I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
11
,
No
.
1
,
Feb
r
u
ar
y
2021
,
p
p
.
107
~
113
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v
1
1
i
1
.
pp
1
0
7
-
113
107
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m
Enha
nced sun
flow
er opti
m
i
z
a
tion
for pla
ce
m
en
t
dis
tribut
ed
g
eneratio
n in dis
t
ribution sy
ste
m
T
hu
a
n
T
ha
nh
Ng
uy
en
F
a
c
u
lt
y
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
T
e
c
h
n
o
lo
g
y
,
In
d
u
strial
Un
iv
e
rsit
y
o
f
Ho
Ch
i
M
in
h
Cit
y
,
V
iet
Na
m
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
A
p
r
2
5
,
2
0
2
0
R
ev
i
s
ed
J
u
n
2
0
,
2
0
2
0
A
cc
ep
ted
J
u
l
1
,
2
0
2
0
In
sta
ll
a
ti
o
n
o
f
d
istr
ib
u
ti
o
n
g
e
n
e
r
a
ti
o
n
(DG
)
in
th
e
d
istri
b
u
ti
o
n
sy
ste
m
g
a
in
s
m
a
n
y
tec
h
n
ica
l
b
e
n
e
f
it
s.
T
o
o
b
tain
m
o
re
b
e
n
e
f
it
s,
th
e
lo
c
a
ti
o
n
a
n
d
siz
e
o
f
D
G
m
u
st
b
e
se
lec
ted
w
it
h
th
e
a
p
p
r
o
p
riate
v
a
lu
e
s.
T
h
is
p
a
p
e
r
p
re
se
n
t
s
a
m
e
th
o
d
f
o
r
o
p
ti
m
izin
g
lo
c
a
ti
o
n
a
n
d
siz
e
o
f
D
G
in
th
e
d
istri
b
u
ti
o
n
sy
s
tem
b
a
s
e
d
o
n
e
n
h
a
n
c
e
d
su
n
f
lo
w
e
r
o
p
ti
m
iz
a
ti
o
n
(ES
F
O)
to
m
in
im
iz
e
p
o
we
r
lo
ss
o
f
th
e
sy
ste
m
.
In
w
h
ich
,
b
a
se
d
o
n
t
h
e
o
p
e
ra
ti
o
n
a
l
m
e
c
h
a
n
ism
s
o
f
th
e
o
rig
in
a
l
su
n
f
lo
w
e
r
o
p
ti
m
iza
ti
o
n
(S
F
O),
a
m
u
tatio
n
tec
h
n
iq
u
e
is
a
d
d
e
d
f
o
r
u
p
d
a
ti
n
g
th
e
b
e
st
p
lan
t
.
T
h
e
c
a
lcu
late
d
re
s
u
lt
s
o
n
th
e
3
3
n
o
d
e
s
tes
t
sy
ste
m
h
a
v
e
sh
o
w
n
th
a
t
ES
F
O
h
a
s
p
ro
f
icie
n
c
y
f
o
r
d
e
term
in
in
g
th
e
b
e
st
l
o
c
a
ti
o
n
a
n
d
s
ize
o
f
D
G
w
it
h
h
ig
h
e
r
q
u
a
li
ty
th
a
n
S
F
O.
T
h
e
c
o
m
p
a
re
d
re
su
lt
s
w
it
h
th
e
p
re
v
io
u
s
m
e
th
o
d
s h
a
v
e
a
lso
sh
o
w
n
th
a
t
ES
F
O o
u
tp
e
rf
o
rm
s to
o
th
e
r
m
e
th
o
d
s
in
term
o
f
p
o
w
e
r
lo
ss
re
d
u
c
ti
o
n
.
A
s
a
re
su
l
t,
ES
F
O
is
a
re
li
a
b
le
a
p
p
ro
a
c
h
fo
r
th
e
DG
o
p
ti
m
iza
ti
o
n
p
ro
b
lem
.
K
ey
w
o
r
d
s
:
Dis
tr
ib
u
tio
n
g
e
n
er
atio
n
E
n
h
a
n
ce
d
s
u
n
f
lo
w
er
o
p
tim
izatio
n
L
o
ca
tio
n
a
n
d
s
ize
P
o
w
er
lo
s
s
Su
n
f
lo
w
er
o
p
ti
m
izatio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
T
h
u
an
T
h
an
h
Ng
u
y
en
,
Facu
lt
y
o
f
E
lectr
ical
E
n
g
in
ee
r
in
g
T
ec
h
n
o
lo
g
y
,
I
n
d
u
s
tr
ial
U
n
i
v
er
s
it
y
o
f
Ho
C
h
i M
in
h
C
it
y
,
No
.
1
2
Ng
u
y
e
n
Van
B
ao
,
W
ar
d
4
,
Go
Va
p
Dis
tr
ict,
Ho
C
h
i
Min
h
C
it
y
,
Viet
Na
m
.
E
m
ail:
n
g
u
y
en
th
a
n
h
th
u
a
n
@
iu
h
.
ed
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
Dis
tr
ib
u
ted
g
en
er
atio
n
s
(
DG
)
is
s
m
all
p
o
w
er
p
lan
t
co
n
n
ec
ted
to
th
e
p
o
w
er
s
y
s
te
m
at
d
is
tr
ib
u
tio
n
v
o
ltag
e
le
v
el
o
r
in
s
talled
clo
s
e
d
to
cu
s
to
m
er
s
[
1
]
.
Fro
m
th
e
o
p
er
atio
n
al
p
er
s
p
ec
tiv
e,
DG
in
s
tallatio
n
is
ab
le
to
b
r
in
g
m
a
n
y
tec
h
n
ical
b
e
n
ef
its
f
o
r
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
s
u
c
h
a
s
p
o
w
er
lo
s
s
r
ed
u
ctio
n
,
v
o
lta
g
e
i
m
p
r
o
v
e
m
e
n
t
an
d
r
eliab
ilit
y
en
h
a
n
cin
g
.
Ho
w
e
v
er
,
th
e
s
e
m
ax
i
m
u
m
b
en
e
f
its
ar
e
o
n
l
y
ac
h
ie
v
ed
w
h
en
DG
is
i
n
s
talled
in
th
e
p
r
o
p
er
p
o
s
itio
n
as
w
ell
as
th
e
ap
p
r
o
p
r
iate
ca
p
ac
ity
,
o
th
er
w
i
s
e
w
r
o
n
g
p
o
s
itio
n
an
d
s
iz
e
o
f
DG
m
a
y
ca
u
s
e
m
o
r
e
tec
h
n
ical
is
s
u
es.
T
h
er
ef
o
r
e
,
o
p
tim
izatio
n
o
f
lo
ca
tio
n
an
d
s
ize
o
f
DG
is
th
e
p
r
o
b
lem
th
at
i
s
attr
ac
ted
b
y
m
an
y
co
n
ce
r
n
s
.
Fo
r
s
o
lv
i
n
g
th
e
DG
o
p
ti
m
iz
atio
n
p
r
o
b
le
m
,
th
er
e
ar
e
v
ar
i
o
u
s
m
et
h
o
d
s
th
a
t
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
.
In
[
2
]
,
g
en
etic
alg
o
r
it
h
m
(
G
A
)
is
p
r
o
p
o
s
ed
t
o
f
in
d
th
e
o
p
ti
m
al
lo
ca
ti
o
n
an
d
s
ize
o
f
DG
to
g
ain
m
o
r
e
r
ev
en
u
e
s
an
d
r
ed
u
ce
im
p
o
s
ed
co
s
ts
[
2
]
.
I
n
[
3
]
,
GA
is
u
s
ed
f
o
r
s
o
lv
i
n
g
th
e
DG
o
p
ti
m
izatio
n
p
r
o
b
le
m
to
r
ed
u
ce
p
o
w
er
lo
s
s
.
Si
m
ilar
l
y
,
i
n
[
4
]
,
G
A
i
s
also
p
r
o
p
o
s
ed
f
o
r
d
eter
m
in
in
g
lo
ca
tio
n
a
n
d
s
ize
o
f
D
G
in
t
h
e
s
m
ar
t
g
r
id
n
et
w
o
r
k
.
In
[
5
]
,
ar
tif
icial
b
ee
co
lo
n
y
m
et
h
o
d
(
A
B
C
)
h
as
b
ee
n
ap
p
lied
to
f
in
d
th
e
ap
p
r
o
p
r
ia
te
p
o
s
itio
n
an
d
s
ize
o
f
DG
in
th
e
d
is
tr
ib
u
tio
n
s
y
s
t
e
m
.
I
n
[
6
]
,
p
o
w
er
lo
s
s
r
ed
u
cti
o
n
is
m
i
n
i
m
ized
b
y
in
s
talli
n
g
DG
b
ased
o
n
h
o
n
e
y
b
ee
m
ati
n
g
o
p
ti
m
izatio
n
(
HB
MO
)
.
In
[
7
]
,
p
a
r
ti
cle
s
w
ar
m
o
p
ti
m
izatio
n
(
P
SO)
is
co
m
b
in
ed
w
it
h
G
A
f
o
r
o
p
tim
izatio
n
o
f
DG
to
r
ed
u
c
e
p
o
w
er
lo
s
s
a
n
d
en
ah
n
ce
v
o
ltag
e
s
tab
ili
t
y
.
I
n
[
8
]
,
P
SO
is
p
r
o
p
o
s
ed
to
s
o
lv
e
th
e
th
e
D
G
o
p
ti
m
izatio
n
p
r
o
b
le
m
co
m
b
i
n
ed
w
i
th
t
h
e
n
e
t
w
o
r
k
r
ec
o
n
f
i
g
u
r
atio
n
.
T
o
s
o
lv
e
th
e
DG
o
p
ti
m
iz
atio
n
p
r
o
b
lem
,
n
o
t
o
n
l
y
co
m
m
o
n
m
et
h
o
d
s
s
u
c
h
as
G
A
,
A
B
C
,
HB
MO
an
d
P
SO
ar
e
u
s
ed
,
b
u
t
al
s
o
m
a
n
y
r
ec
en
tl
y
d
ev
elo
p
ed
alg
o
r
ith
m
s
h
a
v
e
b
ee
n
s
u
cc
e
s
s
f
u
ll
y
ap
p
lied
s
u
c
h
as
w
h
al
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
10
7
-
11
3
108
o
p
tim
izatio
n
al
g
o
r
ith
m
(
W
O
A
)
[
9
,
1
0
]
,
h
ar
m
o
n
y
s
ea
r
ch
(
HS)
[
1
1
,
1
2
]
,
m
o
d
if
ied
cr
o
w
s
ea
r
ch
(
MC
S)
[
1
3
]
,
ad
ap
tiv
e
cu
c
k
o
o
s
ea
r
ch
(
A
C
S
)
[
1
4
]
,
f
ir
e
w
o
r
k
s
al
g
o
r
ith
m
(
F
A
)
[
1
5
]
,
c
oy
o
te
al
g
o
r
ith
m
[
1
6
]
,
u
n
i
f
o
r
m
v
o
ltag
e
d
is
tr
ib
u
tio
n
al
g
o
r
ith
m
(
UV
D)
[
1
7
]
,
h
y
p
er
cu
b
e
an
t
co
lo
n
y
o
p
ti
m
izatio
n
(
HC
A
C
O)
[
1
8
]
,
r
u
n
n
er
r
o
o
t
[
1
9
]
an
d
m
o
d
i
f
ied
p
lan
t
g
r
o
w
t
h
s
i
m
u
latio
n
(
MP
GS)
[
2
0
]
.
C
o
m
p
ar
ed
w
it
h
clas
s
ical
m
e
th
o
d
s
s
u
c
h
as
d
y
n
a
m
i
c
p
r
o
g
r
am
m
i
n
g
[
2
1
]
,
lin
ea
r
p
r
o
g
r
a
m
m
i
n
g
[
2
2
]
an
d
m
i
x
ed
in
t
eg
er
lin
ea
r
p
r
o
g
r
a
m
m
i
n
g
[
2
3
]
,
m
e
th
o
d
s
b
ased
o
n
g
en
er
al
k
n
o
w
led
g
e
s
u
c
h
as
G
A
,
A
B
C
a
n
d
t
h
e
a
f
o
r
e
m
e
n
tio
n
e
d
m
eth
o
d
s
o
f
te
n
g
et
b
etter
q
u
alit
y
r
es
u
lts
w
h
en
a
p
p
l
i
e
d
t
o
t
h
e
D
G
o
p
t
i
m
i
z
a
t
i
o
n
p
r
o
b
l
e
m
.
T
h
e
r
e
f
o
r
e
,
r
e
s
e
a
r
c
h
i
n
g
n
e
w
m
e
t
h
o
d
s
t
o
a
p
p
l
y
t
o
t
h
e
D
G
o
p
t
i
m
i
z
a
t
i
o
n
p
r
o
b
lem
is
al
s
o
a
m
atter
o
f
co
n
ce
r
n
to
s
u
p
p
le
m
e
n
t th
e
p
o
ten
tial
m
et
h
o
d
s
f
o
r
s
o
lv
in
g
t
h
e
p
r
o
b
lem
.
T
h
is
p
ap
er
p
r
esen
ts
a
m
et
h
o
d
to
o
p
ti
m
ize
lo
ca
tio
n
an
d
s
i
ze
o
f
DG
in
t
h
e
d
is
tr
ib
u
tio
n
s
y
s
te
m
to
m
i
n
i
m
ize
p
o
w
er
lo
s
s
b
ased
o
n
e
n
h
a
n
ce
d
s
u
n
f
lo
w
er
o
p
ti
m
iz
atio
n
(
E
SF
O)
.
W
h
er
ein
,
E
SF
O
is
en
h
a
n
ce
d
f
r
o
m
th
e
o
r
ig
i
n
al
s
u
n
f
lo
w
er
o
p
ti
m
iz
atio
n
(
SF
O)
[
2
4
]
.
I
n
[
2
4
]
,
th
e
o
r
ig
in
al
SF
O
i
s
ta
k
en
f
r
o
m
an
id
ea
l
o
f
m
o
v
e
m
en
t
o
f
th
e
s
u
n
f
lo
w
er
p
la
n
t
to
tak
e
s
u
n
l
ig
h
t.
I
n
o
r
d
er
to
ap
p
l
y
f
o
r
s
o
l
v
in
g
t
h
e
o
p
ti
m
izat
i
o
n
p
r
o
b
lem
,
ea
ch
s
u
n
f
lo
w
er
p
lan
t
i
s
co
n
s
id
er
ed
as
s
o
l
u
tio
n
.
T
h
e
b
est
p
lan
t
is
ex
a
m
in
ed
a
s
t
h
e
s
u
n
a
n
d
all
o
f
o
th
er
p
la
n
ts
w
i
ll
m
o
v
e
to
t
h
e
b
est
o
n
e.
B
ase
d
o
n
t
h
e
m
ec
h
an
i
s
m
s
o
f
cr
e
atin
g
n
e
w
p
la
n
ts
o
f
SF
O,
we
p
r
o
p
o
s
ed
to
ad
d
th
e
m
u
tat
io
n
tec
h
n
iq
u
e
to
cr
ea
te
a
n
e
w
p
la
n
t b
y
m
u
tati
n
g
t
h
e
b
est p
lan
t f
o
r
u
p
d
atin
g
t
h
e
b
est s
u
n
f
lo
w
er
p
lan
t.
T
h
e
ef
f
ec
t
iv
e
n
es
s
o
f
th
e
p
r
o
p
o
s
ed
E
SF
O
h
as
b
ee
n
d
e
m
o
n
s
tr
ated
o
n
th
e
3
3
n
o
d
es
test
d
i
s
tr
ib
u
tio
n
s
y
s
te
m
.
T
h
e
ca
lcu
lated
r
esu
lt
is
co
m
p
ar
ed
to
th
at
o
f
SF
O
a
n
d
o
th
er
p
r
ev
io
u
s
m
et
h
o
d
s
.
T
h
e
co
n
tr
ib
u
tio
n
s
o
f
th
is
w
o
r
k
ca
n
b
e
h
i
g
h
lig
h
ted
a
s
f
o
llo
w
s
:
A
m
u
tatio
n
o
f
cr
ea
tin
g
a
n
e
w
p
lan
t f
o
r
u
p
d
atin
g
t
h
e
b
est s
u
n
f
lo
w
er
p
lan
t is p
r
o
p
o
s
ed
f
o
r
E
SF
O.
E
SF
O
is
f
ir
s
t p
r
o
p
o
s
ed
f
o
r
th
e
DG
o
p
ti
m
izatio
n
p
r
o
b
le
m
.
T
h
e
ef
f
ec
ti
v
e
n
ess
o
f
E
SF
O
i
s
ev
alu
a
ted
o
n
th
e
3
3
n
o
d
es test
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
E
SF
O
is
m
o
r
e
e
f
f
ec
t
iv
e
t
h
an
SF
O
as
w
ell
as
t
h
e
p
r
ev
io
u
s
m
et
h
o
d
s
f
o
r
th
e
DG
o
p
ti
m
iza
tio
n
p
r
o
b
lem
i
n
ter
m
s
o
f
t
h
e
o
b
tain
ed
s
o
l
u
tio
n
q
u
alit
y
.
T
h
e
r
est
p
ap
er
is
o
r
g
a
n
ize
d
as
f
o
llo
w
s
:
T
h
e
f
o
llo
w
i
n
g
s
ec
tio
n
s
h
o
w
s
t
h
e
p
r
o
b
lem
o
f
DG
o
p
tim
izatio
n
.
T
h
e
s
ec
tio
n
3
d
e
m
o
n
s
tr
ates
t
h
e
p
r
o
p
o
s
ed
E
SF
O
an
d
its
ap
p
licatio
n
f
o
r
th
e
DG
o
p
ti
m
izatio
n
p
r
o
b
lem
.
T
h
e
s
ec
tio
n
4
p
r
esen
ts
r
esu
l
ts
a
n
d
d
is
cu
s
s
io
n
.
Fi
n
al
y
,
th
e
co
n
cl
u
s
io
n
s
ec
t
io
n
is
d
e
m
o
n
s
tr
ated
.
2.
P
RO
B
L
E
M
O
F
DG
O
P
T
I
M
I
Z
A
T
I
O
N
On
e
o
f
t
h
e
b
ig
g
e
s
t
b
en
e
f
it
s
o
f
in
s
talli
n
g
DG
i
n
t
h
e
d
is
tr
i
b
u
tio
n
s
y
s
te
m
i
s
p
o
w
er
lo
s
s
r
ed
u
ctio
n
.
T
h
e
m
ai
n
g
o
al
o
f
th
e
p
r
o
b
le
m
is
to
m
i
n
i
m
ize
p
o
w
er
lo
s
s
.
I
t i
s
d
eter
m
in
ed
as
f
o
llo
w
s
:
∆
=
∑
,
=
1
(
1
)
w
h
er
e
,
is
p
o
w
er
lo
s
s
o
f
th
e
l
in
e
.
is
n
u
m
b
er
o
f
lin
e
s
in
t
h
e
s
y
s
te
m
.
I
n
s
talli
n
g
DG
i
n
th
e
d
is
tr
ib
u
ti
o
n
s
y
s
te
m
s
h
o
u
ld
b
e
m
ai
n
tai
n
ed
th
e
f
o
llo
w
i
n
g
co
n
s
tr
ai
n
ts
:
Vo
ltag
e
an
d
cu
r
r
e
n
t li
m
it
s
:
{
V
≤
≤
V
;
=
1
÷
≤
,
;
=
1
÷
(
2
)
w
h
er
e
V
an
d
V
ar
e
th
e
lo
w
er
an
d
u
p
p
er
li
m
its
o
f
th
e
n
o
d
e
v
o
lta
g
e.
is
th
e
v
o
lta
g
e
a
m
p
lit
u
d
e
o
f
n
o
d
e
.
an
d
,
ar
e
th
e
lo
ad
ca
r
r
y
i
n
g
co
ef
f
icie
n
t
a
n
d
m
a
x
i
m
u
m
co
e
f
f
icien
t
o
f
t
h
e
li
n
e
.
is
n
u
m
b
er
o
f
n
o
d
es in
t
h
e
s
y
s
te
m
.
DG
s
ize
li
m
its
:
≤
,
;
=
1
÷
(
3
)
w
h
er
e
is
s
ize
o
f
D
G
in
M
W
.
,
is
th
e
m
a
x
i
m
u
m
ca
p
ac
it
y
li
m
it
o
f
DG
.
is
n
u
m
b
er
o
f
D
G
in
s
ta
lled
in
t
h
e
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
3.
E
NH
ANC
E
D
SUNF
L
O
W
E
R
O
P
T
I
M
I
Z
AT
I
O
N
F
O
R
T
H
E
DG
O
P
T
I
M
I
Z
AT
I
O
N
P
RO
B
L
E
M
3
.
1
.
T
he
o
rig
ina
l su
nflo
w
er
o
pti
m
iza
t
io
n
Fo
r
s
o
lv
in
g
th
e
o
p
ti
m
al
p
r
o
b
l
e
m
,
th
e
p
o
p
u
latio
n
o
f
s
u
n
f
lo
w
er
p
lan
t
s
is
u
p
d
ated
b
y
t
h
r
e
e
d
if
f
er
en
t
tech
n
iq
u
es.
T
h
e
f
ir
s
t
o
n
e
is
ca
lled
p
o
llin
atio
n
tec
h
n
iq
u
e.
A
p
ar
t
o
f
th
e
p
o
p
u
latio
n
t
h
a
t
is
d
eter
m
i
n
ed
b
y
th
e
p
o
llin
atio
n
r
ate
is
ch
o
s
e
n
f
o
r
p
o
llin
atio
n
a
n
d
cr
ea
tin
g
n
e
w
p
lan
ts
f
o
r
th
e
n
e
x
t
g
e
n
er
at
io
n
.
T
h
e
p
o
llin
atio
n
tech
n
iq
u
e
to
cr
ea
te
n
e
w
p
la
n
ts
is
d
o
n
e
b
y
t
h
e
co
m
b
i
n
atio
n
o
f
t
w
o
co
n
s
ec
u
t
iv
e
p
la
n
ts
in
t
h
e
p
o
p
u
latio
n
as f
o
llo
w
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
E
n
h
a
n
ce
d
s
u
n
flo
w
er o
p
timiz
a
tio
n
fo
r
p
la
ce
men
t
d
is
tr
ib
u
ted
…
(
Th
u
a
n
Th
a
n
h
N
g
u
ye
n
)
109
=
(
0
,
1
)
.
(
−
+
1
)
+
+
1
;
=
1
÷
.
(
4
)
w
h
er
e
an
d
+
1
ar
e
th
e
p
lan
t
an
d
+
1
in
t
h
e
p
o
p
u
latio
n
.
is
th
e
p
o
llin
atio
n
r
ate
th
a
t
is
ch
o
s
e
n
to
0
.
6
[
2
4
]
.
is
n
u
m
b
er
o
f
p
lan
t
s
i
n
th
e
p
o
p
u
latio
n
.
T
h
e
s
ec
o
n
d
o
n
e
is
ca
ll
ed
th
e
s
u
r
v
iv
al
tec
h
n
iq
u
e.
I
n
t
h
e
r
em
ai
n
d
er
o
f
th
e
p
o
p
u
latio
n
,
a
n
u
m
b
er
o
f
p
lan
ts
w
ill
s
u
r
v
iv
e
an
d
m
a
in
t
ain
o
v
er
th
e
n
e
x
t
g
e
n
er
atio
n
.
T
h
e
r
eten
tio
n
o
f
in
f
o
r
m
atio
n
o
f
a
p
lan
t
th
r
o
u
g
h
th
e
n
ex
t
g
e
n
er
atio
n
i
s
d
eter
m
in
ed
b
y
t
h
e
d
is
ta
n
ce
f
r
o
m
it
s
elf
to
t
h
e
b
est
p
la
n
t.
T
h
e
clo
s
er
to
th
e
b
est
o
n
e
a
p
lan
t
is
,
th
e
g
r
ea
ter
p
r
o
b
ab
il
it
y
th
at
it
w
ill
r
e
m
ai
n
th
e
s
a
m
e
o
v
er
t
h
e
n
e
x
t
g
e
n
er
atio
n
.
T
h
e
d
etails
o
f
cr
ea
ti
n
g
n
e
w
p
lan
t
s
b
y
t
h
e
s
u
r
v
i
v
al
tec
h
n
iq
u
e
is
d
escr
ib
ed
as b
elo
w
:
=
+
(
0
,
1
)
.
(
(
−
)
/
(
‖
−
‖
)
)
;
=
.
÷
.
(
1
−
)
(
5
)
w
h
er
e,
is
th
e
b
est
p
lan
t.
‖
−
‖
is
th
e
E
u
cl
id
ea
n
len
g
t
h
o
f
th
e
−
v
ec
to
r
.
i
s
th
e
d
ea
th
r
ate
t
h
at
is
c
h
o
s
en
to
0
.
1
[
2
4
]
.
T
h
e
last
o
n
e
is
ca
lled
m
o
r
tali
t
y
tech
n
iq
u
e.
I
n
t
h
e
r
e
m
ai
n
d
er
o
f
th
e
p
o
p
u
latio
n
,
a
n
u
m
b
er
o
f
p
lan
ts
th
at
is
d
eter
m
in
ed
b
y
t
h
e
m
o
r
t
alit
y
r
ate
w
ill b
e
d
ied
an
d
r
ep
lace
d
b
y
n
e
w
r
a
n
d
o
m
p
lan
t
s
as
f
o
llo
w
s
:
=
+
(
0
,
1
)
.
(
−
)
;
=
.
(
1
−
)
÷
(
6
)
w
h
er
e
an
d
ar
e
th
e
u
p
p
er
an
d
lo
w
er
b
o
u
n
d
s
o
f
th
e
p
la
n
ts
.
T
h
e
n
e
w
p
la
n
ts
ar
e
v
alid
ated
t
h
e
f
it
n
es
s
f
u
n
ctio
n
a
n
d
t
h
e
y
a
r
e
u
s
ed
to
r
ep
lace
f
o
r
t
h
e
co
r
r
esp
o
n
d
in
g
o
n
es
i
n
th
e
p
o
p
u
latio
n
i
f
t
h
ei
r
q
u
alit
y
i
s
b
etter
t
h
a
n
t
h
e
co
r
r
esp
o
n
d
in
g
o
n
es
’
q
u
alit
y
.
I
n
ad
d
itio
n
,
t
h
e
b
est
s
u
n
f
lo
w
er
p
lan
t is
u
p
d
ated
u
n
t
il th
e
m
ax
i
m
u
m
n
u
m
b
er
o
f
g
e
n
er
atio
n
is
r
ea
c
h
ed
.
3
.
2
.
T
he
enha
nced
s
un
f
lo
w
er
o
pti
m
iza
t
io
n
I
t
ca
n
b
e
s
ee
n
th
at
S
FO
u
s
e
s
th
r
ee
d
if
f
er
en
t
tec
h
n
iq
u
e
s
to
r
en
e
w
t
h
e
p
o
p
u
latio
n
.
I
n
th
e
f
ir
s
t
tech
n
iq
u
e,
t
h
e
m
et
h
o
d
o
f
co
m
b
in
in
g
t
w
o
co
n
s
ec
u
ti
v
e
p
la
n
ts
in
th
e
p
o
p
u
lat
io
n
to
cr
ea
te
a
n
e
w
p
la
n
t.
T
h
e
r
o
le
o
f
th
is
tec
h
n
iq
u
e
is
e
x
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
t
h
e
s
ea
r
ch
s
p
ac
e.
T
h
e
s
ec
o
n
d
tec
h
n
iq
u
e
h
elp
s
to
cr
ea
te
n
e
w
p
lan
ts
th
at
m
o
v
e
to
t
h
e
b
est
p
lan
t.
I
t
h
elp
s
S
FO
to
e
x
p
lo
it
t
h
e
s
ea
r
ch
s
p
ac
e.
Me
an
w
h
i
le,
th
e
f
i
n
al
tech
n
iq
u
e
g
en
er
ate
s
r
an
d
o
m
p
lan
t
s
to
e
x
p
lo
r
e
th
e
s
ea
r
ch
s
p
ac
e
a
n
d
p
r
ev
en
t
t
h
e
SF
O
f
r
o
m
co
n
v
er
g
i
n
g
to
lo
ca
l
o
p
ti
m
al
s
o
lu
tio
n
s
o
o
n
.
B
ased
o
n
t
h
e
ab
o
v
e
m
ec
h
a
n
i
s
m
s
o
f
SF
O,
i
n
th
is
s
tu
d
y
w
e
p
r
o
p
o
s
e
th
e
en
h
a
n
ce
d
s
u
n
f
lo
w
er
o
p
tim
izatio
n
(
E
SF
O)
.
W
h
er
ein
,
a
n
e
w
tec
h
n
iq
u
e
is
s
u
g
g
est
ed
to
cr
ea
te
a
n
e
w
p
lan
t
b
y
m
u
tati
n
g
t
h
e
b
est
o
n
e
.
Af
ter
th
e
n
e
w
p
o
p
u
latio
n
o
f
p
lan
ts
h
as
b
ee
n
cr
ea
ted
f
r
o
m
th
e
th
r
ee
ab
o
v
e
tech
n
iq
u
e
s
,
th
ei
r
f
itn
e
s
s
f
u
n
ctio
n
i
s
ca
lcu
lated
an
d
t
h
e
b
est
p
la
n
t
is
d
eter
m
i
n
ed
.
B
ef
o
r
e
th
e
p
o
p
u
latio
n
is
r
en
e
w
ed
ag
ai
n
i
n
t
h
e
n
e
x
t
g
en
er
atio
n
,
th
e
n
e
w
p
lan
t
is
cr
ea
ted
b
y
m
u
tatio
n
o
f
t
h
e
b
est
p
lan
t.
I
f
t
h
e
n
e
w
p
la
n
t
h
as
b
etter
q
u
a
lit
y
th
a
n
t
h
e
b
est
o
n
e
,
it
is
u
s
ed
to
r
ep
lace
th
e
b
est
p
lan
t,
o
th
er
w
i
s
e
it
w
ill
b
e
d
ie
if
its
q
u
a
lit
y
i
s
w
o
r
s
e
th
a
n
t
h
e
b
est
o
n
e.
T
h
e
n
e
w
p
lan
t is
g
en
er
ated
as
f
o
llo
w
s
:
,
=
,
+
(
0
,
1
)
.
.
(
0
,
1
)
;
=
1
÷
(
7
)
w
h
er
e,
,
an
d
,
ar
e
th
e
co
n
tr
o
l
v
ar
iab
le
o
f
th
e
n
e
w
an
d
b
est
p
lan
ts
.
is
p
r
o
b
lem
d
i
m
e
n
s
io
n
.
is
a
co
n
s
ta
n
t
to
d
eter
m
i
n
e
t
h
e
m
ax
i
m
u
m
c
h
a
n
g
e
li
m
it
o
f
t
h
e
v
ar
iab
le.
(
0
,
1
)
is
a
f
u
n
ctio
n
th
at
r
etu
r
n
s
t
h
e
v
al
u
e
o
f
0
o
r
1
.
I
f
th
e
(
0
,
1
)
is
eq
u
al
to
0
,
th
e
,
is
s
i
m
ilar
to
,
o
th
er
w
i
s
e
th
e
,
w
il
l
b
e
s
et
to
n
e
w
v
alu
e.
T
h
e
v
al
u
e
o
f
(
0
,
1
)
is
d
eter
m
i
n
ed
as f
o
llo
w
s
:
(
0
,
1
)
=
{
1
;
(
0
,
1
)
<
0
;
ℎ
(
8
)
w
h
er
e
is
m
u
ta
tio
n
r
ate
th
at
is
s
elec
ted
to
0
.
2
.
I
t
m
ea
n
s
t
h
at
a
b
o
u
t t
w
en
t
y
p
er
ce
n
t o
f
v
ar
iab
l
es o
f
t
h
e
i
s
r
en
e
w
ed
.
T
h
e
n
e
w
p
la
n
t
i
s
v
a
lid
ated
th
e
f
it
n
es
s
f
u
n
ctio
n
a
n
d
it
w
ill
b
ec
o
m
e
to
t
h
e
b
est
p
lan
t
i
f
i
t
h
as
b
etter
q
u
alit
y
t
h
a
n
th
e
b
es
t o
n
e,
it is
u
s
ed
to
r
ep
lace
th
e
b
est p
lan
t,
o
th
er
w
is
e
it
w
il
l b
e
d
ie.
3
.
3
.
T
he
a
pp
lica
t
io
n o
f
E
SFO
f
o
r
t
he
DG
o
pti
m
iza
t
io
n p
ro
ble
m
Ste
p 1
:
I
n
itializatio
n
Fo
r
ap
p
ly
i
n
g
to
t
h
e
DG
o
p
ti
m
i
za
tio
n
p
r
o
b
lem
,
ea
c
h
s
u
n
f
lo
w
e
r
p
lan
t is p
r
esen
ted
as
f
o
llo
w
s
:
=
[
,
,
,
]
;
=
1
÷
=
1
÷
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
10
7
-
11
3
110
w
h
er
e
an
d
ar
e
lo
ca
tio
n
an
d
s
i
ze
o
f
DG
.
is
n
u
m
b
er
o
f
DG
i
n
s
tal
led
in
t
h
e
d
is
tr
ib
u
tio
n
s
y
s
t
e
m
.
A
t t
h
e
b
eg
i
n
n
in
g
,
t
h
e
in
i
tial p
l
an
ts
ar
e
cr
ea
ted
r
an
d
o
m
l
y
a
s
f
o
llo
w
s
:
=
+
(
0
,
1
)
.
(
−
)
;
=
1
÷
(
1
0
)
w
h
er
e
an
d
f
o
r
ar
e
d
eter
m
i
n
ed
as f
o
llo
w
s
:
{
=
[
,
,
,
]
=
[
,
,
,
]
;
=
1
÷
(
1
1
)
w
h
er
e
,
an
d
,
ar
e
th
e
u
p
p
er
a
n
d
lo
w
er
s
izes
o
f
th
e
DG
.
,
an
d
,
ar
e
th
e
h
i
g
h
e
s
t
an
d
lo
w
es
t n
o
d
es i
n
th
e
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
T
h
en
,
th
e
v
ar
iab
le
p
ar
t
in
d
icat
es
th
e
lo
ca
tio
n
o
f
DG
is
r
o
u
n
d
ed
to
in
teg
er
v
al
u
e
to
m
ap
w
it
h
th
e
D
G
o
p
tim
izatio
n
p
r
o
b
le
m
an
d
t
h
e
s
y
s
te
m
d
ata
i
s
u
p
d
ated
to
ca
lcu
late
t
h
e
f
i
tn
e
s
s
f
u
n
ctio
n
(
)
v
a
l
u
e
as
f
o
llo
w
s
:
=
∆
+
.
[
(
V
−
,
0
)
+
(
−
V
,
0
)
+
(
−
LI
,
0
)
]
(
1
2
)
w
h
er
e,
K
is
p
en
alt
y
co
ef
f
ici
en
t,
an
d
ar
e
th
e
m
i
n
i
m
u
m
a
n
d
m
a
x
i
m
u
m
v
o
lta
g
e
am
p
lit
u
d
e
is
th
e
s
y
s
te
m
.
m
a
x
i
m
u
m
lo
ad
ca
r
r
y
i
n
g
co
ef
f
icie
n
t
in
t
h
e
s
y
s
te
m
.
B
ased
o
n
th
e
v
al
u
e,
th
e
b
est p
lan
t
is
d
eter
m
in
ed
.
Ste
p 2
:
C
r
ea
tin
g
o
f
n
e
w
p
lan
t
s
b
y
u
s
i
n
g
th
e
p
o
lli
n
atio
n
,
s
u
r
v
iv
al
a
n
d
m
o
r
ta
lit
y
tech
n
iq
u
e
s
T
h
e
n
e
w
p
o
p
u
latio
n
o
f
s
u
n
f
lo
w
er
p
la
n
ts
is
g
e
n
er
ated
b
y
u
s
i
n
g
t
h
e
p
o
llin
a
tio
n
,
s
u
r
v
i
v
al
a
n
d
m
o
r
talit
y
tech
n
iq
u
es
as
d
escr
ib
ed
in
eq
u
atio
n
s
(
4
-
6
)
.
W
h
er
ein
,
th
e
v
ar
iab
le
p
ar
t
in
d
icate
s
th
e
lo
ca
tio
n
o
f
DG
o
f
n
e
w
p
lan
ts
i
s
r
o
u
n
d
ed
to
in
te
g
er
v
alu
e.
T
h
e
q
u
alit
y
o
f
n
e
w
p
l
an
ts
is
v
alid
ated
b
y
th
e
f
i
tn
e
s
s
f
u
n
ctio
n
as
(
1
2
)
.
T
h
e
n
e
w
p
la
n
ts
ar
e
u
s
ed
to
r
ep
lace
f
o
r
th
e
co
r
r
esp
o
n
d
in
g
o
n
es
in
th
e
c
u
r
r
en
t
p
o
p
u
latio
n
if
th
eir
q
u
a
lit
y
is
b
etter
th
an
t
h
e
co
r
r
esp
o
n
d
in
g
o
n
es
’
q
u
alit
y
.
Ot
h
er
w
is
e,
t
h
e
y
w
il
l b
e
d
ied
.
T
h
e
f
in
al
p
r
o
ce
d
u
r
e
o
f
t
h
is
s
tep
is
to
u
p
d
ate
th
e
b
es
t
p
lan
t
b
y
co
m
p
ar
in
g
th
e
p
la
n
t
h
av
in
g
t
h
e
b
est
f
it
n
es
s
v
alu
e
w
it
h
t
h
e
b
est
p
l
an
t
o
f
th
e
p
r
ev
io
u
s
g
en
er
atio
n
.
Ste
p 3
: Cre
atin
g
t
h
e
n
e
w
p
la
n
t
b
y
m
u
tati
n
g
t
h
e
b
est p
lan
t
Fro
m
th
e
b
es
t
p
lan
t
d
eter
m
in
ed
in
s
tep
2
,
th
e
n
e
w
p
lan
t
i
s
cr
ea
ted
b
y
u
s
in
g
eq
u
atio
n
(
7
)
.
T
h
en
,
t
h
e
v
ar
iab
le
p
ar
t
in
d
icate
s
t
h
e
lo
ca
tio
n
o
f
DG
o
f
n
e
w
p
lan
ts
is
r
o
u
n
d
ed
to
in
teg
er
v
al
u
e
t
o
m
ap
w
it
h
th
e
DG
o
p
tim
izatio
n
p
r
o
b
le
m
.
Fi
n
all
y
,
its
q
u
ali
t
y
e
v
al
u
ated
b
y
u
s
i
n
g
(
1
2
)
is
co
m
p
ar
ed
w
it
h
t
h
e
b
est
p
lan
t.
T
h
e
b
est
p
lan
t is
u
p
d
ated
o
n
e
m
o
r
e
ti
m
e
if
th
e
q
u
alit
y
o
f
t
h
e
n
e
w
p
la
n
t is b
etter
th
an
t
h
at
o
f
th
e
b
est
p
lan
t.
Ste
p 4
: Ch
ec
k
i
n
g
t
h
e
s
to
p
p
in
g
co
n
d
itio
n
T
h
e
s
to
p
p
in
g
co
n
d
itio
n
i
s
s
et
b
ased
o
n
a
m
ax
i
m
u
m
n
u
m
b
er
o
f
f
it
n
es
s
ev
a
lu
at
io
n
(
MN
FE)
.
I
t
m
ea
n
s
th
at
s
tep
2
an
d
3
w
i
ll b
e
ex
ec
u
ted
u
n
til
n
u
m
b
er
o
f
f
it
n
es
s
ev
a
lu
atio
n
r
ea
c
h
es to
th
e
M
NFE
v
alu
e.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
t
h
is
s
ec
tio
n
,
th
e
p
er
f
o
r
m
a
n
ce
o
f
E
S
FO
i
s
co
m
p
ar
ed
w
it
h
th
e
o
r
i
g
in
a
l
S
FO
i
n
t
h
e
s
a
m
e
p
er
s
o
n
al
co
m
p
u
ter
b
ased
o
n
Ma
tlab
p
latf
o
r
m
.
I
n
ad
d
itio
n
,
t
h
e
ef
f
ec
t
iv
en
e
s
s
o
f
E
SF
O
i
s
also
co
m
p
ar
ed
w
it
h
p
r
ev
io
u
s
DG
o
p
ti
m
izat
io
n
m
et
h
o
d
s
i
n
t
h
e
liter
at
u
r
e.
A
ll
o
f
m
e
th
o
d
s
a
r
e
v
alid
ated
o
n
th
e
3
3
n
o
d
es
d
is
tr
ib
u
tio
n
s
y
s
te
m
as
s
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ig
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t t
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g
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2
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also
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
C
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p
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N:
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tr
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u
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12
11
14
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16
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28
29
30
31
32
33
23
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34
8
21
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15
16
17
25
26
27
28
29
30
31
32
36
37
22
23
24
1
Fig
u
r
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1
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T
h
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3
3
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r
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r
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14
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16
15
18
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26
27
28
29
30
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23
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15
16
17
25
26
27
28
29
30
31
32
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22
23
24
1
DG
DG
DG
Fig
u
r
e
3
.
L
o
ca
tio
n
o
f
D
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o
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ta
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y
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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I
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Vo
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11
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No
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1
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Feb
r
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1
:
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112
C
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e
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t th
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AC
S
[
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.
T
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le
2
.
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o
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f
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p
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M
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R
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I
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5
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lt
s
ar
e
p
r
esen
te
d
in
T
ab
le
2
.
Fro
m
th
e
tab
le,
t
h
e
,
,
an
d
v
alu
e
s
o
b
tain
ed
b
y
E
S
FO
ar
e
b
ett
er
th
an
t
h
o
s
e
o
f
SF
O.
W
h
er
ein
,
t
h
ese
v
al
u
es
o
f
E
SF
O
ar
e
2
.
5
1
5
9
,
0
.
4
7
1
5
,
1
.
2
8
5
7
an
d
0
.
7
4
7
9
lo
w
er
t
h
a
n
t
h
o
s
e
o
f
S
FO,
r
esp
ec
ti
v
el
y
.
Me
an
w
h
ile,
t
h
e
r
u
n
ti
m
e
v
alu
e
o
f
E
SF
O
i
s
o
n
l
y
1
.
0
7
8
5
lo
n
g
er
th
a
n
t
h
at
o
f
SF
O.
I
n
ad
d
itio
n
,
th
e
m
i
n
i
m
u
m
f
it
n
es
s
v
al
u
e
o
b
tain
ed
i
n
ea
c
h
r
u
n
as
s
h
o
w
n
i
n
Fi
g
u
r
e
4
a
s
h
o
w
s
th
at
t
h
e
b
etter
p
er
f
o
r
m
a
n
ce
o
f
E
SF
O
co
m
p
ar
ed
to
SF
O.
I
n
w
h
ich
,
t
h
er
e
ar
e
3
5
r
u
n
s
i
n
to
tal
5
0
r
u
n
s
,
E
S
FO
o
b
tain
ed
a
b
etter
f
it
n
es
s
v
al
u
e
t
h
a
n
th
a
t
of
SF
O
w
h
ile
S
FO
h
a
s
o
n
l
y
f
o
u
n
d
a
b
etter
f
itn
e
s
s
v
a
lu
e
th
an
t
h
at
o
f
E
S
FO
i
n
1
5
r
u
n
s
.
T
h
e
m
a
x
i
m
u
m
,
m
i
n
i
m
u
m
a
n
d
m
ea
n
c
o
n
v
er
g
en
ce
cu
r
v
es
o
f
E
S
FO
an
d
SF
O
in
5
0
r
u
n
s
ar
e
s
h
o
w
n
i
n
F
ig
u
r
e
4
b
.
Fro
m
all
cu
r
v
e
s
o
b
tain
ed
b
y
E
SF
O
ar
e
m
u
c
h
lo
w
er
th
an
co
r
r
esp
o
n
d
in
g
o
n
e
s
o
f
SF
O.
T
h
is
ag
ai
n
co
n
f
ir
m
s
t
h
at
E
SF
O
's
i
m
p
r
o
v
e
m
en
t
s
h
a
v
e
y
ield
ed
m
o
r
e
p
o
s
itiv
e
r
esu
lt
s
th
a
n
SF
O
f
o
r
th
e
DG
o
p
ti
m
iz
atio
n
p
r
o
b
lem
.
(
a)
(
b
)
Fig
u
r
e
4
.
C
o
m
p
ar
is
o
n
o
f
p
er
f
o
r
m
an
ce
o
f
E
SF
O
a
n
d
SF
O,
(
a)
Op
ti
m
al
f
it
n
ess
v
al
u
e
in
5
0
r
u
n
s
an
d
(
b
)
C
o
n
v
er
g
e
n
ce
cu
r
v
es i
n
5
0
r
u
n
s
5.
CO
NCLU
SI
O
N
I
n
t
h
is
p
ap
er
,
E
SF
O
h
as
b
ee
n
s
u
cc
e
s
s
f
u
ll
y
p
r
o
p
o
s
ed
f
o
r
th
e
DG
o
p
ti
m
izatio
n
p
r
o
b
lem
to
m
i
n
i
m
ize
ac
tiv
e
p
o
w
er
lo
s
s
o
f
t
h
e
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
I
n
w
h
ich
,
E
SF
O
h
a
s
b
ee
n
ad
d
ed
th
e
m
u
tatio
n
tec
h
n
iq
u
e
f
o
r
u
p
d
atin
g
t
h
e
b
est
s
u
n
f
lo
w
er
p
lan
t.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
E
SF
O
h
as
b
ee
n
ev
al
u
ated
o
n
th
e
3
3
n
o
d
es
test
s
y
s
te
m
.
T
h
e
o
b
tain
ed
r
esu
lts
co
m
p
ar
ed
w
it
h
t
h
e
o
r
ig
in
al
S
FO
h
a
v
e
s
en
t
a
m
es
s
ag
e
t
h
at
E
SF
O
o
u
tp
er
f
o
r
m
s
to
SF
O
in
ter
m
s
o
f
t
h
e
m
i
n
i
m
u
m
p
o
w
er
lo
s
s
as
w
ell
a
s
i
n
d
ex
es
r
elate
d
to
ef
f
ec
ti
v
en
e
s
s
o
f
an
o
p
ti
m
i
za
tio
n
al
g
o
r
ith
m
s
u
ch
as
m
ax
i
m
u
m
,
m
in
i
m
u
m
a
n
d
m
ea
n
v
al
u
e
s
as
w
ell
a
s
ST
D
o
f
th
e
f
it
n
e
s
s
f
u
n
ctio
n
.
T
h
e
co
m
p
ar
ed
r
esu
lt
s
w
i
th
o
th
er
p
r
ev
io
u
s
m
et
h
o
d
s
h
av
e
also
lead
ed
to
th
e
co
n
clu
s
io
n
th
at
E
SF
O
is
in
o
n
e
o
f
t
h
e
e
f
f
ec
ti
v
e
tec
h
n
iq
u
es
to
t
h
e
D
G
o
p
ti
m
iza
tio
n
p
r
o
b
lem
f
o
r
p
o
w
er
lo
s
s
r
ed
u
ct
io
n
.
T
h
u
s
,
E
SF
O
ca
n
b
e
a
p
o
ten
tial
m
et
h
o
d
f
o
r
s
o
lv
i
n
g
t
h
e
DG
o
p
ti
m
izatio
n
p
r
o
b
lem
f
o
r
p
r
ac
tical
s
y
s
te
m
s
o
r
g
r
ati
f
y
i
n
g
o
th
er
g
o
als.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
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-
8708
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n
h
a
n
ce
d
s
u
n
flo
w
er o
p
timiz
a
tio
n
fo
r
p
la
ce
men
t
d
is
tr
ib
u
ted
…
(
Th
u
a
n
Th
a
n
h
N
g
u
ye
n
)
113
RE
F
E
R
E
NC
E
S
[1
]
K.
A
l
a
n
n
e
a
n
d
A
.
S
a
a
ri,
“
Distrib
u
ted
e
n
e
rg
y
g
e
n
e
ra
ti
o
n
a
n
d
su
sta
i
n
a
b
le
d
e
v
e
lo
p
m
e
n
t,
”
Ren
e
wa
b
le
a
n
d
S
u
st
a
in
a
b
l
e
En
e
rg
y
Rev
iews
,
v
o
l
.
1
0
,
n
o
.
6
,
p
p
.
5
3
9
-
5
5
8
,
2
0
0
6
.
[2
]
S
.
M
.
M
.
K
h
o
rm
a
n
d
ich
a
li
a
n
d
M
.
A
.
Ka
m
a
rp
o
sh
ti
,
“
Op
t
im
a
l
p
lac
e
m
e
n
t
o
f
w
in
d
g
e
n
e
ra
ti
o
n
u
n
it
s
in
o
rd
e
r
t
o
in
c
re
a
se
re
v
e
n
u
e
s
a
n
d
re
d
u
c
e
th
e
im
p
o
se
d
c
o
sts
in
th
e
d
istri
b
u
ti
o
n
sy
ste
m
c
o
n
sid
e
rin
g
u
n
c
e
rtain
ty
,
”
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
C
o
mp
u
t
e
r E
n
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
9
,
n
o
.
6
,
p
p
.
4
5
2
4
-
4
5
3
9
,
2
0
1
9
.
[3
]
A
.
M
u
sa
a
n
d
T
.
J.
T
e
n
g
k
u
Ha
sh
im
,
“
Op
ti
m
a
l
siz
in
g
a
n
d
lo
c
a
ti
o
n
o
f
m
u
lt
ip
le
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
f
o
r
p
o
w
e
r
lo
ss
m
in
i
m
iza
ti
o
n
u
sin
g
g
e
n
e
ti
c
a
lg
o
rit
h
m
,
”
In
d
o
n
e
sia
n
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
C
o
mp
u
ter
S
c
ien
c
e
(
IJ
EE
CS
)
,
v
o
l
.
1
6
,
n
o
.
2
,
p
p
.
9
5
6
-
9
6
3
,
2
0
1
9
.
[4
]
A
.
Ho
b
a
ll
a
h
,
Y.
A
h
m
e
d
,
a
n
d
K.
A
.
S
h
o
u
sh
,
“
Op
ti
m
a
l
u
ti
li
z
a
ti
o
n
o
f
a
u
to
m
a
t
e
d
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
i
n
sm
a
rt
g
rid
u
sin
g
g
e
n
e
ti
c
a
lg
o
rit
h
m
,
”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
E
n
g
i
n
e
e
rin
g
a
n
d
Co
m
p
u
ter
S
c
ien
c
e
(
IJ
EE
CS
)
,
v
o
l.
1
6
,
n
o
.
1
,
p
p
.
82
-
9
1
,
2
0
1
9
.
[5
]
M.
E.
Am
ra
n
e
t
a
l.
,
“
Op
ti
m
a
l
d
istri
b
u
te
d
g
e
n
e
ra
ti
o
n
in
g
re
e
n
b
u
i
ld
in
g
a
ss
e
ss
m
e
n
t
to
wa
rd
s
li
n
e
lo
ss
re
d
u
c
ti
o
n
f
o
r
M
a
la
y
sia
n
p
u
b
li
c
h
o
sp
it
a
l,
”
Bu
l
letin
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
In
fo
rm
a
t
ics
(
BE
EI)
,
v
o
l.
8
,
n
o
.
4
,
p
p
.
1
1
8
0
-
1
1
8
8
,
2
0
1
9
.
[6
]
N.
G
h
a
d
im
i,
“
Us
in
g
HBMO
A
l
g
o
rit
h
m
to
O
p
ti
m
a
l
S
izin
g
&
S
it
ti
n
g
o
f
Distrib
u
ted
G
e
n
e
ra
ti
o
n
i
n
P
o
w
e
r
S
y
ste
m
,
”
Bu
ll
e
ti
n
o
f
El
e
c
trica
l
E
n
g
in
e
e
rin
g
a
n
d
I
n
fo
rm
a
t
ics
(
BE
EI)
,
v
o
l.
3
,
n
o
.
1
,
p
p
.
1
-
8
,
2
0
1
4
.
[7
]
M
.
H.
M
o
ra
d
i
a
n
d
M
.
A
b
e
d
in
i,
“
A
c
o
m
b
in
a
ti
o
n
o
f
g
e
n
e
ti
c
a
lg
o
rit
h
m
a
n
d
p
a
rti
c
le
s
wa
r
m
o
p
ti
m
iz
a
t
io
n
f
o
r
o
p
ti
m
a
l
DG
lo
c
a
ti
o
n
a
n
d
siz
in
g
i
n
d
istri
b
u
ti
o
n
sy
ste
m
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
P
o
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
3
4
,
n
o
.
1
,
p
p
.
6
6
-
7
4
,
2
0
1
2
.
[8
]
B.
M
u
k
h
o
p
a
d
h
y
a
y
a
n
d
D.
Da
s,
“
M
u
lt
i
-
o
b
jec
ti
v
e
d
y
n
a
m
ic
a
n
d
sta
ti
c
re
c
o
n
f
ig
u
ra
ti
o
n
w
it
h
o
p
ti
m
iz
e
d
a
ll
o
c
a
ti
o
n
o
f
PV
-
DG
a
n
d
b
a
tt
e
ry
e
n
e
r
g
y
sto
ra
g
e
s
y
ste
m
,
”
Ren
e
wa
b
le a
n
d
S
u
sta
i
n
a
b
le E
n
e
rg
y
Rev
iews
,
v
o
l.
1
2
4
,
2
0
2
0
.
[9
]
M
.
N.
M
o
rsh
id
i
,
e
t
a
l.
,
“
W
h
a
le
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
b
a
se
d
tec
h
n
i
q
u
e
f
o
r
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
in
sta
ll
a
ti
o
n
in
d
istri
b
u
ti
o
n
sy
ste
m
,
”
Bu
ll
e
ti
n
o
f
E
lec
trica
l
En
g
in
e
e
rin
g
a
n
d
In
f
o
rm
a
ti
c
s
(
BE
EI)
,
vo
l.
7
,
n
o
.
3
,
p
p
.
4
4
2
-
4
4
9
,
2
0
1
8
.
[1
0
]
J.
P
.
S
ri
d
h
a
r
a
n
d
R
.
P
ra
k
a
sh
,
“
M
u
lt
i
-
o
b
jec
ti
v
e
w
h
a
le
o
p
ti
m
iza
ti
o
n
b
a
se
d
m
in
im
iza
ti
o
n
o
f
lo
ss
,
m
a
x
i
m
iz
a
ti
o
n
o
f
v
o
lt
a
g
e
sta
b
il
it
y
c
o
n
sid
e
rin
g
c
o
st
o
f
D
G
f
o
r
o
p
ti
m
a
l
siz
in
g
a
n
d
p
lac
e
m
e
n
t
o
f
D
G
,
”
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
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
),
v
o
l.
9
,
n
o
.
2
,
p
p
.
8
3
5
-
8
3
9
,
2
0
1
9
.
[1
1
]
S
.
M
.
A
li
,
P
.
S
.
Ba
b
u
,
a
n
d
B.
G
u
ru
s
e
k
h
a
r,
“
Re
c
o
n
f
ig
u
ra
ti
o
n
w
it
h
S
im
u
lt
a
n
e
o
u
s
DG
in
sta
ll
a
ti
o
n
to
Im
p
ro
v
e
th
e
V
o
l
tag
e
P
r
o
f
il
e
in
Distrib
u
ti
o
n
N
e
tw
o
rk
u
sin
g
Ha
r
m
o
n
y
S
e
a
rc
h
A
l
g
o
rit
h
m
,
”
Bu
ll
e
ti
n
o
f
E
lec
trica
l
E
n
g
i
n
e
e
rin
g
a
n
d
In
fo
rm
a
t
ics
(
BE
EI)
,
vo
l.
4
,
n
o
.
4
,
p
p
.
2
5
7
-
2
7
3
,
2
0
1
5
.
[1
2
]
R.
S
.
Ra
o
,
e
t
a
l.
,
“
P
o
w
e
r
L
o
ss
M
in
im
iza
ti
o
n
i
n
Distrib
u
ti
o
n
S
y
ste
m
Us
in
g
Ne
t
w
o
rk
Re
c
o
n
f
i
g
u
ra
ti
o
n
i
n
t
h
e
P
re
se
n
c
e
o
f
Distrib
u
ted
G
e
n
e
ra
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
Po
we
r S
y
ste
m,
vo
l.
2
8
,
n
o
.
1
,
p
p
.
3
1
7
-
3
2
5
,
2
0
1
3
.
[1
3
]
M
.
A
b
d
e
lb
a
d
e
a
,
T
.
A
.
Bo
g
h
d
a
d
y
,
a
n
d
D.
K.
Ib
ra
h
im
,
“
En
h
a
n
c
in
g
a
c
ti
v
e
ra
d
ial
d
istri
b
u
ti
o
n
n
e
tw
o
rk
s
b
y
o
p
ti
m
a
l
siz
in
g
a
n
d
p
lac
e
m
e
n
t
o
f
D
G
s
u
sin
g
m
o
d
if
ied
c
ro
w
se
a
rc
h
a
lg
o
rit
h
m
,
”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
Co
m
p
u
ter
S
c
ie
n
c
e
(
IJ
EE
CS
)
,
v
o
l.
1
6
,
n
o
.
3
,
p
p
.
1
1
7
9
-
1
1
8
8
,
2
0
1
9
.
[1
4
]
T
.
T
.
Ng
u
y
e
n
,
A
.
V
.
T
ru
o
n
g
,
a
n
d
T
.
A
.
P
h
u
n
g
,
“
A
n
o
v
e
l
m
e
th
o
d
b
a
se
d
o
n
a
d
a
p
ti
v
e
c
u
c
k
o
o
se
a
rc
h
f
o
r
o
p
ti
m
a
l
n
e
tw
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
a
n
d
d
ist
rib
u
te
d
g
e
n
e
ra
ti
o
n
a
ll
o
c
a
ti
o
n
i
n
d
istri
b
u
ti
o
n
n
e
tw
o
rk
,
”
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 &
En
e
rg
y
S
y
ste
ms,
v
o
l
.
7
8
,
p
p
.
8
0
1
-
8
1
5
,
2
0
1
6
.
[1
5
]
A
.
M
.
I
m
ra
n
,
M
.
Ko
w
s
a
l
y
a
,
a
n
d
D.
P
.
K
o
th
a
ri,
“
A
n
o
v
e
l
in
teg
ra
ti
o
n
tec
h
n
iq
u
e
f
o
r
o
p
ti
m
a
l
n
e
t
w
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
a
n
d
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
p
lac
e
m
e
n
t
in
p
o
w
e
r
d
istri
b
u
ti
o
n
n
e
tw
o
rk
s,”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
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.
6
3
,
p
p
.
4
6
1
-
4
7
2
,
2
0
1
4
.
[1
6
]
T
.
N
.
T
o
n
,
e
t
a
l
.
,
“
O
p
t
i
m
a
l
l
o
c
a
t
i
o
n
a
n
d
s
i
z
e
o
f
d
i
s
t
r
i
b
u
t
e
d
g
e
n
e
r
a
t
o
r
s
i
n
a
n
e
l
e
c
r
i
c
d
i
s
t
r
i
b
u
t
i
o
n
s
y
s
t
e
m
b
a
s
e
d
o
n
a
n
o
v
e
l
m
e
t
a
h
e
u
r
i
s
t
i
c
a
l
g
o
r
i
t
h
m
,
”
E
n
g
i
n
e
e
r
i
n
g
,
T
e
c
h
n
o
l
o
g
y
&
A
p
p
l
i
e
d
S
c
i
e
n
c
e
R
e
s
e
a
r
c
h
,
v
o
l
.
1
0
,
n
o
.
1
,
p
p
.
5
3
2
5
-
5
3
2
9
,
2
0
2
0
.
[1
7
]
A
.
Ba
y
a
t,
A
.
Ba
g
h
e
ri,
a
n
d
R
.
N
o
ro
o
z
ian
,
“
Op
ti
m
a
l
siti
n
g
a
n
d
si
z
in
g
o
f
d
istri
b
u
te
d
g
e
n
e
ra
ti
o
n
a
c
c
o
m
p
a
n
ied
b
y
re
c
o
n
f
ig
u
ra
ti
o
n
o
f
d
istri
b
u
ti
o
n
n
e
tw
o
rk
s
f
o
r
m
a
x
i
m
u
m
lo
ss
re
d
u
c
ti
o
n
b
y
u
sin
g
a
n
e
w
UV
D
A
-
b
a
se
d
h
e
u
risti
c
m
e
th
o
d
,
”
I
n
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
E
n
e
rg
y
S
y
s
te
ms,
v
o
l.
7
7
,
p
p
.
3
6
0
-
3
7
1
,
2
0
1
6
.
[1
8
]
M
.
R.
Na
y
a
k
,
“
Op
ti
m
a
l
F
e
e
d
e
r
Re
c
o
n
f
ig
u
ra
ti
o
n
o
f
Distrib
u
ti
o
n
S
y
st
e
m
w
it
h
Distrib
u
ted
Ge
n
e
ra
ti
o
n
Un
it
s
u
si
n
g
HC
-
A
C
O,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
n
El
e
c
trica
l
E
n
g
i
n
e
e
rin
g
a
n
d
I
n
fo
rm
a
ti
c
s,
v
o
l
.
6
,
n
o
.
1
,
p
p
.
1
0
7
-
1
2
8
,
2
0
1
4
.
[1
9
]
A
.
V
.
T
ru
o
n
g
,
e
t
a
l
.
,
“
T
w
o
sta
tes
f
o
r
o
p
ti
m
a
l
p
o
siti
o
n
a
n
d
c
a
p
a
c
it
y
o
f
d
istri
b
u
ted
g
e
n
e
ra
to
rs
c
o
n
si
d
e
rin
g
n
e
tw
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
f
o
r
p
o
w
e
r
lo
ss
m
i
n
im
iza
ti
o
n
b
a
se
d
o
n
r
u
n
n
e
r
ro
o
t
a
lg
o
rit
h
m
,
”
En
e
rg
ie
s,
v
o
l.
1
2
,
n
o
.
1
,
2
0
1
9
.
[2
0
]
R.
Ra
jara
m
,
K.
S
a
th
ish
Ku
m
a
r,
a
n
d
N.
Ra
jas
e
k
a
r,
“
P
o
w
e
r
s
y
ste
m
re
c
o
n
f
ig
u
ra
ti
o
n
in
a
ra
d
ial
d
ist
rib
u
ti
o
n
n
e
tw
o
rk
f
o
r
re
d
u
c
in
g
lo
ss
e
s
a
n
d
to
im
p
ro
v
e
v
o
lt
a
g
e
p
ro
f
il
e
u
sin
g
m
o
d
if
ied
p
lan
t
g
ro
w
th
si
m
u
latio
n
a
lg
o
rit
h
m
w
it
h
Distrib
u
te
d
G
e
n
e
ra
ti
o
n
(DG
),
”
En
e
rg
y
Rep
o
rts,
v
o
l
.
1
,
p
p
.
1
1
6
-
1
2
2
,
2
0
1
5
.
[2
1
]
N.
Kh
a
les
i,
N.
Re
z
a
e
i,
a
n
d
M
.
R.
Ha
g
h
if
a
m
,
“
D
G
a
ll
o
c
a
ti
o
n
w
i
th
a
p
p
li
c
a
ti
o
n
o
f
d
y
n
a
m
ic
p
ro
g
ra
m
m
in
g
f
o
r
lo
ss
re
d
u
c
ti
o
n
a
n
d
re
li
a
b
il
it
y
im
p
ro
v
e
m
e
n
t,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r
a
n
d
E
n
e
rg
y
S
y
ste
ms
,
v
o
l
.
3
3
,
n
o
.
2
,
p
p
.
2
8
8
-
2
9
5
,
2
0
1
1
.
[2
2
]
A
.
Ke
a
n
e
a
n
d
M
.
O’Malley
,
“
Op
ti
m
a
l
a
ll
o
c
a
ti
o
n
o
f
e
m
b
e
d
d
e
d
g
e
n
e
ra
ti
o
n
o
n
d
istri
b
u
ti
o
n
n
e
tw
o
rk
s,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
o
l.
2
0
,
n
o
.
3
,
p
p
.
1
6
4
0
-
1
6
4
6
,
2
0
0
5
.
[2
3
]
Y.
M
.
A
t
w
a
,
e
t
a
l.
,
“
Op
ti
m
a
l
Re
n
e
wa
b
le
R
e
so
u
rc
e
s
M
ix
f
o
r
Distrib
u
ti
o
n
S
y
ste
m
En
e
rg
y
L
o
ss
M
in
imiz
a
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
vo
l.
2
5
,
n
o
.
1
,
p
p
.
3
6
0
-
3
7
0
,
2
0
1
0
.
[2
4
]
G
.
F
.
G
o
m
e
s,
S
.
S
.
d
a
C
u
n
h
a
,
a
n
d
A
.
C.
A
n
c
e
lo
tt
i,
“
A
su
n
f
lo
we
r
o
p
ti
m
iza
ti
o
n
(
S
F
O)
a
lg
o
rit
h
m
a
p
p
li
e
d
to
d
a
m
a
g
e
id
e
n
ti
f
ica
ti
o
n
o
n
lam
in
a
ted
c
o
m
p
o
site p
late
s,”
E
n
g
i
n
e
e
rin
g
wi
th
C
o
mp
u
ter
s,
v
o
l
.
3
5
,
n
o
.
2
,
p
p
.
6
1
9
-
6
2
6
,
2
0
1
9
.
[2
5
]
M
.
E.
Ba
ra
n
a
n
d
F
.
F
.
W
u
,
“
Ne
t
wo
rk
re
c
o
n
f
ig
u
ra
ti
o
n
in
d
istri
b
u
ti
o
n
s
y
ste
m
s
f
o
r
lo
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
.
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