TELKOM
NIKA
, Vol.12, No
.2, June 20
14
, pp. 315~3
2
4
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i2.1977
315
Re
cei
v
ed
Jan
uary 6, 2014;
Re
vised Ap
ril
7, 2014; Accepted April 2
2
, 2014
Stability Improvement of Single Machine using ANFIS-
PSS Based on Feedback-linearization
I Made Ginar
s
a
1
, Osea Ze
bua
2
1
Dept. of Electrical En
gin
eeri
ng, Mataram U
n
iversit
y
Jln. Maja
pah
it No. 62 Matara
m,
T
e
lp/fax+
62
370 63
67
55
2
Dept. of Electrical En
gin
eeri
ng, Univ
ersit
y
of Lampu
ng
Jln. Prof. SumantriBro
j
on
eg
o
r
o No. 1, Band
ar Lamp
u
n
g
,
T
e
lp. +
62 72
17
0
160
9
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:
1
kadekgi
n@
yaho
o.com;
2
oseaz8
9
@
y
a
h
o
o
.com
A
b
st
r
a
ct
Electrical
pow
er system (EP
S
) operati
on
a
l
w
a
ys follow
s
l
oad c
han
ges
w
h
ich occur w
i
thin ti
me.
Loa
d cha
n
g
e
s
and
disturb
anc
es caus
e EPS
oper
ation to
fi
nd a n
e
w
bal
a
n
ce p
o
int a
nd
before c
an re
a
c
h
the new
b
a
la
nc
e po
int, the rot
o
r spe
ed w
ill s
w
ing aro
u
n
d
its
synchro
nous s
pee
d. This p
h
e
n
o
m
e
non c
aus
es
the stability of
the EPS oper
ation decreas
e
significantl
y, m
o
r
eover, when the
di
sturbance
is large the
m
a
c
h
ine tend
to become unstable. To ov
ercome this
problem
,
it is
nec
essary to add a power syst
em
stabili
z
e
r (PSS
). This research
proposes ANFIS-PSS based
on feedback-
lineari
z
a
t
i
on to
stabili
z
e
t
he E
PS
oper
ation. F
e
e
dback-
lin
eari
z
a
t
ion is
a
non
li
near c
ont
ro
l techn
i
qu
e w
h
ic
h fee
dback
a
nd l
i
m
its sev
e
ral
outputs in or
der to make the nonlinear syst
em
acts as
a
linear system
. Data from
conventional P
S
S
is
used to tra
i
n
and to
upd
ate
ANFIS-PSS para
m
eters.
Si
mu
lati
on res
u
lt
s show
an i
m
prove
m
ent of
the
stability of sin
g
l
e machi
ne
mo
del suc
h
as de
creasi
ng in
ma
ximu
m magn
itu
de of rotor spe
edat the val
ue
of
0.466 ra
d/s an
d to reduce th
e
time settli
ng to
5.6 s.
Ke
y
w
ords
: stability, PSS, ANFIS,
feedback-
l
i
ne
ari
z
a
t
i
on, se
ttling time red
u
c
ing
1. Introduc
tion
Electri
c
po
wer sy
stem
s have intri
s
ically natural
a
nd sh
ould
be mod
e
lled
using
a
nonlin
eardifferential e
quati
on.Co
nventio
nal linea
r co
ntrol ha
s lim
ited ability, so it is able
to
stabili
ze a pl
ant due to d
y
namic (smal
l
) distu
r
ba
nce and work with one p
o
int operatio
n only
[1].Some efforts
have been done to
reduce the
rotor oscillation
in power
sy
stem
s by usi
ng
power
syst
em stabilizer
(PSS) based on
neura
l
network (NN), such
as,heuri
s
tic-dynamic-
prog
ram
m
ing
[2], adaptive
NN [3] and
re
curre
n
t
NN
[4
].Nonline
a
r control schem
e
was appli
e
d
to
control st
eam
turbine
valve in a m
u
ltimachi
ne p
o
wer system
usi
n
g the ge
omet
rical
differe
ntial
method
[5]. So, stabili
zat
i
on of
a m
u
l
t
imachin
e
p
o
w
er
system
via excitation
co
ntrol
u
s
in
g
decentrali
ze
d
feedb
ack-li
n
eari
z
ation
wa
s a
b
le to
re
d
u
ce
roto
r o
scillation ag
ain
s
t dynami
c
a
n
d
transi
ent di
st
urba
nces. In
put si
gnal
co
ntrol
wa
s
ob
served
by lo
cal mea
s
u
r
em
ent only [6].
PSS
desi
gn u
s
in
g
feedba
ck-lin
eari
z
ation
in
nonlin
ear
p
o
we
r
system
model
by con
s
id
erin
g the
magnitud
e
li
mit of control
signal
have
been d
one
b
y
Liu et al. [7]. Robu
st con
t
rol tech
niqu
e
via
Lyapun
ov method
wa
s u
s
ed to im
pro
v
e the stab
ili
ty of a nonli
near
po
we
r
system
whe
n
the
power sy
ste
m
was fo
rced
by
heavily disturb
a
n
c
e
s
[8].
ANFIS alg
o
ri
thm is a
me
thod
whi
c
h t
heir
pa
ramet
e
rs a
r
e
obta
i
ned
autom
atically b
y
learni
ng p
r
o
c
ess via data
training. In
rece
nt
years,
some A
N
FIS
algorith
m
ha
ve been
wid
e
ly
use
d
to
cont
rol th
e
cha
o
s and
voltag
e
coll
ap
se
in
power sy
ste
m
. Com
b
inati
on of
compo
s
ite
controlle
r-static var comp
ensator
ba
se
d on
ANFIS
algo
rithm
h
a
ve be
en
used to
su
ppre
s
s
cha
o
s, volta
ge coll
ap
se,
and al
so t
o
add lo
adi
ng ma
rgin i
n
a po
wer
system [9]-[
11].
Furthe
rmo
r
e,
by applying a PID-loop
based A
N
F
I
S to
the system
sthat was obtain
ed
the
improvem
ent
of tran
sie
n
t voltage resp
onse [12]
-[1
3
]. Desi
gn a
n
d
digital
sim
u
lation of A
N
FIS-
PSS with a real power deviation was
us
ed as
an
input for the A
N
FIS-PSS.It
was
obtained that
the ANFIS-PSS was
able
to damp the
local and inter-area oscillat
i
ons
[14]. Also, the first order
Sugeno model has been used to design ANFIS-
PSS andthis model can be able to damp local
and inte
r-are
a
oscillatio
n
s [15]. Dampi
ng of ro
tor o
scill
ation h
a
s been
don
e
by usin
g lay
e
re
d
recurrent
net
work-ba
s
e
d
PID-SVC co
n
t
roller
[16
]. S
V
C
controlled
by
NN was
use
d
to
enh
a
n
ce
dynamic
stabi
lity of power system [17].
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 2, June 20
14: 315 – 32
4
316
This pa
pe
r is organi
ze
d a
s
follows: Single ma
chin
e
model co
nn
ected to infin
i
te bus is
explained i
n
Section 2. A
N
FIS power
system stab
ili
zer ba
se
d on
control n
online
a
r via feedb
a
c
k-
lineari
z
atio
n
method i
s
de
tailed in
Sect
ion 3. Sim
u
la
tion re
sult
an
d an
alysi
s
a
r
e de
scrib
ed i
n
Section 4. Fin
a
lly, the concl
u
sio
n
is provided in the la
st section.
2. Single Machine Model
Conn
ected to Infinite Bu
s
A single
ma
chin
e mod
e
l
whi
c
h u
s
ed
in this rese
arch con
s
ist
s
of turbine,
gene
rato
r
(ma
c
hin
e
), e
x
citation syst
em (excite
r),
automat
ic v
o
ltage regula
t
or (AVR) an
d external li
ne
con
n
e
c
ted to
infinite bu
s [1
8]. This m
o
d
e
l is ill
ustrate
d
in Fig
u
re 1
and its pa
ra
meters a
r
e li
sted
in Table
1. A synch
r
o
n
o
u
s g
ene
rato
r is mod
e
led
by usin
g a
voltage (
) be
hind a
dire
ct
r
e
ac
ta
nc
e
(
). Steam or gas turbine funct
i
on conve
r
tst
herm
a
l energ
y
to mechani
cal ene
rgy or
torque (
T
m
). Synchrono
us generator
p
r
odu
ce
s termi
nal voltage
(
V
)
at a bu
s machin
e through
excitation sy
stem. Single machi
ne conn
e
c
ted to infi
nite bus i
s
expressed by formula Eqs.(1)-(5).
(1)
(2)
(3)
(4)
(5)
whe
r
e
T
m
,
,
,
0
,
D
and
M
are the m
e
cha
n
ical torq
ue, roto
r angl
e, rotor
spe
e
d
, synchro
u
n
ous
spe
ed, damp
i
ng con
s
tant
and inertia
con
s
tant, resp
ectively.Thevaria
bel
s
I
d
,
I
q
and
V
t
are
con
s
trai
ned b
y
Eqs. (6)-(8
), resp
ectively.
sin
0
(6)
cos
0
(7)
(8)
Table 1. Power System Pa
ramete
rs
x
d
x
d
x
q
t
d
0
0.8958
0.1198
0.8645
6.0
H t
a
K
A
0
6.0 0.01
20.0
377
Dfw
t
e
r
e
x
e
0.0125
0.314
0.025
0.085
sin
(9)
cos
(10
)
whe
r
e
V
d
,
V
q
and
V
t
are the
dire
ct, qu
adrature
and
termi
nal voltag
e
s
, re
pe
ctively. Whil
e,
I
d
an
d
I
q
are the di
re
ct and qu
adratu
r
e cu
rrents.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Stability Im
provem
ent of Single Machine Us
ing ANFIS
-
PSS Based .
... (I Made Ginarsa)
317
Figure 1. Single-m
a
chine
model equipped by PSS.
3. ANFIS-PS
S
Based on
Feedb
ack
-lineariza
t
ion Design
3.1. Feedba
c
k
-lineari
z
atio
n method
Nonli
nea
r co
ntrol techniqu
e feedba
ck-li
neari
z
atio
n m
e
thod is a te
chni
cal p
r
o
c
e
dure th
at
state feed
ba
ck
of a no
n
linear
syste
m
, whe
r
e
some outp
u
ts of the syst
em are bo
u
nded
(co
n
st
rain
ed).
This meth
od
made the
system be
have
as a lin
ear
system [19].
Whe
n
some
of
variable
s
su
ch
as
I
d
,
I
q
an
d
V
t
,
are
not
state varia
b
le
s, a tran
sfo
r
mationis
nee
ded to ma
ke
that
variable
s
be
came state va
riable
s
. Singl
e machi
ne
m
odel that exp
r
esse
d by variable
s
in Eq
s.
(2)-(5) i
s
tra
n
s
form
ed into t
he mod
e
l that
expre
s
sed
b
y
v
a
riable
s
in
Eqs. (1
1)
-(
14
).Part from thi
s
,
the state vari
able (
) in Eq. (1) is still the same.
sin
cos
sin
cos
sin
′
cos
′
′
(11
)
′
′
sin
′
cos
(12
)
(13
)
(14
)
whe
r
e
.In addition, definition of con
s
tant
s from
k
1
to
k
28
are given in
Appendix B.
3.2 Lineariza
t
ion proce
s
s
es of inpu
t-o
utpu
t contro
ller
The
sin
g
le
m
a
chi
ne
whi
c
h
is conn
ecte
d
to t
hei
nfinite
bu
s i
s
a
sin
g
le in
put-sing
l
e outp
u
t
(SISO) n
onlin
ear
co
ntrol
problem. In thi
s
re
sea
r
ch,
sp
eed
roto
r (
) variable
is u
s
ed a
s
an o
b
je
ct
control.By defining
, the control obje
c
ti
ve is regulat
ed towa
rd ze
ro value. To obtain
the rotor
sp
e
ed d
e
viation
(
e
) that
co
n
nect to
control si
gnal
(
u
) it isrequired to differentiate
e
several time
s until the
control
sign
al
(
u
)
is
a
p
pea
r
e
d
.
D
e
r
i
va
tive
p
r
oc
es
ses
ar
e
s
h
ow
n a
s
follows
:
(15
)
(16
)
(17
)
(18
)
Derivative proce
s
s of the error from
to
aregive
n in Appen
dix A. Variab
el
X
is i
n
itial
state vari
able
wh
ich
co
nsi
s
ts o
f
rotor angl
e
(
),rotor spee
d (
),quadrat
ure
axis volta
ge
(
E
q
),field volt
age
(
E
fd
)
an
d output volt
age of AV
R
(
V
r
), respe
c
tively. The st
ate varia
bel
is
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 2, June 20
14: 315 – 32
4
318
c
h
os
en
as a
control objec
tive. In this cas
e
, the
c
ontrol s
i
gnal
(
u
)a
p
peared
at the
fourth
de
riva
tive
of
,
(
).By this pro
c
e
s
s the system beca
m
e a
fourth
-order feed
ba
ck-lineari
z
e
d
system. Since
uncontroll
ed state
varia
bel
sat
i
sf
y
, state variabl
e
is bound
ed
wh
enstate va
ria
b
le
was able to st
abilize
0
.Next step is to define refe
ren
c
e sign
als (
x
d
) and erro
r sig
nals (
e
).
Figure 2. Fee
dba
ck-line
a
ri
zation
co
ntrol
techni
que tha
t
was imple
m
ented in si
ngl
e machi
ne
model.
(19
)
̅
̅
̅
(20
)
whe
r
e
T
is ve
ctor tra
n
spo
s
e. The dynam
ics of
the sy
stem are exp
r
e
s
sed a
s
follo
ws:
(21
)
;
(22);
(23
)
(24
)
In this research, the lin
e freque
ncy
(
f
) is 60 Hz
. So,
0
is a
con
s
tant
value at 2
6
0
=
377
rad/s.
The
r
ef
ore, all
of its derivative
s
have zero
va
lues.
Id
eal control sig
nal
v
was chos
en as
follow:
̅
(25
)
Whe
r
e
K
v
is the gain vector.
, where
a
1
,
a
2
,
a
3
and
a
4
are the
para
m
eters
o
f
the gain
ve
ctor. The
para
m
eters
a
1
,
a
2
,
a
3
an
d
a
4
are
cho
s
e
n
p
r
ope
rly to ma
ke th
e
clo
s
ed
-loo
p system sta
b
l
e
. Then, theclo
sed
-
lo
o
p
dynamical sy
stem wa
s transfo
rme
d
into a
linear
system
without mag
n
itude con
s
traint (
u
=
v
).
̅
̅
0
1
0
0
0
0
1
0
00
01
̅
(26
)
By choosi
ng
the para
m
ete
r
s
a
1
,
a
2
,
a
3
and
a
4
p
r
o
perl
y
, the system in Eq. (26
)
tendst
o
asymptoticall
y
stable
(
e
0
)
. Since th
e a
c
tual
cont
rol
sign
al is
a su
bjec to
mag
n
i
t
ude contraints,
the applie
d control si
gnal
(
u
) i
s
given by
|
|
|
|
(27
)
Whe
r
e the
u
max
is the maximumallo
wed
control sig
nal
magnitude.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Stability Im
provem
ent of Single Machine Us
ing ANFIS
-
PSS Based .
... (I Made Ginarsa)
319
3.3. ANFIS-P
SS Design Proces
ses
An ANFIS-P
SS wa
s d
e
si
g
ned
usi
ng i
d
e
a
l control
sig
nal
(
v
)a
nd rot
o
r sp
eed
a
s
i
nputs, and
control signal
from PSS a
s
the output. Each
input
s of the ANFIS-PSS have five membership
function
s. The membe
r
ship function
that
used to state each inputs a
r
e
Gauss type 2
membe
r
ship
function. Ea
ch input
s u
s
e
d
five lingui
stic vari
abel
s
such
as:
nega
tive high (NH),
negative
l
o
w (NL
)
, ze
ro (Z
E),
po
sitive
lo
w (PL)
an
d
p
o
sitive hi
gh
(PH) to
exp
r
e
s
s the
value
of
the
input sig
nal.
Fuzzy mod
e
l Taka
gi-Su
geno (T-S)
i
s
used to impleme
n
t the fuzzy infe
rence
system.Th
e
output of th
e ANFIS PS
S is a
sig
n
a
l co
ntrol
(
V
pss
)
and 25 rules with
li
n
ear
membe
r
ship functio
n
are u
s
ed to imple
m
ent the outp
u
t signal.
Learning
stag
es are don
e by using off-li
ne me
thod
wi
th 4000 data
matrix input-o
utputs. In
this
stage
th
e data
i
s
structured
in
m
a
trix form
a
s
[
v
V
pss
], where
v
,
, are
the i
nput
si
gnal
control ideal
and input rot
o
r sp
eed, re
spectively.
V
pss
is the output control
sign
al from ANFIS-
PSS.The proposed ANFI
S-PSSis
applied to a s
i
ngle
machine c
onnec
ted to infinite bus as
shown in Fi
gure 3.Architecture
and input-output
surf
ace
cont
rol of ANFIS-PSS are shown i
n
Figure 4 (a
) a
nd 4 (b
), re
sp
ectively.
Figure 3. Implementation of
the ANFIS-PSS
to improve stability of single machine.
Figure4 (a
). Archite
c
tu
re of fuzzy Suge
no
with two inpu
t (
v
,
) and one output (
V
p
s
s
).
Figure 4 (b). Input-output su
rface control
of ANFIS-PSS
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ISSN: 16
93-6
930
TELKOM
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Vol. 12, No. 2, June 20
14: 315 – 32
4
320
4. Results a
nd Analy
s
is
To demonstrate the performance of
the A
N
FIS-P
SS to improve stability i
n
a si
ngl
e
machi
ne n
o
n
linear m
odel,
t
he system i
s
impl
e
m
ente
d
and exam
ined u
s
ing
Matlab/Simuli
nk
7.9.0.529 [20]
on an Intel Core 2
Duo E6
550 23
3 GHz PC comp
uter.
The
simulatio
n
wa
s
perfo
rmed by fo
rci
n
g the
single
machi
ne
with
addition
al torque
(
T
m
) at
the value of 0
.
1 pu and at time of 100 m
s
. The respo
n
se
s were ob
serve
d
in spe
ed roto
r (
) a
nd
rotor an
gle (
). From Figu
re 5, it is s
hown that the maximum magni
tude (
M
max
) of the rotor sp
e
e
d
wa
s a
c
hi
eved
at the val
ue
of 0.555
ra
d/s fo
r
the
sin
g
l
e ma
chin
e
without eq
uipp
ed by th
e PS
S.
Mean
while, t
he m
a
ximum
magnitud
e
o
c
cured
(
t
max
) at
time of
0.4
s. Furthe
rmo
r
e
,
this
re
spo
n
se
wa
s damp
ed,
so its re
spo
n
se a
c
hi
eved
the steady
state with settling time of 27.5 s. From t
he
Figure 5 we
can
see that the
response of the singl
e machi
ne
without equi
pped by PSS very
oscillate.Thi
s
oscillation can be
occured becaus
e the system naturally has insuf
f
iction dampi
ng
component to damp the
rotor os
cillati
on when the system is di
sturbed. Next
, ANFIS-PSS is
prop
osed to
pro
d
u
c
e a
n
addition
al signal. Thi
s
a
dditional
sig
nal is u
s
ed
to modul
ate
the
automatic vol
t
age
reg
u
lato
r (AV
R
) to
produ
ce
dam
ping to
rqu
e
co
mpone
nt thro
ugh th
e
excit
e
r
system. So,
the dampi
ng
torque
co
m
pone
nt is
u
s
ed to dam
p
the roto
r o
s
cillation. And, the
respon
se
of
the p
r
opo
se
d
co
ntrolle
r i
s
also
comp
ared to th
e
re
spon
se
of con
v
entional PS
S
(CPSS) in order to valid of
the s
i
mulation result.
Maximum m
a
gnitude, time
of the m
a
ximum ma
gnit
ude
occu
rre
d
and
settling
time ofthe
CPSS response
was achieved at the value of
0.492 rad/s,
time of 0.37 s and 7.89 s,
respe
c
tively. Mean
while, t
he re
sp
on
se
of the pro
p
o
s
ed co
ntroll
er
wa
s a
c
hieve
d
at the valu
e o
f
0.466
rad/s,
time of 0.33
s an
d 5.6
s, for
the ma
ximum magn
itude, time o
f
the maximum
magnitude occured and
set
t
ling time, respectively.It
is
shown that the propo
sed controller
i
s
able
to redu
ce the
maximum m
agnitud
e
and
settling time
of the rotor
speed
re
spon
se. The re
sp
o
n
se
of the propo
sed co
ntrolle
r i
s
better tha
n
the other
cont
rolle
rs.
Figure 5. Respon
ses of single machine
without
PSS, conventional
-PSS, and ANFIS-PSS
is com
p
a
r
ed t
o
obtain their
respe
c
tive pe
rforma
nces.
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TELKOM
NIKA
ISSN:
1693-6
930
Stability Im
provem
ent of Single Machine Us
ing ANFIS
-
PSS Based .
... (I Made Ginarsa)
321
Figure 6. Control signal
s produced by the conven
tional PSS and ANFIS-PSS.
Figure 7. Re
spon
se
s of rotor angl
e for resp
ective con
t
rollers.
Figure 6
sho
w
s the
sig
nal
control p
a
ttern
(
u
(
V
pss
))
from CPSS and
the propos
e
d
PSS. This
s
i
gnal was
us
ed to modulate AVR in the exc
i
tation s
y
s
t
em.It is
s
h
own that the maximum
magnitud
e
(
u
(
V
pss
)) of the sign
al cont
rol
was le
ss tha
n
the magnit
ude con
s
train
t
(
u
maks
=
0.5 pu).
The
control
si
gnal that pr
oduced
by the PSS is bounded.By this
result it
is guaranteed that the
sy
st
em i
s
st
a
b
le.
The re
sp
on
se of the roto
r angle i
s
sh
own in Fig
u
re 7. Figure
7 sho
w
s the
maximum
magnitude of
the CPSS and proposed PSS was achi
eved at the values
of 0.
191 and 0.1396
rad, respectiv
e
ly. In addition, the settling ti
me of the CPSS and proposed PSS was achieved at
the time
s of
7
.
97 an
d
5.6
s, re
sp
ectively.Mean
while
,
t
he re
spo
n
se
of
the sin
g
le machi
n
e
with
out
PSS oscillated in more than 28 s and the maximu
m magnitude was more than 0.22 rad. From
the rotor angl
e response,
we
see that the proposed
PSS gives
better response than the other
controlle
r.
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93-6
930
TELKOM
NIKA
Vol. 12, No. 2, June 20
14: 315 – 32
4
322
5. Conclusio
n
Powe
r sy
ste
m
s al
ways o
perate
in a
balan
ce
co
n
d
ition bet
we
en po
we
r de
mand a
n
d
sup
p
ly. Balan
c
ing
op
eratio
n of p
o
wer
systems ca
n b
e
di
sturb
ed
b
y
load
or
stru
cture
chan
ge
s.
Whe
n
the
op
erationi
su
nba
lance, this co
ndition
ca
use
s
the
rotor sp
eed
rea
c
h
o
s
cillation
mod
e
.
In
this research ANFIS-PSS based
on feedback-linearization i
s
pro
posed to i
m
prove
stability of
rotor oscillati
on of single
machi
ne.Gauss type
2 m
e
mbership function i
s
used to implem
ent
respe
c
tive ANFIS param
eters. Th
e ANFIS par
am
eters
are o
b
t
ained autom
atically by using
learni
ng processes. The
si
mulati
on
shows that the proposed PSS is
able to im
prove
stabilit
y of
singl
e ma
chi
ne
whe
r
e
the
settling
time
is
achieved
at the time
s
of 5.6 a
nd
5.
59s for the
rotor
spe
ed an
d rotor angl
e resp
on
se
s, re
spe
c
tively. Finally, the maximum mag
n
itude of the
proposed PSS is obtained at the
values of 0.466 and 0.1396 rad/
s
for the rotor speed and rotor
angle.
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Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Stability Im
provem
ent of Single Machine Us
ing ANFIS
-
PSS Based .
... (I Made Ginarsa)
323
[19]
Che
ng
D, T
a
rn T
J
, Isidori A. Globa
l E
x
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a
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Li
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nli
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i
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ans. on Auto
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9b).
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h
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ang
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9.
Abbrev
iation and Sy
mbol
ANFIS Adaptive
neu
ro-fu
z
zy
inference system
H
Inertia
co
nsta
nt
AVR
Automatic vol
t
age reg
u
lato
r
t
d
0
Dire
ct
-
a
x
i
s t
i
me con
s
t
ant
PSS
Power system stabilizer
0
Initial rotor angle
CPSS
Conventional
PSS
e
Erro
r
sig
nal
r
e
netwo
rk
re
sistance
u
(
V
pss
) Control
sig
nal
x
e
Network
re
actance
v
Ideal
co
ntrol
s
Appendix
A:
Feedb
ack-lin
eari
z
ation
For the sake of simplicity the variab
el
sin
cos
sin
cos
sin
cos
(A1)
sin
2
cos
2
2
cos
sin
(A2)
2
cos
2
2
sin
2
cos
sin
cos
sin
cos
sin
2
2
2
2
(A3)
s
i
n
2
2
6
cos
2
6
4
cos
sin
2
3
2
2
sin
cos
3
3
cos
sin
cos
sin
sin
cos
2
2
sin
cos
2
sin
cos
2
2
2
2
(A4)
sinα
co
sα
2
(A5)
co
s
sin
(A6)
Appe
ndix B
:
Con
s
tant calculation
k
1
-
k
28
′
;
′
;
′
′
;
′
;
;
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 2, June 20
14: 315 – 32
4
324
;
;
;
;
2
;
;
;
′
;
;
′
;
;
;
;
;
;
2
2
;
2
2
;
;
2
2
2
;
2
2
;
2
2
;
;
;
Evaluation Warning : The document was created with Spire.PDF for Python.