TELK
OMNIKA
Indonesian
Journal
of
Electrical
Engineering
V
ol.
14,
No
.
3,
J
une
2015,
pp
.
363
375
DOI:
10.11591/telk
omnika.v12.i9.4678
363
Fuzzy
Logic
PSS
Assisted
b
y
Neighboring
Signals
to
Mitigate
the
Electr
omec
hanical
W
a
ve
Pr
opa
gation
in
P
o
wer
Systems
Mahmoud
N.
Ali
*
F
aculty
of
Engineer
ing,
Shoubr
a,
Benha
Univ
ersity
108
Shoubr
a
st.,
Cairo
,
Egypt.
*
e-mail:
mahmoud.nour@f
eng.b
u.edu.eg
Abstract
This
paper
deals
with
the
mitigation
of
e
lectromechanical
w
a
v
e
propagation
in
po
w
er
systems
.
Dif-
f
erent
con
v
entional
controllers
addressed
this
prob
lem,
such
as
the
con
v
entional
PSS
and
the
con
v
entional
fuzzy
logic
PSS
.
In
this
paper
,
the
fuzzy
logic
PSS
is
assisted
b
y
auxiliar
y
signals
from
the
fuzzy
logic
PSS
of
the
interconnected
machines
to
augment
the
damping
of
electromechanical
w
a
v
e
propagation
and
the
associated
oscillations
.
The
neighbor
ing
machines
speed
d
e
viation
and
its
der
iv
ativ
es
signals
are
e
xploited
through
the
fuzzy
logic
PSS
to
assist
the
local
fuzzy
logic
PSS
.
The
disturbance
propagation
and
reflection
phenomena
are
considered
in
the
desig
n
of
the
adopted
str
ategy
.
The
efficacy
of
the
proposed
assistance
of
the
con
v
entional
fuzzy
logic
PSS
are
e
xamined
through
diff
erent
sim
ulation
results
.
K
e
yw
or
ds:
Electromechanical
w
a
v
e
propagation,
fuzzy
logic
PSS
,
interconnected
machines
Cop
yright
c
2015
Institute
of
Ad
v
anced
Engineering
and
Science
.
All
rights
reser
v
ed.
1.
Intr
oduction
P
o
w
er
systems
are
contin
ually
subjected
to
diff
erent
co
ntingencies
and
r
andom
e
v
ents
.
The
po
w
er
balance
betw
een
gener
ation
and
loads
is
essential
to
get
a
stab
le
oper
ation
of
a
po
w
er
system.
The
mismatch
betw
een
the
gener
ator
mechanical
and
el
ectr
ical
po
w
er
f
orces
the
gener
ator
rotor
to
de
viate
from
the
synchronous
ref
erence
fr
ame
.
This
elect
romechanical
distur-
bance
propagates
throug
h
the
entire
netw
or
k
as
an
electromechanical
w
a
v
e
with
a
cer
tain
speed
of
propagation
[1]
[2].
Sim
ulation
results
[3]
[4]
and
e
xper
imental
obser
v
ations
[5]
emphasiz
ed
this
phenomenon,
where
its
speed
of
propagation
depends
on
the
gener
ators
and
tr
ansmission
system
par
ameters
[2].
The
propagat
ion
of
the
electromechanical
w
a
v
e
stresses
diff
erent
equipments
in
po
w
er
systems
,
e
.g.
gener
ators
and
tr
ansf
or
mers
.
The
protection
systems
ma
y
be
subjected
to
a
tem-
por
ar
y
violation
of
their
limits
which
ma
y
cause
une
xpected
gener
ator
and/or
tr
ansmission
line
tr
ipping,
and
consequently
,
the
cascading
f
ailure
occurs
[6].
Pre
v
entiv
e
and
emergency
control
str
ategies
w
ere
used
to
a
v
oid
the
dr
a
wbac
ks
of
the
electromechanical
w
a
v
e
propa
gation
[7]
[8].
The
pre
v
entiv
e
control
str
ategies
urge
to
oper
ate
the
system
with
high
secur
ity
margins
to
decrease
the
possibility
of
gener
ator
tr
ipping.
The
emer-
gency
control
str
ategies
tak
e
th
e
suitab
le
actions
in
case
of
sensing
the
in
itiation
of
a
disturbance
to
lessen
the
potential
eff
ect
of
its
propagation
[8].
The
con
v
entional
po
w
er
system
stabiliz
er
(PSS)
has
been
used
man
y
y
ears
ago
to
dampen
electromechanical
oscillations
in
po
w
er
systems
.
It
acts
through
the
e
xcitation
system
in
such
a
w
a
y
that
the
speed
de
viation
gener
ates
a
component
of
electr
ical
torque
to
assist
the
damping
torque
,
where
the
lac
k
of
sufficient
damping
torque
results
in
o
sc
i
llator
y
instability
[9].
PSS
is
also
used
to
mitigate
the
spatial
propagation
of
the
electromechanical
disturbance
in
po
w
er
sys-
tems
[10].
Based
on
wide
area
measurements
(W
AM),
some
impro
v
ements
of
the
con
v
entional
PSS
w
ere
proposed
through
centr
aliz
ed
and
decentr
aliz
ed
str
ategies
to
m
itigate
the
electromechanical
Receiv
ed
F
ebr
uar
y
19,
2015;
Re
vised
Ma
y
1,
2015;
Accepted
Ma
y
14,
2015
Evaluation Warning : The document was created with Spire.PDF for Python.
364
ISSN:
2302-4046
disturbance
propagation
in
po
w
er
systems
[11]
[12].
The
con
v
entional
fuzzy
logic
po
w
er
sys-
tem
stabiliz
er
(FLPSS)
w
as
eff
ectiv
ely
emplo
y
ed
to
e
xt
inguish
the
propagated
electromechanical
disturbance
in
po
w
er
systems
[12].
In
[13],
a
z
ero
reflection
controller
str
ategy
to
quench
the
propagation
of
electromechani-
cal
disturbance
w
as
proposed.
The
str
ategy
in
[13]
w
as
analogous
to
the
impedance
matching
to
inhibit
reflection
of
tr
a
v
eling
electromagnetic
w
a
v
es
in
tr
ansmission
lines
.
As
the
disturbance
occurs
at
an
y
place
of
the
system
tends
to
propagate
to
the
entire
system
and
tends
to
be
reflected
upon
reaching
the
system
boundar
ies
,
the
proposed
str
ategy
in
this
paper
e
xploits
this
nature
of
th
e
disturbance
.
As
the
speed
de
viation
gener
ates
a
propor-
tional
component
of
electr
ical
torque
through
the
con
v
entional
PSS
or
through
the
con
v
entional
fuzzy
logic
PSS
,
the
neighbor
ing
speed
de
viation
signal
cou
ld
be
e
xploited,
through
a
FLPSS
,
to
gener
ate
electr
ical
torque
to
suppor
t
damping
of
the
coming
and
reflected
disturbance
.
F
rom
the
vie
wpoint
of
disturbance
location,
the
nearest
to
the
first
place
of
disturbance
are
the
f
oremost
machines
,
and
the
late
s
t
machines
are
the
fur
thest.
Th
rough
the
FLPSS
,
the
speed
de
viation
signals
of
the
f
oremost
machines
can
assist
the
damping
of
the
propagated
disturbance
in
the
later
machines
.
With
the
order
re
v
ersed,
t
he
speed
de
viation
signals
of
the
latest
machines
also
can
assist
the
f
oremost
machines
,
through
the
FLPSS
,
to
atten
uate
the
reflected
disturbance
.
The
paper
is
organiz
ed
as
f
ollo
ws
.
Section
2.
introduces
the
system
modeling
and
f
or-
malization
of
the
prob
lem
of
electromechanical
w
a
v
e
propagation.
Section
3.
demonstr
ates
the
proposed
str
ategy
to
impro
v
e
the
mitigation
of
electromechanical
w
a
v
e
propagation.
Section
4.
presents
a
perf
or
mance
e
v
aluation
of
the
proposed
str
ategy
.
Finally
,
Section
5.
concludes
.
The
appendix
presents
the
par
ameters
of
the
benchmar
k
po
w
er
system
used
in
the
sim
ulations
.
2.
System
modeling
and
pr
ob
lem
f
ormalization
This
section
introduces
the
detailed
gener
ator
modeling
and
the
fuzzy
logic
based
po
w
er
system
stabiliz
er
control.
Some
dr
a
wbac
ks
of
the
the
prob
lem
of
electromechanical
w
a
v
e
propa-
gation
are
e
xplained.
2.1.
Generator
modeling
Diff
erent
models
can
represent
synchronous
machines
depending
on
the
deg
ree
of
de-
tails
[9]
[14].
The
adopted
detailed
model
ar
e
represented
b
y
the
f
ollo
wing
dynamic
equations
[14]:
_
E
0
q
=
1
T
0
d
0
(
E
0
q
+
(
x
d
x
d
)
i
d
+
E
f
d
)
(1)
_
E
0
d
=
1
T
0
q
0
(
E
0
d
(
x
q
x
q
)
i
q
)
(2)
_
=
!
0
!
(3)
_
!
=
1
2
H
(
T
m
T
e
D
!
)
(4)
T
e
=
E
0
d
i
d
+
E
0
q
i
q
+
(
x
d
x
q
)
i
d
i
q
(5)
i
q
=
<
e
f
1
r
a
+
j
x
[(
E
0
q
+
j
E
0
d
)
(
v
q
+
j
v
d
)]
g
(6)
i
d
=
=
m
f
1
r
a
+
j
x
[(
E
0
q
+
j
E
0
d
)
(
v
q
+
j
v
d
)]
g
(7)
where
E
0
q
is
the
q-axis
inter
nal
v
oltage
in
pu
,
E
d
0
is
the
d-axis
inter
nal
v
oltage
in
pu
,
v
q
is
the
q-axis
ter
minal
v
oltage
in
pu
,
v
d
is
the
d-axis
ter
minal
v
oltage
in
pu
,
i
q
is
the
q-axis
current
in
pu
,
i
d
is
the
d-axis
current
in
pu
,
T
m
is
the
mechanical
torque
in
pu
,
T
e
is
the
electr
ical
torque
in
pu
,
E
f
d
is
the
field
v
oltage
in
pu
,
is
the
rotor
angle
in
r
ad
,
!
is
the
speed
de
viation
in
pu
,
!
0
is
the
rotor
r
ated
angular
speed
in
r
ad=s
,
x
d
is
the
d-axis
tr
ansient
reactance
in
pu
,
x
=
x
d
=
x
q
,
x
d
is
TELK
OMNIKA
V
ol.
14,
No
.
3,
J
une
2015
:
363
375
Evaluation Warning : The document was created with Spire.PDF for Python.
TELK
OMNIKA
ISSN:
2302-4046
365
the
d-axis
synchronous
reactance
in
pu
,
x
q
is
the
q-axis
tr
ansient
reactance
in
pu
,
x
q
is
the
q-axis
synchronous
reactance
in
pu
,
r
a
is
the
gener
ator
inter
nal
resistance
in
pu
,
T
0
d
0
is
the
ope
n
circuit
d-axis
time
constant
in
s
,
T
0
q
0
is
the
open
circuit
q-axis
time
constant
in
s
and
D
is
the
damping
constant
in
pu
.
2.2.
Generator
contr
ol
and
fuzzy
logic
PSS
T
o
counter
act
the
rotor
angle
and
speed
de
viations
,
induced
from
the
gener
ator
po
w
er
imbalance
,
tw
o
pr
incipal
controls
ha
v
e
been
e
v
olv
ed
f
or
synchronous
gener
ato
rs
,
which
are
the
pr
ime
mo
v
er
control
and
e
xcitation
control.
The
mathematical
models
of
these
controllers
can
be
f
ound
in
[9]
[14].
Con
v
entionally
,
PSS
is
added
to
the
e
xcitation
system
to
dampen
po
w
er
system
oscilla-
tions
.
A
fine
tuning
of
PSS
par
ameters
giv
es
a
satisf
actor
y
atten
uation
of
the
electromechanical
disturbance
propagation
in
po
w
er
systems
[10]
[12]
.
Fuzzy
logic
po
w
er
system
stabiliz
er
can
replace
the
con
v
entional
PSS
and
can
pro
vide
more
satisf
actor
y
damping
f
or
diff
erent
modes
of
electromechanical
oscillations
[15]
[16]
and
f
or
the
disturbance
propagation
in
po
w
er
systems
[12].
The
con
v
entional
PSS
emplo
ys
fix
ed
par
ameter
model
based
on
system
linear
ization
or
optimization
methods
.
Such
a
fix
ed-par
ameter
PSS
is
widely
used
in
po
w
er
systems
and
has
made
a
g
reat
contr
ib
ution
in
enhancing
po
w
er
system
dynamics
[17].
As
po
w
er
systems
are
dynamic
systems
and
their
oper
ation
is
of
a
stochastic
nature
,
the
con
v
entional
fix
ed-par
ameter
PSS
can
be
replaced
b
y
a
fuzzy
logic
based
PSS
[18].
Fuzzy
logic
is
con
s
i
dered
as
a
po
w
erful
tool
in
encounter
ing
challenging
prob
lems
in
po
w
er
systems
because
of
its
capability
to
handle
imprecise
,
v
ague
or
’fuzzy’
inf
or
mation
[19].
Fuzzy
logic
implements
human
e
xper
iences
and
pref
erences
with
the
adjustment
of
membership
functions
and
fuzzy
r
ules
.
Fuzzy
membership
functions
can
ha
v
e
diff
erent
shapes
,
e
.g.,
tr
iangular
,
tr
apez
oidal
or
Gaussian,
depending
on
the
pref
erence
and/or
the
e
xper
ience
of
the
designer
.
The
fuzzy
r
ules
,
which
descr
ibe
relationships
in
a
linguistic
sense
,
are
typically
wr
itten
as
antecedent
consequent
pairs
of
(IF-THEN)
statements
.
A
b
loc
k
diag
r
am
of
a
fuzzy
controller
is
sho
wn
in
Figure
1
[20],
in
which
the
input
and
the
output
of
the
fuzzy
controller
are
cr
isp
.
The
fuzzification
process
con
v
er
ts
each
piece
of
input
data
to
deg
rees
of
membership
.
The
r
ule
base
introduces
the
designer’
s
e
xper
ience
in
linguistic
relationships
.
In
the
inf
erence
engine
,
the
application
of
an
implication
method
and
the
agg
regation
of
all
outputs
,
related
to
the
fuzzy
r
ules
,
are
perf
or
med
to
get
the
output
fuzzy
set.
The
resulting
fuzzy
set
m
ust
be
con
v
er
ted
to
a
n
umber
that
can
be
sent
to
the
process
as
a
control
signal,
which
is
called
the
defuzzification
oper
at
ion.
All
the
processes
in
the
dashed
bo
x
(see
Figure
1)
are
called
fuzzy
inf
erence
system
[21]
[22].
I
nput
(
c
r
i
s
p)
F
uz
z
i
f
i
c
a
t
i
o
n
O
ut
pu
t
(
c
r
i
s
p)
D
e
f
uz
z
i
f
i
c
a
t
i
o
n
R
ul
e
ba
s
e
I
n
f
e
r
e
nc
e
e
ng
i
ne
Figure
1.
Bloc
k
diag
r
am
of
a
fuzzy
controller
.
Empir
ical
kno
wledge
and
engineer
ing
intuition
pla
y
an
impor
tant
role
in
choosing
the
lin-
guistic
v
ar
ia
b
les
and
their
membership
functions
.
Based
on
the
pre
vious
e
xper
iences
introduced
in
[23]
[24]
[18],
the
input
signals
are
chosen
as
speed
de
viation
(
!
)
and
its
der
iv
ativ
e
(
_
!
)
and
the
output
signal
(
V
f
l
pss
)
is
added
to
the
e
xcitation
system
ref
erence
v
oltage
.
The
speed
Evaluation Warning : The document was created with Spire.PDF for Python.
366
ISSN:
2302-4046
de
viation
der
iv
ativ
e
(
_
!
)
can
be
calculated
from
the
f
ollo
wing
relation
[23]:
_
!
=
!
n
+1
!
n
t
(8)
where
!
n
is
the
speed
de
viation
at
step
n
,
!
n
+1
is
the
speed
de
viation
at
step
n
+
1
and
t
is
time
of
step
of
integ
r
ation.
2.3.
The
electr
omec
hanical
wa
ve
pr
opa
gation
pr
ob
lems
The
phenomenon
of
electromechanical
w
a
v
e
propagation
has
significant
eff
ects
on
the
po
w
er
systems
and
their
protection
systems
.
As
the
disturbance
propagation
imposes
a
de
viation
of
the
gener
ator’
s
rotor
angle
from
its
steady-state
v
alue
,
the
po
w
er
tr
ansf
ers
in
the
netw
or
k
is
disturbed.
The
po
w
er
flo
w
betw
een
b
us
i
and
b
us
j
in
a
pure
inductiv
e
line
is
giv
en
b
y
th
e
f
ollo
wing
relation:
P
f
ij
=
P
max
sin
ij
0
(9)
where
P
f
ij
is
the
po
w
er
flo
w
betw
een
b
us
i
and
b
us
j
,
ij
0
is
the
steady
state
angle
diff
erence
and
P
max
is
the
maxim
um
po
w
er
tr
ansf
er
,
which
is
giv
en
b
y
the
f
ollo
wing
relation:
P
max
=
j
V
g
i
jj
V
g
j
j
X
ij
(10)
where
j
V
g
i
j
and
j
V
g
j
j
are
the
magnitude
of
the
inter
nal
v
oltage
of
the
tw
o
machines
i
and
j
and
X
ij
is
the
reactance
of
the
connecting
line
.
Thus
,
the
de
viation
in
rotor
angle
results
in
a
change
in
po
w
er
tr
ansf
er
,
which
could
be
significant
and
could
impact
the
po
w
er
system
oper
ation
[12].
The
eff
ects
of
the
electromechanical
disturbance
propagation
on
protection
systems
w
ere
presented
in
[25],
where
such
a
propagation
often
e
xposes
remote
rela
ying
systems
to
f
alse
re-
sponses
.
The
de
viation
in
the
po
w
er
flo
w
causes
a
de
viation
in
the
current,
which
aff
ects
the
op-
er
ation
of
the
o
v
er-current
rela
ys
and
also
aff
ects
the
apparent
impedance
which,
consequently
,
aff
ects
the
oper
ation
of
the
distance
rela
ys
[25].
The
propagation
of
the
electromechanical
dis-
turbance
ma
y
tr
ip
o
v
er-current
rela
ys
and/or
distance
rela
ys
because
of
the
tr
ansient
violation
of
their
pic
k-up
settings
.
This
unplanned
tr
ipping
of
protection
rela
ys
could
disconnect
one
or
some
components
of
the
po
w
er
system,
which
ma
y
lead
to
other
disturbances
[12].
3.
Pr
oposed
strategy
of
assisted
FLPSS
In
the
proposed
str
ategy
,
the
phenomenon
of
propagation
and
reflection
of
electrome-
chanical
w
a
v
e
in
po
w
er
systems
a
re
e
xploited.
The
str
ategy
is
based
on
the
injection
of
the
output
signal
of
neighbor
ing
FLPSS
as
e
xtr
a
inputs
to
the
e
xcitation
system
besides
the
FLPSS
of
the
local
machine
to
impro
v
e
the
dampin
g
of
electromechanical
w
a
v
e
propagation
and
the
associated
oscillations
.
More
specifically
,
the
e
xcitation
system
of
machine
(
n
)
has
m
ulti
FLPSS
signals
,
which
are
the
local
FLPSS
signal
(
V
f
l
pss
n
)
and
the
FLPSS
signals
of
all
electr
ically
connected
machines
(
V
f
l
pss
m
)
w
eighted
b
y
a
gain
K
m
as
sho
wn
in
Figure
2.
The
same
str
ategy
is
applied
at
all
other
machines
.
Basing
on
the
phenomenon
of
disturbance
propagation
and
i
ts
reflection
upon
reaching
system
boundar
ies
,
this
str
ategy
is
de
v
eloped.
Suppose
that
machine
n
is
electr
ically
connected
to
machine
m
(which
represents
one
or
more
machines)
and
it
is
firstly
subjected
to
a
disturbance
.
The
FLPSS
of
machine
n
add
e
xtr
a
damping
through
the
e
xcitation
system
of
machine
m
besides
the
local
FLPSS
of
this
machine
to
coun
ter
act
the
propagated
disturbance
.
Also
,
the
FLPSS
of
machine
m
add
e
xtr
a
damping
besides
the
local
FLPSS
of
machine
n
,
through
the
e
xcitation
system,
to
counter
act
the
reflected
disturbance
.
This
inter-assistance
betw
een
the
interconnected
machines
helps
in
damping
the
propagated
and
the
reflected
disturbance
.
Nor
mally
,
a
time
dela
y
is
implied
f
or
the
disturbance
to
reach
diff
erent
machines
,
where
,
the
f
oremost
aff
ected
machines
are
the
nearest
to
the
f
ault
location
and
the
last
aff
ected
machines
are
the
most
f
ar
.
This
can
TELK
OMNIKA
V
ol.
14,
No
.
3,
J
une
2015
:
363
375
Evaluation Warning : The document was created with Spire.PDF for Python.
TELK
OMNIKA
ISSN:
2302-4046
367
_
_
n
m
Figure
2.
A
schematic
diag
r
am
of
the
proposed
str
ategy
of
modifications
of
the
fuzzy
logic
PSS
.
be
disregarded
f
or
neighbor
ing
machines
with
small
electr
ical
distance
,
where
the
time
dela
y
is
small.
T
o
adjust
the
gains
K
n
and
K
m
,
an
optimization
toolbo
x
of
MA
TLAB
(FMINCON)
is
used
to
minimiz
e
an
objectiv
e
function,
F
obj
,
which
is
giv
en
as
f
ollo
ws:
F
obj
=
n
X
i
=1
Z
t
f
0
(
!
i
)
2
dt
(11)
where
n
is
the
total
n
umber
of
machines
in
oper
ation
and
t
f
is
the
per
iod
of
sim
ulation.
4.
P
erf
ormance
e
v
aluation
of
the
pr
oposed
strategy
This
section
presents
the
perf
or
mance
e
v
aluation
of
the
proposed
str
ategy
through
the
sim
ulation
of
the
unif
or
m
tw
o-dimensional
(2-D)
model
[11].
The
perf
or
mance
is
quantitativ
ely
assessed
through
perf
or
mance
inde
x
es
.
4.1.
unif
orm
2-D
system
A
gener
al
regular
tw
o-dimension
(2-D)
g
r
id
is
sho
wn
in
Figure
3.
It
consists
of
8
8
nodes
,
where
one
gener
ator
and
a
shunt
load
ar
e
connected
to
each
node
.
The
model
has
identical
tr
ansmission
lines
connecting
tw
o
adjacent
nodes
Z
tl
,
and
identical
loads
at
each
node
,
which
is
modeled
as
constant
impedance
Z
l
.
The
disturbance
is
initiated
through
a
sequence
of
e
v
ents
as
f
ollo
ws:
Bef
ore
t
=
0
:
1
s
,
the
system
is
in
steady
state
.
At
t
=
0
:
1
s
,
the
gene
r
ator
(1
;
1)
,
which
has
coordinates
in
the
g
r
id
x
=
1
,
y
=
1
,
is
lost.
The
initiated
disturbance
propagates
to
the
entire
netw
or
k
in
tw
o
dimensions
x
and
y
.
The
propagated
disturbance
in
rotor
angle
and
rotor
speed
of
the
64
gener
ators
of
the
2-D
model
are
sho
wn
in
Figures
4
and
5,
where
all
the
machines
are
equipped
with
the
pr
ime
mo
v
er
controller
and
the
e
xcitation
system
without
FLPSS
.
These
Figures
sho
w
that
the
distur-
bance
occurs
at
the
first
location
causes
the
electromechanical
oscillation
near
this
location.
It
propagates
allo
v
er
the
netw
or
k
causing
oscillations
at
each
gener
ator
and
upon
reaching
bound-
ar
ies
,
it
is
reflected
bac
k
to
the
first
place
causing
a
ne
w
disturbance
propagating
to
the
entire
netw
or
k.
4.2.
Application
of
the
con
ventional
FLPSS
to
the
unif
orm
2-D
system
F
or
the
studied
test
system,
se
v
en
linguistic
v
ar
iab
les
are
proposed
f
or
each
input
and
output
v
ar
iab
les
,
which
are:
LP
(large
positiv
e),
MP
(medium
positiv
e),
SP
(small
positiv
e),
VS
(v
er
y
small),
SN
(small
negativ
e),
MN
(medium
negativ
e)
and
LN
(large
negativ
e)
[23].
The
typical
membership
functions
ma
y
be
chosen
as
tr
iangular
,
tr
apez
oidal,
bell
shaped,
etc.
In
the
sim
ulation
of
the
application
of
the
FLPSS
to
the
2-D
test
system,
a
bell
shaped
mem-
Evaluation Warning : The document was created with Spire.PDF for Python.
368
ISSN:
2302-4046
Figure
3.
P
o
w
er
system
netw
or
k
sim
ulated
arr
anged
in
a
g
r
id
of
tw
o
dimensions
.
bership
functions
are
chosen
f
or
all
t
he
inputs
and
output
v
ar
iab
les
.
The
membership
functions
of
the
tw
o
inputs
(
!
and
_
!
)
and
the
output
(
V
f
l
pss
)
are
sho
wn
in
Figures
6
and
7,
respectiv
ely
.
A
set
of
r
ules
,
which
defines
the
relation
betw
een
the
inputs
and
the
output
of
the
FLPSS
is
e
xtr
acted
from
the
pre
vious
e
xper
ience
of
designing
th
e
PSS
[18]
[23]
[24],
which
are
presented
in
T
ab
le
1.
T
ab
le
1.
Decision
tab
le
f
or
the
output
of
fuzzy
logic
PSS
.
P
P
P
P
P
P
P
P
!
_
!
LN
MN
SN
VS
SP
MP
LP
LP
VS
SP
MP
LP
LP
LP
LP
MP
SN
VS
SP
MP
MP
LP
LP
SP
MN
SN
VS
SP
SP
MP
LP
VS
MN
MN
SN
VS
SP
MP
MP
SN
LN
MN
SN
SN
VS
SP
MP
MN
LN
LN
MN
MN
SN
VS
SP
LN
LN
LN
LN
LN
MN
SN
VS
There
are
diff
erent
methods
f
or
finding
the
fuzzy
output,
e
.g.,
minim
um-maxim
um
and
maxim
um-product
methods
[22]
[23].
In
these
sim
ulations
,
the
minim
um-maxim
um
method
is
adopted.
The
fuzzy
output
of
each
r
ule
is
obtained
and
all
outputs
are
agg
regated
and
defuzzified
to
get
the
final
output
of
the
FLPSS
.
There
are
diff
erent
techniques
f
or
defuzzification
of
fuzzy
quantities
such
as
the
maxim
um
method,
the
height
method,
and
the
centroid
method,
where
the
later
is
the
most
widespread
one
,
and
it
is
adopted
in
these
sim
ulations
.
4.3.
Application
of
the
pr
oposed
strategy
to
the
unif
orm
2-D
system
T
o
e
v
aluate
the
application
of
the
proposed
str
ategy
,
the
rotor
angle
and
rotor
speed
de
viation
responses
are
e
xamined
to
e
v
aluate
the
eff
ectiv
eness
of
this
str
ategy
.
First,
the
responses
of
all
rotor
angles
,
ref
erred
to
the
angle
of
machine
(8,8),
and
rotor
TELK
OMNIKA
V
ol.
14,
No
.
3,
J
une
2015
:
363
375
Evaluation Warning : The document was created with Spire.PDF for Python.
TELK
OMNIKA
ISSN:
2302-4046
369
Figure
4.
Propagation
of
electromechanical
w
a
v
e
in
rotor
angle
,
ref
erred
to
the
rotor
angle
of
machine
(8
;
8)
,
throughout
the
2-D
test
system
without
FLPSS
.
Figure
5.
Propagation
of
electromechanical
w
a
v
e
in
rotor
speed
throughout
the
2-D
test
po
w
er
system
without
FLPSS
.
speed
de
viation,
when
applying
the
con
v
entional
FLPSS
,
are
sho
wn
in
Figures
8
and
9
respec-
tiv
ely
.
When
applying
the
proposed
str
ategy
,
introduced
in
section
3.,
the
ne
w
responses
of
machines’
angles
and
speed
de
viations
are
sho
wn
in
Figures
10
and
11
respectiv
ely
.
Putting
Figures
8,
9,
10
and
11
in
perspectiv
e
,
sho
ws
the
impro
v
ement
achie
v
ed
when
applying
the
proposed
str
ategy
of
the
FLPSS
.
T
o
allo
w
a
quantitativ
e
e
v
aluation
of
the
the
proposed
str
ategy
,
perf
or
mance
inde
x
es
(
t
)
and
!
(
t
)
are
proposed.
The
y
are
defined
as
f
ollo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
370
ISSN:
2302-4046
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
0
0.2
0.4
0.6
0.8
1
∆
ω
Degree of membership
LN
MN
SN
VS
SP
MP
LP
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0
0.2
0.4
0.6
0.8
1
d(
∆
ω
)/dt
Degree of membership
LN
MN
SN
VS
SP
MP
LP
Figure
6.
Membership
function
of
the
fuzzy
inp
uts
(the
speed
de
viation
(
!
)
and
the
der
iv
ativ
e
of
speed
de
viation
(
_
!
)).
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
0
0.2
0.4
0.6
0.8
1
∆
V
flpss
Degree of membership
LN
MN
SN
VS
SP
MP
LP
Figure
7.
Membership
function
of
the
fuzzy
output
(
V
f
l
pss
).
TELK
OMNIKA
V
ol.
14,
No
.
3,
J
une
2015
:
363
375
Evaluation Warning : The document was created with Spire.PDF for Python.
TELK
OMNIKA
ISSN:
2302-4046
371
Figure
8.
Rotor
angle
response
f
or
all
machine
(ref
err
ed
to
machine(8,8))
with
applying
the
con-
v
entional
FLPSS
.
Figure
9.
Rotor
speed
de
viation
of
all
machines
with
applying
the
con
v
entional
FLPSS
.
(
t
)
=
n
X
i
=1
(
i
(
t
)
C
O
I
(
t
))
2
(12)
!
(
t
)
=
n
X
i
=1
(
!
i
(
t
)
!
C
O
I
(
t
))
2
(13)
These
perf
or
mance
inde
x
es
consider
tw
o
char
acter
istics;
First,
the
div
ergence
from
the
center
of
iner
tia
(
C
O
I
)
of
rotor
angle
and
speed
de
viation.
Second,
the
speed
of
the
controller
to
mitigate
the
disturbance
propagation
i.e
.,
the
time
required
f
or
the
perf
or
mance
inde
x
to
reach
z
ero
.
Evaluation Warning : The document was created with Spire.PDF for Python.
372
ISSN:
2302-4046
Figure
10.
Rotor
angle
of
all
machines
(ref
erred
to
machine(8,8))
when
applying
the
proposed
str
ategy
of
FLPSS
.
Figure
11.
Rotor
speed
de
viation
of
all
machines
when
applying
the
proposed
str
ategy
of
FLPSS
.
T
o
allo
w
quantitativ
e
compar
ison
betw
een
the
con
v
entional
PSS
,
the
con
v
entional
FLPSS
and
the
prop
osed
str
ategy
of
FLPSS
,
the
perf
or
mance
inde
x
es
f
or
speed
de
viation
and
f
or
rotor
angle
are
presen
ted
in
Figures
12
and
13
respectiv
ely
.
A
lthough
the
con
v
entional
FLPSS
in-
troduces
some
damping
f
or
the
propagation
of
electromechanical
w
a
v
e
,
the
proposed
str
ategy
of
FLPSS
add
an
additional
damping
f
or
this
propagation
and
f
or
the
associated
oscillations
.
TELK
OMNIKA
V
ol.
14,
No
.
3,
J
une
2015
:
363
375
Evaluation Warning : The document was created with Spire.PDF for Python.