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1.
I
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I
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6
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T
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KOM
NI
KA
T
elec
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m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
1
,
Feb
r
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ar
y
2
0
2
1
:
3
0
1
-
3
0
9
302
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to
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[
1
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[
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e
in
d
icate
d
th
e
ad
v
an
tag
es
o
f
B
SA
co
m
p
ar
ed
t
o
o
th
er
alg
o
r
ith
m
s
s
u
ch
as
g
en
er
atio
n
o
f
ef
f
icien
t
ly
tr
ial
p
o
p
u
latio
n
s
,
b
ala
n
ce
b
e
twee
n
ex
p
lo
r
atio
n
an
d
ex
p
l
o
itatio
n
,
th
e
ef
f
icien
t
cr
o
s
s
o
v
er
o
p
e
r
ato
r
an
d
th
e
s
im
p
ly
im
p
lem
en
t.
M
o
r
eo
v
er
in
[
1
9
,
2
0
]
,
B
SA
h
as
d
em
o
n
s
tr
ated
th
e
h
ig
h
er
p
er
f
o
r
m
an
ce
th
a
n
p
a
r
ticle
s
war
m
o
p
t
im
izatio
n
,
d
if
f
er
en
tial
e
v
o
lu
tio
n
alg
o
r
ith
m
,
f
ir
ef
ly
alg
o
r
ith
m
an
d
ar
tif
icial
b
ee
co
lo
n
y
f
o
r
1
6
b
e
n
ch
m
ar
k
p
r
o
b
lem
s
.
I
n
ad
d
itio
n
,
B
SA
h
as
also
s
h
o
wn
its
p
er
f
o
r
m
an
ce
f
o
r
s
o
m
e
p
r
o
b
le
m
s
in
p
o
wer
s
y
s
tem
f
ield
s
u
c
h
as
d
is
tr
ib
u
ted
g
en
er
atio
n
p
lace
m
en
t
[
2
1
]
,
ec
o
n
o
m
ic
lo
ad
d
is
p
atch
[
2
2
,
2
3
]
a
n
d
n
etwo
r
k
r
ec
o
n
f
ig
u
r
atio
n
[
2
4
]
.
I
n
th
is
s
tu
d
y
,
im
p
r
o
v
ed
B
SA
(
I
B
SA)
is
p
r
o
p
o
s
ed
f
o
r
s
ea
r
ch
i
n
g
th
e
o
p
tim
al
n
etwo
r
k
c
o
n
f
ig
u
r
atio
n
o
f
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
to
r
e
d
u
ce
p
o
wer
lo
s
s
.
W
h
er
ein
,
in
o
r
d
er
to
ap
p
ly
I
B
SA
f
o
r
th
e
n
et
wo
r
k
co
n
f
ig
u
r
atio
n
p
r
o
b
lem
,
a
s
ta
r
tin
g
s
o
l
u
tio
n
is
f
ir
s
t
d
eter
m
in
ed
b
y
a
h
e
u
r
is
tic
r
u
le
in
p
o
we
r
s
y
s
tem
.
T
h
en
,
t
h
e
s
tar
tin
g
s
o
lu
tio
n
is
as
s
ig
n
ed
to
th
e
in
itializatio
n
p
o
p
u
latio
n
o
f
I
B
SA.
T
h
e
ef
f
ec
tiv
en
ess
o
f
I
B
SA
f
o
r
th
e
n
etwo
r
k
c
o
n
f
ig
u
r
atio
n
p
r
o
b
lem
is
co
m
p
ar
ed
with
B
SA,
PS
O,
FA
an
d
o
th
e
r
tech
n
i
q
u
es
in
th
e
liter
atu
r
e
o
n
two
d
i
s
tr
ib
u
tio
n
n
etwo
r
k
s
co
n
s
is
tin
g
o
f
th
e
3
3
-
n
o
d
e
an
d
6
9
-
n
o
d
e
s
y
s
tem
s
.
B
ased
o
n
th
e
p
er
f
o
r
m
an
ce
o
f
I
B
SA
f
o
r
two
test
s
y
s
tem
s
,
th
e
m
ain
h
ig
h
lig
h
ts
o
f
th
is
wo
r
k
a
r
e
f
o
llo
ws:
−
I
B
SA is f
ir
s
t p
r
o
p
o
s
ed
f
o
r
t
h
e
n
etwo
r
k
co
n
f
ig
u
r
a
tio
n
p
r
o
b
lem
to
m
in
im
ize
p
o
wer
lo
s
s
.
−
T
h
e
s
tar
tin
g
n
etwo
r
k
co
n
f
ig
u
r
atio
n
is
p
r
o
p
o
s
ed
f
o
r
I
B
SA
to
en
h
an
ce
th
e
ef
f
icien
cy
o
f
I
B
S
A
f
o
r
th
e
n
etwo
r
k
co
n
f
ig
u
r
atio
n
p
r
o
b
lem
.
−
I
B
SA
o
u
tp
er
f
o
r
m
s
B
SA,
PS
O
an
d
FA
in
ter
m
s
o
f
s
u
cc
ess
r
ate
an
d
o
b
tain
ed
s
o
lu
tio
n
q
u
a
lity
f
o
r
f
i
n
d
in
g
o
p
tim
al
n
etwo
r
k
co
n
f
ig
u
r
atio
n
.
−
I
B
SA c
an
f
in
d
th
e
b
e
tter
n
etw
o
r
k
co
n
f
ig
u
r
atio
n
c
o
m
p
ar
e
d
to
s
o
m
e
p
r
ev
i
o
u
s
m
eth
o
d
s
.
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
o
f
th
e
n
etwo
r
k
r
ec
o
n
f
i
g
u
r
atio
n
p
r
o
b
lem
in
th
is
s
tu
d
y
is
to
m
in
im
ize
p
o
wer
lo
s
s
o
f
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
I
t
is
ca
lcu
lated
as f
o
llo
ws:
min
ob
j
=
∑
∆
P
=
1
(
1
)
wh
er
e
∆
P
is
p
o
wer
lo
s
s
o
f
th
e
i
th
b
r
an
ch
.
is
n
u
m
b
er
o
f
b
r
an
c
h
e
s
o
f
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
I
n
s
t
allin
g
DG
in
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
s
h
o
u
l
d
b
e
m
ain
tain
ed
t
h
e
f
o
llo
win
g
c
o
n
s
tr
ain
ts
:
−
R
ad
ial
to
p
o
lo
g
y
: th
is
co
n
s
t
r
ain
t is satis
f
ied
b
y
th
e
b
elo
w
eq
u
atio
n
[
2
5
]
:
|
(
)
|
=
1
(
2
)
wh
er
e
,
(
)
is
d
eter
m
i
n
an
t
o
f
m
atr
ix
.
is
a
m
atr
ix
th
at
s
im
u
lates
th
e
co
n
n
ec
tio
n
o
f
a
n
etwo
r
k
co
n
f
ig
u
r
atio
n
.
−
Vo
ltag
e
an
d
c
u
r
r
en
t lim
its
:
{
,
≤
≤
,
;
=
1
÷
≤
,
;
=
1
÷
(
3
)
wh
er
e
,
an
d
,
ar
e
th
e
lo
wer
an
d
u
p
p
er
p
er
m
itted
r
a
n
g
es
v
o
lta
g
e.
is
th
e
v
o
ltag
e
am
p
litu
d
e
o
f
th
e
ith
n
o
d
e.
an
d
,
ar
e
cu
r
r
en
t
an
d
r
ated
cu
r
r
en
t
o
f
th
e
ith
b
r
an
c
h
.
is
n
u
m
b
e
r
o
f
b
u
s
es
o
f
th
e
d
is
t
r
ib
u
tio
n
n
etwo
r
k
.
T
h
e
a
d
ap
tiv
e
f
u
n
ctio
n
(
)
o
f
th
e
n
etwo
r
k
r
ec
o
n
f
i
g
u
r
atio
n
p
r
o
b
lem
is
d
eter
m
in
ed
b
ased
o
n
th
e
o
b
jectiv
e
f
u
n
ctio
n
an
d
in
e
q
u
al
ity
co
n
s
tr
ain
ts
as f
o
llo
ws:
=
ob
j
+
.
[
(
,
−
,
0
)
+
(
ma
x
(
/
,
)
−
1
,
0
)
]
(
4
)
wh
er
e
is
a
p
en
alty
co
ef
f
icien
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
Op
tima
l d
is
tr
ib
u
tio
n
n
etw
o
r
k
co
n
fig
u
r
a
tio
n
u
s
in
g
… (
Th
u
a
n
Th
a
n
h
N
g
u
ye
n
)
303
3.
I
M
P
RO
V
E
D
B
ACK
T
R
AC
K
I
NG
SE
AR
CH
AL
G
O
RI
T
H
M
F
O
R
E
L
E
C
T
RIC D
I
S
T
RIB
U
T
I
O
N
NE
T
WO
RK
RE
CO
NF
I
G
U
RATI
O
N
T
h
er
e
ar
e
m
an
y
f
ac
to
r
s
th
at
a
f
f
ec
t
th
e
o
u
tc
o
m
e
o
f
an
o
p
tim
a
l
alg
o
r
ith
m
s
u
c
h
as
s
ea
r
ch
m
e
ch
an
is
m
s
,
co
n
tr
o
l
p
a
r
am
eter
s
,
in
itial
in
itialized
p
o
p
u
latio
n
s
.
I
n
th
is
s
tu
d
y
,
th
e
in
itial
in
itializatio
n
p
o
p
u
latio
n
o
f
B
SA
is
im
p
r
o
v
e
d
to
en
h
an
ce
e
f
f
icien
c
y
o
f
B
SA.
Step
1
: G
en
er
ate
r
an
d
o
m
ly
t
h
e
p
o
p
u
latio
n
o
f
s
o
lu
tio
n
s
.
,
=
,
+
(
0
,
1
)
.
(
,
−
,
)
;
=
1
,
…
,
;
=
1
,
…
,
(
5
)
W
h
er
e
,
,
is
th
e
jth
v
ar
ia
b
le
o
f
th
e
ith
s
o
lu
tio
n
.
,
an
d
,
ar
e
u
p
p
e
r
a
n
d
lo
wer
lim
its
o
f
th
e
j
th
v
ar
ia
b
le
o
f
th
e
ith
s
o
lu
tio
n
.
an
d
ar
e
p
o
p
u
latio
n
s
ize
an
d
d
im
en
s
io
n
o
f
th
e
o
p
tim
izatio
n
p
r
o
b
lem
.
E
ac
h
s
o
lu
tio
n
cr
ea
ted
is
ad
ju
s
ted
f
o
r
m
ap
p
i
n
g
with
th
e
n
etwo
r
k
r
ec
o
n
f
ig
u
r
atio
n
as f
o
llo
ws:
=
[
]
(
6
)
Step
2
: Fin
d
th
e
s
tar
tin
g
s
o
lu
ti
o
n
(
)
.
Fro
m
th
e
p
o
p
u
latio
n
cr
ea
ted
r
a
n
d
o
m
ly
as
(
5
)
,
a
g
o
o
d
s
o
lu
tio
n
to
th
e
n
etwo
r
k
r
ec
o
n
f
ig
u
r
atio
n
p
r
o
b
le
m
is
ass
ig
n
ed
to
th
e
p
o
p
u
latio
n
t
o
im
p
r
o
v
e
th
e
q
u
ality
o
f
th
e
o
r
ig
in
al
p
o
p
u
latio
n
.
T
h
is
s
o
lu
tio
n
is
d
ete
r
m
in
ed
b
y
th
e
h
eu
r
is
tic
r
u
l
e
o
f
th
e
p
o
w
er
s
y
s
tem
th
at
o
p
en
in
g
t
h
e
b
r
an
ch
with
th
e
s
m
allest
cu
r
r
e
n
t
in
a
clo
s
ed
-
lo
o
p
n
etwo
r
k
,
th
e
clo
s
ed
-
lo
o
p
n
et
wo
r
k
will
b
ec
o
m
e
a
r
ad
ial
n
etwo
r
k
th
at
h
as
th
e
s
m
allest
p
o
wer
lo
s
s
[
1
0
]
.
T
o
d
eter
m
in
e
th
e
s
tar
tin
g
s
o
lu
tio
n
,
th
e
f
ir
s
t
o
p
en
s
witch
o
f
th
e
o
r
ig
in
al
n
etwo
r
k
c
o
n
f
ig
u
r
atio
n
is
clo
s
ed
an
d
th
e
lo
ad
f
lo
w
p
r
o
b
lem
is
r
u
n
f
o
r
th
e
s
y
s
tem
with
a
lo
o
p
.
T
h
e
n
,
th
e
s
witch
th
at
ex
it
s
th
e
s
m
allest
cu
r
r
en
t
in
th
e
lo
o
p
is
o
p
en
ed
to
s
u
b
s
titu
te
f
o
r
th
e
f
ir
s
t
o
p
en
s
witch
.
T
h
is
p
r
o
ce
s
s
is
ca
r
r
ied
o
u
t
u
n
til
th
e
f
in
al
o
p
en
s
witch
o
f
t
h
e
o
r
ig
in
al
n
etwo
r
k
co
n
f
ig
u
r
atio
n
is
r
ep
lace
d
b
y
a
n
ew
s
witch
.
T
h
en
s
o
lu
tio
n
is
s
u
b
s
titu
ted
f
o
r
a
r
a
n
d
o
m
s
o
lu
tio
n
o
f
th
e
in
i
tial p
o
p
u
latio
n
as f
o
llo
ws:
1
=
(
7
)
wh
er
e
,
1
is
a
r
an
d
o
m
s
o
lu
tio
n
s
elec
ted
f
r
o
m
th
e
in
itial p
o
p
u
la
tio
n
.
Fro
m
th
e
p
o
p
u
latio
n
c
r
ea
ted
,
th
e
a
d
ap
tiv
e
f
u
n
ctio
n
o
f
ea
ch
s
o
lu
tio
n
is
v
al
id
ated
b
y
(
4
)
an
d
th
e
b
est
so
-
f
a
r
s
o
lu
tio
n
(
)
with
th
e
b
est
ad
a
p
tiv
e
f
u
n
ctio
n
v
alu
e
(
)
is
d
eter
m
in
e
d
.
Fu
r
th
er
m
o
r
e,
B
SA
is
also
u
s
ed
a
n
o
th
er
p
o
p
u
latio
n
ca
lled
h
is
to
r
ical
p
o
p
u
latio
n
t
o
s
er
v
e
f
o
r
g
e
n
er
atin
g
n
ew
s
o
lu
tio
n
s
.
T
h
u
s
,
ea
ch
s
o
lu
tio
n
o
f
t
h
e
h
is
to
r
ical
p
o
p
u
latio
n
(
ℎ
)
is
g
en
er
ated
at
th
e
b
eg
in
n
in
g
b
y
u
s
in
g
(
5
)
a
n
d
(
6
).
Step
3
: Red
ef
in
e
th
e
h
is
to
r
ical
p
o
p
u
latio
n
.
T
h
e
ea
ch
s
o
lu
tio
n
in
th
e
h
is
to
r
ical
p
o
p
u
latio
n
is
r
ed
ef
in
e
d
as f
o
llo
ws:
ℎ
=
{
;
2
<
3
ℎ
;
ℎ
;
=
1
,
…
,
(
8
)
wh
er
e
,
2
an
d
3
ar
e
two
r
an
d
o
m
n
u
m
b
er
s
in
[
0
,
1
]
.
T
h
e
s
o
lu
tio
n
s
in
th
e
h
is
to
r
ical
p
o
p
u
latio
n
is
p
er
m
u
ted
as
f
o
llo
ws:
ℎ
=
ℎ
4
(
)
;
=
1
,
…
,
(
9
)
wh
er
e
4
is
a
v
ec
to
r
co
n
tain
in
g
a
r
an
d
o
m
p
er
m
u
tatio
n
o
f
1
:
.
Step
4
: G
en
er
ate
n
ew
p
o
p
u
lati
o
n
.
Firstl
y
,
tem
p
o
r
ar
y
n
ew
s
o
lu
tio
n
s
ca
lled
(
)
ar
e
g
en
er
ated
as f
o
llo
ws:
=
+
.
5
.
(
ℎ
−
)
;
=
1
,
…
,
(
1
0
)
wh
er
e
,
4
is
a
r
an
d
o
m
n
u
m
b
er
in
[
0
,
1
]
.
is
a
s
ca
le
co
ef
f
icien
t
th
at
is
s
et
to
3
[
1
8
]
.
Seco
n
d
l
y
,
th
e
n
ew
p
o
p
u
latio
n
(
_
)
ar
e
g
e
n
er
ated
as f
o
llo
ws:
_
,
=
{
,
;
,
=
1
,
;
ℎ
;
=
1
,
…
,
;
=
1
,
…
,
(
1
1
)
wh
er
ein
,
is
th
e
.
b
in
ar
y
m
atr
ix
.
All
o
f
elem
en
ts
o
f
is
f
ir
s
t
s
et
to
0
.
T
h
en
s
o
m
e
o
f
ele
m
en
ts
ar
e
ad
ju
s
ted
to
1
as f
o
llo
ws:
{
,
(
1
:
.
6
.
)
=
1
;
7
<
8
,
(
)
=
1
;
ℎ
;
=
1
,
…
,
(
1
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
3
0
1
-
3
0
9
304
wh
er
e
,
(
1
:
.
6
.
)
is
a
v
ec
to
r
co
n
tain
in
g
a
r
an
d
o
m
p
er
m
u
tatio
n
o
f
1
:
.
6
.
.
is
a
m
ix
-
r
ate
co
ef
f
icie
n
t.
6
,
7
an
d
8
ar
e
r
an
d
o
m
n
u
m
b
er
s
in
[
0
,
1
]
.
(
)
is
a
in
teg
er
r
an
d
o
m
n
u
m
b
er
in
[
1
,
].
E
ac
h
n
ew
s
o
lu
tio
n
in
th
e
p
o
p
u
latio
n
is
ch
ec
k
ed
a
n
d
co
r
r
e
cte
d
its
lim
it a
s
f
o
llo
ws:
_
,
=
{
,
;
_
,
<
,
,
;
_
,
>
,
_
,
;
ℎ
;
=
1
,
…
,
;
=
1
,
…
,
(
1
3
)
Step
5
: u
p
d
ate
t
h
e
p
o
p
u
latio
n
f
o
r
n
e
x
t g
en
e
r
atio
n
.
T
h
e
n
ew
p
o
p
u
latio
n
is
r
o
u
n
d
ed
to
in
teg
er
v
alu
e
b
y
u
s
in
g
(
6
)
an
d
v
alid
ate
d
th
e
ad
ap
tiv
e
f
u
n
ctio
n
b
y
(
4
)
an
d
th
e
p
o
p
u
latio
n
is
u
p
d
ated
f
o
r
th
e
n
e
x
t g
en
e
r
atio
n
b
ased
o
n
th
e
s
elec
tio
n
tech
n
iq
u
e
as
f
o
llo
ws:
=
{
_
;
(
_
)
<
(
)
;
ℎ
;
=
1
,
…
,
(
1
4
)
=
{
(
_
)
;
(
_
)
<
(
)
(
)
;
ℎ
;
=
1
,
…
,
(
1
5
)
Step
6
:
u
p
d
ate
t
h
e
b
est s
o
-
f
ar
s
o
lu
tio
n
.
B
ased
o
n
th
e
ad
ap
tiv
e
f
u
n
ctio
n
v
alu
e
o
f
th
e
p
o
p
u
latio
n
,
th
e
b
e
s
t
s
o
lu
tio
n
(
)
with
th
e
b
est
a
d
a
p
tiv
e
f
u
n
ctio
n
v
alu
e
(
)
i
s
d
eter
m
in
e
d
.
T
h
en
th
e
b
est s
o
-
f
a
r
s
o
lu
tio
n
is
u
p
d
ated
as b
ello
w:
=
{
;
<
;
ℎ
(
1
6
)
=
{
;
min
(
)
<
;
ℎ
(
1
7
)
Step
7
: sto
p
s
ea
r
ch
in
g
p
r
o
ce
s
s
.
T
h
e
s
tep
s
3
to
6
will
b
e
p
e
r
f
o
r
m
ed
u
n
til
th
e
m
a
x
im
u
m
g
en
er
atio
n
(
)
r
ea
ch
es.
T
h
en
t
h
e
b
est
s
o
f
ar
s
o
lu
tio
n
is
c
o
n
s
id
er
ed
as
t
h
e
o
p
tim
al
s
o
lu
tio
n
o
f
th
e
p
r
o
b
lem
.
T
h
e
p
s
eu
d
o
-
c
o
d
e
o
f
I
B
SA
f
o
r
s
o
lv
in
g
th
e
n
etwo
r
k
r
ec
o
n
f
ig
u
r
atio
n
p
r
o
b
l
em
is
s
h
o
wn
in
Fig
u
r
e
1
.
// Step 1: Generate randomly the population of solutions
Generate randomly the current population by using (5)
Modify the generat
ed population by using (6)
// Step 2: Find the starting solution
For
i
= 1
to
number of the original open switches of the distribution system
do
Close the ith original open switch to form a loop for the distribution system
Run power load flow
Open the swit
ch in the loop with the smallest current
Save the open switch as the variable
ith for the starting solution
End for
Assign the starting solution to the current population by using (7)
Validate the adaptive function of each solution is validated by (4)
Dete
rm
in
e
th
e
be
st
so
-
fa
r
so
lu
ti
on
(
)
wi
th
th
e
be
st
ad
ap
ti
ve
function
value
(
)
Generate the historical population by using (5) and (6)
Set the current generation equal to zero
While
the current generation <
do
// Step 3: Redefine the historical po
pulation
Redefine the historical population
by using (8)
Permute the historical population by using (9)
// Step 4: Generate new population
Generate new population by using (11)
Check and correct the bound of new population by using (13)
// Step 5: update
the population for next generation
Modify the
generated population by using (6)
Validate the adaptive function of each solution is validated by (4)
Update the current population by using (14) and (15)
// Step 6: update the best so
-
far solution
Update the b
est so
-
far solution by using (16) and (17)
In
crease the current generation
End while
Fig
u
r
e
1
.
T
h
e
p
s
eu
d
o
-
co
d
e
o
f
I
B
SA f
o
r
s
o
lv
in
g
th
e
n
etwo
r
k
r
ec
o
n
f
ig
u
r
atio
n
p
r
o
b
lem
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
Op
tima
l d
is
tr
ib
u
tio
n
n
etw
o
r
k
co
n
fig
u
r
a
tio
n
u
s
in
g
… (
Th
u
a
n
Th
a
n
h
N
g
u
ye
n
)
305
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
o
r
d
er
to
ev
alu
ate
th
e
ef
f
ec
tiv
en
ess
o
f
I
B
SA
f
o
r
th
e
n
et
wo
r
k
r
ec
o
n
f
ig
u
r
atio
n
p
r
o
b
lem
,
two
test
s
y
s
tem
s
ar
e
u
s
ed
to
r
ec
o
n
f
ig
u
r
e
in
clu
d
in
g
th
e
3
3
-
n
o
d
e
a
n
d
6
9
-
n
o
d
e
s
y
s
tem
s
as sh
o
wn
in
Fi
g
u
r
e
2
.
T
h
e
d
ata
o
f
two
test
s
y
s
tem
s
ar
e
r
ef
er
en
ce
d
f
r
o
m
[
2
6
,
2
7
]
,
r
esp
ec
tiv
ely
.
T
h
e
r
ated
cu
r
r
en
t
o
f
b
r
a
n
ch
es
f
o
r
two
test
s
y
s
tem
s
is
s
et
to
2
5
0
A
an
d
1
5
0
A,
r
e
s
p
ec
tiv
ely
.
T
h
e
n
etwo
r
k
r
ec
o
n
f
ig
u
r
atio
n
p
r
o
g
r
am
is
d
ev
elo
p
ed
o
n
th
e
Ma
tlab
s
o
f
twar
e
an
d
ex
ec
u
ted
o
n
a
p
er
s
o
n
al
co
m
p
u
ter
with
4
GB
o
f
R
AM
an
d
C
PU
co
r
e
-
i5
2
.
4
GH.
T
h
e
p
o
wer
f
lo
w
b
ased
o
n
t
h
e
New
to
n
-
R
ap
h
s
o
n
m
et
h
o
d
is
u
s
ed
f
o
r
ca
lcu
lat
i
n
g
p
o
wer
lo
s
s
,
v
o
ltag
e
a
n
d
c
u
r
r
en
t
p
r
o
f
iles
o
f
t
h
e
s
y
s
tem
s
[
2
8
]
.
Fo
r
th
e
co
n
t
r
o
l
p
ar
am
eter
s
o
f
I
B
SA,
p
o
p
u
latio
n
s
ize
,
d
im
en
s
io
n
an
d
n
u
m
b
er
o
f
m
ax
im
u
m
g
en
er
atio
n
s
ar
e
ch
o
s
en
to
2
0
,
5
an
d
1
5
0
,
r
e
s
p
ec
tiv
el
y
.
T
h
e
m
ix
-
r
ate
co
ef
f
icien
t
in
(
1
2
)
is
ch
o
s
en
b
y
0
.
7
[
2
4
]
.
Mo
r
e
o
v
er
,
i
n
o
r
d
e
r
to
d
em
o
n
s
tr
ate
ef
f
ec
tiv
en
ess
o
f
i
m
p
r
o
v
e
m
en
t
o
f
I
B
SA,
th
e
o
r
ig
in
al
B
SA,
P
SO
an
d
F
A
h
av
e
b
ee
n
also
im
p
le
m
en
ted
f
o
r
th
e
n
etwo
r
k
r
e
co
n
f
ig
u
r
atio
n
p
r
o
b
lem
to
c
o
m
p
ar
e
with
I
B
SA.
T
h
e
p
ar
a
m
eter
s
o
f
B
SA
f
o
r
two
test
s
y
s
tem
s
ar
e
ch
o
s
en
id
e
n
tical
to
th
o
s
e
o
f
I
B
SA
m
ea
n
wh
ile
f
o
r
PS
O,
th
e
1
,
2
,
an
d
ar
e
ch
o
s
en
to
2
,
2
,
2
0
an
d
1
5
0
,
r
esp
ec
tiv
ely
.
Fo
r
F
A,
th
e
an
d
co
ef
f
icien
ts
ar
e
s
et
to
1
[
2
9
,
3
0
]
.
T
h
e
m
a
x
im
u
m
n
u
m
b
er
o
f
e
v
alu
atio
n
th
e
ad
a
p
t
iv
e
f
u
n
ctio
n
(
MN
E
)
is
u
s
ed
as
th
e
s
to
p
co
n
d
itio
n
in
s
tead
o
f
th
e
n
u
m
b
er
o
f
m
ax
i
m
u
m
g
en
er
atio
n
s
b
ec
au
s
e
in
ea
ch
g
en
er
atio
n
,
th
er
e
ar
e
×
n
ew
in
d
iv
id
u
als
cr
ea
ted
an
d
ev
alu
ated
th
e
ad
a
p
tiv
e
f
u
n
ctio
n
t
h
at
is
d
if
f
er
en
t
f
r
o
m
th
e
I
B
SA,
B
SA
an
d
PS
O
alg
o
r
ith
m
s
(
o
n
ly
n
ew
in
d
iv
id
u
als
ar
e
cr
ea
ted
in
ea
ch
g
en
er
atio
n
)
.
T
h
e
MN
E
v
alu
e
o
f
FA
is
s
et
to
3
,
0
0
0
s
im
ilar
to
I
B
SA,
B
SA
an
d
PS
O
wh
ich
is
d
eter
m
i
n
ed
b
y
×
.
Du
e
to
th
is
ch
a
r
ac
ter
,
th
e
co
n
v
er
g
en
ce
cu
r
v
es
o
f
FA
wi
ll
n
o
t
b
e
u
s
ed
to
c
o
m
p
ar
e
with
th
e
r
e
m
ain
in
g
alg
o
r
ith
m
s
.
T
h
e
s
tar
tin
g
s
o
lu
tio
n
o
f
two
te
s
t
s
y
s
tem
s
i
s
d
eter
m
in
ed
b
y
I
B
SA
s
h
o
wn
in
T
ab
le
1
.
C
o
m
p
ar
ed
to
th
e
in
itial
co
n
f
ig
u
r
atio
n
,
p
o
wer
l
o
s
s
ca
u
s
ed
b
y
th
e
s
tar
tin
g
co
n
f
ig
u
r
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T
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307
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3
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Op
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,
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Fig
u
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6
(
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.
Similar
to
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3
3
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,
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m
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m
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in
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6
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s
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ab
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4
.
Op
tim
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n
etwo
r
k
c
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n
f
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r
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f
o
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th
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6
9
-
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d
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s
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s
tem
M
e
t
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O
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∑
∆
(
k
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6
9
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7
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1
3
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4
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5
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3
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TELA
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3
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5
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5
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6
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1
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1
5
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5
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6
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1
,
5
8
9
8
.
6
3
5
6
.
1
4
%
0
.
9
4
9
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
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n
C
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m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
3
0
1
-
3
0
9
308
(
a)
(
b
)
Fig
u
r
e
6
.
C
u
r
r
e
n
t a
n
d
v
o
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e
o
f
th
e
6
9
-
n
o
d
e
d
is
tr
ib
u
tio
n
s
y
s
tem
;
(
a)
b
r
a
n
ch
cu
r
r
en
t a
n
d
(
b
)
n
o
d
e
v
o
ltag
e
5.
CO
NCLU
SI
O
N
I
n
th
is
p
ap
e
r
,
th
e
o
p
tim
al
m
eth
o
d
o
f
elec
tr
ic
d
is
tr
ib
u
tio
n
n
etwo
r
k
c
o
n
f
i
g
u
r
atio
n
f
o
r
p
o
wer
lo
s
s
r
ed
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ctio
n
u
s
in
g
I
B
SA
is
p
r
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ted
.
C
o
m
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r
ed
with
B
SA,
th
e
in
itializatio
n
p
o
p
u
latio
n
o
f
I
B
SA
is
m
o
d
if
ied
b
y
ass
ig
n
in
g
a
g
o
o
d
s
o
lu
t
io
n
th
at
f
o
u
n
d
b
y
th
e
h
eu
r
is
tic
r
u
le
in
th
e
p
o
wer
s
y
s
tem
.
T
h
e
ef
f
icien
cy
o
f
I
B
SA
o
n
th
e
33
-
n
o
d
e
a
n
d
6
9
-
n
o
d
e
s
y
s
tem
s
s
h
o
ws
th
at
I
B
SA
o
u
tp
er
f
o
r
m
s
B
SA
in
ter
m
s
o
f
s
u
cc
ess
f
u
l
r
ate
an
d
o
b
tain
ed
s
o
lu
tio
n
q
u
ality
.
Ab
o
u
t
th
e
s
u
cc
ess
r
ate,
I
B
S
A
ca
n
f
in
d
th
e
o
p
tim
al
co
n
f
ig
u
r
atio
n
with
s
u
cc
ess
r
ate
o
f
9
0
%
an
d
9
2
% f
o
r
th
e
3
3
-
n
o
d
e
a
n
d
6
9
-
n
o
d
e
s
y
s
tem
s
m
ea
n
wh
ile
th
is
in
d
ex
o
f
B
SA f
o
r
two
test
s
y
s
tem
s
is
o
n
ly
6
4
% a
n
d
7
4
%,
r
esp
ec
tiv
ely
.
T
h
e
co
m
p
a
r
is
o
n
s
o
f
I
B
SA w
ith
PS
O,
FA a
n
d
o
t
h
er
m
et
h
o
d
s
in
th
e
liter
a
tu
r
e
also
s
h
o
w
t
h
at
I
B
SA
i
s
b
etter
th
an
s
o
m
e
p
r
ev
io
u
s
m
eth
o
d
s
.
T
h
er
ef
o
r
e,
I
B
SA
is
o
n
e
o
f
ef
f
ec
tiv
e
m
eth
o
d
s
f
o
r
d
eter
m
in
in
g
th
e
o
p
tim
al
n
etwo
r
k
co
n
f
ig
u
r
atio
n
.
Fo
r
f
u
tu
r
e
wo
r
k
,
I
B
SA c
an
b
e
ap
p
lied
f
o
r
s
o
lv
in
g
th
e
n
etwo
r
k
r
ec
o
n
f
ig
u
r
atio
n
p
r
o
b
lem
with
v
ar
y
in
g
lo
ad
s
to
r
ed
u
ce
e
n
er
g
y
lo
s
s
o
r
s
o
lv
in
g
th
e
n
etwo
r
k
r
ec
o
n
f
ig
u
r
atio
n
p
r
o
b
lem
co
n
s
id
er
i
n
g
th
e
d
is
tr
ib
u
ted
g
e
n
er
atio
n
s
to
r
ed
u
ce
p
o
wer
lo
s
s
o
r
en
e
r
g
y
l
o
s
s
.
RE
F
E
R
E
NC
E
S
[1
]
A.
Ab
u
r,
“
A
m
o
d
ifi
e
d
l
in
e
a
r
p
r
o
g
ra
m
m
in
g
m
e
th
o
d
f
o
r
d
istri
b
u
t
i
o
n
sy
ste
m
re
c
o
n
fig
u
ra
ti
o
n
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
Po
we
r a
n
d
En
e
rg
y
S
y
st
e
ms
,
v
o
l.
1
8
,
n
o
.
7
,
p
p
.
4
6
9
-
4
7
4
,
1
9
9
6
.
[2
]
F
.
Ll
o
re
n
s
-
Ib
o
rra
,
J.
Ri
q
u
e
lme
-
S
a
n
to
s,
a
n
d
E.
R
o
m
e
ro
-
Ra
m
o
s,
“
M
i
x
e
d
-
in
teg
e
r
li
n
e
a
r
p
r
o
g
ra
m
m
in
g
m
o
d
e
l
fo
r
so
l
v
i
n
g
re
c
o
n
fig
u
ra
ti
o
n
p
r
o
b
lem
s
in
la
rg
e
-
sc
a
le
d
istri
b
u
ti
o
n
sy
ste
m
s,”
El
e
c
tric
Po
we
r
S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
8
8
,
p
p
.
1
3
7
-
1
4
5
,
2
0
1
2
.
[3
]
A.
Au
g
u
g
l
iaro
,
L.
Du
s
o
n
c
h
e
t
,
a
n
d
S
.
M
a
n
g
i
o
n
e
,
“
Op
ti
m
a
l
re
‐c
o
n
f
ig
u
ra
ti
o
n
o
f
d
istr
ib
u
ti
o
n
n
e
two
rk
fo
r
lo
ss
re
d
u
c
ti
o
n
u
sin
g
n
o
n
‐l
in
e
a
r
p
r
o
g
ra
m
m
i
n
g
,
”
Eu
ro
p
e
a
n
T
ra
n
sa
c
ti
o
n
s o
n
E
lec
trica
l
Po
we
r
,
v
o
l
.
1
,
n
o
.
6
,
p
p
.
3
1
7
-
3
2
4
,
1
9
9
1
.
[4
]
J.
A.
Tay
lo
r
a
n
d
F
.
S
.
Ho
v
e
r,
“
Co
n
v
e
x
m
o
d
e
ls
o
f
d
istri
b
u
ti
o
n
sy
ste
m
re
c
o
n
fig
u
ra
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
o
l.
2
7
,
n
o
.
3
,
p
p
.
1
4
0
7
-
1
4
1
3
,
2
0
1
2
.
[5
]
A.
M
e
rl
in
a
n
d
H.
Ba
c
k
,
“
S
e
a
rc
h
fo
r
a
m
in
ima
l
lo
ss
o
p
e
ra
ti
n
g
sp
a
n
n
i
n
g
tree
c
o
n
f
ig
u
ra
ti
o
n
i
n
a
n
u
r
b
a
n
p
o
we
r
d
istri
b
u
ti
o
n
sy
ste
m
,
”
Pr
o
c
e
e
d
in
g
in
5
t
h
p
o
we
r
sy
ste
m
c
o
m
p
u
t
a
ti
o
n
c
o
n
f
(P
S
CC),
Ca
m
b
rid
g
e
,
UK
,
v
o
l.
1
,
p
p
.
1
-
1
8
,
1
9
7
5
.
[6
]
S
.
Civ
a
n
lar,
J.
J.
G
ra
in
g
e
r,
H.
Yin
,
a
n
d
S
.
S
.
H.
Lee
,
“
Distrib
u
t
io
n
fe
e
d
e
r
re
c
o
n
fig
u
ra
ti
o
n
fo
r
l
o
ss
re
d
u
c
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r De
li
v
e
ry
,
v
o
l.
3
,
n
o
.
3
,
p
p
.
1
2
1
7
-
1
2
2
3
,
1
9
8
8
.
[7
]
D.
S
h
irm
o
h
a
m
m
a
d
i
a
n
d
H.
W
.
Ho
n
g
,
“
Re
c
o
n
fi
g
u
ra
ti
o
n
o
f
e
lec
tr
ic
d
istri
b
u
ti
o
n
n
e
two
r
k
s
fo
r
re
sistiv
e
li
n
e
lo
ss
e
s
re
d
u
c
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r De
li
v
e
ry
,
v
o
l.
4
,
n
o
.
2
,
p
p
.
1
4
9
2
-
1
4
9
8
,
1
9
8
9
.
[8
]
J.
Z.
Z
h
u
,
“
Op
ti
m
a
l
re
c
o
n
fi
g
u
ra
ti
o
n
o
f
e
lec
tri
c
a
l
d
istri
b
u
ti
o
n
n
e
tw
o
rk
u
si
n
g
t
h
e
re
fin
e
d
g
e
n
e
ti
c
a
lg
o
rit
h
m
,
”
E
lec
tric
Po
we
r S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
6
2
,
n
o
.
1
,
p
p
.
3
7
-
4
2
,
2
0
0
2
.
[9
]
A.
M
.
Ot
h
m
a
n
,
A.
A.
El
-
F
e
r
g
a
n
y
,
a
n
d
A.
Y.
Ab
d
e
laz
iz,
“
Op
ti
m
a
l
Re
c
o
n
fig
u
ra
ti
o
n
Co
m
p
risin
g
Vo
lt
a
g
e
S
tab
il
it
y
Asp
e
c
t
Us
in
g
En
h
a
n
c
e
d
Bin
a
ry
P
a
rti
c
le
S
wa
rm
Op
ti
m
iza
ti
o
n
Alg
o
rit
h
m
,
”
El
e
c
tric
Po
we
r
Co
mp
o
n
e
n
ts
a
n
d
S
y
ste
ms
,
v
o
l.
4
3
,
n
o
.
1
4
,
p
p
.
1
6
5
6
-
1
6
6
6
,
2
0
1
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
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p
u
t E
l Co
n
tr
o
l
Op
tima
l d
is
tr
ib
u
tio
n
n
etw
o
r
k
co
n
fig
u
r
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tio
n
u
s
in
g
… (
Th
u
a
n
Th
a
n
h
N
g
u
ye
n
)
309
[1
0
]
T.
Th
a
n
h
N
g
u
y
e
n
,
T
.
T.
N
g
u
y
e
n
,
a
n
d
N.
A
.
Ng
u
y
e
n
,
“
Op
ti
m
a
l
Ne
two
rk
Re
c
o
n
fig
u
ra
ti
o
n
t
o
Re
d
u
c
e
P
o
we
r
Lo
ss
Us
in
g
a
n
In
it
ial
S
e
a
rc
h
in
g
P
o
in
t
fo
r
Co
n
ti
n
u
o
u
s G
e
n
e
ti
c
Alg
o
r
it
h
m
,
”
C
o
mp
lex
it
y
,
v
o
l.
2
0
2
0
,
2
0
2
0
.
[1
1
]
T.
T.
Tran
,
K
.
H.
Tr
u
o
n
g
,
a
n
d
D.
N.
Vo
,
“
S
to
c
h
a
stic
fra
c
tal
se
a
rc
h
a
lg
o
rit
h
m
fo
r
re
c
o
n
fi
g
u
ra
ti
o
n
o
f
d
istri
b
u
ti
o
n
n
e
two
rk
s wit
h
d
istri
b
u
ted
g
e
n
e
ra
t
io
n
s,”
A
in
S
h
a
ms
En
g
in
e
e
rin
g
J
o
u
rn
a
l
,
n
o
.
11
,
n
o
.
2
,
p
p
.
3
8
9
-
4
0
7
,
2
0
1
9
.
[1
2
]
M
.
F
.
Ab
d
El
-
sa
lam
,
E.
Be
sh
r,
a
n
d
M
.
B.
Et
e
ib
a
,
“
A
n
e
w
h
y
b
r
id
tec
h
n
iq
u
e
fo
r
m
in
imiz
i
n
g
p
o
we
r
lo
ss
e
s
in
a
d
istri
b
u
ti
o
n
s
y
ste
m
b
y
o
p
ti
m
a
l
si
z
in
g
a
n
d
siti
n
g
o
f
d
istri
b
u
ted
g
e
n
e
ra
to
rs
with
n
e
tw
o
rk
re
c
o
n
fig
u
ra
t
io
n
,
”
E
n
e
rg
ies
,
v
o
l.
1
1
,
n
o
.
1
2
,
2
0
1
8
.
[1
3
]
K.
Ja
sth
i
a
n
d
D.
Da
s,
“
S
imu
lt
a
n
e
o
u
s d
istri
b
u
ti
o
n
s
y
ste
m
re
c
o
n
fig
u
ra
ti
o
n
a
n
d
DG
siz
in
g
a
lg
o
r
it
h
m
with
o
u
t
l
o
a
d
fl
o
w
so
lu
ti
o
n
,
”
IET
Ge
n
e
ra
t
io
n
,
T
r
a
n
s
miss
io
n
a
n
d
Distrib
u
ti
o
n
,
v
o
l.
1
2
,
n
o
.
6
,
p
p
.
1
3
0
3
-
1
3
1
3
,
2
0
1
8
.
[1
4
]
H.
Ka
rimia
n
fa
rd
a
n
d
H.
Ha
g
h
i
g
h
a
t,
“
An
in
i
ti
a
l
-
p
o
in
t
stra
teg
y
f
o
r
o
p
ti
m
izi
n
g
d
istri
b
u
ti
o
n
sy
ste
m
re
c
o
n
fig
u
ra
ti
o
n
,
”
El
e
c
tric P
o
we
r S
y
st
e
ms
Res
e
a
rc
h
,
v
o
l.
1
7
6
,
2
0
1
9
.
[1
5
]
K.
S
.
S
a
m
b
a
iah
a
n
d
T.
Ja
y
a
b
a
ra
th
i,
“
Op
ti
m
a
l
re
c
o
n
fi
g
u
ra
ti
o
n
a
n
d
re
n
e
wa
b
le
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
a
ll
o
c
a
ti
o
n
i
n
e
lec
tri
c
d
istri
b
u
ti
o
n
sy
ste
m
s,”
In
t
e
rn
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Amb
ien
t
E
n
e
rg
y
,
p
p
.
1
-
2
9
,
2
0
1
9
.
[1
6
]
T.
T.
Ng
u
y
e
n
,
“
El
e
c
tri
c
d
istri
b
u
ti
o
n
n
e
two
rk
re
c
o
n
fi
g
u
ra
ti
o
n
f
o
r
p
o
we
r
lo
ss
re
d
u
c
ti
o
n
b
a
se
d
o
n
r
u
n
n
e
r
ro
o
t
a
lg
o
rit
h
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
En
g
i
n
e
e
rin
g
(IJ
ECE
)
,
v
o
l.
1
0
,
n
o
.
5
,
p
p
.
5
0
1
6
-
5
0
2
4
,
2
0
2
0
.
[1
7
]
H.
Ah
m
a
d
i
a
n
d
J.
R.
M
a
rtí
,
“
M
in
imu
m
-
l
o
ss
n
e
tw
o
rk
re
c
o
n
fi
g
u
ra
ti
o
n
:
A
m
in
im
u
m
sp
a
n
n
in
g
tree
p
ro
b
lem
,
”
S
u
sta
in
a
b
le E
n
e
rg
y
,
Gr
id
s
a
n
d
N
e
two
rk
s
,
v
o
l
.
1
,
p
p
.
1
-
9
,
2
0
1
5
.
[1
8
]
P
.
Civ
icio
g
l
u
,
“
Ba
c
k
trac
k
in
g
S
e
a
rc
h
Op
ti
m
iza
ti
o
n
Alg
o
r
it
h
m
f
o
r
n
u
m
e
rica
l
o
p
t
imiz
a
ti
o
n
p
r
o
b
l
e
m
s,”
Ap
p
li
e
d
Ma
t
h
e
ma
ti
c
s a
n
d
Co
mp
u
ta
ti
o
n
,
v
o
l.
2
1
9
,
n
o
.
1
5
,
p
p
.
8
1
2
1
-
8
1
4
4
,
2
0
1
3
.
[1
9
]
B.
A.
Ha
ss
a
n
a
n
d
T
.
A
.
Ra
sh
i
d
,
“
Op
e
ra
ti
o
n
a
l
fra
m
e
wo
rk
f
o
r
re
c
e
n
t
a
d
v
a
n
c
e
s
i
n
b
a
c
k
trac
k
i
n
g
se
a
rc
h
o
p
ti
m
isa
ti
o
n
a
lg
o
rit
h
m
:
A
sy
ste
m
a
ti
c
re
v
iew
a
n
d
p
e
rfo
rm
a
n
c
e
e
v
a
lu
a
ti
o
n
,
”
A
p
p
li
e
d
M
a
t
h
e
ma
ti
c
s
a
n
d
C
o
mp
u
ta
t
io
n
,
v
o
l.
3
7
0
,
2
0
2
0
.
[2
0
]
B.
A.
Ha
ss
a
n
a
n
d
T
.
A.
Ra
sh
i
d
,
“
Da
tas
e
ts
o
n
sta
ti
stica
l
a
n
a
ly
sis
a
n
d
p
e
rfo
rm
a
n
c
e
e
v
a
l
u
a
ti
o
n
o
f
b
a
c
k
trac
k
in
g
se
a
rc
h
o
p
ti
m
isa
ti
o
n
a
l
g
o
rit
h
m
c
o
m
p
a
re
d
with
it
s c
o
u
n
terp
a
rt
a
lg
o
rit
h
m
s,”
Da
ta
i
n
Brief
,
v
o
l.
2
8
,
2
0
2
0
.
[2
1]
A.
El
-
F
e
rg
a
n
y
,
“
M
u
lt
i
-
o
b
jec
ti
v
e
Allo
c
a
ti
o
n
o
f
M
u
lt
i
-
t
y
p
e
Distrib
u
t
e
d
G
e
n
e
ra
to
rs
a
lo
n
g
Distrib
u
ti
o
n
Ne
two
rk
s
Us
in
g
Ba
c
k
trac
k
in
g
S
e
a
rc
h
Alg
o
rit
h
m
a
n
d
F
u
z
z
y
E
x
p
e
rt
Ru
les
,
”
El
e
c
tric
Po
we
r
Co
mp
o
n
e
n
ts
a
n
d
S
y
ste
ms
,
v
o
l.
5
0
0
8
,
n
o
.
Ja
n
u
a
ry
,
p
p
.
1
-
1
6
,
2
0
1
5
.
[2
2
]
K.
Bh
a
tt
a
c
h
a
rjee
,
A.
B
h
a
tt
a
c
h
a
r
y
a
,
a
n
d
S
.
Ha
ld
e
r
n
e
e
De
y
,
“
Ba
c
k
trac
k
in
g
se
a
rc
h
o
p
ti
m
iza
ti
o
n
b
a
se
d
e
c
o
n
o
m
ic
e
n
v
iro
n
m
e
n
tal
p
o
we
r
d
is
p
a
tch
p
r
o
b
lem
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
Po
we
r
a
n
d
En
e
rg
y
S
y
ste
ms
,
v
o
l.
7
3
,
p
p
.
8
3
0
-
8
4
2
,
2
0
1
5
.
[2
3
]
M
.
M
o
d
iri
-
De
l
sh
a
d
a
n
d
N.
A.
R
a
h
im,
“
S
o
lv
in
g
n
o
n
-
c
o
n
v
e
x
e
c
o
n
o
m
ic
d
isp
a
tch
p
ro
b
lem
v
ia
b
a
c
k
t
ra
c
k
in
g
se
a
rc
h
a
lg
o
rit
h
m
,
”
En
e
rg
y
,
v
o
l.
7
7
,
p
p
.
3
7
2
-
3
8
1
,
2
0
1
4
.
[2
4
]
N.
T.
Th
u
a
n
,
P
.
N.
Hie
p
,
T.
V.
A
n
h
,
P
.
A.
T
u
a
n
,
a
n
d
N.
T.
Th
a
n
g
,
“
A
Ba
c
k
trac
k
in
g
S
e
a
rc
h
Alg
o
rit
h
m
fo
r
Distrib
u
t
io
n
Ne
two
rk
Re
c
o
n
fi
g
u
ra
ti
o
n
P
ro
b
lem
,
”
AE
T
A
2
0
1
5
:
Rec
e
n
t
Ad
v
a
n
c
e
s
in
El
e
c
trica
l
E
n
g
i
n
e
e
rin
g
a
n
d
R
e
la
ted
S
c
ien
c
e
s
,
L
e
c
tu
re
No
tes
in
El
e
c
trica
l
E
n
g
i
n
e
e
rin
g
3
7
1
,
p
p
.
2
2
3
-
2
3
0
,
2
0
1
5
.
[2
5
]
A.
Y.
Ab
d
e
laz
iz,
F
.
M
.
M
o
h
a
m
e
d
,
S
.
F
.
M
e
k
h
a
m
e
r,
a
n
d
M
.
A.
L.
B
a
d
r,
“
Distr
ib
u
t
io
n
sy
ste
m
re
c
o
n
fig
u
ra
ti
o
n
u
sin
g
a
m
o
d
ifi
e
d
Tab
u
S
e
a
rc
h
a
lg
o
rit
h
m
,
”
El
e
c
tric P
o
we
r S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
8
0
,
n
o
.
8
,
p
p
.
9
4
3
-
9
5
3
,
2
0
1
0
.
[2
6
]
M
.
E
.
Ba
ra
n
a
n
d
F
.
F
.
W
u
,
“
Ne
tw
o
rk
re
c
o
n
fi
g
u
ra
ti
o
n
in
d
istri
b
u
ti
o
n
sy
ste
m
s
f
o
r
l
o
ss
re
d
u
c
ti
o
n
a
n
d
l
o
a
d
b
a
lan
c
in
g
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r De
l
ive
ry
,
v
o
l.
4
,
n
o
.
2
.
p
p
.
1
4
0
1
-
1
4
0
7
,
1
9
8
9
.
[2
7
]
H.
-
D.
Ch
ian
g
a
n
d
R.
Je
a
n
-
Ju
m
e
a
u
,
“
Op
ti
m
a
l
n
e
two
r
k
re
c
o
n
f
ig
u
r
a
ti
o
n
s
i
n
d
istr
ib
u
ti
o
n
sy
ste
m
s:
P
a
rt
2
:
S
o
lu
t
io
n
a
lg
o
rit
h
m
s a
n
d
n
u
m
e
rica
l
re
su
lt
s,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r D
e
l
ive
ry
,
v
o
l.
5
,
n
o
.
3
,
p
p
.
1
5
6
8
-
1
5
7
4
,
1
9
9
0
.
[2
8
]
R.
D.
Zi
m
m
e
rm
a
n
,
C.
E.
M
u
ril
l
o
-
S
a
n
c
h
e
z
,
a
n
d
R
.
J.
T
h
o
m
a
s,
“
M
ATP
OWE
R:
S
tea
d
y
-
S
tate
Op
e
ra
t
io
n
s,
P
la
n
n
i
n
g
,
a
n
d
An
a
l
y
sis
T
o
o
ls
f
o
r
P
o
we
r
S
y
ste
m
s
Re
se
a
rc
h
a
n
d
Ed
u
c
a
ti
o
n
,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
P
o
we
r
S
y
ste
ms
,
v
o
l
.
2
6
,
n
o
.
1
,
p
p
.
1
2
–
1
9
,
2
0
1
1
.
[2
9
]
X.
Ya
n
g
,
"
Na
tu
re
-
In
s
p
ired
M
e
ta
h
e
u
risti
c
Alg
o
r
it
h
m
s,
"
S
e
c
o
n
d
E
d
i.
L
u
n
ive
r P
re
ss
,
2
0
1
0
.
[3
0
]
X.
S
.
Ya
n
g
,
“
F
irefly
a
l
g
o
rit
h
m
,
sto
c
h
a
stic
tes
t
fu
n
c
ti
o
n
s
a
n
d
d
e
si
g
n
o
p
ti
m
iza
ti
o
n
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Bi
o
-
In
sp
ire
d
C
o
mp
u
ta
t
io
n
,
v
o
l.
2
,
n
o
.
2
,
p
p
.
7
8
-
8
4
,
2
0
1
0
.
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