I
nte
rna
t
io
na
l J
o
urna
l o
f
Adv
a
nces in Applie
d Science
s
(
I
J
AAS)
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
2
0
,
p
p
.
101
~
1
0
9
I
SS
N:
2
2
5
2
-
8
8
1
4
,
DOI
: 1
0
.
1
1
5
9
1
/i
j
aa
s
.
v
9
.
i2
.
p
p
1
0
1
-
109
101
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
a
a
s
.
ia
esco
r
e.
co
m
Pas
serine sw
a
rm
o
pti
m
i
z
a
tion a
lg
o
rith
m
for so
lv
ing
opti
m
a
l
reactiv
e pow
er dispa
tch
pro
ble
m
L
enin
K
a
na
g
a
s
a
ba
i
De
p
a
rtme
n
t
o
f
EE
E,
P
ra
sa
d
V
.
P
o
tl
u
ri
S
id
d
h
a
rt
h
a
In
stit
u
te o
f
T
e
c
h
n
o
lo
g
y
,
In
d
ia
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
an
3
,
2
0
20
R
ev
i
s
ed
Feb
11
,
2
0
20
A
cc
ep
ted
Mar
1
4
,
2
0
20
T
h
is
p
a
p
e
r
p
re
se
n
ts
P
a
ss
e
rin
e
S
w
a
r
m
Op
ti
m
iza
ti
o
n
A
lg
o
rit
h
m
(
P
S
OA
)
f
o
r
so
lv
in
g
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
p
r
o
b
lem
.
T
h
is
a
lg
o
rit
h
m
is
b
a
se
d
o
n
b
e
h
a
v
io
u
r
o
f
so
c
ial
c
o
m
m
u
n
ica
ti
o
n
s
o
f
P
a
ss
e
rin
e
b
ird
.
Ba
sic
a
ll
y
,
P
a
ss
e
rin
e
b
ird
h
a
s
th
re
e
c
o
m
m
o
n
b
e
h
a
v
io
u
rs:
se
a
rc
h
b
e
h
a
v
io
u
r,
a
d
h
e
re
n
c
e
b
e
h
a
v
io
u
r
a
n
d
e
x
p
e
d
it
i
o
n
b
e
h
a
v
io
u
r.
T
h
r
o
u
g
h
t
h
e
sh
a
re
d
c
o
m
m
u
n
ica
ti
o
n
s
P
a
ss
e
rin
e
b
ird
w
il
l
se
a
rc
h
f
o
r
th
e
f
o
o
d
a
n
d
a
ls
o
ru
n
a
w
a
y
f
ro
m
h
u
n
ters
.
By
u
sin
g
th
e
P
a
ss
e
rin
e
b
ir
d
c
o
m
m
u
n
ica
ti
o
n
s
a
n
d
b
e
h
a
v
io
u
r
,
f
iv
e
b
a
sic
ru
les
h
a
v
e
b
e
e
n
c
re
a
ted
in
th
e
P
S
OA
a
p
p
ro
a
c
h
to
so
lv
e
th
e
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
p
ro
b
lem
.
Ke
y
a
sp
e
c
t
is
to
re
d
u
c
e
th
e
re
a
l
p
o
w
e
r
lo
ss
a
n
d
a
lso
to
k
e
e
p
th
e
v
a
riab
les
w
it
h
in
th
e
li
m
it
s.
P
ro
p
o
se
d
P
a
ss
e
rin
e
S
w
a
r
m
O
p
ti
m
iza
ti
on
A
l
g
o
rit
h
m
(P
S
OA
)
h
a
s
b
e
e
n
tes
t
e
d
in
sta
n
d
a
rd
IE
EE
3
0
b
u
s
tes
t
s
y
ste
m
a
n
d
sim
u
latio
n
s
re
su
lt
s
re
v
e
a
l
a
b
o
u
t
th
e
b
e
tt
e
r
p
e
rf
o
rm
a
n
c
e
o
f
th
e
p
ro
p
o
se
d
a
lg
o
rit
h
m
in
re
d
u
c
in
g
th
e
re
a
l
p
o
w
e
r
lo
ss
a
n
d
e
n
h
a
n
c
in
g
th
e
sta
ti
c
v
o
lt
a
g
e
sta
b
il
it
y
m
a
r
g
in
.
K
ey
w
o
r
d
s
:
Op
ti
m
al
P
ass
er
in
e
b
ir
d
R
ea
cti
v
e
p
o
w
er
S
w
ar
m
-
i
n
telli
g
e
n
ce
T
r
an
s
m
is
s
io
n
lo
s
s
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
L
e
n
in
Ka
n
a
g
asab
ai
Dep
ar
t
m
en
t
o
f
E
E
E
,
P
r
asad
V.
P
o
tlu
r
i
Sid
d
h
ar
th
a
I
n
s
ti
tu
te
o
f
T
ec
h
n
o
lo
g
y
,
Kan
u
r
u
,
Vij
a
y
a
w
ad
a,
An
d
h
r
a
P
r
ad
esh
-
5
2
0
0
0
7
,
I
n
d
ia
.
E
m
ail:
g
k
len
i
n
@
g
m
ai
l.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
Op
ti
m
al
r
ea
cti
v
e
p
o
w
er
d
is
p
atch
p
r
o
b
lem
i
s
s
u
b
j
ec
t
to
n
u
m
b
er
o
f
u
n
ce
r
tai
n
tie
s
an
d
at
least
in
th
e
b
est
ca
s
e
to
u
n
ce
r
tai
n
t
y
p
ar
a
m
eter
s
g
iv
e
n
in
t
h
e
d
e
m
a
n
d
an
d
ab
o
u
t
th
e
av
ailab
ilit
y
e
q
u
iv
ale
n
t
a
m
o
u
n
t
o
f
s
h
u
n
t
r
ea
ctiv
e
p
o
w
er
co
m
p
e
n
s
ato
r
s
.
Op
ti
m
al
r
ea
cti
v
e
p
o
w
e
r
d
is
p
atch
p
la
y
s
a
m
aj
o
r
r
o
le
f
o
r
th
e
o
p
er
atio
n
o
f
p
o
w
er
s
y
s
te
m
s
,
an
d
i
t
s
h
o
u
l
d
b
e
ca
r
r
ied
o
u
t
in
a
p
r
o
p
er
m
a
n
n
er
,
s
u
c
h
th
at
s
y
s
te
m
r
eliab
ilit
y
is
n
o
t
g
o
t
af
f
ec
ted
.
T
h
e
m
ain
o
b
j
ec
tiv
e
o
f
th
e
o
p
ti
m
al
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
is
to
m
ai
n
tai
n
th
e
le
v
el
o
f
v
o
lta
g
e
an
d
r
ea
ctiv
e
p
o
w
er
f
lo
w
w
i
th
i
n
th
e
s
p
ec
if
ied
li
m
it
s
u
n
d
e
r
v
ar
io
u
s
o
p
er
atin
g
co
n
d
it
i
o
n
s
an
d
n
et
w
o
r
k
co
n
f
i
g
u
r
atio
n
s
.
B
y
u
ti
lizin
g
a
n
u
m
b
er
o
f
co
n
tr
o
l
to
o
ls
s
u
c
h
a
s
s
w
itc
h
in
g
o
f
s
h
u
n
t
r
ea
ct
iv
e
p
o
w
er
s
o
u
r
ce
s
,
ch
an
g
i
n
g
g
e
n
er
ato
r
v
o
ltag
es
o
r
b
y
ad
j
u
s
tin
g
tr
an
s
f
o
r
m
er
tap
-
s
etti
n
g
s
th
e
r
ea
cti
v
e
p
o
w
er
d
is
p
atch
ca
n
b
e
d
o
n
e.
B
y
d
o
in
g
o
p
ti
m
al
ad
j
u
s
t
m
e
n
t
o
f
t
h
es
e
co
n
tr
o
ls
i
n
d
i
f
f
er
en
t
lev
el
s
,
t
h
e
r
ed
is
tr
ib
u
t
io
n
o
f
t
h
e
r
ea
cti
v
e
p
o
w
e
r
w
o
u
ld
m
i
n
i
m
ize
tr
a
n
s
m
i
s
s
io
n
lo
s
s
es.
T
h
is
p
r
o
ce
d
u
r
e
f
o
r
m
s
a
n
o
p
ti
m
al
r
ea
cti
v
e
p
o
w
er
d
is
p
atch
p
r
o
b
le
m
an
d
it
h
as
a
m
aj
o
r
in
f
l
u
e
n
ce
o
n
s
ec
u
r
e
an
d
ec
o
n
o
m
ic
o
p
er
atio
n
o
f
p
o
w
er
s
y
s
te
m
s
.
Var
io
u
s
m
at
h
e
m
atica
l
tec
h
n
iq
u
e
s
lik
e
th
e
g
r
ad
ien
t
m
et
h
o
d
A
ls
a
c
et
al
.
L
ee
et
al
an
d
lin
ea
r
p
r
o
g
r
a
m
m
i
n
g
m
an
g
o
li
et
al
[
1
-
7
]
h
av
e
b
ee
n
ad
o
p
ted
to
s
o
lv
e
t
h
e
o
p
ti
m
al
r
ea
cti
v
e
p
o
w
er
d
is
p
atch
p
r
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b
le
m
.
B
o
th
th
e
g
r
ad
ien
t
a
n
d
Ne
w
to
n
m
e
th
o
d
s
h
as
t
h
e
d
if
f
ic
u
lt
y
i
n
h
a
n
d
lin
g
in
eq
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ali
t
y
co
n
s
tr
ai
n
t
s
.
I
f
lin
ea
r
p
r
o
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r
am
m
in
g
is
ap
p
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e
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p
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t
-
o
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tp
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t
f
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to
b
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ex
p
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ess
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as
a
s
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o
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li
n
ea
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f
u
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s
w
h
ic
h
m
o
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t
l
y
lead
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s
s
o
f
ac
cu
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ac
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.
T
h
is
p
ap
er
f
o
r
m
u
late
s
b
y
co
m
b
in
in
g
b
o
th
t
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e
r
ea
l
p
o
w
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lo
s
s
m
i
n
i
m
izatio
n
a
n
d
m
a
x
i
m
izatio
n
o
f
s
ta
tic
v
o
lta
g
e
s
tab
ili
t
y
m
ar
g
in
(
SVSM)
as
t
h
e
o
b
j
ec
tiv
es.
G
l
o
b
al
o
p
tim
izat
io
n
h
as
r
ec
ei
v
e
d
ex
ten
s
i
v
e
r
esear
ch
atte
n
tio
n
,
an
d
a
g
r
ea
t
n
u
m
b
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8814
I
n
t J
A
d
v
A
p
p
l Sci
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
2
0
:
1
0
1
–
109
102
o
f
m
eth
o
d
s
h
a
v
e
b
ee
n
ap
p
lied
to
s
o
lv
e
th
i
s
p
r
o
b
le
m
.
Ma
n
y
E
v
o
lu
tio
n
ar
y
a
lg
o
r
it
h
m
s
Ap
ar
aj
ita
Mu
k
h
er
j
ee
et
al.
,
Hu
et
al
.
,
Ma
h
aletc
h
u
m
i
et
al.
,
S
u
lai
m
a
n
et
al.
,
P
an
d
i
ar
aj
an
et
al.
,
h
av
e
b
ee
n
alr
ea
d
y
p
r
o
p
o
s
ed
to
s
o
lv
e
th
e
r
ea
cti
v
e
p
o
w
er
f
lo
w
p
r
o
b
le
m
.
T
h
is
p
ap
er
p
r
esen
ts
P
ass
e
r
in
e
S
w
ar
m
Op
ti
m
izatio
n
A
l
g
o
r
ith
m
(
P
SO
A
)
f
o
r
s
o
lv
i
n
g
o
p
ti
m
al
r
ea
cti
v
e
p
o
w
er
d
is
p
atc
h
p
r
o
b
le
m
.
T
h
is
alg
o
r
ith
m
i
s
b
ased
o
n
b
e
h
av
io
u
r
o
f
s
o
cial
co
m
m
u
n
icatio
n
s
o
f
P
ass
er
i
n
e
b
ir
d
A
n
d
er
s
o
n
et
al.
,
B
ar
n
ar
d
et
al
.
,
B
ea
u
ch
a
m
p
et
al.
,
B
ed
n
ek
o
f
f
et
al.
,
C
o
o
len
et
al.
[
8
-
1
3
]
.
B
asicall
y
P
ass
er
i
n
e
b
ir
d
h
as
t
h
r
ee
co
m
m
o
n
b
eh
av
io
u
r
s
:
s
ea
r
c
h
b
eh
a
v
io
u
r
,
a
d
h
er
en
ce
b
eh
a
v
io
u
r
an
d
ex
p
ed
itio
n
b
eh
av
io
u
r
.
T
h
r
o
u
g
h
t
h
e
s
h
ar
ed
co
m
m
u
n
ica
t
io
n
s
P
ass
er
in
e
b
ir
d
w
il
l
s
ea
r
ch
f
o
r
th
e
f
o
o
d
an
d
also
r
u
n
a
w
a
y
f
r
o
m
h
u
n
ter
s
[
1
4
-
2
0
]
.
B
y
u
s
i
n
g
th
e
P
as
s
er
in
e
b
ir
d
co
m
m
u
n
ica
tio
n
s
an
d
b
eh
av
io
u
r
,
f
iv
e
b
as
ic
r
u
les
h
a
v
e
b
ee
n
cr
ea
ted
in
th
e
P
SOA
ap
p
r
o
ac
h
to
s
o
lv
e
th
e
o
p
tim
al
r
ea
cti
v
e
p
o
w
er
d
is
p
atch
p
r
o
b
lem
.
Ke
y
asp
ec
t
is
to
r
ed
u
ce
th
e
r
ea
l
p
o
w
er
lo
s
s
an
d
also
to
k
ee
p
th
e
v
ar
iab
les
w
ith
in
t
h
e
li
m
its
.
P
r
o
p
o
s
ed
P
ass
er
in
e
S
w
ar
m
Op
ti
m
izatio
n
A
l
g
o
r
ith
m
(
P
SO
A
)
h
as
b
ee
n
test
ed
i
n
s
tan
d
ar
d
I
E
E
E
3
0
b
u
s
test
s
y
s
t
e
m
an
d
s
i
m
u
lat
io
n
s
r
esu
lt
s
r
ev
ea
l
ab
o
u
t
t
h
e
b
etter
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
it
h
m
in
r
ed
u
ci
n
g
th
e
r
e
al
p
o
w
er
lo
s
s
a
n
d
en
h
a
n
ci
n
g
t
h
e
s
tatic
v
o
lta
g
e
s
t
ab
ilit
y
m
ar
g
i
n
.
2.
VO
L
T
A
G
E
S
T
AB
I
L
I
T
Y
E
VALUA
T
I
O
N
o
d
al
an
al
y
s
i
s
f
o
r
v
o
ltag
e
s
tab
ilit
y
e
v
al
u
atio
n
;
Mo
d
al
an
a
l
y
s
i
s
is
o
n
e
a
m
o
n
g
b
est
m
et
h
o
d
s
f
o
r
v
o
ltag
e
s
tab
ilit
y
e
n
h
an
ce
m
e
n
t i
n
p
o
w
e
r
s
y
s
te
m
s
.
T
h
e
s
tead
y
s
tate
s
y
s
te
m
p
o
w
er
f
lo
w
ar
e
g
i
v
en
b
y
(
1)
.
[
∆
P
∆
Q
]
=
[
J
p
θ
J
pv
J
q
θ
J
QV
]
[
∆
∆
]
(
1
)
W
h
er
e
Δ
P
=
I
n
cr
e
m
en
ta
l c
h
a
n
g
e
i
n
b
u
s
r
ea
l p
o
w
er
.
Δ
Q
=
I
n
cr
e
m
e
n
tal
c
h
a
n
g
e
i
n
b
u
s
r
ea
cti
v
e
P
o
w
er
in
j
ec
tio
n
Δ
θ
=
in
cr
e
m
en
ta
l c
h
a
n
g
e
i
n
b
u
s
v
o
lta
g
e
an
g
le.
Δ
V
=
I
n
cr
e
m
e
n
tal
c
h
a
n
g
e
i
n
b
u
s
v
o
ltag
e
Ma
g
n
i
tu
d
e
J
p
θ
,
J
P
V
,
J
Qθ
,
J
QV
j
ac
o
b
ia
n
m
atr
ix
ar
e
t
h
e
s
u
b
-
m
a
tr
ix
e
s
of
th
e
S
y
s
te
m
v
o
ltag
e
s
tab
ilit
y
is
af
f
ec
ted
b
y
b
o
t
h
P
an
d
Q.
T
o
r
ed
u
ce
(
1
)
,
let
Δ
P
=
0
,
th
en
.
∆
Q
=
[
J
QV
−
J
Q
θ
J
P
θ
−
1
J
PV
]
∆
V
=
J
R
∆
V
(
2
)
∆
V
=
J
−
1
−
∆
Q
(
3
)
W
h
er
e
J
R
=
(
J
QV
−
J
Q
θ
J
P
θ
−
1
J
PV
)
(
4
)
J
R
is
ca
lled
th
e
r
ed
u
ce
d
J
ac
o
b
ian
m
atr
i
x
o
f
th
e
s
y
s
te
m
.
Mo
d
es o
f
Vo
ltag
e
in
s
tab
ilit
y
:
Vo
ltag
e
Stab
il
it
y
c
h
ar
ac
ter
is
t
ics
o
f
t
h
e
s
y
s
te
m
h
a
v
e
b
ee
n
id
en
ti
f
ied
b
y
co
m
p
u
ti
n
g
th
e
E
ig
en
v
al
u
es
an
d
E
ig
en
v
ec
to
r
s
.
L
et
J
R
=
ξ
˄
η
(
5
)
Wh
er
e,
ξ =
r
ig
h
t e
i
g
e
n
v
ec
to
r
m
a
tr
ix
o
f
J
R
η
=
lef
t e
i
g
e
n
v
ec
to
r
m
a
tr
ix
o
f
J
R
∧
=
d
iag
o
n
al
eig
e
n
v
al
u
e
m
atr
i
x
o
f
J
R
an
d
J
R
−
1
=
ξ
˄
−
1
η
(
6
)
Fro
m
(
5
)
an
d
(
8
)
,
w
e
h
a
v
e
∆
V
=
ξ
˄
−
1
η
∆
Q
(
7
)
O
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
d
v
A
p
p
l Sci
I
SS
N:
2
2
5
2
-
8814
P
a
s
s
erin
e
s
w
a
r
m
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
fo
r
s
o
lvin
g
o
p
tima
l
…
(
K
a
n
a
g
a
s
a
b
a
i Len
in
)
103
∆
V
=
∑
ξ
i
η
i
λ
i
I
∆
Q
(
8
)
W
h
er
e
ξi
is
th
e
it
h
co
lu
m
n
r
i
g
h
t e
ig
e
n
v
ec
to
r
an
d
η
t
h
e
ith
r
o
w
le
f
t
ei
g
en
v
ec
to
r
o
f
J
R
.
λi
is
th
e
i
th
E
i
g
e
n
v
al
u
e
o
f
J
R
.
T
h
e
ith
m
o
d
al
r
ea
ctiv
e
p
o
w
er
v
ar
iatio
n
is
,
∆
Q
mi
=
K
i
ξ
i
(
9
)
w
h
er
e,
K
i
=
∑
ξ
ij
2
j
−
1
(
1
0
)
W
h
er
e
ξj
i is th
e
j
th
ele
m
e
n
t o
f
ξi
T
h
e
co
r
r
esp
o
n
d
in
g
it
h
m
o
d
al
v
o
ltag
e
v
ar
iatio
n
i
s
∆
V
mi
=
[
1
λ
i
⁄
]
∆
Q
mi
(
1
1
)
If
|
λi
|
=0
th
e
n
th
e
i
th
m
o
d
al
v
o
ltag
e
w
ill co
llap
s
e
.
I
n
(
1
0
)
,
let
Δ
Q
=
ek
w
h
er
e
ek
h
as a
ll it
s
ele
m
en
t
s
ze
r
o
ex
ce
p
t th
e
k
t
h
o
n
e
b
ei
n
g
1
.
T
h
en
,
∆
V
=
∑
ƞ
1k
ξ
1
λ
1
i
(
1
2
)
ƞ
1k
k
th
ele
m
e
n
t o
f
ƞ
1
V
–
Q
s
en
s
i
tiv
it
y
at
b
u
s
k
∂
V
K
∂
Q
K
=
∑
ƞ
1k
ξ
1
λ
1
i
=
∑
P
ki
λ
1
i
(
1
3
)
3.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
T
h
e
o
b
j
ec
tiv
es
o
f
th
e
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
p
r
o
b
lem
is
to
m
i
n
i
m
ize
th
e
s
y
s
te
m
r
ea
l
p
o
w
er
lo
s
s
an
d
m
ax
i
m
ize
th
e
s
tatic
v
o
lta
g
e
s
t
ab
ilit
y
m
ar
g
i
n
s
(
SV
SM)
.
3
.
1
.
M
ini
m
iza
t
io
n o
f
re
a
l po
w
er
l
o
s
s
Min
i
m
izatio
n
o
f
t
h
e
r
ea
l p
o
w
e
r
lo
s
s
(
P
lo
s
s
)
in
tr
an
s
m
i
s
s
io
n
l
in
es i
s
m
at
h
e
m
atica
l
l
y
s
tated
as
(
1
4
)
.
P
l
o
s
s
=
∑
g
k
(
V
i
2
+
V
j
2
−
2
V
i
V
j
c
o
s
θ
ij
)
n
k
=
1
k
=
(
i
,
j
)
(
14)
W
h
er
e
n
is
th
e
n
u
m
b
er
o
f
tr
an
s
m
i
s
s
io
n
lin
e
s
,
g
k
i
s
t
h
e
c
o
n
d
u
ctan
ce
o
f
b
r
an
c
h
k
,
V
i
an
d
Vj
ar
e
v
o
ltag
e
m
a
g
n
i
tu
d
e
at
b
u
s
i a
n
d
b
u
s
j
,
an
d
θij
is
th
e
v
o
lta
g
e
an
g
le
d
if
f
er
en
ce
b
et
w
ee
n
b
u
s
i a
n
d
b
u
s
j
.
Min
i
m
izatio
n
o
f
Vo
lta
g
e
Dev
i
atio
n
.
Min
i
m
iza
tio
n
o
f
t
h
e
v
o
l
tag
e
d
ev
iatio
n
m
a
g
n
it
u
d
es (
V
D)
at
lo
ad
b
u
s
es
is
m
at
h
e
m
a
ticall
y
s
tated
as
(
1
5
)
.
Min
i
m
ize
VD
=
∑
|
V
k
−
1
.
0
|
nl
k
=
1
(
1
5
)
W
h
er
e
n
l is t
h
e
n
u
m
b
er
o
f
lo
a
d
b
u
s
s
es a
n
d
Vk
is
t
h
e
v
o
ltag
e
m
ag
n
it
u
d
e
at
b
u
s
k
.
3
.
2
.
Sy
s
t
e
m
co
n
s
t
ra
ints
T
h
e
f
o
llo
w
i
n
g
i
s
an
o
b
j
ec
tiv
e
f
u
n
ctio
n
th
a
t e
x
p
er
ien
ce
s
co
n
s
tr
ain
ts
.
a.
L
o
ad
f
lo
w
eq
u
alit
y
co
n
s
tr
ain
ts
:
P
Gi
–
P
Di
−
V
i
∑
V
j
nb
j
=
1
[
G
ij
c
os
θ
ij
+
B
ij
s
in
θ
ij
]
=
0
,
i
=
1
,
2
…
.
,
nb
(
1
6
)
Q
Gi
−
Q
Di
−
V
i
∑
V
j
nb
j
=
1
[
G
ij
s
in
θ
ij
+
B
ij
c
os
θ
ij
]
=
0
,
i
=
1
,
2
…
.
,
nb
(
1
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8814
I
n
t J
A
d
v
A
p
p
l Sci
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
2
0
:
1
0
1
–
109
104
w
h
er
e,
n
b
is
th
e
n
u
m
b
er
o
f
b
u
s
e
s
,
P
G
an
d
QG
ar
e
th
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
o
f
th
e
g
e
n
er
ato
r
,
P
D
an
d
QD
ar
e
th
e
r
ea
l
an
d
r
ea
ctiv
e
lo
ad
o
f
th
e
g
en
er
ato
r
,
an
d
Gij
an
d
B
ij
ar
e
th
e
m
u
tu
al
co
n
d
u
ctan
ce
an
d
s
u
s
ce
p
tan
ce
b
et
w
ee
n
b
u
s
i a
n
d
b
u
s
j
.
b.
Gen
er
ato
r
b
u
s
v
o
lta
g
e
(
VGi)
i
n
eq
u
alit
y
co
n
s
tr
ain
t:
V
Gi
m
i
n
≤
V
Gi
≤
V
Gi
m
ax
,
i
∈
ng
(
1
8
)
c.
L
o
ad
b
u
s
v
o
lta
g
e
(
V
L
i)
in
eq
u
alit
y
co
n
s
tr
ain
t:
V
Li
m
i
n
≤
V
Li
≤
V
Li
m
ax
,
i
∈
nl
(
1
9
)
d.
S
w
itc
h
ab
le
r
ea
ctiv
e
p
o
w
er
co
m
p
e
n
s
atio
n
s
(
QC
i)
i
n
eq
u
alit
y
co
n
s
tr
ain
t:
Q
Ci
m
i
n
≤
Q
Ci
≤
Q
Ci
m
ax
,
i
∈
nc
(
2
0
)
e.
R
ea
cti
v
e
p
o
w
er
g
e
n
er
a
tio
n
(
Q
Gi)
in
eq
u
ali
t
y
co
n
s
tr
ai
n
t:
Q
Gi
m
i
n
≤
Q
Gi
≤
Q
Gi
m
ax
,
i
∈
ng
(
2
1
)
f.
T
r
an
s
f
o
r
m
er
s
tap
s
etti
n
g
(
T
i)
i
n
eq
u
alit
y
co
n
s
tr
ain
t:
T
i
m
i
n
≤
T
i
≤
T
i
m
ax
,
i
∈
nt
(
2
2
)
g.
T
r
an
s
m
is
s
io
n
li
n
e
f
lo
w
(
S
L
i)
i
n
eq
u
alit
y
co
n
s
tr
ain
t:
S
Li
m
i
n
≤
S
Li
m
ax
,
i
∈
nl
(2
3)
W
h
er
e,
n
c,
n
g
a
n
d
n
t a
r
e
n
u
m
b
er
s
o
f
th
e
s
w
i
tch
ab
le
r
ea
cti
v
e
p
o
w
er
s
o
u
r
ce
s
,
g
e
n
er
ato
r
s
an
d
tr
an
s
f
o
r
m
er
s
.
4.
P
ASSE
RIN
E
B
I
RD
S
WAR
M
H
YP
O
T
H
E
SI
S
T
h
e
Pas
s
er
in
e
b
ir
d
Fig
u
r
e
1
s
o
cial
b
eh
av
io
r
’
s
ca
n
b
e
w
r
itten
as f
o
ll
o
w
s
:
a)
R
u
le
1
.
E
v
e
r
y
P
ass
er
in
e
b
ir
d
h
as
ch
o
i
ce
t
o
alt
er
b
e
tw
ee
n
th
e
a
d
h
er
en
ce
b
eh
av
i
o
u
r
an
d
s
e
ar
ch
b
eh
av
io
u
r
.
W
h
eth
e
r
th
e
P
ass
er
in
e
b
i
r
d
s
ea
r
ch
es
o
r
in
o
b
s
e
r
v
an
c
e,
it
is
m
o
l
d
e
d
as
a
s
t
o
ch
ast
ic
d
ec
is
io
n
.
b)
R
u
le
2
.
W
h
i
le
s
ea
r
ch
,
ea
ch
Pa
s
s
er
in
e
b
i
r
d
c
an
p
r
o
m
p
tly
r
ec
o
r
d
an
d
r
en
o
v
at
e
its
p
r
ev
i
o
u
s
m
o
s
t
o
u
ts
tan
d
in
g
ex
p
e
r
i
en
ce
an
d
th
e
s
w
ar
m
s
’
p
r
ev
i
o
u
s
m
o
s
t
o
u
ts
tan
d
in
g
ex
p
er
i
en
ce
a
b
o
u
t
f
o
o
d
a
r
ea
.
T
h
is
in
f
o
r
m
atio
n
h
as
b
e
en
u
s
e
d
to
d
is
c
o
v
e
r
f
o
o
d
.
So
cial
in
f
o
r
m
atio
n
is
s
h
ar
ed
r
a
p
i
d
ly
am
o
n
g
th
e
w
h
o
le
s
w
ar
m
.
c)
R
u
le
3
.
Du
r
in
g
ad
h
e
r
en
c
e,
e
v
er
y
P
ass
e
r
in
e
w
ill
attem
p
t
to
m
o
v
e
n
ea
r
t
o
th
e
ce
n
t
r
e
o
f
th
e
s
w
ar
m
.
T
h
is
b
eh
av
i
o
u
r
c
an
b
e
em
b
r
o
i
d
e
r
e
d
b
y
th
e
in
ter
f
e
r
en
c
e
tem
p
ted
b
y
th
e
r
iv
al
r
y
am
o
n
g
s
w
ar
m
.
T
h
e
P
ass
er
in
e
w
ith
th
e
u
p
p
er
m
o
s
t
r
ese
r
v
es
w
o
u
l
d
b
e
m
o
r
e
p
r
o
n
e
t
o
lie
n
ea
r
er
t
o
th
e
ce
n
t
r
e
o
f
th
e
s
w
ar
m
.
d)
R
u
le
4
.
W
h
il
e
f
ly
in
g
Pas
s
e
r
in
e
m
ay
o
f
ten
ch
an
g
e
b
e
tw
ee
n
g
en
er
a
tin
g
an
d
s
p
o
n
g
in
g
.
T
h
e
Pas
s
e
r
in
e
w
ith
th
e
u
p
p
er
m
o
s
t
r
es
e
r
v
es
w
o
u
ld
b
e
a
c
r
e
at
o
r
,
w
h
ile
th
e
o
n
e
w
ith
th
e
b
o
tt
o
m
m
o
s
t
r
ese
r
v
es
w
o
u
ld
b
e
a
s
p
o
n
g
e
r
.
Pas
s
e
r
in
e
h
av
e
r
e
s
er
v
es
b
etw
ee
n
th
e
u
p
p
e
r
m
o
s
t
an
d
b
o
tt
o
m
m
o
s
t
r
ese
r
v
es
w
o
u
ld
r
an
d
o
m
ly
ch
o
o
s
e
t
o
b
e
c
r
ea
t
o
r
an
d
s
p
o
n
g
er
.
e)
R
u
le
5
.
C
r
ea
t
o
r
s
w
ith
d
esir
e
s
e
ar
ch
f
o
r
f
o
o
d
.
Sp
o
n
g
e
r
s
w
o
u
ld
r
an
d
o
m
ly
f
o
llo
w
a
cr
ea
t
o
r
t
o
s
ea
r
ch
f
o
r
f
o
o
d
.
B
y
th
e
ab
o
v
e
R
u
les
th
e
m
ath
em
atica
l m
o
d
el
f
o
r
th
e
p
r
o
b
l
em
h
as b
ee
n
d
ev
el
o
p
e
d
,
A
ll
N
v
ir
tu
a
l
P
ass
er
in
e
b
ir
d
,
p
o
r
t
r
ay
ed
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y
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eir
p
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ti
o
n
Z
_
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i
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tim
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r
f
o
o
d
an
d
f
ly
in
an
o
r
g
an
i
ze
d
s
p
a
ce
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
d
v
A
p
p
l Sci
I
SS
N:
2
2
5
2
-
8814
P
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u
r
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1
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ir
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2
ca
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e
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r
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(
24)
as f
o
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s
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ca
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e
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ar
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ass
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ar
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o
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er
v
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ce
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4
.
2
.
Adherence
be
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v
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ur
R
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3
i
n
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icate
s
t
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at
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as
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er
in
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w
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ld
tr
y
to
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C
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f
th
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w
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m
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n
d
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e
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d
in
ev
itab
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n
te
n
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h
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er
.
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h
u
s
,
ea
c
h
P
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ca
n
n
o
t
d
ir
ec
tl
y
m
o
v
e
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th
e
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e
n
tr
e
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th
e
s
w
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m
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h
is
d
r
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ca
n
b
e
w
r
itte
n
as
f
o
llo
w
s
:
,
+
1
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1
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(
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7
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W
h
er
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≠
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is
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er
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d
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1
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2
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t
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[
0
,
2
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d
e
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Fit
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1
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F2
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T
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h
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it
h
p
ass
er
i
n
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8814
I
n
t J
A
d
v
A
p
p
l Sci
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
2
0
:
1
0
1
–
109
106
4
.
3
.
E
x
peditio
n be
ha
v
io
ur
P
ass
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in
e
m
a
y
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l
y
to
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t
h
er
ar
ea
s
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e
to
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n
tle
s
s
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o
n
s
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W
h
e
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t
h
e
P
ass
er
i
n
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ar
r
i
v
ed
at
a
n
in
n
o
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s
ite,
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e
y
w
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ld
ag
ain
s
ea
r
ch
f
o
r
f
o
o
d
.
So
m
e
P
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cr
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s
w
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ld
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r
ch
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P
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s
.
B
y
t
h
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R
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l
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4
th
e
cr
ea
to
r
s
a
n
d
s
p
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er
s
ca
n
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e
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etac
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f
r
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t
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s
w
a
r
m
.
T
h
e
b
eh
av
io
r
s
o
f
th
e
cr
ea
to
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s
an
d
s
p
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n
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er
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n
b
e
w
r
it
te
n
as f
o
llo
w
s
:
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+
1
=
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+
(
0
,
1
)
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(
2
8
)
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1
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,
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d
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o
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Gau
s
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ta
n
d
ar
d
d
ev
iatio
n
1
,
∈
[
1
,
2
,
3
,
.
.
,
]
,
≠
.
(
∈
[
0
,
2
]
)
m
ea
n
s
th
at
th
e
s
p
o
n
g
er
w
o
u
ld
f
o
llo
w
th
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to
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to
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ea
r
ch
f
o
r
f
o
o
d
.
W
e
ass
u
m
e
th
at
ea
ch
P
ass
er
in
e
f
l
y
to
alter
n
ativ
e
p
lace
ev
er
y
GH
(
p
o
s
itiv
e
in
teg
er
)
u
n
i
t in
ter
v
al.
4
.
4
.
P
a
s
s
er
ine bir
d Sw
a
r
m
o
pti
miza
t
io
n Alg
o
rit
h
m
f
o
r
o
pti
m
a
l r
ea
ct
iv
e
po
w
er
dis
pa
t
ch
pro
ble
m
E
n
ter
:
P
:
th
e
n
u
m
b
er
o
f
i
n
d
iv
i
d
u
als
(
p
ass
er
i
n
e)
b
o
u
n
d
ed
in
t
h
e
p
o
p
u
latio
n
,
Q:
t
h
e
u
t
m
o
s
t
n
u
m
b
er
o
f
iter
atio
n
s
,
GH
:
th
e
r
ate
o
f
r
ep
eti
tio
n
o
f
P
ass
er
i
n
e
e
x
p
ed
itio
n
b
eh
a
v
io
r
s
’
,
K:
t
h
e
p
r
o
b
ab
ilit
y
o
f
s
ea
r
ch
i
n
g
f
o
r
f
o
o
d
,
M,
N,
f
1
,
f
2
,
GH:
ar
e
f
iv
e
co
n
s
tan
t p
ar
a
m
eter
s
,
=
0
; I
n
itial
ize
th
e
p
o
p
u
latio
n
Ass
es
s
m
en
t
o
f
th
e
N
i
n
d
i
v
id
u
a
ls
’
f
it
n
es
s
v
al
u
e,
an
d
f
in
d
t
h
e
m
o
s
t o
u
t
s
ta
n
d
in
g
s
o
l
u
tio
n
While
(
<
)
If
(
%
≠
0
)
For
=
1
:
If
(
0
,
1
)
<
At that juncture Passerine searches for food (24)
Else
The Pas
serine keep surveillance (25)
End if
End for
Else
Classifying swarms as creators and spongers.
For
=
1
:
If
is a creator
Then Create (28)
Else
It will be Sponger (29)
End if
End for
End if
C
alcu
late
i
n
n
o
v
ati
v
e
s
o
lu
tio
n
s
.
I
f
th
e
i
n
n
o
v
ati
v
e
s
o
lu
tio
n
s
ar
e
g
r
ea
ter
to
th
eir
p
r
ev
io
u
s
o
n
e
s
,
r
en
o
v
ate
t
h
e
m
.
F
in
d
t
h
e
cu
r
r
e
n
t
m
o
s
t o
u
t
s
tan
d
i
n
g
s
o
lu
t
io
n
t=t+1;
End while
Output:
The individual with the finest objective function value in the population
5.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
T
h
e
ef
f
icien
c
y
o
f
t
h
e
p
r
o
p
o
s
ed
P
ass
er
in
e
S
w
ar
m
Op
ti
m
izatio
n
Alg
o
r
it
h
m
(
P
SO
A
)
m
et
h
o
d
is
d
em
o
n
s
tr
ated
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y
test
i
n
g
it
o
n
s
tan
d
ar
d
I
E
E
E
-
3
0
b
u
s
s
y
s
te
m
.
T
h
e
I
E
E
E
-
3
0
b
u
s
s
y
s
te
m
h
a
s
6
g
en
er
ato
r
b
u
s
es,
2
4
lo
ad
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u
s
es
an
d
4
1
tr
an
s
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i
s
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io
n
lin
e
s
o
f
w
h
ic
h
f
o
u
r
b
r
an
ch
e
s
ar
e
(
6
-
9
)
,
(
6
-
1
0
)
,
(
4
-
1
2
)
an
d
(
2
8
-
2
7
)
-
ar
e
w
it
h
t
h
e
tap
s
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g
tr
an
s
f
o
r
m
er
s
.
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h
e
lo
w
er
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o
lta
g
e
m
a
g
n
it
u
d
e
li
m
it
s
at
all
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u
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e
s
ar
e
0
.
9
5
p
.
u
.
an
d
th
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u
p
p
er
li
m
it
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ar
e
1
.
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f
o
r
all
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u
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a
n
d
1
.
0
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p
.
u
.
f
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al
l
t
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b
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s
es
an
d
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ef
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e
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ce
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s
.
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h
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i
m
u
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&
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a
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r
esp
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l v
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it w
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p
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p
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b
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a
s
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s
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a
m
u
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-
o
b
j
ec
tiv
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ti
m
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p
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w
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b
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p
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w
er
lo
s
s
a
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d
m
ax
i
m
u
m
v
o
ltag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
d
v
A
p
p
l Sci
I
SS
N:
2
2
5
2
-
8814
P
a
s
s
erin
e
s
w
a
r
m
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
fo
r
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lvin
g
o
p
tima
l
…
(
K
a
n
a
g
a
s
a
b
a
i Len
in
)
107
s
tab
ilit
y
m
ar
g
i
n
o
f
t
h
e
s
y
s
te
m
w
er
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o
p
ti
m
ized
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i
m
u
lta
n
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s
l
y
.
T
ab
le
2
in
d
icate
s
t
h
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o
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t
in
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tab
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s
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n
g
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co
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tr
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l
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b
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s
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in
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o
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tai
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s
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1
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.
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g
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eq
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f
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co
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iv
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n
i
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ab
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3
.
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as
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s
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s
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ab
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1
.
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esu
lts
o
f
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SO
A
–
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tim
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8814
I
n
t J
A
d
v
A
p
p
l Sci
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
2
0
:
1
0
1
–
109
108
T
ab
le
4
.
L
i
m
it
v
io
latio
n
c
h
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k
in
g
o
f
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tate
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ar
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ab
le
5
.
C
o
m
p
ar
is
o
n
o
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ea
l p
o
w
er
lo
s
s
M
e
t
h
o
d
M
i
n
i
m
u
m
l
o
ss
(
M
W
)
Ev
o
l
u
t
i
o
n
a
r
y
p
r
o
g
r
a
mm
i
n
g
[
2
1
]
5
.
0
1
5
9
G
e
n
e
t
i
c
a
l
g
o
r
i
t
h
m
[
2
2
]
4
.
6
6
5
R
e
a
l
c
o
d
e
d
G
A
w
i
t
h
L
i
n
d
e
x
a
s SV
S
M
[
2
3
]
4
.
5
6
8
R
e
a
l
c
o
d
e
d
g
e
n
e
t
i
c
a
l
g
o
r
i
t
h
m
[
2
4
]
4
.
5
0
1
5
P
r
o
p
o
se
d
P
S
O
A
me
t
h
o
d
4.
2
5
0
2
6.
CO
NCLU
SI
O
N
I
n
th
is
p
a
p
e
r
,
Pas
s
e
r
in
e
b
i
r
d
Sw
ar
m
Op
tim
izatio
n
(
P
S
OA
)
alg
o
r
i
th
m
h
as
b
ee
n
s
u
cc
ess
f
u
lly
im
p
lem
en
ted
t
o
s
o
lv
e
o
p
tim
al
r
e
ac
tiv
e
p
o
w
er
d
is
p
at
ch
p
r
o
b
l
em
.
B
y
u
s
in
g
t
h
e
P
as
s
er
in
e
b
i
r
d
co
m
m
u
n
icatio
n
s
an
d
b
eh
a
v
io
u
r
,
f
i
v
e
b
as
ic
r
u
le
s
h
av
e
b
ee
n
cr
ea
ted
i
n
th
e
P
S
OA
ap
p
r
o
ac
h
to
s
o
l
v
e
t
h
e
o
p
ti
m
al
r
ea
cti
v
e
p
o
w
er
d
is
p
atch
p
r
o
b
le
m
.
Ke
y
a
s
p
ec
t
is
to
r
ed
u
ce
t
h
e
r
ea
l
p
o
w
er
lo
s
s
a
n
d
also
to
k
ee
p
th
e
v
ar
iab
le
s
w
it
h
i
n
t
h
e
li
m
its
.
P
r
o
p
o
s
ed
P
ass
er
in
e
S
w
ar
m
O
p
ti
m
izatio
n
A
l
g
o
r
ith
m
(
P
SO
A
)
h
as
b
ee
n
test
ed
in
s
ta
n
d
ar
d
I
E
E
E
3
0
b
u
s
te
s
t
s
y
s
te
m
an
d
s
i
m
u
lat
io
n
s
r
es
u
lt
s
r
ev
ea
l
ab
o
u
t
th
e
b
etter
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
in
r
ed
u
c
in
g
th
e
r
ea
l p
o
w
er
lo
s
s
a
n
d
en
h
a
n
cin
g
t
h
e
s
tatic
v
o
lta
g
e
s
tab
il
it
y
m
ar
g
i
n
.
RE
F
E
R
E
NC
E
S
[1
]
O.A
lsa
c
,
a
n
d
B.
S
c
o
tt
,
“
Op
t
im
a
l
lo
a
d
f
lo
w
w
it
h
ste
a
d
y
sta
te se
c
u
rit
y
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
.
P
AS
,
p
p
.
7
4
5
-
7
5
1
,
1
9
7
3
.
[2
]
L
e
e
K
.
Y
.
,
P
a
ru
Y
.
M
.
,
Oritz
J
.
L
.,
“
A
u
n
it
e
d
a
p
p
ro
a
c
h
t
o
o
p
ti
m
a
l
re
a
l
a
n
d
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
p
o
we
r A
p
p
a
ra
tu
s
a
n
d
sy
ste
ms
,
P
A
S
-
104
,
p
p
.
1
1
4
7
-
1
1
5
3
,
1
9
8
5
.
[3
]
A.
M
o
n
ti
c
e
ll
i
,
M
.
V
.
F
P
e
re
ira
,
S
.
G
ra
n
v
il
le
.
,
“
S
e
c
u
r
it
y
c
o
n
stra
in
e
d
o
p
t
im
a
l
p
o
w
e
r
f
lo
w
w
it
h
p
o
st
c
o
n
ti
n
g
e
n
c
y
c
o
rre
c
ti
v
e
re
sc
h
e
d
u
li
n
g
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
y
ste
ms
,
P
W
RS
-
2
,
n
o
.
1
,
p
p
.
1
7
5
-
1
8
2
,
1
9
8
7
.
[4
]
De
e
b
N
,
S
h
a
h
i
d
e
h
p
u
r
S
.
M
.,
“
L
in
e
a
r
re
a
c
ti
v
e
p
o
w
e
r
o
p
ti
m
iza
ti
o
n
in
a
larg
e
p
o
w
e
r
n
e
tw
o
rk
u
sin
g
th
e
d
e
c
o
m
p
o
siti
o
n
a
p
p
ro
a
c
h
,”
I
EE
E
T
r
a
n
s
a
c
ti
o
n
s o
n
p
o
we
r sy
ste
m
,
v
o
l.
5
,
n
o
.
2
,
p
p
.
4
2
8
-
4
3
5
,
1
9
9
0
.
[5
]
E.
Ho
b
so
n
.,
“
Ne
tw
o
rk
c
o
n
sra
in
e
d
re
a
c
ti
v
e
p
o
w
e
r
c
o
n
tro
l
u
sin
g
li
n
e
a
r
p
ro
g
ra
m
m
in
g
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
p
o
we
r
sy
ste
ms
,
P
A
S
-
99
,
n
o
.
4,
pp
.
8
6
8
-
8
7
7
,
1
9
8
0
.
[6
]
K.
Y
Lee
,
Y.
M
P
a
rk
,
a
n
d
J.
L
Oritz,
“
F
u
e
l
-
c
o
st
o
p
ti
m
iza
ti
o
n
f
o
r
b
o
t
h
re
a
l
a
n
d
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
e
s
,
”
IEE
Pro
c
,
v
o
l.
1
3
1
C,
n
o
.
3
,
p
p
.
85
-
93
,
1
9
8
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
d
v
A
p
p
l Sci
I
SS
N:
2
2
5
2
-
8814
P
a
s
s
erin
e
s
w
a
r
m
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
fo
r
s
o
lvin
g
o
p
tima
l
…
(
K
a
n
a
g
a
s
a
b
a
i Len
in
)
109
[7
]
M
.
K.
M
a
n
g
o
li
,
a
n
d
K.Y.
L
e
e
,
“
Op
ti
m
a
l
re
a
l
a
n
d
re
a
c
ti
v
e
p
o
w
e
r
c
o
n
tro
l
u
sin
g
li
n
e
a
r
p
r
o
g
ra
m
m
in
g
,
”
El
e
c
tr.P
o
we
r
S
y
st.R
e
s
,
v
o
l.
2
6
,
p
p
.
1
-
1
0
,
1
9
9
3
.
[8
]
A
p
a
ra
ji
ta
M
u
k
h
e
rjee
,
V
iv
e
k
a
n
a
n
d
a
M
u
k
h
e
rjee
,
“
S
o
lu
ti
o
n
o
f
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
b
y
c
h
a
o
ti
c
k
ril
l
h
e
rd
a
lg
o
rit
h
m
,”
IET
Ge
n
e
r.
T
ra
n
sm
.
Distrib
,
v
o
l.
9
,
no
.
1
5
,
p
p
.
2
3
5
1
-
2
3
6
2
,
2
0
1
5
.
[9
]
Hu
,
Z.
,
W
a
n
g
,
X
.
&
T
a
y
lo
r,
G
,
“
S
to
c
h
a
stic
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
:
F
o
rm
u
latio
n
a
n
d
s
o
lu
ti
o
n
m
e
th
o
d
,”
El
e
c
tr.
Po
we
r E
n
e
rg
y
S
y
st
,
v
o
l.
3
2
,
p
p
.
6
1
5
-
6
2
1
.
2
0
1
0
.
[1
0
]
M
a
h
a
letc
h
u
m
i
A
/P
M
o
rg
a
n
,
No
r
Ru
l
Ha
sm
a
A
b
d
u
ll
a
h
,
M
o
h
d
He
rw
a
n
S
u
laim
a
n
,
M
a
h
f
u
z
a
h
M
u
sta
f
a
a
n
d
R
o
sd
iy
a
n
a
S
a
m
a
d
,
“
Co
m
p
u
tatio
n
a
l
i
n
telli
g
e
n
c
e
tec
h
n
iq
u
e
f
o
r
sta
ti
c
V
A
R
c
o
m
p
e
n
sa
to
r
(S
V
C)
in
sta
ll
a
ti
o
n
c
o
n
sid
e
rin
g
m
u
lt
i
-
c
o
n
ti
n
g
e
n
c
ies
(N
-
m)
,
”
AR
PN
J
o
u
rn
a
l
o
f
E
n
g
i
n
e
e
rin
g
a
n
d
Ap
p
li
e
d
S
c
ien
c
e
s
,
v
o
l.
1
0
,
no
.
2
2
,
De
c
2
0
1
5
.
[1
1
]
M
o
h
d
He
rw
a
n
S
u
laim
a
n
,
Zu
rian
i
M
u
sta
f
fa
,
Ha
m
d
a
n
Da
n
i
y
a
l,
M
o
h
d
Ru
slli
m
M
o
h
a
m
e
d
a
n
d
O
m
a
r
Alim
a
n
,
“
S
o
lv
in
g
Op
ti
m
a
l
Re
a
c
ti
v
e
P
o
w
e
r
P
lan
n
i
n
g
P
ro
b
lem
Util
izin
g
Na
tu
re
In
sp
ired
Co
m
p
u
ti
n
g
T
e
c
h
n
iq
u
e
s
,
”
AR
PN
J
o
u
rn
a
l
o
f
En
g
i
n
e
e
rin
g
a
n
d
A
p
p
li
e
d
S
c
ien
c
e
s
,
v
o
l
.
1
0
,
no
.
2
1
,
p
p
.
9
7
7
9
-
9
7
8
5
,
No
v
2
0
1
5
.
[1
2
]
M
o
h
d
He
rw
a
n
S
u
laim
a
n
,
W
o
n
g
L
o
In
g
,
Zu
rian
i
M
u
sta
f
f
a
a
n
d
M
o
h
d
R
u
slli
m
M
o
h
a
m
e
d
,
“
G
r
e
y
W
o
lf
Op
ti
m
i
z
e
r
f
o
r
S
o
lv
in
g
Eco
n
o
m
ic
Disp
a
tch
P
ro
b
lem
w
it
h
V
a
lv
e
-
L
o
a
d
in
g
Eff
e
c
t
s
,
”
AR
PN
J
o
u
r
n
a
l
o
f
E
n
g
in
e
e
rin
g
a
n
d
Ap
p
li
e
d
S
c
ien
c
e
s
,
v
o
l
.
1
0
,
no
.
2
1
,
p
p
.
9
7
9
6
-
9
8
0
1
,
No
v
2
0
1
5
.
[1
3
]
P
a
n
d
iara
jan
,
K.
&
Ba
b
u
lal,
C.
K.,
“
F
u
z
z
y
h
a
r
m
o
n
y
se
a
r
c
h
a
lg
o
rit
h
m
b
a
se
d
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
f
o
r
p
o
w
e
r
s
y
ste
m
se
c
u
rit
y
e
n
h
a
n
c
e
m
e
n
t
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
El
e
c
tric P
o
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r E
n
e
rg
y
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y
st
,
v
o
l.
7
8
,
p
p
.
7
2
-
7
9
.
2
0
1
6
.
[1
4
]
M
u
sta
f
fa
,
Z.
,
S
u
laim
a
n
,
M
.
H.,
Yu
so
f
,
Y.,
Ka
m
a
ru
lza
m
a
n
,
S
.
F.,
“
A
n
o
v
e
l
h
y
b
rid
m
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tah
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risti
c
a
lg
o
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it
h
m
f
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sh
o
rt
term
lo
a
d
f
o
re
c
a
stin
g
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
S
imu
l
a
ti
o
n
:
S
y
ste
ms
,
S
c
ien
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e
a
n
d
T
e
c
h
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o
lo
g
y
,
v
ol
.
1
7
,
n
o
.
4
1
,
pp.
6
.
1
-
6
.
6
.
2
0
1
7
.
[1
5
]
A
n
d
e
rso
n
,
T
.
R.
,
“
Bio
lo
g
y
o
f
th
e
u
b
i
q
u
it
o
u
s
h
o
u
se
sp
a
rr
o
w
:
F
ro
m
g
e
n
e
s
to
p
o
p
u
latio
n
s
,”
Ox
fo
rd
:
O
x
fo
rd
Un
ive
rs
i
ty
Pre
ss
,
2
0
0
6
.
[1
6
]
Ba
rn
a
rd
,
C.
J.,
&
S
i
b
ly
,
R.
M
.
,
“
P
ro
d
u
c
e
rs
a
n
d
sc
ro
u
n
g
e
rs:
A
g
e
n
e
ra
l
m
o
d
e
l
a
n
d
i
ts
a
p
p
li
c
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ti
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n
t
o
c
a
p
ti
v
e
f
lo
c
k
s
o
f
h
o
u
se
s
p
a
rro
w
s
,”
An
ima
l
Be
h
a
v
i
o
r
,
v
o
l.
2
9
,
p
p
.
5
4
3
-
5
5
0
,
2
0
1
8
.
[1
7
]
Be
a
u
c
h
a
m
p
,
G
.
“
T
h
e
e
ff
e
c
t
o
f
g
ro
u
p
siz
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n
m
e
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n
f
o
o
d
i
n
ta
k
e
ra
te
in
b
ird
s
,
”
Bi
o
lo
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ica
l
R
e
v
iews
,
v
o
l.
7
3
,
p
p
.
4
4
9
-
472
,
1
9
9
8
.
[1
8
]
Be
a
u
c
h
a
m
p
,
G
.
,
“
G
ro
u
p
-
siz
e
e
ff
e
c
ts
o
n
v
ig
il
a
n
c
e
:
A
se
a
r
c
h
f
o
r
m
e
c
h
a
n
is
m
s
,”
Beh
a
v
io
ra
l
Pro
c
e
ss
e
s
,
v
o
l.
6
3
,
p
p
.
1
1
1
-
121
,
2
0
0
3
.
[1
9
]
Be
d
n
e
k
o
ff
,
B.
A
.
,
&
L
i
m
a
,
S
.
L
.
,
“
Ra
n
d
o
m
n
e
ss
,
c
h
a
o
s
a
n
d
c
o
n
f
u
sio
n
i
n
t
h
e
stu
d
y
o
f
a
n
ti
p
re
d
a
to
r
v
ig
il
a
n
c
e
,”
T
re
n
d
s
in
Eco
l
o
g
y
a
n
d
Ev
o
lu
t
io
n
,
v
o
l.
1
3
,
p
p
.
2
8
4
-
2
8
7
,
1
9
9
8
.
[2
0
]
Co
o
len
,
I.
,
G
irald
e
a
u
,
L
.
A
.
,
&
L
a
v
o
ie,
M
.
,
“
He
a
d
p
o
siti
o
n
a
s
a
n
i
n
d
ica
to
r
o
f
p
r
o
d
u
c
e
r
a
n
d
sc
ro
u
n
g
e
r
tac
ti
c
s
in
a
g
ro
u
n
d
-
f
e
e
d
in
g
b
ird
,”
A
n
ima
l
Be
h
a
v
io
r
,
v
o
l.
6
1
,
p
p
.
8
9
5
-
9
0
3
,
2
0
0
1
.
d
o
i:
1
0
.
1
0
0
6
/an
b
e
.
2
0
0
0
.
1
6
7
8
.
[2
1
]
W
u
Q
H,
M
a
J
T
.
“
P
o
w
e
r
s
y
s
tem
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
is
p
a
tch
u
sin
g
e
v
o
lu
ti
o
n
a
ry
p
ro
g
ra
m
m
in
g
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
p
o
we
r sy
ste
ms
,
v
o
l.
10
,
n
o
.
3
,
p
p
.
1
2
4
3
-
1
2
4
8
,
1
9
9
5
.
[2
2
]
S
.
Du
ra
iraj
,
D.
De
v
a
ra
j
,
P
.
S
.
K
a
n
n
a
n
,
“
G
e
n
e
ti
c
a
lg
o
rit
h
m
a
p
p
li
c
a
ti
o
n
s
to
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
w
it
h
v
o
lt
a
g
e
sta
b
il
it
y
e
n
h
a
n
c
e
m
e
n
t
,
”
IE(
I)
J
o
u
rn
a
l
-
EL
,
v
ol
.
8
7
,
S
e
p
t
2
0
0
6
.
[2
3
]
D.De
v
a
ra
j
,
“
I
m
p
ro
v
e
d
g
e
n
e
ti
c
a
lg
o
rit
h
m
f
o
r
m
u
lt
i
-
o
b
jec
ti
v
e
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
p
ro
b
lem
,
”
Eu
ro
p
e
a
n
T
ra
n
sa
c
ti
o
n
s
o
n
e
lec
trica
l
p
o
we
r
,
v
o
l.
17
,
p
p
.
5
6
9
-
5
8
1
,
2
0
0
7
.
[2
4
]
P
.
A
ru
n
a
Je
y
a
n
th
y
a
n
d
Dr.
D.
De
v
a
r
a
j
.,
“
Op
ti
m
a
l
Re
a
c
ti
v
e
P
o
w
e
r
Disp
a
tch
f
o
r
V
o
lt
a
g
e
S
tab
i
l
it
y
En
h
a
n
c
e
m
e
n
t
Us
in
g
Re
a
l
Co
d
e
d
G
e
n
e
ti
c
A
lg
o
rit
h
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Co
mp
u
ter
a
n
d
El
e
c
trica
l
E
n
g
i
n
e
e
r
in
g
,
v
o
l.
2
,
n
o
.
4
,
p
p
.
1
7
9
3
-
8
1
6
3
,
A
u
g
2
0
1
0
.
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