I
n
d
o
n
es
i
a
n
J
o
u
rn
a
l
o
f
E
l
ect
ri
ca
l
E
n
g
i
n
eer
i
n
g
a
n
d
C
o
mp
u
t
er
S
ci
en
ce
V
o
l
.
9
,
No
.
1
,
Ja
n
u
ar
y
2
01
8
,
pp
.
1
23
~
13
0
IS
S
N
:
250
2
-
47
52
,
D
O
I
:
10.
115
91
/
i
j
eecs
.
v
9
.
i
1
.
p
p
1
23
-
1
30
1
23
Jo
u
r
n
al
h
om
e
pa
ge
:
h
t
t
p
:
/
/
i
a
e
s
c
o
r
e
.
c
o
m
/
j
o
u
r
n
a
l
s
/
i
n
d
e
x
.
p
h
p
/
i
j
e
e
c
s
G
rav
i
t
at
i
o
na
l
S
ea
rc
h A
l
go
r
i
t
hm
B
a
s
e
d T
e
c
hni
que f
or
V
o
l
t
a
ge
St
a
bi
l
i
t
y I
mpr
ove
me
nt
M
o
ha
m
a
d
K
h
a
i
r
uz
z
a
m
a
n
M
o
ha
m
a
d
Z
a
m
a
ni
1
,
I
s
m
a
i
l
M
u
s
i
r
i
n
2
,
M
o
ha
m
a
d
Sa
br
i
O
m
a
r
3
,
Sa
i
f
ul
I
z
w
a
n
Sul
i
m
a
n
4
,
N
o
r
A
z
ur
a
M
d
.
G
ha
ni
5
,
N
u
r
A
zw
a
n
M
o
h
a
med
K
a
ma
r
i
6
1,2,3,4
F
a
c
ul
t
y
of
E
l
e
c
t
ri
c
a
l
E
ngi
n
e
e
ri
ng,
U
ni
v
e
rs
i
t
i
T
e
knol
ogi
M
A
RA
,
40000 S
ha
h
A
l
a
m
,
S
e
l
a
ngor,
M
a
l
a
y
s
i
a
5
F
a
c
ul
t
y
of Com
put
e
r
&
M
a
t
he
m
a
t
i
c
a
l
S
c
i
e
nc
e
s
,
U
ni
ve
rs
i
t
i
T
e
kno
l
ogi
M
A
RA
,
400
00 S
ha
h A
l
a
m
,
S
e
l
a
ngor
,
M
a
l
a
y
s
i
a
6
D
e
pa
rt
m
e
nt
of E
l
e
c
t
ri
c
a
l
,
E
l
e
c
t
r
oni
c
&
S
y
s
t
e
m
s
E
ngi
ne
e
ri
ng,
F
a
c
ul
t
y
of E
ngi
ne
e
ri
ng
a
nd
Bui
l
t
E
nvi
ronm
e
nt
,
U
ni
ve
rs
i
t
i
K
e
ba
ngs
a
a
n M
a
l
a
y
s
i
a
A
rt
i
cl
e
I
n
f
o
A
B
S
T
RA
C
T
Ar
t
i
c
l
e
h
i
s
t
o
r
y
:
R
ecei
v
ed
Ju
l
y
1
9,
2
01
7
Re
v
i
s
e
d
O
ct
20
,
20
1
7
A
ccep
t
e
d
N
ov
7
,
20
1
7
V
ol
t
a
ge
i
ns
t
a
bi
l
i
t
y
prob
l
e
m
ha
s
be
e
n know
n a
s
a
s
i
gni
fi
c
a
nt
t
hr
e
a
t
t
o pow
e
r
s
y
s
t
e
m
ope
ra
t
i
o
n s
i
nc
e
i
t
s
oc
c
u
rre
nc
e
c
a
n l
e
a
d
t
o pow
e
r i
nt
e
rru
pt
i
on.
T
h
i
s
phe
nom
e
non c
a
n be
du
e
t
o
unc
o
nt
rol
l
a
b
l
e
l
oa
d
i
nc
re
m
e
nt
,
l
i
ne
a
nd ge
ne
r
a
t
o
r
out
a
ge
c
on
t
i
ng
e
nc
i
e
s
or unpl
a
n
n
ed
l
o
ad
cu
r
t
ai
l
m
en
t
. O
p
t
i
m
a
l
r
ea
ct
i
v
e p
o
w
er
di
s
pa
t
c
h
i
nvol
v
i
ng re
a
c
t
i
v
e
po
w
e
r s
upport
c
a
n be
on
e
of
t
h
e
opt
i
ons
for
i
m
provi
ng vol
t
a
ge
s
t
a
bi
l
i
t
y
o
f a
pow
e
r s
y
s
t
e
m
,
w
hi
c
h a
l
s
o re
qui
re
s
opt
i
m
i
z
a
t
i
on pr
oc
e
s
s
.
O
pt
i
m
a
l
s
i
z
i
ng a
nd l
o
c
a
t
i
on c
a
n of re
a
c
t
i
ve
pow
e
r
s
upport
c
a
n a
voi
d t
he
s
y
s
t
e
m
from
e
xpe
ri
e
nc
i
ng
ove
r
-
c
om
pe
ns
a
t
e
d or unde
r
-
c
om
pe
ns
a
t
e
d p
he
nom
e
na
.
T
he
pre
s
e
nc
e
of
o
pt
i
m
i
z
a
t
i
on
t
e
c
hni
que
s
ha
s
he
l
pe
d
s
ol
vi
ng
non
-
opt
i
m
a
l
phe
nom
e
non,
ne
ve
r
t
he
l
e
s
s
s
om
e
s
e
t
ba
c
ks
ha
ve
a
l
s
o be
e
n
e
xpe
r
i
e
nc
e
d
i
n t
e
rm
s
of i
na
c
c
ura
c
y
a
n
d
s
tu
c
k
in
lo
c
a
l o
p
tim
a
.
Th
is
pa
pe
r pre
s
e
n
t
s
t
he
a
pp
l
i
c
a
t
i
on
of G
ra
vi
t
a
t
i
ona
l
S
e
a
rc
h A
l
gori
t
hm
(G
S
A
)
t
e
c
hn
i
que
i
n a
t
t
e
m
pt
t
o s
ol
v
e
o
pt
i
m
a
l
r
e
a
c
t
i
v
e
pow
e
r di
s
pa
t
c
h
probl
e
m
i
n
t
e
rm
s
of re
a
c
t
i
ve
pow
e
r s
upport
for vol
t
a
ge
s
t
a
bi
l
i
t
y
i
m
prove
m
e
nt
.
O
p
tim
iz
a
tio
n
proc
e
s
s
t
e
s
t
e
d on IE
E
E
14
-
bus
Re
l
i
a
bi
l
i
t
y
T
e
s
t
S
y
s
t
e
m
(RT
S
)
ha
s
re
ve
a
l
e
d
i
t
s
s
upe
ri
ori
t
y
w
i
t
h s
i
gni
fi
c
a
nt
pr
om
i
s
i
ng re
s
ul
t
s
i
n t
e
rm
s
of
v
o
lta
g
e
s
ta
b
ili
t
y
im
p
r
o
v
e
m
e
n
t
in
th
e
te
s
t
s
y
s
te
m
.
Ke
y
wo
r
d
s
:
G
r
a
v
i
t
a
t
i
o
n
a
l
S
e
a
r
c
h
A
l
g
o
r
i
t
h
m
O
p
t
i
m
al
R
eact
i
v
e
P
o
w
er
D
i
s
p
a
t
c
h
V
o
l
t
a
g
e
S
t
a
b
i
l
i
t
y
L
o
a
d
I
n
d
e
x
Copy
r
i
ght
©
201
8
Ins
t
i
t
ut
e
o
f
A
d
v
anc
e
d
E
ngi
n
e
e
r
i
ng and S
c
i
e
nc
e
.
A
l
l
ri
g
h
t
s re
se
rv
e
d
.
C
or
r
e
s
po
n
di
n
g
A
u
t
h
or
:
M
o
h
am
ad
K
h
a
i
r
u
zzam
an
M
o
h
am
ad
Z
am
an
i
,
F
a
c
u
l
t
y
o
f
E
l
e
c
t
r
i
c
a
l
E
n
g
i
n
e
e
r
i
n
g
,
U
ni
ve
r
s
i
t
i
T
e
k
nol
ogi
M
A
R
A,
40
000
S
h
a
h
A
la
m
,
S
e
la
n
go
r
,
Ma
la
ys
ia
.
E
m
a
i
l
:
m
ohd_
kha
i
r
uz
z
a
m
a
n@
y
a
h
oo
.
c
om
1.
I
N
T
R
O
D
U
C
T
I
O
N
A
s
i
de
o
f
t
he
r
m
a
l
ove
r
l
oa
d a
nd a
ngl
e
i
ns
t
a
bi
l
i
t
y
i
s
s
ue
,
v
ol
t
a
ge
i
ns
t
a
bi
l
i
t
y
ha
s
be
e
n k
n
ow
n t
o be
a
m
a
jor
i
s
s
ue
i
n
a
p
o
w
e
r
s
y
s
t
e
m
ope
r
a
t
i
on
.
V
ol
t
a
ge
i
n
s
t
a
bi
l
i
t
y
c
a
n be
obs
e
r
ve
d
i
n t
e
r
m
s
of
p
r
og
r
e
s
s
i
ve
r
e
d
uc
t
i
o
n
of
vol
t
a
ge
l
e
ve
l
w
hi
c
h
e
ve
nt
ua
l
l
y
l
e
a
ds
t
o
s
y
s
t
e
m
di
s
r
u
pt
i
o
n
due
t
o
vol
t
a
ge
c
o
l
l
a
ps
e
phe
n
om
e
non
[
1]
.
V
ol
t
a
ge
i
ns
t
a
bi
l
i
t
y
c
a
n oc
c
ur
du
e
t
o va
r
i
ous
r
e
a
s
on
s
s
u
c
h a
s
hi
ghl
y
s
t
r
e
s
s
e
d p
ow
e
r
s
y
s
t
e
m
,
hi
g
h l
oa
di
n
g i
n a
p
owe
r
s
y
s
t
e
m
,
e
xt
e
ns
i
ve
us
a
ge
of
s
h
u
nt
c
om
pe
ns
a
t
i
on
de
vi
c
e
,
s
w
i
t
c
hi
ng
of
l
oa
d
s
a
n
d
p
r
o
t
e
c
t
i
v
e d
e
v
i
ces
as
w
el
l
as
i
m
p
r
o
p
er
r
e
act
i
v
e p
o
w
e
r
s
u
p
p
o
r
t
[
2
]
-
[
4
]
.
I
n
r
ecen
t
y
ear
s
,
b
l
ack
o
u
t
s
o
cc
u
r
r
en
ce
s
ha
ve
be
e
n
r
e
po
r
t
e
d
d
ue
t
o
u
n
d
e
t
e
c
t
e
d
p
r
o
g
r
e
s
s
i
ve
r
e
d
uc
t
i
o
n
i
n
v
ol
t
a
ge
s
t
a
bi
l
i
t
y
i
n
po
w
e
r
s
y
s
t
e
m
s
[
5]
.
I
n
or
de
r
t
o i
m
pr
o
ve
t
he
v
ol
t
a
ge
s
t
a
bi
l
i
t
y
of
a
po
w
e
r
s
y
s
t
e
m
,
opt
im
a
l
r
e
a
c
t
i
ve
po
we
r
di
s
pa
t
c
h c
a
n be
e
m
pl
oy
e
d.
S
e
v
e
r
a
l
r
e
s
e
a
r
c
he
r
s
ha
ve
i
m
pl
e
m
e
nt
e
d
va
r
i
ou
s
opt
i
m
i
z
a
ti
on t
e
c
hni
que
t
o s
o
l
ve
o
pt
i
m
a
l
r
e
a
c
t
i
ve
po
w
e
r
di
s
pa
t
c
h
pr
o
bl
e
m
.
I
n
[
6]
,
G
e
ne
t
i
c
A
l
go
r
i
t
hm
(
G
A
)
ha
s
be
e
n i
m
pl
e
m
e
nt
e
d t
o
s
o
l
ve
o
pt
i
m
a
l
r
e
a
c
t
i
ve
p
ow
e
r
di
s
pa
t
c
h p
r
obl
e
m
i
n m
i
nim
i
z
i
ng t
h
e
t
ot
a
l
po
w
e
r
l
os
s
i
n
I
E
E
E
3
0
-
b
us
s
y
s
t
e
m
.
On t
he
ot
he
r
h
a
nd
,
G
A
ha
s
be
e
n i
m
pl
e
m
e
nt
e
d i
n [
7]
f
or
s
ol
vi
n
g
opt
i
m
a
l
r
e
a
c
t
i
ve
powe
r
di
s
pa
t
c
h
pr
o
bl
e
m
t
o im
pr
o
ve
v
ol
t
a
ge
pr
of
i
l
e
o
f
a
p
r
act
i
cal
I
n
d
i
a
n
p
o
w
er
s
y
s
t
e
m
.
T
h
e r
es
ear
ch
c
om
pa
r
e
s
t
he
o
pt
im
i
z
e
d r
e
s
ul
t
s
us
i
ng
GA
w
i
t
h
opt
i
m
i
z
a
t
i
on
r
e
s
ul
t
s
pr
o
vi
de
d by
L
i
ne
a
r
P
r
o
gr
a
m
m
i
ng (
L
P
)
t
e
c
hni
que
,
w
hi
c
h
r
e
ve
a
l
e
d t
ha
t
G
A
i
s
c
a
pa
bl
e
t
o
pr
od
uc
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
25
02
-
475
2
I
n
d
one
s
i
a
n
J
E
l
e
c
E
n
g
&
C
o
m
p
S
c
i
,
V
o
l
.
9
,
N
o
.
1
,
J
an
u
ar
y
20
1
8
:
1
23
–
13
0
1
24
hi
g
he
r
q
ua
l
i
t
y
r
e
s
ul
t
s
c
om
pa
r
e
d t
o L
P
.
A
ut
h
or
s
i
n [
8]
ha
s
a
t
t
e
m
pt
e
d t
o s
ol
ve
t
he
s
a
m
e
pr
o
bl
e
m
s
a
s
i
n
[
7]
by
us
i
n
g P
a
r
t
i
c
l
e
S
wa
r
m
O
pt
i
m
iz
a
t
i
on (
P
S
O
)
t
e
c
hni
que
a
n
d c
om
pa
r
a
t
i
ve
s
t
udy
w
a
s
c
o
nd
uc
t
e
d
w
i
t
h r
e
s
pe
c
t
t
o
L
P
t
e
c
h
ni
q
ue
,
r
e
s
ul
t
i
n
g i
n
P
S
O
pr
o
vi
di
n
g be
t
t
e
r
r
e
s
ul
t
s
c
om
pa
r
e
d t
o
L
P
.
P
S
O
w
a
s
f
u
r
t
he
r
i
m
pr
o
ve
d
by
s
ev
er
al
r
es
ea
r
c
h
er
s
w
h
er
e au
t
h
o
r
s
i
n
[
9
]
h
as
i
m
pl
e
m
e
nt
e
d m
odi
f
i
e
d
E
vol
ut
i
ona
r
y
P
S
O
(
E
P
S
O
)
t
o
s
ol
v
e
o
p
t
i
m
al
r
eact
i
v
e p
o
w
e
r
d
i
s
p
at
ch
p
r
o
b
l
em
w
h
i
l
e au
t
h
o
r
s
i
n
[
1
0
]
h
as
m
o
d
i
f
i
ed
t
h
e accel
e
r
at
i
o
n
co
e
f
f
i
ci
en
t
o
f
P
S
O
t
e
c
h
ni
q
ue
w
hi
c
h t
he
n
pr
od
uc
e
a
t
e
c
h
ni
que
k
n
ow
n a
s
P
S
O
wi
t
h
t
i
m
e
va
r
y
i
ng
a
c
c
e
l
e
r
a
t
i
on
c
oe
f
f
i
c
i
e
n
t
s
(
P
SO
-
T
V
A
C
)
.
As
i
de
o
f
t
he
m
e
nt
i
one
d
t
e
c
h
n
i
que
s
,
s
e
ve
r
a
l
ot
he
r
t
e
c
h
ni
qu
e
s
w
hi
c
h
ha
s
b
e
e
n i
m
pl
e
m
e
nte
d t
o
s
o
l
v
e
o
p
t
i
m
a
l
r
e
a
c
t
i
v
e
p
o
w
e
r
d
i
s
p
a
t
c
h
p
r
o
b
l
e
m
a
r
e
A
r
t
i
f
i
c
i
a
l
Be
e
Co
l
o
n
y
[
1
1
]
,
C
u
c
k
o
o
S
e
a
r
c
h
A
l
g
o
r
i
t
h
m
[
1
2]
a
n
d
A
nt
C
ol
o
ny
O
pt
i
m
i
z
a
t
i
on
[
1
3]
.
Cl
a
s
s
i
c
a
l
o
p
t
i
m
i
z
a
t
i
o
n
t
e
c
h
n
i
q
u
e
s
u
c
h
a
s
L
P
,
N
o
n
-
L
i
n
e
ar
P
r
o
g
r
am
m
i
n
g
,
Q
u
ad
r
at
i
c P
r
o
g
r
am
m
i
n
g
a
nd
N
e
w
t
on
P
r
o
g
r
a
m
m
i
ng ha
s
be
e
n i
m
p
l
e
m
e
nt
e
d t
o s
ol
ve
o
pt
i
m
a
l
r
e
a
c
t
i
ve
p
ow
e
r
di
s
pa
t
c
h p
r
obl
e
m
.
H
o
we
ve
r
,
t
he
s
e
c
l
a
s
s
i
c
a
l
t
e
c
hni
que
s
s
u
f
f
e
r
f
r
om
dr
a
w
ba
c
ks
s
uc
h a
s
i
ns
e
c
ur
e
c
o
n
v
e
r
g
e
n
c
e
,
s
e
n
s
i
t
i
v
i
t
y
t
o
s
e
a
r
c
h
s
t
a
r
t
i
n
g
p
o
i
n
t
[
1
0
]
,
d
i
f
f
i
c
u
l
t
i
e
s
o
n
h
a
n
d
l
i
n
g
p
r
o
b
l
e
m
w
i
t
h
d
i
s
c
r
e
t
e
v
a
r
i
a
b
l
e
s
[
6
]
,
a
n
d
d
i
f
f
i
c
u
l
t
y
t
o
s
o
l
v
e
t
he
p
r
obl
e
m
du
e
t
o
t
he
n
o
nl
i
n
e
a
r
i
t
y
of
t
he
pr
obl
e
m
[
9]
.
I
n
t
hi
s
s
t
udy
,
G
S
A
w
a
s
e
m
pl
oy
e
d
i
n
t
he
a
t
t
e
m
pt
t
o
s
ol
ve
opt
i
m
al
r
eact
i
v
e
p
o
w
e
r
d
i
s
p
at
ch
p
r
o
b
l
em
i
n
o
r
d
e
r
t
o
i
m
p
r
o
v
e
t
h
e
v
o
l
t
a
g
e
s
t
a
b
i
l
i
t
y
o
f
I
E
E
E
1
4
-
B
u
s
R
T
S
.
A
p
re
-
de
ve
l
ope
d
v
ol
t
a
ge
s
t
a
bi
l
i
t
y
i
nde
x t
e
r
m
e
d
a
s
V
o
l
t
a
g
e
S
t
a
b
i
l
i
t
y
L
o
a
d
I
n
d
e
x
(
V
L
S
I
)
d
e
v
e
l
o
p
e
d
b
y
T
.
K
.
A
b
d
u
l
Ra
h
m
a
n
e
t
.
a
l
[
1
5
]
w
a
s
u
t
i
l
i
z
e
d
a
s
t
h
e
i
n
d
i
c
a
t
o
r
.
I
n t
h
i
s
pa
pe
r
,
3 c
a
s
e
s
t
udi
e
s
a
r
e
c
ons
i
de
r
e
d
w
hi
c
h i
n
vol
ve
s
t
he
m
a
ni
pul
a
t
i
o
n o
f
l
oa
d a
t
t
he
w
e
a
ke
s
t
bus
i
n t
he
s
y
s
t
e
m
.
R
e
s
ul
t
s
ob
t
a
i
ne
d f
r
om
t
he
s
t
udy
r
e
ve
a
l
e
d t
he
f
e
a
s
i
bi
l
i
t
y
of
GS
A
i
n
pr
o
duc
i
ng
pr
o
m
i
s
i
ng
r
e
s
u
l
t
s
.
2.
R
E
S
E
AR
C
H
M
ETH
O
D
2
.
1
.
P
ro
b
l
em
F
o
rmu
l
at
i
on
I
n
t
hi
s
s
t
udy
,
t
he
a
i
m
of
t
he
o
pt
im
i
z
a
t
i
on
pr
oc
e
s
s
i
s
t
o
i
m
pr
o
ve
t
he
vol
t
a
g
e
s
t
a
bi
l
i
t
y
i
n
t
he
s
y
s
t
e
m
by
m
i
nim
i
z
i
ng t
he
v
ol
t
a
ge
s
t
a
bi
l
i
t
y
i
nde
x
of
t
he
w
e
a
ke
s
t
b
us
i
n t
he
s
y
s
t
e
m
.
He
nc
e
,
t
he
ob
j
e
c
t
i
ve
f
unc
t
i
on
o
f
t
h
e
opt
i
m
i
z
a
ti
on
pr
oc
e
s
s
c
a
n
be
e
xp
r
e
s
s
e
d
as
:
=
(
)
(
1)
w
h
e
r
e
V
S
L
I
i
s
t
h
e
v
a
l
u
e
o
f
v
o
l
t
a
g
e
s
t
a
b
i
l
i
t
y
o
f
t
h
e
w
e
a
k
e
s
t
b
u
s
i
n
t
h
e
s
y
s
t
e
m
.
D
u
r
i
n
g
t
h
e
o
p
t
i
m
i
zat
i
o
n
p
r
o
c
es
s
,
a c
r
u
ci
al
c
o
n
s
t
r
ai
n
t
n
eed
s
t
o
b
e s
at
i
s
f
i
ed
w
h
er
e t
h
e t
o
t
al
r
eact
i
v
e
po
w
e
r
pr
o
duc
e
d by
t
he
ge
ne
r
a
t
i
on u
ni
t
Q
_
g a
nd t
ot
a
l
r
e
a
c
t
i
ve
p
ow
e
r
i
nje
c
t
e
d t
o t
he
t
e
s
t
s
y
s
t
e
m
Q
_i
n
j s
h
ou
l
d
cat
er
t
h
e
r
eact
i
v
e l
o
a
d
d
em
a
n
d
Q
_
d
em
an
d
an
d
t
h
e
r
eact
i
v
e
p
o
w
er
l
o
s
s
i
n
t
h
e s
y
s
t
e
m
Q
_
l
o
s
s
.
I
t
can
b
e
ex
p
r
es
s
e
d
as
:
+
=
∑
+
∑
(
2)
2.
2.
G
r
a
vi
t
at
i
on
al
S
e
ar
c
h
A
l
gor
i
t
h
m
(
G
S
A
)
G
S
A
w
as
f
i
r
s
t
i
n
t
r
o
d
u
ce
d
b
y
E
s
m
a
t
R
as
h
ed
i
,
H
o
s
s
ei
n
N
ezam
ab
ad
i
-
po
ur
a
n
d S
a
e
id
S
ar
y
azd
i
i
n
20
0
9 [
1
4]
.
T
hi
s
opt
i
m
i
z
a
t
i
on t
e
c
hni
q
ue
i
s
ins
pi
r
e
d
by
l
a
w of
gr
a
vi
t
y
a
nd m
a
s
s
i
nt
e
r
a
c
t
i
on.
M
a
s
s
e
s
i
n G
S
A
(
F
igu
r
e
1)
w
i
l
l
obe
y
2
m
a
i
n
l
a
w
w
hi
c
h
i
s
t
he
l
a
w
o
f
g
r
a
vi
t
y
a
nd
l
a
w
of
m
ot
i
on.
F
o
r
de
t
a
i
l
e
d
e
x
pl
a
n
a
t
i
on
a
bo
ut
G
S
A t
e
c
hni
q
u
e
s
r
e
ga
r
di
ng a
bo
ut
i
t
s
l
a
ws
a
nd a
l
go
r
i
t
hm
,
t
he
br
i
e
f
de
s
c
r
i
pt
i
o
n o
f
t
he
m
e
c
ha
ni
c
s
of
G
S
A
t
e
c
hni
q
ue
i
s
di
s
c
us
s
e
d
a
s
t
he
f
ol
l
o
wi
n
gs
.
S
t
e
p
1
:
A
g
e
n
t
s
i
n
i
t
i
a
l
i
z
a
t
i
o
n
C
ons
i
de
r
i
ng a
s
y
s
t
e
m
w
hi
c
h c
on
s
i
s
t
s
of
N a
ge
nt
s
,
t
he
i
ni
t
i
a
l
pos
i
t
i
on o
f
t
he
a
ge
nt
s
i
n dt
h di
m
e
ns
i
on
i
s
d
ef
i
n
ed
a
s
f
o
l
l
o
w
s
:
=
1
,
…
,
,
…
,
=
1
,
2
,
…
,
(
3)
w
he
r
e
n
i
s
t
he
num
be
r
of
di
m
e
ns
i
o
ns
o
f
t
he
opt
i
m
i
z
a
ti
on
pr
obl
e
m
.
S
t
e
p
2:
E
va
l
ua
t
e
f
i
t
ne
s
s
va
l
ue
of
t
he
a
ge
nt
s
A
t
t
h
i
s
s
t
e
p
,
t
h
e
f
i
t
n
e
s
s
v
a
l
u
e
f
o
r
e
a
c
h
a
g
e
n
t
i
n
t
h
e
s
y
s
t
e
m
i
s
e
v
a
l
u
a
t
e
d
.
I
n
t
h
i
s
s
t
u
d
y
,
t
h
e
f
i
t
n
e
s
s
va
l
ue
i
s
V
S
L
I
a
nd
i
t
i
s
de
t
e
r
m
i
ne
d
f
r
om
t
h
e
c
u
r
r
e
nt
p
os
i
t
i
on
o
f
t
he
a
ge
nt
.
S
t
e
p
3
:
U
p
d
a
t
e
o
f
g
r
a
v
i
t
a
t
i
o
n
a
l
c
o
n
s
t
a
n
t
,
b
e
s
t
f
i
t
n
e
s
s
,
w
o
r
s
t
f
i
t
n
e
s
s
a
n
d
a
g
e
n
t
m
a
s
s
I
n
t
h
i
s
s
t
e
p
,
t
h
e
c
u
r
r
e
n
t
g
r
a
v
i
t
a
t
i
o
n
a
l
c
o
n
s
t
a
n
t
G
(t
) i
s
u
p
d
a
t
e
d
.
T
h
e
v
a
l
u
e
o
f
G(t
) i
s
re
l
a
t
e
d
b
a
s
e
d
o
n
t
h
e
i
n
i
t
i
a
l
i
t
e
r
a
t
i
o
n
n
u
m
b
e
r
t
0
,
c
u
r
r
e
n
t
i
t
e
r
a
t
i
o
n
n
u
m
b
e
r
t
a
n
d
c
o
n
s
t
a
n
t
β
.
L
a
t
e
r
o
n
,
t
h
e
b
e
s
t
f
i
t
n
e
s
s
a
n
d
t
h
e
w
o
r
s
t
f
i
t
n
e
s
s
i
n
c
u
r
r
e
n
t
i
t
e
r
a
t
i
o
n
i
s
d
e
f
i
n
e
d
.
I
n
t
h
i
s
s
t
u
d
y
,
t
h
e
b
e
s
t
f
i
t
n
e
s
s
b
e
s
t
f
i
t
(
t
)
i
s
d
ef
i
n
e
d
as
t
h
e l
o
w
es
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
one
s
i
a
n
J
E
l
e
c
E
n
g
&
C
o
m
p
S
c
i
IS
S
N
:
250
2
-
47
52
G
r
av
i
t
at
i
on
al
Se
a
r
c
h
A
l
g
or
i
t
hm
B
as
e
d
T
e
c
h
ni
q
ue
f
o
r
V
ol
t
a
ge
S
t
a
b
i
l
i
t
y
…
(
M
.
K
.
M
oha
m
ad
Z
am
an
i
)
1
25
f
i
t
n
e
s
s
v
a
l
u
e
w
h
i
l
e
t
h
e
w
o
r
s
t
f
i
t
n
e
s
s
w
o
r
s
t
f
i
t
(
t
)
i
s
d
e
f
i
n
e
d
a
s
t
h
e
h
i
g
h
e
s
t
f
i
t
n
e
s
s
v
a
l
u
e
.
F
i
n
a
l
l
y
,
t
h
e
a
g
e
n
t
m
a
s
s
M
i
(
t
)
f
o
r
t
he
a
ge
nt
s
i
s
t
he
n
c
om
put
e
d
ba
s
e
d
on
t
he
f
i
t
ne
s
s
va
l
ue
f
i
t
i
(
t
)
,
be
s
t
f
i
t
ne
s
s
va
l
u
e
a
nd
t
he
w
or
s
t
f
i
t
ne
s
s
v
al
u
e.
(
)
=
(
0
)
×
0
(
4)
(
)
=
m
i
n
∈
{
1
,
…
,
}
(
)
(
5)
(
)
=
ma
x
∈
{
1
,
…
,
}
(
)
(
6)
(
)
=
(
)
−
(
)
(
)
−
(
)
(
7)
(
)
=
(
)
∑
(
)
=
1
(
8)
S
t
e
p
4
:
Co
m
p
u
t
a
t
i
o
n
o
f
t
o
t
a
l
f
o
r
c
e
i
n
e
v
e
r
y
d
i
r
e
c
t
i
o
n
D
u
r
i
n
g t
hi
s
s
t
e
p,
t
he
f
or
c
e
a
c
t
i
ng o
n i
t
h a
ge
nt
f
r
om
jt
h a
ge
nt
a
t
dt
h
di
m
e
ns
i
on
F
_i
j^
d
(
t
)
w
i
l
l
b
e
cal
cu
l
at
ed
b
as
ed
o
n
t
h
e
act
i
v
e g
r
a
v
i
t
at
i
o
n
al
m
as
s
r
el
at
e
d
t
o
j
t
h
ag
e
n
t
M
aj
(
t
)
,
p
as
s
i
v
e g
r
a
v
i
t
at
i
o
n
al
m
as
s
r
e
l
a
t
e
d
t
o
i
t
h
a
g
e
n
t
M
p
i
(
t
)
,
E
u
c
l
i
d
i
a
n
d
i
s
t
a
n
c
e
b
e
t
w
e
e
n
i
t
h
a
g
e
n
t
a
n
d
j
t
h
a
g
e
n
t
Ri
j
(
t
)
a
s
w
e
l
l
a
s
s
m
a
l
l
co
n
s
t
an
t
ε.
=
=
=
=
1
,
…
,
(
9)
(
)
=
−
2
=
1
(
10
)
(
)
=
(
)
×
(
)
×
(
)
(
)
×
×
(
)
−
(
)
(
11
)
S
t
e
p
5
:
Co
m
p
u
t
a
t
i
o
n
o
f
a
c
c
e
l
e
r
a
t
i
o
n
a
n
d
v
e
l
o
c
i
t
y
N
ex
t
,
t
h
e
accel
er
at
i
o
n
o
f
t
h
e
a
g
en
t
s
a
_
i
^
d
(
t
)
i
s
co
m
p
u
t
ed
.
A
ccel
er
at
i
o
n
o
f
t
h
e
ag
e
n
t
s
ar
e
d
et
er
m
i
n
ed
by
t
he
t
ot
a
l
f
or
c
e
a
c
t
i
ng o
n i
t
h a
ge
nt
F
_i
^
d
(
t
)
o
ve
r
t
he
i
ne
r
t
i
a
l
m
a
s
s
of
i
th a
ge
nt
M
_i
i
(
t
)
.
T
he
n,
t
he
ve
l
oc
i
t
y
of
t
he
a
ge
nt
v
_i
^
d i
s
up
da
t
e
d
ba
s
e
d
o
n t
h
e accel
er
at
i
o
n
o
f
t
h
e a
g
en
t
s
an
d
t
h
e i
n
f
l
u
e
n
ce
o
f
r
a
n
d
o
m
i
zat
i
o
n
w
h
e
re
〖
r
an
d
〗
_i
i
s
a
r
a
n
dom
n
um
be
r
i
n
t
he
i
n
t
e
r
va
l
of
0
t
o
1.
(
)
=
×
(
)
=
1
,
≠
(
12
)
(
)
=
(
)
(
)
(
13
)
(
+
1
)
=
×
(
)
+
(
)
(
14
)
S
t
e
p
6:
A
ge
nt
s
pos
i
t
i
o
n
u
pda
t
e
A
f
t
e
r
t
h
e
v
e
l
o
c
i
t
y
o
f
t
h
e
a
g
e
n
t
s
h
a
s
b
e
e
n
u
p
d
a
t
e
d
,
t
h
e
n
t
h
e
p
o
s
i
t
i
o
n
o
f
t
h
e
a
g
e
n
t
x
_
i
^d
w
i
l
l
a
l
s
o
b
e
up
da
t
e
d
ba
s
e
d
on
t
he
a
ge
nt
ve
l
oc
i
t
y
.
(
+
1
)
=
(
)
+
(
+
1
)
(
15
)
S
t
ep
7
:
C
o
n
v
er
g
en
ce
T
es
t
N
o
w
,
t
h
e
a
l
g
o
r
i
t
h
m
w
i
l
l
c
h
e
c
k
t
h
e
t
e
r
m
i
n
a
t
i
o
n
c
r
i
t
e
r
i
a
o
f
t
h
e
o
p
t
i
m
i
z
a
t
i
o
n
p
r
o
c
e
s
s
.
I
f
t
h
e
o
p
t
i
m
i
zat
i
o
n
p
r
o
ces
s
h
as
r
ea
ch
i
t
s
m
a
x
i
m
u
m
i
t
e
r
a
t
i
o
n
l
i
m
i
t
,
t
h
e
o
p
t
i
m
i
z
a
t
i
o
n
p
r
o
c
e
s
s
c
a
n
b
e
t
e
r
m
i
n
a
t
e
d
.
O
t
h
e
r
w
i
s
e
,
t
h
e
a
l
g
o
r
i
t
h
m
w
i
l
l
p
r
o
c
e
e
d
b
a
c
k
t
o
s
t
e
p
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
25
02
-
475
2
I
n
d
one
s
i
a
n
J
E
l
e
c
E
n
g
&
C
o
m
p
S
c
i
,
V
o
l
.
9
,
N
o
.
1
,
J
an
u
ar
y
20
1
8
:
1
23
–
13
0
1
26
F
i
g
u
r
e
1
.
F
l
o
w
Ch
a
r
t
o
f
G
S
A
2.
3.
V
ol
t
age
S
t
ab
i
l
i
t
y
L
oa
d
I
n
d
e
x
V
ol
t
a
ge
s
t
a
bi
l
i
t
y
i
nde
x
u
s
e
d
i
n
t
hi
s
pa
pe
r
i
s
a
n
i
n
de
x
de
ve
l
ope
d
by
T
.
K
.
Ab
d
ul
R
a
hm
a
n
[
1
5]
i
n
1
99
5
kn
o
w
n a
s
V
ol
t
a
ge
S
t
a
bi
l
i
t
y
L
oa
d
I
n
de
x (
V
S
L
I
)
.
V
S
L
I
c
a
n be
i
m
pl
e
m
e
nt
e
d t
o de
t
e
r
m
i
ne
t
he
vol
t
a
ge
s
t
a
bi
l
i
t
y
a
t
a
l
oa
d
bu
s
a
nd
i
de
nt
i
f
y
t
he
w
e
a
ke
s
t
bu
s
i
n a
p
ow
e
r
s
y
s
t
e
m
.
I
n
F
i
g
u
r
e
2,
V
_t
h
i
s
t
he
ope
n
c
i
r
c
ui
t
v
ol
t
a
ge
r
e
pr
e
s
e
nt
by
n
o
l
oa
d
vol
t
a
ge
a
n
d
a
n
gl
e
,
V
_o
a
n
d
θ
_o
r
e
s
pe
c
t
i
ve
l
y
.
W
hi
l
e
V
_L
a
n
d
θ
_
L
i
s
l
oa
d
v
ol
t
a
ge
a
nd
a
ngl
e
vi
e
w
f
r
o
m
e
a
c
h
l
oa
d
b
u
s
.
V
_
o,
θ
_
o,
V
_L
,
a
nd
θ
_L
w
e
r
e
c
a
l
c
ul
a
t
e
d
us
i
n
g
l
oa
d
f
l
o
w
a
na
l
y
s
i
s
.
I
n
VS
L
I
,
a
bus
w
i
t
h
vol
t
a
ge
s
t
a
bi
l
i
t
y
i
nde
x c
l
os
e
t
o
1
.
0
0 i
s
c
o
ns
i
de
r
e
d a
s
t
he
c
r
i
t
i
c
a
l
bus
.
O
n t
h
e
ot
he
r
ha
n
d,
vol
t
a
ge
s
t
ab
i
l
i
t
y
i
n
d
ex
l
es
s
er
t
h
an
1
.
0
0
i
m
p
l
i
es
l
es
s
w
eak
b
u
s
i
n
t
h
e s
y
s
t
e
m
.
V
S
L
I
can
b
e e
x
p
r
e
s
s
ed
m
at
h
e
m
at
i
cal
l
y
as
:
=
4
c
o
s
(
−
)
−
2
c
o
s
(
−
)
2
0
2
(
16
)
F
ig
ur
e
2.
E
q
ui
va
l
e
nt
T
he
ve
ni
n
c
i
r
c
ui
t
vi
e
w
f
r
om
e
a
c
h
l
oa
d
3.
R
E
S
U
L
T
S
A
ND
A
N
A
L
Y
S
I
S
I
n t
hi
s
s
t
u
dy
,
3
c
a
s
e
s
t
udi
e
s
h
a
ve
be
e
n c
o
nd
uc
t
e
d w
hi
c
h i
n
vol
ve
d m
a
ni
pu
l
a
t
i
on of
t
he
l
o
a
di
n
g a
t
t
he
w
e
a
ke
s
t
b
us
i
n
t
he
gi
ve
n
c
o
n
di
t
i
on.
C
a
s
e
s
t
udi
e
s
w
hi
c
h c
o
nd
uc
t
e
d
i
n t
he
s
t
udy
a
r
e
a
c
t
i
v
e
l
o
a
d
m
a
n
i
p
u
l
a
t
i
o
n
,
r
e
a
c
t
i
v
e
l
o
a
d
m
a
n
i
p
u
l
a
t
i
o
n
a
n
d
m
a
n
i
p
u
l
a
t
i
o
n
o
n
b
o
t
h
a
c
t
i
v
e
a
n
d
r
e
a
c
t
i
v
e
l
o
a
d
.
T
h
e
o
p
t
i
m
i
z
a
t
i
o
n
r
e
s
u
l
t
s
f
o
r
e
a
c
h
c
a
s
e
s
t
u
d
y
i
s
di
s
c
u
s
s
e
d
i
n
t
he
s
e
c
t
i
o
n
3.
1,
3.
2
a
n
d
3.
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
one
s
i
a
n
J
E
l
e
c
E
n
g
&
C
o
m
p
S
c
i
IS
S
N
:
250
2
-
47
52
G
r
av
i
t
at
i
on
al
Se
a
r
c
h
A
l
g
or
i
t
hm
B
as
e
d
T
e
c
h
ni
q
ue
f
o
r
V
ol
t
a
ge
S
t
a
b
i
l
i
t
y
…
(
M
.
K
.
M
oha
m
ad
Z
am
an
i
)
1
27
3.
1.
M
an
i
p
u
l
a
t
i
on
o
f
ac
t
i
ve
l
oa
d
d
e
m
an
d
I
n
t
h
i
s c
a
se
st
u
d
y
,
t
he
a
c
t
i
ve
l
oa
d
de
m
a
nd i
s
m
a
ni
pul
a
t
e
d
whe
r
e
t
he
l
oa
d
i
s
s
u
b
je
c
t
e
d t
o i
nc
r
e
m
e
nt
.
D
u
r
i
n
g t
hi
s
c
a
s
e
,
b
us
1
4 ha
s
be
e
n de
t
e
r
m
ine
d t
o
be
t
he
w
e
a
ke
s
t
b
us
.
T
he
a
c
t
i
ve
l
oa
d a
t
b
us
1
4 ha
s
be
e
n
i
nc
r
e
a
s
e
d
up
t
o
2.
5 t
i
m
e
s
i
t
s
n
om
i
na
l
l
oa
di
ng
va
l
ue
.
T
he
l
oa
ds
a
t
ot
he
r
b
u
s
es
a
r
e m
ai
n
t
ai
n
ed
as
i
n
n
o
m
i
n
a
l
ope
r
a
t
i
n
g
c
on
d
i
t
i
on.
U
p
o
n t
he
c
om
pl
e
t
i
on
of
t
he
opt
i
m
i
z
a
ti
on p
r
oc
e
s
s
,
i
t
c
a
n be
o
bs
e
r
ve
d t
ha
t
G
S
A ha
s
s
uc
c
e
s
s
f
ul
l
y
im
pr
o
ve
t
he
v
ol
t
a
ge
s
t
a
bi
l
i
t
y of
t
he
s
y
s
t
e
m
by
s
ol
vi
n
g
o
pt
i
m
a
l
r
e
a
c
t
i
ve
p
owe
r
di
s
pa
t
c
h
pr
o
bl
e
m
by
r
e
duc
i
n
g
t
he
va
l
ue
o
f
V
S
L
I
f
or
a
l
l
l
oa
di
ng c
o
n
di
t
i
ons
.
A
s
t
he
l
oa
d m
ul
t
i
pl
i
e
r
i
nc
r
e
a
s
e
s
,
t
he
va
l
ue
of
V
S
L
I
a
l
s
o
i
n
c
r
e
a
s
e
d
.
H
o
w
e
v
e
r
,
s
o
l
v
i
n
g
o
p
t
i
m
a
l
r
e
a
c
t
i
v
e
p
o
w
e
r
d
i
s
p
a
t
c
h
h
a
s
i
m
p
r
o
v
e
d
t
h
e
v
o
l
t
a
g
e
s
t
a
b
i
l
i
t
y
a
t
b
u
s
1
4
,
he
nc
e
m
a
ki
ng
e
xt
r
a
l
oa
di
n
g a
t
bus
14
po
s
s
i
bl
e
.
O
p
t
i
m
i
z
a
t
i
o
n
r
e
s
u
l
t
s
u
s
i
n
g
G
S
A
i
s
p
r
e
s
e
n
t
e
d
i
n
T
a
b
l
e
1
a
n
d
g
r
a
p
h
i
cal
l
y
p
r
e
s
en
t
ed
as
i
n
F
i
g
u
r
e
3
.
T
a
b
l
e
1
.
O
p
t
i
m
i
z
a
t
i
o
n
r
e
s
u
l
t
s
f
o
r
a
c
t
i
v
e
l
o
a
d
m
a
n
i
p
u
l
a
t
i
o
n
c
o
n
d
i
t
i
o
n
L
o
ad
m
u
ltip
lier
at
bus
14
P
re
-
o
p
ti
m
iz
ed
VSL
I
Po
s
t
-
o
p
ti
m
iz
ed
VSL
I
1
.0
0.
1001
0.
0003
1
.1
0.
1257
0.
0377
1
.2
0.
1690
0.
0632
1
.3
0.
2091
0.
0842
1
.4
0.
2637
0.
1188
1
.5
0.
3172
0.
1518
1
.6
0.
3840
0.
1982
1
.7
0.
4490
0.
2430
1
.8
0.
5187
0.
3008
1
.9
0.
5919
0.
3569
2
.0
0.
6672
0.
4182
2
.1
0.
7428
0.
4842
2
.2
0.
8162
0.
5543
2
.3
0.
8841
0.
6275
2
.4
0.
9422
0.
7025
2
.5
0.
9840
0.
7774
F
i
g
u
r
e
3
.
V
S
L
I
v
a
l
u
e
s
a
t
d
i
f
f
e
r
e
n
t
a
c
t
i
v
e
l
o
a
d
m
u
l
t
i
p
l
i
e
r
3.
2.
M
an
i
p
u
l
a
t
i
on
o
f
r
e
ac
t
i
v
e
l
oa
d
d
e
m
a
n
d
I
n
t
hi
s
c
a
s
e
s
t
udy
,
t
he
r
e
a
c
t
i
ve
l
oa
d
de
m
a
nd
a
t
t
he
w
e
a
ke
s
t
bus
i
n
t
he
s
y
s
t
e
m
i
s
m
a
ni
pu
l
a
t
e
d.
B
us
14
w
a
s
f
ou
n
d t
o b
e
t
he
we
a
ke
s
t
bus
i
n t
he
s
y
s
t
e
m
dur
i
n
g t
he
nom
i
na
l
c
on
di
t
i
on.
T
he
r
e
a
c
t
i
ve
l
oa
d de
m
a
nd w
a
s
i
nc
r
e
a
s
e
d
a
t
t
h
e
hi
g
he
s
t
va
l
ue
p
os
s
i
bl
e
a
n
d
t
he
v
o
l
t
a
g
e
s
t
a
b
i
l
i
t
y
a
t
t
h
e
b
u
s
i
s
o
b
s
e
r
v
e
d
.
A
f
t
er
t
h
e o
p
t
i
m
i
zat
i
o
n
p
r
o
ce
s
s
h
as
b
een
c
o
n
d
u
ct
ed
,
G
S
A
h
as
s
u
cces
s
f
u
l
l
y
s
o
l
v
e
d
o
p
t
i
m
al
r
eact
i
v
e
po
w
e
r
di
s
pa
t
c
h t
o
i
m
pr
ove
t
he
vol
t
a
ge
s
t
a
bi
l
i
t
y
a
t
bus
1
4
of
t
he
t
e
s
t
s
y
s
t
e
m
.
I
t
c
a
n
be
obs
e
r
ve
d
t
h
a
t
a
s
t
he
r
eact
i
v
e l
oa
d
i
s
i
nc
r
e
a
s
e
d
,
t
h
e
v
ol
t
a
ge
s
t
a
bi
l
i
t
y
i
nde
x
w
a
s
a
l
s
o i
nc
r
e
a
s
e
d
f
o
r
bot
h
pr
e
-
o
pt
i
m
i
z
e
d
a
n
d po
s
t
-
opt
i
m
i
z
e
d c
on
di
t
i
on.
H
ow
e
v
e
r
,
t
he
p
os
t
-
o
p
t
im
i
z
e
d vol
t
a
g
e
s
t
a
bi
l
i
t
y
i
nde
x va
l
ue
r
e
m
a
i
ns
l
ow
e
r
t
ha
n t
he
p
r
e
-
o
p
t
i
m
i
z
e
d
v
o
l
t
a
g
e
s
t
a
b
i
l
i
t
y
i
n
d
e
x
,
w
h
i
c
h
i
m
p
l
i
e
s
t
h
e
s
u
c
c
e
s
s
o
f
G
S
A
.
T
h
e
o
p
t
i
m
i
z
a
t
i
o
n
r
e
s
u
l
t
i
s
t
a
b
u
l
a
t
e
d
i
n
T
a
bl
e
2
a
nd
i
t
i
s
de
pi
c
t
e
d
i
n
F
i
gu
r
e
4.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
25
02
-
475
2
I
n
d
one
s
i
a
n
J
E
l
e
c
E
n
g
&
C
o
m
p
S
c
i
,
V
o
l
.
9
,
N
o
.
1
,
J
an
u
ar
y
20
1
8
:
1
23
–
13
0
1
28
T
a
b
l
e
2
.
O
p
t
i
m
i
z
a
t
i
o
n
r
e
s
u
l
t
s
f
o
r
r
e
a
c
t
i
v
e
l
o
a
d
m
a
n
i
p
u
l
a
t
i
o
n
c
o
n
d
i
t
i
o
n
L
o
ad
m
u
ltip
lier
at
bus
14
P
re
-
o
p
ti
m
iz
ed
VSL
I
Po
s
t
-
o
p
ti
m
iz
ed
VSL
I
8
0.
9152
0.
6613
8
.1
0.
9251
0.
6702
8
.2
0.
9349
0.
6791
8
.3
0.
9447
0.
6881
8
.4
0.
9543
0.
6972
8
.5
0.
9637
0.
7064
8
.6
0.
9730
0.
7157
8
.7
0.
9819
0.
7252
8
.8
0.
9902
0.
7348
8
.9
0.
9975
0.
7446
F
i
g
u
r
e
4
.
V
S
L
I
v
a
l
u
e
s
a
t
d
i
f
f
e
r
e
n
t
r
e
a
c
t
i
v
e
l
o
a
d
m
u
l
t
i
p
l
i
e
r
3.
3.
M
an
i
p
u
l
a
t
i
on
o
f
ac
t
i
ve
an
d
r
e
ac
t
i
ve
l
oa
d
d
e
m
an
d
I
n t
hi
s
c
o
n
di
t
i
on,
bot
h r
e
a
l
a
nd r
e
a
c
t
i
ve
l
oa
d de
m
a
nd
of
t
he
w
e
a
k
e
s
t
bus
i
n t
h
e
s
y
s
t
e
m
i
s
m
a
ni
pul
a
t
e
d a
nd
G
S
A i
s
i
m
pl
e
m
e
nt
e
d t
o s
ol
ve
opt
i
m
a
l
r
e
a
c
t
i
ve
po
we
r
di
s
pa
t
c
h p
r
o
bl
e
m
.
H
e
r
e
,
bu
s
14
ha
s
b
een
i
d
e
n
t
i
f
i
ed
t
o
b
e t
h
e w
ea
k
es
t
b
u
s
i
n
t
h
e
s
y
s
t
e
m
.
D
u
r
i
n
g
t
h
e
o
p
t
i
m
i
z
a
t
i
o
n
p
r
o
c
e
s
s
,
t
h
e
a
c
t
i
v
e
a
n
d
r
e
a
c
t
i
v
e
l
oa
d
ha
s
be
e
n
i
nc
r
e
a
s
e
d
i
n
s
t
e
ps
a
n
d
t
he
v
ol
t
a
ge
s
t
a
bi
l
i
t
y
i
nde
x
va
l
ue
i
s
o
b
s
e
r
ve
d.
U
p
o
n c
om
pl
e
t
i
on
of
o
pt
i
m
i
z
a
t
i
on
pr
oc
e
s
s
,
i
t
c
a
n be
o
b
s
e
r
ve
d t
ha
t
G
S
A
ha
s
s
uc
c
e
s
s
f
ul
l
y
s
ol
ve
op
t
i
m
a
l
r
e
a
c
t
i
v
e
p
o
w
e
r
d
i
s
p
a
t
c
h
f
o
r
v
o
l
t
a
g
e
s
t
a
b
i
l
i
t
y
i
m
p
r
o
v
e
m
e
n
t
p
r
o
b
l
e
m
.
T
h
e
r
e
s
u
l
t
s
y
i
e
l
d
e
d
b
y
t
h
e
opt
i
m
i
z
a
ti
on p
r
oc
e
s
s
s
ho
ws
t
ha
t
t
he
v
ol
t
a
ge
s
t
a
bi
l
i
t
y
i
nde
x
a
t
b
us
14
o
f
t
he
t
e
s
t
s
y
s
t
e
m
ha
s
be
e
n i
m
pr
o
ve
d
t
hr
ou
g
h r
e
d
uc
t
i
on o
f
t
he
v
ol
t
a
ge
s
t
a
bi
l
i
t
y
inde
x
va
l
ue
.
A
t
m
a
xim
u
m
l
o
a
di
n
g,
t
he
p
os
t
-
o
p
t
i
m
i
z
e
d
v
o
l
t
a
g
e
s
t
a
bi
l
i
t
y
i
nde
x
va
l
ue
ha
s
b
e
e
n s
i
g
ni
f
i
c
a
n
t
r
e
d
uc
t
i
on
,
w
hi
c
h e
n
a
bl
e
s
f
u
r
t
he
r
l
oa
di
ng a
t
t
he
b
u
s
.
T
he
opt
i
m
i
z
a
ti
on
r
e
s
ul
t
s
a
n
d
i
t
s
gr
a
phi
c
a
l
r
e
p
r
e
s
e
nt
a
t
i
on
i
s
p
r
o
vi
de
d
i
n
T
a
bl
e
3
a
nd
F
i
g
u
r
e
5
r
e
s
pe
c
t
i
ve
l
y
.
T
a
b
l
e
3
.
O
p
t
i
m
i
z
a
t
i
o
n
r
e
s
u
l
t
s
f
o
r
a
c
t
i
v
e
a
n
d
r
e
a
c
t
i
v
e
l
o
a
d
m
a
n
i
p
u
l
a
t
i
o
n
c
o
n
d
i
t
i
o
n
L
o
ad
m
u
ltip
lier
at
bus
14
P
re
-
o
p
ti
m
iz
ed
VSL
I
Po
s
t
-
o
p
ti
m
iz
ed
VSL
I
1
.0
0.
1453
0.
0096
1
.1
0.
1801
0.
0615
1
.2
0.
2315
0.
0941
1
.3
0.
2864
0.
1296
1
.4
0.
3470
0.
1631
1
.5
0.
4057
0.
2096
1
.6
0.
4692
0.
2612
1
.7
0.
5366
0.
3108
1
.8
0.
6069
0.
3654
1
.9
0.
6787
0.
4247
2
.0
0.
7503
0.
4881
2
.1
0.
8196
0.
5551
2
.2
0.
8837
0.
6248
2
.3
0.
9389
0.
6961
2
.4
0.
9800
0.
7673
2
.5
0.
9996
0.
8364
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
one
s
i
a
n
J
E
l
e
c
E
n
g
&
C
o
m
p
S
c
i
IS
S
N
:
250
2
-
47
52
G
r
av
i
t
at
i
on
al
Se
a
r
c
h
A
l
g
or
i
t
hm
B
as
e
d
T
e
c
h
ni
q
ue
f
o
r
V
ol
t
a
ge
S
t
a
b
i
l
i
t
y
…
(
M
.
K
.
M
oha
m
ad
Z
am
an
i
)
1
29
F
i
gu
r
e
5.
V
S
L
I
v
a
l
u
e
s
a
t
d
i
f
f
e
r
e
n
t
a
c
t
i
v
e
a
n
d
r
e
a
c
t
i
v
e
l
o
a
d
m
u
l
t
i
p
l
i
e
r
4.
C
O
N
CL
U
S
I
O
N
A
t
t
he
e
n
d
of
t
he
s
t
udy
,
i
t
c
a
n
be
c
o
nc
l
u
de
d
t
ha
t
GS
A
ha
s
s
uc
c
e
s
s
f
ul
l
y
s
ol
ve
opt
i
m
a
l
r
e
a
c
t
i
ve
p
owe
r
d
i
s
p
a
t
c
h
t
o
i
m
p
r
o
v
e
v
o
l
t
a
g
e
s
t
a
b
i
l
i
t
y
i
n
t
h
e
s
y
s
t
e
m
.
F
r
o
m
a
l
l
c
a
s
e
s
t
u
d
i
e
s
c
o
n
d
u
c
t
ed
i
n
t
h
e p
ap
er
,
G
S
A
h
a
s
pr
o
vi
de
d e
xc
e
l
l
e
nt
pos
t
-
o
pt
i
m
i
z
e
d r
e
s
ul
t
s
i
n t
e
r
m
s
of
vol
t
a
ge
s
t
a
bi
l
i
t
y
im
pr
ove
m
e
nt
on t
he
we
a
ke
s
t
bus
i
n a
po
w
e
r
s
y
s
t
e
m
.
I
t
c
a
n a
l
s
o
be
c
onc
l
ude
d t
ha
t
opt
i
m
a
l
r
e
a
c
t
i
ve
p
ow
e
r
di
s
p
a
t
c
h c
a
n i
m
pr
ove
v
ol
t
a
ge
s
t
a
bi
l
i
t
y
i
nde
x
i
n
a
po
w
e
r
sy
st
e
m
.
A
C
K
N
O
W
L
E
D
G
E
ME
NT
T
he
a
ut
h
o
r
s
wo
ul
d l
i
ke
t
o
a
c
kn
owl
e
dge
t
he
I
ns
t
i
t
ut
e
of
R
e
s
e
a
r
c
h M
a
na
ge
m
e
nt
a
nd I
n
no
va
t
i
o
n
(IR
M
I
) Ui
T
M
,
S
h
a
h
Al
a
m
,
S
e
l
a
n
g
o
r,
M
a
l
a
y
s
i
a
fo
r t
h
e
f
i
n
a
n
c
i
a
l
s
u
p
p
o
rt
o
f
t
h
i
s
re
s
e
a
rc
h
.
T
h
i
s
re
s
e
a
rc
h
i
s
s
up
p
or
t
e
d by
I
R
M
I
u
nde
r
B
E
S
T
AR
I
R
es
ear
ch
G
r
a
n
t
S
ch
em
e w
i
t
h
p
r
o
j
ect
co
d
e:
6
0
0
-
IR
M
I/
M
Y
R
A
5
/
3
/
BE
S
T
A
RI
(
0
2
7
/
2
0
1
7
)
.
R
EF
ER
E
N
C
ES
[1]
G
ha
ffa
rz
a
de
h N
,
A
kba
ri
M
,
K
h
an
j
an
zad
eh
A
.
D
i
s
t
ri
but
e
d ge
n
e
ra
t
i
on a
l
l
o
c
a
t
i
o
n t
o i
m
prove
s
t
e
a
d
y
s
t
a
t
e
vol
t
a
g
e
s
t
a
bi
l
i
t
y
of di
s
t
ri
but
i
on n
e
t
w
orks
us
i
ng I
m
pe
ri
a
l
i
s
t
C
o
m
p
e
tit
iv
e
A
lg
o
r
ith
m
.
Int
e
r
nat
i
ona
l
J
our
nal
of
A
ppl
i
e
d
P
ow
e
r
E
ngi
ne
e
r
i
ng
.
20
13
;
2
(
2
)
:
71
-
78
.
[2]
L
of P
A
,
A
nde
rs
s
on G
,
Hi
l
l
DJ
.
V
ol
t
a
ge
s
t
a
bi
l
i
t
y i
ndi
c
e
s
for s
t
r
e
s
s
e
d pow
e
r s
y
s
t
e
m
s
.
IE
E
E
T
r
ans
ac
t
i
ons
on
P
o
w
er
S
ys
t
em
s
.
1993
;
8
(
1
)
:
326
-
335
.
[3]
Cut
s
e
m
T
V
.
V
o
l
t
a
g
e
i
ns
t
a
bi
l
i
t
y
:
phe
nom
e
na
,
c
o
unt
e
rm
e
a
s
ure
s
,
a
nd a
n
a
l
y
s
i
s
m
e
t
hods
.
P
r
oc
e
e
d
i
ngs
of
t
h
e
I
E
E
E
.
2000
;
88
(
2
):
208
-
227
.
[4]
M
a
rt
ol
i
a
T
,
Ve
r
m
a
MK
.
V
ol
t
a
g
e
s
t
a
b
i
l
i
t
y
ba
s
e
d
form
a
t
i
on of
v
ol
t
a
g
e
c
on
t
rol
a
r
e
a
s
c
ons
i
d
e
ri
ng
i
m
pa
c
t
o
f
c
ont
i
ng
e
nc
i
e
s
.
I
nt
e
r
nat
i
onal
J
ou
r
nal
of
A
ppl
i
e
d P
owe
r
E
ng
i
ne
e
r
i
ng
.
2012
;
1
(
3
)
:
11
5
-
122.
[5]
S
i
ngh S
P
,
S
i
ngh S
P
.
On
-
l
i
ne
a
s
s
e
s
s
m
e
nt
of vol
t
a
ge
s
t
a
bi
l
i
t
y
us
i
n
g S
y
nc
hroph
a
s
or t
e
c
hno
l
og
y
.
In
done
s
i
an
J
our
nal
of
E
l
e
c
t
r
i
c
al
E
ngi
ne
e
r
i
n
g and Com
put
e
r
Sc
i
e
n
c
e
.
2017
;
8
(
1
):
1
-
8
.
[6]
V
ă
duva
A
M
,
Bul
a
c
C
.
Ne
w e
v
ol
ut
i
onar
y
al
gor
i
t
hm
m
e
t
hod f
or
s
ol
v
i
ng opt
i
m
al
r
e
ac
t
i
v
e
powe
r
di
s
pat
c
h
pr
obl
e
m
.
Int
e
rna
t
i
ona
l
Confe
r
e
nc
e
on A
ppl
i
e
d
a
n
d T
he
or
e
t
i
c
a
l
E
l
e
c
t
r
i
c
i
t
y
(ICA
T
E
).
Cra
i
ova
.
2016
:
1
-
6.
[7]
Ra
y
udu K
,
Y
e
s
ura
t
na
m
G
, J
a
y
al
ax
m
i
A
.
Im
pr
ov
i
ng v
ol
t
age
s
t
abi
l
i
t
y
by
opt
i
m
al
r
e
ac
t
i
v
e
pow
e
r
di
s
pat
c
h
bas
e
d on ge
n
e
t
i
c
al
gor
i
t
hm
and
l
i
ne
ar
pr
ogr
am
m
i
ng t
e
c
hni
que
.
20
16 Int
e
rn
a
t
i
on
a
l
Confe
re
nc
e
on
E
l
e
c
t
ri
c
a
l
,
E
l
e
c
t
roni
c
s
,
a
nd O
pt
i
m
i
z
a
t
i
o
n
T
e
c
hni
que
s
(IC
E
E
O
T
).
Che
nn
a
i
.
2
016
:
1357
-
1362.
[8]
Ra
y
udu K
,
Y
e
s
u
ra
t
na
m
G
,
A
li M
,
J
a
y
a
la
x
m
i A
.
O
pt
i
m
al
r
e
ac
t
i
v
e
powe
r
di
s
pat
c
h bas
e
d on par
t
i
c
l
e
s
war
m
opt
i
m
i
z
at
i
on and
L
P
t
e
c
hni
qu
e
.
2
016 Int
e
rna
t
i
ona
l
Confe
re
n
c
e
on
E
m
e
rgi
ng T
e
c
hn
ol
ogi
c
a
l
T
r
e
nds
(ICE
T
T
)
.
K
o
lla
m
.
2016
:
1
-
7
.
[9]
F
er
r
ei
r
a
E
C
, N
et
o
M
S
I
, A
s
ad
a E
N
.
M
e
ta
h
e
u
r
is
tic
s
tr
a
t
e
gi
e
s
f
or
s
ol
v
i
ng t
he
O
pt
i
m
al
R
e
ac
t
i
v
e
P
owe
r
D
i
s
pat
c
h
wi
t
h di
s
c
r
e
t
e
v
ar
i
abl
e
s
.
2016 12t
h
IE
E
E
In
t
e
rn
a
t
i
o
na
l
Confe
r
e
nc
e
on Indus
t
r
y
A
ppl
i
c
a
t
i
ons
(
I
NDUS
C
ON)
.
Curi
t
i
ba
.
2016
:
1
-
6
.
[10]
M
e
da
ni
K
BO
,
S
a
y
a
h S
.
O
pt
i
m
al
r
e
ac
t
i
v
e
pow
e
r
di
s
pat
c
h us
i
ng par
t
i
c
l
e
s
wa
r
m
o
p
tim
iz
a
tio
n
w
ith
tim
e
va
r
yi
n
g
a
cc
el
er
a
t
i
o
n
co
ef
f
i
ci
en
t
s
.
2016 8t
h Int
e
rna
t
i
ona
l
Conf
e
re
nc
e
on M
ode
l
l
i
ng
,
Ide
nt
i
fi
c
a
t
i
on a
nd
Cont
rol
(ICM
IC
).
A
l
gi
e
rs
.
2
016
:
780
-
785
.
[11]
Ra
y
udu K
,
Y
e
s
ura
t
na
m
G
,
J
a
ya
l
a
xm
i
A
.
A
r
t
i
f
i
c
i
al
B
e
e
Col
on
y
al
gor
i
t
hm
f
or
opt
i
m
al
r
ea
ct
i
ve p
o
w
er
di
s
pat
c
h t
o i
m
pr
ov
e
v
ol
t
ag
e
s
t
abi
l
i
t
y
.
2016 Int
e
rna
t
i
on
a
l
Confe
r
e
nc
e
on Ci
rc
u
i
t
,
P
ow
e
r a
nd Co
m
put
i
ng
T
e
c
hno
l
ogi
e
s
(I
CCP
CT
).
N
ag
er
co
i
l
.
2016
:
1
-
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
25
02
-
475
2
I
n
d
one
s
i
a
n
J
E
l
e
c
E
n
g
&
C
o
m
p
S
c
i
,
V
o
l
.
9
,
N
o
.
1
,
J
an
u
ar
y
20
1
8
:
1
23
–
13
0
1
30
[12]
S
ul
a
i
m
a
n M
H
,
M
us
t
a
ffa
Z
.
Cu
c
k
oo Se
ar
c
h
A
l
go
r
i
t
hm
as
an opt
i
m
i
z
e
r
f
or
O
pt
i
m
al
R
e
ac
t
i
v
e
P
o
w
e
r Di
sp
a
t
c
h
pr
obl
e
m
s
.
2017 3rd Int
e
rna
t
i
on
a
l
Confe
r
e
nc
e
o
n Cont
rol
,
A
ut
o
m
a
t
i
on a
nd Robot
i
c
s
(ICCA
R).
N
a
g
oy
a
.
2017
:
735
-
739
.
[13]
Ra
y
udu K
,
Y
e
s
ura
t
na
m
G
,
J
a
y
a
l
a
xm
i
A
.
A
nt
c
ol
ony
opt
i
m
i
z
at
i
o
n al
gor
i
t
hm
bas
e
d opt
i
m
al
r
e
ac
t
i
v
e
powe
r
di
s
pat
c
h t
o i
m
pr
ov
e
v
ol
ta
g
e
s
ta
b
ilit
y
.
2017 Int
e
rna
t
i
on
a
l
Confe
r
e
nc
e
on Ci
rc
u
i
t
,
P
ow
e
r a
nd Co
m
put
i
ng
T
e
c
hno
l
ogi
e
s
(I
CCP
CT
).
K
o
l
l
am
.
2017
:
1
-
6
.
[14]
Ra
s
hi
di
E
,
N
e
z
a
m
a
ba
di
-
pour H
,
S
a
r
y
a
z
di
S
.
G
S
A
:
A
G
ra
vi
t
a
t
i
o
na
l
S
e
a
rc
h A
l
go
ri
t
hm
.
Inf
or
m
at
i
on Sc
i
e
nc
e
s
.
2009
;
179
(
13
)
:
2
232
-
2248
.
[15]
Ra
hm
a
n T
K
A
,
J
a
s
m
on G
B
.
A
ne
w t
e
c
hni
qu
e
f
or
v
ol
t
ag
e
s
t
abi
l
i
t
y
anal
y
s
i
s
i
n a powe
r
s
y
s
t
e
m
and
i
m
pr
ov
e
d
l
oadf
l
ow al
gor
i
t
hm
f
or
di
s
t
r
i
but
i
on ne
t
wor
k
.
P
ro
c
e
e
d
i
ngs
of E
M
P
D
'
95.
,
1995 In
t
e
rna
t
i
ona
l
Conf
e
re
nc
e
on
E
ne
rg
y
M
a
n
a
ge
m
e
nt
a
nd
P
ow
e
r
D
e
l
i
ve
r
y
,
1995
.
Si
nga
pore
.
1995
;
2:
714
-
719
.
Evaluation Warning : The document was created with Spire.PDF for Python.