tem
s
an
d
n
eu
r
al
n
etwo
r
k
s
(
NN)
,
an
d
d
ee
p
r
ein
f
o
r
ce
m
e
n
t
lear
n
in
g
(
DR
L
)
ar
e
g
ain
in
g
in
cr
ea
s
in
g
atten
tio
n
in
win
d
tu
r
b
in
e
c
o
n
tr
o
l
d
u
e
to
t
h
eir
ad
ap
tab
ilit
y
an
d
d
ata
-
d
r
iv
en
n
atu
r
e.
T
h
ese
m
eth
o
d
s
ca
n
lear
n
co
m
p
lex
n
o
n
lin
ea
r
r
elat
io
n
s
h
ip
s
,
ad
ap
t
to
ch
an
g
in
g
co
n
d
itio
n
s
,
an
d
en
h
a
n
ce
co
n
tr
o
l
r
o
b
u
s
tn
ess
.
W
h
ile
th
ey
o
f
f
er
p
r
o
m
is
in
g
alter
n
ativ
es
to
co
n
v
e
n
tio
n
al
o
p
tim
izatio
n
-
b
ased
tech
n
iq
u
e
s
lik
e
p
ar
ticle
s
war
m
o
p
tim
i
za
tio
n
(
PSO
)
an
d
g
en
etic
alg
o
r
ith
m
(
GA
)
[
1
4
]
,
wh
ich
o
f
ten
s
u
f
f
er
f
r
o
m
lo
ca
l
o
p
tim
a
an
d
h
ig
h
co
m
p
u
tatio
n
al
co
s
ts
,
AI
m
eth
o
d
s
also
p
r
esen
t
ch
allen
g
es
r
elate
d
to
tr
ain
in
g
d
ata
r
eq
u
i
r
em
en
ts
,
r
ea
l
-
tim
e
d
ep
lo
y
m
en
t
,
an
d
h
ar
d
war
e
c
o
m
p
atib
ilit
y
[
1
5
]
.
T
o
p
r
o
v
id
e
a
clea
r
er
o
v
e
r
v
iew
o
f
co
n
t
r
o
l
s
tr
ateg
ies,
T
ab
le
1
p
r
esen
ts
a
c
o
m
p
ar
ativ
e
a
n
aly
s
is
b
ased
o
n
k
ey
cr
iter
ia
s
u
c
h
as
ac
cu
r
ac
y
,
r
o
b
u
s
tn
ess
,
co
m
p
u
tatio
n
al
d
em
a
n
d
,
an
d
r
ea
l
-
tim
e
f
ea
s
ib
ilit
y
.
T
h
is
c
o
m
p
ar
is
o
n
h
ig
h
lig
h
ts
th
e
tr
ad
e
-
o
f
f
s
b
etwe
en
tr
a
d
itio
n
al,
o
p
tim
izatio
n
-
b
ased
,
a
n
d
in
tellig
en
t c
o
n
tr
o
l m
eth
o
d
s
.
Desp
ite
ad
v
an
ce
m
en
ts
in
co
n
tr
o
l
s
tr
ateg
ies
f
o
r
g
r
id
-
c
o
n
n
ec
ted
PMSG
win
d
tu
r
b
in
es,
ch
allen
g
es
r
em
ain
with
class
ical
PI
co
n
tr
o
ller
s
,
an
d
ad
v
an
ce
d
m
eth
o
d
s
lik
e
b
ac
k
s
tep
p
in
g
an
d
m
o
d
el
p
r
e
d
ictiv
e
co
n
tr
o
l
(
MPC
)
f
ac
e
lim
itatio
n
s
.
W
h
ile
b
ac
k
s
tep
p
in
g
co
n
tr
o
l
o
f
f
er
s
r
o
b
u
s
tn
ess
f
o
r
n
o
n
li
n
ea
r
s
y
s
tem
s
,
its
co
m
p
u
tatio
n
al
co
m
p
lex
ity
ca
n
h
in
d
er
im
p
lem
e
n
tatio
n
in
h
ig
h
er
-
o
r
d
e
r
s
y
s
tem
s
.
On
th
e
o
th
er
h
an
d
,
MPC
p
r
o
v
id
es
s
tr
o
n
g
p
er
f
o
r
m
a
n
ce
i
n
h
an
d
lin
g
m
u
lti
-
v
ar
iab
le
co
n
s
tr
ain
ts
b
u
t
s
tr
u
g
g
les
with
its
r
elian
ce
o
n
ac
cu
r
ate
m
o
d
els
an
d
h
ig
h
c
o
m
p
u
tatio
n
al
d
em
an
d
s
,
lim
itin
g
r
ea
l
-
tim
e
ap
p
licab
ilit
y
.
T
h
ese
g
ap
s
u
n
d
er
s
co
r
e
th
e
n
ee
d
f
o
r
a
d
etailed
co
m
p
ar
is
o
n
o
f
B
ac
k
s
tep
p
in
g
an
d
MPC
s
tr
ateg
ies,
f
o
cu
s
in
g
o
n
th
eir
t
r
ad
e
-
o
f
f
s
in
r
o
b
u
s
tn
ess
,
co
m
p
u
tatio
n
al
e
f
f
icien
cy
,
an
d
ad
ap
tab
ilit
y
f
o
r
d
y
n
am
ic
g
r
i
d
-
co
n
n
ec
ted
PMSG
s
y
s
tem
s
.
T
h
is
r
esear
ch
aim
s
to
ad
d
r
ess
th
ese
g
ap
s
th
r
o
u
g
h
a
c
o
m
p
ar
ativ
e
a
n
aly
s
is
o
f
b
o
t
h
co
n
tr
o
l m
eth
o
d
s
.
T
h
is
r
esear
ch
p
ap
er
is
m
eth
o
d
ically
s
tr
u
ctu
r
ed
to
p
r
o
v
id
e
a
t
h
o
r
o
u
g
h
ex
am
i
n
atio
n
o
f
cu
r
r
e
n
t
co
n
t
r
o
l
s
tr
ateg
ies
in
DD
-
P
MSG
s
.
Sec
tio
n
1
th
e
in
tr
o
d
u
ctio
n
,
u
n
d
er
s
co
r
es
th
e
cr
itical
n
ee
d
f
o
r
p
r
e
cise
cu
r
r
en
t
co
n
tr
o
l
in
DD
-
PMSGs
,
cr
itiq
u
es
th
e
l
im
itatio
n
s
o
f
co
n
v
en
tio
n
al
an
d
ad
v
an
ce
d
co
n
tr
o
l
m
eth
o
d
s
,
wh
ile
also
o
u
tlin
in
g
th
e
r
esear
ch
o
b
jectiv
es
an
d
co
n
tr
ib
u
tio
n
s
.
I
n
s
ec
tio
n
2
th
e
p
ap
er
d
elin
ea
tes
th
e
ar
ch
it
ec
tu
r
e
o
f
th
e
win
d
tu
r
b
in
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I
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&
C
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g
I
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N:
2088
-
8
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DD
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P
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RB
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SYS
T
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Fig
u
r
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1
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s
tr
ates
th
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p
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S.
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ty
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n
co
m
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r
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e
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r
im
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m
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ts
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r
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,
a
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PMSG,
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d
a
p
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ter
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k
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to
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ter
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B
B
C
S).
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h
is
B
B
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s
s
en
tially
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ed
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ts
:
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r
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r
(
MSC
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d
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ter
(
GSC
)
,
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lin
k
.
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n
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t
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th
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f
r
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cy
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h
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p
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izatio
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g
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to
th
e
elec
tr
ical
g
r
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d
s
y
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tem
[
1
6
]
.
Fig
u
r
e
1
.
T
h
e
s
u
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g
ested
W
T
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ch
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2
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1
.
Wind
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m
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T
h
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x
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ca
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(
1
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[
1
7
]
:
=
1
2
3
(
,
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1
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s
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,
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in
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icate
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th
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o
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f
icien
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ef
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s
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itch
an
g
le,
an
d
d
en
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tes th
e
tip
-
s
p
ee
d
r
atio
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
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m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
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r
20
25
:
5
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T
h
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p
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co
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icien
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ep
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o
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g
win
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g
y
[
1
8
]
.
T
h
at
is
co
n
d
itio
n
al
o
n
th
e
tip
-
s
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ich
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d
as:
=
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(
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,
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2
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116
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4
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5
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21
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0
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0068
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w
ith
:
1
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08
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035
1
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3
Ω
r
ep
r
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ts
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e
r
o
t
o
r
’
s
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g
u
lar
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ile
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its
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ad
iu
s
.
2
.
2
.
DD
-
P
M
SG
m
o
del
I
n
o
r
d
e
r
to
tr
an
s
f
o
r
m
win
d
tu
r
b
in
e
m
ec
h
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ical
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er
g
y
in
to
e
lectr
ical
en
er
g
y
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th
e
DD
-
PMSG m
o
d
el
is
r
eq
u
ir
ed
.
T
h
is
m
o
d
el
in
clu
d
e
s
k
ey
elec
tr
o
m
ag
n
etic
eq
u
ati
o
n
s
an
d
d
y
n
a
m
ics
o
f
th
e
g
e
n
er
ato
r
.
T
h
e
s
tato
r
v
o
ltag
e
eq
u
atio
n
s
in
th
e
d
-
q
f
r
am
e
ar
e
[
1
9
]
:
=
+
−
(
4
)
=
+
−
(
5
)
w
h
er
e
t
h
e
d
-
a
x
is
an
d
q
-
a
x
is
p
ar
ts
o
f
s
tato
r
v
o
ltag
e
ar
e
ca
lle
d
an
d
,
r
esp
ec
tiv
ely
.
T
h
e
d
-
a
x
is
an
d
q
-
ax
is
p
ar
ts
o
f
th
e
s
tato
r
cu
r
r
e
n
t
ar
e
ca
lled
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d
.
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h
e
d
-
ax
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d
q
-
ax
is
p
ar
ts
o
f
s
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f
lu
x
lin
k
a
g
e
ar
e
ca
lle
d
an
d
,
r
esp
ec
tiv
ely
.
T
h
e
s
tato
r
r
esis
tan
ce
is
d
en
o
ted
b
y
.
T
h
e
s
tato
r
’
s
elec
tr
ical
a
n
g
u
lar
v
el
o
city
is
d
en
o
ted
b
y
.
T
h
e
f
o
llo
win
g
ar
e
th
e
f
lu
x
lin
k
ag
e
eq
u
atio
n
s
:
=
+
(
6
)
=
(
7
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w
h
er
e
an
d
ar
e
th
e
in
d
u
ctan
c
es
o
f
th
e
s
tato
r
’
s
d
-
ax
is
a
n
d
q
-
ax
is
.
T
h
e
p
er
m
an
e
n
t
m
a
g
n
et
f
lu
x
lin
k
a
g
e
is
d
en
o
ted
b
y
.
W
e
ca
n
f
ig
u
r
e
o
u
t
th
e
s
tato
r
c
u
r
r
en
t
b
e
h
av
io
r
f
r
o
m
th
ese
m
o
d
els.
B
y
s
witch
in
g
th
e
v
o
ltag
e
eq
u
atio
n
s
ar
o
u
n
d
an
d
ad
d
in
g
th
e
f
lu
x
c
o
u
p
lin
g
e
q
u
atio
n
s
in
s
tead
,
we
g
et:
=
1
(
−
+
)
−
(
8
)
=
1
(
−
+
)
(
9
)
A
cr
u
cial
elem
en
t o
f
en
er
g
y
c
o
n
v
er
s
io
n
,
th
e
elec
tr
o
m
a
g
n
eti
c
to
r
q
u
e
ca
n
b
e
ca
lc
u
lated
as:
=
2
3
(
−
)
(1
0
)
T
h
e
d
y
n
am
ic
b
eh
a
v
io
r
o
f
th
e
g
en
er
ato
r
is
ex
p
lain
ed
b
y
(1
1
)
:
Ω
=
ℎ
−
−
Ω
(1
1
)
T
h
e
elec
tr
o
m
a
g
n
etic
to
r
q
u
e
i
s
in
d
icate
d
b
y
,
an
d
s
tan
d
s
f
o
r
th
e
g
en
er
at
o
r
’
s
n
u
m
b
er
o
f
p
o
l
e
p
air
s
,
th
e
g
en
er
at
o
r
’
s
m
o
m
e
n
t
o
f
in
er
tia
is
d
en
o
ted
b
y
,
T
h
e
d
am
p
i
n
g
co
e
f
f
icien
t,
w
h
ich
r
ep
r
esen
ts
m
ec
h
an
ical
lo
s
s
es,
is
r
ep
r
esen
ted
b
y
,
wh
er
ea
s
th
e
tu
r
b
in
e
to
r
q
u
e
is
r
ep
r
esen
ted
b
y
ℎ
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
N
o
n
lin
ea
r
b
a
ck
s
tep
p
in
g
a
n
d
mo
d
el
p
r
ed
ictive
co
n
tr
o
l fo
r
g
r
id
-
co
n
n
ec
ted
…
(
A
d
il E
l
K
a
s
s
o
u
mi
)
5095
2
.
3
.
DC
lin
k
m
o
delin
g
T
h
e
r
ec
tifie
r
an
d
th
e
in
v
er
ter
a
r
e
co
n
n
ec
te
d
b
y
th
e
DC
lin
k
.
T
h
e
DC
lin
k
v
o
ltag
e
is
g
iv
e
n
b
y
[
2
0
]
:
=
1
∫
(
−
)
(1
2
)
T
h
e
DC
lin
k
'
s
ca
p
ac
itan
ce
is
r
ep
r
esen
ted
b
y
.
T
h
e
r
ec
tifie
r
cu
r
r
e
n
t
is
.
T
h
e
in
v
er
ter
cu
r
r
en
t
o
n
th
e
d
-
ax
is
is
d
en
o
ted
b
y
.
2
.
4
.
G
rid
-
s
ide c
o
nv
er
t
er
(
inv
er
t
er
)
m
o
del
T
h
e
in
v
er
te
r
co
n
v
er
ts
DC
p
o
wer
b
ac
k
t
o
AC
f
o
r
g
r
id
i
n
ter
co
n
n
ec
tio
n
v
ia
R
L
f
ilter
.
T
h
e
g
r
id
v
o
ltag
e
eq
u
atio
n
s
in
th
e
f
r
am
e
a
r
e
[
2
1
]
:
=
−
−
+
(1
3
)
=
−
−
−
(1
4
)
Her
e,
th
e
d
-
ax
is
an
d
q
-
ax
is
co
m
p
o
n
e
n
ts
o
f
th
e
in
v
er
ter
v
o
ltag
e
ar
e
d
en
o
te
d
b
y
an
d
,
r
es
p
ec
tiv
ely
,
th
e
d
-
ax
is
an
d
q
-
ax
is
c
o
m
p
o
n
en
t
s
o
f
t
h
e
in
v
er
ter
cu
r
r
en
t
a
r
e
d
en
o
ted
b
y
th
e
an
d
,
an
d
ar
e
th
e
r
esis
tan
ce
an
d
in
d
u
ctan
ce
o
f
t
h
e
f
ilter
,
an
d
is
th
e
elec
tr
ical
a
n
g
u
lar
v
elo
city
o
f
th
e
g
r
id
.
3.
NO
NL
I
N
E
AR
B
ACK
S
T
E
P
P
I
NG
CO
NT
RO
L
O
F
T
H
E
DD
-
P
M
SG
WI
ND
T
U
RB
I
N
E
C
o
n
tr
o
llin
g
th
e
MSC
an
d
t
h
e
GSC
is
a
v
er
y
im
p
o
r
ta
n
t
p
ar
t
o
f
m
a
k
in
g
s
u
r
e
th
at
a
wi
n
d
en
er
g
y
co
n
v
er
s
io
n
s
y
s
tem
(
W
E
C
S
)
s
y
s
tem
wo
r
k
s
well
a
n
d
ef
f
icien
tly
.
Fo
r
t
h
e
MSC
,
its
k
ey
f
u
n
c
tio
n
is
to
m
ax
im
ize
win
d
en
er
g
y
ca
p
tu
r
e.
T
h
is
is
ac
h
iev
ed
b
y
im
p
le
m
en
tin
g
m
a
x
im
u
m
p
o
wer
p
o
in
t tr
ac
k
in
g
(
MPPT)
b
ased
o
n
th
e
g
en
er
ato
r
'
s
s
p
ee
d
,
alo
n
g
s
id
e
m
an
ag
in
g
t
o
r
q
u
e
o
r
p
o
wer
c
o
n
tr
o
l.
C
o
n
v
er
s
ely
,
th
e
GSC
is
r
esp
o
n
s
ib
le
f
o
r
a
r
an
g
e
o
f
cr
itical
f
u
n
ctio
n
s
:
it
r
eg
u
lates
th
e
v
o
ltag
e
o
f
th
e
D
C
b
u
s
,
m
an
ag
es
th
e
g
r
id
'
s
r
ea
ctiv
e
p
o
wer
,
en
s
u
r
es
g
r
id
s
y
n
c
h
r
o
n
izatio
n
,
a
n
d
m
a
in
tain
s
o
p
er
atio
n
d
u
r
in
g
g
r
id
f
au
lts
(
f
au
lt
r
id
e
-
th
r
o
u
g
h
(
FR
T
)
)
[
2
2
]
.
A
ty
p
ica
l
co
n
tr
o
l sch
em
e
u
s
in
g
a
n
o
n
lin
ea
r
b
ac
k
s
tep
p
in
g
s
tr
ateg
y
is
g
i
v
en
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
No
n
lin
ea
r
b
ac
k
s
tep
p
in
g
co
n
tr
o
l
f
o
r
MSC
an
d
GSC
3
.
1
.
M
SC c
o
ntr
o
l by
no
nli
nea
r
ba
ck
s
t
eppin
g
ba
s
ed
o
n
o
ptim
a
l t
o
rque
co
ntr
o
l
M
P
P
T
T
h
e
o
b
jectiv
e
o
f
th
e
MSC
i
s
t
o
co
n
tr
o
l
th
e
PMSG
to
ex
tr
ac
t
m
ax
im
u
m
p
o
wer
f
r
o
m
th
e
win
d
.
T
h
is
is
ac
h
iev
ed
b
y
a
d
ju
s
tin
g
th
e
t
o
r
q
u
e
o
f
th
e
g
en
er
at
o
r
.
Op
tim
al
to
r
q
u
e
co
n
tr
o
l
(
OT
C
)
is
im
p
l
em
en
ted
f
o
r
MPPT.
T
h
e
o
p
tim
al
to
r
q
u
e
r
ef
er
e
n
ce
(
)
is
d
e
r
iv
ed
b
ased
o
n
th
e
wi
n
d
s
p
ee
d
an
d
th
e
ch
ar
a
cter
is
tics
o
f
th
e
win
d
tu
r
b
in
e.
B
ased
o
n
t
h
e
c
o
n
n
ec
t
i
o
n
b
etw
ee
n
wi
n
d
s
p
ee
d
a
n
d
th
e
t
ip
s
p
ee
d
r
ati
o
,
a
n
d
b
y
s
u
b
s
t
it
u
ti
n
g
wit
h
its
o
p
ti
m
al
v
al
u
e
a
n
d
eq
u
ati
n
g
t
h
e
p
o
w
er
c
o
ef
f
i
cie
n
t
to
i
ts
m
ax
i
m
u
m
v
al
u
e
[
2
3
]
,
we
d
e
r
i
v
e
(1
5
)
:
=
1
2
5
3
(1
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
0
9
1
-
5
1
0
5
5096
T
h
u
s
,
th
e
r
e
f
er
en
ce
f
o
r
elec
tr
o
m
ag
n
etic
to
r
q
u
e,
d
e
n
o
ted
as
,
is
f
o
r
m
u
lated
in
th
e
f
o
llo
win
g
m
an
n
er
:
=
Ω
2
(1
6
)
T
h
e
r
ef
er
e
n
ce
cu
r
r
en
ts
ar
e
d
e
f
in
ed
as:
{
∗
=
0
∗
=
2
3
1
∗
(1
7
)
3
.
2
.
M
SC c
o
ntr
o
l us
ing
no
nli
nea
r
ba
ck
s
t
eppin
g
a
pp
ro
a
ch
Fro
m
Fig
u
r
e
2
,
it
ca
n
b
e
s
ee
n
th
at
th
e
s
tato
r
cu
r
r
en
ts
ca
n
b
e
co
n
tr
o
lled
b
y
an
d
,
h
en
ce
th
e
s
tato
r
cu
r
r
en
ts
er
r
o
r
s
ar
e
ex
p
r
e
s
s
ed
as
[
2
4
]
:
{
=
∗
−
=
∗
−
(1
8
)
w
h
er
e
∗
an
d
∗
ar
e
th
e
cu
r
r
e
n
t c
o
m
p
o
n
e
n
t r
ef
er
e
n
ce
s
.
B
ased
o
n
(
1
7
)
a
n
d
(
1
8
)
,
we
ca
n
wr
ite:
{
=
−
1
(
−
+
)
=
∗
−
1
(
−
−
−
)
(
19
)
T
h
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
is
ch
o
s
en
as g
iv
en
in
:
{
=
1
2
(
2
+
2
)
>
0
=
+
(2
0
)
Fu
r
th
er
m
o
r
e
,
co
ef
f
icien
ts
Υ
an
d
Υ
m
u
s
t b
e
p
o
s
itiv
e
to
en
s
u
r
e
th
e
s
y
s
tem
s
tab
ilit
y
[
2
5
]
.
=
−
2
−
2
<
0
(2
1
)
T
h
e
s
tato
r
cu
r
r
e
n
ts
tr
ac
k
in
g
e
r
r
o
r
s
ar
e
ac
h
ie
v
ed
if
o
n
ly
th
e
f
o
llo
win
g
d
/q
v
o
ltag
e
r
e
f
er
en
ce
s
ar
e
ch
o
s
en
:
{
∗
=
+
−
∗
=
+
+
+
+
∗
(2
2
)
3
.
3
.
G
SC c
o
ntr
o
l us
ing
no
nli
nea
r
ba
ck
s
t
eppin
g
a
pp
ro
a
ch
T
h
e
e
r
r
o
r
s
i
n
t
h
e
d
i
r
e
c
t
a
n
d
q
u
a
d
r
a
t
u
r
e
g
r
i
d
c
u
r
r
e
n
t
s
c
a
n
b
e
d
e
s
c
r
i
b
e
d
u
s
i
n
g
t
h
e
f
o
l
l
o
w
i
n
g
f
o
r
m
u
l
a
s
[
2
6
]
:
{
=
∗
−
=
∗
−
(2
3
)
u
s
in
g
(
1
3
)
an
d
(
1
4
)
,
we
o
b
tain
:
{
=
∗
−
1
(
−
−
+
)
=
−
1
(
−
−
)
(2
4
)
t
h
e
f
o
llo
win
g
f
o
r
m
u
la
p
r
o
v
id
e
s
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
:
{
=
1
2
(
2
+
2
)
>
0
=
+
(2
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
N
o
n
lin
ea
r
b
a
ck
s
tep
p
in
g
a
n
d
mo
d
el
p
r
ed
ictive
co
n
tr
o
l fo
r
g
r
id
-
co
n
n
ec
ted
…
(
A
d
il E
l
K
a
s
s
o
u
mi
)
5097
F
u
r
th
er
m
o
r
e
,
to
en
s
u
r
e
th
e
s
y
s
tem
'
s
s
tab
ilit
y
,
th
e
co
ef
f
icien
ts
Υ
′
an
d
Υ
′
m
u
s
t b
e
p
o
s
itiv
e.
=
−
′
2
−
′
2
<
0
(2
6
)
T
h
e
tr
ac
k
in
g
er
r
o
r
s
o
f
th
e
g
r
id
cu
r
r
en
ts
ca
n
b
e
attain
ed
p
r
o
v
id
ed
th
at
th
e
d
/q
v
o
ltag
e
r
ef
e
r
e
n
ce
s
ar
e
s
elec
ted
:
{
∗
=
′
+
∗
+
+
−
∗
=
′
+
+
(2
7
)
4.
M
O
DE
L
P
RE
DIC
T
I
V
E
CO
NT
RO
L
T
h
e
p
r
e
d
ictiv
e
co
n
tr
o
l
a
p
p
r
o
a
ch
,
s
p
ec
if
ically
m
o
d
el
p
r
ed
icti
v
e
co
n
tr
o
l
(
MPC
)
,
h
as g
ain
ed
s
ig
n
if
ican
t
im
p
o
r
tan
ce
in
p
o
wer
c
o
n
v
er
te
r
s
an
d
elec
tr
ic
d
r
iv
e
s
y
s
tem
s
[
2
7
]
,
[
2
8
]
.
MPC
u
tili
ze
s
a
m
at
h
em
atica
l
m
o
d
el
f
o
r
p
r
ed
ictin
g
h
o
w
a
p
r
o
ce
s
s
will
b
eh
a
v
e
in
th
e
f
u
t
u
r
e
i
n
r
elatio
n
to
a
ce
r
tain
c
o
n
tr
o
l
v
a
r
iab
le.
T
h
e
g
o
al
is
to
d
eter
m
in
e
th
e
o
p
tim
al
ac
tio
n
b
y
m
in
im
izin
g
a
p
r
e
d
ef
in
e
d
c
o
s
t
f
u
n
ctio
n
,
b
ased
o
n
s
et
o
p
t
im
izatio
n
cr
iter
ia.
On
e
v
ar
ian
t
o
f
MPC
,
k
n
o
wn
as
p
r
ed
ictiv
e
d
ea
d
b
e
at
co
n
tr
o
l
,
ad
ju
s
ts
th
e
co
n
tr
o
l
v
a
r
iab
le
r
ap
id
ly
to
m
atch
t
h
e
r
ef
er
en
ce
in
p
u
t.
Ho
we
v
er
,
it
i
s
s
en
s
itiv
e
to
ch
an
g
es
in
s
y
s
tem
p
ar
am
eter
s
an
d
d
is
tu
r
b
a
n
ce
s
.
I
n
co
n
tr
ast,
MPC
is
f
av
o
r
ed
f
o
r
its
ab
ilit
y
to
e
f
f
ec
tiv
ely
h
an
d
le
co
m
p
lex
,
n
o
n
lin
ea
r
s
y
s
tem
s
with
co
n
s
tr
ain
ts
,
as
it
p
r
ed
icts
s
y
s
tem
b
eh
av
io
r
u
s
in
g
a
m
ath
em
atica
l m
o
d
el
an
d
o
p
tim
izes
co
n
tr
o
l a
ctio
n
s
ac
c
o
r
d
in
g
ly
[
2
9
]
.
T
h
er
e
ar
e
two
ty
p
es
o
f
MPC
f
o
r
p
o
wer
co
n
v
er
ter
s
:
co
n
tin
u
o
u
s
co
n
tr
o
l
s
et
MPC
(
C
C
S
-
MPC
)
an
d
FC
S
-
MP
C
.
A
m
o
d
u
lato
r
is
n
ec
ess
ar
y
f
o
r
C
C
S
-
MPC
to
f
li
p
b
etwe
en
s
tates,
en
s
u
r
in
g
a
co
n
s
is
ten
t
s
witch
in
g
f
r
eq
u
e
n
cy
.
Ho
wev
er
,
it
f
ac
es
ch
allen
g
es
d
u
e
to
th
e
co
m
p
le
x
ity
o
f
o
p
tim
izatio
n
p
r
o
b
lem
s
ar
is
in
g
f
r
o
m
m
o
d
e
l
n
o
n
lin
ea
r
ities
.
T
h
e
d
is
cr
ete
f
e
atu
r
e
o
f
s
tatic
co
n
v
er
ter
s
,
wh
i
ch
h
a
v
e
a
lim
ited
q
u
an
tity
o
f
s
tates
th
at
s
witch
,
is
ex
p
lo
ited
b
y
FC
S
-
MPC
.
T
h
is
r
ed
u
ce
s
th
e
co
m
p
u
tatio
n
al
d
em
an
d
s
f
o
r
p
r
ed
ictio
n
an
d
p
r
o
ce
s
s
in
g
.
I
n
FC
S
-
MPC
,
th
ese
d
is
cr
ete
s
tates
ar
e
th
e
o
n
ly
s
tates
th
at
ca
n
b
e
p
r
ed
icted
;
t
h
e
id
ea
l
s
tate
o
r
v
o
ltag
e
v
ec
to
r
f
o
r
co
n
tr
o
l
is
ch
o
s
en
in
an
o
p
tim
i
za
tio
n
s
tag
e.
T
h
e
ef
f
ec
tiv
en
es
s
o
f
th
is
m
eth
o
d
d
ep
en
d
s
o
n
an
ac
cu
r
ate
s
y
s
tem
m
o
d
el
an
d
a
well
-
d
ef
in
ed
c
o
s
t
f
u
n
ctio
n
.
T
h
e
im
p
lem
en
tatio
n
o
f
FC
S
-
MPC
co
n
s
is
ts
o
f
f
o
u
r
k
ey
s
tep
s
[
3
0
]
,
[
3
1
]
:
a.
R
ef
er
en
ce
ca
lcu
latio
n
:
d
ep
e
n
d
in
g
o
n
th
e
p
a
r
ticu
lar
ap
p
licatio
n
,
th
is
p
h
ase
en
tails
d
eter
m
in
in
g
th
e
r
ef
er
en
ce
c
o
n
tr
o
l
v
alu
e
∗
(
)
,
wh
ich
m
ay
b
e
to
r
q
u
e,
f
l
u
x
,
p
o
wer
,
v
o
ltag
e,
an
d
cu
r
r
en
t.
b.
Pre
d
ictio
n
:
Her
e,
th
e
co
n
v
er
ter
s
witch
in
g
s
tate
co
m
b
in
atio
n
s
(
)
,
s
y
s
tem
ch
ar
ac
ter
is
tics
,
an
d
th
e
d
is
cr
ete
tim
e
(
DT
)
m
o
d
el
ar
e
u
s
ed
to
p
r
e
d
ict
th
e
f
u
t
u
r
e
v
al
u
es o
f
th
e
co
n
tr
o
l v
a
r
iab
les
(
+
1
)
.
c.
E
x
tr
ap
o
latio
n
: I
n
th
is
s
tag
e,
p
r
esen
t a
n
d
p
ast s
am
p
le
v
alu
es
∗
(
)
,
∗
(
−
1
)
ar
e
u
s
ed
to
p
r
ed
ict
th
e
f
u
t
u
r
e
v
alu
e
o
f
t
h
e
r
ef
e
r
en
ce
co
n
tr
o
l
v
ar
iab
le
∗
(
+
1
)
.
d.
C
o
s
t
f
u
n
ctio
n
m
in
im
izatio
n
:
T
h
is
f
u
n
ctio
n
,
r
e
p
r
esen
ted
as
=
∗
(
+
1
)
−
(
+
1
)
,
s
ee
k
s
to
m
in
im
ize
th
e
er
r
o
r
b
etwe
en
th
e
p
r
ed
icted
a
n
d
ex
t
r
ap
o
lated
r
ef
er
en
ce
s
.
4
.
1
.
M
P
C
us
ing
f
ini
t
e
co
ntr
o
l set
f
o
r
M
SC
T
h
e
d
is
cr
ete
PMSG
m
o
d
el
is
u
s
ed
b
y
th
e
MPC
alg
o
r
ith
m
.
T
o
s
im
p
lify
th
e
a
n
aly
s
is
,
a
f
o
r
war
d
E
u
le
r
ap
p
r
o
x
im
atio
n
ap
p
r
o
ac
h
,
wh
ic
h
tak
es
in
co
n
s
id
er
atio
n
th
e
f
u
tu
r
e
s
am
p
le
(
k
+
1
)
as
well
as
th
e
p
r
esen
t
s
am
p
le
(
k
)
,
is
ad
o
p
ted
in
t
h
is
s
tu
d
y
.
T
h
is
ap
p
r
o
ac
h
is
g
iv
en
as
[
3
2
]
:
{
(
)
}
=
≈
(
+
)
−
(
)
;
∈
{
,
}
(2
8
)
T
h
e
(2
8
)
m
ay
b
e
m
a
d
e
s
im
p
le
r
as
:
(
+
1
)
≈
(
)
+
{
(
)
}
=
(
29
)
F
o
llo
win
g
th
e
n
ec
ess
ar
y
d
is
cr
etiza
tio
n
p
r
o
ce
s
s
,
th
e
DT
m
o
d
el
o
f
th
e
PMSG c
an
b
e
g
iv
en
a
s
[
2
3
]
:
[
(
+
1
)
(
+
1
)
]
=
(
)
[
(
)
(
)
]
+
[
(
)
(
)
]
+
(
)
(3
0
)
w
ith
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
0
9
1
-
5
1
0
5
5098
{
(
)
≈
[
+
(
)
]
≈
[
1
−
(
)
−
(
)
1
−
]
≈
≈
[
0
0
]
≈
(
)
≈
[
0
−
(
)
]
(3
1
)
T
ak
in
g
in
to
ac
co
u
n
t
th
e
DT
m
o
d
el
o
f
t
h
e
PMSG
as
d
escr
ib
e
d
b
y
(
3
0
)
,
th
e
f
u
tu
r
e
s
tates
o
f
th
e
PMSG
cu
r
r
en
ts
ar
e
f
o
r
ec
asted
b
y
d
eter
m
in
in
g
th
eir
s
u
b
s
eq
u
en
t
v
alu
es.
C
o
n
s
eq
u
en
tly
,
th
e
f
o
r
ec
asted
d
ir
ec
t
a
n
d
q
u
ad
r
atu
r
e
(
)
ax
is
cu
r
r
en
ts
ca
n
b
e
d
elin
ea
ted
as
[
3
3
]
:
[
(
+
1
)
(
+
1
)
]
=
(
)
[
(
)
(
)
]
+
[
(
)
(
)
]
+
(
)
(3
2
)
w
h
er
e
th
e
v
a
r
iab
le
’
s
p
r
ed
icted
v
alu
e
is
in
d
icate
d
b
y
th
e
s
u
p
e
r
s
cr
ip
t
.
T
h
e
MSC
v
o
ltag
e
p
r
ed
ictio
n
s
,
an
d
,
ar
e
d
er
iv
ed
b
ased
o
n
s
witch
in
g
s
tates
an
d
th
e
DC
-
l
in
k
v
o
ltag
e
(
)
th
r
o
u
g
h
t
h
e
m
o
d
el
d
escr
ib
ed
as:
[
(
)
(
)
]
=
(
)
[
(
)
(
)
]
(3
3
)
T
h
e
v
o
ltag
e
ac
r
o
s
s
th
e
ca
p
ac
it
o
r
is
d
e
n
o
ted
b
y
(
)
,
an
d
,
(
)
s
ig
n
if
ies
th
e
s
tate
o
f
s
witch
in
g
alo
n
g
th
e
/
ax
is
.
T
h
e
f
o
r
m
al
ex
p
r
ess
io
n
is
p
r
esen
ted
as:
[
(
)
(
)
]
=
[
(
)
(
)
−
(
)
(
)
]
2
3
[
1
−
1
2
−
1
2
0
√
3
2
−
√
3
2
]
[
(
)
(
)
(
)
]
(3
4
)
B
y
in
co
r
p
o
r
atin
g
(
3
2
)
i
n
to
(
3
3
)
,
we
d
er
iv
e
th
e
m
o
d
el
f
o
r
th
e
p
r
ed
icted
s
tato
r
cu
r
r
en
ts
:
[
(
+
1
)
(
+
1
)
]
=
(
)
[
(
)
(
)
]
+
(
(
)
[
(
)
(
)
]
)
+
(
)
(3
5
)
C
o
n
v
er
s
ely
,
th
e
cu
r
r
e
n
t
r
e
f
er
e
n
ce
s
at
th
e
(
)
s
am
p
lin
g
in
s
tan
t
a
r
e
p
r
o
jecte
d
to
th
e
(
+
1
)
s
am
p
lin
g
in
s
tan
t
th
r
o
u
g
h
th
e
a
p
p
licatio
n
o
f
f
ir
s
t
-
o
r
d
er
L
ag
r
a
n
g
e
ex
t
r
ap
o
latio
n
[
3
4
]
.
{
̇
̂
∗
(
+
1
)
=
2
∗
(
)
−
∗
(
−
1
)
̇
̂
∗
(
+
1
)
=
2
∗
(
)
−
∗
(
−
1
)
(3
6
)
I
n
th
is
s
itu
atio
n
,
̇
̂
∗
r
ep
r
esen
ts
t
h
e
ex
tr
ap
o
lated
r
e
f
er
en
ce
cu
r
r
en
ts
,
an
d
̇
̂
∗
s
ig
n
if
ies
th
e
g
e
n
er
a
to
r
'
s
r
ef
er
en
ce
cu
r
r
en
ts
.
Un
d
er
all
o
p
e
r
atio
n
al
co
n
d
itio
n
s
,
th
e
d
ir
ec
t
cu
r
r
e
n
t
∗
is
s
e
t
to
ze
r
o
in
o
r
d
er
to
p
r
eser
v
e
a
u
n
ity
p
o
wer
f
ac
to
r
.
Me
an
wh
ile,
∗
is
d
eter
m
in
ed
th
r
o
u
g
h
MPPT
c
o
n
tr
o
l.
Ultim
ately
,
to
r
ed
u
ce
th
e
d
is
cr
ep
an
c
y
b
etwe
en
th
e
p
r
e
d
icted
an
d
ex
tr
ap
o
lated
r
ef
e
r
en
ce
c
u
r
r
en
ts
,
th
e
f
o
llo
win
g
c
o
s
t f
u
n
ctio
n
is
im
p
lem
en
ted
[
3
5
]
:
(
)
=
[
̇
̂
∗
(
+
1
)
−
(
+
1
)
]
2
−
[
̇
̂
∗
(
+
1
)
−
(
+
1
)
]
2
(3
7
)
4
.
2
.
M
P
C
us
ing
f
ini
t
e
co
ntr
o
l set
f
o
r
G
SC
Usi
n
g
th
e
s
am
e
m
eth
o
d
ap
p
li
ed
to
estab
lis
h
th
e
MSC
p
r
ed
ictiv
e
co
n
tr
o
ller
,
th
e
GSC
co
s
t
f
u
n
ctio
n
ca
n
b
e
f
o
r
m
u
lated
as
[
3
5
]
:
(
)
=
[
̇
̂
∗
(
+
1
)
−
(
+
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2
−
[
̇
̂
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(
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−
(
+
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2
(3
8
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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a
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…
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5099
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u
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d
e
p
icts
th
e
o
v
er
all
f
r
am
ewo
r
k
o
f
th
e
MPC
ap
p
lied
to
th
e
PMSG w
in
d
en
er
g
y
co
n
v
er
s
io
n
s
y
s
tem
.
Fig
u
r
e
3
.
Ov
e
r
v
iew
d
iag
r
am
o
f
MPC
im
p
lem
en
tatio
n
in
th
e
PMSG w
in
d
en
er
g
y
co
n
v
er
s
io
n
s
y
s
tem
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
s
tu
d
y
c
o
m
p
a
r
es
two
a
d
v
an
ce
d
c
o
n
tr
o
l
s
tr
ateg
ies,
B
SC
an
d
MPC
f
o
r
c
o
n
tr
o
llin
g
b
o
th
MSC
an
d
GSC
in
a
p
er
m
an
en
t
m
ag
n
et
s
y
n
ch
r
o
n
o
u
s
g
en
e
r
ato
r
(
PMSG)
-
b
ased
W
T
S
co
n
n
ec
ted
to
t
h
e
p
o
wer
g
r
id
.
T
h
e
win
d
tu
r
b
in
e
o
p
er
ates
with
v
a
r
iab
le
win
d
s
p
ee
d
s
b
etwe
en
8
.
9
m
/s
a
n
d
1
2
.
1
5
m
/s
as
s
h
o
w
n
in
Fig
u
r
e
4
,
an
d
th
e
s
y
s
tem
's p
ar
am
eter
s
ar
e
o
u
tlin
ed
in
T
ab
le
2
.
Fig
u
r
e
4
.
W
in
d
p
r
o
f
ile
T
ab
le
2
.
Per
f
o
r
m
an
ce
co
m
p
a
r
is
o
n
: b
ac
k
s
tep
p
in
g
v
s
FC
S
-
MP
C
M
e
t
r
i
c
B
S
C
F
C
S
-
M
P
C
S
e
t
t
l
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g
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me
(
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e
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d
)
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.
4
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s
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O
v
e
r
sh
o
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t
(
To
r
q
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e
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.
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%
2
.
3
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t
e
a
d
y
-
S
t
a
t
e
Er
r
o
r
2
.
7
r
p
m
0
.
9
r
p
m
TH
D
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r
i
d
C
u
r
r
e
n
t
)
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.
4
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%
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.
2
1
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S
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d
.
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v
.
(
T
o
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e
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1
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3
8
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m
0
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9
N
m
C
o
m
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u
t
a
t
i
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n
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i
me
/
S
t
e
p
<
0
.
4
ms
>
1
.
2
ms
5
.
1
.
K
ey
f
ind
ing
s
T
h
e
p
r
im
ar
y
aim
o
f
th
is
s
tu
d
y
was
to
co
m
p
ar
e
th
e
p
er
f
o
r
m
an
ce
o
f
two
ad
v
an
ce
d
co
n
tr
o
l
s
tr
ateg
ies
u
s
ed
in
g
r
id
-
co
n
n
ec
ted
win
d
en
er
g
y
s
y
s
tem
s
:
th
e
FC
S
-
MPC
an
d
th
e
s
tan
d
ar
d
n
o
n
lin
ea
r
B
SC
.
T
h
is
co
m
p
ar
is
o
n
was
co
n
d
u
cted
u
n
d
er
v
a
r
y
in
g
win
d
c
o
n
d
itio
n
s
an
d
s
y
s
tem
p
ar
a
m
eter
f
lu
ct
u
atio
n
s
to
ev
al
u
ate
th
e
r
o
b
u
s
tn
ess
an
d
ef
f
ec
tiv
en
ess
o
f
ea
c
h
a
p
p
r
o
ac
h
i
n
r
ea
lis
tic
o
p
er
atin
g
en
v
ir
o
n
m
en
ts
.
T
h
e
FC
S
-
MP
C
s
tr
ateg
y
lev
er
ag
es
p
r
ed
ictiv
e
m
o
d
elin
g
an
d
o
p
tim
izatio
n
t
o
an
ticip
ate
s
y
s
tem
b
eh
av
io
r
an
d
s
elec
t
o
p
tim
al
co
n
tr
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
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I
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t J E
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&
C
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p
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g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
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1
-
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1
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5
5100
ac
tio
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s
in
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ea
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tim
e.
T
h
is
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les
it
to
ac
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iev
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u
p
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io
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er
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ce
i
n
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o
th
d
y
n
am
i
c
an
d
s
tead
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s
tate
co
n
d
itio
n
s
.
I
n
p
ar
ticu
lar
,
it
d
em
o
n
s
tr
ated
b
etter
t
r
ac
k
in
g
o
f
s
et
p
o
i
n
ts
an
d
m
o
r
e
r
eli
ab
le
co
n
t
r
o
l
d
u
r
in
g
d
is
tu
r
b
an
ce
s
an
d
p
ar
am
eter
v
ar
iatio
n
s
.
I
n
c
o
n
tr
ast,
th
e
B
SC
ap
p
r
o
ac
h
,
wh
ile
n
o
n
lin
ea
r
an
d
m
ath
em
atica
ll
y
r
ig
o
r
o
u
s
,
is
less
co
m
p
u
tatio
n
a
lly
d
em
an
d
in
g
b
u
t
d
o
es
n
o
t
i
n
co
r
p
o
r
ate
p
r
ed
ictiv
e
f
ea
t
u
r
es.
As
a
r
esu
lt,
B
SC
s
h
o
wed
lim
itatio
n
s
in
m
ain
tai
n
in
g
o
p
tim
al
p
e
r
f
o
r
m
an
ce
u
n
d
er
r
a
p
id
ly
c
h
an
g
in
g
co
n
d
itio
n
s
,
h
ig
h
lig
h
tin
g
t
h
e
tr
ad
e
-
o
f
f
b
etwe
en
c
o
n
tr
o
l
p
r
ec
is
io
n
an
d
co
m
p
u
tatio
n
al
c
o
m
p
lex
ity
.
5
.
2
.
Set
po
int
t
ra
c
k
ing
s
ce
na
rio
I
n
th
e
s
ce
n
ar
io
o
f
s
et
p
o
in
t
tr
ac
k
in
g
,
th
e
win
d
s
p
ee
d
was
v
ar
ied
ac
co
r
d
in
g
to
th
e
p
r
o
f
ile
s
h
o
wn
in
Fig
u
r
e
4
,
lead
in
g
to
c
h
an
g
es
i
n
th
e
g
en
er
ato
r
'
s
m
ec
h
an
ical
s
p
ee
d
.
As
s
h
o
wn
in
Fig
u
r
e
5
(
a
)
,
th
e
PMSG
s
p
ee
d
cu
r
v
es
clo
s
ely
f
o
llo
w
th
e
win
d
p
r
o
f
ile
b
u
t
ex
h
ib
it
s
m
o
o
th
er
d
y
n
am
ics
d
u
e
to
th
e
h
ig
h
m
a
ch
in
e
in
er
tia.
B
o
th
co
n
tr
o
l
s
tr
ateg
ies
s
u
cc
ess
f
u
lly
en
s
u
r
ed
th
e
W
T
ex
tr
ac
ted
m
ax
im
u
m
p
o
wer
,
co
n
f
ir
m
in
g
t
h
e
ef
f
ec
tiv
e
n
ess
o
f
th
e
MPPT
m
eth
o
d
.
Ho
wev
er
,
b
etter
tr
ac
k
in
g
was
d
em
o
n
s
tr
ated
b
y
th
e
FC
S
-
MPC
ap
p
r
o
ac
h
,
g
u
a
r
an
teein
g
m
o
r
e
r
eliab
le
p
er
f
o
r
m
an
ce
i
n
a
r
an
g
e
o
f
win
d
s
itu
atio
n
s
.
Fig
u
r
e
5
(
b
)
s
h
o
ws
th
e
PMSG
to
r
q
u
e,
wh
ich
m
ir
r
o
r
s
th
e
m
ec
h
an
ical
s
p
ee
d
.
T
h
e
to
r
q
u
e
i
s
s
m
o
o
th
er
with
MPC
co
n
tr
o
l,
r
ed
u
ci
n
g
m
ec
h
an
ical
s
tr
ess
an
d
en
h
a
n
cin
g
th
e
tu
r
b
in
e'
s
lo
n
g
ev
ity
.
T
h
e
r
ed
u
ctio
n
in
to
r
q
u
e
r
ip
p
les
in
d
icate
s
th
e
ef
f
ec
tiv
en
ess
o
f
b
o
th
c
o
n
tr
o
l
s
tr
ateg
ies,
b
u
t
MPC
p
r
o
v
id
ed
a
m
o
r
e
co
n
s
is
ten
t
an
d
s
m
o
o
th
er
to
r
q
u
e
p
r
o
f
ile,
lea
d
in
g
to
b
etter
p
er
f
o
r
m
a
n
ce
in
ter
m
s
o
f
r
ed
u
cin
g
m
ec
h
an
ical
we
ar
.
(
a)
(
b
)
Fig
u
r
e
5
.
PMSG
(
a)
m
ec
h
an
ic
al
s
p
ee
d
an
d
(
b
)
elec
tr
o
m
ag
n
et
ic
to
r
q
u
e
5
.
3
.
Curre
nt
co
ntr
o
l per
f
o
rm
a
nc
e
Fig
u
r
es
6
(
a)
an
d
6
(
b
)
s
h
o
w
th
e
m
ac
h
in
e
-
s
id
e
d
ir
ec
t
an
d
q
u
a
d
r
atu
r
e
cu
r
r
en
ts
.
W
h
ile
th
e
d
ir
ec
t
cu
r
r
en
t
o
s
cillates
ar
o
u
n
d
ze
r
o
(
Fig
u
r
e
6
(
a)
,
th
e
q
u
ad
r
atu
r
e
cu
r
r
en
t
F
ig
u
r
e
6
(
b
)
)
is
p
r
o
p
o
r
tio
n
al
to
t
h
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e.
T
h
e
MPC
s
tr
ateg
y
f
o
l
lo
ws
th
e
r
ef
e
r
en
ce
c
u
r
r
e
n
t
p
r
o
f
iles
m
o
r
e
p
r
ec
is
ely
t
h
an
B
SC
,
h
ig
h
lig
h
tin
g
its
s
u
p
er
io
r
c
o
n
tr
o
l
ac
cu
r
ac
y
an
d
p
r
e
d
ictiv
e
ca
p
a
b
ilit
ies.
T
h
e
s
m
o
o
th
r
esp
o
n
s
e
o
f
th
e
MPC
s
tr
ateg
y
en
s
u
r
e
s
o
p
tim
al
o
p
er
atio
n
with
m
in
im
al
d
ev
iatio
n
f
r
o
m
th
e
d
esire
d
v
alu
es.
(
a)
(
b
)
Fig
u
r
e
6
.
C
o
m
p
a
r
is
o
n
o
f
s
tato
r
cu
r
r
e
n
t tr
ac
k
in
g
p
er
f
o
r
m
a
n
ce
(
a)
m
ac
h
i
n
e
-
s
id
e
d
ir
ec
t c
u
r
r
en
t a
n
d
(
b
)
m
ac
h
i
n
e
-
s
id
e
q
u
ad
r
atu
r
e
cu
r
r
en
t
Evaluation Warning : The document was created with Spire.PDF for Python.