In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
Vol.
11, No.
1, Mar
ch 2020,
pp.
10~23
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
5
9
1
/ij
ped
s
.
v11
.
i
1.pp
1
0
-2
3
10
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
Performance enhancements of
D
F
IG
wind turbine using
fu
zzy-feedback li
nea
r
ization cont
r
o
ller augmented by hi
gh-
g
ai
n
observer
Kada
B
ou
reg
u
i
g
1
,
A
b
d
e
lla
h
M
ansouri
2
,
Ah
me
d
Ch
ou
ya
3
1
Oran
U
n
i
vers
ity
o
f
S
c
i
en
ce
and
Tech
nol
og
y
-
M
o
ham
e
d
Bou
d
ia
f
UST
O-
MB
,
A
l
g
e
r
i
a
2
Nat
i
o
n
al
P
o
l
y
t
ech
ni
c Un
iv
e
r
sit
y
O
ran,
Al
g
eria
3
Dep
a
rtm
e
nt of Elect
rical
En
g
ineer
ing,
D
jil
l
a
l
i
B
ou
naam
a Un
iv
ers
i
t
y
,
A
lg
e
r
ia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
A
pr 17,
2
0
1
9
Re
vise
d Ju
l 2
2
,
201
9
Ac
ce
p
t
ed
Au
g
1
2
,
2
019
Th
is
p
aper
p
ro
p
o
s
e
s
a
feed
back
l
in
e
a
ri
zati
o
n
co
ntro
l
o
f
d
o
ubly
fe
d
in
du
c
t
io
n
gen
e
rator
bas
e
d
win
d
e
nerg
y
s
y
stem
s
f
o
r
im
p
r
ovin
g
d
ecou
p
l
e
d
co
n
tr
o
l
o
f
t
h
e
acti
v
e
and
r
eactiv
e
po
wers
s
tato
r.
I
n
o
r
der
to
e
nh
an
ce
dyn
am
ic
pe
rform
a
nc
e
of
t
he
c
o
n
t
r
o
l
ler
s
t
u
d
ied
,
t
he
a
dop
ted
con
t
rol
i
s
r
ei
nf
orced
b
y
a
f
u
z
z
y
l
o
g
i
c
c
o
ntrol
l
e
r
.
Thi
s
a
p
p
ro
ac
h
is
d
e
s
ig
ne
d
with
ou
t
a
n
y
mo
de
l
of
r
o
t
o
r
fl
ux
est
i
mation.
T
he
d
iffi
culty
o
f
me
as
u
r
in
g
o
f
r
otor
f
lu
x
is
o
v
e
rco
m
e
b
y
us
ing
hi
gh
g
ai
n
ob
server.
The
s
t
abilit
y
of
t
he
n
on
l
i
ne
ar
o
bserver
i
s
pr
o
v
e
d
b
y
the
Ly
apu
nov
t
h
e
o
r
y.
N
um
erical
s
im
u
l
a
t
i
ons
u
sin
g
M
ATLA
B-S
I
M
U
LINK
sh
ow
n
cl
early
t
h
e
r
o
bus
tn
ess
of
t
h
e
p
ro
po
sed
con
t
rol
,
p
arti
cula
rl
y
t
o
t
h
e
d
i
s
t
u
r
ba
nc
e
re
je
c
t
io
n
a
n
d
p
a
ra
me
tric
v
a
r
ia
tio
ns
c
o
m
pa
re
d
with
t
he
conventional
method.
K
eyw
ord
s
:
DF
I
G
F
e
edbac
k
l
ine
a
riza
t
i
o
n
c
o
n
tr
ol
Fu
zz
y
l
ogi
c
H
i
g
h
gai
n
obse
r
ver
Lya
p
u
n
ov sta
b
il
ity
Th
is
is a
n
o
p
en
acces
s a
r
ticle u
n
d
e
r t
h
e
CC
BY-S
A
li
cens
e
.
Corres
pon
d
i
n
g
Au
th
or:
Ka
d
a
Bou
re
gu
ig
,
O
r
a
n
U
niversi
t
y
of
S
c
i
e
nce
an
d
Tech
no
l
o
g
y
-
M
oh
am
ed Bo
u
d
i
a
f
,
U
S
TO
-MB,
BP
1505 E
l
M
'N
aoue
r,
3
1
000
O
r
a
n
,
A
l
ge
ria.
Em
ail:
kada.
b
o
u
reg
u
i
g
@
u
niv-
usto.dz
1.
I
N
TR
OD
U
C
TI
O
N
The
wind
e
ner
gy
i
s
a
p
ollution
-free
and
ef
f
ect
ive
s
o
urce. There
fore
, a
win
d
p
o
w
er ge
n
er
atio
n s
y
st
em
bec
o
me
s
o
n
e
o
f
t
he
p
o
t
e
n
t
i
a
l
s
ourc
e
s
o
f
a
l
t
e
r
nat
i
ve
e
ner
g
y
for
the
fut
u
re
[
1].
Ene
r
gy
c
o
n
sum
p
ti
on
o
ve
r
th
e
l
a
st
c
en
tu
ry
h
as
i
n
c
re
as
ed
s
i
g
nif
i
c
a
nt
ly
due
t
o
th
e
g
r
ea
t
i
ndu
s
trial
i
za
tio
n.
R
e
cen
tl
y,
p
ar
t
i
c
u
l
a
r
i
n
t
e
re
st
h
as
b
e
en
g
i
v
en
t
o
g
e
n
e
rat
i
ng
e
l
ect
ri
ci
t
y
f
ro
m
ren
e
wab
l
e
en
erg
y
s
ou
r
ce
s.
O
f
al
l
re
newa
bl
e
source
s,
w
i
n
d
e
n
erg
y
ho
lds t
h
e
la
rge
s
t
m
a
r
k
e
t
s
har
e
a
n
d
i
s
ex
pec
t
e
d
t
o
ma
inta
i
n
r
api
d
g
r
o
w
t
h
i
n
t
h
e
co
mi
ng
y
e
a
rs
[
2
]
.
Win
d
e
ne
rg
y
syste
m
s
ha
ve
r
ece
ive
d
c
o
n
si
d
e
r
a
ble
a
t
t
e
n
tio
n
o
v
e
r
t
he
p
as
t
dec
a
de
a
s
one
o
f
t
h
e
mos
t
p
r
o
m
i
sing
r
ene
w
abl
e
ene
r
g
y
s
o
u
rc
es
due
t
o
ne
ga
tiv
e
e
n
v
i
r
onm
en
t
a
l i
n
fl
u
e
nce
s
a
nd the
h
i
gh
c
o
st o
f c
o
n
v
e
n
t
i
on
a
l
ene
r
gy
s
o
urc
e
s. In
th
i
s
c
onte
x
t,
s
ever
al
c
o
u
n
tri
e
s
have
t
urne
d
to
e
x
p
lor
e
t
he
w
in
d
e
ne
rg
y
s
ector,
lead
i
ng
r
e
se
arc
h
ers
to
c
on
d
u
ct
rese
arc
h
t
o
im
pro
v
e
t
h
e
e
f
fi
cienc
y
a
nd
p
o
w
er
o
f
e
l
ec
tro
m
ec
hani
c
a
l
c
o
nver
s
io
n
a
n
d
qua
lit
y
o
f
p
ro
vi
d
i
n
g
e
n
e
r
g
y
[
3
]
.
T
o
m
e
e
t
e
n
e
r
g
y
n
e
e
d
s
,
i
t
i
s
i
m
p
e
r
a
t
i
v
e
t
o
f
i
n
d
a
d
j
u
s
t
e
d
an
d
fle
x
ibl
e
s
ol
ut
i
ons
b
y
red
u
c
i
n
g
en
e
r
gy
con
s
um
pt
io
n
o
r
i
nc
rea
s
in
g
en
e
r
gy
pr
od
uc
tio
n
b
y
a
dd
i
ng
p
o
w
e
r
p
l
a
n
t
s
or
i
mpr
ovin
g
t
he
e
ff
i
c
ie
nc
y
o
f
e
x
i
s
tin
g
in
sta
l
lat
i
o
n
s
.
In
a
d
d
i
t
i
on,
t
he
d
y
n
a
m
ic
i
m
p
ro
vem
e
nt
o
f
the
perf
orma
nce
o
f
r
enew
a
b
le
e
n
e
r
gy
s
y
stem
s,
w
hos
e
no
n-l
i
ne
ar
c
hara
cteris
t
i
cs
a
re
p
art
i
cu
larl
y
impor
ta
n
t
,
espec
i
a
l
l
y
w
i
t
h
t
h
e
r
a
p
i
d
g
r
o
w
t
h
o
f
t
h
e
i
r
u
s
e
.
T
h
e
r
e
f
o
r
e
,
the
c
o
ntr
o
l
of
t
he
W
in
d
P
o
w
e
r
Con
v
er
sio
n
S
ystem
(WECS
)
b
a
s
e
d
o
n
d
o
u
b
l
y
fee
d
i
n
d
u
c
t
ion
ge
ne
rat
o
r
(DF
I
G)
w
ith
i
nt
e
r
m
itte
n
t
i
n
p
u
t
w
i
n
d
s
pee
d
i
s
pa
rtic
ula
r
i
ntere
s
t
i
n
t
he
e
nerg
y
an
d
c
o
nt
r
o
l
c
o
m
m
un
i
tie
s.
D
F
I
G
s
are
pote
n
tia
l
c
a
n
d
i
da
t
e
s
for
h
i
g
h
p
o
w
er
w
i
nd
s
y
s
t
e
m
s
be
ca
u
s
e
t
h
ey
c
an
g
en
e
r
a
t
e
re
ac
t
i
v
e
c
u
r
re
n
t
a
nd
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Perf
orm
anc
e enh
a
n
ce
m
e
n
t
s
o
f
D
F
IG
wind tu
rb
ine usi
ng fuz
z
y-fe
ed
back
lin
e
a
r
i
za
t
i
on …
(K
ad
a
Bo
ure
g
u
i
g)
11
pro
duce
c
o
n
s
t
a
nt
freq
u
enc
y
pow
e
r
f
or
v
ar
ia
bl
e
s
p
ee
d
o
p
e
ra
tion.
H
o
w
e
ver,
t
he
m
a
i
n
disa
dva
nt
a
g
e
of
t
he
D
F
I
G
i
s
it
s
bru
s
hes
an
d
sl
i
p
r
ings
s
truc
ture
,
w
h
i
c
h
i
n
v
o
l
ves
pe
rm
anent
ma
in
t
e
nanc
e
a
nd
r
e
duce
s
t
he
l
i
f
e
t
i
m
e
of
t
he
m
achi
n
e
[4].
T
h
i
s
ty
pe
o
f
ge
ne
rat
o
rs
h
as
b
ee
n
w
i
del
y
u
se
d
fo
r
wi
nd
s
y
s
t
e
ms
[
5
]
.
Th
e
co
nt
ro
l
and
opera
tio
n
o
f
t
hese
s
ys
t
e
ms
h
as
b
ee
n
t
h
e
sub
j
ec
t
of
m
a
ny
resea
r
c
h
proje
c
t
s
i
n
r
ec
ent
year
s
[6]
.
I
n
t
h
i
s
perspe
c
tive
,
v
a
r
io
us
s
t
u
d
i
es
h
ave
be
en
p
r
o
pose
d
i
n
[7-9]
t
o
c
o
n
t
r
ol
w
in
d
t
u
rb
in
e
sy
st
ems
b
a
se
d
DFIG
f
ro
m
the
clas
sica
l
c
o
nfi
gura
t
ion
s
b
y
a
p
plic
a
tio
n
of
F
i
e
ld
o
r
i
e
n
t
e
d
c
on
t
r
o
l
(
F
O
C)
s
t
r
ate
gy.
H
ow
e
v
er,
t
h
e
WT-D
F
I
G
is
h
ig
hly
n
onl
i
n
ea
r system
,
wi
t
h
s
tro
n
g
c
ou
p
lin
gs
b
e
t
w
een
t
he d
if
fe
re
n
t
v
ari
a
bl
es
o
f
t
h
e sy
st
ems.
I
n
t
h
i
s
c
o
n
t
e
x
t,
m
any
n
o
n
l
ine
a
r
c
o
n
t
r
o
l
m
e
tho
d
s
have
b
e
e
n
deve
l
op
ed.
P
e
ngha
n
Li
e
t
a
l
[
1
0
]
pro
poses
a
n
o
n
l
i
n
e
a
r
c
o
ntr
o
ller
base
d
o
n
s
t
a
t
e
f
ee
d
b
ac
k
li
near
i
z
a
t
i
on
stra
t
e
gy
t
o
r
e
d
uce
su
b-sy
nc
h
r
onous
c
o
nt
rol
in
t
e
racti
o
n
in
s
e
ri
e
s
-comp
e
n
s
a
t
e
d
doub
ly
f
e
d
i
ndu
c
t
io
n
g
e
n
e
r
at
or
(
D
F
I
G
)-ba
sed w
i
n
d
p
o
w
er
p
la
nts.
I
n
[1
1
]
t
h
e a
u
t
h
o
r
s have
use
d
a r
o
b
u
st n
onl
i
n
ea
r fee
dba
c
k
l
inea
r
i
zat
i
o
n
c
ontr
o
l
l
er
base
d
s
lid
in
g m
o
de
con
t
ro
l
to
r
el
ie
ve
s
ub-s
ync
hr
on
o
u
s
c
o
n
t
ro
l
in
tera
ct
i
on
i
n
d
o
u
b
l
y-fe
d
in
d
u
ct
i
o
n
ge
nera
tor
ba
se
d
w
i
n
d
far
m
s
con
n
ec
ted
to
s
eries-c
o
mpe
n
sa
ted
tran
sm
iss
i
o
n
l
i
n
e
s
.
The
t
w
o
a
f
o
remen
t
io
n
e
d
w
o
rk
s
sh
o
w
g
ood
perform
ance
s.
H
ow
e
v
e
r
,
t
h
e
aut
h
ors
d
i
d
no
t
use
a
n
o
n
l
i
nea
r
m
ode
l
a
n
d
D
F
IG
W
i
nd
T
u
r
b
ine
c
o
ntr
o
l
sc
hem
e
is
b
ase
d
on ve
c
t
or c
o
n
t
r
ol.
In add
i
tio
n,
the
s
t
a
t
e
s of
t
he
D
F
I
G
a
re supp
ose
d
to be
m
ea
sur
e
d.
D
jil
lal
i
e
t
a
l
[
1
2
]
ha
ve
u
se
d
N
e
ura
l
I
npu
t-O
u
t
p
ut
F
e
e
d
b
ac
k
Li
n
ea
ri
zat
ion
C
ont
rol
.
T
h
e
n
eu
ral
con
t
ro
l
l
er
i
s
ba
se
d
o
n
a
R
e
c
u
rr
en
t
H
i
g
h
O
rde
r
N
e
u
ral
N
e
tw
ork,
t
ra
ine
d
w
i
t
h
an
E
xte
nde
d
K
a
lma
n
F
il
ter
.
T
h
i
s
las
t
m
eth
od
us
es
a
s
im
pl
e
P
I
c
ontr
o
ller
t
o
d
ef
ine
t
h
e
co
n
t
rol
l
aw
d
efine
d
b
y
a
re
l
a
ti
on
sh
ip
lin
ki
n
g
t
h
e
n
ew
i
n
t
e
r
n
a
l
i
n
p
u
t
s
t
o
t
h
e
p
h
y
s
i
c
a
l
i
n
p
u
t
s
.
T
h
e
s
a
m
e
s
t
r
a
t
e
g
y
c
o
n
t
r
ol
h
as
b
ee
n
a
p
p
lie
d
i
n
[
13]
b
a
s
ed
on
the
line
a
r
qua
dra
tic
r
eg
u
l
ator
(
LQ
R).
D
u
e
t
o
t
he
l
i
m
ita
tio
ns
p
re
se
n
t
e
d
b
y
the
tw
o
lin
e
a
r
con
t
ro
llers
t
he
P
I
a
nd
the
L
Q
R
w
h
ic
h
ha
ve
a
l
ow
r
obus
t
n
ess
to
p
ar
am
eter
v
ar
i
a
t
i
o
n
s
as
w
ell
as
to
u
n
b
ala
n
c
e
d
grid
vol
ta
ge
w
h
i
c
h
h
a
v
e
di
r
e
c
t
effec
t
s
o
n
t
he
dyna
mic
pe
rfo
rm
anc
e
o
f
t
h
e
syste
m
,
a
n
d
p
o
ses
se
r
io
us
p
r
o
b
l
em
s,
s
uc
h
a
s
o
sc
i
l
l
a
tio
ns
o
f
t
h
e
st
a
t
or
pow
er
a
nd
t
he
g
e
n
er
at
or
t
orq
u
e,
w
hic
h
a
re
d
e
t
rim
e
nta
l
t
o
t
he
m
ec
han
i
ca
l
s
y
s
t
e
m
a
nd
t
h
e
e
l
e
c
t
rica
l
netw
ork
[1
4].
In
t
hi
s
p
a
p
e
r
t
h
e
Fe
ed
b
a
ck
lin
e
a
r
i
zat
ion
t
ech
ni
q
u
e
i
s
co
mb
in
ed
w
i
t
h
F
u
z
z
y
l
og
ic
t
o
form
F
uz
zy-
F
e
edbac
k
L
i
n
e
a
riza
tio
n
Co
ntr
o
l
l
er
a
ppl
ied
t
o
a
n
o
n
-l
i
n
e
a
r
m
odel
o
f
D
F
IG
t
o
impr
ov
e
the
pe
rfor
ma
nc
e
o
f
t
h
e
syste
m
s
uc
h
a
s
t
he
r
e
s
po
nse
t
i
m
e
,
r
obus
t
n
es
s
a
g
a
i
nst para
me
ter
v
aria
t
i
o
n
s
a
n
d
t
he
s
e
n
s
i
t
i
v
i
t
y
to
per
t
ur
b
a
tio
ns
(u
nb
a
l
an
ced
g
ri
d
vo
lt
ag
e
)
.
Th
i
s
n
e
w
m
e
t
hod
i
s
aug
m
en
t
e
d
b
y
Hig
h
G
ain
Ob
serv
er
(
HG
O)
m
ai
n
l
y
us
ed
t
o
est
i
ma
t
e
g
e
n
era
t
o
r
r
otor
f
lu
x,
b
a
s
ed
o
n
t
h
e
m
easure
m
ent
o
f
r
oto
r
c
u
rrents
,stator
v
o
lta
ge
s
a
nd
t
h
e
m
e
c
h
anica
l
spee
d.
T
he
e
ffec
t
i
v
e
n
e
s
s
o
f
t
he
p
rop
o
se
d
c
ontr
o
l
l
er
i
s
c
o
m
p
are
d
t
o
the
c
o
n
v
e
n
t
i
ona
l
F
e
edbac
k
l
i
n
e
a
r
i
za
t
i
o
n
con
t
ro
l b
y
s
im
ula
t
i
o
n
resu
lts
i
n
Mat
l
a
b
S
imul
i
nk.
2.
MODELING OF S
T
U
D
I
E
D
S
Y
S
T
EM
A
s
s
how
n
in
F
ig
ure
1
t
h
e
s
y
ste
m
i
s
c
o
m
pos
e
d
o
f
t
w
o
pa
rts;
t
he
f
irst
i
s
th
e
c
onve
rs
ion
o
f
t
he
k
ine
t
ic
ene
r
g
y
o
f
t
h
e
win
d
i
nto
m
e
c
h
an
ica
l
e
n
e
rgy
via
a
t
u
rb
ine
a
nd
the
s
ec
on
d
is
t
he
c
o
nver
s
io
n
of
t
he
m
ec
han
i
ca
l
ene
r
g
y
a
t
the
leve
l
of
t
he
t
u
r
bine
s
ha
f
t
i
n
t
o
elec
t
r
i
c
a
l
e
n
e
rgy
v
i
a
a
dou
b
l
e-f
eed
g
e
n
era
t
o
r
.
Th
e
st
ato
r
i
s
con
n
ec
ted
d
i
rec
tly
t
o
t
h
e
gr
i
d
a
nd
i
t
s
ro
tor
a
l
s
o
v
ia
a
s
t
a
t
i
c
con
v
er
t
e
r
wh
i
c
h
al
lows
d
e
l
i
v
e
r
i
n
g
the
nec
e
ssary
c
o
nt
rol
vo
lt
ag
es o
f
t
h
e
st
at
o
r
p
o
w
ers.
F
i
gure
1
. S
yst
e
m
under
st
u
d
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
10
– 23
12
2.1.
Turb
ine
mod
e
l
The
a
e
rod
yna
m
i
c
po
w
e
r
app
e
a
r
in
g at
t
he
ro
t
or
o
f t
h
e
t
u
rb
i
n
e is
th
e
n
wri
tt
en
[
15
].
P
ρC
λ,
β
SV
(1)
Where
:
ρ
i
s
t
h
e
a
i
r
dens
it
y an
d
S
the
s
w
e
pt surfa
ce
ar
e
a
of
t
he
t
ur
bi
ne (
π
R
V
i
s
t
h
e
w
i
nd
spe
e
d
(
m
/s),
C
λ
,
β
i
s
the
pow
er
c
o
e
fficie
nt
o
f
the
turbine
,
λ
i
s
the
tip
s
pee
d
r
a
t
io
a
nd
β
is the
p
i
tc
h
ang
l
e.
The
tip
s
pee
d
r
atio
i
s
:
λ
ω
(2)
wher
e:
R
i
s
th
e
ra
di
us
o
f
t
h
e
turbi
n
e
(
m
)
a
n
d
ω
i
s
the
speed
t
urbi
ne
(
rad/s).
F
igure
2
show
s
the
cur
v
e
of
t
h
e
pow
er
coe
ffic
i
e
nt
v
ers
u
s
λ
for a
c
onsta
nt
v
a
l
u
e
of the
p
itch
a
n
g
l
e
β.
F
i
gure
2.
Ty
pi
c
a
l c
u
rve
of p
o
w
e
r
c
oeffi
c
ien
t
.
2.2.
Dy
n
a
mi
que mo
d
el
o
f DFIG
The
m
a
them
at
i
c
a
l
m
ode
l
s
o
f t
h
re
e
DFIG phase
s
in t
he P
ar
k
fr
am
e
are writt
en a
s fol
l
ows [16]
:
⎩
⎪
⎪
⎨
⎪
⎪
⎧
v
R
i
φ
ω
φ
v
R
i
φ
ω
φ
v
R
i
φ
ω
ω
φ
v
R
i
φ
ω
ω
φ
(3)
⎩
⎪
⎨
⎪
⎧
φ
L
i
M
i
φ
L
i
M
i
φ
L
i
M
i
φ
L
i
M
i
(
4
)
Where
R
,
R
are
t
h
e
rotor
and
st
ator
r
e
s
i
s
ta
nc
e
s
,
r
e
spec
t
i
ve
ly
;
L
,
L
,
M
a
r
e
t
he
r
otor,
stat
or
a
nd
mutua
l
i
n
d
u
c
ta
nces,
re
spect
i
v
el
y
;
i
,
i
are
the
st
a
t
or
–r
ot
or
c
ur
rent
c
ompo
ne
nts;
v
,
v
a
r
e
t
h
e
com
p
o
n
e
n
t
s
o
f
the
stat
or–ro
t
or
vol
t
a
ge;
φ
,
φ
are
the
stat
or–ro
t
or
f
lux
c
o
mp
one
n
t
s
;
ω
,
ω
ar
e
th
e
rota
ti
n
g
and
s
t
a
t
or
p
ulsa
t
i
ons,
r
e
s
pe
cti
v
e
l
y.
The
mode
l
of
D
FIG
ac
cordi
n
g to t
he
r
ot
or c
ompo
ne
nts
i
s
r
epr
e
sen
ted
b
y
t
he fo
llow
i
n
g
e
qua
t
i
o
n
s [
15].
⎩
⎪
⎪
⎨
⎪
⎪
⎧
a
i
ω
i
a
φ
a
ωφ
a
v
a
v
ω
i
a
i
a
φ
a
ωφ
a
v
a
v
φ
R
i
ω
φ
ωφ
v
φ
R
i
ω
φ
ωφ
v
(5)
0
5
10
15
0
0.1
0.2
0.3
0.4
0.5
T
i
p s
p
e
e
d
ra
t
i
o
Po
w
e
r
co
e
f
f
i
ci
e
n
t
C
p
B=
0
°
B=
2
°
B=
4
°
B=
6
°
B=
8
°
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Perf
orm
anc
e enh
a
n
ce
m
e
n
t
s
o
f
D
F
IG
wind tu
rb
ine usi
ng fuz
z
y-fe
ed
back
lin
e
a
r
i
za
t
i
on …
(K
ad
a
Bo
ure
g
u
i
g)
13
wher
e
a
σ
σ
,
a
σ
,
a
σ
,
a
σ
σ
,σ
1
,
b
R
,
C
,
C
,
T
,
T
σ
i
s t
h
e di
sp
e
r
sio
n
c
o
e
f
fi
ci
en
t
Th
e el
ect
ro
me
c
h
ani
cal
dy
n
a
mi
c
e
q
u
a
t
i
on
i
s t
h
e
n
gi
v
en
by
ω
φ
i
φ
i
C
C
(6)
w
h
er
e
P
is
t
he
numbe
r
of
p
o
l
e
pa
irs;
J
i
s
th
e
iner
tia
o
f
t
h
e
sha
f
t
,
C
i
s
th
e
torq
ue
o
n
t
h
e
gene
rat
o
r
.A
l
l
fric
ti
on
s on
th
i
s
shaf
t
a
re
incl
ude
d
i
n
C
.
We
put
i
,i
,
φ
,
φ
,
ω
x
,x
,x
,x
,x
The sys
t
em
(6) is then
w
rit
t
en
i
n the
form
:
x
f
x
g
x
u
(7)
Where
f
x
⎩
⎪
⎪
⎨
⎪
⎪
⎧
f
x
a
v
f
x
a
v
f
x
v
f
x
v
f
x
(
8
)
u
v
v
;
g
x
a
0
10
0
0a
01
0
(9)
An
d
f
x
a
x
ω
x
a
x
a
x
x
a
v
,
f
x
ω
x
a
x
a
x
a
x
x
a
v
f
x
b
x
ω
x
x
x
,
f
x
b
x
ω
x
x
x
f
x
C
x
x
x
x
C
C
C
3.
FEEDBACK LINE
A
R
I
Z
A
TION
C
ONTROL
To
d
e
v
e
l
o
p
n
o
n
li
nea
r
c
on
tro
l
o
f
t
h
e
ac
ti
ve
a
nd
r
ea
ct
ive
p
o
w
ers
o
f
s
t
a
t
o
r
,
t
h
e
f
e
e
d
b
a
c
k
l
i
n
e
a
r
i
z
a
t
i
o
n
st
r
a
te
gy
is
p
r
o
pose
d
.
T
h
is
t
e
c
hn
ique
c
on
s
i
s
t
s
t
o
t
rans
for
m
nonl
i
n
ea
r
syst
em
s
into
line
a
r
one
s,
s
o
tha
t
l
i
n
e
a
r
con
t
ro
l
t
ech
n
i
q
u
es
c
a
n
b
e
a
p
p
lie
d.
T
h
i
s
tech
ni
q
u
e
is
p
oss
i
b
l
e
t
hro
u
g
h
c
ha
nge
o
f
varia
b
le
s
a
nd
b
y
c
h
o
o
s
in
g
a
su
i
t
a
b
le
c
o
n
tr
o
l
i
np
u
t
[
17].A
ccor
d
in
g
t
o
t
h
e
m
ode
l
of
t
h
e
D
F
I
G
devel
ope
d
a
b
o
v
e,
a
nd
r
eca
ll
in
g
t
h
at
t
he
refere
nce
i
s
c
h
o
se
n
s
o
tha
t it
s
com
p
o
n
en
t
(
d
)
c
o
inc
i
de
s
w
i
th
t
h
e
st
a
t
o
r
vol
ta
g
e
v
e
c
t
o
r,
t
hi
s
sy
st
e
m
h
as
a
s
i
npu
t
varia
b
l
e
s
t
h
e v
o
lta
ge
a
pp
lied to
t
he rot
or
v
v
a
nd
as outp
u
t var
i
ab
les t
h
e
a
c
t
i
v
e
and
r
eac
tive
pow
e
r
a
t
the
st
a
t
or
P
,Q
d
ef
in
ed
b
y:
P
v
i
v
i
Q
v
i
v
i
(
10)
Th
e
st
ato
r
p
owers’
c
o
n
t
r
o
l
l
aw
i
s
c
o
mput
ed
a
cco
rdi
ng
t
o
t
h
e
r
ot
or
c
ur
rent
m
ea
su
r
e
m
e
nt
a
n
d
est
i
ma
t
e
d
rot
o
r
flu
x
.
The
l
a
t
t
e
r
c
om
es
f
r
o
m
the
pr
o
p
ose
d
h
i
gh
g
a
i
n
o
b
serv
e
r
.
S
ubsti
tu
tin
g
i
a
nd
i
i
n
(10)
b
y
th
ei
r c
o
un
t
e
rp
art
s
e
x
t
ract
ed
f
ro
m t
h
e
t
w
o
l
a
st
e
qu
at
io
ns o
f
(4)
, one has:
P
v
φ
v
φ
Q
v
φ
v
φ
(11)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
10
– 23
14
A
r
rangin
g
(
11)
P
φ
v
v
φ
v
v
Q
φ
v
v
φ
v
v
(12)
D
i
ffere
n
tia
t
i
n
g
(
12) unt
il
a
n
inp
u
t
a
ppear
s
P
v
v
v
v
Q
v
v
v
v
(13)
Wri
t
e
the
la
st e
qua
tio
n a
s
fo
l
l
o
w
s
P
v
v
v
v
v
v
Q
v
v
v
v
v
v
(14)
It
i
s d
e
si
re
d
to
re
g
ul
a
t
e
th
e out
put
q
u
a
nt
it
i
e
s
P
and
Q
to t
heir
r
espec
t
ive
re
fer
e
nce
va
l
u
e
P
and
Q
F
o
r this p
urp
o
s
e
d
efin
in
g t
h
e
adj
u
s
t
m
e
n
t
e
rror
s
e
P
P
e
Q
Q
(15)
D
e
fi
ni
ng
the i
n
pu
t o
f
t
he D
F
I
G
syste
m
u
u
u
v
v
(16)
Rew
r
i
t
i
ng (
1
4
)
in the
ma
tri
x
for
m
P
Q
v
v
v
v
v
v
v
v
u
u
(17)
Rew
r
i
t
i
ng t
h
e
new
i
n
pu
ts
V
an
d
V
in
t
he f
orm
(1
8)
P
V
Q
V
(18)
F
r
om (19)
w
e ca
n w
r
i
t
e
P
Q
0
0
V
V
(19)
F
r
om (17)
and
(18)
t
he
c
o
n
tr
o
l
l
a
w
is gi
ve
n
as
v
v
E
x
Ax
V
V
(20)
wh
ere
A
x
v
v
v
v
a
nd
E
x
v
v
v
v
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Perf
orm
anc
e enh
a
n
ce
m
e
n
t
s
o
f
D
F
IG
wind tu
rb
ine usi
ng fuz
z
y-fe
ed
back
lin
e
a
r
i
za
t
i
on …
(K
ad
a
Bo
ure
g
u
i
g)
15
The
re
fer
e
nce
ac
tive
pow
er
P
s
i
s
g
e
n
era
t
e
d
by
MP
P
T
a
nd
the
r
eac
t
i
ve
p
o
w
er
Q
s
is
d
ef
ine
d
by
th
e
gri
d
t
o
sup
por
t
the
ne
tw
or
k
vo
l
t
a
g
e
.
T
o
fo
llow
t
h
e
tra
j
ec
t
o
r
y
o
f
∗
a
nd
Q
∗
,
w
e
use
a
PI
c
ontr
o
l
l
e
r
impo
sed
t
o
t
he li
n
ea
rize
d
syst
em
[
17].
The
new
i
n
p
u
t v
i
s
g
i
v
e
n
by
V
V
P
∗
k
e
k
e
dt
Q
∗
k
e
k
e
dt
(21)
4.
HI
GH GAIN OBSERVER FOR FLU
X
E
S
T
IMA
T
ION
We
i
nte
n
d
to
c
ons
truc
t
s
u
c
h
a
n
o
b
se
rver
,
bas
e
d
o
n
t
he
m
e
a
s
u
rem
e
nt
o
f
the
rotor
c
u
rr
ents,
speed
a
n
d
vo
lta
ge
s [15]
the
p
ri
nci
p
l
e
is show
n in
F
i
gur
e
3.
F
i
gure
3.
R
o
t
or
f
lu
x o
b
serva
t
i
on
stra
teg
y
.
The
est
i
ma
t
e
d
fl
u
x
c
om
p
o
ne
n
t
s
φ
,
φ
a
re
u
se
d
i
n
t
he
c
om
pu
ta
ti
o
n
o
f
t
h
e
F
B
L
la
w
.
We
p
ropos
e
to imp
le
me
nt
a
r
ot
or
fl
ux
obse
r
ver
in orde
r
to
stu
dy i
t
s pro
p
e
r
ti
e
s
.
F
r
om the
m
ode
l
(7)
and a
ssumin
g
t
he
c
on
sta
n
t vel
o
c
i
ty (
Ω
= 0)
,
w
i
t
h
Ω
ω
we
ca
n
write
:
X
A
Ω
XB
v
(22)
wh
ere
X
i
i
φ
φ
(23)
A
Ω
,
B
a
nd
v
a
r
e
g
i
v
en
b
y
v
v
v
v
v
(
24)
A
Ω
a
ω
a
pa
Ω
ω
R
0
a
0
R
pa
Ω
0
ω
p
Ω
a
ω
p
Ω
0
;
B
a
0
a
0
0
0
0
a
0
0
0
1
0
a
0
1
(25)
Th
us,
at
c
onsta
nt
Ω
,
the
mode
l
is
line
a
r,
w
hi
ch
i
s
a
pa
rticu
l
ar
case
of
t
he
f
or
m
of
i
njec
tio
n
of
t
he
ou
tpu
t
a
n
d
of t
h
e ou
t
p
u
t
de
r
iv
a
tive
.
I
n
t
his
pa
rt,
w
e
a
r
e
i
n
t
e
r
este
d
i
n
t
he
w
ork
pre
s
e
n
t
e
d
in
[
18,
1
9
]
w
h
i
c
h
d
e
a
l
w
i
t
h
t
h
e
s
y
n
t
h
e
s
i
s
o
f
obs
erve
rs w
ith
h
i
g
h gai
n
f
or loc
al
ly
o
b
s
erva
ble
s
y
st
e
m
s.
The
n
it is p
oss
i
ble
t
o
m
ake
ou
t
the f
o
l
l
ow
i
n
g c
h
an
ge
o
f va
ri
abl
es:
z
Φ
x
h
L
h
(26)
z
I
z
a
ω
I
a
a
p
Ω
φ
(27)
F
o
r the
s
e
c
h
an
ges,
m
od
e
l
(7)
take
s
t
he f
oll
o
w
i
n
g
for
m:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
10
– 23
16
⎩
⎨
⎧
z
z
a
v
a
v
z
a
ω
z
a
v
a
v
a
a
p
Ω
R
z
ω
p
Ω
a
a
p
Ω
z
a
ω
z
v
(28)
We
put
z
z
z
z
i
i
z
φ
φ
0
00
w
ith
10
01
;
01
1
0
;
ψ
v
,v
,
Ω
,z
ψ
v
,v
,
Ω
,z
ψ
φ
v
,v
,
Ω
,z
,z
(29)
ψ
v
,v
,Ω
,z
a
v
a
v
ψ
v
,v
,Ω
,
z
,z
z
(30)
Th
a
t
t
ra
n
s
fo
rms t
h
e no
nli
n
ea
r sy
st
em (2
8
)
i
n
t
o
a l
o
c
a
l
sy
s
t
em o
f pyra
m
ida
l
c
oor
di
na
tes
z
z
ψ
v
,v
,z
y
C
z
(31)
Wit
h
t
he
o
u
t
pu
t
vect
or
C
,
0
The
n
the
f
ol
lo
w
i
n
g
sys
tem
z
z
ψ
z
,
z
S
θ
C
Cz
y
(32)
I
s
e
xpo
nen
t
ia
l obs
e
r
ver
of
t
he
syst
e
m
w
ith
S
θ
i
s
t
h
e
ma
t
r
i
x
d
ef
in
ed
b
y
S
θ
S
θ
θ
θ
θ
2
θ
(
33)
With
θ
0
Is
t
h
e
un
iq
ue
s
o
l
ut
ion
o
f
the
fol
l
o
w
i
ng
L
yap
u
n
o
v
a
l
g
e
b
raic
e
q
u
at
io
n:
θ
S
θ
S
θ
S
θ
C
C
(34)
4.1.
Th
e
orem
The
fu
nc
t
i
o
n
ψ
is gl
oba
l
l
y L
i
pc
hi
t
z
ian w
i
t
h
r
e
s
pec
t
t
o
z
un
ifo
r
mly
wi
th
r
espect to
v
and
v
‖
ψ
z
,
v
,v
ψ
z,
v
,v
‖
‖
z
z
‖
(35)
4.2.
Pr
o
of
of
stab
il
ity an
ay
l
s
is an
d
ob
s
erve
r
co
nv
erg
e
nce
C
ons
ide
r
the
er
r
or
ez
z
(36)
I
t
s
dy
nam
i
c
s
is
give
n b
y
e
S
θ
C
C
e
ψ
z
,
v
,v
ψ
z,
v
,v
(37)
Le
t’s cons
i
d
er
the f
o
l
l
o
w
i
n
g
Lya
pun
ov
func
ti
o
n
ca
n
d
i
da
te
V
e
e
S
θ
e
(38)
I
t
s
deriva
t
i
ve
i
s
V
e
e
S
θ
ee
S
θ
e
(39)
e
S
θ
C
C
ψ
z
,
v
,v
ψ
z,
v
,v
S
θ
e
e
S
θ
S
θ
C
C
e
ψ
z
,
v
,v
ψ
z,
v
,v
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Perf
orm
anc
e enh
a
n
ce
m
e
n
t
s
o
f
D
F
IG
wind tu
rb
ine usi
ng fuz
z
y-fe
ed
back
lin
e
a
r
i
za
t
i
on …
(K
ad
a
Bo
ure
g
u
i
g)
17
e
S
θ
2
C
C
S
θ
2
e
S
θ
ψ
z
,
v
,v
ψ
z,
v
,v
V
e
e
θ
S
θ
C
C
e
2
e
S
θ
ψ
z
,
v
,v
ψ
z,
v
,v
(40)
Usi
n
g
in
e
q
u
a
l
ity
C
C0
a
nd the
o
re
m
(1)
we
can
i
nc
re
ase
V
e
as
follo
w
i
n
g
:
V
e
e
θ
S
θ
e2
e
S
θ
e
θ
2
Ve
(41)
Th
is gua
ra
ntee
s the
ex
po
ne
nt
ia
l sta
b
i
lit
y o
f
t
he ob
s
e
r
ver
for θ
2
t
h
i
s c
o
ncl
u
de
s the
pro
o
f.
4.3.
Ob
s
er
ver
in
t
h
e
in
i
tial c
oord
i
n
a
tes
The
o
b
ser
v
a
tio
n
x
o
f
t
h
e st
at
e
x
for
t
he m
ode
l (
7
) is ob
t
a
i
ne
d
by
:
x
Φ
z
(42)
Tha
t
z
Φ
x
i
m
p
l
y
Φ
I
s
a
m
e
t
hod
o
f
syn
t
hes
i
zi
n
g
th
e
observe
r e
xpr
essed
i
n
x
x
f
x
g
x,
v
Φ
S
θ
C
Cx
y
(
43)
O
r
in t
h
e
pan
o
ra
mic
for
m
:
⎣
⎢
⎢
⎢
⎡
ı
̂
ı
̂
φ
φ
⎦
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎡
a
ı
̂
ω
ı
̂
a
φ
a
p
Ωφ
ω
ı
̂
a
ı
̂
a
p
Ωφ
a
φ
R
ı
̂
ω
p
Ω
φ
R
ı
̂
ω
p
Ω
φ
⎦
⎥
⎥
⎥
⎤
a
0
a
0
0
0
0
a
0
0
0
1
0
a
0
1
v
v
v
v
1
0
0
1
0
0
0
0
a
ω
ω
a
a
a
p
Ω
a
p
Ω
a
2
θ
0
02
θ
θ
0
0
θ
ı
̂
i
ı
̂
i
(44)
The
D
F
I
G
c
ontro
l
sche
me
u
sin
g
c
on
ve
n
tio
n
a
l
fe
e
dbac
k
l
in
e
a
riza
ti
on
(
CF
B
L
)
asso
ci
at
ed
w
i
t
h
HGO
is
s
h
o
w
n
i
n F
i
gur
e4.
F
i
gure.
4.D
F
IG c
ontr
o
l schem
e
u
sing
co
n
v
en
ti
o
n
al fee
d
b
ac
k
linea
r
i
z
at
i
on c
o
n
t
ro
l (
C
F
B
L)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
10
– 23
18
5.
FUZ
Z
Y-FE
EDB
A
CK
L
INEARI
Z
A
T
I
ON CONTROL
F
u
zz
y
l
o
gi
c
c
o
nt
r
o
l
has
bee
n
w
ide
l
y
use
d
i
n
r
ece
nt
y
e
a
r
s
du
e
to
i
t
s
s
im
p
lic
i
t
y of
i
m
p
lem
e
nta
t
i
o
n
a
n
d
i
t
s
a
bil
i
t
y
t
o
c
o
n
t
r
ol
nonl
in
ea
r
sy
st
e
m
s,
w
h
i
c
h
g
iv
e
s
b
e
t
t
e
r
p
e
rform
ance
under
param
e
ter
va
riat
i
ons
a
n
d
vo
lta
ge d
is
t
u
rb
ance
s [2
0]
.
Base
d
o
n
t
he
s
t
u
d
y
o
f
fuz
z
y
log
i
c
c
o
n
t
ro
l
de
scr
i
be
d
i
n
[
21]
,
[6
]
w
e
w
ill
pr
o
c
ee
d
t
o
i
t
s
a
p
p
l
i
ca
t
i
o
n
t
o
D
F
I
G
b
a
s
e
d
o
n
t
h
e
e
q
u
a
t
i
o
n
(
1
9
)
o
r
w
e
c
o
n
s
i
d
e
r
o
u
r
s
y
s
t
e
m
a
s
a
sim
p
le
i
n
t
e
g
ra
tor
w
h
ic
h
fac
i
l
ita
t
e
s
t
h
e
sy
nt
h
e
si
s
of
t
his
co
nt
rol
wh
ere
we
w
i
l
l
h
a
v
e
t
w
o
re
gu
l
a
to
rs
o
n
e
a
c
h
o
f
t
h
e
loo
p
s,
t
ha
t
of
t
he
a
ct
i
v
e
pow
er
a
nd
tha
t
o
f
the r
eac
tive
p
o
w
e
r
. F
igure
5 show
s t
h
e
princ
i
p
l
e o
f
t
he
pr
o
pos
e
d
m
ethod.
F
i
gure
5.
D
FIG
contro
l sc
he
m
e
usin
g
pr
opose
d
fuz
z
y
-fee
dba
c
k
l
in
ea
ri
zat
ion
c
o
nt
rol
(P
FB
L)
The
tw
o
m
o
st
s
i
gnif
i
c
a
n
t
q
u
a
n
t
i
t
ie
s
t
o
a
na
ly
z
e
t
he
b
eha
v
i
o
r
of
the
sys
t
e
m
n
am
ely
t
h
e
power
e
r
r
or
e
,
and
its va
r
ia
t
i
o
n
de
,
a
re
c
h
o
s
en
as t
w
o
i
npu
t
s
o
f t
h
e
re
g
u
l
a
to
r by
Fu
z
z
y
l
ogi
c
c
o
nt
r
oll
e
r FLC.
e
P
P
e
Q
Q
(45)
C
ons
ide
r
f
or
e
a
c
h
va
r
i
a
b
le
o
f
m
e
a
s
urem
ent
(the
e
rr
or
a
n
d
t
he
v
a
riation
of
t
he
e
rr
or)
3
m
e
m
b
er
s
h
ip
fu
nc
ti
o
n
s no
te
d {
N
, EZ, P
}
w
ith:
N
e
ga
t
i
ve
,
A
bou
t Ze
ro, P
osi
tive
presented in F
i
gure
6
.
F
i
gure
6.
Mem
bersh
i
p f
u
nct
i
o
n
s
The
rule
base
s
o
f p
o
w
e
r
contr
o
l
l
e
r’s a
re illus
t
rate
d
by t
h
e
fo
l
low
i
n
g
T
ab
le 1:
Table
1.
B
as
is
o
f
fuzzy
control rules
U
e
N
E
Z
P
de
N
N
N
E
Z
EZ
N
E
Z
P
P
EZ
P
P
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Perf
orm
anc
e enh
a
n
ce
m
e
n
t
s
o
f
D
F
IG
wind tu
rb
ine usi
ng fuz
z
y-fe
ed
back
lin
e
a
r
i
za
t
i
on …
(K
ad
a
Bo
ure
g
u
i
g)
19
F
o
r
the
de
fuzz
ifica
t
i
o
n
of
t
he
o
ut
p
u
t
var
i
a
b
le
s
o
f
t
he
s
yste
m,
we
u
se
t
he
m
eth
o
d
o
f
t
h
e
c
e
n
t
er
o
f
grav
it
y (
C
O
G
)
[2
2
]
.
u
∑
.
∑
(46)
The
pro
p
o
s
ed
c
on
tro
l
is re
prese
n
t
e
d i
n
F
igur
e 7.
F
i
gur
e 7.
F
uzzy-
f
ee
d
b
ac
k
lin
e
a
riza
tio
n
co
nt
rol
com
b
ine
d
w
it
h hi
g
h
ga
i
n
obse
r
ver
6.
SIMU
L
A
TIONS A
N
D
RESUL
T
S
I
n
w
ha
t
fo
l
l
ow
s
w
e
w
il
l
st
ud
y
t
h
e
per
f
orm
a
nce
s
(
Re
fe
renc
e
trac
k
ing,
d
istur
b
a
n
ce
s
e
n
sit
i
v
it
y
a
n
d
ro
bu
stn
e
ss)
f
o
r
d
i
ffe
rent
c
o
n
t
r
o
l
l
e
rs
m
en
t
i
on
e
d
a
bov
e
co
nv
en
ti
o
na
l
fe
ed
bac
k
l
i
n
ea
riza
tio
n
c
o
ntr
o
l
(C
F
B
L)
and
pr
op
ose
d
F
uzzy-
F
ee
dbac
k
L
i
n
ear
i
z
a
t
i
o
n
contr
o
l (
P
F
B
L)
u
si
n
g
t
h
e rotor
f
l
ux obser
v
er.
6.1.
Reference
trac
k
i
ng
Th
is
t
e
s
t
co
ns
i
s
t
s
i
n
m
a
k
i
n
g
a
c
ha
nge
i
n
t
h
e
ac
t
i
ve
a
n
d
r
e
a
c
t
i
v
e
po
we
r
se
tp
v
a
l
u
e
s
w
h
i
l
e
m
a
i
n
t
aini
ng
the
dri
v
e
s
p
ee
d
o
f
t
he
g
ene
r
ator
c
o
n
sta
n
t.
F
igure
8
i
l
l
u
st
ra
t
e
s
t
he
b
e
h
a
v
i
o
r
o
f
act
i
v
e
and
r
eac
tive
p
o
w
e
rs
s
t
a
t
o
r
.
B
y
e
x
a
m
i
n
i
n
g
t
h
i
s
f
i
g
u
r
e
,
i
t
c
a
n
b
e
s
e
e
n
a
g
o
o
d
r
e
f
e
r
e
n
c
e
t
rac
k
ing
w
i
t
h
a
l
e
ss
r
i
pp
les
for
t
h
e
p
r
op
ose
d
me
tho
d
c
om
pa
re
d
w
i
t
h
the
c
o
nve
n
t
i
o
nal
me
tho
d
.
The
dec
o
upl
in
g be
t
w
ee
n t
h
e
tw
o pow
ers i
s
i
dea
l
l
y
n
ote
d
for
the
pro
p
o
s
ed
m
etho
d
c
o
n
t
r
a
ry
t
o
t
h
e
c
o
n
v
e
n
t
i
ona
l
me
tho
d
w
e
not
i
ce
t
he
a
ppear
a
n
ce
o
f
a
stat
i
c
e
rr
or
a
t
ti
m
e
s
of
s
t
e
p
c
h
a
n
ge
(
see
F
i
gure
9).
In
F
ig
ure
1
0
,
t
h
e
ob
serve
r
's
p
er
form
anc
e
i
s
i
l
l
u
s
t
rate
d
w
h
e
n
t
he
e
s
t
i
m
at
ed
r
ot
or
fl
u
x
es a
nd re
al flu
xe
s ar
e subs
tan
t
ia
lly
i
d
e
n
t
i
c
al for
the
d
q a
xi
s.
F
i
gure
8.
R
e
s
pons
e
s
o
f
act
i
v
e
a
nd re
ac
t
i
ve
p
ow
er
s
0.
6
0.8
1
1.2
1.4
1.6
-2
-1
0
1
2
x 10
6
Ti
m
e
(
s
)
Qs
(
V
a
r
)
PF
B
L
CF
B
L
Qs
-
r
e
f
0.6
0.8
1
1.
2
1.4
1.6
-2
-1
0
1
2
x 10
6
Ti
m
e
(
s)
P
s
(
wa
tt)
PF
BL
CF
B
L
Ps
-
r
e
f
Evaluation Warning : The document was created with Spire.PDF for Python.