Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
6,
N
o
.
4
,
D
ecem
b
er 20
1
5
, pp
. 78
1~
78
7
I
S
SN
: 208
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9
4
7
81
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Unknown Input Observer fo
r a Doubly Fed Induction
Generator Subject to
Disturbances
Samir Abdelmalek*
,
**, Li
nda Bar
a
z
a
ne
*,
Ab
delkader
Lar
a
bi*
*Industrial and
Electrical S
y
stems Labor
ator
y
,
Faculty
of Electr
onics
and
Co
mputer, University
of Scien
ces
and
Techno
log
y
Hou
a
riBoumedien
e
,
B. P. 32 El -
Alia, 16111
, B
a
b -
Ezzou
a
r. Algiers, Alger
i
a
**Unité d
e
Dév
e
loppement d
e
s E
quipements Solaires (UDES) EP
ST
CDER, 4241
5, Tipaza, Algér
i
e
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 22, 2015
Rev
i
sed
O
c
t 11
, 20
15
Accepted Oct 26, 2015
This paper deals with the prob
lem design of an unknown inp
u
t observer
(UIO) for a Dou
b
ly
Fed Inductio
n Genera
tor (DFIG) subject to disturbances
.
These disturban
ces can be
con
s
ider
ed as unknown inputs (UI
)
. The state
s
p
ace m
odel of t
h
e DF
IG is
obtained from
the vol
tage equ
a
t
i
ons
of the s
t
ator
and rotor.
Then
, this latter
is us
ed for the design of an unknown input
observer (UIO) in order to
estim
ate bo
th th
e state and
the unkno
wn inputs of
the DF
IG. F
u
rtherm
ore, th
e UI
O gains
are
co
m
puted b
y
s
o
lv
ing a s
e
t
of
line
a
r m
a
trix
ine
qualit
ies (
L
MIs). Sim
u
lations r
e
sults are g
i
ven
t
o
show the
performance and
the eff
ectiven
ess of the proposed method.
Keyword:
D
oub
ly f
e
d
indu
ctio
n g
e
n
e
r
a
to
r
Lin
ear m
a
trix
in
equ
a
lities
State space m
odel
U
nkn
own
input o
b
serv
er
Vol
t
a
ge
eq
uat
i
ons
Copyright ©201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Samir Abdelmalek,
Industrial and
Electrical Sy
ste
m
s Laboratory, Faculty of E
l
ectronics
and Com
puter, Uni
v
ersity
of Sciences
an
d Tech
no
logy H
o
u
a
r
i
Bo
u
m
ed
ien
e
, B.
P.
32
El
-
A
lia, 161
11
, Bab -
Ezzo
u
a
r
.
A
l
g
i
er
s,
A
l
g
e
r
i
a
Uni
t
é
de
Dével
o
p
p
em
ent
des
Eq
ui
pem
e
nt
s Sol
a
i
r
es
(U
DES
)
EP
ST C
D
ER
,
4
2
4
1
5
,
Ti
paza
, Al
géri
e
Em
a
il: sa
mir_
au
t@yahoo
.fr
1.
INTRODUCTION
In
d
u
ct
i
o
n
ge
ne
rat
o
r
s
are
o
n
e
of
t
h
e
m
o
st
pop
ul
ar
electric m
achines use
d
in wi
nd turbines.
Wi
nd
turbines base
d
on the
doubly
fed inducti
on
gene
rator (D
FIG) ha
s receive
d increasi
ng at
tention in the recent
y
ears,
d
u
e t
o
i
t
s
rem
a
rkabl
e
a
dva
nt
age
s
ove
r
ot
her
wi
nd
turb
in
e system
s [1
],
th
e in
crease of
po
wer cap
t
ure
[2], their ca
pa
city to operate
at di
ffere
nt ra
nge
of the
wind spee
d, th
e a
b
ility to control active and
reactive
po
we
rs
[3]
.
Ho
weve
r,
D
F
I
G
-
b
ase
d
win
d
tu
r
b
ines
can
be
s
u
bject t
o
disturba
nces
which can ha
ve as
s
o
urce:
m
easurem
ent
noi
ses
,
se
nso
r
s
and act
uat
o
rs
faul
t
s
, es
peci
al
l
y
t
o
vol
t
a
ge
d
i
ps [
4
]
.
The
s
e
di
st
ur
ba
nces, c
a
n be
co
nsid
er
ed
as
u
nkn
own
inputs, h
a
v
e
adv
e
rse eff
ects on
t
h
e
n
o
r
m
al b
e
hav
i
or
o
f
t
h
e
r
e
al syste
m
an
d th
eir
esti
m
a
tes can
b
e
u
s
ed
to
co
nceiv
e
syste
m
s
o
f
d
i
agn
o
s
tic an
d
co
n
t
r
o
l [5
]. Ro
bu
st ob
serv
er
s ar
e pr
oposed
to
estim
a
te sim
u
ltaneously states
and actuat
o
r faults for
v
a
r
i
ous class
o
f
lin
ear
an
d non
lin
ear syste
m
s [
6
]-[
10
].
Recently, diagnosis a
n
d esti
mation faults a
r
e bec
o
m
i
ng very im
porta
nt to e
n
sure a
good s
upe
rvisi
on
of t
h
e sy
st
em
s and g
u
ara
n
t
e
e
t
h
e safet
y
of hum
an ope
rat
o
rs an
d equi
pm
ent
’
s, e
v
en i
f
s
y
st
em
s are becom
i
ng
m
o
re an
d m
o
re co
m
p
lex
.
In th
is resp
ect,
a larg
e nu
m
b
er
o
f
d
i
agno
stic m
e
th
o
d
s for
sen
s
o
r
s of i
n
du
ction
mach
in
es
h
a
v
e
pr
opo
sed in
[11
]
-
[
13
].
Faul
t
di
a
g
n
o
si
s an
d St
at
e est
i
m
a
ti
on
of
i
n
d
u
ct
i
o
n
m
achines has
attracted c
o
ns
id
erab
le in
terest, as
t
h
ey
are
oft
e
n
use
d
i
n
p
r
act
i
cal
cont
rol
sy
st
e
m
s [14]
. F
D
I i
n
se
ns
or
fa
ul
t
s
of i
n
d
u
ct
i
o
n m
achi
n
es
i
s
nece
ssary
si
nce co
nt
r
o
l
s
y
st
em
s rel
y
on t
h
e i
n
f
o
rm
at
i
on p
r
ovi
ded
by
m
easured
si
g
n
a
l
s
. In
[
15]
, t
h
e aut
h
ors
ha
ve
st
udi
e
d
t
h
e FD
I p
r
obl
e
m
of i
n
d
u
ct
i
o
n
m
achi
n
es. Si
n
ce DFI
G
ca
n
be su
b
j
ect
t
o
d
i
ffere
nt
ki
nds
of
faul
t
s
as st
u
d
i
e
d i
n
[1
6]
.
A
u
t
h
ors
i
n
[
1
7]
-[
19]
,
f
o
cus
o
n
c
u
r
r
ent
sens
or
fa
ul
t
det
ect
i
on a
n
d
i
s
ol
at
i
on
(F
DI
) a
n
d c
ont
rol
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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IJPE
DS Vol. 6,
No.
4,
December
2015: 781 – 787
78
2
reconfi
g
uration curre
nt for
DFIG.
They
h
a
ve u
s
ed t
w
o
Lue
nbe
rge
r
ob
serve
r
s to
ge
n
e
rate resid
u
als
fo
r the
cu
rren
t sensors. A p
r
op
o
s
ed alg
o
r
ith
m
fo
r fau
lt id
en
tifi
catio
n
is d
e
sign
ed
to
iso
l
ate cu
rren
t sensor fau
lts
in
stato
r
o
r
in
ro
tor
.
I
n
[2
0
]-[2
1
]
,
h
a
v
e
studied
th
e ef
f
ect
o
f
cur
r
e
n
t
senso
r
f
a
u
lt o
n
a do
ub
ly f
e
d
inductio
n
m
achi
n
e (D
FI
M
)
. I
n
[2
2]
, a
new F
D
I al
go
r
i
t
h
m
of st
at
or
cur
r
ent
se
nso
r
s
and s
p
eed se
n
s
or
faul
t
s
det
e
ct
i
on
pr
o
b
l
e
m
has pr
o
pose
d
fo
r
Perm
anent
M
a
gnet
sy
nc
h
r
o
n
ous m
achi
n
e d
r
i
v
es
w
h
ere si
m
u
l
a
t
i
o
n an
d
expe
rim
e
ntal results are reported.
In
[23]
presents a si
gna
l
-base
d
approa
ch to
detect and isolate the
fa
ult in
stato
r
cu
rr
en
t
an
d vo
ltag
e
senso
r
s of
t
h
e
D
F
IG
.
The c
ont
ri
b
u
t
i
on
o
f
t
h
i
s
pa
p
e
r f
o
c
u
ses
on
t
h
e de
si
g
n
o
f
t
h
e U
I
O
t
o
e
s
t
i
m
a
t
e
bot
h o
f
st
at
e an
d
u
nkn
own
inp
u
t
s. Th
ese unk
now
n
i
n
pu
ts ar
e co
n
s
i
d
er
ed
in
t
h
is work, as fa
ul
ts affecte the st
ator
voltage
s of the
DFIG a
n
d t
h
eir estim
a
tes can
be
use
d
to c
o
n
cei
ve sy
st
em
s
of
di
a
g
n
o
st
i
c
a
n
d
co
nt
r
o
l
.
Thi
s
wo
rk
i
s
o
r
ga
ni
zed
as
fol
l
ows.
I
n
Sect
i
o
n
2, sy
st
em
descri
pt
i
o
n a
n
d
m
odel
i
ng are
p
r
esent
e
d.
I
n
Sect
i
o
n
3
,
f
o
r
m
ul
at
i
on
pr
obl
em
i
s
di
scus
se
d.
The
n
,
i
n
Sec
t
i
on
4,
si
m
u
l
a
t
i
on
res
u
l
t
s
a
r
e c
o
n
d
u
ct
ed
t
o
e
v
al
uat
e
t
h
e pe
rf
o
r
m
a
nce o
f
t
h
e
p
r
o
p
o
s
e
d
ob
ser
v
er
. Fi
nal
l
y
, t
h
e c
o
ncl
u
si
o
n
s a
n
d
fut
u
re
wo
rks
are
gi
ven
i
n
Sect
i
o
n
5.
2.
SYSTE
M
DESC
RIPTIO
N AN
D MO
DE
LING
In
a
DFIG-b
ased
wi
n
d
turb
ine, as sho
w
n
in
Fig
.
1
,
th
e
g
e
nerato
r is co
up
l
e
d
to
th
e
wind
tu
rb
in
e ro
tor
t
h
r
o
u
g
h
a gea
r
bo
x. T
h
e st
at
o
r
of t
h
e
DF
IG i
s
directly connected to the
gri
d
and the
rot
o
r side is connec
t
ed to
a bac
k
-t
o-
bac
k
co
nve
rt
er
vi
a s
l
i
p
-ri
n
g
s
[
24]
.
Fi
gu
re
1.M
ode
l
of
DF
I
G
-
b
ase
d
wi
n
d
t
u
r
b
i
n
e.
2.
1. DFI
G
m
o
del
For the
DFIG, the dy
nam
i
c
voltage
s of the stator
(
s
V
and
s
V
) and those
of
the rotor (
r
V
and
r
V
) in th
e
g
e
n
e
ral
(
)
refe
rence
fra
m
e
are res
p
ec
tively expresse
d as
[25]:
d
d
d
d
d
d
d
d
s
ss
s
s
s
s
ss
s
s
s
rr
r
r
r
r
rr
r
r
r
r
VR
I
ΦΦ
t
VR
I
ΦΦ
t
VR
I
ΦΦ
t
VR
I
ΦΦ
t
1
The stator a
n
d
rot
o
r
(
)
flu
x
es,
s
,
s
,
r
and
r
are gi
v
e
n
by
:
s
ss
m
r
s
ss
m
r
rr
r
m
s
rr
r
m
s
Φ
Li
L
i
Φ
Li
L
i
Φ
Li
L
i
Φ
Li
L
i
2
Whe
r
e,
s
V
,
s
V
,
r
V
and
r
V
stator and
rot
o
r i
n
(
) vo
ltag
e
s;
s
I
,
s
I
,
r
I
and
r
I
stato
r
and rot
o
r
in (
) curre
nts; ,
s
,
s
,
r
and
r
stator an
d
roto
r in (
) flu
x
es;
s
R
,
r
R
stator
and rotor
per phase
resistance
;
s
L
,
r
L
cyclic stator and
rot
o
r i
n
ductances.
2.2.
DFI
G
State space
mode
l
In t
h
i
s
pape
r, t
h
em
at
hem
a
ti
cal
m
odel
devel
o
ped
of
t
h
e DF
I
G
i
s
deri
ved
fr
om
t
h
e vol
t
a
ge
equat
i
o
ns
of t
h
e stato
r
a
n
d r
o
to
r
(f
or
m
o
re details see
([
17
-
19]
)
.
Based
o
n
(
1
),
(2
) a
n
d
(3
),
the
DF
IG
m
odel is exp
r
e
ssed
in the
refe
re
nc
e (
) fram
e, as the
following:
Wi
nd
Tur
b
i
n
e
Gea
r
B
o
x
DC
Bu
s
Cont
r
o
l
Sy
s
t
e
m
Co
n
t
r
o
l
Sy
st
em
DC
Bu
s
AC
AC
AC
‐
DC
DC
‐
AC
DFIG
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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S
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4
Unk
n
ow
n
I
n
p
u
t
Obs
e
rver f
o
r
a
Do
u
b
l
y
Fe
d I
n
d
u
ct
i
o
n
Gene
rat
o
r
S
u
b
j
ect
t
o
Di
st
ur
ba
nces
(
S
a
m
i
r
A
b
del
m
al
ek)
78
3
2
2
1
()
1
()
ss
mm
r
m
m
m
m
s
ss
r
r
s
r
ss
r
s
r
s
s
s
r
s
s
mm
m
m
r
m
m
s
ss
r
r
s
r
sr
s
s
sr
s
s
r
rm
s
mm
r
ss
sr
r
r
dI
R
L
p
R
L
L
p
L
II
I
I
u
u
dt
L
L
L
L
L
L
L
L
L
dI
R
Lp
L
p
R
L
L
II
I
I
u
u
d
t
LL
L
L
LL
L
L
L
dI
L
R
Lp
R
II
I
dt
L
L
L
L
1
()
1
()
mm
rs
r
s
r
sr
r
r
ms
mm
m
r
m
ss
s
r
r
s
r
rs
r
r
s
r
r
pL
Iu
u
LL
L
dI
LR
Lp
p
R
L
II
I
I
u
u
dt
L
L
L
L
L
L
L
3
The state s
p
ace
m
odel of the
DFIG is
gi
ven
by:
()
(
)
()
()
()
()
()
mi
n
x
tA
x
t
B
u
t
R
u
t
yt
C
x
t
4
Whe
r
e,
m
is the
m
echanical
speed
of the rot
o
r,
p
i
s
t
h
e nu
m
b
er of pol
e
pai
r
s, a
nd t
h
e
m
a
t
r
i
ces
()
m
A
,
B
and
C
a
r
e e
x
presse
d as
fol
l
ows :
2
22
22
()
1
()
sm
m
r
m
m
m
s
ss
r
s
r
s
m
sm
m
m
m
r
sr
s
r
RL
p
R
L
L
p
IJ
I
J
LL
L
L
L
L
A
RL
L
p
p
IJ
I
J
LL
L
L
,
2
2
1
m
sr
r
L
I
LL
B
I
L
,
22
2
0
T
C
I
01
10
J
The state vector
T
ss
r
r
xI
I
I
I
, consists
of the stator currents a
n
d rot
o
r c
u
rre
n
t
com
pone
nt
s.
The co
nt
rol
i
nput
s
T
ss
uu
u
are the rotor voltage com
ponents. The m
easure
d
di
st
ur
ba
nces (
U
n
k
n
o
w
n
i
n
p
u
t
s
)
T
in
r
r
uu
u
are t
h
e st
at
or
v
o
l
t
a
ge c
o
m
pone
nt
s.
It
i
s
cl
ear
fr
om
t
h
e
represen
tatio
n
as in
(4), th
at t
h
e system
m
a
trix
A is
va
ry
i
n
g
t
i
m
e
and de
pe
nds
o
n
t
h
e m
e
chani
cal
r
o
t
o
r
spee
d
m
. In
t
h
is p
a
p
e
r,
letu
s con
s
id
er t
h
at
the DFIG operates
at a
fi
xed-s
p
ee
d (
mm
e
c
).
3.
PROBLEM FORMUL
ATION
UIO’s
goal is to estim
a
te the system
s
t
ates wh
er
e so
me in
pu
ts ar
e
un
kno
wn
.
Au
th
or
s in
[
2
6
]
,
dem
onst
r
at
ed t
h
at
t
h
e c
o
nve
n
t
i
onal
L
u
en
be
r
g
er
o
b
ser
v
e
r
is no
t su
itab
l
e to ov
erco
m
e
u
nkn
own
inpu
ts.
Using
t
h
e est
i
m
a
t
e
d st
at
es and t
h
e k
n
o
w
n i
n
p
u
t
s
, t
h
e u
n
k
n
o
w
n
i
n
put
s are rec
o
ns
t
r
uct
e
d [
3
]
.
Th
e bl
ock
di
agra
m
of a
UI
O
wi
t
h
rec
o
nst
r
uct
i
o
n
of t
h
e
un
k
n
o
w
n i
n
put
s
i
s
gi
ve
n i
n
Fi
gu
re
3.
F
o
r t
h
e
sy
st
em
as i
n
(1
),
t
h
e
U
I
O i
s
as
fo
llows[27
]
:
()
()
()
()
ˆ
()
()
()
zt
N
z
t
G
u
t
L
y
t
xt
z
t
E
y
t
5
Whe
r
e
is a new state of t
h
e
obs
erver,
y
t
h
e
out
put
vect
o
r
,
u t
h
e
kn
o
w
n i
n
p
u
t
vect
or
, N
i
s
a st
abl
e
m
a
t
r
i
x
. M
a
t
r
i
ces N
,
G,
L a
n
d E
are
t
h
e
o
b
s
erve
r
gai
n
s
.
T
h
e m
a
t
r
i
ces N,
K,
G
a
n
d
E
h
a
ve t
o
be
desi
gne
d i
n
s
u
ch
a
w
a
y th
at
ˆ
()
x
t
co
nve
r
g
es as
ym
pt
ot
i
cal
l
y
t
o
()
x
t
.
As a con
s
equ
e
n
c
e, th
e ob
serv
er erro
r will con
v
e
rge
to zero.
Fi
gu
re 2.
U
n
kn
ow
n In
p
u
t
Obs
e
rve
r
fo
r
a DF
I
G
s
u
b
j
ect
t
o
di
st
ur
bance
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
208
8-8
6
9
4
IJPE
DS Vol. 6,
No.
4,
December
2015: 781 – 787
78
4
Let us
de
fine t
h
e state estim
a
tion e
r
ror as:
ˆ
()
()
()
et
x
t
x
t
6
B
y
usi
n
g
(5
) a
n
d
(
6
)
,
t
h
e
st
at
e
estim
a
tion error e
(
t)
becom
e
s:
()
()
(
)
()
nx
et
z
t
I
E
C
x
t
7
By settin
g
()
nx
PI
E
C
, t
h
e
dy
nam
i
cs of t
h
e est
i
m
ati
on e
r
r
o
r
i
s
gi
ven
by
t
h
e
fol
l
o
wi
n
g
equat
i
o
n:
()
()
(
)
()
(
)
()
in
et
N
e
t
G
P
B
ut
P
N
L
C
N
P
x
t
P
R
u
8
Th
eo
rem
.
1
. Th
e n
ecessary an
d
su
fficien
t
co
nd
itio
ns for th
e ex
isten
ce
o
f
UIO
(5) of syste
m
(4
) are
[2
7-
2
8
]
:
a)
N is stab
le (eig
(N)
0);
b)
ra
nk
(CR) =
ran
k
(R
) =
dim
(
y
)
;
c)
Th
e
p
a
ir
(
(
I
n
x
+
EC)A
,
C
) is ob
serv
ab
le.
If
t
h
e fo
llowing
relatio
n
s
are satisfied
:
LC
P
A
N
C
9a
GP
B
9b
()
0
nx
IE
C
R
9c
B
a
sed on
(
9
c)
y
i
el
d
t
o
:
()
ER
C
R
10
whe
r
e
(C
R
)
+ i
s
t
h
e
ge
neral
i
z
ed i
n
ve
rse m
a
tri
x
of
(C
R
)
an
d
can
be
gi
ve
n
a
s
:
()
()
()
()
T
TT
C
R
CR
CR
CR
11
Fin
a
lly, all m
a
t
r
ices N,
K,
G an
d E are
d
e
fi
n
e
d
in th
e
fo
llo
wi
n
g
equ
a
tion
s
:
1
()
()
()
TT
E
R
CR
CR
CR
12a
1
()
()
(
)
TT
nx
PI
R
C
R
C
R
C
R
12b
GP
B
12c
NP
A
K
C
12d
LK
N
E
12e
The state estimation e
r
ror is then
refine
d a
s
:
()
()
et
N
e
t
(13)
3
.
1
.
Sta
b
ility and co
nv
erg
ence co
nditions
Based
on
th
e ab
ov
e
UI
o
b
serv
er, th
e fo
llowin
g
th
eorem
wi
ll g
i
v
e
th
e fau
l
t esti
m
a
tio
n
alg
o
rith
m
an
d
th
e cond
itio
n
s
th
at gu
aran
tee
th
e stab
ility o
f
erro
r system
(1
3
)
.
The
o
rem
.
2. T
h
e U
I
O
(5
) f
o
r
a DFI
G
sy
st
em
wi
t
h
i
nput
s
un
k
n
o
w
n (
4
) e
x
i
s
t
s
an
d t
h
ei
r
est
i
m
a
t
i
o
n
er
ro
r
(
13)
conv
erg
e
s asym
p
t
o
tically to
zero
,
if and
o
n
l
y
if, th
e
p
a
ir
(A,C) is detectabl
e
. This
observer is
asy
m
p
t
o
tically
stab
le if ex
ists a p
o
s
itiv
e d
e
fi
n
ite sy
mmetric
m
a
trix
P
and matrices
ii
WP
K
such that the
fo
llowing
LM
I ho
ld
s:
0
,
1
,
.
..,
TT
T
ii
i
i
A
PP
A
C
W
W
C
i
r
(14)
Th
e so
lu
tion of th
e in
eq
u
a
lity (14
)
can th
en
b
e
o
b
t
ai
n
e
d
u
s
ing
L
MI cond
itio
n
s
.
Ob
serv
er
g
a
in
s can
becalculated from
1
ii
K
PW
. T
h
en, c
o
nsequently
ˆ
()
x
t
will asym
p
t
o
tical
l
y
co
nv
erg
e
to
()
x
t
and
()
in
ut
to
ˆ
()
in
ut
.
3.
2.
Unk
o
wn i
nput estim
a
ti
on
I
n
o
r
d
e
r
t
o
ob
tain
th
e un
know
n
inpu
ts
ˆ
()
in
ut
, we
com
b
i
n
i
ng (
4
)
and (
1
5)
, t
h
e
un
k
n
o
w
n i
n
put
s are
expresse
d as
the followi
ng:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Unk
n
ow
n
I
n
p
u
t
Obs
e
rver f
o
r
a
Do
u
b
l
y
Fe
d I
n
d
u
ct
i
o
n
Gene
rat
o
r
S
u
b
j
ect
t
o
Di
st
ur
ba
nces
(
S
a
m
i
r
A
b
del
m
al
ek)
78
5
ˆ
()
()
()
()
()
dx
t
N
z
t
L
yt
G
u
t
E
yt
dt
15
ˆˆ
()
(
)
()
in
ut
R
N
R
G
B
u
R
L
y
R
E
y
R
A
x
t
16
4.
SIM
U
LATI
O
N
AN
D DIS
C
USSI
ON
RE
S
U
LTS
I
n
o
r
d
e
r
t
o
v
a
lid
ate th
e pr
oposed
appr
o
a
ch
e, th
e
m
o
d
e
l (
4
)
w
ith
th
e p
a
r
a
meter
s
in
[9
-1
0
]
is u
s
ed
as a
cont
rol
l
e
d
sy
st
em
i
n
t
h
e si
m
u
l
a
t
i
on st
udi
es
. The
st
u
d
i
e
s
were c
o
nd
uct
e
d i
n
M
a
t
l
a
b
us
i
ng
4t
h
-
o
r
der
R
u
n
g
e-
Kut
t
a
m
e
t
hod
wi
t
h
t
h
e
fi
xed
st
ep si
ze
of
0
.
0
1
s
.
Fi
g
u
re
.
3
re
prese
n
t
s
t
h
e m
easure
d
st
at
or
and
r
o
t
o
r c
u
r
r
e
n
t
s
of
t
h
e DF
IG
an
d
t
h
ei
r est
i
m
at
ed base
d o
n
t
h
e
UI
O, a
nd i
n
Fi
gu
re.
4 i
s
re
prese
n
t
e
d t
h
e
dy
nam
i
c errors
of t
h
e
states.
Fig
u
re
3
.
Sim
u
latio
n
resu
lts
of
o
r
ig
i
n
al states and
t
h
eir esti
mated
.
Figure
4. The
e
r
rors
bet
w
een s
t
ates and their
estim
a
ted.
It can
be clearly obse
r
ved from
the sim
u
lation res
u
lts th
at
th
e states estimatio
n
g
e
n
e
rated
fro
m
th
e
UI
O c
o
n
v
e
r
ge
rapi
dl
y
t
o
t
h
os
e sim
u
l
a
t
e
by
t
h
e
DFI
G
sy
st
e
m
. In ad
di
t
i
on,
we ca
n see i
n
Fi
g
u
res
4,
t
h
a
t
t
h
e
e
s
ti
ma
t
i
o
n
er
ror
s
ar
e
v
e
r
y
w
e
ak
.
4.
1.
Un
kn
ow
n
Inpu
t E
s
ti
ma
ti
on
Fig
u
r
e
s. 5 and 6
r
e
pr
esen
t the un
kno
wn
i
n
pu
ts an
d
t
h
eir esti
m
a
tes, with
th
eir
d
y
n
a
m
i
c
erro
rs .
The
si
m
u
latio
n
r
e
sults sh
ow
t
h
e
g
o
o
d
estim
a
tio
n
o
f
th
ese
un
know
n inp
u
t
s.
0
5
10
-1
0
0
-5
0
0
50
10
0
Ti
m
e
s
[
s
]
I
s
[A
]
DF
IG
UI
O
0
5
10
-4
0
-2
0
0
20
40
Ti
m
e
s
[
s
]
I
s
[A
]
DF
IG
UI
O
0
5
10
-1
0
0
-5
0
0
50
10
0
Ti
m
e
s
[
s
]
I
r
[A
]
DF
IG
UI
O
0
5
10
-4
0
-2
0
0
20
40
Ti
m
e
s
[
s
]
I
r
[A
]
DF
IG
UI
O
0
5
10
-2
-1
0
1
2
x 1
0
-1
3
Ti
m
e
s
[
s
]
r
s
0
5
10
-4
-2
0
2
4
x 1
0
-1
3
Ti
m
e
s
[
s
]
r
s
0
5
10
-1
-0
.
5
0
0.
5
1
x 1
0
-1
2
Ti
m
e
s
[
s
]
r
r
0
5
10
-1
-0
.
5
0
0.
5
1
x 1
0
-1
2
Ti
m
e
s
[
s
]
r
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
208
8-8
6
9
4
IJPE
DS Vol. 6,
No.
4,
December
2015: 781 – 787
78
6
Fig
u
r
e
5
.
Un
kno
wn
i
n
pu
t
s
V
an
d its
esti
m
a
ted
ˆ
in
s
u
.
Fig
u
r
e
6
.
Un
kno
wn
i
n
pu
t
s
V
an
d its
esti
m
a
ted
ˆ
in
s
u
.
Th
e sim
u
latio
n r
e
su
lts show
a go
od
esti
m
a
ti
o
n
of
bo
th
stat
e and
u
nkn
own in
pu
ts
b
y
u
s
ing
th
e UIO
.
5.
CO
NCL
USI
O
N
In t
h
i
s
pa
pe
r, t
h
e
pr
obl
em
of
desi
g
n
i
n
g t
h
e
u
n
k
n
o
w
n
i
n
p
u
t
obs
er
ver
(
U
I
O
) f
o
r a
D
F
I
G
w
h
i
c
h s
u
bject
to disturba
nce
is treated. Thes
e unkn
own i
n
puts affects the
states of th
e DFI
G
. Th
e
Un
kn
own
In
pu
t Obser
v
er
(UIO)
d
e
sign
p
r
ob
lem
is fo
rm
u
l
a
t
ed
as a set o
f
lin
ea
r con
s
train
t
s
wh
ich
can
be easily so
lv
ed
u
s
ing lin
ear
matrix
in
equ
a
li
ties (LMIs) tech
n
i
q
u
e
.
S
o
l
v
i
n
g a
set
of
LM
I
s
, t
h
e
U
I
O ca
n
be
desi
g
n
e
d
.
A
n
a
ppl
i
cat
i
o
n
b
a
sed
on a
DF
I
G
i
s
prese
n
t
e
d t
o
e
v
al
uat
e
t
h
e
pe
rf
orm
a
nce
and the effectiveness of th
e pr
o
pos
ed o
b
ser
v
e
r
.
T
h
e
o
b
s
erv
e
r is app
lied
to estim
a
t
e b
o
t
h
stator
an
d ro
tor
cu
rren
t
s
w
ith
u
nkno
wn
i
n
pu
ts
which
d
e
scr
i
bed
b
y
th
e
stato
r
v
o
ltag
e
s. Th
e sim
u
latio
n
resu
lts sho
w
a go
od
esti
m
a
ti
o
n
of
bo
th
stat
e and
u
nkn
own in
pu
ts.
REFERE
NC
ES
[1]
Singh M, Khadkikar V, Chand
r
a A. Grid s
y
n
c
hroniz
a
tion wit
h
harm
onics and react
ive pow
er com
p
ensatio
n
capab
ility
of a p
e
rmanent magnet s
y
nchronous generator-b
ased variable speed wind energ
y
conver
s
ion sy
stem.
IET
Power E
l
ec
tron
. 2011;
4(1):122–
130.
[2]
Heier S. Grid
Integration of
Wind Energ
y
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