In
te
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ation
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l Jou
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Elec
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Vo
l
.
1
0
, No
.
2
, Ju
n
e
20
1
9
, p
p
.
1
1
1
0
~
1
122
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
2.pp1110-1122
1110
Jou
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Robust c
oor
dinated control usi
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kstepping of fl
y
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energy storage system and D
F
IG
for pow
er smoothing in wind
power plants
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o
ha
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a
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i
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a
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Mo
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Rese
arch
Ce
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ter
o
f
E
ngi
neering
and
Heal
th
S
ciences
and
Tech
no
lo
g
i
es (STIS),
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ig
h Norm
a
l
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cho
o
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f
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echn
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ohamm
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o
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occo
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Rese
arch
Cent
e
r
of E
ng
ineeri
n
g
and
Heal
th S
cie
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ces
and
Tech
no
lo
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(
STIS
),
H
i
gher
Nati
on
al
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ch
oo
l
of
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o
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puter
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nce an
d S
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s A
n
a
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i
s
,
Moham
m
e
d
V
U
n
ivers
ity, M
o
rocco
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
Jan
2
, 2019
Re
vise
d Mar
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201
9
Ac
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ar 1
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019
Th
is
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o
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he
w
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u
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power
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s
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K
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Wi
n
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ne
r
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y
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Mo
ham
e
d N
a
d
our,
R
e
sear
ch Ce
n
t
e
r
for
Engi
nee
r
ing
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d
Healt
h
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cienc
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s a
n
d Tec
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o
l
ogi
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s
,
H
i
g
h
N
orm
a
l
Scho
o
l
of Te
ch
n
i
cal
E
duc
a
t
io
n, Moh
am
m
e
d V
U
n
iver
si
t
y,
Ense
t,
B
.
P
. ،6
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v
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nue
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e
s
F
orce
s
Arm
ées Ro
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ale
s
,
Ra
b
a
t 10
1
0
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Morocco
.
Em
ail:
moha
me
d.nad
o
u
r@u
m
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t
.
m
a
1.
I
N
TR
OD
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C
TI
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En
viro
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ta
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ene
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s,
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i
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ai
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f
t
h
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wable
source
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w
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h
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ic
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ly
affec
t
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i
cal
n
e
t
w
o
r
k
opera
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n
d
st
a
b
il
it
y
[1].
T
her
efor
e,
t
he
W
E
C
S
must
q
uic
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ly
t
a
k
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par
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ces rat
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s pa
ssi
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c
har
g
es from
the pow
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s
ys
t
e
m
view
p
o
in
t [
2
].
V
a
rious
c
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n
f
i
gura
t
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av
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bee
n
r
ec
com
e
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o
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d
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r
t
o
r
e
du
ce
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ut
put
p
ow
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v
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iat
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.
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prac
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a
l
s
o
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co
ns
ists on all
o
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tin
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a
s
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rm
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ne
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r
g
y
s
tor
a
ge
(
S
M
ES
)
[3]
,
s
uper
c
a
p
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c
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s
[4]
or
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lyw
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y
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t
o
r
a
g
e
s
y
s
t
e
m
(
F
E
S
S
)
[
5
]
,
a
s
a
n
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
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IS
S
N
:
2088-
86
94
Ro
bu
s
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o
or
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a
te
d co
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g
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e
l
e
n
er
gy sto
r
a
g
e
sy
st
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m
… (Moham
e
d
Nad
o
u
r
)
1
111
a
d
dit
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o
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a
l
reserv
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th
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it
i
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t
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c
a
s
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o
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d
efi
c
ienc
y.
Re
fe
re
nce
[6],
p
resen
t
s
a
c
o
mpa
r
ati
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dy
a
n
d
a
t
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g
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f
u
l
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ver
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w
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ic
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l
a
n
d
e
c
onom
ic
perform
ance
on
t
h
e
a
v
a
i
l
a
bl
e
ener
g
y
s
t
o
rag
e
t
e
c
h
n
o
l
ogie
s
.
For
i
ns
tance
,
w
ith
t
he
ir
h
ig
h
e
f
fic
i
e
n
c
y
,
bo
t
h
h
igh
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a
nd
e
n
e
rgy
de
ns
itie
s,
a
n
d
l
on
ger
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y
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i
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g
life,
t
he
F
ES
Ss
offer
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ompe
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i
t
i
v
e
o
p
t
i
on
ove
r
t
h
e
alter
n
a
t
i
v
es
[
7]
.
A
m
ong
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y
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a
nt
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or
ks,
i
n
[
2]
a
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ES
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i
s
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syn
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ac
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ne
(
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M
S
M
)
base
d
w
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d
p
ow
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p
l
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i
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or
der
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m
oot
h
an
d
i
m
prove
t
he
o
u
t
p
u
t
pow
er
q
u
a
l
i
t
y
.
C
l
a
s
s
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c
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l
P
I
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o
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l
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a
w
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t
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a
f
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z
z
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l
o
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i
c
s
u
p
erv
i
sor
are
used
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or
t
he
p
ow
er
f
l
o
w
ma
nage
me
nt
b
etw
e
e
n
t
he
F
ES
S
and
the
e
l
e
c
trica
l
g
r
i
d
w
h
il
e
c
ons
i
der
i
n
g
t
h
e
st
o
r
age
de
vice
s
ta
te
o
f
c
h
a
r
g
e
(S
oC).
F
ew
h
ave
be
e
n
t
he
s
tu
die
s
t
ha
t
su
gge
st
e
d
a
p
r
o
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ta
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l
e
a
p
p
l
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c
a
t
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o
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o
f
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t
o
a
D
F
I
G
U
R
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T
h
e
a
u
t
h
o
r
i
n
[
8
]
h
as
p
resent
ed
a
s
ol
uti
o
n
t
h
at
c
on
si
sts
o
n
c
onn
ec
ti
ng
t
h
e
F
E
S
S
t
o
t
h
e
D
C
b
u
s
t
h
r
o
u
g
h
a
n
A
C
/
D
C
con
v
er
t
e
r
i
n
o
rde
r
t
o
st
udy
t
h
e
effec
t
s
of
r
e
a
c
tive
a
nd
a
c
t
i
v
e
pow
e
r
q
u
a
l
ity
i
mpro
ve
me
nt
o
n
loa
d
v
o
l
tage
s
us
i
n
g
P
I
c
on
trol
l
e
rs.
H
o
w
e
ve
r,
t
r
a
ditio
na
l
c
o
n
t
ro
l
sc
hem
e
s
do
n
ot
a
l
w
a
y
s
pr
ovi
de
p
lea
s
ing
re
s
u
l
t
s,
s
i
n
c
e
t
he
y
on
ly
guara
nt
e
e
t
h
e
a
ppr
opria
t
e
t
rac
k
ing
r
e
sp
ons
e
a
t
a
c
ert
a
in
o
pe
rat
i
n
g
p
o
i
n
t
for
w
h
ic
h
the
c
o
n
t
ro
l
la
w
w
a
s
alre
ad
y d
e
sig
n
e
d.
W
here
as, w
hen a pa
ram
e
tric
var
i
a
tio
n
i
s
regis
tere
d, w
hic
h
is
us
ua
l
l
y t
h
e case
d
u
e es
pec
i
a
l
l
y
to m
o
d
e
lli
ng
unc
erta
in
t
i
es a
n
d
som
e p
h
y
s
i
c
a
l
p
he
nom
ena,
the
p
er
fo
rman
c
e
o
f
PI-b
a
s
e
d
co
n
t
r
ol
s
ch
eme
ri
sk
t
o
be
i
n
s
ura
b
l
e
a
n
d
gra
ve
ly de
t
er
i
o
r
a
ted.
A
c
cordi
n
gl
y,
i
n
a
t
te
mp
t
to
m
eet
h
ighe
r
p
e
rforma
n
ce
s,
t
hi
s
p
a
per
p
re
sent
s
a
c
oor
din
a
ted
ro
bust
con
t
ro
l
of
a
F
ES
S
associate
d
t
o
a
DFIG-based
w
i
n
d
t
u
rb
i
n
e
us
i
n
g
a
s
ys
t
e
mat
i
c
a
nd
r
e
c
u
r
si
v
e
m
e
t
ho
dol
ogy
use
d
f
or
n
o
n
l
i
ne
ar
s
yste
ms
c
on
t
r
o
l
know
n
as
b
a
c
k
s
t
ep
p
i
ng
(BS
)
[
9].
O
w
i
n
g
t
o
t
h
i
s
t
e
c
hn
i
que,
the
fe
e
dbac
k
con
t
ro
l
law
th
a
t
g
uara
nte
e
s
t
h
e
sys
t
em
ove
r
a
ll
be
ha
vi
or
a
nd
s
t
a
b
i
l
i
t
y
can
b
e
e
ffi
c
i
en
tl
y
el
ab
o
r
at
ed
.
Fi
gu
re
1
show
s
t
h
e
bas
i
c
con
f
i
g
ura
tio
n
o
f
t
he
s
ys
te
m
,
w
here
t
he
s
ta
tor
w
i
n
d
i
ng
s
of
t
h
e
D
F
I
G
ar
e
st
r
a
ig
htf
o
rw
ar
d
l
y
lin
ke
d
t
o
t
he
g
rid,
w
hi
le
i
ts
r
ot
or
w
i
n
d
i
ngs
a
r
e
l
i
nke
d
via
a
b
a
c
k-
to-ba
c
k
con
v
er
t
e
r.
T
h
e
D
FIG
side
c
on
ve
rter
DSC
is
u
se
d
to
c
o
n
tr
ol
t
he
g
e
n
er
ate
d
r
e
act
i
v
e
an
d
ac
tive
p
o
we
rs
f
o
l
l
o
w
i
n
g
a
m
a
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
(MPP
T)
a
lg
or
ithm
.
T
h
e
e
le
c
t
rical
n
e
t
w
o
rk
s
ide
c
o
n
v
e
r
ter
N
S
C
is
use
d
t
o
kee
p
c
o
n
s
t
an
t
the
D
C
b
us
v
ol
ta
ge
regardless
o
f
the
dire
ct
io
n
and
ma
gn
itu
d
e
o
f
t
h
e
po
we
r.
F
i
n
al
l
y
,
th
e
f
l
y
w
he
el
s
i
d
e
conv
ert
e
r
FSC
i
s
c
o
n
t
ro
ll
ed
in
o
r
d
er
t
o
sm
oo
th
t
he
w
in
d
-
in
duce
d
f
luc
t
uat
i
o
n
s
a
n
d
to
i
m
p
ro
ve
t
he
qua
lit
y
o
f
t
he
o
u
t
pu
t
a
c
t
i
ve
pow
er
.
S
i
m
u
l
a
t
i
o
n
r
e
s
ul
ts
p
e
rform
ed
i
n
M
a
tla
b/S
i
m
u
l
i
n
k
ver
i
fy
t
h
e
p
e
r
f
orm
a
nc
e
of
t
he
p
r
o
pose
d
c
o
n
tr
ol
s
che
m
es,
in
term
s of
o
u
t
pu
t
p
o
w
e
r
sm
ooth
i
n
g
,
dy
nam
i
c
resp
onse
an
d r
obus
t
n
es
s ag
ainst
p
a
ramet
r
i
c
vari
a
ti
o
n
.
F
i
gure
1.
S
tud
i
e
d
sys
tem
The
res
t
o
f
the
pap
e
r
is
a
rranged
a
s
f
o
l
l
o
w
s
:
S
e
c
t
i
o
n
2
p
r
e
s
e
n
t
s
the
mo
de
l
l
i
n
g
o
f
t
he
w
i
nd
tur
b
i
n
e
,
the
D
F
IG
a
nd
t
h
e
F
E
S
S
.
T
he
p
ro
pose
d
c
on
tr
ol
s
tra
t
e
g
i
e
s
of
t
he
M
S
C
,
t
h
e
G
S
C,
a
nd
t
h
e
F
S
C
ar
e
disc
us
se
d
i
n
deta
i
l
s
i
n
S
e
c
t
i
o
n
2
.
S
i
mula
t
i
o
n
a
n
d
i
n
t
er
pr
etat
io
n
of
t
he
r
e
s
u
lts
i
n
S
ecti
o
n
3.
F
ina
l
l
y
,
a
co
nc
l
u
s
i
o
n
i
n
S
e
ctio
n 4.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
111
0 –
1
1
22
1
112
2.
DYNA
M
I
C M
O
DELLING OF THE S
T
UDIE
D
S
Y
S
T
E
M
2.1.
W
i
n
d
t
ur
bi
ne
m
o
d
el
The
a
e
rody
na
m
i
c
pow
er
h
a
r
ves
t
ed
by
t
h
e
w
i
n
d
t
urb
i
ne
P
c
an
b
e
expre
ssed
a
s
f
unct
i
on
o
f
t
h
e
pow
er
c
o
eff
i
ci
ent
C
a
s fo
l
l
ow
s [10-1
2
]
:
3
hp
w
i
n
d
p
PC
,
P
0
.
5
C
,
A
v
,
T
R
v
(
1
)
Where
v
is
t
he
w
ind
spe
e
d,
i
s
t
h
e
a
i
r
density
a
nd
A
repr
esents
t
he
s
w
e
pt
a
r
ea,
R
i
s
the
b
lade
s
radi
us
a
n
d
i
s
t
h
e
tu
rbi
n
e
rot
a
t
i
on
a
l
s
p
eed
.
Th
e
co
ef
fi
ci
ent
repr
esen
ts
t
he
a
erod
yna
mic
ef
ficie
n
c
y
o
f
t
h
e
tur
b
ine
,
w
hich
a
ppr
oache
d
i
n th
is w
ork
b
y
th
e
e
xpre
s
si
o
n
b
e
l
l
o
w
[
9
]
:
p
3
3
11
6
0
.4
06
0
.
07
3
5
C
0
.51
0
9
0
.4
5
e
xp
2
1
0.
0
8
1
0.
0
8
1
(
2
)
Whe
r
e,
t
he an
g
le of
or
i
e
n
t
a
tion of the
b
la
de
s and λ
is the tip spee
d
rati
o. More
ove
r, the a
erod
yna
mic t
o
rq
ue
is
o
b
ta
ine
d
fr
o
m
by [9]
:
3
h
hp
tT
P
Av
CC
,
2
(3)
N
e
glec
tin
g
t
h
e
ela
s
tic
i
t
y,
f
ricti
o
n
a
nd
ene
r
g
y
l
osses.
T
he
g
ear
b
o
x
th
at
i
s
used
t
o
ada
p
t
the
r
o
t
a
tio
na
l
spee
d
to t
ha
t
of t
he
g
ener
at
or
ca
n be
m
o
d
e
l
l
e
d us
in
g
G
a
ga
i
n
r
ati
o
a
s fo
ll
ow
s
:
me
c
T
h
g
G;
C
G
C
(4)
F
i
nal
l
y
,
t
h
e
m
odel i
s
c
omple
t
e
d
by t
h
e
fun
d
a
m
ental
e
qua
t
i
o
n
of
d
yna
mic
[13]
:
me
c
gg
e
m
m
e
c
d
JC
C
f
dt
(5)
2.2.
DFIG Mo
d
el
T
h
e
D
F
I
G
m
o
d
e
l
i
s
e
s
t
a
b
l
i
s
h
e
d
u
s
i
n
g
t
h
e
d
y
n
a
m
i
c
e
q
u
a
t
i
o
n
s
o
f
t
h
e
st
a
t
or
a
nd
r
o
t
or
c
ur
rents,
vo
lta
ge
s,
a
nd fluxe
s
re
present
e
d
in a
t
w
o
-p
h
a
se
dq re
fer
e
nce
fr
am
e
[9,
14]:
sd
sd
.
s
s
d
s
s
q
sq
sq
.
s
s
q
s
s
d
rd
rd
.
r
rd
r
r
q
rq
rq
.
r
rq
r
r
d
d
vR
i
dt
d
vR
i
dt
d
vR
i
dt
d
vR
i
dt
;
sd
.
s
sd
rd
sq
.
s
sq
rq
rd
.
r
rd
s
d
rq
.
r
rq
s
q
Li
M
i
Li
M
i
Li
M
i
Li
M
i
(6)
Wh
e
r
e,
,
,
,
,
a
nd
b
ei
n
g
r
espec
t
i
v
e
l
y
t
h
e
st
a
t
or
a
nd
ro
t
o
r
curr
ents,
v
o
lta
ge
s,
a
n
d
gene
ra
ted
fl
u
x
e
s.
a
nd
r
epre
se
n
t
t
he
a
n
g
u
l
ar
s
pe
ed
o
f
th
e
rotating
fie
l
d
associa
t
e
d
r
espe
ctive
l
y
to
t
h
e
rotor
and
to
t
he
s
tator
(rad/s).
S
i
milarly,
,
,
,
and
a
re
s
t
a
tor
r
e
sista
n
ce
and
i
n
c
u
c
t
a
n
ce
a
n
d
r
oto
r
resista
n
ce
a
n
d
in
d
u
cta
n
ce
r
espective
l
y. Whe
rea
s
,
M repr
es
ents t
h
e
m
ut
u
a
l
i
n
du
ct
a
n
c
e
.
T
h
e
r
ea
ct
iv
e
and
a
c
tiv
e
pow
er
as
w
e
ll as
e
lec
t
r
o
m
a
g
n
e
t
i
c
t
orq
u
e
ca
n be
g
ive
n
by,
w
it
h p
be
i
ng
t
he pai
r
of
pol
es:
s
s
s
s
ds
d
s
qs
q
s
s
s
s
qs
d
s
ds
q
PR
e
v
i
v
i
v
i
QI
m
v
i
v
i
v
i
;
e
m
sq
rd
sd
rq
s
M
Cp
i
i
L
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Ro
bu
s
t
c
o
or
d
i
n
a
te
d co
nt
ro
l usin
g
b
a
c
k
s
t
ep
p
i
n
g
o
f
f
l
y
w
he
e
l
e
n
er
gy sto
r
a
g
e
sy
st
e
m
… (Moham
e
d
Nad
o
u
r
)
11
1
3
2.3.
FES
S
mod
elin
g an
d
si
z
i
n
g
F
E
SS
ope
rate
s
as
a
n
ene
r
gy
r
e
ser
v
e
t
h
a
t
s
tor
e
s
th
e
e
n
ergy
i
n
a
ki
ne
tic
f
or
m
i
n
a
h
i
gh-s
p
eed
s
p
i
nni
ng
m
a
ss
coup
le
d
t
o
t
he
s
ha
f
t
o
f
an
e
l
e
c
t
rica
l
m
a
chi
n
e
tha
t
p
r
o
vi
de
s
an
e
l
e
ct
ro
me
ch
a
n
i
c
a
l
i
n
t
e
r
f
a
ce
b
et
wee
n
t
he
fl
yw
hee
l
a
nd
t
he
s
yste
m
[1].
D
urin
g
t
h
e
ch
a
r
gi
ng
pr
o
c
es
s
,
t
he
m
a
c
h
i
ne
w
orks
a
s
a
m
o
tor
to
s
pe
e
d
up
th
e
rota
ti
o
n
al m
o
tion
of t
he fl
y
w
h
ee
l
a
nd
t
h
e
r
e
f
ore i
n
c
r
ea
s
i
n
g
t
h
e
s
t
ored ene
r
gy, the
n, the
fl
y
w
h
e
e
l
re
m
a
i
n
s
in t
h
e
st
a
n
d
b
y
m
ode. Whe
rea
s
,
o
n
-
d
em
and, t
he
m
ac
hi
ne
s
e
r
ves as
a
g
e
n
er
a
t
o
r
a
n
d
d
e
c
e
l
e
r
a
te
t
h
e
fl
y
w
h
e
e
l r
e
tr
i
e
v
i
n
g
the
stor
ed
e
ne
r
gy
in
to
t
he
s
ys
t
e
m
.
The
a
m
oun
t
of
e
ner
gy
s
t
ore
d
i
n
a
flyw
he
el
d
e
p
e
n
ds
on
t
h
e
m
a
ss
and
the f
o
rm
(r
e
prese
n
t
e
d b
y
f
lyw
h
eel
i
ne
rti
a
J
) a
nd the
ro
tat
i
ona
l
speed
[6]:
2
fw
fw
fw
E0
.
5
J
,
(8)
H
o
w
e
ve
r,
f
or
s
afet
y
re
aso
n
s,
t
he
a
cce
ssi
b
le
k
ine
tic
e
ne
rg
y
i
s
lim
i
t
e
d
b
y
an
d
w
h
i
c
h
are
r
e
spec
tive
l
y the
m
a
xim
u
m
a
nd m
i
nim
u
m
speed
o
f
t
h
e
fl
yw
hee
l
[1
5],
gi
v
i
n
g
t
hat
:
22
fw1
f
w
f
w
m
ax
fw
m
i
n
E0
.
5
J
,
(9)
The
f
l
yw
he
el
i
nert
ia
i
s
de
te
r
m
ine
d
u
sin
g
t
h
e
e
xpress
i
o
n
b
elow
,
a
f
ter
se
lectin
g
the
stor
age
sys
t
em
m
axim
um
pow
er
ca
p
aci
ty
store
d duri
n
g a
c
e
rtain Δt, whic
h is ide
nt
ica
l
t
o the elec
t
r
i
c
al m
otor rated pow
er
.
Whic
h
in t
h
i
s
ap
pl
i
c
a
t
io
n, c
ons
ide
r
ed
l
ow
e
r
tha
n 2
0
%
the
D
F
I
G
based w
i
n
d
tur
b
ine
ra
t
e
d p
o
w
e
r:
fw
1
rI
M
fw
22
22
fw
m
a
x
f
w
m
i
n
fw
max
f
w
m
i
n
2E
2P
t
J
(10)
I
n
t
h
i
s
w
o
rk,
t
h
e
fl
yw
he
e
l
e
x
c
ha
nge
s
t
h
e
e
n
ergy
w
i
t
h
t
he
s
ys
tem
b
y
m
e
ans
of
a
n
i
n
d
u
c
t
i
o
n
m
ac
hi
ne
(IM).
I
t
i
s
e
sse
nt
ia
l
for
t
h
e
I
M
t
o
o
p
era
t
e
in
i
ts
f
i
e
ld-
w
ea
k
e
n
ing
re
gio
n
,
at
a
r
o
t
a
tio
na
l
spee
d
r
a
n
g
i
n
g
be
t
w
ee
n
15
0
0
a
nd
30
0
0
rpm
,
w
her
e
i
t
s
r
a
t
e
d
pow
e
r
i
s
alw
a
ys
a
v
a
il
a
b
l
e
[
1]
.
Ther
efor
e,
t
he
r
e
g
u
l
a
t
i
on
of
t
he
f
l
u
x
i
s
con
d
u
cte
d
i
n ac
corda
n
ce
w
ith
t
he
follow
i
n
g
con
tro
l
la
w
:
s
r
r
r
ated
m
r
s
rr
e
f
r
r
r
ated
m
r
m
3V
L
;i
f
M
;i
f
(1
1)
Whe
r
e,
a
nd
a
re
r
e
s
p
e
c
t
i
v
ely
t
h
e
rot
o
r
and
t
h
e
st
at
o
r
r
at
ed
f
l
u
x
e
s
,
a
nd
b
e
i
n
g
t
h
e
m
e
asure
d
and
t
h
e r
a
ted
rota
t
i
o
n
a
l
s
peed
o
f th
e
IM,
and
V
is th
e
sta
t
or
ra
t
e
d
vol
ta
ge.
3.
PROPOS
E
D
CONTROL S
T
R
ATEGIES
3.1.
MSC
co
n
t
ro
l
In
o
rd
er
t
o
d
e
c
o
upl
e
t
h
e
co
nt
ro
l
of
s
t
a
t
o
r
re
act
i
v
e
a
n
d
acti
v
e
po
wers,
a
f
i
e
l
d
o
r
i
e
nt
ed
c
o
n
t
r
ol
s
ch
e
m
e
is
a
do
pte
d
,
ali
g
n
i
ng
t
h
e
d-a
x
i
s
w
ith
t
he
s
tat
o
r
fl
u
x
(
;
0
).
M
ore
over,
b
y
n
e
g
le
cti
ng
the
sta
t
or
resista
n
ce
,
w
h
i
c
h
is
a
r
a
tio
na
l
appro
x
i
m
a
ti
on
f
or
h
ig
h
p
o
w
e
r
ge
n
e
r
a
t
o
r
s
[
9
]
,
w
e
d
e
t
e
r
m
i
n
e
t
h
e
s
t
a
t
e
m
o
d
e
l
o
f
the DF
IG
a
s fol
l
ows
:
s
rq
r
r
q
r
d
rq
rq
r
r
q
r
d
1s
PV
R
I
I
IV
R
I
I
zP
;
rd
r
r
d
r
q
s
rd
rq
r
r
d
2s
QV
R
I
I
IV
R
I
I
q
zQ
Wi
t
h
:
2
s
rs
rs
s
sr
sr
VM
M
1;
;
LL
LL
MV
1
gL
;
g
;
.
LL
(12)
Th
e
b
a
c
k
st
epp
i
ng
(
BS)
b
a
si
cal
ly
u
se
s
the
so-
cal
led
(vir
tua
l
c
o
n
t
r
o
l
v
a
r
i
a
b
l
e
s
(
V
C
V
s
)
)
t
o
sy
st
emat
i
call
y
d
is
sac
o
ci
at
e
a
n
o
nl
in
e
a
r
c
o
m
p
l
ex
c
o
n
t
r
ol
s
ch
e
m
e
in
to
s
im
pler
d
e
s
ig
n
pr
o
b
lem
[
9
].
T
he
c
on
tro
l
des
i
g
n
i
s
d
i
v
i
d
e
d
in
t
o
m
ult
i
p
le
s
te
ps.
In
e
ve
ry
s
te
p,
w
e
virt
ua
ll
y
de
a
l
w
ith
a
s
in
gle
in
pu
t
s
i
n
g
le
o
u
t
pu
t
sub
s
ys
tem
,
so
t
h
at eac
h
ste
p
p
rov
i
des
a
re
fe
renc
e
f
o
r
the
ne
xt
one. The c
o
ntr
o
l law
tha
t
g
ua
ran
t
ee
s
the o
v
era
l
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9 :
111
0 –
112
2
1
114
sy
st
em
b
eh
avio
u
r
a
n
d
st
a
b
i
lit
y
can
b
e
b
u
ilt
u
p
i
n
a
con
s
t
r
u
c
tiv
e
m
a
n
n
er
u
s
i
n
g
L
ya
pu
n
o
v
fu
nc
ti
on
s.
A
s
it
is
show
n
in
F
i
g
ure
2
T
h
e
bloc
k
dia
g
ra
m
of
D
S
C
c
on
tro
l
i
n
v
ol
ves
a
n
ope
n
lo
op
M
P
P
T
[1
6]
u
se
d
to
e
s
t
a
b
l
i
s
h
t
h
e
op
tim
al
a
c
tive
pow
er
r
efere
n
ce
in
o
rde
r
t
o
m
a
x
i
mize
t
h
e
c
o
nve
rt
e
d
p
ow
er
by
a
d
j
u
s
t
i
n
g
the
w
i
n
d
t
ur
bi
ne
me
cha
n
ic
al
t
o
it
s
o
p
t
i
m
al
v
alue,
a
n
d
tw
o
seria
l
c
o
n
tro
l
l
o
o
ps.
The
oute
r
l
oo
p
pro
v
i
de
s
t
h
e
V
C
V
s
(
the
references
o
f
curr
ents)
via
the
rea
c
tiv
e
an
d
a
c
ti
ve
p
ow
er
c
on
tr
o
l
.
Wh
i
l
e
t
h
e
in
ner
l
o
o
p
p
r
o
vide
s
t
h
e
actua
l
con
t
ro
l va
ria
b
l
e
s (r
ot
or
vol
ta
g
e
s)
[
17,
18].
F
i
gure
2.
D
S
C
c
on
t
r
o
l
a)
C
u
r
r
e
n
ts
r
ef
er
e
n
c
e
s
c
o
m
pu
t
a
ti
o
n
F
i
rst, w
e
defin
e
the err
ors va
riab
les, w
ith
a
nd
be
i
ng re
sp
e
c
ti
ve
ly t
he r
efere
n
ces of t
h
e
stator
rea
c
ti
ve
a
nd a
c
tive
p
o
w
e
r.
T
h
e
n
w
e
se
l
e
c
t th
e
chose
n
L
yap
u
n
o
v f
unc
tio
ns
(
LF
s)
s
uch t
h
a
t
:
sr
s
1
1s
r
s
2
2s
r
s
s
r
s
eP
P
e
P
P
eQ
Q
e
Q
Q
;
22
1.
1
2
.
2
11
Ve
V
e
22
(
1
3
)
The
deri
va
ti
ve
o
f Lya
pun
o
v
f
unc
t
i
o
n
ca
n
be
w
r
itte
n
:
sr
1.
1
11
r
q
r
r
q
r
d
2.
2
22
r
d
r
r
d
r
d
sr
Ve
e
e
P
V
R
I
I
Ve
e
e
Q
V
R
I
I
(
1
4)
A
c
c
o
rdi
n
g
to
t
he
B
S
the
o
ry,
V
a
nd
V
m
ust
be
s
t
r
ict
l
y
ne
ga
t
i
v
e
t
o
e
n
sure
t
he
s
t
a
bi
lit
y
o
f
t
hi
s
f
i
r
s
t
step.
Thus,
V
b
e
and
V
b
e
.
The c
u
rrents
refere
nces
a
re
obta
i
ne
d
usin
g (
14):
sr
rq
r
s
1
1
rq
rd
rr
rd
r
s
2
2
rd
rd
sr
rr
11
IP
b
e
V
I
RR
11
IQ
b
e
V
I
RR
(
1
5)
b)
Rot
o
r
v
o
l
t
a
ge
s c
o
mp
u
t
at
i
o
n
W
e
d
e
f
i
n
e
t
h
e
erro
rs
v
a
r
i
a
b
l
es
,
n
o
ti
ng
t
h
a
t
th
e
V
C
Vs
d
ete
r
mi
n
e
d
by
(1
5)
a
re
t
he
d
e
s
ir
ed
v
a
r
ia
b
l
e
in
th
i
s
s
te
p, a
nd w
e
selec
t the
L
F
s for this ste
p
such
t
hat
:
rq
r
r
q
3
3r
q
r
r
q
rd
r
r
d
4
4r
d
r
r
d
eI
I
e
I
I
eI
I
e
I
I
;
22
2
2
3.
1
3
4.
2
4
11
Ve
e
V
e
e
22
(
1
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Ro
bu
s
t
c
o
or
d
i
n
a
te
d co
nt
ro
l usin
g
b
a
c
k
s
t
ep
p
i
n
g
o
f
f
l
y
w
he
e
l
e
n
er
gy sto
r
a
g
e
sy
st
e
m
… (Moham
e
d
Nad
o
u
r
)
1
115
In
o
rd
e
r
t
o
i
n
su
re
a
s
t
a
bl
e
t
r
ac
k
i
ng
p
erf
o
rman
ce
t
h
e
d
e
r
iv
at
iv
e
o
f
the
LF
s
must
b
e
ne
ga
t
i
ve.
F
i
na
ll
y,
o
w
i
n
g
t
o
(16)
t
he
c
o
n
t
r
ol
v
o
ltage
s ar
e give
n
b
y
:
-a
)
22
1
s1
1
s
3
3
22
4
s2
2
s
4
4
Vb
e
b
e
0
Vb
e
b
e
0
;
-b
)
rq
r
rq
r
s
3
3
1
r
rq
rd
rd
r
rd
r
s
4
4
2
r
rd
rd
1
Vb
e
I
e
R
I
I
1
Vb
e
I
e
R
I
I
(17)
No
ti
ng
t
h
a
t
b
s1
,
b
s2
,
b
s3
a
nd b
s4
ar
e
posi
t
i
ve
c
ons
tan
t
s c
a
l
l
e
d
t
he
B
S
c
o
eff
i
c
i
e
n
t
s
,
used
t
o e
n
s
u
r
e a f
a
s
t
dyn
ami
c
respo
n
se
a
n
d
t
he
sta
bi
lit
y o
f
t
he ove
ra
ll sy
st
em
.
3.2.
GSC
control
The
G
S
C
i
s
c
onnec
t
e
d
t
o
t
h
e
gr
id
t
hr
ou
gh
a
fi
l
t
er
(
re
si
st
or-in
d
uctor
circuit
R
,
L
.
F
i
gur
e
3
show
s
the
b
l
oc
k
d
i
a
g
ra
m
of
N
S
C
c
on
tro
l
t
ha
t
in
v
o
l
v
es
t
w
o
c
onse
c
ut
i
v
e
c
o
nt
rol
l
o
op
s.
T
h
e
out
er
l
oop
p
rovide
s
t
h
e
VCVs
(
t
h
e
r
e
f
e
rences
o
f
the
f
i
lter
output
c
urrents
(
an
d
)
via
the
re
acti
v
e
a
nd
ac
t
i
ve
p
ow
e
r
c
ontro
l.
Wh
i
l
e
the
inne
r
loop
pro
v
i
de
s
the
actua
l
co
ntr
o
l
varia
b
le
s
(the
f
i
l
ter
outpu
t
vo
l
t
a
g
es
and
))
.
T
h
i
s
syste
m
can
b
e repr
esente
d
in
a
dq
refere
nce
fr
am
e by
th
e
foll
ow
i
n
g equa
ti
on
[1
9]:
td
td.
t
t
d
t
s
t
t
q
s
d
tq
tq.
t
t
q
t
s
t
t
d
s
q
dI
VR
I
L
L
I
V
dt
dI
VR
I
L
L
I
V
dt
(
1
8
)
A
ve
ct
or
c
ontr
o
l
is
u
se
d
to
a
chie
ve
a
n
in
de
pen
d
e
n
t
c
o
n
t
ro
l
o
f
t
he
a
ct
i
v
e
pow
er
a
n
d
t
h
e
r
e
acti
v
e
pow
er
a
nd
e
x
c
h
an
ge
d
be
tw
e
e
n
t
h
e
N
S
C
a
nd
t
h
e
gri
d
.
B
y
a
lig
n
i
n
g
t
he
q
-a
xis
of
t
he
p
a
r
k
refere
nce
fr
am
e
w
i
t
h
netw
ork
vo
l
t
ag
e
e
q
u
i
va
l
e
n
t
v
e
c
tor,
t
hu
s,
.
0
a
n
d
.
.
,
t
h
e
m
o
d
e
l
o
f
t
h
e
s
y
s
t
e
m
c
a
n
b
e
d
e
t
e
r
m
i
n
e
d
a
s
fo
l
lo
ws:
s
t.
tq
t
t
q
s
t
t
d
s
t
tq
.
tq
t
t
q
s
t
t
d
s
t
1.
t
.
V
PV
R
I
L
I
V
L
1
IV
R
I
L
I
V
L
zP
;
s
td
t
t
d
s
t
t
q
t.
t
td
.
td
t
t
d
s
t
t
q
t
2.
t
.
V
QV
R
I
L
I
L
1
IV
R
I
L
I
L
zQ
(
1
9)
F
i
gure
3.
N
S
C
c
on
t
r
o
l
a)
Curr
ent
s
r
e
f
e
r
en
ce
s
co
mp
u
t
ati
o
n
We
def
ine
(
e
,
e
) re
presen
ti
n
g
t
he
e
rr
ors var
i
a
b
le
s, w
e
choose
th
e
LF
s
such t
ha
t:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9 :
111
0 –
112
2
1
116
tr
t
1
1t
r
t
2
2t
r
t
tr
t
eP
P
e
P
P
eQ
Q
e
Q
Q
;
2
11
2
11
1
Ve
2
1
Ve
2
(
2
0
)
Li
kew
i
se,
ap
pl
yi
n
g
t
he
s
am
e
pri
n
ci
p
l
e
use
d
f
or
t
he
D
S
C
c
o
n
tr
ol,
t
h
e
V
CV
s
t
h
a
t
g
u
a
ra
nt
ee
a
s
t
a
bl
e
t
r
a
c
ki
ng
i
n
the f
i
r
s
t
co
n
t
ro
l lo
o
p
ca
n
be
d
e
ter
m
ine
d
s
uc
h
that
:
-a
)
'2
1
s1
1
'2
4
s2
2
Vb
e
0
Vb
e
0
;
-b
)
'
t
tr
tq
r
.
s
1
1
t
q
s
t
t
d
s
fs
'
t
td
r
.
s
2
2
t
d
s
t
t
q
tr
fs
L
1
IP
b
e
V
L
I
V
RV
L
1
IQ
b
e
V
L
I
RV
(
2
1)
b)
Rot
o
r
v
o
l
t
a
ge
s
co
mp
u
t
at
i
o
n
The
V
C
V
s
d
et
erm
i
ned
prev
i
o
us
l
y
a
re
the
d
e
s
ired
v
aria
b
l
e
for
thi
s step.
We def
ine
:
tq
r
t
q
3
3t
q
r
t
q
td
r
t
d
4
4t
d
r
t
d
eI
I
e
I
I
eI
I
e
I
I
;
22
31
3
22
42
4
1
Ve
e
2
1
Ve
e
2
(22)
S
i
m
i
la
rl
y, the
con
tro
l
la
w
tha
t e
n
s
u
r
e
s gl
oba
l
sta
b
i
l
ity
o
f
the
s
ys
t
e
m
is
w
ritte
n suc
h
:
-a
)
'2
'
2
3
s1
1
s
3
3
'2
'
2
4
s2
2
s
4
4
Vb
e
b
e
0
Vb
e
b
e
0
;
-b
)
s
tq
r
f
q
r
s
2
2
1
t
tt
q
s
tt
d
t
s
td
r
t
d
r
s
4
4
3
t
tt
d
s
tt
q
t
V
Vb
e
I
e
L
R
I
L
I
L
V
Vb
e
I
e
L
R
I
L
I
L
(
2
3)
c)
DC-l
ink v
i
l
t
a
g
e co
ntr
o
l
N
e
glec
ti
n
g
t
he
c
onv
e
r
ters
l
osse
s.
W
ith
P
,
P
and
P
b
ei
ng
respe
c
tive
l
y
t
h
e
rot
o
r,
t
he
D
C-b
u
s
a
n
d
t
h
e
FESS
act
iv
e po
wer Fi
gu
re 4
W
e h
a
v
e
:
ct
s
s
t
PP
P
P
(
2
4
)
Wi
t
h
:
2
dc
cd
c
d
c
dU
(
t
)
d1
PC
U
(
t
)
C
U
(
t
)
dt
2
d
t
(
2
5
)
A
c
c
o
rdi
n
g
to (24)
an
d
(
25),
w
e
w
rite:
dc
t
r
s
t
c
dc
dU
(
t
)
P
P
P
IC
dt
U
(
t
)
(
2
6
)
F
i
gure
4. D
C-li
nk v
o
lta
ge
c
o
n
t
ro
l
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Ro
bu
s
t
c
o
or
d
i
n
a
te
d co
nt
ro
l usin
g
b
a
c
k
s
t
ep
p
i
n
g
o
f
f
l
y
w
he
e
l
e
n
er
gy sto
r
a
g
e
sy
st
e
m
… (Moham
e
d
Nad
o
u
r
)
1
117
3.3.
FS
C con
t
ro
l
The
F
S
C
con
t
rol
i
t
i
s
used
t
o
m
a
nage
t
h
e
s
t
o
rage
d
e
v
ice
o
p
er
at
i
o
n
s
o
as
t
o
s
t
ore
the
e
n
er
gy
w
h
e
n
ava
ila
b
l
e,
a
nd
t
o
r
e
st
o
r
e
i
t
b
a
c
k
to
t
he
s
ys
te
m
in
t
he
o
p
pos
ite
c
a
s
e
.
T
h
e
b
l
o
c
k
d
i
a
g
r
a
m
o
f
F
S
C
c
o
n
t
r
o
l
i
s
show
n
in
F
i
g
u
r
e
5
it
i
nvo
lve
s
t
w
o
c
o
n
t
rol
lo
ops
i
.e.
t
h
e
ou
te
r
loop
that
p
rovides
the
VCV
s
(
t
h
e
references
o
f
the
s
t
at
or
o
u
t
p
u
t
curr
en
ts
and
)
via
the
ro
tat
i
ona
l
sp
eed
a
n
d
direc
t
f
l
ux
co
n
t
ro
l,
a
nd
the
i
n
n
e
r
l
oo
p
t
h
at
p
rovi
d
e
s
t
h
e a
c
t
u
al
c
ont
ro
l
v
a
ri
a
b
l
e
s (t
h
e
o
u
t
pu
t
volt
a
ge
s
an
d
))
.
F
i
gure
5.
B
l
o
c
k
d
i
a
gram
of th
e
FS
C
contro
l
The
re
ac
t
i
ve
a
nd
act
i
v
e
po
w
e
r
at the
p
o
i
n
t
o
f c
o
m
m
on c
o
u
p
l
i
ng (
PC
C
)
a
r
e
g
i
v
en
by
:
gs
t
gs
t
PP
P
QQ
P
(27)
We
d
e
f
i
n
e
:
ms
r
ms
r
PP
P
QQ
P
(28)
Wh
e
r
e
(
Q
;P
,
(
Q
;P
a
n
d
(
Q
;P
b
eing
t
h
e
reac
t
i
ve
a
n
d
a
c
t
i
v
e
pow
er
p
r
ovide
d
i
n
t
he
s
ta
t
o
r,
t
h
e
rot
o
r
a
nd
the
filte
r,
r
espec
tiv
e
l
y.
K
now
in
g
the
a
d
jus
t
e
d
p
ow
e
r
P
d
esired
t
o
be
i
n
j
ec
t
e
d
in
to
t
he
g
r
i
d,
t
he
pow
er
re
f
er
ence
of
the F
E
SS c
ontr
o
l
can
b
e
determ
i
n
ed u
si
ng t
h
e
f
ol
low
i
n
g
e
xpress
i
on [6
]
:
st
k
g
r
m
PP
P
(29)
Th
e
r
efo
r
e,
w
i
t
h
E
b
e
i
n
g
t
he
e
n
e
rgy
i
n
it
ia
ll
y
s
t
ored
i
n
t
h
e
fl
y
w
hee
l
.
W
e
d
e
t
erm
i
n
e
t
h
e
to
ta
l
pow
er
s
t
o
r
e
d
in
the f
l
yw
he
e
l
us
i
n
g
:
fw
r
f
w
0
s
t
k
EE
P
d
t
(30)
Fi
n
a
lly
, t
h
e sp
eed
ref
e
r
e
n
c
e
ca
n
b
e d
e
d
u
ced
u
sin
g
th
e
e
x
p
r
ess
i
o
n
(11)
:
fw
r
fw
r
fw
2E
J
(31)
In
o
r
d
er
t
o
a
c
h
ieve
a
s
e
p
a
r
a
t
e
con
t
ro
l
the
r
o
ta
ti
ona
l
s
p
ee
d
and
t
he
f
l
u
x
c
o
m
p
o
n
e
n
t
o
f
t
he
I
M,
w
e
a
d
opte
d
a
fie
l
d
or
i
e
n
t
e
d
c
ontro
l
sc
hem
e
,
by
a
lig
ni
n
g
t
he
d
-ax
i
s
of
t
he
p
a
rk
r
eference
f
ra
m
e
w
ith
r
ot
or
f
l
ux,
s
uch
t
h
a
t
,
0
.
Ba
se
d o
n
th
e
IM m
odel
g
i
ve
n i
n
[20]
w
e
dete
rm
i
n
e
the s
t
at
m
od
e
l
o
f
th
e
I
M
a
s
foll
ow
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
111
0 –
1
1
22
1
118
rr
rs
q
sd
sq
sq
sq
sq
sd
sd
rs
1
fC
I
JJ
J
II
V
II
p
I
p
I
M
L
y
;
rd
sd
r
2
sq
s
q
sd
sd
rd
sq
rd
s
2r
MI
IV
II
p
I
M
L
y
(32)
Whe
r
e,
p r
epresen
t
s
the p
o
l
e
pairs
an
d:
22
2
rr
r
r
2
rs
r
r
s
r
sr
MR
L
R
R
Mp
M
M
1;
;
;
;
.
LL
L
L
L
L
LL
a)
C
u
r
ren
t
s
re
f
e
r
en
c
e
s
c
o
m
p
u
t
a
t
i
o
n
We
def
ine
(
e
,
e
) re
presen
ti
n
g
t
he
e
rr
ors var
i
a
b
le
s a
n
d
w
e
s
elec
t
th
e
lya
p
un
o
v
f
unc
t
i
o
n
s
uc
h t
h
at:
r
1
1r
2
2r
r
e
f
r
rr
e
f
r
ee
ee
;
2
11
2
22
1
Ve
2
1
Ve
2
(
33
)
Li
kew
i
se,
app
l
y
i
ng
t
he
s
a
m
e
princ
i
ple
us
ed
f
or
t
he
M
S
C
-G
S
C
c
ont
r
o
l,
t
he
V
CV
s
tha
t
g
ua
ran
t
e
e
the
asym
p
t
o
t
ic
s
ta
b
i
l
ity
o
f the
first c
o
nt
r
o
l
l
o
o
p
c
a
n
be
det
e
rm
ine
d
suc
h
t
ha
t:
-a
)
''
2
1
s1
1
''
2
2
s2
2
Vb
e
0
Vb
e
0
;
-
b)
"
rr
r
sq
r
1
1
r
"
sd
r
2
2
r
rr
e
f
fC
1J
Ik
e
JJ
1
Ik
e
M
(34)
b)
Rot
o
r
v
o
l
t
a
ge
s c
o
mp
u
t
at
i
o
n
A
g
ai
n,
the
V
CV
s
de
term
ine
d
previ
o
u
s
l
y
a
re
t
h
e
d
es
ire
d
inp
u
t
v
ar
i
a
bl
e
i
n
this
s
tep.
W
e
de
fi
ne
t
he
e
rrors
(
e
,
e
)
and
Lyap
un
ov fu
nc
ti
on
su
c
h
tha
t
:
rq
r
r
q
3
3r
q
r
r
q
rd
r
r
d
4
4r
d
r
r
d
eI
I
e
I
I
eI
I
e
I
I
;
22
31
3
22
42
4
1
Ve
e
2
1
Ve
e
2
(
3
5
)
The
co
ntro
l
la
w
t
ha
t i
n
s
u
r
e
s the
sta
bi
lit
y o
f
t
he ove
ra
ll sy
st
e
m
,
c
an
b
e de
t
e
rm
ined b
y
:
-a
)
"2
"
2
3
s1
1
s
3
3
"2
"
2
4
s2
2
s
4
4
Vb
e
b
e
0
Vb
e
b
e
0
;
-
b)
"
rq
r
sq
r
s
r
1
1
s
3
3
"
rd
r
sd
r
s
2
2
s
4
4
VL
I
e
b
e
J
VL
I
M
e
b
e
(34)
W
h
ere:
2
s
d
sq
sq
1
s
q
r
sd
2
s
d
r
sq
rr
II
I
I
p
pI
M
I
pI
M
4.
SIMU
L
A
TION
R
ESULT
S
S
i
mulat
i
o
n
st
u
d
ie
s
ar
e
per
f
orm
e
d
w
ith
t
he
s
ys
tem
cha
r
ac
t
e
ristic
s
pr
ese
n
te
d
i
n
T
ab
le
1
i
n
A
ppen
d
i
x.
A
l
l
s
i
m
u
l
a
t
i
o
n
a
r
e
r
u
n
w
i
t
h
t
h
e
s
a
m
e
w
i
n
d
p
r
o
f
i
l
e
t
h
a
t
v
a
r
i
e
s
a
ro
und
a
n
a
v
e
r
ag
e
sp
eed
o
f
8
.
9
m/
s
f
o
r
a
5
0
s
ec
dura
t
i
o
n,
a
s show
n
in
F
igure
6.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Ro
bu
s
t
c
o
or
d
i
n
a
te
d co
nt
ro
l usin
g
b
a
c
k
s
t
ep
p
i
n
g
o
f
f
l
y
w
he
e
l
e
n
er
gy sto
r
a
g
e
sy
st
e
m
… (Moham
e
d
Nad
o
u
r
)
1
119
Wh
en
u
sing
a
MPP
T
st
rat
e
gy,
t
h
e
a
cti
v
e
powe
r
d
e
l
iv
e
r
e
d
b
y
t
h
e
w
in
d tur
b
i
n
e
is cor
resp
on
d
i
ng
to t
he
cube
o
f
the
w
i
nd
spe
ed.
Mea
n
i
n
g
tha
t
a
s
m
a
ll
var
iat
i
o
n
i
n
t
he
w
ind
cau
se
s
a
sign
ifi
c
a
n
t
va
ri
a
t
i
o
n
in
t
h
e
o
utp
u
t
p
o
w
e
r
.
F
i
gu
re
7
s
ho
ws
t
h
e
D
FIG
st
a
t
o
r
a
c
t
iv
e
po
wer
a
n
d
a
nd
Fi
gu
r
e
8
s
h
o
w
s
i
t
s
r
e
a
c
t
i
v
e
p
o
w
e
r
c
u
r
v
e
s
re
sp
ec
ti
v
e
ly
.
I
n
t
h
i
s
wo
rk
,
t
h
e
l
a
tt
e
r
i
s
ma
i
n
t
a
in
ed
e
qu
al
t
o
z
e
r
o
i
n
o
r
d
e
r
k
e
e
p
a
u
n
i
t
ar
y
pow
e
r
f
ac
tor
at
P
C.
I
n
brief,
t
he
r
esu
l
t
s
d
e
m
o
n
stra
t
e
t
he
v
a
l
idne
s
s
o
f
t
h
e
MS
C
prop
ose
d
co
n
t
ro
l
sc
hem
e
,
bein
g
t
h
a
t
t
he
o
u
t
pu
t
s
enc
o
u
n
te
r
flaw
le
ss
ly
t
he
ir
r
efe
r
enc
e
s
a
n
d
a
l
l
t
r
acki
n
g
e
rrors
c
on
verge
to
zer
o
asym
pto
t
i
call
y
.
M
o
re
o
v
e
r
,
th
e
refere
nce
of
t
h
e
F
ES
S
pow
er
P
d
e
t
erm
i
ned
us
in
g
Eq.4
2,
w
hic
h
c
orre
spon
d
s
t
o
t
h
e
d
i
ffe
r
enc
e
b
et
ween
P
w
hich
i
s
the
ne
t
p
o
w
e
r
int
e
nde
d
to
b
e
de
live
r
e
d
t
o
th
e
g
r
id
a
n
d
P
t
h
e
t
ot
a
l
g
en
e
r
at
ed
p
o
w
er,
a
s
i
t
i
s
show
n
i
n
F
i
gur
e
9.
I
n
F
i
gure
10
a
n
d
F
i
g
u
re
11,
t
he
r
e
s
u
l
ts
s
how
t
he
e
ffec
ti
ve
ness
of
t
he
F
S
C
c
ontr
o
l
sc
he
me
,
gi
ve
n
t
h
a
t
t
he
F
ES
S
out
pu
t
p
o
w
e
r
P
a
nd
the
ins
t
a
n
t
a
neo
u
s
r
o
t
a
t
i
o
n
a
l
s
pee
d
p
r
ese
n
t
an
e
x
c
el
l
e
nt
t
ra
ck
i
n
g
respo
n
se.
The
st
or
age
de
vic
e
i
s
in
i
t
i
a
l
l
y
c
ha
rge
d
w
it
h
E
a
nd
ro
tate
a
t
an
i
ni
tia
l
spee
d
of
200
m/s,
i
t
ac
cele
r
ate
to
s
t
o
re
e
ne
rgy
w
h
en
t
he
o
u
t
pu
t
p
o
w
e
r
P
i
s
pos
iti
ve,
and
de
ce
l
e
rate
t
o
ge
nera
te
it
i
n
t
he
o
p
pos
ite
ca
se
.
F
i
gur
e
1
2
a
n
d
F
igur
e
1
3
p
in
po
in
ts
t
he
e
ffic
ie
nc
y
t
h
e
G
S
C
c
o
n
t
r
o
l
s
t
ra
t
e
g
y
.
F
i
gur
e
12
ill
us
trate
t
h
e
D
C
bus
r
eg
ula
t
ion,
w
hi
c
h
i
s
u
s
ed
t
o
m
a
i
n
ta
i
n
a
c
ons
ta
n
t
v
o
l
tage
,
a
nd
F
i
gure
13
sh
ow
s
t
h
a
t
t
h
e
r
e
active
p
o
w
e
r
Q
exc
h
a
n
ged
be
t
w
e
e
n
t
h
e
G
S
C
a
nd
the
e
l
ec
tri
cal
n
e
t
w
o
r
k
c
o
nver
g
e
s
t
o
i
t
s
r
e
f
e
r
e
n
c
e
t
h
a
t
i
s
l
i
k
e
w
i
s
e
c
h
o
s
e
n
t
o
be
zer
o.
Th
e
tot
a
l
a
c
t
i
ve
p
o
w
e
r
i
nj
ect
ed
t
o
th
e
po
we
r
sy
st
em
P
w
ith
a
nd
w
i
t
h
o
u
t
i
ncl
u
d
i
ng the
F
E
S
S
s
upp
ort
is
s
how
n
i
n
F
i
gure
1
4
.
A
s
e
xpe
cte
d
,
t
h
e
p
o
w
e
r
i
njec
t
e
d
w
i
t
h
out
t
h
e
s
u
pp
ort
o
f
t
he
s
t
o
rage
d
e
v
ice
is
h
i
ghl
y
fl
uc
tua
t
in
g d
u
e
to ra
n
d
o
m nat
u
re of the
w
i
n
d
. O
n the ot
her han
d
, the qua
li
ty of t
h
e ou
tp
u
t
p
ow
e
r
ge
n
era
t
e
d
by
the
ar
range
me
n
t
(
D
F
IG
p
lus
F
E
S
S
)
a
t
the
PC
C
i
s
c
ompa
rati
ve
ly
s
m
oo
t
h
e
r
,
and
P
r
e
m
ains
a
t
the
desi
gna
te
d
reference
P
w
h
i
c
h
c
ho
se
n
to
b
e
eq
u
a
l
to
775k
W
i
n
t
hi
s
c
a
se
o
f
stud
y
.
H
owe
v
er
,
a
low
pass
fil
t
er
c
a
n
b
e
use
d
to
de
term
ine
P
f
or
l
on
g-te
rm F
ES
S
opera
tio
n.
I
n
o
rde
r
e
val
u
ate
the
im
pro
v
em
ent
ach
ie
v
e
d
by
a
p
p
l
yi
n
g
t
he
p
ro
p
ose
d
c
on
tro
l
a
l
g
o
r
i
t
hm
s,
it
i
s
part
icu
l
ar
ly
i
m
por
tan
t
t
o
ana
l
yz
e
t
h
e
syste
m
p
er
form
anc
e
u
nder
par
a
m
e
tri
c
v
ar
i
a
t
i
on,
s
i
n
ce
u
sua
lly
m
achi
n
es
para
me
ters
a
re
e
xpose
d
t
o
m
a
ny
ina
c
c
u
r
acie
s
d
ue
t
o
th
e
a
dop
te
d
i
d
e
n
t
i
fi
c
a
t
io
n
m
e
t
h
o
d
o
lo
gy,
m
easur
ing
dev
i
ce
s
or
s
e
v
era
l
n
a
t
ur
al
p
h
e
nome
n
a.
T
her
e
fore,
t
o
d
e
m
o
n
s
t
rate
t
he
s
ys
t
e
m
abil
i
t
y
t
o
r
ea
ct
a
ga
in
st
t
h
i
s
kind
of
d
is
t
u
rba
n
ce
s,
w
e
com
p
ar
e
d
t
he
p
ro
p
o
se
d
bac
k
ste
p
p
i
ng
c
o
n
t
r
o
l
ap
proa
c
h
w
it
h
c
o
n
v
e
n
t
i
ona
l
P
I
c
ont
rol
l
ers
for
the
MS
C
and
t
h
e
FS
C
contr
o
l.
T
hi
s
tes
t
,
cons
i
s
t
o
f
m
od
i
f
y
i
n
g
t
h
e
DF
IG
’s
m
ode
l
para
me
ters
s
uc
h
that
(
R
1
.
5
R
;
L
1
.
2
L
;
L
1
.
2
L
)
and
the
F
E
SS-IM’s
m
odel
param
e
ters
i
n
a
way
that
(
R
1.5
R
; R
1
.
5
R
).
F
i
gur
e
15,
F
igure
1
6
a
nd
F
i
gur
e
1
7
s
h
o
w
re
spe
c
t
i
v
e
l
y
t
he
D
F
I
G
stator
a
c
t
i
v
e
P
s
a
nd
rea
c
ti
ve
pow
er
Q
s
a
n
d
t
he
F
ES
S
out
pu
t
p
o
w
e
r.
A
c
c
ordin
g
l
y
,
t
h
e
tes
t
c
on
firm
t
he
r
ob
us
t
n
ess
of
t
he
p
ro
pos
e
d
bac
k
ste
p
pi
n
g
c
on
t
r
o
l
s
tra
t
eg
y
com
p
are
d
t
o
P
I
c
ont
r
o
ller
s
.
Be
in
g
t
ha
t
t
h
e
la
tter
ha
ve
s
h
o
w
n
h
i
gh
se
ns
i
t
i
v
it
y
t
o
w
a
r
d
s
p
a
r
a
m
e
t
r
i
c
v
a
r
i
a
t
i
o
n
,
a
s
t
a
t
i
c
e
r
r
o
r
a
p
p
e
a
r
s
i
n
t
h
e
F
E
S
S
-IM
c
ontro
l,
not
ab
l
y
a
t
t
h
e
o
u
t
put
p
ow
er
,
w
h
er
eas
t
he
p
e
r
for
m
a
n
c
e
h
a
s
b
een
c
ompl
e
t
el
y
dete
ri
orat
ed
f
or
t
h
e
D
F
I
G
c
o
n
t
r
o
l
.
O
n
t
h
e
o
t
h
e
r
h
a
n
d
,
B
S
c
o
nt
roll
e
r
s
p
r
e
s
ent
an
e
xq
u
i
si
t
e
d
i
s
tu
rb
ance
r
ej
ec
t
i
on
a
n
d
a
l
l
t
h
e
o
u
t
p
ut
s
c
onv
e
r
ge
c
o
r
re
c
t
l
y
t
o
t
h
ei
r
des
i
g
n
a
t
ed
r
efe
r
enc
e
s.
F
i
gure
6
:
W
i
n
d
spee
d pro
f
ile
Fi
g
u
r
e 12
. Re
a
c
t
i
v
e po
wer at
t
h
e
o
utp
u
t
of
GSC
Evaluation Warning : The document was created with Spire.PDF for Python.