I
nte
rna
t
io
na
l J
o
urna
l o
f
Ro
bo
t
ics a
nd
Aut
o
m
a
t
io
n (
I
J
R
A)
Vo
l.
8
,
No
.
2
,
J
u
n
e
201
9
,
p
p
.
77
~
88
I
SS
N:
2089
-
4
8
5
6
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
r
a
.
v
8
i
2
.
p
p
7
7
-
88
77
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
co
r
e.
co
m/jo
u
r
n
a
ls
/in
d
ex
.
p
h
p
/
I
JR
A
O
pti
m
a
l
T
CSC
pl
a
ce
m
en
t
for con
g
estio
n
m
a
na
g
e
m
e
nt
in
deregu
la
ted
po
w
er sy
ste
m
s usin
g
a
ntlion o
pti
m
i
z
a
t
io
n alg
o
rith
m
M
a
j
id
M
o
a
zz
a
m
i
1
,
H
o
s
s
ein S
ha
hin
za
deh
2
,
G
ev
o
rk
B
.
G
ha
re
hp
et
ia
n
3
,
Abo
lf
a
zl
Sh
a
f
iei
4
1
S
m
a
rt
M
icro
g
rid
Re
se
a
rc
h
Ce
n
ter,
Na
jaf
a
b
a
d
Bra
n
c
h
,
Isla
m
ic
A
z
a
d
Un
iv
e
rsity
,
Na
ja
f
a
b
a
d
,
Ira
n
4
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
Na
jaf
a
b
a
d
Bra
n
c
h
,
Isla
m
ic
A
z
a
d
Un
iv
e
rsit
y
,
Na
ja
f
a
b
a
d
,
Ira
n
2
,
3
De
p
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
Am
ir
k
a
b
ir
Un
iv
e
rsit
y
o
f
Tec
h
n
o
l
o
g
y
(
T
e
h
ra
n
P
o
ly
te
c
h
n
ic),
T
e
h
ra
n
,
Ira
n
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
an
2
9
,
2
0
1
9
R
ev
i
s
ed
A
p
r
2
,
2
0
1
9
A
cc
ep
ted
A
p
r
1
6
,
2
0
1
9
Co
n
g
e
stio
n
m
a
n
a
g
e
m
e
n
t
is
o
n
e
o
f
th
e
i
m
p
o
rtan
t
issu
e
s
in
th
e
d
e
re
g
u
late
d
p
o
w
e
r
s
y
ste
m
s.
T
h
e
re
a
re
se
v
e
ra
l
m
e
th
o
d
s
to
e
li
m
in
a
te
c
o
n
g
e
stio
n
.
Util
izin
g
F
A
C
T
S
d
e
v
ic
e
s
is
a
n
a
p
p
ro
p
riate
o
p
ti
o
n
f
o
r
larg
e
-
s
c
a
le
a
n
d
q
u
ick
c
o
n
tro
l
o
f
f
lo
ws
o
f
tran
s
m
issio
n
li
n
e
s.
F
A
C
T
S
d
e
v
ice
s
su
c
h
a
s
T
h
y
risto
r
Co
n
tr
o
ll
e
d
S
e
ries
Ca
p
a
c
it
o
r
(T
CS
C)
c
a
n
h
e
lp
to
m
it
ig
a
te
th
e
tran
sm
it
ti
n
g
f
lo
w
o
f
p
o
w
e
r
in
th
e
c
o
n
g
e
ste
d
li
n
e
s,
w
h
ich
le
a
d
s
to
a
n
in
c
re
a
se
in
th
e
n
e
t
w
o
rk
lo
a
d
in
g
a
b
il
it
y
a
s
we
ll
a
s
re
d
u
c
ti
o
n
o
f
b
o
th
l
o
ss
e
s
a
n
d
p
r
o
d
u
c
ti
o
n
c
o
sts.
Du
e
to
th
e
c
o
n
sid
e
ra
b
ly
h
ig
h
p
rice
o
f
F
A
CTS
d
e
v
ice
s,
it
is
i
m
p
o
rtan
t
to
d
e
term
in
e
th
e
ir
o
p
ti
m
u
m
lo
c
a
ti
o
n
o
n
t
h
e
n
e
tw
o
rk
.
A
c
c
o
rd
in
g
ly
,
in
th
is
p
a
p
e
r,
th
e
A
n
tl
io
n
o
p
ti
m
iza
ti
o
n
a
lg
o
ri
th
m
(AL
O)
h
a
s
b
e
e
n
e
m
p
lo
y
e
d
to
c
o
n
d
u
c
t
a
c
o
n
g
e
stio
n
m
a
n
a
g
e
m
e
n
t
a
n
a
l
y
sis
to
d
e
ter
m
in
e
th
e
o
p
ti
m
a
l
lo
c
a
ti
o
n
f
o
r
th
e
in
st
a
ll
a
ti
o
n
o
f
T
CS
C,
w
h
ich
is
sim
u
late
d
o
n
a
n
IEE
E
1
4
-
b
u
s
tes
t
sy
ste
m
su
b
jec
t
to
sa
ti
sfy
th
e
c
o
n
stra
i
n
ts
o
f
th
e
m
a
rk
e
t
e
n
v
i
ro
n
m
e
n
t.
K
ey
w
o
r
d
s
:
An
tlio
n
o
p
ti
m
izatio
n
C
o
n
g
esti
o
n
m
a
n
a
g
e
m
e
n
t
F
A
C
T
S d
ev
ices
Op
ti
m
al
p
lace
m
en
t
T
C
SC
Co
p
y
rig
h
t
©
2
0
1
9
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ma
j
id
Mo
az
za
m
i,
Dep
ar
t
m
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
I
s
la
m
ic
A
za
d
U
n
iv
er
s
it
y
o
f
N
aj
af
ab
ad
,
Dan
es
h
g
ah
B
l
v
d
,
Naj
af
ab
ad
,
I
s
f
a
h
a
n
,
P
o
s
t c
o
d
e:
8
5
1
4
1
4
3
1
3
1
,
I
r
an
.
E
m
ail:
m
_
m
o
az
za
m
i
@
p
el.
iau
n
.
ac
.
ir
1.
I
NT
RO
D
UCT
I
O
N
I
n
r
ec
en
t
d
ec
ad
es,
an
im
p
o
r
ta
n
t
s
tr
u
c
tu
r
al
r
ef
o
r
m
h
as
b
ee
n
m
ad
e
in
m
a
n
y
p
o
w
er
s
y
s
te
m
s
,
w
h
ich
h
a
s
ch
an
g
ed
t
h
e
p
o
w
er
in
d
u
s
tr
y
f
r
o
m
a
tr
ad
itio
n
al
s
tr
u
ct
u
r
e
t
o
a
r
estru
ct
u
r
ed
m
o
d
er
n
o
n
e.
T
h
is
f
u
n
d
a
m
e
n
ta
l
ch
an
g
e
i
n
s
tr
u
ct
u
r
e
an
d
o
p
er
atio
n
al
r
u
le
s
h
av
e
b
ec
o
m
e
p
er
v
a
s
iv
e
v
er
y
s
o
o
n
t
h
r
o
u
g
h
o
u
t
t
h
e
w
o
r
ld
.
T
h
e
f
o
r
m
er
is
ca
lled
r
estr
u
ct
u
r
in
g
o
f
p
o
w
er
s
y
s
te
m
s
,
a
n
d
th
e
latter
i
s
c
alled
d
er
eg
u
latio
n
.
I
n
th
i
s
r
e
g
ar
d
,
th
e
g
e
n
e
r
atio
n
,
tr
an
s
m
is
s
io
n
,
d
i
s
tr
ib
u
tio
n
s
e
g
m
en
ts
a
n
d
en
er
g
y
s
er
v
ice
s
wer
e
s
ep
ar
ated
f
r
o
m
ea
ch
o
t
h
e
r
in
t
h
e
f
ir
s
t
s
tep
.
T
h
en
th
e
g
e
n
er
atio
n
a
n
d
d
is
tr
ib
u
tio
n
s
ec
to
r
s
w
er
e
d
iv
id
ed
in
to
s
ev
er
al
i
n
d
ep
en
d
en
t
co
m
p
an
ies
w
h
ich
m
a
y
h
av
e
g
o
v
er
n
m
e
n
tal
o
r
n
o
n
-
g
o
v
er
n
m
e
n
tal
o
w
n
er
s
h
ip
s
o
r
m
a
y
b
e
p
r
iv
ate
eq
u
ities
.
Su
b
s
eq
u
e
n
tl
y
,
ea
ch
o
n
e
o
f
t
h
e
g
en
er
ati
n
g
a
n
d
d
is
tr
ib
u
tio
n
c
o
m
p
a
n
ies
w
a
s
allo
w
ed
to
co
m
p
e
te
w
ith
o
th
er
co
m
p
a
n
ies
i
n
th
e
w
h
o
l
esale
elec
tr
icit
y
m
ar
k
et
to
ex
ch
an
g
e
elec
tr
ical
en
er
g
y
as
a
s
eller
o
r
a
b
u
y
er
.
T
h
er
ef
o
r
e,
th
e
i
n
cr
ea
s
e
i
n
co
m
p
e
titi
v
en
e
s
s
o
f
elec
tr
icit
y
c
o
m
m
er
ce
h
as
ca
u
s
ed
t
h
e
f
a
ir
p
r
ice
o
f
elec
tr
icit
y
w
h
ic
h
is
d
eter
m
in
ed
b
ased
o
n
th
e
s
u
p
p
l
y
a
n
d
d
e
m
an
d
tr
ad
e
-
o
f
f
m
ec
h
a
n
i
s
m
w
h
ic
h
p
r
o
v
id
es
b
o
th
s
id
es
o
f
th
e
tr
ad
e
w
it
h
t
h
e
lev
el
o
f
s
at
is
f
a
ctio
n
.
T
h
e
r
ed
u
ctio
n
o
f
g
en
er
atio
n
co
s
ts
,
t
h
e
i
m
p
r
o
v
e
m
e
n
t
in
an
c
illar
y
s
er
v
ice
s
q
u
alit
y
,
a
n
d
i
m
p
r
o
v
e
m
e
n
t
i
n
d
em
a
n
d
-
s
id
e
s
ati
s
f
ac
tio
n
ar
e
o
th
er
b
en
ef
i
ts
o
f
r
estr
u
ct
u
r
in
g
in
p
o
w
er
i
n
d
u
s
tr
y
.
T
h
e
tr
an
s
m
is
s
io
n
n
et
w
o
r
k
i
s
a
m
aj
o
r
o
b
s
tacle
f
o
r
th
e
d
er
eg
u
la
tio
n
o
f
th
e
p
o
w
er
s
y
s
te
m
s
b
ec
a
u
s
e
o
f
t
w
o
r
ea
s
o
n
s
.
T
h
e
f
ir
s
t
r
ea
s
o
n
is
r
e
s
p
ec
t
to
th
e
tech
n
ical
i
s
s
u
es,
wh
ich
i
m
p
lie
s
t
h
at
it
is
n
o
t
p
o
s
s
ib
le
to
s
ep
ar
ate
th
e
tr
an
s
m
is
s
io
n
n
et
w
o
r
k
li
k
e
g
en
er
atio
n
o
r
d
is
tr
ib
u
tio
n
s
ec
to
r
s
to
m
a
k
e
it
co
m
p
et
iti
v
e.
I
n
ad
d
itio
n
,
th
e
r
eq
u
i
s
ite
o
f
t
h
e
e
x
is
te
n
ce
o
f
a
p
r
o
p
er
c
o
m
p
eti
tio
n
b
et
w
ee
n
p
o
w
er
p
r
o
v
id
er
s
i
n
s
u
p
p
l
y
i
n
g
elec
tr
ici
t
y
i
s
t
h
e
f
air
a
n
d
n
o
t
co
n
tr
o
lled
in
ter
co
n
n
ec
tio
n
s
a
cr
o
s
s
th
e
p
o
w
er
g
r
id
[
1
-
2
]
.
A
lt
h
o
u
g
h
t
h
e
co
n
ce
p
t
o
f
tr
a
n
s
m
i
s
s
io
n
n
et
w
o
r
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l.
8
,
No
.
2
,
J
u
n
e
2
0
1
9
:
77
–
88
78
co
n
g
es
tio
n
alr
ea
d
y
ex
i
s
ts
in
tr
ad
itio
n
al
p
o
w
er
s
y
s
te
m
s
,
th
e
ter
m
“
c
o
n
g
esti
o
n
”
h
as
b
ee
n
r
aised
as
th
e
d
er
eg
u
latio
n
o
f
t
h
e
elec
tr
icit
y
in
d
u
s
tr
y
h
as
b
ee
n
s
tar
ted
.
T
h
e
m
ea
n
in
g
o
f
co
n
g
es
tio
n
i
s
th
e
u
s
e
o
f
tr
a
n
s
m
i
s
s
io
n
n
et
w
o
r
k
b
e
y
o
n
d
th
e
p
er
m
i
s
s
ib
le
o
p
er
atin
g
r
an
g
e.
T
h
e
co
n
g
esti
o
n
o
f
tr
an
s
m
i
s
s
io
n
lin
e
s
ca
n
p
r
ev
en
t
s
u
p
p
lier
s
f
r
o
m
m
a
k
i
n
g
a
n
e
w
co
n
tr
ac
t
,
an
d
ca
u
s
e
t
h
e
i
m
p
o
s
s
ib
ili
t
y
o
f
e
x
ec
u
t
io
n
o
f
ex
is
ti
n
g
co
n
tr
ac
ts
,
a
s
w
ell
as
cu
r
tail
m
en
ts
,
m
o
n
o
p
o
ly
o
f
p
r
ices
in
s
o
m
e
ar
ea
s
,
d
a
m
a
g
e
to
elec
tr
ical
eq
u
ip
m
e
n
t
i
n
th
e
s
y
s
te
m
d
u
e
to
u
n
p
la
n
n
ed
lo
ad
s
h
ed
d
i
n
g
,
p
r
ice
s
p
ik
e,
in
cr
ea
s
e
i
n
t
h
e
p
r
ice
o
f
elec
tr
ical
en
er
g
y
i
n
s
o
m
e
lo
c
atio
n
s
,
etc.
[
3
-
4
]
.
T
h
er
e
ar
e
m
an
y
w
a
y
s
to
r
ed
u
c
e
tr
an
s
m
is
s
io
n
co
n
g
es
tio
n
.
T
h
e
u
tili
za
tio
n
o
f
F
AC
T
S
d
ev
ice
s
is
o
n
e
o
f
th
e
m
o
s
t
e
f
f
ec
ti
v
e
w
a
y
s
.
Uti
lizin
g
F
AC
T
S
d
ev
ices
f
o
r
c
o
n
g
es
tio
n
m
a
n
ag
e
m
e
n
t
p
u
r
p
o
s
es
is
v
er
y
u
s
ef
u
l
b
ec
au
s
e
t
h
e
li
m
itatio
n
o
n
o
p
ti
m
u
m
p
o
w
er
f
lo
w
d
u
e
to
th
e
p
o
w
er
tr
a
n
s
m
is
s
io
n
co
n
s
tr
ai
n
t
i
s
b
asicall
y
r
e
m
o
v
ab
le
b
y
t
h
e
p
o
w
er
f
lo
w
co
n
tr
o
l.
T
C
SC
is
o
n
e
o
f
t
h
e
m
o
s
t
u
til
ized
k
i
n
d
s
o
f
th
e
F
A
C
T
S
d
ev
ices
th
at
ca
n
b
e
u
s
ed
to
ab
s
o
r
b
o
r
g
en
er
ate
r
ea
ctiv
e
p
o
w
er
.
T
C
SC
ca
n
c
o
n
tr
o
l
th
e
tr
an
s
m
is
s
io
n
p
o
w
er
o
f
th
e
lin
e
th
r
o
u
g
h
af
f
ec
tin
g
o
n
t
h
e
i
m
p
ed
a
n
ce
o
f
th
e
tar
g
et
li
n
e.
An
ad
v
a
n
ta
g
e
o
f
u
s
i
n
g
th
i
s
eq
u
ip
m
e
n
t
is
its
q
u
ick
in
s
tallatio
n
co
m
p
ar
ed
to
th
e
co
n
s
tr
u
ctio
n
o
f
a
n
e
w
tr
an
s
m
i
s
s
io
n
li
n
e.
T
h
er
ef
o
r
e,
th
e
u
tili
za
tio
n
o
f
th
e
s
e
d
ev
ices
to
eli
m
i
n
ate
o
r
r
ed
u
ce
co
n
g
es
tio
n
in
t
h
e
s
h
o
r
t te
r
m
is
j
u
s
ti
f
iab
l
e
an
d
s
en
s
ib
le.
I
n
r
ec
en
t
y
ea
r
s
,
t
h
e
d
eter
m
i
n
atio
n
o
f
t
h
e
s
ize
a
n
d
th
e
o
p
ti
m
al
lo
ca
tio
n
o
f
t
h
ese
d
ev
i
ce
s
in
t
h
e
n
et
w
o
r
k
s
h
av
e
d
r
a
w
n
a
p
ar
tic
u
lar
atte
n
tio
n
to
t
h
is
s
u
b
j
ec
t
as
an
o
p
ti
m
i
za
tio
n
p
r
o
b
le
m
.
Va
r
io
u
s
m
et
h
o
d
s
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
f
in
d
i
n
g
t
h
e
o
p
tim
a
l size
an
d
lo
ca
tio
n
o
f
T
C
S
C
r
eg
ar
d
to
it
s
g
en
er
atio
n
c
ap
ac
it
y
,
lo
s
s
e
s
,
a
n
d
co
s
ts
,
an
d
v
ar
io
u
s
ar
ticles
h
a
v
e
b
ee
n
p
u
b
lis
h
ed
in
th
is
co
n
tex
t.
I
n
[
5
]
,
a
s
en
s
itiv
i
t
y
a
n
al
y
s
i
s
o
f
th
e
ac
ti
v
e
p
o
w
er
f
lo
w
p
er
f
o
r
m
an
ce
i
n
d
ex
(
P
I
in
d
ex
)
h
as
b
ee
n
u
s
ed
f
o
r
T
C
SC
an
d
T
C
P
A
R
o
p
ti
m
al
l
o
ca
tin
g
.
A
cc
o
r
d
in
g
to
th
i
s
m
et
h
o
d
,
T
C
SC
s
h
o
u
ld
b
e
in
s
talled
i
n
a
li
n
e
t
h
at
h
a
s
th
e
m
o
s
t
n
eg
ati
v
e
s
e
n
s
it
iv
i
t
y
f
ac
to
r
,
an
d
T
C
P
AR
s
h
o
u
ld
b
e
in
s
talled
in
a
lin
e
t
h
at
h
as
t
h
e
la
r
g
es
t
v
al
u
e
o
f
s
e
n
s
it
iv
i
t
y
f
ac
to
r
s
o
th
at
th
e
in
s
t
allatio
n
o
f
F
AC
T
S
d
ev
ices
i
n
th
e
tar
g
et
li
n
e
m
u
s
t
p
r
o
v
id
e
th
e
lo
w
e
s
t
co
s
t
an
d
eli
m
i
n
ate
t
h
e
co
n
g
e
s
tio
n
.
I
n
[
6
]
,
an
ap
p
r
o
ac
h
is
in
tr
o
d
u
ce
d
to
f
in
d
t
h
e
o
p
ti
m
al
lo
ca
tio
n
o
f
T
C
SC
s
u
b
j
ec
t
to
r
ed
u
ce
th
e
co
n
g
e
s
tio
n
co
s
t
(
C
C
)
in
a
co
m
p
etiti
v
e
elec
tr
icit
y
m
ar
k
e
t
co
n
s
id
er
i
n
g
s
h
ad
o
w
p
r
ices.
I
n
t
h
is
p
ap
er
,
th
e
p
er
f
o
r
m
a
n
ce
i
n
d
ex
f
o
r
T
C
S
C
p
lace
m
e
n
t
i
s
a
co
m
b
i
n
atio
n
o
f
li
n
es
'
p
o
w
er
s
en
s
it
iv
i
t
y
f
ac
to
r
an
d
s
h
ad
o
w
p
r
ices.
I
n
[
7
]
,
t
w
o
o
p
tio
n
s
o
f
lo
ad
s
h
ed
d
in
g
an
d
u
tili
zi
n
g
T
C
S
C
h
av
e
b
ee
n
e
v
al
u
ated
to
m
an
a
g
e
co
n
g
es
tio
n
i
n
a
b
ilater
al
b
ased
p
o
w
er
m
ar
k
e
t.
I
n
[
8
]
,
th
e
e
f
f
ec
t
s
o
f
t
h
e
T
C
SC
o
n
t
h
e
co
n
g
e
s
tio
n
an
d
p
r
ices
i
n
a
n
elec
tr
icit
y
m
ar
k
et
in
cl
u
d
in
g
b
ilater
al
co
n
tr
ac
ts
ar
e
in
v
est
ig
ated
an
d
a
L
MP
-
b
ased
ap
p
r
o
a
ch
is
u
s
ed
.
I
n
[
9
]
,
a
s
tu
d
y
o
n
t
h
e
o
p
ti
m
al
lo
ca
tio
n
o
f
th
e
T
C
S
C
f
o
r
co
n
g
esti
o
n
m
a
n
a
g
e
m
en
t
in
a
n
elec
tr
i
cit
y
m
ar
k
et
b
ased
o
n
s
en
s
it
iv
it
y
an
a
l
y
s
is
a
n
d
co
n
s
id
er
in
g
t
w
o
g
o
als
o
f
r
ed
u
cin
g
t
h
e
to
tal
r
ea
cti
v
e
lo
s
s
e
s
o
f
th
e
s
y
s
te
m
an
d
r
ed
u
ci
n
g
t
h
e
ac
tiv
e
p
o
w
er
f
lo
w
p
er
f
o
r
m
a
n
ce
i
n
d
ex
(
P
I
in
d
ex
)
h
as
b
ee
n
co
n
d
u
cted
.
I
n
[
1
0
]
,
t
h
e
au
t
h
o
r
s
h
a
v
e
p
r
o
p
o
s
ed
a
n
ew
m
et
h
o
d
b
ased
o
n
th
e
to
tal
F
AC
T
S
an
n
u
al
i
n
co
m
e
a
n
d
co
s
t
p
er
tain
i
n
g
to
T
C
S
C
s
u
b
j
ec
t
to
d
eter
m
i
n
e
i
ts
o
p
ti
m
al
lo
ca
tio
n
i
n
o
r
d
er
to
m
a
n
a
g
e
co
n
g
e
s
tio
n
i
n
th
e
r
estr
u
ctu
r
ed
elec
tr
icit
y
m
ar
k
ets.
I
n
[
1
1
]
,
T
C
SC
i
s
u
ti
liz
ed
in
th
e
elec
tr
icit
y
m
ar
k
et
to
i
m
p
r
o
v
e
t
h
e
ab
ilit
y
o
f
th
e
s
y
s
te
m
to
tr
an
s
m
it
m
o
r
e
p
o
w
er
.
I
n
th
i
s
p
ap
er
,
th
e
s
e
n
s
it
iv
i
t
y
a
n
al
y
s
i
s
is
u
s
ed
f
o
r
T
C
SC
p
lace
m
e
n
t.
I
n
[
1
2
]
,
m
u
lt
i
-
o
b
j
ec
tiv
e
p
ar
tic
le
s
w
ar
m
o
p
ti
m
izat
io
n
al
g
o
r
ith
m
(
MO
P
SO)
an
d
s
eq
u
en
tial
q
u
ad
r
atic
p
r
o
g
r
a
m
m
i
n
g
(
SQP
)
h
a
v
e
b
ee
n
e
m
p
lo
y
ed
w
i
th
r
e
g
ar
d
to
th
e
v
o
ltag
e
s
tab
ilit
y
i
n
d
ex
i
n
o
p
tim
a
l lo
ca
tin
g
o
f
F
AC
T
S d
ev
ices
f
o
r
co
n
g
e
s
tio
n
m
an
a
g
e
m
en
t.
I
n
[
1
3
]
,
a
n
e
w
m
et
h
o
d
f
o
r
th
e
T
C
SC
lo
ca
ti
n
g
is
p
r
ese
n
ted
in
o
r
d
er
to
ab
s
o
r
b
th
e
m
a
x
i
m
u
m
tr
a
n
s
m
ittab
le
p
o
w
er
b
y
th
e
lo
ad
s
th
r
o
u
g
h
t
h
e
n
et
w
o
r
k
’
s
b
r
an
ch
e
s
.
I
n
[
1
4
]
,
th
e
au
t
h
o
r
s
h
av
e
f
o
cu
s
ed
o
n
t
h
e
tr
an
s
m
is
s
io
n
co
s
t
an
d
i
m
p
r
o
v
i
n
g
i
t
b
y
i
n
s
ta
llin
g
t
h
e
T
C
SC
.
I
n
[
1
5
-
1
6
]
,
an
o
p
ti
m
izatio
n
m
e
th
o
d
is
p
r
o
p
o
s
ed
to
f
i
n
d
th
e
b
est
lo
ca
tio
n
to
in
s
t
all
T
C
SC
r
eg
ar
d
to
m
a
x
i
m
izi
n
g
t
h
e
lo
ad
ab
ilit
y
o
f
t
h
e
Ma
l
a
y
s
ia
n
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
b
ased
o
n
ev
o
lu
tio
n
a
r
y
o
p
ti
m
izatio
n
tec
h
n
iq
u
e.
B
esid
es,
th
e
in
cr
ea
s
e
i
n
th
e
n
e
t
w
o
r
k
lo
ad
in
g
w
it
h
r
esp
ec
t
to
th
e
i
m
p
licatio
n
s
o
f
i
n
s
talli
n
g
a
s
er
ies
o
f
ca
p
a
cito
r
s
is
in
v
es
tig
a
ted
u
s
i
n
g
t
h
e
p
ar
ticle
s
w
ar
m
alg
o
r
ith
m
b
ased
o
n
b
ir
d
s
’
f
lo
c
k
b
eh
a
v
io
r
.
I
n
[
1
7
]
,
th
e
p
ar
ticle
s
w
ar
m
o
p
ti
m
izatio
n
al
g
o
r
ith
m
(
P
SO)
h
a
s
b
ee
n
u
s
ed
to
f
i
n
d
t
h
e
o
p
ti
m
al
v
al
u
e
an
d
t
h
e
o
p
ti
m
al
lo
ca
tio
n
o
f
T
C
S
C
a
n
d
SV
C
i
n
o
r
d
er
to
i
n
cr
ea
s
e
t
h
e
r
eliab
ilit
y
o
f
t
h
e
s
y
s
te
m
.
I
n
[
1
8
]
,
th
e
a
u
th
o
r
s
h
av
e
u
s
ed
t
h
e
b
ac
ter
ial
f
o
r
ag
i
n
g
al
g
o
r
ith
m
to
o
p
ti
m
iz
e
F
AC
T
S
d
ev
ices.
I
n
r
ec
en
t
y
ea
r
s
,
n
e
w
e
v
o
lu
tio
n
ar
y
al
g
o
r
it
h
m
s
s
u
ch
a
s
b
at
alg
o
r
ith
m
(
B
A
)
[
1
9
]
,
g
lo
ww
o
r
m
s
w
ar
m
o
p
ti
m
izatio
n
alg
o
r
ith
m
(
GS
O)
[
2
0
]
,
g
r
av
it
y
s
ea
r
ch
al
g
o
r
ith
m
(
GS
A
)
[
2
1
]
,
g
r
a
y
w
o
l
f
al
g
o
r
ith
m
(
GW
O)
[
2
2
]
,
Sh
u
f
f
led
f
r
o
g
leap
in
g
a
lg
o
r
it
h
m
(
SF
L
A
)
[
2
3
]
,
b
io
g
eo
g
r
ap
h
y
-
b
a
s
ed
o
p
ti
m
izatio
n
(
B
B
O)
alg
o
r
ith
m
[
2
4
]
,
an
d
b
ig
b
a
n
g
-
b
ig
cr
u
n
c
h
(
B
B
B
C
)
o
p
tim
izatio
n
alg
o
r
ith
m
[
2
5
]
h
av
e
b
ee
n
w
id
el
y
u
s
ed
to
s
o
lv
e
o
p
ti
m
izat
io
n
p
r
o
b
lem
s
i
n
p
o
w
er
s
y
s
te
m
o
p
er
a
tio
n
an
d
m
ar
k
et
an
al
y
s
is
.
I
n
t
h
e
p
r
ese
n
t
ar
tic
l
e,
a
n
e
w
m
et
h
o
d
is
p
r
o
p
o
s
ed
w
h
ic
h
i
s
o
b
tain
ed
b
y
m
er
g
i
n
g
th
e
AL
O
al
g
o
r
it
h
m
an
d
o
p
ti
m
al
p
o
w
er
f
lo
w
,
an
d
th
is
ap
p
r
o
ac
h
i
s
e
m
p
l
o
y
ed
to
d
eter
m
in
e
th
e
o
p
ti
m
al
T
C
SC
lo
ca
tio
n
.
T
h
e
s
i
m
u
la
tio
n
is
e
x
ec
u
ted
o
n
I
E
E
E
1
4
-
bu
s
test
s
y
s
te
m
s
h
o
w
s
ab
ilit
y
a
n
d
ef
f
ec
tiv
e
n
e
s
s
o
f
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4856
Op
tima
l tc
s
c
p
la
ce
men
t fo
r
co
n
g
esti
o
n
ma
n
a
g
eme
n
t in
d
ereg
u
la
ted
p
o
w
er sys
tem
s
…
(
Ma
jid
Mo
a
z
z
a
mi
)
79
2.
M
O
DE
L
I
N
G
AN
D
F
O
RM
U
L
AT
I
O
N
O
F
T
CS
C
I
N
O
P
T
I
M
AL
L
O
AD
F
L
O
W
E
Q
U
AT
I
O
N
S
2
.
1
.
St
a
t
ic
m
o
delin
g
o
f
T
CS
C
Fig
u
r
e
1
s
h
o
w
s
th
e
π
m
o
d
el
o
f
a
tr
an
s
m
i
s
s
io
n
li
n
e
t
h
at
is
in
s
talled
b
et
w
ee
n
t
h
e
b
u
s
i
an
d
th
e
b
u
s
j
.
Ass
u
m
e
t
h
at
t
h
e
co
m
p
lex
v
o
ltag
e
at
t
h
e
i
th
b
u
s
a
n
d
j
th
b
u
s
ar
e
d
ef
i
n
ed
as
ii
V
an
d
jj
V
r
esp
ec
t
iv
el
y
.
T
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
tr
an
s
m
is
s
io
n
f
r
o
m
b
u
s
i
to
j
is
r
ep
r
esen
ted
in
(
1
)
an
d
(
2
)
:
2
c
o
s
s
i
n
i
j
i
i
j
i
j
i
j
i
j
i
j
i
j
P
V
G
V
V
G
B
(
1
)
2
(
)
s
i
n
c
o
s
i
j
i
i
j
s
h
i
j
i
j
i
j
i
j
i
j
Q
V
B
B
VV
G
B
(
2
)
Si
m
i
lar
l
y
,
t
h
e
ac
tiv
e
a
n
d
r
ea
cti
v
e
p
o
w
er
tr
an
s
m
is
s
io
n
f
r
o
m
b
u
s
j
to
i
b
u
s
i
s
s
h
o
w
n
as (
3
)
an
d
(
4
)
:
2
c
o
s
s
i
n
j
i
j
i
j
i
j
i
j
i
j
i
j
i
j
P
V
G
V
V
G
B
(
3
)
2
(
)
s
i
n
c
o
s
j
i
j
i
j
s
h
i
j
i
j
i
j
i
j
i
j
Q
V
B
B
V
V
G
B
(
4
)
T
h
e
tr
an
s
m
is
s
io
n
li
n
e
m
o
d
el
w
it
h
i
n
co
r
p
o
r
atin
g
a
T
C
SC
t
h
at
is
lo
ca
ted
b
et
w
ee
n
th
e
b
u
s
e
s
i
an
d
j
is
d
ep
icted
in
Fi
g
u
r
e
2
.
I
n
t
h
e
s
t
ea
d
y
s
tate,
T
C
S
C
is
co
n
te
m
p
l
ated
as
a
s
tat
ic
r
ea
ctan
ce
w
i
t
h
t
h
e
v
a
lu
e
o
f
-
jx
c
.
T
h
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
e
r
tr
an
s
m
is
s
io
n
f
r
o
m
t
h
e
i
th
b
u
s
to
t
h
e
j
th
b
u
s
(
an
d
al
s
o
co
n
t
r
ar
i
w
is
e)
r
e
g
ar
d
to
p
r
esen
t o
f
T
C
S
C
is
m
o
d
elled
as (
5
)
to
(
8
)
:
2
'
'
'
c
o
s
s
i
n
C
i
j
i
i
j
i
j
i
j
i
j
i
j
i
j
P
V
G
V
V
G
B
(
5
)
2
'
'
'
(
)
s
i
n
c
o
s
C
i
j
i
i
j
s
h
i
j
i
j
i
j
i
j
i
j
Q
V
B
B
V
V
G
B
(
6
)
2
'
'
'
c
o
s
s
i
n
C
i
j
j
i
j
i
j
i
j
i
j
i
j
i
j
P
V
G
V
V
G
B
(
7
)
2
'
'
'
(
)
s
i
n
c
o
s
C
i
j
i
i
j
s
h
i
j
i
j
i
j
i
j
i
j
Q
V
B
B
V
V
G
B
(
8
)
B
u
s
-
i
B
u
s
-
j
Y
=
G
+
j
B
i
j
i
j
i
j
j
B
s
h
j
B
s
h
B
u
s
-
i
B
u
s
-
j
i
j
i
j
i
j
j
B
s
h
j
B
s
h
Z
=
R
+
j
X
-
j
X
c
Fig
u
r
e
1
.
T
h
e
tr
an
s
m
i
s
s
io
n
lin
e
m
o
d
el
Fig
u
r
e
2
.
T
h
e
tr
an
s
m
i
s
s
io
n
lin
e
m
o
d
el
w
it
h
p
r
esen
ce
o
f
T
C
SC
W
h
er
e
G
′
ij
a
n
d
B
′
ij
ar
e
(9
-
10)
:
2
'2
i
j
i
j
i
j
i
j
C
G
r
r
x
x
(
9
)
2
'2
i
j
i
j
C
i
j
i
j
C
B
x
x
r
x
x
(
1
0
)
T
h
e
v
ar
iatio
n
o
f
th
e
l
in
e
’
s
f
l
o
w
d
u
e
to
s
er
ies
ca
p
ac
ita
n
ce
ca
n
b
e
r
ep
r
esen
ted
as
a
li
n
e
w
i
th
o
u
t
a
s
er
ies
ca
p
ac
itan
ce
w
it
h
f
lo
w
i
n
g
p
o
w
er
at
th
e
i
n
j
ec
tin
g
a
n
d
r
ec
eiv
in
g
ter
m
i
n
a
ls
o
f
th
e
lin
e,
as
s
h
o
w
n
i
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l.
8
,
No
.
2
,
J
u
n
e
2
0
1
9
:
77
–
88
80
Fig
u
r
e
3
.
T
h
e
in
j
ec
ted
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
to
th
e
b
u
s
i
(
P
i
C
,
Q
i
C
(
an
d
to
th
e
j
th
b
u
s
(
P
j
C
,
Q
j
C
)
ca
n
b
e
o
b
tain
ed
b
y
(
1
1
)
to
(
1
4
)
[
2
6
-
2
8
]
:
2
c
o
s
s
i
n
C
i
i
i
j
i
j
i
j
i
j
i
j
i
j
P
V
G
V
V
G
B
(
1
1
)
2
c
o
s
s
i
n
C
j
j
i
j
i
j
i
j
i
j
i
j
i
j
P
V
G
V
V
G
B
(
1
2
)
2
c
o
s
s
i
n
C
i
i
i
j
i
j
i
j
i
j
i
j
i
j
Q
V
B
V
V
G
B
(1
3
)
2
s
i
n
c
o
s
C
j
j
i
j
i
j
i
j
i
j
i
j
i
j
Q
V
B
V
V
G
B
(1
4
)
W
h
er
e
G
ij
an
d
B
ij
ar
e
(
1
5
-
1
6
)
:
2
2
2
2
2
i
j
C
i
j
C
i
j
i
j
i
j
i
j
i
j
C
G
x
r
x
x
r
x
r
x
x
(
1
5
)
2
2
2
2
2
2
i
j
C
i
j
i
j
C
i
j
i
j
i
j
i
j
i
j
C
B
x
r
x
x
r
r
x
r
x
x
(
1
6
)
B
u
s
-
i
B
u
s
-
j
i
j
i
j
i
j
Z
=
R
+
j
X
S
i
c
S
j
c
Fig
u
r
e
3
.
T
C
SC
in
j
ec
tio
n
m
o
d
el
2
.
2
.
O
ptim
a
l lo
a
d f
lo
w
equa
t
io
ns
T
h
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
m
a
y
c
o
n
tain
ec
o
n
o
m
ic,
s
ec
u
r
it
y
o
r
en
v
ir
o
n
m
e
n
tal
asp
ec
t
s
o
f
p
o
w
er
s
y
s
te
m
s
th
at
m
u
s
t b
e
s
o
l
v
ed
b
y
a
p
r
o
p
e
r
o
p
tim
iza
tio
n
al
g
o
r
ith
m
.
I
n
r
e
ce
n
t
y
ea
r
s
,
r
eg
ar
d
to
th
e
r
aisi
n
g
o
f
t
h
e
co
n
ce
p
t o
f
r
estru
ct
u
r
in
g
an
d
d
er
eg
u
latio
n
in
t
h
e
elec
tr
ici
t
y
i
n
d
u
s
tr
y
,
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
is
m
o
s
tl
y
d
e
f
i
n
ed
as
th
e
m
i
n
i
m
izatio
n
o
f
th
e
g
e
n
er
at
i
o
n
co
s
t
(
ec
o
n
o
m
ic
asp
ec
ts
o
f
th
e
s
y
s
te
m
)
as
w
el
l
as
m
a
x
i
m
izatio
n
o
f
th
e
r
eliab
ilit
y
o
f
t
h
e
s
y
s
te
m
(
s
ec
u
r
it
y
o
f
t
h
e
s
y
s
te
m
)
.
1
F
(
x
)
m
i
n
G
i
N
iG
i
cP
(
(
17)
W
h
er
e
F
(
x
)
is
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
th
at
m
u
s
t
b
e
o
p
tim
ized
,
x
is
th
e
s
tate
v
ar
iab
les,
N
G
is
th
e
n
u
m
b
er
o
f
n
e
t
w
o
r
k
g
en
er
ato
r
s
,
c
i
(
P
Gi
)
is
th
e
g
en
er
atio
n
co
s
t
o
f
u
n
it
i
.
I
n
g
e
n
er
al,
o
u
r
g
o
al
is
to
o
p
ti
m
ize
th
e
o
b
j
ec
tiv
e
f
u
n
c
tio
n
b
y
a
s
u
itab
le
s
o
lu
tio
n
an
d
s
atis
f
y
i
n
g
t
h
e
p
r
ev
aili
n
g
co
n
s
tr
ain
t
s
o
f
t
h
e
s
y
s
te
m
(
p
h
y
s
ical
co
n
s
tr
ain
ts
,
w
h
ic
h
li
m
it
t
h
e
p
o
w
er
g
en
er
atio
n
an
d
av
aila
b
ilit
y
o
f
tr
an
s
m
is
s
io
n
lin
e
s
’
ca
p
ac
ities
,
an
d
th
e
co
n
s
tr
ain
ts
i
m
p
o
s
ed
o
n
elec
tr
i
ca
l
d
ev
ices
u
s
ed
i
n
p
o
w
er
g
r
id
s
an
d
s
y
s
te
m
o
p
er
atio
n
al
s
tr
at
eg
ies).
I
f
th
e
T
C
S
C
is
lo
ca
ted
i
n
th
e
li
n
e
b
et
w
ee
n
b
u
s
e
s
i
an
d
j
,
t
h
en
t
h
e
p
o
w
er
b
alan
ce
eq
u
atio
n
f
o
r
th
e
n
o
d
es
i
a
n
d
j
w
o
u
ld
b
e
ex
p
r
ess
ed
as
(
1
8
-
21)
:
,0
ii
T
C
S
C
i
G
D
i
P
V
P
P
P
(
18)
,0
ii
T
C
S
C
i
G
D
i
Q
V
Q
Q
Q
(
1
9
)
,0
jj
T
C
S
C
j
G
D
j
P
V
P
P
P
(
2
0
)
,0
jj
T
C
S
C
j
G
D
j
Q
V
Q
Q
Q
(
2
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4856
Op
tima
l tc
s
c
p
la
ce
men
t fo
r
co
n
g
esti
o
n
ma
n
a
g
eme
n
t in
d
ereg
u
la
ted
p
o
w
er sys
tem
s
…
(
Ma
jid
Mo
a
z
z
a
mi
)
81
W
h
er
e
P
Gi
an
d
Q
Gi
ar
e
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
in
t
h
e
n
o
d
e
i
,
P
Gj
an
d
Q
Gj
ar
e
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
i
n
t
h
e
n
o
d
e
j
,
P
Di
an
d
Q
Di
ar
e
th
e
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
co
n
s
u
m
ed
b
y
th
e
d
e
m
a
n
d
i
n
t
h
e
n
o
d
e
i
,
P
Dj
an
d
Q
Dj
ar
e
th
e
ac
tiv
e
an
d
r
ea
cti
v
e
p
o
w
er
o
f
t
h
e
lo
ad
s
in
t
h
e
n
o
d
e
j
,
P
i
TCSC
an
d
Q
i
TCSC
ar
e
th
e
ac
tiv
e
an
d
r
ea
cti
v
e
in
j
ec
tio
n
p
o
w
er
b
y
T
C
S
C
to
th
e
n
o
d
e
i
,
P
j
TCSC
an
d
Q
j
TCSC
ar
e
th
e
ac
tiv
e
an
d
r
ea
cti
v
e
in
j
ec
tio
n
p
o
w
er
b
y
T
C
SC
to
th
e
n
o
d
e
j
.
T
h
e
co
n
s
tr
ain
ts
o
f
th
e
p
r
o
b
lem
ar
e
al
s
o
ex
p
r
ess
e
d
in
th
e
f
o
llo
w
i
n
g
(
2
2
-
26)
:
m
a
x
,
i
j
i
j
S
V
S
(
2
2
)
m
i
n
m
a
x
i
i
i
G
G
G
P
P
P
(
2
3
)
m
i
n
m
a
x
i
i
i
G
G
G
Q
Q
Q
(
2
4
)
m
i
n
m
a
x
i
i
G
i
V
V
V
(
2
5
)
m
i
n
m
a
x
C
C
C
X
X
X
(
2
6
)
T
h
e
(
2
2
)
s
h
o
w
s
t
h
e
li
m
itatio
n
o
f
t
h
e
ap
p
ar
en
t
p
o
w
er
t
h
r
o
u
g
h
th
e
lin
e
w
h
er
e
S
ij
is
t
h
e
ap
p
ar
en
t
p
ass
in
g
p
o
w
er
t
h
r
o
u
g
h
t
h
e
tr
an
s
m
i
s
s
io
n
li
n
e
b
et
w
ee
n
b
u
s
es
i
an
d
j
,
an
d
S
ij
max
is
its
m
ax
i
m
u
m
b
o
u
n
d
ar
y
.
T
h
e
(
2
3
)
an
d
(
2
4
)
ex
p
lain
th
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
g
e
n
er
atio
n
li
m
itatio
n
s
s
o
t
h
at
P
Gi
m
in
an
d
P
Gi
max
i
m
p
l
y
o
n
th
e
m
in
i
m
u
m
an
d
m
ax
i
m
u
m
ac
t
iv
e
p
o
w
er
g
e
n
er
atio
n
b
o
u
n
d
ar
ies
in
b
u
s
i
,
Q
Gi
min
a
n
d
Q
Gi
max
ar
e
th
e
m
i
n
i
m
u
m
a
n
d
m
ax
i
m
u
m
r
ea
c
tiv
e
p
o
w
er
g
e
n
er
atio
n
li
m
its
in
t
h
e
b
u
s
i
.
T
h
e
(
2
5
)
s
h
o
w
s
th
e
v
o
ltag
e
r
an
g
e
li
m
ita
tio
n
w
h
er
e
V
i
min
a
n
d
V
i
ma
x
d
eter
m
in
e
th
e
m
in
i
m
u
m
an
d
m
ax
i
m
u
m
li
m
i
ts
o
f
t
h
e
p
er
m
i
s
s
ib
le
v
o
lta
g
e
r
an
g
e
in
t
h
e
b
u
s
i
.
T
h
e
(
2
6
)
s
h
o
w
s
th
e
li
m
ita
tio
n
o
f
th
e
T
C
SC
r
ea
ct
an
ce
w
h
er
e
X
C
min
an
d
X
C
max
ar
e
th
e
m
i
n
i
m
u
m
a
n
d
m
ax
i
m
u
m
o
f
T
C
S
C
r
ea
c
tan
ce
[
2
9
-
3
0
]
.
T
h
e
o
p
tim
al
p
o
w
er
f
lo
w
o
p
ti
m
iz
atio
n
p
r
o
b
le
m
i
s
f
o
r
m
u
lated
as f
o
llo
w
s
:
m
a
x
m
i
n
m
i
n
1
1
1
1
1
m
a
x
m
a
x
m
i
n
m
i
n
m
a
x
m
a
x
m
i
n
m
1
1
1
GG
L
i
i
i
i
i
i
i
i
j
G
i
i
i
G
G
G
G
i
i
G
i
i
G
i
i
i
i
i
i
NN
N
NN
T
C
S
C
T
C
S
C
i
G
P
i
G
D
i
Q
i
G
D
i
L
i
j
i
j
P
G
G
i
i
i
i
j
i
N
N
N
P
G
G
Q
G
G
Q
G
G
V
i
i
j
i
i
L
C
P
P
P
P
P
Q
Q
Q
Q
S
S
P
P
P
P
P
P
P
P
V
i
n
m
a
x
m
a
x
11
i
NN
i
V
i
i
ii
V
V
V
(
27
)
W
h
er
e
an
d
µ
d
en
o
te
th
e
L
ag
r
a
n
g
ian
co
e
f
f
icien
ts
o
f
th
e
eq
u
ali
t
y
a
n
d
in
eq
u
a
lit
y
co
n
s
tr
ain
ts
r
esp
ec
tiv
el
y
,
ea
ch
o
f
w
h
ich
h
as
a
n
ec
o
n
o
m
ic
i
n
ter
p
r
etatio
n
.
T
h
e
m
o
s
t
i
m
p
o
r
tan
t
o
n
e
is
P
,
w
h
ic
h
i
s
t
h
e
in
s
ta
n
ta
n
eo
u
s
p
r
ice
o
r
n
o
d
al
p
r
ice
o
r
l
o
ca
tio
n
al
m
ar
g
i
n
al
p
r
ice
(
LMP
)
.
A
cc
o
r
d
in
g
l
y
,
b
y
co
n
s
id
er
in
g
t
h
e
p
r
esen
ce
o
f
T
C
SC
i
n
th
e
n
et
wo
r
k
,
th
e
o
v
er
all
co
s
t f
u
n
ctio
n
w
il
l b
e
m
ad
e
u
p
o
f
t
w
o
p
ar
ts
:
T
h
e
co
s
t o
f
p
o
w
er
g
en
er
ati
n
g
at
th
e
p
lan
t.
T
h
e
co
s
t o
f
in
v
e
s
t
m
en
t r
elate
d
to
th
e
T
C
SC
.
Th
u
s
,
t
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
o
f
t
h
e
s
y
s
te
m
r
ep
r
esen
t
s
t
h
e
m
i
n
i
m
izatio
n
o
f
th
e
co
s
t
o
f
g
en
er
atio
n
(
ec
o
n
o
m
ic
asp
ec
ts
o
f
t
h
e
s
y
s
te
m
)
an
d
th
e
co
s
t o
f
th
e
T
C
S
C
i
n
s
tal
latio
n
:
1
F
(
x
)
m
i
n
G
i
N
t
i
G
T
C
S
C
i
C
P
C
(
2
8
)
2
.
3
.
Ca
lcula
t
i
o
n o
f
L
M
P
a
n
d c
o
ng
estio
n a
na
ly
s
is
T
o
ca
lcu
late
th
e
co
n
g
esti
o
n
co
s
t
in
ea
ch
li
n
e,
th
e
L
MP
p
r
ice
d
if
f
er
en
ce
b
et
w
ee
n
t
w
o
b
u
s
es
m
u
s
t
b
e
m
u
ltip
lied
b
y
th
e
f
lo
w
o
f
p
o
wer
p
ass
in
g
th
r
o
u
g
h
th
e
li
n
e.
i
j
i
j
(
2
9
)
i
j
i
j
i
j
C
C
P
(
3
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l.
8
,
No
.
2
,
J
u
n
e
2
0
1
9
:
77
–
88
82
W
h
er
e
i
d
en
o
tes
th
e
lo
ca
tio
n
al
m
ar
g
in
al
p
r
ice
i
n
t
h
e
i
th
b
u
s
,
j
s
h
o
w
s
t
h
e
lo
ca
tio
n
a
l
m
ar
g
in
al
p
r
ice
in
t
h
e
j
th
b
u
s
,
ij
in
d
icate
s
t
h
e
m
ar
g
i
n
al
p
r
ice
d
i
f
f
er
en
ce
b
et
w
ee
n
b
u
s
es
i
an
d
j
,
P
ij
r
ep
r
esen
ts
t
h
e
f
lo
w
o
f
p
ass
in
g
p
o
w
er
th
r
o
u
g
h
t
h
e
li
n
e
i
-
j
,
an
d
C
ij
i
s
th
e
co
n
g
e
s
t
io
n
co
s
t
o
f
th
e
l
in
e
i
-
j
.
A
cc
o
r
d
in
g
l
y
,
t
h
e
to
tal
co
n
g
es
tio
n
co
s
t c
a
n
b
e
ca
lcu
la
ted
as in
(
3
1
)
[
3
1
-
3
2
]
:
L
N
i
j
i
j
ij
T
C
C
P
(
(
31)
3.
ANT
L
I
O
N
O
P
T
I
M
I
Z
A
T
I
O
N
AL
G
O
RI
T
H
M
An
tlio
n
o
p
ti
m
izatio
n
(
A
LO
)
m
et
h
o
d
is
a
n
o
v
el
n
a
tu
r
e
-
i
n
s
p
ir
ed
alg
o
r
ith
m
t
h
at
i
s
in
tr
o
d
u
ce
d
b
y
Mir
j
alili
in
2
0
1
5
[
3
3
]
.
T
h
e
A
LO
alg
o
r
ith
m
m
i
m
ics
t
h
e
h
u
n
tin
g
m
ec
h
an
is
m
o
f
an
t
lio
n
s
i
n
n
atu
r
e.
Fi
v
e
m
ai
n
s
tep
s
o
f
h
u
n
tin
g
p
r
e
y
s
u
ch
a
s
th
e
r
a
n
d
o
m
w
al
k
o
f
an
t
s
,
b
u
i
ld
in
g
tr
ap
s
,
en
tr
ap
m
en
t
o
f
a
n
t
s
in
tr
ap
s
,
ca
tch
in
g
p
r
ey
s
,
an
d
r
e
-
b
u
ild
i
n
g
tr
ap
s
ar
e
i
m
p
le
m
e
n
ted
.
T
h
er
e
ar
e
s
ev
er
al
d
if
f
er
en
t
s
p
ec
ies
o
f
an
t
s
ar
o
u
n
d
th
e
w
o
r
ld
i
n
n
atu
r
e.
An
tlio
n
s
b
elo
n
g
to
th
e
M
y
r
m
eleo
n
tid
ae
f
a
m
i
l
y
a
n
d
Neu
r
o
p
t
er
a
o
r
d
er
(
n
et
-
w
i
n
g
ed
in
s
ec
t
s
)
.
T
h
e
lif
ec
y
cle
o
f
a
n
tlio
n
s
i
n
cl
u
d
es
t
w
o
m
ai
n
p
h
a
s
es:
lar
v
ae
a
n
d
ad
u
lt.
A
n
at
u
r
al
to
tal
li
f
esp
an
ca
n
tak
e
u
p
to
3
y
ea
r
s
,
w
h
ic
h
m
o
s
tl
y
o
cc
u
r
s
i
n
lar
v
ae
to
b
ec
o
m
e
a
n
ad
u
lt
an
t.
T
h
e
an
t
lio
n
lar
v
ae
p
er
io
d
m
o
s
tl
y
p
ass
ed
o
n
w
al
k
i
n
g
r
o
u
tes
o
n
s
a
n
d
an
d
leav
es
to
f
in
d
a
g
o
o
d
p
lace
f
o
r
b
u
ild
i
n
g
tr
a
p
s
.
Du
r
i
n
g
t
h
e
h
u
n
ti
n
g
p
r
o
ce
s
s
,
an
an
tlio
n
lar
v
a
d
ig
s
a
co
n
e
-
s
h
ap
ed
p
it
in
s
o
f
t
s
an
d
.
As
illu
s
tr
ated
i
n
F
i
g
u
r
e
4
,
af
te
r
d
ig
g
in
g
th
e
tr
ap
,
th
e
lar
v
ae
h
id
e
u
n
d
er
n
ea
th
t
h
e
b
o
tto
m
o
f
t
h
e
co
n
e,
an
d
w
ait
s
f
o
r
th
e
p
r
e
y
(
a
n
ts
an
d
o
th
er
k
in
d
s
o
f
i
n
s
ec
t
s
)
to
b
e
tr
ap
p
e
d
in
th
e
p
it.
Fig
u
r
e
4
.
Hu
n
t
in
g
b
eh
a
v
io
r
o
f
an
tlio
n
On
ce
t
h
e
an
t
lio
n
r
ea
lizes
th
at
a
p
r
ey
i
s
in
t
h
e
tr
ap
,
it
tr
ies
t
o
ca
tch
it.
Ho
w
ev
er
,
i
f
th
e
p
r
e
y
tr
ies
t
o
escap
e
f
r
o
m
t
h
e
tr
ap
,
t
h
e
a
n
tli
o
n
i
n
telli
g
e
n
tl
y
t
h
r
o
w
s
s
an
d
s
t
o
w
ar
d
s
to
ed
g
e
o
f
t
h
e
p
it
to
s
li
d
e
th
e
p
r
e
y
i
n
to
t
h
e
b
o
tto
m
o
f
t
h
e
p
it.
T
h
e
m
at
h
e
m
atica
l
m
o
d
el
o
f
an
t
s
a
n
d
a
n
tlio
n
s
i
s
d
is
cu
s
s
ed
in
t
h
e
f
o
llo
w
in
g
p
ar
t:
3
.
1
.
Ra
nd
o
m
w
a
l
k
s
o
f
a
nts
T
h
e
r
an
d
o
m
w
al
k
s
o
f
an
t
s
f
o
r
s
ea
r
ch
i
n
g
f
o
o
d
in
th
e
n
at
u
r
e
ca
n
b
e
ex
p
r
ess
ed
b
y
(
3
2
)
:
2
(
)
=
[
0
,
c
u
m
s
u
m
(
2
(
)
-
1
)
,
c
u
m
s
u
m
(
2
(
)
-
1
)
,
.
.
.
,
c
u
m
s
u
m
(
2
(
)
-
1
)
]
1n
X
t
r
t
r
t
r
t
(
(
32)
W
h
er
e
cu
m
s
u
m
i
s
t
h
e
c
u
m
u
la
tiv
e
s
u
m
an
d
N
i
s
t
h
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
,
t
s
h
o
ws
t
h
e
s
tep
o
f
r
an
d
o
m
w
al
k
an
d
r
(
t
)
is
a
s
t
o
ch
asti
c
f
u
n
ctio
n
d
ef
i
n
ed
as (
3
3
)
.
1
r
a
n
d
>
0
.
5
()
0
r
a
n
d
0
.
5
if
rt
if
(
(
33)
W
h
er
e
t
s
h
o
w
s
t
h
e
s
tep
o
f
r
a
n
d
o
m
w
al
k
an
d
r
an
d
is
a
r
an
d
o
m
n
u
m
b
er
g
e
n
er
ated
in
t
h
e
in
ter
v
al
o
f
[
0
,
1
]
.
T
h
e
p
o
s
itio
n
o
f
an
t is p
r
esen
ted
i
n
th
e
f
o
llo
w
in
g
m
atr
i
x
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4856
Op
tima
l tc
s
c
p
la
ce
men
t fo
r
co
n
g
esti
o
n
ma
n
a
g
eme
n
t in
d
ereg
u
la
ted
p
o
w
er sys
tem
s
…
(
Ma
jid
Mo
a
z
z
a
mi
)
83
2
2
2
1
,
1
1
,
1
,
d
,
1
2
,
2
2
,
d
A
n
t
n
,
1
n
,
n
,
d
A
A
A
A
A
A
M
A
A
A
(
(
34)
W
h
er
e
M
Ant
is
th
e
m
atr
ix
f
o
r
s
av
in
g
t
h
e
p
o
s
itio
n
o
f
ea
ch
a
n
t,
A
i,
j
s
h
o
w
s
t
h
e
v
al
u
e
o
f
t
h
e
j
-
th
v
ar
iab
le
o
f
i
-
th
an
t,
n
is
th
e
n
u
m
b
er
o
f
an
ts
a
n
d
d
is
t
h
e
n
u
m
b
er
o
f
v
ar
iab
les.
T
h
e
o
b
j
ec
tiv
e
f
u
n
c
tio
n
o
f
ea
c
h
a
n
t
is
s
av
ed
in
M
OA
m
atr
ix
.
2
2
,
,
.
.
.
,
,
,
.
.
.
,
,
,
.
.
.
,
1
,
1
1
,
1
,
d
2
,
1
2
,
2
2
,
d
OA
n
,
1
n
,
n
,
d
f
A
A
A
f
A
A
A
M
f
A
A
A
(
(
35
)
w
h
er
e
f
d
en
o
tes t
h
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
.
2
2
2
1
,
1
1
,
1
,
d
,
1
2
,
2
2
,
d
A
n
t
l
i
o
n
n
,
1
n
,
n
,
d
A
L
A
L
A
L
A
L
A
L
A
L
M
A
L
A
L
A
L
(
(
36
)
W
h
er
e
M
Antlion
is
th
e
m
atr
i
x
f
o
r
s
av
i
n
g
th
e
p
o
s
it
io
n
o
f
ea
ch
an
tlio
n
,
AL
i,
j
s
h
o
w
s
t
h
e
j
-
th
v
a
lu
e
o
f
i
-
th
an
tlio
n
,
n
is
t
h
e
n
u
m
b
er
o
f
an
tlio
n
s
,
a
n
d
d
is
th
e
n
u
m
b
er
o
f
v
ar
iab
les.
T
h
e
o
b
j
ec
tiv
e
f
u
n
c
tio
n
o
f
ea
ch
a
n
t
is
s
av
ed
in
M
OA
m
atr
ix
.
Si
m
i
lar
ly
,
th
e
o
b
j
ec
tiv
e
f
u
n
c
tio
n
o
f
ea
ch
an
tl
io
n
is
s
av
ed
i
n
M
OAL
m
a
tr
ix
.
2
2
,
,
.
.
.
,
,
,
.
.
.
,
,
,
.
.
.
,
1
,
1
1
,
1
,
d
2
,
1
2
,
2
2
,
d
O
A
L
n
,
1
n
,
n
,
d
f
A
L
A
L
A
L
f
A
L
A
L
A
L
M
f
A
L
A
L
A
L
(
(
37
)
I
n
o
r
d
er
to
k
ee
p
th
e
r
an
d
o
m
w
al
k
s
in
s
id
e
th
e
s
ea
r
c
h
s
p
ac
e,
a
n
o
r
m
alize
r
f
u
n
ctio
n
i
s
e
m
p
lo
y
ed
s
h
o
w
n
i
n
(
3
8
)
.
tt
i
i
i
i
t
ii
t
ii
X
a
b
c
Xc
da
(
(
38
)
W
h
er
e
a
i
is
t
h
e
m
i
n
i
m
u
m
o
f
r
an
d
o
m
w
al
k
o
f
i
-
th
v
ar
iab
le,
b
i
is
t
h
e
m
a
x
i
m
u
m
o
f
r
an
d
o
m
w
al
k
i
n
i
-
th
v
ar
iab
le,
c
t
i
is
t
h
e
m
i
n
i
m
u
m
o
f
i
-
th
v
ar
iab
le
at
t
-
th
iter
atio
n
,
an
d
d
t
i
i
n
d
icate
s
t
h
e
m
ax
i
m
u
m
o
f
i
-
th
v
ar
iab
le
at
t
-
th
iter
atio
n
.
3
.
2
.
T
ra
pp
ing
in a
ntlio
n’s pi
t
T
h
e
m
at
h
e
m
atica
l
m
o
d
el
o
f
th
e
tr
ap
p
ed
an
ts
in
th
e
a
n
tlio
n
's t
r
ap
s
is
p
r
esen
ted
b
y
(
3
9
)
an
d
(
4
0
)
.
t
t
t
ij
c
A
n
t
l
i
o
n
c
(
(
39
)
t
t
t
ij
d
A
n
t
l
i
o
n
d
(
(
40
)
W
h
er
e
c
t
i
s
t
h
e
m
i
n
i
m
u
m
o
f
all
v
ar
iab
les
a
t
t
-
th
iter
atio
n
,
d
t
i
n
d
icate
s
t
h
e
v
ec
to
r
in
c
lu
d
in
g
th
e
m
ax
i
m
u
m
o
f
all
v
ar
iab
les
at
t
-
th
iter
atio
n
,
c
t
j
is
th
e
m
i
n
i
m
u
m
o
f
all
v
ar
iab
les
f
o
r
i
-
th
an
t,
d
t
j
is
th
e
m
a
x
i
m
u
m
o
f
all
v
ar
iab
les
f
o
r
i
-
th
an
t,
an
d
A
n
tlio
n
t
j
s
h
o
w
s
t
h
e
s
elec
ted
p
o
s
itio
n
o
f
th
e
j
-
th
a
n
tlio
n
at
t
-
th
iter
at
io
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l.
8
,
No
.
2
,
J
u
n
e
2
0
1
9
:
77
–
88
84
3
.
3
.
B
uil
din
g
t
ra
p
I
n
o
r
d
er
to
m
o
d
el
th
e
a
n
tlio
n
s
’
s
h
u
n
ti
n
g
ca
p
ab
ilit
y
d
u
r
i
n
g
t
h
e
o
p
tim
izat
io
n
p
r
o
ce
s
s
,
a
r
o
u
lette
w
h
ee
l
is
e
m
p
lo
y
ed
.
T
h
is
m
ec
h
a
n
is
m
g
iv
e
s
h
ig
h
ch
a
n
ce
s
to
t
h
e
f
itter
an
tlio
n
s
f
o
r
ca
tch
in
g
an
ts
.
3
.
4
.
Sli
din
g
a
nts t
o
w
a
rd
a
ntl
io
n
W
it
h
t
h
e
m
ec
h
a
n
i
s
m
s
p
r
o
p
o
s
ed
s
o
f
ar
,
a
n
tlio
n
s
ar
e
ab
le
to
b
u
ild
tr
ap
s
p
r
o
p
o
r
tio
n
al
to
th
eir
f
it
n
es
s
an
d
an
ts
ar
e
r
eq
u
ir
ed
to
m
o
v
e
r
an
d
o
m
l
y
.
Mo
r
eo
v
er
,
an
tlio
n
s
s
h
o
o
t
s
an
d
s
o
u
t
w
ar
d
s
th
e
ce
n
ter
o
f
th
e
p
it
to
s
lid
es
d
o
w
n
t
h
e
tr
ap
p
ed
an
t
t
h
at
i
s
tr
y
i
n
g
to
e
s
ca
p
e.
E
q
u
a
tio
n
s
(
4
1
)
an
d
(
4
2
)
ex
p
r
ess
ed
th
e
m
ath
e
m
atica
l
m
o
d
el
o
f
an
t
s
'
s
lid
e
d
o
w
n
an
d
tr
ap
p
ed
in
th
e
an
tlio
n
'
s
tr
ap
.
tt
c
c
I
(
(
41
)
tt
d
d
I
(
(
42
)
w
h
er
e
I
d
en
o
te
th
e
ca
lcu
lated
r
atio
,
o
b
tain
ed
b
y
(
4
3
)
[
3
3
]
.
1
0
.
w
I
t
T
(
(
43
)
W
h
er
e
t
is
t
h
e
cu
r
r
en
t
iter
atio
n
,
T
is
th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
,
an
d
w
i
s
a
co
n
s
t
an
t
d
ef
i
n
ed
b
ased
o
n
th
e
cu
r
r
en
t i
ter
atio
n
an
d
is
o
b
tain
ed
b
y
(
4
4
)
.
2
>
0
.
1
3
>
0
.
5
4
>
0
.
7
5
5
>
0
.
9
6
>
0
.
9
5
i
f
t
T
i
f
t
T
w
i
f
t
T
i
f
t
T
i
f
t
T
(
(
44
)
3
.
5
.
Ca
t
ching
prey
a
nd
re
-
bu
ild
i
ng
t
he
pit
T
h
e
f
in
al
s
ta
g
e
o
f
h
u
n
t
i
s
wh
en
an
a
n
t
(
p
r
e
y
)
r
ea
ch
e
s
t
h
e
b
o
tto
m
o
f
t
h
e
p
it
a
n
d
is
ca
u
g
h
t
in
th
e
an
tlio
n
’
s
j
a
w
.
Af
ter
th
is
s
t
ag
e,
th
e
an
t
lio
n
p
u
ll
s
th
e
p
r
ey
i
n
s
id
e
th
e
s
a
n
d
an
d
co
n
s
u
m
e
s
its
b
o
d
y
.
Fo
r
m
i
m
ic
k
i
n
g
th
i
s
p
r
o
ce
s
s
,
i
t
is
a
s
s
u
m
ed
th
a
t
ca
tc
h
i
n
g
p
r
e
y
o
cc
u
r
w
h
e
n
a
n
ts
b
ec
o
m
es
f
it
ter
(
g
o
es
in
s
id
e
s
an
d
)
th
a
n
its
co
r
r
esp
o
n
d
in
g
a
n
tlio
n
.
An
an
tlio
n
is
th
e
n
r
eq
u
ir
ed
to
u
p
d
ate
its
p
o
s
itio
n
to
t
h
e
latest
p
o
s
itio
n
o
f
th
e
h
u
n
ted
an
t to
en
h
a
n
ce
its
c
h
an
ce
o
f
ca
tch
i
n
g
n
e
w
p
r
e
y
.
E
q
u
atio
n
(
4
5
)
is
p
r
o
p
o
s
ed
in
th
i
s
r
eg
ar
d
.
(
)>
t
t
t
j
i
i
A
n
t
l
i
o
n
A
n
t
i
f
f
A
n
t
f
(
(
45
)
W
h
er
e
t
s
h
o
w
s
t
h
e
c
u
r
r
en
t
i
ter
atio
n
,
A
n
tlio
n
t
j
s
h
o
w
s
th
e
p
o
s
itio
n
o
f
s
elec
ted
j
-
th
an
tli
o
n
at
t
-
th
iter
atio
n
,
an
d
A
n
t
t
i
in
d
icate
s
t
h
e
p
o
s
itio
n
o
f
i
-
th
an
t a
t
t
-
th
ite
r
atio
n
.
3
.
6
.
E
litis
m
E
liti
s
m
i
s
a
n
i
m
p
o
r
tan
t
ch
a
r
ac
ter
is
tic
o
f
ev
o
l
u
tio
n
ar
y
a
l
g
o
r
ith
m
s
t
h
at
allo
w
s
t
h
e
o
p
ti
m
izat
io
n
alg
o
r
ith
m
to
s
elec
t
a
n
d
u
s
e
th
e
b
est
s
o
l
u
tio
n
o
b
tai
n
ed
at
an
y
s
ta
g
e
o
f
o
p
ti
m
izatio
n
p
r
o
ce
s
s
.
Sin
ce
,
i
n
o
p
tim
izatio
n
p
r
o
ce
s
s
a
n
tlio
n
i
s
co
n
s
id
er
ed
as
eli
te,
it
s
h
o
u
l
d
b
e
ab
le
to
af
f
ec
t
t
h
e
m
o
v
e
m
en
ts
o
f
al
l
t
h
e
a
n
t
s
(
p
r
ey
s
)
d
u
r
i
n
g
iter
atio
n
s
.
T
h
er
ef
o
r
e,
it
is
ass
u
m
ed
th
at
e
v
er
y
an
t
r
an
d
o
m
l
y
w
al
k
s
ar
o
u
n
d
a
s
elec
ted
an
tlio
n
b
y
th
e
r
o
u
lette
w
h
ee
l a
n
d
th
e
elit
e
s
i
m
u
lta
n
eo
u
s
l
y
.
T
h
e
m
a
th
e
m
ati
ca
l
m
o
d
el
o
f
th
is
b
eh
a
v
io
r
is
as (
4
6
)
.
2
t
t
t
i
A
E
A
n
t
R
R
(
(
46
)
W
h
er
e
R
t
A
is
th
e
r
an
d
o
m
w
al
k
ar
o
u
n
d
th
e
an
t
lio
n
s
elec
ted
b
y
th
e
r
o
u
let
te
w
h
ee
l
at
t
-
th
ite
r
atio
n
,
R
t
E
is
th
e
r
an
d
o
m
w
alk
ar
o
u
n
d
th
e
elite
at
t
-
th
iter
atio
n
,
an
d
An
t
t
i
in
d
icate
s
t
h
e
p
o
s
itio
n
o
f
i
-
th
a
n
t
at
t
-
th
iter
atio
n
[
3
4
,
3
5
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4856
Op
tima
l tc
s
c
p
la
ce
men
t fo
r
co
n
g
esti
o
n
ma
n
a
g
eme
n
t in
d
ereg
u
la
ted
p
o
w
er sys
tem
s
…
(
Ma
jid
Mo
a
z
z
a
mi
)
85
4.
SI
M
UL
AT
I
O
N
AN
D
RE
SU
L
T
S
I
n
th
i
s
p
ap
er
,
I
E
E
E
1
4
-
b
u
s
te
s
t
s
y
s
te
m
is
u
s
ed
f
o
r
s
i
m
u
lat
i
o
n
.
T
h
is
s
y
s
te
m
co
n
s
is
t
s
o
f
5
g
en
er
ato
r
s
,
1
1
lo
ad
s
,
1
7
tr
an
s
m
is
s
io
n
lin
e
s
a
n
d
3
li
n
es
o
f
tr
an
s
f
o
r
m
er
s
.
T
h
e
s
in
g
le
-
li
n
e
d
ia
g
r
a
m
o
f
th
i
s
n
et
w
o
r
k
is
s
h
o
w
n
in
Fi
g
u
r
e
5
.
T
h
e
in
f
o
r
m
atio
n
o
n
th
i
s
n
e
t
w
o
r
k
is
al
s
o
g
i
v
en
i
n
T
ab
les 1
to
3
.
I
n
th
i
s
m
et
h
o
d
,
t
w
o
ca
s
e
s
ar
e
in
v
e
s
ti
g
ated
:
T
C
SC
is
n
o
t i
n
s
ta
lled
in
t
h
e
s
y
s
te
m
a
n
d
th
e
co
n
g
es
tio
n
co
n
s
t
r
ain
t f
o
r
tr
an
s
m
is
s
io
n
li
n
es i
s
i
m
p
o
s
ed
.
T
h
e
lin
es h
a
v
e
co
n
g
est
io
n
co
n
s
tr
ain
t
s
an
d
T
C
SC
h
as b
ee
n
ad
d
ed
to
th
e
s
y
s
te
m
.
I
n
t
h
e
f
ir
s
t
ca
s
e,
i
n
w
h
ic
h
th
e
s
y
s
te
m
d
o
es
n
o
t
h
av
e
T
C
SC
,
th
e
to
tal
co
s
t
o
f
g
e
n
er
atio
n
i
s
8
,
1
5
6
.
8
1
(
$
/h
)
,
an
d
th
e
to
tal
c
o
n
g
es
tio
n
co
s
t i
s
1
1
8
1
.
3
2
(
$
/h
)
.
T
h
u
s
,
t
h
e
to
tal
co
s
t
w
ill
b
e
9
3
3
8
.
1
3
(
$
/h
)
.
I
n
t
h
e
s
ec
o
n
d
ca
s
e,
a
f
ter
t
h
e
o
p
ti
m
i
za
tio
n
is
ex
ec
u
ted
,
t
h
e
o
p
ti
m
al
lo
ca
tio
n
a
n
d
s
i
ze
o
f
t
h
e
T
C
S
C
is
in
v
e
s
ti
g
ated
.
T
h
e
lin
e
2
is
d
eter
m
i
n
ed
as
t
h
e
b
est
p
lace
to
in
s
tall,
a
n
d
X
TC
SC
is
eq
u
a
l
to
-
1
0
.
5
8
.
I
n
ad
d
iti
o
n
,
th
e
to
tal
co
s
t
o
f
g
en
er
atio
n
i
n
t
h
e
s
ec
o
n
d
ca
s
e
is
8
0
6
1
.
4
6
(
$
/h
)
,
th
e
to
tal
co
n
g
e
s
tio
n
co
s
t
is
8
1
6
.
32
(
$
/h
)
.
T
h
u
s
,
t
h
e
to
tal
co
s
t
w
il
l
b
e
8
8
7
7
,
7
8
(
$
/h
)
.
T
h
er
e
f
o
r
e,
w
ith
th
e
in
s
tallat
io
n
o
f
T
C
SC
in
th
e
s
y
s
te
m
,
t
h
e
p
r
o
f
it
w
i
l
l
b
e
eq
u
al
to
4
6
0
.
3
5
(
$
/h
)
.
Fig
u
r
e
6
s
h
o
w
s
t
h
e
LMP
f
o
r
all
b
u
s
es
i
n
t
h
e
t
w
o
s
t
u
d
ied
ca
s
es.
A
cc
o
r
d
in
g
l
y
,
in
a
ll
b
u
s
e
s
,
asid
e
f
r
o
m
b
u
s
es
3
an
d
8
,
t
h
e
LMP
p
r
ice
is
r
ed
u
ce
d
.
I
n
Fig
u
r
e
7
,
t
h
e
tr
a
n
s
m
is
s
io
n
p
o
w
er
t
h
r
o
u
g
h
t
h
e
n
et
w
o
r
k
lin
e
s
is
s
h
o
w
n
i
n
t
w
o
ca
s
es
.
T
ab
le
1
.
C
o
s
t
f
u
n
ctio
n
c
o
e
f
f
ic
i
en
ts
a
n
d
e
n
er
g
y
s
ale
b
id
d
in
g
s
P
max
P
m
i
n
P
r
i
c
e
(
$
/
M
W
h
)
γ
β
α
B
u
s
N
o
.
3
3
2
0
35
0
.
0
4
7
4
3
20
0
1
1
4
0
0
36
0
.
2
3
9
1
20
0
2
1
0
0
0
38
0
.
0
3
7
3
5
.
4
0
3
1
0
0
0
60
0
.
0
2
40
0
6
1
0
0
0
40
0
.
0
3
35
0
8
T
ab
le
2
.
C
h
ar
ac
ter
is
tics
o
f
a
tr
an
s
m
i
s
s
io
n
l
in
e
L
i
n
e
N
o
.
Bu
s
S
e
ndi
ng
Bu
s
R
e
c
e
i
v
i
ng
R
e
si
st
a
n
c
e
(
p
.
u
)
R
e
a
c
t
a
n
c
e
(
p
.
u
)
1
1
2
0
.
0
1
9
3
8
0
.
0
5
9
1
7
2
1
5
0
.
0
5
4
0
3
0
.
2
2
3
0
4
3
2
3
0
.
0
4
6
9
9
0
.
1
9
7
9
7
4
2
4
0
.
0
5
8
1
1
0
.
1
7
6
3
2
5
2
5
0
.
0
5
6
9
5
0
.
1
7
3
8
8
6
3
4
0
.
0
6
7
0
1
0
.
1
7
1
0
3
7
4
5
0
.
0
1
3
3
5
0
.
0
4
2
1
1
8
4
7
0
.
0
0
0
.
2
0
9
1
2
9
4
9
0
.
0
0
0
.
5
5
6
1
8
10
5
6
0
.
0
0
0
.
2
5
2
0
2
11
6
11
0
.
0
9
4
9
8
0
.
1
9
8
9
12
6
12
0
.
1
2
2
9
1
0
.
2
5
5
8
1
13
6
13
0
.
0
6
6
1
5
0
.
1
3
0
2
7
14
7
8
0
.
0
0
0
.
1
7
6
1
5
15
7
9
0
.
0
0
0
.
1
1
0
0
1
16
9
10
0
.
0
3
1
8
1
0
.
0
8
4
5
0
17
9
14
0
.
1
2
7
1
1
0
.
2
7
0
3
8
18
10
11
0
.
0
8
2
0
5
0
.
1
9
2
0
7
19
12
13
0
.
2
2
0
9
2
0
.
1
9
9
8
8
20
13
14
0
.
1
7
0
9
3
0
.
3
4
8
0
2
T
ab
le
3
.
Data
o
f
b
u
s
es
[
3
6
]
B
u
s
N
o
.
P
G
e
n
(
p
.
u
)
Q
G
e
n
(
p
.
u
)
P
Co
n
(
p
.
u
)
Q
Co
n
(
p
.
u
)
B
u
s
t
y
p
e
Q
M
a
x,
ge
n
(
p
.
u
)
Q
M
i
n,
ge
n
(
p
.
u
)
1
2
.
3
2
0
.
0
0
0
.
0
0
0
.
0
0
PV
1
0
.
0
-
1
0
.
0
2
0
.
4
-
0
.
4
2
4
0
.
2
1
7
0
0
.
1
2
7
0
S
w
i
n
g
0
.
5
-
0
.
4
3
0
.
0
0
0
.
0
0
0
.
9
4
2
0
0
.
1
9
0
0
PV
0
.
4
0
.
0
0
4
0
.
0
0
0
.
0
0
0
.
4
7
8
0
0
.
0
0
PQ
0
.
0
0
0
.
0
0
5
0
.
0
0
0
.
0
0
0
.
0
7
6
0
0
.
0
1
6
0
PQ
0
.
0
0
0
.
0
0
6
0
.
0
0
0
.
0
0
0
.
1
1
2
0
0
.
0
7
5
0
PV
0
.
2
4
-
0
.
0
6
7
0
.
0
0
0
.
0
0
0
.
0
0
0
.
0
0
PQ
0
.
0
0
0
.
0
0
8
0
.
0
0
0
.
0
0
0
.
0
0
0
.
0
0
PV
0
.
2
4
-
0
.
0
6
9
0
.
0
0
0
.
0
0
0
.
2
9
5
0
0
.
1
6
6
0
PQ
0
.
0
0
0
.
0
0
10
0
.
0
0
0
.
0
0
0
.
0
9
0
0
0
.
0
5
8
0
PQ
0
.
0
0
0
.
0
0
11
0
.
0
0
0
.
0
0
0
.
0
3
5
0
0
.
0
1
8
0
PQ
0
.
0
0
0
.
0
0
12
0
.
0
0
0
.
0
0
0
.
0
6
1
0
0
.
0
1
6
0
PQ
0
.
0
0
0
.
0
0
13
0
.
0
0
0
.
0
0
0
.
1
3
5
0
0
.
0
5
8
0
PQ
0
.
0
0
0
.
0
0
14
0
.
0
0
0
.
0
0
0
.
1
4
9
0
0
.
0
5
0
0
PQ
0
.
0
0
0
.
0
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l.
8
,
No
.
2
,
J
u
n
e
2
0
1
9
:
77
–
88
86
G
C
G
e
n
.
2
2
G
e
n
.
3
3
5
G
G
e
n
.
1
C
4
G
e
n
.
4
6
7
8
C
9
1
3
1
4
1
0
1
1
1
2
1
Fig
u
r
e
5
.
I
E
E
E
1
4
-
b
u
s
s
y
s
te
m
Fig
u
r
e
6
.
L
o
ca
tio
n
al
m
ar
g
i
n
al
p
r
ices
w
it
h
o
r
w
it
h
o
u
t T
C
SC
i
n
th
e
I
E
E
E
1
4
-
b
u
s
test
n
et
w
o
r
k
.
Fig
u
r
e
7
.
T
r
an
s
m
i
s
s
io
n
ac
ti
v
e
p
o
w
er
o
f
lin
e
s
w
it
h
o
r
w
it
h
o
u
t T
C
SC
i
n
th
e
I
E
E
E
1
4
-
b
u
s
test
n
et
w
o
r
k
5.
CO
NCLU
SI
O
N
Ser
ies
F
AC
T
S
d
ev
ices
ca
n
h
elp
to
in
cr
ea
s
e
p
o
w
er
s
y
s
te
m
s
ec
u
r
it
y
b
y
co
n
tr
o
lli
n
g
th
e
p
o
w
er
f
lo
w
p
ass
in
g
th
r
o
u
g
h
tr
a
n
s
m
i
s
s
io
n
lin
e
s
.
Ne
v
er
t
h
eles
s
,
t
h
eir
c
o
n
s
id
er
ab
l
y
h
i
g
h
co
s
t
o
f
th
e
m
n
ec
es
s
itate
s
t
h
e
ac
cu
r
ate
p
lace
m
e
n
t
a
n
d
s
izi
n
g
o
f
th
e
m
.
I
n
t
h
i
s
s
t
u
d
y
,
a
co
m
b
in
ed
m
et
h
o
d
is
e
m
p
lo
y
ed
to
o
p
tim
ize
th
e
T
C
S
C
p
ar
am
eter
s
an
d
d
eter
m
i
n
e
it
s
ap
p
r
o
p
r
iate
lo
ca
tio
n
to
r
ed
u
ce
th
e
co
s
t
o
f
co
n
g
e
s
tio
n
a
n
d
to
d
im
i
n
is
h
t
h
e
g
en
er
atio
n
co
s
t
in
p
o
w
er
g
r
id
.
T
h
e
r
esu
lt o
f
u
s
i
n
g
AL
O
al
g
o
r
ith
m
a
n
d
o
p
ti
m
al
p
o
w
er
f
lo
w
o
n
an
I
E
E
E
1
4
-
b
u
s
test
s
y
s
te
m
i
s
co
m
p
ar
ed
in
t
wo
ca
s
es
o
f
w
i
th
a
n
d
w
it
h
o
u
t
T
C
S
C
.
T
h
e
r
esu
lt
s
s
h
o
w
th
a
t
r
esp
ec
t
to
th
e
o
p
ti
m
a
l
in
s
ta
llatio
n
o
f
T
C
S
C
(
lin
e
2
)
,
th
e
to
tal
co
s
t
w
ill
d
ec
r
ea
s
e
f
r
o
m
9
3
3
8
.
1
3
(
$
/h
)
to
8
8
7
7
.
7
8
(
$
/h
)
.
T
h
is
m
ea
n
s
th
at
t
h
e
p
r
o
f
it
w
i
ll
b
e
eq
u
al
t
o
4
6
0
.
3
5
(
$
/
h
)
.
T
h
er
ef
o
r
e,
in
co
n
g
es
tio
n
m
a
n
ag
e
m
e
n
t
m
et
h
o
d
,
d
esp
ite
th
e
f
ac
t
th
at
F
AC
T
S
d
ev
ices
ar
e
ex
p
en
s
i
v
e,
t
h
e
o
p
ti
m
al
u
s
e
o
f
t
h
ese
ele
m
e
n
ts
(
r
eg
ar
d
to
th
e
b
est
F
A
C
T
S
t
y
p
e
s
elec
tio
n
an
d
ch
o
o
s
i
n
g
t
h
e
b
est
in
s
tallatio
n
lo
ca
tio
n
)
m
iti
g
a
tes
th
e
co
n
g
e
s
tio
n
a
n
d
m
ak
e
a
p
r
o
p
er
c
o
n
g
esti
o
n
m
an
a
g
e
m
e
n
t
p
o
s
s
ib
le.
T
h
er
ef
o
r
e,
u
tili
zi
n
g
th
e
s
e
d
ev
ice
s
f
o
r
co
n
g
esti
o
n
m
an
a
g
e
m
e
n
t
h
as
a
h
ig
h
er
p
r
io
r
it
y
th
an
o
t
h
er
m
et
h
o
d
s
.
RE
F
E
R
E
NC
E
S
[1
]
F
Bo
u
g
o
u
f
fa
,
L
.
,
&
Ch
a
g
h
i,
A
.
,
“
Op
ti
m
a
l
Co
o
rd
in
a
ti
o
n
o
f
DO
CR
f
o
r
Ra
d
ial
Distrib
u
ti
o
n
S
y
ste
m
s
in
P
re
se
n
c
e
o
f
T
CS
C
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
,
7
(2
),
3
1
1
,
2
0
1
6
.
[2
]
Ku
m
a
r,
P
.
,
“
En
h
a
n
c
e
m
e
n
t
o
f
p
o
w
e
r
q
u
a
li
t
y
b
y
a
n
a
p
p
li
c
a
ti
o
n
F
A
C
T
S
d
e
v
ice
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
,
6
(
1
),
1
0
,
2
0
1
5
.
[3
]
Ku
m
a
riCh
,
N.
R.
,
&
S
e
k
h
a
r,
K.
C.
,
“
Op
ti
m
a
l
P
lac
e
m
e
n
t
o
f
T
CS
C
Ba
se
d
o
n
S
e
n
si
ti
v
it
y
A
n
a
l
y
sis
f
o
r
Co
n
g
e
stio
n
M
a
n
a
g
e
m
e
n
t,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
E
lec
trica
l
a
n
d
Co
mp
u
ter
E
n
g
i
n
e
e
rin
g
,
6
(
5
),
2
0
4
1
.,
2
0
1
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.