In
te
r
n
ation
a
l Jou
rn
al
of Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJPED
S
)
V
o
l.
11, N
o
.
1, Mar
c
h 20
20,
p
p
.
302~
3
0
8
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v11
.
i
1.pp
3
02-
30
8
3
02
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
Differen
tial game theory with
FP
A optimi
zation in multi-area
p
o
wer system
S
.
Kh
ad
arval
i
1
, V.
M
a
dhusu
d
ha
n
2
, R
.
Kiranmayi
3
1,
3
Dep
a
rt
m
e
nt
o
f
Electri
cal an
d Elect
roni
cs
Engineerin
g,
J
a
wah
a
rlal
Nehru
Tech
no
log
i
cal Univ
ersity,
India.
2
Dep
a
rtm
e
n
t
o
f
Elect
rical
and
Electron
i
cs
En
gi
ne
erin
g,
VN
R VJ
IET,
India.
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Au
g
2
7
,
2
019
Re
vise
d N
ov
9
,
2019
A
c
c
e
pte
d
D
ec
2, 201
9
Th
e di
s
t
rib
u
tion
g
e
nerati
on
pen
e
trat
ion
i
n
creases
d
u
e t
o
t
h
e
increas
ed n
eed
of
po
wer.
T
h
ese penet
r
atio
n cau
ses p
r
ob
le
m
o
f
f
r
eq
uen
c
y dev
i
at
ion
s
.
In this
pap
e
r th
e in
m
u
l
t
i
-
are
a
po
wer sy
st
em th
e
com
b
inatio
n
of
renew
a
bl
e
energy
reso
urces i
s
propos
ed.
H
e
re
t
h
e
area
1
& area
2 are
t
h
erm
a
l p
o
wer pl
ant.
Hy
dro
po
wer generat
i
o
n
p
l
ant is
tak
e
n in
area-3 &
area
-4. Rene
wab
l
e energy
sy
st
e
m
i
s
con
s
idered
i
n
area-5.
H
e
re
t
h
e cyb
e
r security
attack
is
t
a
ken
as
chan
ge i
n
power
i
n
th
e
entire
a
r
ea
.
This can
make
th
e
power blo
c
k
out o
r
wro
n
g
data
e
n
try
.
Here d
i
ff
eren
tia
l
gam
e
t
h
eo
ry
-bas
ed p
r
obl
em
f
o
rm
u
l
ati
o
n
is do
ne. The
P
I
co
nt
ro
l
l
er and
diff
erential game theory w
i
th
flower
pollinat
ion are
c
o
mpared f
o
r
perf
or
ma
nce of
f
a
s
t
res
ponse
. The
MAT
L
AB
20
17
b is u
s
ed
f
o
r b
u
ild
in
g
t
h
e areas
and
pro
g
ram
m
i
n
g
t
h
e al
go
rithm
.
K
eyw
ord
s
:
F
l
ow
e
r
poll
i
na
t
i
o
n
op
tim
i
z
a
t
ion
Game
t
h
eo
r
y
Lo
ad
f
r
eq
u
e
n
c
y
co
nt
rol
Mu
lt
i-ar
ea
power
syst
e
m
D
i
ffe
re
nt
ia
l G
a
me
theor
y
Th
is
is a
n
o
p
en acces
s a
r
ti
cle u
n
d
e
r t
h
e
CC
B
Y
-S
A
li
cens
e
.
Corres
pon
d
i
n
g
Au
th
or:
S. K
h
a
d
arva
li,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
and Ele
c
t
ron
i
cs
E
n
gi
nee
r
i
n
g
,
Jaw
a
harlal
N
e
hru
Tech
no
l
o
g
i
cal U
n
ive
r
sit
y
,
A
n
an
ta
pur
am
u
,
India.
Em
ail: kha
dar.
vl
@
g
ma
i
l
.
c
om
1.
I
N
TR
OD
U
C
TI
O
N
The
p
o
w
e
r syst
e
m
sec
u
rit
y
is very impor
t
a
nt
iss
u
e n
o
w
a
da
ys a
s
the dis
t
r
i
bu
t
i
o
n
ge
nera
ti
on
pene
tr
at
ion.
Even
sma
l
l c
o
m
p
o
n
e
n
t
fa
il
ure
bri
ngs
mor
e
lo
ss in pow
er
. Thi
s
m
a
y
affect
the
com
p
le
te pow
e
r
syste
m
.
The
w
i
de
a
r
ea
c
o
n
t
r
o
l
and
m
oni
t
o
ri
n
g
pr
od
uc
es
the
se
curi
ty
in
rec
e
nt
p
o
w
e
r
syst
em
s. F
o
r
that
p
h
as
or
me
asure
m
e
n
t
(P
MU
)
uni
t
s
,
circui
t bre
a
ker
s
and
dis
t
r
i
b
u
te
d
g
e
nera
t
o
rs us
es the c
o
mm
u
n
ica
t
io
n i
n
t
e
rfa
ces to
ma
ke sure the syste
m
secur
i
t
y
.
The
s
e
se
curi
ty
s
y
s
t
em
s
use c
y
be
r ne
tw
ork
as com
m
unica
tio
n pro
t
oco
l
t
h
er
e i
s
a poss
i
b
i
lit
y of cybe
r-a
t
t
a
c
k
.
A
ttac
k
e
r
s i
n
je
c
t
false da
ta i
n
j
ecti
o
n
a
s
disc
u
ssed i
n
[1].
Eaves
d
rop
p
i
n
g
e
s
t
i
m
a
t
e
in [2]
den
i
es
t
h
e se
rvice
a
tta
ck
o
n
the
c
o
m
m
unic
a
t
ion
me
dium
as in [
3
]. A
n
al
ysi
s
of
ris
k
is d
one
in
[4-
6
].
R
e
ce
ntl
y
t
h
e
c
yber
-
at
tac
k
is d
o
ne
in the wea
k
er system
. The bi
nary o
n
-o
ff puls
e
s ar
e c
r
eated i
n
[7] as
cybe
r-
attac
k
w
h
ic
h
ca
n trip
g
e
nera
t
o
r
s
. F
a
lse
data
in
jec
t
io
n m
a
ke
s the
P
M
U
to pr
ovide
w
r
on
g
data
t
o
pow
e
r
syste
m
con
t
ro
l. This c
a
uses t
h
e c
e
ntr
a
l c
o
n
t
r
o
l un
i
t
to o
p
era
t
e
fa
l
s
e
l
y.
Thi
s
cause
s
b
l
a
c
k
o
u
t
s
an
d ec
on
omica
l
losses
[8].
In [11] it
is disc
ussin
g
t
h
a
t
ste
a
lth
y attac
k
mode
l
w
h
ich
c
o
rrupts
t
h
e sma
r
t
cir
c
uit
br
ea
kers.
The
v
a
ria
t
io
n of
r
e
new
a
b
l
e
ener
g
y
r
e
sourc
e
s
due
t
o
na
t
u
re the pow
e
r
sys
t
em
must be
ca
pab
l
e of
adj
u
s
tin
g t
h
e outp
u
t co
n
t
ro
l of mult
i
a
r
ea
pow
e
r
syst
e
m
.
Gener
a
l
l
y, the p
o
w
e
r system
cons
i
s
ts
o
f
c
o
al,
hydr
o
and
gas. Man
y
m
e
tho
d
s
a
r
e use
d
to c
o
n
t
ro
l
t
h
e pow
e
r
system
i
n
mul
t
i
ar
ea
[12,
1
7
-2
5
]
. In [13,1
4
] kee
p
in
g
con
t
ro
ls as
sam
e
m
u
lt
i
are
a
w
ith
mult
ip
le
source
s ar
e c
o
n
s
ide
r
ed.
I
n
th
is pa
pe
r
th
e fl
ow
e
r
pol
l
i
n
a
tio
n o
p
tim
i
z
a
t
io
n
al
g
o
ri
thm i
s
used for so
l
v
i
ng the
gam
e
th
eory base
d
ob
jec
t
i
v
e fu
nc
tio
ns. A
nd here
th
e
d
i
str
i
bu
t
i
o
n
sys
t
em
is co
ns
idere
d
w
i
th m
u
lt
i
are
a
pow
er
syste
m
c
onsis
t o
f
hy
dro an
d s
t
ea
m uni
t. The
ch
ange
s
in so
lar
sys
t
em
cr
eate
s
t
h
e
sy
ste
m
t
o
be w
eak.
It m
a
kes t
h
e gr
id a
s
prey
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
r
i
S
y
st
IS
S
N
:
2088-
86
94
D
i
f
f
e
r
e
n
t
i
al
ga
m
e
theory
w
ith
FP
A opt
i
m
i
z
a
t
i
o
n
i
n
m
u
l
t
i-
ar
e
a
po
wer sys
t
e
m
(S.
Khadar
v
a
l
i
)
3
03
for cyber
-
at
tac
k
s.
The new
s
o
l
u
ti
on me
th
o
d
give
s
t
h
e
faster response
i
n
tha
t
con
d
i
t
i
on
c
o
mpa
r
ed to ol
d
me
tho
d
s.
It reduc
es
t
h
e vu
lne
r
abi
l
ity o
f
a
t
ta
c
k
.
Th
is pape
r i
s
orga
n
i
z
e
d l
i
ke Con
t
ro
ller
t
desig
n
in
se
ct
ion 2,
F
l
ow
er
p
o
ll
i
n
at
ion a
l
gor
i
t
h
m
i
n
sec
tio
n
3,
results an
d
d
i
sc
uss
i
o
n
i
n
se
ctio
n
4 and
last
sec
t
i
on w
ith c
onc
l
u
sio
n
.
2.
CONT
ROLLER D
E
S
I
GN
A
c
cordi
n
g to the pr
ob
lem
and s
itua
t
i
o
n ma
ny
ga
me
t
h
e
o
r
i
es are
a
v
aila
b
l
e.
I
n
thi
s
p
a
per,
“
t
he
no
nzer
o-s
u
m non-
c
o
o
p
era
tiv
e
differe
n
t
ia
l
ga
me
s” a
r
e used.
“
N
onze
r
o su
m”
explai
ns t
h
at it
c
o
nsis
ts of more
tha
n
tw
o pla
y
e
r
s, the
sum
of
a
l
l t
h
e
pl
a
y
ers’
in
de
x of
p
e
rfor
ma
nce
i
s
ze
ro or a
c
o
ns
tan
t
. A
nd colla
bor
a
tio
n
betw
ee
n the
p
l
a
y
e
r
s is d
i
ffic
u
l
t
to
e
n
forc
e [1
5],
hence
f
ort
h
t
h
e
pl
a
y
ers ar
e expec
t
ed
no
t
t
o
co
oper
a
te i
n
or
der
t
o
mi
ni
mi
z
e
t
h
ei
r
i
n
d
i
v
i
du
al
pe
rfo
rman
c
e
i
nde
x
.
Ta
ke a
system
w
i
t
h
N
pl
a
y
ers defi
ned b
y
t
h
e l
i
nea
r
d
i
ffere
n
tia
l
eq
ua
t
i
o
n
a
s
show
n
be
low
∑
(1)
wher
e
wher
e
∈
is state
vara
b
l
e
ve
ct
or
∈
is a
c
ont
r
o
l
st
r
a
teg
y
v
e
c
t
or use
d
by it
h
pl
aye
r
∈
a
nd
∈
a
nd ea
ch
p
l
a
y
e
r
desires to
minimiz
e
h
i
s ow
n
quadra
t
ic
P
e
rform
ance
inde
x,
i.e
., cost
func
t
i
o
n
.
In
this
p
a
per
w
e
ado
p
t
t
h
e
fo
l
l
o
w
in
g
type
co
st
func
t
i
o
n
for
si
m
p
lic
i
t
y.
(2)
wh
ere
is sym
m
e
t
r
i
c
sem
i
-po
s
i
t
i
v
e
defi
n
ite
is syme
tric
po
si
tive
def
i
n
ite
ma
t
r
i
x
Assum
e
cur
r
ent va
lu
e of sys
t
em
st
a
t
e vec
t
o
r
is ava
ila
bl
e
for all
the
p
l
aye
r
s,
then t
h
e co
ns
tan
t
li
nea
r
fe
ed
bac
k
con
t
r
o
l
s
t
rate
g
y
use
d
by i
t
h pl
a
y
er ca
n
be expre
sse
d
as
(3)
ℎ
,…
.
,
) belo
ngs t
o
t
h
e
se
t
,…,
|
∑
3.
FLOWER POLLINATIO
N
AL
GORIT
HM
The
r
e are
tw
o i
m
porta
n
t
st
e
p
s in
t
h
is
al
gor
it
h
m
as i
t
i
s
giv
e
n
in
[16], they
a
r
e
“
g
lo
ba
l pol
li
nat
i
on an
d
l
o
c
a
l
po
llin
a
t
i
o
n
”
. Th
e fi
rs
t
st
ep
a
n
d
flo
w
e
r
c
o
nst
a
n
c
y
c
a
n
b
e
re
p
r
e
s
e
n
t
e
d
mat
h
emati
c
a
lly
a
s
∗
(4)
wh
ere
x
is t
h
e
po
l
l
en i
or
sol
u
t
i
on vec
t
or x
_
i
a
t
it
e
r
a
t
i
o
n
t,
g
∗
is
the curren
t
best
solu
ti
on
f
o
u
n
d am
ong al
l
sol
u
t
i
ons
at th
e
curren
t
iterat
io
n
,
L
i
s
the
str
e
n
g
th
of
th
e poll
ina
t
io
n
,
wh
ich
essen
t
i
a
lly
is a ste
p
siz
e
.
S
i
nce inse
c
t
s
m
a
y go a lon
g
e
r dista
n
ce
w
ith va
rio
u
s d
i
s
t
a
n
ce
s/ste
p
s, it u
s
es a L´
evy fl
i
ght t
o
mim
i
c
th
i
s
char
ac
ter
i
s
tic pr
ofess
i
ona
l
l
y.
S
o
, draw L>0 from
a
levy
di
s
t
rib
u
tio
n as
show
n be
l
o
w
,
~
≫
≫
0
(5)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t J P
o
w
E
l
e
c
&
Dr
i S
y
st
V
o
l.
11,
N
o
.
1,
Mar
202
0 :
302
–
308
30
4
Pseu
do co
de
:
Objec
tiv
e
mi
n
J
i
(
x
)
,
x = (
x1,
x2,
…,
xd)
I
n
i
tia
liz
a
a
p
o
p
u
l
a
tio
n of
n fl
o
w
e
r
s
/
po
l
l
n g
a
m
etes w
i
t
h
ra
n
dom
so
lu
ti
ons
F
i
nd t
h
e
bes
t
sol
u
tio
n
g
_
in
the
i
n
iti
a
l
pop
ulat
io
n
D
e
fi
ne a
swit
c
h
prob
ab
i
l
i
ty
p
∈
0, 1
whi
l
e
(
t<
Ma
xGe
n
era
tio
n
)
for
i = 1 :
n
(a
ll
n
f
l
ow
e
rs in
th
e
p
opu
l
a
t
i
on
)
if
rand
<
p,
Draw
a
(
d-
dim
e
ns
io
n
a
l
)
ste
p
vec
t
o
r
L
wh
i
c
h
obey
s
a
L
’
e
v
y
di
st
r
i
bu
tio
n
Gl
ob
al
po
l
l
i
nat
i
o
n
v
i
a
∗
(6
)
else
D
r
aw
f
r
om
a
un
i
f
orm
distr
i
b
u
ti
on
i
n
[0,
1
]
Ra
nd
om
ly c
h
o
o
s
j an
d
k
am
o
ng al
l
so
lu
t
i
o
n
s
D
o
loc
a
l
p
o
ll
i
n
ati
on v
i
a
ℇ
End if
Ev
al
uat
e
n
e
w
so
l
u
t
i
on
s
I
f
ne
w
so
lut
i
o
n
s
are be
t
t
e
r
,
up
da
te
t
h
e
m
in
th
e
pop
u
l
a
tio
n
End fo
r
Fi
nd t
h
e
curre
nt be
st so
l
u
t
i
on
g*
End while
4.
RESU
L
T
S A
ND
DIS
C
U
S
S
I
ON
Sc
enar
i
o
1 is
ta
ken a
s
re
newa
bl
e
e
n
erg
y
-f
ou
r area system
e
x
ecu
t
i
o
n
,
sc
ena
r
io 2
i
s
t
a
ke
n
as four-a
rea
,
tw
o hy
dr
o
& tw
o the
r
ma
l syste
m
,
scena
r
io 3 is taken
as five-
a
r
e
a,
wher
e
ther
m
a
l,
hy
dr
o an
d r
e
new
a
ble
e
n
er
g
y
ar
e
hyb
r
i
d.
The sa
fe
ty
r
i
sk
i
s
f
o
r
m
ed a
t
the
r
e
ne
w
a
ble e
n
er
gy
pl
a
c
e
due
to
the
f
r
eque
nc
y ch
a
n
ge &
pow
e
r
cha
nge
ar
e
c
o
mpa
r
ed
(
w
hi
c
h
is o
t
he
r
w
ise know
n as w
e
a
k
gr
i
d
c
o
n
d
it
i
on)
.
A
n
d
it
c
a
n be see
n
tha
t
di
ff
er
e
n
tia
l
ga
m
e
theor
y
w
o
r
k
s
st
a
b
l
e
e
v
e
n
w
i
t
h
c
yber
tr
ea
t
pr
o
duce
d
.
The d
i
ffe
r
en
t t
ype
s of co
n
t
ro
llers ar
e cons
i
d
er
ed
as di
ffe
r
e
nt ca
ses here
. Case1 is wor
k
s with PI
c
o
n
t
r
o
ller
,
case
2 i
s
w
o
r
k
s
w
i
t
h
R
o
b
u
s
t
con
t
r
o
l
l
er
.
F
i
gu
r
e
1
show
s
the
pr
op
osed t
e
st
syste
m
w
i
t
h
f
i
ve-
a
r
e
a
inc
l
ud
i
ng s
o
lar
.
F
i
gur
e
s
2,
4,
6,
8,
10 & 12 sh
ow
s t
h
e
ti
e
lin
e
po
w
e
r
of
t
h
r
ee se
par
a
t
e
sc
e
n
a
r
i
o
s and ca
ses.
F
i
gur
es
3,
5,
7,
9,
11 a
nd
13 s
how
s the
f
r
e
q
u
e
n
cy de
v
i
a
t
i
o
n of
thr
e
e
se
par
a
te sce
n
ar
io
s and ca
ses.
He
r
e
it is sh
ow
n
tha
t
a
l
l
the
tie
line
pow
e
r
& f
r
e
que
ncy
ar
e
pr
odu
c
e
d a
s
z
e
r
o
w
h
ich de
pic
t
s
t
h
e
con
t
r
o
lla
b
ili
t
y
.
But th
e
sett
l
i
n
g
t
i
m
e
is d
i
ss
i
m
i
l
ar f
o
r e
ach
scena
r
io
s
an
d c
o
rre
sp
o
n
d
i
n
g c
a
ses.
The
se
curi
t
y
threa
t
is re
so
l
v
ed
a
n
d t
h
e
sys
t
em
sta
b
i
l
i
t
y
i
s
ach
i
e
ve
d
a
nd i
t
als
o
show
n
i
n
fi
g
u
r
e
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J P
o
w
Elec
& D
r
i
S
y
st
I
S
S
N
: 2088-
86
94
Di
f
f
ere
n
t
i
a
l
game theory wi
th
FPA optimiz
ation
in multi-
ar
ea pow
e
r
sys
t
e
m
(S. K
h
adar
v
a
l
i
)
3
05
F
i
gur
e
1.
Pr
op
ose
d
test s
y
ste
m
w
ith 5
ar
e
a
s inc
l
ud
i
ng s
o
lar
F
i
gur
e
2.
Tie
l
i
ne
pow
er
in p.
u w
i
t
h
P
I
c
ont
r
o
ller
(scen
a
rio
I
-
cas
e
I)
F
i
gur
e
3.
F
r
eque
nc
y de
vi
a
t
i
o
n in
hz w
i
th P
I
con
t
r
o
l
l
e
r
(
s
ce
nar
i
o 1-
ca
se
I
)
0
2
0
4
0
6
0
8
0
100
12
0
1
4
0
16
0
1
80
2
0
0
T
i
m
e
in
secs
-8
-6
-4
-2
0
2
4
6
10
-3
area 1
area 2
area 3
area 4
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
I
n
t
J
P
o
w
Elec
& Dr
i
S
y
st V
o
l.
11,
N
o
.
1, Ma
r 202
0
:
302
–
30
8
30
6
F
i
gure 4. Ti
e
li
ne
pow
er i
n
p.
u
w
i
t
h
rob
u
st c
o
n
t
ro
l
l
e
r
(sce
nario 1-
cas
e
II
)
F
i
gure
5.
Fr
equenc
y
de
via
t
i
o
n in hz
w
i
th ro
bus
t
c
ontr
o
l
l
er
(sc
e
nar
i
o
1-ca
se
I
I)
F
i
gure
6. Tie
li
n
e
pow
e
r
in
p.
u w
i
t
h
P
I
c
ontr
o
lle
r
(sc
e
nar
i
o 2-ca
s
e
I)
F
i
gure 7. Fre
quenc
y de
via
t
i
on in
hz w
i
t
h
P
I
controll
er (sce
nario
2-case I)
F
i
gure 8. Ti
e
li
ne
pow
e
r
i
n
p.
u
w
i
t
h
r
o
b
u
st c
o
n
t
ro
lle
r
(
s
c
e
na
rio 2-
case
II)
F
i
gure 9. Fre
quenc
y de
via
t
i
o
n
in
hz w
i
t
h
ro
bus
t
con
t
ro
l
l
er
(scenari
o
2-
ca
se
I
I
)
0
2
0
4
0
6
0
8
0
100
120
140
160
180
200
T
i
m
e
in secs
-0
.8
-0
.6
-0
.4
-0
.2
0
0.2
0.4
0.6
0.8
a
r
ea 1
a
r
ea 2
a
r
ea 3
a
r
ea 4
c
han
ge
in
Fr
e
que
nc
y
i
n
H
Z
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
r
i
S
y
st
IS
S
N
:
2088-
86
94
D
i
f
f
e
r
e
n
t
i
al
ga
m
e
theory
w
ith
FP
A opt
i
m
i
z
a
t
i
o
n
i
n
m
u
l
t
i-
ar
e
a
po
wer sys
t
e
m
(S.
Khadar
v
a
l
i
)
3
07
F
i
gure
1
0
. Tie
l
i
ne p
o
w
e
r in
p
.
u w
i
t
h
P
I
cont
rol
l
er
(sc
e
nar
i
o 3-ca
s
e
I)
F
i
gur
e 1
1
.
F
r
e
que
nc
y de
via
t
i
on i
n
h
z
w
i
t
h
P
I
c
o
nt
roll
er (sc
e
n
ario
3
-
ca
se
I)
Fi
g
u
r
e
12
. Ti
e
l
i
n
e
po
we
r i
n
p.u
wi
t
h
ro
bu
st
c
o
nt
roll
e
r
(scenario 3-cas
e
I
I)
F
i
gur
e 1
3
.
F
r
e
que
nc
y de
via
t
i
on i
n
h
z
w
i
t
h
r
obus
t
c
ontro
l
l
er (scenari
o
3-ca
se
II)
Ta
b
l
e
-
1 show
s
the compa
r
iso
n
of the resul
t
s
taken fr
om a
ll
t
h
e three
sce
n
ari
o
s
a
nd
t
h
e tw
o
c
a
ses
stud
ies.
it sh
o
w
s
tha
t
t
h
e ca
s
e
II of a
l
l t
h
e
t
h
ree
sc
enar
ios
perform
s
be
t
t
e
r
i
n
rise
ti
me,
se
t
t
li
ng
t
i
m
e and
p
eak
ti
m
e
w
h
ic
h a
r
e
si
g
n
i
f
ic
a
n
t i
n
t
h
e
perfo
r
m
a
n
c
e
of
t
h
e
sy
nam
i
c ope
rat
i
o
n
of
pow
er
syste
m
.
Tab
l
e
1
.
P
e
rform
ance
c
o
mpa
r
ison
t
a
b
l
e
S
cen
a
r
i
o
1
Sc
e
n
ar
i
o
2
Sc
e
n
ar
i
o
3
P
I
R
obust
PI
R
obust
PI
R
obust
R
i
s
e
T
i
m
e
(s)
4.
1134
0.
0339
27
0.
465
9
0.
0339
27
2.
0968
0.
0
388
71
S
e
tt
lin
g
T
i
m
e
(s)
21.
502
10.
611
26.
42
1
8.
1247
34.
451
1
6
.
685
S
e
ttl
in
g
M
i
n
0.
1411
7
0.
1411
7
0.
046908
0.
0467
7
0.
0630
62
0.
015
Se
t
tlingMa
x
0.
2614
3
0.
2580
3
21.
32
7
21.
415
25.
779
2
6
.
341
Ove
r
shoot
85.
183
82.
769
45192
4540
7
4031
5
1.
7
524e
+
05
Unde
r
s
hoot
0
0 0
0 0
0
P
e
a
k
0.
2614
3
0.
2580
3
21.
32
7
21.
415
25.
779
2
6
.
341
Pe
a
k
T
i
m
e
(
s
)
5.
6118
2.
3388
3.
378
5
1.
3073
9.
5024
3
.
1117
5.
CONCL
U
S
ION
The
P
I
contr
o
l
l
er and rob
u
s
t
c
o
n
t
r
o
l us
i
n
g d
i
ffe
r
en
tia
l gam
e
t
h
e
o
ry w
i
t
h
F
l
ow
er
pol
li
na
tio
n
alg
o
ri
t
h
m is
u
s
ed t
o
sol
v
e t
h
e pro
b
l
em
of
se
curi
ty
a
t
t
a
c
k
cre
a
ted a
t
t
h
e mul
t
i
-
are
a
power
sys
t
em
. Th
e
perform
ance
l
i
k
e sett
lin
g t
i
m
e
rise time
a
nd
pe
ak ti
m
e
sho
w
s
the
r
obustn
ess of the new
con
t
ro
l sys
t
em
and i
t
is de
p
i
cte
d
t
h
a
t
i
n
a
ll
t
h
e
sc
e
n
arios case
I
I
, the st
a
b
i
l
i
t
y is
a
t
t
a
ine
d
i
n
sm
al
ler
time
com
p
a
r
ed to
c
a
se I.
So, the
c
o
nt
roll
e
r
p
r
o
v
e
s
t
h
at
t
h
e mu
lt
i
-
are
a
wi
t
h
ren
e
wab
l
e reso
u
r
ces
st
abl
e
ev
e
n
in
cy
b
e
r-a
t
t
a
ck
.
0
2
0
4
0
6
0
8
0
1
00
120
140
1
60
180
2
00
T
i
me in secs
-1
.
5
-1
-0
.
5
0
0.
5
1
1.
5
2
2.
5
ar
ea 1
ar
ea 2
ar
ea 3
ar
ea 4
ar
ea 5
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
I
n
t
J
P
o
w
Elec
& Dr
i
S
y
st V
o
l.
11,
N
o
.
1, Ma
r 202
0
:
302
–
30
8
30
8
REFE
RENCES
[1]
Y.
Li
u,
P.
Ni
ng, an
d
M.
K.
Reiter,
“F
als
e
d
a
ta in
ject
ion attack
s agai
nst
stat
e estimatio
n in
e
l
ectric
po
wer
gri
d
s,
”
in
Pr
oc. 1
6
t
h
A
C
M Co
nf.
Co
m
p
u
t
.
Comm
un
. S
e
c
u
rity
,
Ch
icag
o,
IL, US
A,
pp.
21
–3
2
,
20
09.
[2]
M.
El-Halabi,
A.
Farraj,
H.
Ly,
a
n
d D.
Ku
nd
ur,
“A disto
r
ti
on
-th
e
oreti
c
p
e
rs
pect
ive f
o
r
redu
nd
ant m
e
teri
ng secu
rity
in s
m
art gri
d
,” i
n
Pr
oc.
I
E
E
E
C
a
n.
Con
f
. E
l
ect.
Compu
t
.
E
n
g.
(CCECE)
, Mo
n
t
r
eal
, Can
a
da,
Ap
r./
M
ay
, pp
.
1
–
5
,
20
12
.
[3]
D.
Kundur,
“Po
w
er system relia
bili
t
y
,
securi
ty and
s
t
ability
,
c
l
as
s no
tes for
E
C
E
1
518:
Seminar
in ide
n
tity, pr
iva
c
y
and
secu
rity
,” Dept
. El
ect.
Co
m
p
u
t
.
En
g
.
,
Un
iv.
To
ron
t
o,
To
ronto,
ON,
Canad
a
,
2
0
1
4
.
[4]
S.
Sridh
a
r,
A. H
a
hn
, a
n
d G.
Ma
nima
ra
n
,
“Cyb
er-p
hys
ical
securi
ty
fo
r elect
ric power gri
d
,”
Pr
oc
.
I
E
E
E
,
vol.
100
,
no
.
1
,
pp
. 2
1
0
–224,
Jan
.
20
12
[5]
A. Hah
n
and
G.
M
a
n
i
m
a
ran,
“
C
y
b
er att
ack
exp
o
s
u
re ev
alu
a
tio
n
f
r
am
e
w
ork
f
o
r
t
h
e
sm
art
gri
d
,”
IEE
E
Tr
an
s.
S
m
art
Gr
id
,
Vo
l.
2
,
No.
4,
pp
. 8
35–
84
3,
Dec.
2
0
1
1
[6]
R. P
.
Reza
ei
, P
.
Hi
nes, an
d
M
.
Ep
ps
tein,
“Estim
a
tin
g
cascad
in
g fail
ure
ris
k
w
ith
ran
d
o
m
ch
emis
t
r
y,”
IEE
E
Tr
an
s
.
Power Sys
t
.
,
V
o
l.
30
, N
o
.
5,
p
p
.
2
7
26–
27
35
,
S
e
p.
20
15
[7]
S
.
Liu,
B.
Chen,
T.
Z
ournto
s
,
D.
Ku
nd
ur,
an
d
K.
Bu
tler-P
urry
,
“A coo
r
di
na
t
e
d
m
u
lti
-
sw
itch
attack f
o
r cascad
in
g
f
a
il
ures in
sm
art gri
d
,”
IE
EE
T
r
ans
.
S
m
art
G
r
i
d
, vo
l. 5
,
n
o
.
3, p
p
.
11
83
–11
95
,
M
a
y
20
14.
[8]
T.
L
i
u e
t
al.,
“A
bnormal
t
r
a
ffic-inde
xed state
estimation:
A cyb
e
r– ph
ysical
fu
si
o
n
appro
ach f
o
r
sm
art gri
d
a
t
t
ack
det
ectio
n,
”
F
u
t
u
re G
e
n
e
r.
Com
p
ut.
S
y
s
t
.
,
vol.
49
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4
–
1
0
3
, A
ug.
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015
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[9]
M
.
Es
malif
a
l
a
k, L
.
Li
u
,
N. N
g
u
y
en
,
R. Zhen
g, an
d
Z.
H
a
n,
“D
etecti
ng steal
th
y
f
a
ls
e d
a
ta i
n
ject
io
n
usin
g
m
achi
n
e
learn
i
ng
i
n
sm
art g
r
id
,
”
IE
EE Sys
t
.
J
.
,
DOI:
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0
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1
1
0
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M
.
E
s
m
a
lif
a
lak
,
Z
.
Han,
and
L
.
So
ng
,
“Effect
of
stealt
hy
b
a
d d
a
ta in
jecti
o
n
o
n
netw
ork
co
nges
t
i
on in
m
a
rk
et-bas
ed
power s
y
stem
,”
in
P
r
oc
. I
EEE
Wi
reless
Commun
.
Netw. Con
f
.
,
S
h
a
n
g
h
ai,
Ch
i
n
a, 2
0
1
2
,
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68
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4
7
2.
[11]
S.
L
i
u
,
B.
Ch
e
n
, D
.
Ku
nd
ur,
T. Zo
urn
t
o
s
, a
n
d K.
Bu
tl
er-P
urry,
“
P
ro
gres
si
ve
swit
c
hi
ng
attack
s f
o
r insti
g
ating
cascad
ing
f
a
i
l
u
r
es
in
smart g
r
id,”
in
Proc.
IE
EE
Po
wer En
ergy Soc.
Gen.
M
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V
a
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ver,
BC,
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H. Shayeghi
,
H.
A.
S
h
ayanf
a
r
and A. Ja
lili
,
"L
oad f
r
equenc
y control
s
t
rat
e
gi
es
:
a stat
e-o
f
-the-art survey
f
o
r
t
h
e
research
er,
"
En
e
r
g
y
Con
v
e
r
sion
an
d
Man
ag
e
m
e
n
t
,
vo
l.
5
0
,
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4
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353
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e
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11
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K.
S
.
S. Ra
makri
s
hna1,
P. Sharma and
T.
S.
B
h
atti, "Au
t
omatic
generat
i
on c
o
nt
rol
of interconne
ct
ed
power syste
m
with
d
i
v
e
rse s
ourc
e
s
of p
o
wer generat
i
on
,
"
Interna
t
i
o
n
a
l Jo
ur
na
l
o
f
En
gi
neeri
ng Sci
e
nce
an
d
T
ech
nol
og
y
,
vol.
2,
n
o
. 5,
p
p
.
51
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,
20
10
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K. P.
S
.
P
a
rm
ara,
S. M
a
jhi
an
d
D
.
P.
K
o
t
h
ari,
"Lo
a
d
f
r
eq
uency
co
ntrol o
f
a
reali
s
t
i
c
pow
er
syst
em
w
i
t
h
m
u
lti-
so
urce p
o
wer
generat
i
o
n
,
"
Electrica
l P
o
wer
an
d E
n
er
gy
S
y
stems
, vo
l. 4
2
,
no
. 1
,
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4
2
6
-
433
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ov.
20
12
.
[15]
J.
C.
En
gw
erda,
L
Q
d
y
na
mic
op
ti
miza
t
i
o
n
a
n
d
di
ff
e
r
e
n
tia
l
ga
me
s
. Ne
w
Yo
rk
: Wile
y,
20
05
[16]
Xi
n-s
h
e Yang
, “Fl
o
w
e
r
P
o
llin
a
t
io
n alg
o
rithm f
o
r Gl
ob
al Optimi
zati
on”,
Un
c
o
nv
e
n
tion
a
l
C
o
mpu
t
a
t
io
n
an
d Natu
ra
l
C
o
m
p
u
t
at
i
o
n 2
0
1
2
,
L
e
c
t
ur
e
N
o
t
e
s
i
n
C
o
m
p
ut
er
S
c
i
e
n
c
e
,
Vo
l.
7445,
pp
. 24
0-2
4
9
,
2
012
.
[17]
N. E. Y.
Kouba, M. Menaa,
M.
Ha
sni
and
M.
Boudour, "Load
Frequency
Control in m
u
lti-
area
po
w
e
r sys
t
em bas
e
d
on
F
u
zzy
Lo
g
i
c-P
I
D
Co
nt
ro
ller,"
2
0
1
5
I
E
EE
In
te
rn
at
io
na
l
Co
n
f
e
r
e
n
c
e
on
Smar
t E
n
e
r
gy
Grid
Eng
i
n
e
e
r
in
g
(S
EG
E)
,
Os
hawa,
ON
, 2
0
15
,
p
p
.
1-6.
[18]
BAO
,
Y
Q
., LI,
Y.
,
W
ANG,
B. et
a
l
. “Dem
and
re
spons
e
f
o
r
f
r
equency control of
m
u
lti-area pow
e
r sys
t
em
”
J
.
Mo
d.
Po
wer S
y
st.
Cle
a
n E
n
er
gy
(
2
017)
5: 2
0
.
[19]
Rabi
ndra Kumar
Sahu, Tulasicha
n
dra Sekhar
Gor
r
ipot
u
,
S
i
dhart
h
a
Panda
,
“Au
t
omati
c
generat
i
on cont
rol
of
multi-
area po
wer sy
s
t
em
s wit
h
divers
e energ
y
s
o
u
r
ces us
in
g
T
eac
hin
g
Learni
ng
Based
Optim
i
zatio
n
al
go
rit
h
m
”
,
En
gi
neeri
ng Science a
n
d
T
echno
lo
gy,
an
Inter
nati
o
n
a
l Jou
r
na
l,
V
o
l.
1
9
,
No.
1,
p
p
.
11
3-1
3
4
, 20
16
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[20]
Zen
g
, Gu
o-Q
i
an
g
& Xi
e,
Xiao
-Qin
g &
Ch
en,
M
i
n
-
Ro
ng. “A
n
Ad
apt
i
ve M
o
d
e
l P
r
edictiv
e
L
o
ad F
r
equ
e
ncy
Con
t
ro
l
Method f
o
r
Mu
lti-
Area Interconnect
ed Power S
y
st
ems wi
t
h
Ph
otovoltai
c
Ge
nerati
ons”
E
n
er
g
i
es
.
Vol.
10,
2
017.
1
0
.3
39
0/e
n
10
11
18
40
.
[21]
J.
Dev
e
ndra
Ku
mar,
M
r
.
M
. S
a
nto
s
h Ki
ran,
“
M
ulti
Area L
o
ad Frequ
e
ncy
Con
t
rol
i
n
P
o
wer
S
y
stem
s via
Intern
al
Mo
de
l C
o
n
t
ro
l
S
c
he
me
using
Mo
de
l-Ord
e
r
Re
du
c
t
io
n”
,
In
t
e
rna
t
i
o
n
a
l
Jo
ur
na
l
of Advan
ced
Res
e
arch
i
n
El
ectrical,
El
ectro
n
i
cs
a
n
d
Ins
t
r
u
m
e
ntati
on En
gi
neeri
ng,
V
o
l
.
2, Iss
u
e 1
2
, Decem
ber 2
0
1
3
, p
a
ges
64
43
-645
4.
[22]
Isha Garg, “Multi-Area
Load F
r
eq
uency C
o
nt
rol
I
m
ple
m
ent
a
t
i
on in
Deregul
at
ed Power Syste
m
”,
Internation
a
l
Jou
r
n
a
l
o
f
Soft
Com
putin
g
a
nd En
gi
neer
ing (
I
JSCE)
, v
o
l.
2
,
no.
2
,
20
12
.
[23]
Goma
a
Haroun
AH,
Li
YY,
“A
novel op
t
i
mi
zed hybrid
f
u
z
z
y
l
ogic inte
lligent PI
D control
l
er f
o
r
an
interconnect
ed
m
u
lti
-
a
r
ea
pow
er sy
s
t
em w
i
th
p
h
ysi
cal co
nstrain
t
s and
bo
il
er d
y
nam
i
cs
”,
ISA Tr
ans
.
V
o
l 71
(Pt 2
)
pp
. 3
6
4
-
379,
20
17
.
[24]
To
pn
o, P
r
e
t
t
y
&
Chanan
a,
S
a
urabh
,
“Lo
a
d
f
r
equen
c
y con
t
ro
l
o
f
a
two
-
area mu
lti-s
o
u
r
ce
p
o
wer
syst
em u
s
i
ng a tilt
inte
gr
a
l
de
r
i
v
a
ti
ve
c
o
ntrol
l
e
r
”
J
o
ur
na
l o
f
Vib
r
ati
o
n
an
d Co
n
t
ro
l
.
V
o
l
24,
2
016.
[25]
H.D. M
a
t
h
u
r
an
d
H.
V
.
M
a
n
j
u
n
a
t
h,
“
F
req
u
en
cy s
t
ab
ili
zati
o
n
u
s
in
g
f
u
zzy l
ogic-b
a
sed
con
t
rol
l
er fo
r
m
u
lti
-area po
we
r
syst
e
m
”,
T
h
e S
o
u
t
h
Pa
cif
i
c Jo
ur
n
a
l
o
f
Natur
a
l S
c
i
e
nce
,
vol
. 4
,
pp.
2
2
-3
0,
200
7.
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