T
E
L
KO
M
N
I
KA
T
e
lec
om
m
u
n
icat
ion
,
Com
p
u
t
i
n
g,
E
lec
t
r
on
ics
an
d
Cont
r
ol
Vol.
18
,
No.
3
,
J
une
2020
,
pp.
1582
~
1599
I
S
S
N:
1693
-
6930,
a
c
c
r
e
dit
e
d
F
ir
s
t
G
r
a
de
by
Ke
me
nr
is
tekdikti
,
De
c
r
e
e
No:
21/E
/KP
T
/2018
DO
I
:
10.
12928/
T
E
L
KO
M
NI
KA
.
v18i3.
13466
1582
Jou
r
n
al
h
omepage
:
ht
tp:
//
jour
nal.
uad
.
ac
.
id/
index
.
php/T
E
L
K
OM
N
I
K
A
S
t
oc
h
ast
ic
r
e
n
e
w
ab
le
e
n
e
r
gy
r
e
sou
r
c
e
s i
n
t
e
gr
a
t
e
d
m
u
lti
-
o
b
j
e
c
t
iv
e
op
t
i
m
al
p
ow
e
r
f
lo
w
S
u
n
d
ar
am
B
.
P
an
d
ya,
Hi
t
e
s
h
R.
Jar
iwala
De
pa
r
tm
e
nt
of
E
lec
tr
ica
l
E
nginee
r
ing,
S
.
V
.
Na
ti
o
na
l
I
ns
ti
tut
e
of
T
e
c
hnology
,
I
nd
ia
Ar
t
icle
I
n
f
o
AB
S
T
RA
CT
A
r
ti
c
le
h
is
tor
y
:
R
e
c
e
ived
J
ul
2
,
2019
R
e
vis
e
d
J
a
n
3
0
,
2020
Ac
c
e
pted
F
e
b
26
,
2020
T
h
e
m
o
d
er
n
s
t
at
e
o
f
el
ec
t
ri
ca
l
s
y
s
t
em
co
n
s
i
s
t
s
t
h
e
c
o
n
v
e
n
t
i
o
n
al
g
en
era
t
i
n
g
u
n
i
t
s
al
o
n
g
w
i
t
h
t
h
e
s
o
u
rces
o
f
re
n
ew
a
b
l
e
en
er
g
y
.
T
h
e
p
ro
p
o
s
ed
ar
t
i
c
l
e
reco
mmen
d
s
a
me
t
h
o
d
f
o
r
t
h
e
s
o
l
u
t
i
o
n
o
f
s
i
n
g
l
e
a
n
d
m
u
l
t
i
-
o
b
j
ect
i
v
e
o
p
t
i
ma
l
p
o
w
er
fl
o
w
,
i
n
t
e
g
rat
i
n
g
w
i
n
d
an
d
s
o
l
ar
o
u
t
p
u
t
en
e
rg
y
w
i
t
h
t
ra
d
i
t
i
o
n
a
l
co
al
-
b
as
e
d
g
e
n
erat
i
n
g
s
t
at
i
o
n
s
.
In
t
h
e
f
i
rs
t
p
ar
t
o
f
t
h
e
art
i
c
l
e,
t
h
e
t
w
o
w
i
n
d
p
o
w
er
p
l
an
t
s
an
d
o
n
e
s
o
l
ar
PV
p
o
w
er
p
l
a
n
t
s
are
i
n
c
o
rp
o
r
at
ed
w
i
t
h
t
h
e
t
h
ermal
po
w
er
p
l
an
t
s
.
T
h
e
o
p
t
i
mal
p
o
w
er
fl
o
w
p
ro
b
l
em
o
f
s
i
n
g
l
e
an
d
c
o
n
f
l
i
ct
i
n
g
mu
l
t
i
-
o
b
j
ect
i
v
e
s
are
t
ak
e
n
w
i
t
h
t
h
i
s
s
ce
n
ari
o
.
T
h
e
s
ec
o
n
d
p
ar
t
o
f
t
h
e
p
ap
er,
s
o
l
ar
p
o
w
er
p
l
a
n
t
i
s
re
p
l
ace
d
w
i
t
h
a
n
o
t
h
er
w
i
n
d
p
o
w
er
p
l
an
t
w
i
t
h
t
h
e
co
n
v
e
n
t
i
o
n
al
co
a
l
-
b
a
s
ed
p
o
w
er
p
l
an
t
s
.
T
h
e
t
ec
h
n
o
-
e
co
n
o
mi
c
an
a
l
y
s
i
s
are
d
o
n
e
w
i
t
h
t
h
i
s
s
t
at
e
o
f
el
ec
t
r
i
ca
l
s
y
s
t
em.
In
p
ro
p
o
s
ed
w
o
r
k
,
l
o
g
n
o
rmal
an
d
w
ei
b
u
l
l
p
ro
b
ab
i
l
i
t
y
d
i
s
t
ri
b
u
t
i
o
n
f
u
n
c
t
i
o
n
s
are
a
l
s
o
u
t
i
l
i
ze
d
fo
r
p
red
i
ct
i
n
g
s
o
l
a
r
an
d
w
i
n
d
o
u
t
p
u
t
s
,
res
p
ec
t
i
v
el
y
.
A
n
o
n
-
d
o
m
i
n
a
t
ed
m
u
l
t
i
-
o
b
j
ect
i
v
e
mo
t
h
f
l
ame
o
p
t
i
mi
zat
i
o
n
t
ec
h
n
i
q
u
e
i
s
u
s
ed
fo
r
t
h
e
o
p
t
i
m
i
zat
i
o
n
i
s
s
u
e.
T
h
e
fu
zz
y
d
eci
s
i
o
n
-
ma
k
i
n
g
ap
p
r
o
ach
i
s
ap
p
l
i
e
d
fo
r
ex
t
ract
i
n
g
t
h
e
b
es
t
co
m
p
ro
m
i
s
e
s
o
l
u
t
i
o
n
.
T
h
e
res
u
l
t
s
are
v
a
l
i
d
at
e
d
t
h
o
u
g
h
ad
ap
t
ed
I
E
E
E
-
3
0
b
u
s
t
e
s
t
s
y
s
t
em,
w
h
i
ch
i
s
i
n
co
r
p
o
ra
t
ed
w
i
t
h
w
i
n
d
an
d
s
o
l
ar
g
en
er
at
i
n
g
p
l
an
t
s
.
K
e
y
w
o
r
d
s
:
M
e
ta
-
h
e
ur
is
ti
c
s
P
r
ob
a
bil
it
y
de
ns
it
y
f
unc
ti
on
S
olar
P
V
e
ne
r
gy
S
tocha
s
ti
c
W
ind
unit
s
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
r
t
i
c
l
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e
.
C
or
r
e
s
pon
din
g
A
u
th
or
:
S
unda
r
a
m
B
.
P
a
ndya
,
De
pa
r
tm
e
nt
of
E
lec
tr
ica
l
E
nginee
r
ing,
S
.
V
.
Na
ti
ona
l
I
ns
ti
tut
e
of
T
e
c
hnology
,
S
u
r
a
t,
I
ndi
a
.
E
mail:
s
unda
r
a
mpandya
@gmail.
c
om
L
I
S
T
OF
NOM
E
NC
L
AT
UR
E
O
PF
O
p
t
i
ma
l
Po
w
er
F
l
o
w
T
G
T
h
erma
l
G
en
erat
o
r
W
G
W
i
n
d
G
en
er
at
o
r
PV
Ph
o
t
o
V
o
l
t
ai
c
ISO
In
d
e
p
en
d
en
t
Sy
s
t
em
O
p
erat
o
r
PD
F
Pro
b
a
b
i
l
i
t
y
D
e
n
s
i
t
y
Fu
n
ct
i
o
n
BCS
Bes
t
Co
m
p
ro
m
i
s
e
So
l
u
t
i
o
n
MO
MFO
Mu
l
t
i
-
O
b
j
ect
i
v
e
Mo
t
h
F
l
ame
O
p
t
i
m
i
zat
i
o
n
MO
O
PF
Mu
l
t
i
-
O
b
j
ect
i
v
e
O
p
t
i
mal
P
o
w
er
Fl
o
w
Po
w
er
o
u
t
p
u
t
o
f
ℎ
t
h
ermal
u
n
i
t.
,
Sch
ed
u
l
e
d
p
o
w
er
fro
m
ℎ
w
i
n
d
p
o
w
er
u
n
i
t
,
Sch
ed
u
l
e
d
p
o
w
er
fro
m
ℎ
s
o
l
ar
P
V
u
n
i
t
,
A
ct
u
al
av
a
i
l
a
b
l
e
p
o
w
er
fro
m
ℎ
w
i
n
d
p
o
w
er
u
n
i
t
,
A
ct
u
al
av
a
i
l
a
b
l
e
p
o
w
er
fro
m
ℎ
s
o
l
ar
P
V
u
n
i
t
D
i
rec
t
co
s
t
co
eff
i
ci
e
n
t
fo
r
ℎ
w
i
n
d
p
o
w
er
u
n
i
t
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
Stochas
ti
c
r
e
ne
w
able
e
ne
r
gy
r
e
s
ou
r
c
e
s
int
e
gr
ated
multi
-
objec
ti
v
e
…
(
S
undar
am
B
.
P
andy
a
)
1583
ℎ
D
i
rec
t
co
s
t
co
eff
i
ci
e
n
t
fo
r
ℎ
s
o
l
ar
PV
u
n
i
t
,
Res
erv
e
co
s
t
c
o
effi
c
i
en
t
fo
r
o
v
eres
t
i
ma
t
i
o
n
o
f
w
i
n
d
p
o
w
er
fro
m
ℎ
u
n
i
t
,
Pen
al
t
y
co
s
t
c
o
effi
c
i
en
t
fo
r
u
n
d
ere
s
t
i
mat
i
o
n
o
f
w
i
n
d
p
o
w
er
fro
m
ℎ
u
n
i
t
,
Res
erv
e
co
s
t
c
o
effi
c
i
en
t
fo
r
o
v
eres
t
i
ma
t
i
o
n
o
f
s
o
l
ar
p
o
w
er
fro
m
ℎ
u
n
i
t
,
Pen
al
t
y
co
s
t
c
o
effi
c
i
en
t
fo
r
u
n
d
ere
s
t
i
mat
i
o
n
o
f
s
o
l
ar
p
o
w
er
fro
m
ℎ
u
n
i
t
Carb
o
n
t
ax
i
n
$
/
t
o
n
n
e
So
l
ar
i
rra
d
i
a
n
ce
i
n
W
m
2
⁄
(
)
Pro
b
a
b
i
l
i
t
y
o
f
w
i
n
d
s
p
eed
m/
s
(
)
Pro
b
a
b
i
l
i
t
y
o
f
s
o
l
ar
i
rrad
i
an
ce
W
m
2
⁄
.
Rat
ed
o
u
t
p
u
t
p
o
w
er
o
f
a
w
i
n
d
t
u
rb
i
n
e
Rat
ed
o
u
t
p
u
t
p
o
w
er
o
f
t
h
e
s
o
l
ar
P
V
p
l
a
n
t
,
W
ei
b
u
l
l
PD
F
s
cal
e
an
d
s
h
ap
e
p
arame
t
ers
re
s
p
ec
t
i
v
el
y
,
L
o
g
n
o
rmal
PD
F
mea
n
an
d
s
t
a
n
d
ar
d
d
ev
i
at
i
o
n
res
p
ect
i
v
e
l
y
Real
p
o
w
er
l
o
s
s
i
n
t
h
e
g
r
i
d
Cu
mu
l
at
i
v
e
v
o
l
t
ag
e
d
ev
i
at
i
o
n
i
n
a
g
r
i
d
1.
I
NT
RODU
C
T
I
ON
T
h
e
o
p
t
i
m
a
l
p
o
w
e
r
f
l
o
w
(
O
P
F
)
p
l
a
y
a
v
i
t
a
l
r
o
l
e
i
n
o
b
t
a
i
n
i
n
g
r
e
g
u
l
a
t
i
o
n
a
n
d
o
p
e
r
a
t
i
o
n
a
l
m
a
n
a
g
e
m
e
n
t
o
f
t
h
e
e
l
e
c
t
r
i
c
a
l
g
r
i
d
.
T
h
e
r
o
o
t
f
o
c
u
s
o
f
O
P
F
i
s
t
o
f
i
n
d
o
u
t
t
h
e
o
p
e
r
a
t
i
o
n
a
l
r
e
g
i
o
n
o
f
t
h
e
e
l
e
c
t
r
i
c
a
l
n
e
t
w
o
r
k
b
y
o
p
t
i
m
i
z
i
n
g
t
h
e
c
e
r
t
a
i
n
o
b
j
e
c
t
i
v
e
a
l
o
n
g
w
i
t
h
n
o
n
-
v
i
o
l
a
t
i
n
g
e
q
u
a
l
i
t
y
a
n
d
i
n
e
q
u
a
l
i
t
y
b
o
u
n
d
s
.
I
t
w
a
s
f
i
r
s
t
i
n
t
r
o
d
u
c
e
d
b
y
C
a
r
p
e
n
t
i
e
r
[
1
]
.
L
a
s
t
f
e
w
y
e
a
r
s
,
m
a
n
y
s
t
o
c
h
a
s
t
i
c
t
e
c
h
n
i
q
u
e
s
h
a
v
e
b
e
e
n
p
r
o
p
o
s
e
d
i
n
[
2
-
1
2
]
f
o
r
t
h
e
O
P
F
p
r
o
b
l
e
m
.
W
hil
e
a
bove
-
mentioned
c
it
a
ti
ons
c
ons
ider
only
c
las
s
ica
l
ge
ne
r
a
ti
ng
unit
s
.
An
e
lec
tr
ica
l
s
ys
tem
c
ompr
is
ing
wind
a
nd
ther
mal
powe
r
unit
s
ha
s
c
ur
r
e
ntl
y
be
e
n
c
ons
ider
e
d
in
s
e
a
r
c
h
o
f
opti
mum
ge
ne
r
a
ti
ng
c
os
t
in
s
ome
of
the
a
r
t
i
c
l
e
s
.
Gbe
s
t
dir
e
c
ted
a
r
ti
f
icia
l
be
e
c
olony
(
GA
B
C
)
is
put
in
us
e
d
in
[
13]
f
or
the
e
nha
nc
e
m
e
nt
of
OPF
output
s
obtaine
d
in
e
a
r
li
e
r
a
r
ti
c
les
us
ing
s
a
me
e
xpe
r
im
e
ntal
a
r
r
a
nge
ment
.
In
[
14
]
int
r
oduc
e
d
a
modi
f
ied
ba
c
ter
ia
f
or
a
ging
a
ppr
oa
c
h
(
M
B
F
A)
a
nd
pr
opos
e
d
a
doubly
f
e
d
induction
ge
ne
r
a
tor
(
DFI
G
)
s
tr
uc
tur
e
in
the
OPF
a
ge
nda
to
e
xpr
e
s
s
bounds
on
VA
R
powe
r
pr
oduc
ti
on
c
a
pa
c
it
y.
Anothe
r
VA
R
powe
r
c
ompens
a
ti
ng
de
vice
,
s
tatic
s
ync
hr
onous
c
ompens
a
tor
(
S
T
AT
C
OM
)
is
int
e
gr
a
ti
ng
wi
th
[
15]
f
or
a
ne
twor
k
ha
vin
g
ther
mal
a
nd
wind
unit
s
.
Als
o,
the
OPF
is
s
ue
wa
s
s
olved
with
the
he
lp
of
a
nt
c
olony
opti
mi
z
a
ti
on
(
AC
O)
a
s
we
ll
a
s
M
B
F
A.
S
hi
e
t
a
l
.
[
16]
int
r
oduc
e
d
a
pa
tt
e
r
n
f
or
the
f
or
mul
a
ti
on
of
the
c
os
t
of
wind
powe
r
.
Ge
ne
r
a
to
r
s
s
c
he
duli
ng
pr
oblem
f
or
e
c
onomi
c
dis
pa
tch
is
a
us
ua
l
pr
oblem
f
or
a
uti
li
ty
ha
vin
g
wind
powe
r
a
nd
ther
mal
unit
s
.
J
a
br
a
nd
P
a
l
[
17
]
of
f
e
r
e
d
a
s
tocha
s
ti
c
model
of
wind
powe
r
pr
oduc
ti
on
.
I
n
a
ddit
ional
,
while
s
olvi
ng
the
s
im
il
a
r
is
s
ue
,
M
is
hr
a
e
t
al
.
[
18]
invol
ve
d
D
F
I
G
model
of
wind
tur
bine.
W
e
i
a
t
a
l
.
[
19
]
int
r
oduc
e
d
dyna
mi
c
e
c
onomi
c
dis
pa
tch
(
DE
D)
s
tr
uc
tur
e
c
ompr
is
ing
a
wide
r
a
nge
of
wi
nd
e
ne
r
gy
with
r
is
k
r
e
s
e
r
ve
li
mi
ts
.
Dube
y
[
20]
include
d
va
lve
-
point
loading
e
f
f
e
c
t
of
ge
ne
r
a
ti
ng
unit
a
nd
e
mi
s
s
ion
in
DE
D
s
tr
uc
tur
e
.
OP
F
s
c
he
duli
ng
s
ys
tem
f
or
a
s
oli
tar
y
hybr
id
ne
twor
k
ha
ving
s
olar
P
V,
ba
tt
e
r
y
a
nd
the
dies
e
l
ge
ne
r
a
ti
ng
unit
is
e
xplaine
d
in
[
21]
.
P
umped
hydr
o
s
tor
a
ge
is
pr
e
s
e
nted
in
[
22
]
a
s
a
s
ubs
ti
tut
e
s
tor
a
ge
f
or
the
s
a
me
s
tanda
lone
hybr
id
ne
twor
k
c
ompr
is
ing
of
a
wind
ge
ne
r
a
ti
ng
uni
t
,
a
s
olar
P
V
,
a
nd
a
dies
e
l
ge
ne
r
a
ti
ng
unit
.
N
ow
a
d
a
ys
,
th
e
m
a
j
o
r
c
ha
l
le
ng
e
i
n
pow
e
r
s
ys
te
m
i
s
a
n
i
nt
e
g
r
a
t
in
g
t
he
r
e
ne
wa
b
le
e
ne
r
gy
s
ou
r
c
e
s
li
ke
w
i
nd
a
nd
s
o
la
r
P
V
p
ow
e
r
i
n
p
owe
r
g
r
i
d
.
T
he
s
i
ng
le
a
n
d
m
u
lt
i
-
o
bje
c
t
i
ve
o
pt
i
ma
l
p
owe
r
f
lo
w
i
nc
lud
i
ng
wi
th
t
he
r
e
n
e
wa
bl
e
e
ne
r
g
y
s
o
u
r
c
e
s
f
oc
us
e
d
t
he
ma
xi
m
um
a
t
ten
t
io
n
.
T
he
a
u
t
ho
r
’
s
in
f
lue
nc
e
i
n
t
h
is
p
a
pe
r
,
a
r
e
a
s
f
o
l
low
s
:
−
T
h
is
a
r
t
ic
le
is
d
e
v
ote
d
t
o
the
m
a
t
he
ma
ti
c
a
l
mo
de
li
ng
o
f
t
he
s
i
ng
le
a
nd
m
ul
ti
-
ob
je
c
t
iv
e
O
P
F
p
r
o
bl
e
ms
i
nc
lud
i
ng
c
om
p
let
e
un
c
e
r
t
a
i
n
ty
m
od
e
l
in
g
o
f
t
he
r
m
a
l
p
la
nts
,
win
d
p
owe
r
p
la
nts
a
nd
s
ol
a
r
P
V
p
owe
r
p
la
nt
in
the
f
i
r
s
t
pa
r
t
.
−
C
a
lc
ul
a
t
i
ons
a
nd
mo
de
l
in
g
o
f
the
d
i
f
f
e
r
e
n
t
p
r
oba
bi
li
t
y
d
e
ns
it
y
f
u
nc
ti
ons
c
o
mp
r
is
i
ng
th
e
s
t
oc
ha
s
ti
c
w
ind
a
n
d
s
ola
r
po
we
r
p
la
nts
.
−
I
n
s
e
c
on
d
p
a
r
t
s
ol
a
r
p
owe
r
p
lan
t
is
r
e
pla
c
e
d
w
it
h
t
h
e
w
in
d
po
we
r
p
la
nt
a
n
d
f
i
na
ll
y
f
in
d
o
ut
t
he
s
ol
ut
io
n
of
s
in
gl
e
a
n
d
m
u
lt
i
-
o
bj
e
c
ti
ve
O
P
F
p
r
ob
le
m
w
it
h
t
he
c
om
pa
r
a
t
iv
e
t
e
c
h
no
-
e
c
o
no
m
ic
a
na
lys
is
.
−
T
h
e
no
n
-
do
m
ina
te
d
s
o
r
t
in
g
M
ot
h
F
l
a
me
O
pt
im
iz
a
t
io
n
te
c
h
ni
que
is
a
p
p
li
e
d
f
or
f
i
nd
in
g
s
ol
ut
io
ns
o
f
s
in
gle
a
n
d
m
u
lt
i
-
o
bj
e
c
ti
ve
O
P
F
p
r
ob
le
ms
i
nc
lu
di
ng
s
t
oc
h
a
s
t
ic
r
e
ne
wa
b
le
e
ne
r
gy
s
ou
r
c
e
s
l
ik
e
w
in
d
a
nd
s
ol
a
r
P
V
pow
e
r
.
T
he
f
u
r
ther
s
e
c
ti
ons
of
the
a
r
ti
c
le
a
r
e
a
r
r
a
nge
d
a
s
:
s
e
c
ti
on
2
c
ons
is
t
of
the
a
na
lys
is
of
mathe
matica
l
models
c
ontaining
a
f
o
r
mul
a
ti
on
of
unc
e
r
tainti
e
s
i
n
s
olar
a
nd
wind
e
n
e
r
gy
outcome
s
r
e
ga
r
ding
O
P
F
pr
oblem.
S
e
c
ti
on
3
incl
ude
s
dis
c
us
s
ion
on
the
objec
ti
ve
s
whic
h
is
to
be
opti
mi
z
e
d.
E
xplana
ti
on
a
nd
a
ppli
c
a
ti
on
of
mul
ti
-
objec
ti
ve
M
F
O
a
ppr
oa
c
h
a
r
e
e
xplaine
d
in
s
e
c
ti
on
4
.
Nume
r
ica
l
r
e
s
ult
s
a
nd
dis
c
us
s
ion
a
r
e
pr
e
s
e
nted
in
s
e
c
ti
on
5
a
nd
c
onc
lus
ive
notes
given
in
s
e
c
ti
on
6
.
2.
M
AT
HE
M
A
T
I
CA
L
M
ODE
L
S
T
he
e
leme
ntar
y
inf
or
mation
da
ta
o
f
mod
if
ied
I
E
E
E
-
30
bus
powe
r
s
ys
tem
c
ons
ider
ing
the
ther
mal
powe
r
plants
a
nd
r
e
ne
wa
ble
r
e
s
our
c
e
s
is
s
hown
in
T
a
b
le
1
.
T
he
bus
nu
mber
5,
bus
number
11
a
nd
bus
number
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1582
-
1599
1584
13
a
r
e
r
e
plac
e
d
with
the
r
e
ne
wa
ble
s
our
c
e
s
.
All
the
ther
m
a
l
plants
,
wind
a
nd
s
olar
plants
c
ont
r
ibut
e
to
the
tot
a
l
c
os
t
of
ge
ne
r
a
ti
on
.
T
he
c
os
t
of
the
c
onve
nti
ona
l
the
r
mal
ge
ne
r
a
ti
ng
plants
a
nd
the
r
e
ne
wa
ble
s
our
c
e
s
p
lants
a
r
e
de
s
c
r
ibed
in
the
be
low
s
e
c
ti
on.
T
a
ble
1.
T
he
main
c
ha
r
a
c
ter
is
ti
c
s
of
the
s
ys
tem
unde
r
s
tudy
I
te
ms
Q
ua
nt
it
y
D
e
ta
il
s
B
us
e
s
30
[
23]
B
r
a
nc
he
s
41
[
23]
T
he
r
ma
l
ge
ne
r
a
to
r
s
(
T
G
1;
T
G
2;
T
G
3)
3
B
us
e
s
:
1 (
s
w
in
g)
, 2 a
nd 8
W
in
d ge
ne
r
a
to
r
s
(
W
G
1;
W
G
2)
2
B
us
e
s
:
5
a
nd 11
S
ol
a
r
P
V
uni
t
(
S
P
V
)
or
W
in
d ge
ne
r
a
to
r
(
W
G
3)
1
B
us
:
13
C
ont
r
ol
va
r
ia
bl
e
s
24
-
C
onne
c
te
d l
oa
d
-
283.4
M
W
, 126.2 M
V
A
r
2.
1.
Cos
t
of
t
h
e
r
m
al
p
owe
r
u
n
i
t
s
T
he
ther
mal
ge
ne
r
a
ti
ng
unit
s
ope
r
a
ti
ng
with
the
f
o
s
s
il
f
ue
ls
a
nd
non
-
c
onve
xit
y
c
o
ntaining
numer
ous
s
we
ll
s
be
c
a
u
s
e
of
the
e
xis
tenc
e
of
s
tac
king
im
pa
c
ts
of
the
va
lve
point
.
T
he
r
ippl
e
e
f
f
e
c
t
upon
the
c
os
t
c
ur
ve
is
include
d
a
s
r
e
dr
e
s
s
ing
s
inus
oids
with
qua
dr
a
ti
c
c
o
s
ts
.
S
c
ientif
ica
ll
y,
the
c
os
t
in
$/hr
ha
ving
a
va
lve
-
point
e
f
f
e
c
t
is
tr
e
a
te
d
a
s
:
(
)
=
∑
+
+
2
+
|
×
s
in
(
×
(
−
)
)
|
=
1
(
1)
whe
r
e
,
a
nd
a
r
e
the
c
os
t
c
oe
f
f
icie
nts
f
or
ℎ
ther
mal
p
owe
r
plant.
Als
o
a
nd
a
r
e
the
c
os
t
c
oe
f
f
icie
nts
be
c
a
us
e
of
va
lve
point
e
f
f
e
c
t.
2.
2.
E
m
is
s
ion
T
he
non
-
r
e
ne
wa
b
le
e
ne
r
gy
s
ou
r
c
e
s
r
e
lea
s
e
tox
ic
ga
s
e
s
in
the
a
tm
os
p
he
r
e
du
r
i
ng
p
owe
r
ge
n
e
r
a
ti
on
.
T
he
dis
c
h
a
r
ge
o
f
NO
x
a
n
d
S
ox
r
is
e
s
w
it
h
a
n
i
nc
r
e
a
s
e
in
t
he
r
mal
pla
nts
out
puts
a
s
ind
ica
ted
i
n
(
2
)
.
E
m
is
s
ion
in
tones
pe
r
h
our
(
t
o
n/h
r
)
c
a
n
be
de
te
r
mi
ne
d
a
s
:
E
m
is
s
io
n
=
∑
[
(
+
+
2
)
×
0
.
01
+
(
)
]
=
1
(
2)
whe
r
e
,
,
,
,
a
nd
a
r
e
the
e
mi
s
s
ion
c
oe
f
f
icie
nts
with
r
e
s
pe
c
t
to
the
ℎ
ther
mal
unit
.
T
he
va
lues
of
ther
mal
c
os
t
c
oe
f
f
icie
nts
a
nd
e
mi
s
s
ion
c
oe
f
f
icie
nts
of
the
r
mal
powe
r
plants
a
r
e
dis
playe
d
in
T
a
ble
2
.
T
a
ble
2.
C
os
t
c
oe
f
f
icie
nts
a
nd
e
mi
s
s
ion
c
oe
f
f
icie
nt
s
of
the
s
ys
tem
unde
r
s
tudy
G
e
ne
r
a
to
r
B
us
1
1
0
2
0
.00375
18
0.037
4.091
-
5.554
6.49
0.0002
6.667
2
2
0
1.75
0.0175
16
0.038
2.543
-
6.047
5.638
0.0005
3.333
3
8
0
3.25
0.00834
12
0.045
5.326
-
3.55
3.38
0.002
2
2.
3.
Dir
e
c
t
c
os
t
of
s
t
oc
h
as
t
ic
r
e
n
e
wabl
e
p
lan
t
s
T
he
r
e
ne
wa
ble
s
our
c
e
s
a
r
e
s
tocha
s
ti
c
in
n
a
tur
e
a
nd
it
is
ve
r
y
dif
f
icult
to
int
e
g
r
a
te
thes
e
s
our
c
e
s
int
o
the
powe
r
gr
id
.
T
he
wind
a
nd
s
olar
powe
r
unit
s
a
r
e
c
ontr
oll
e
d
th
r
ough
the
indepe
nde
nt
s
ys
tem
ope
r
a
tor
(
I
S
O)
.
S
o
the
pr
ivate
ope
r
a
to
r
ha
s
to
make
the
a
g
r
e
e
ment
with
the
gr
id
f
or
a
c
e
r
tain
a
mount
o
f
s
c
he
duled
powe
r
.
T
he
I
S
O
mus
t
be
s
us
taine
d
the
s
c
he
duled
powe
r
.
I
f
the
s
e
r
e
ne
wa
ble
f
a
r
ms
a
r
e
not
a
ble
to
maintain
the
s
c
he
duled
powe
r
,
I
S
O
is
r
e
s
pons
ibl
e
f
o
r
the
de
f
icie
nc
y
of
the
powe
r
.
S
o
the
s
pinni
ng
r
e
s
e
r
ve
s
uppli
e
s
the
powe
r
,
if
powe
r
de
mand
a
r
is
e
.
T
his
s
pinni
ng
r
e
s
e
r
ve
a
dds
e
xtr
a
c
os
t
f
or
the
I
S
O
a
nd
thi
s
c
ondit
ion
is
ter
med
a
s
ove
r
e
s
ti
mation
of
the
r
e
ne
wa
ble
s
our
c
e
s
li
ke
wind
a
nd
s
olar
P
V
f
a
r
ms
.
S
im
i
lar
ly,
in
oppos
it
e
wa
y
,
i
f
thes
e
r
e
ne
wa
ble
s
our
c
e
s
pr
oduc
e
d
mor
e
powe
r
c
ompar
e
d
to
the
s
c
he
duled
p
owe
r
,
it
c
a
n
be
wa
s
ted
be
c
a
us
e
of
non
-
uti
li
z
a
ti
on
.
S
o
the
I
S
O
mus
t
tol
e
r
a
te
the
pe
n
a
lt
y
c
ha
r
ge
.
T
hus
,
the
dir
e
c
t
c
os
t
of
the
non
-
c
onve
nti
ona
l
unit
s
a
ll
ied
with
the
s
c
he
duled
powe
r
,
ove
r
e
s
ti
mation
c
os
t
be
c
a
us
e
of
the
s
pinni
ng
r
e
s
e
r
ve
a
nd
the
pe
na
lt
y
c
os
t
be
c
a
u
s
e
of
the
unde
r
e
s
ti
mation.
Dir
e
c
t
c
os
t
r
e
late
d
to
the
wind
f
a
r
ms
f
r
om
the
ℎ
powe
r
plant
is
modele
d
with
the
,
s
c
he
duled
powe
r
f
r
om
the
s
a
me
s
our
c
e
s
a
s
:
,
(
,
)
=
,
(
3)
whe
r
e
indi
c
a
te
the
dir
e
c
t
c
os
t
c
oe
f
f
icie
nt
a
nd
,
is
tr
e
a
ted
a
s
the
s
c
he
duled
powe
r
o
f
the
ℎ
powe
r
plant
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
Stochas
ti
c
r
e
ne
w
able
e
ne
r
gy
r
e
s
ou
r
c
e
s
int
e
gr
ated
multi
-
objec
ti
v
e
…
(
S
undar
am
B
.
P
andy
a
)
1585
S
im
il
a
r
ly,
the
d
ir
e
c
t
c
os
t
r
e
late
d
to
the
s
olar
P
V
f
a
r
ms
f
r
om
ℎ
powe
r
plant
is
de
mons
tr
a
ted
with
the
,
s
c
he
duled
powe
r
f
r
om
the
s
a
me
s
our
ces
as
:
,
(
,
)
=
ℎ
,
(
4)
whe
r
e
ℎ
indi
c
a
tes
the
dir
e
c
t
c
os
t
c
oe
f
f
icie
nt
a
nd
,
is
tr
e
a
ted
a
s
the
s
c
he
duled
pow
e
r
of
the
ℎ
powe
r
plant.
2.
4.
Unce
r
t
ain
r
e
n
e
wabl
e
win
d
p
owe
r
c
os
t
Ow
ing
to
the
unc
e
r
tainty
of
t
he
wind
,
oc
c
a
s
ionally
the
wind
f
a
r
m
p
r
oduc
e
s
the
les
s
a
mount
of
the
powe
r
a
s
c
ompar
e
d
to
s
c
he
duled
powe
r
.
S
ometi
mes
,
it
may
be
pos
s
ibl
e
that
a
c
tual
powe
r
pr
ovided
by
wind
f
a
r
m
may
not
be
s
a
ti
s
f
ying
the
de
mand
a
nd
ha
ve
l
owe
r
va
lues
.
S
uc
h
powe
r
is
known
a
s
ove
r
e
s
ti
mat
e
d
powe
r
by
a
n
indete
r
mi
na
te
r
e
s
our
c
e
.
T
he
ne
twor
k
I
S
O
s
hould
r
e
qui
r
e
a
s
pinni
ng
r
e
s
e
r
ve
to
c
ope
up
with
thi
s
type
o
f
unc
e
r
tainty
a
nd
de
li
ve
r
c
onti
nuous
powe
r
s
our
c
e
to
the
e
nd
us
e
r
s
.
T
he
c
os
t
of
obli
ga
ti
ng
a
r
e
s
e
r
ve
ge
ne
r
a
tor
to
f
ulf
il
l
the
ove
r
e
s
ti
mate
d
powe
r
is
na
med
a
s
r
e
s
e
r
ve
c
os
t.
R
e
s
e
r
ve
c
os
t
f
or
the
ℎ
wind
unit
is
f
o
r
mul
a
ted
by
:
,
(
,
−
,
)
=
,
(
,
−
,
)
=
,
∫
(
,
−
,
)
(
,
)
,
,
0
(
5)
whe
r
e
,
,
r
e
pr
e
s
e
nts
a
r
e
s
e
r
ve
c
os
t
c
oe
f
f
icie
nt
r
e
ga
r
di
ng
ℎ
wind
unit
,
,
is
the
de
f
ini
te
a
c
c
e
s
s
ibl
e
powe
r
f
r
om
the
s
a
me
unit
.
(
,
)
r
e
pr
e
s
e
nts
the
wind
powe
r
p
r
o
ba
bil
it
y
de
ns
it
y
f
unc
ti
on
f
or
ℎ
wind
unit
.
Oppos
it
e
to
the
ove
r
e
s
ti
mation
c
ondit
ion,
it
may
be
pos
s
ibl
e
that
the
a
c
tual
powe
r
pr
ovided
by
the
wind
f
a
r
m
is
higher
f
r
om
the
de
mand
va
lue.
S
uc
h
a
s
c
e
na
r
io
is
c
a
ll
e
d
unde
r
e
s
ti
mate
d
powe
r
.
T
h
e
lef
tover
powe
r
will
be
los
t
i
f
ther
e
is
n
ot
a
ny
p
r
ovis
ion
f
or
c
ontr
oll
ing
the
ou
tput
powe
r
f
r
om
th
e
r
mal
uni
ts
.
I
S
O
s
hould
be
pa
id
a
pe
na
lt
y
c
ha
r
ge
r
e
ga
r
ding
the
e
xc
e
s
s
powe
r
.
P
e
na
lt
y
c
ha
r
ge
f
or
the
ℎ
wind
unit
is
given
by
:
,
(
,
−
,
)
=
,
(
,
−
,
)
=
,
∫
(
,
−
,
)
(
,
)
,
,
,
(
6)
whe
r
e
,
,
r
e
pr
e
s
e
nts
a
pe
na
lt
y
c
os
t
c
oe
f
f
icie
nt
of
ℎ
wi
nd
unit
,
,
gives
the
s
pe
c
if
ied
ou
tput
powe
r
of
th
e
s
a
me
unit
.
2.
5.
Unce
r
t
ain
r
e
n
e
wabl
e
s
olar
P
V
p
owe
r
c
os
t
S
olar
P
V
unit
a
ls
o
ha
s
a
n
ir
r
e
gular
a
nd
unc
e
r
tain
ge
ne
r
a
ti
on.
I
n
f
a
c
t,
the
tac
ti
c
f
o
r
unde
r
e
s
ti
mation
a
nd
ove
r
e
s
ti
mation
of
s
olar
powe
r
will
be
s
im
il
a
r
to
the
c
a
s
e
of
wind
powe
r
.
T
hough,
r
a
diation
o
f
s
o
lar
tr
a
il
s
lognor
mal
P
DF
[
23]
,
unli
ke
a
s
of
wind
powe
r
s
u
pply
that
is
popular
f
o
r
tr
a
il
ing
W
e
ibul
l
P
DF
,
f
or
e
a
s
e
in
c
omput
a
ti
on,
a
pe
na
lt
y
a
s
we
ll
a
s
r
e
s
e
r
ve
c
os
t
s
tr
uc
tur
e
s
we
r
e
made
a
c
c
or
ding
to
the
idea
e
xplaine
d
in
[
23]
.
R
e
s
e
r
ve
c
os
t
of
ℎ
s
olar
P
V
unit
c
a
n
be
wr
it
ten
a
s
:
,
(
,
−
,
)
=
,
(
,
−
,
)
=
,
∗
(
,
<
,
)
∗
[
,
−
(
,
<
,
)
]
(
7)
whe
r
e
,
is
the
r
e
s
e
r
ve
c
os
t
c
oe
f
f
icie
nt
r
e
ga
r
ding
ℎ
s
o
lar
P
V
unit
,
,
is
the
de
f
ini
te
a
c
c
e
s
s
ibl
e
pow
e
r
f
r
om
the
s
a
me
unit
.
(
,
<
,
)
s
hows
the
pos
s
ibi
li
ty
of
s
olar
output
powe
r
de
f
icie
nc
y
incide
nc
e
with
r
e
s
pe
c
t
to
s
c
he
duled
outp
ut
powe
r
(
,
)
,
(
,
<
,
)
s
hows
the
a
nti
c
ipation
to
the
s
olar
P
V
output
powe
r
lowe
r
than
,
.
P
e
n
a
lt
y
c
os
t
of
unde
r
-
e
s
ti
mation
of
ℎ
s
olar
P
V
unit
c
a
n
be
given
by
:
,
(
,
−
,
)
=
,
(
,
−
,
)
=
,
∗
(
,
>
,
)
∗
[
(
,
>
,
)
−
,
]
(
8)
w
h
e
r
e
,
r
e
p
r
e
s
e
n
t
s
t
h
e
c
o
e
f
f
i
c
i
e
n
t
o
f
p
e
n
a
l
t
y
c
o
s
t
r
e
g
a
r
d
i
n
g
ℎ
s
o
l
a
r
P
V
u
n
i
t
,
(
,
>
,
)
s
h
o
ws
t
h
e
p
o
s
s
i
b
i
l
i
t
y
o
f
s
o
l
a
r
o
u
t
p
u
t
i
n
e
x
c
e
s
s
w
i
t
h
r
e
s
p
e
c
t
t
o
t
h
e
s
c
h
e
d
u
l
e
d
o
u
t
p
u
t
p
o
w
e
r
(
,
)
,
(
,
>
,
)
s
h
o
w
s
t
h
e
a
n
t
i
c
i
p
a
t
i
o
n
o
f
s
o
l
a
r
P
V
o
u
t
p
u
t
p
o
w
e
r
h
i
g
h
e
r
t
h
a
n
,
.
2.
6.
Unce
r
t
ain
t
y
m
o
d
e
ls
of
s
t
oc
h
as
t
ic
win
d
/s
olar
p
o
we
r
I
n
a
da
pted
I
E
E
E
-
30
bus
c
a
s
e
s
tudy,
the
ther
mal
ge
ne
r
a
ti
ng
unit
s
whic
h
a
r
e
loca
ted
a
t
bus
-
5
a
nd
bus
-
1
1,
r
e
plac
e
d
by
wind
powe
r
ge
ne
r
a
ti
ng
unit
s
.
Da
ta
of
pr
opos
e
d
W
e
ibul
l
s
ha
pe
(
)
a
nd
s
c
a
le
(
)
pa
r
a
mete
r
s
we
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1582
-
1599
1586
dis
playe
d
in
T
a
ble
3
.
W
e
ibul
l
f
it
ti
ng
a
nd
wind
f
r
e
que
nc
y
dis
tr
ibut
ions
in
F
igur
e
s
1
(
a
)
a
nd
1
(
b)
a
r
e
a
c
hieve
d
by
taking
8000
M
onte
-
C
a
r
lo
s
c
e
na
r
ios
.
T
he
S
tanda
r
d
given
in
[
23
]
ins
tr
uc
ts
the
de
s
ign
ne
c
e
s
s
it
y
of
wind
tur
bines
a
nd
s
tate
s
maximum
t
ur
bulent
c
las
s
I
A
that
is
ve
r
i
f
ied
to
ope
r
a
te
a
t
highes
t
ye
a
r
ly
a
ve
r
a
ge
wind
ve
locity
of
10
mete
r
s
/s
e
c
a
t
hub
he
ight
.
S
pe
c
ial
f
oc
us
is
f
or
taking
s
ha
pe
(
)
a
nd
s
c
a
le
(
)
pa
r
a
mete
r
s
of
win
d
f
a
r
ms
a
s
highes
t
W
e
ibul
l
P
DF
mea
n
va
lue
s
tuck
ne
a
r
10.
I
n
a
ddit
io
n
,
va
r
ious
P
DF
pa
r
a
mete
r
s
f
or
t
wo
wind
f
a
r
ms
de
pict
the
a
c
c
ur
a
te
topogr
a
phica
l
va
r
iety
o
f
loca
ti
ons
.
T
his
is
ve
r
y
we
ll
known
that
the
dis
tr
i
buti
on
of
wind
s
pe
e
d
tr
a
c
ks
W
e
ibul
l
pr
oba
bil
it
y
de
ns
it
y
f
unc
ti
on
(
P
DF
)
.
T
a
ble
3.
P
DF
pa
r
a
mete
r
s
of
wind
a
nd
s
ol
ar
P
V
pla
nts
W
in
d powe
r
ge
ne
r
a
ti
ng pla
nt
s
S
ol
a
r
P
V
pl
a
nt
W
in
d
f
a
r
m#
N
o. of
tu
r
bi
ne
s
R
a
te
d powe
r
,
(
M
W
)
W
e
ib
ul
l
P
D
F
pa
r
a
me
te
r
s
W
e
ib
ul
l
me
a
n,
R
a
te
d powe
r
,
(
M
W
)
L
ognor
ma
l
P
D
F
pa
r
a
me
te
r
s
L
ognor
ma
l
me
a
n,
1 (
bus
5)
25
75
=
9,
=
2
=
7.976 m/
s
50 (
bus
13)
=
6,
=
0.6
=
483
W
m
2
⁄
2 (
bus
11)
20
60
=
10,
=
2
=
8.862 m/
s
OR
3 (
bus
13)
17
51
=
9,
=
2
=
7.976 m/
s
W
in
d powe
r
ge
ne
r
a
ti
ng pla
nt
a
t
B
us
-
13 (
P
a
r
t
-
2)
(
a
)
(
b)
F
igur
e
1.
W
e
ibul
l
P
DF
f
or
wind
f
a
r
m
loca
ted
a
t
(
a
)
B
us
-
5,
(
b)
B
us
-
11
T
he
pos
s
ibi
li
ty
o
f
wind
ve
locity
mete
r
/s
e
c
pur
s
uing
W
e
ibul
l
P
DF
including
s
ha
pe
f
a
c
tor
(
)
a
nd
s
c
a
le
f
a
c
tor
(
)
c
a
n
be
c
a
lcula
ted
a
s
:
(
)
=
(
)
(
)
(
−
1
)
−
(
)
0
<
<
∞
(
9)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
Stochas
ti
c
r
e
ne
w
able
e
ne
r
gy
r
e
s
ou
r
c
e
s
int
e
gr
ated
multi
-
objec
ti
v
e
…
(
S
undar
am
B
.
P
andy
a
)
1587
m
e
a
n
of
W
e
ibul
l
dis
tr
ibut
ion
is
s
tate
d
a
s
:
=
∗
(
1
+
−
1
)
(
10)
whe
r
e
ga
mm
a
f
unc
ti
on
Γ
(
)
is
given
by
:
(
)
=
∫
−
−
1
∞
0
(
11
)
T
he
r
mal
unit
c
oupled
to
bus
number
-
13
of
I
E
E
E
-
30
bus
ne
twor
k
is
s
ubs
ti
tut
e
d
with
the
s
olar
p
lant.
T
he
ge
ne
r
a
ti
on
by
the
s
our
c
e
is
r
e
li
a
nt
on
s
olar
ir
r
a
dianc
e
(
)
that
tr
a
c
ks
logno
r
mal
P
DF
[
23]
.
T
he
pos
s
ibi
li
ty
of
the
s
olar
ir
r
a
dianc
e
(
)
pur
s
uing
lognor
mal
P
DF
ha
ving
mea
n
a
nd
s
tanda
r
d
de
viation
c
a
n
be
given
a
s
:
(
)
=
1
√
2
{
−
(
−
)
2
2
2
}
fo
r
>
0
(
12)
m
e
a
n
of
logno
r
mal
dis
tr
ibut
ion
c
a
n
be
g
iven
by:
=
(
+
2
2
⁄
)
(
13)
F
igur
e
2
s
pe
c
if
ies
a
dis
tr
ibut
ion
o
f
f
r
e
que
nc
y
a
nd
l
ognor
mal
f
it
ti
ng
of
s
olar
i
r
r
a
dianc
e
by
s
im
ulating
t
he
M
onte
C
a
r
lo
s
c
e
na
r
io,
taking
r
e
f
e
r
e
nc
e
va
lue
of
8000.
T
a
ble
3
s
tate
s
the
nomi
na
ted
W
e
ibul
l
a
nd
lognor
mal
P
DF
pa
r
a
mete
r
s
.
F
or
wind
a
nd
s
olar
P
V
powe
r
s
e
e
in
th
e
[
23]
.
F
igur
e
2.
L
ognor
mal
P
D
F
f
o
r
the
s
olar
plant
loca
ted
a
t
bus
-
13
3.
OB
JE
CT
I
VE
S
OF
OP
T
I
M
I
Z
AT
I
ON
T
he
opt
im
a
l
powe
r
f
low
c
ontains
the
objec
ti
ve
s
of
opti
mal
a
c
ti
ve
powe
r
dis
pa
tch
a
nd
opti
mal
r
e
a
c
ti
ve
powe
r
dis
pa
tch.
I
n
thi
s
s
e
c
ti
on,
the
objec
ti
ve
s
of
opti
mal
powe
r
f
low
with
wind
a
nd
s
olar
powe
r
p
lants
a
r
e
incor
por
a
ted
a
s
f
oll
ows
;
3.
1.
M
in
i
m
izat
ion
of
t
ot
al
f
u
e
l
c
os
t
in
c
lu
d
in
g
r
e
n
e
wabl
e
e
n
e
r
gy
r
e
s
ou
r
c
e
s
T
he
OPF
objec
ti
ve
is
modele
d
by
int
e
g
r
a
ti
ng
e
ve
r
y
c
os
t
f
unc
ti
on
that
a
r
e
dis
c
us
s
e
d
e
a
r
li
e
r
.
I
n
the
f
ir
s
t
objec
ti
ve
,
the
c
os
t
of
wind
a
nd
s
olar
powe
r
p
lants
a
r
e
a
dde
d
to
the
c
onve
nti
ona
l
the
r
mal
powe
r
plant
s
.
W
h
il
e
,
e
mi
s
s
ion
c
os
t
i
s
not
c
ons
ider
e
d.
Ne
xt
objec
ti
ve
f
unc
ti
on
is
f
or
mul
a
ted
by
including
e
mi
s
s
ion
c
os
t
to
a
na
lyze
the
c
ha
nge
in
ge
ne
r
a
ti
on
s
c
he
dule
a
t
the
ti
me
o
f
i
m
pos
it
ion
c
a
r
bon
tax.
Obje
c
ti
ve
1:
M
ini
mi
z
e
-
1
=
(
)
+
∑
[
,
(
,
)
+
,
(
,
−
,
)
+
,
(
,
−
=
1
,
)
]
+
∑
[
,
(
,
)
+
,
(
,
−
,
)
+
,
(
,
−
,
)
]
=
1
(
14)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1582
-
1599
1588
whe
r
e
a
nd
r
e
pr
e
s
e
nt
the
no.
of
wind
unit
s
a
nd
s
ol
a
r
P
V
unit
s
in
a
gr
id
,
r
e
s
pe
c
ti
ve
ly.
R
e
maining
c
os
t
p
a
r
a
mete
r
s
a
r
e
de
ter
mi
ne
d
f
r
om
(
1)
a
nd
(
3
)
to
(
8
)
.
3.
2.
M
in
i
m
izat
ion
of
t
ot
al
f
u
e
l
c
os
t
p
lu
s
c
ar
b
on
E
m
is
s
ion
t
ax
in
c
lu
d
in
g
r
e
n
e
wabl
e
e
n
e
r
gy
r
e
s
ou
r
c
e
s
Now
a
da
ys
,
s
ome
of
the
c
ountr
ies
a
r
e
p
r
e
s
s
ur
izing
the
whole
powe
r
ut
il
it
y
to
dim
ini
s
h
the
c
a
r
bon
dis
c
ha
r
ge
to
c
ont
r
ol
the
global
wa
r
mi
ng
[
23]
.
I
n
o
r
de
r
to
ins
pir
e
ve
ntur
e
in
c
lea
ne
r
wa
ys
of
powe
r
s
uc
h
a
s
s
olar
a
nd
wind,
c
a
r
bon
tax
(
)
is
c
ha
r
ge
d
on
dis
c
ha
r
ge
d
of
pe
r
unit
gr
e
e
nhous
e
s
mokes
.
T
he
e
mi
s
s
ion
c
os
t
(
in
$/hr
)
is
de
noted
by
(
2
)
:
E
mi
s
s
ion
c
os
t,
=
Obje
c
ti
ve
2
:
mi
nim
ize
-
2
=
1
+
(
15)
3.
3.
M
in
i
m
izat
ion
of
vo
lt
age
d
e
via
t
ion
wit
h
r
e
n
e
wabl
e
e
n
e
r
gy
r
e
s
ou
r
c
e
s
B
us
volt
a
ge
is
a
s
tandout
a
mong
the
highes
t
im
p
e
r
a
ti
ve
s
a
f
e
ty
a
nd
a
dmi
nis
tr
a
ti
on
s
upe
r
io
r
it
y
li
s
ts
.
T
he
e
nha
nc
ing
volt
a
ge
pr
of
i
le
will
be
a
c
quir
e
d
by
li
mi
ti
ng
the
de
viations
in
volt
a
ge
of
P
Q
bus
f
r
o
m
1.
0
f
or
e
ve
r
y
unit
.
T
he
ob
je
c
ti
ve
f
unc
ti
on
will
be
give
n
by
;
Obje
c
ti
ve
3:
m
ini
mi
z
e
-
3
=
∑
|
−
1
.
0
|
=
1
(
16)
whe
r
e
s
hows
the
no.
o
f
load
(
P
Q)
bus
e
s
,
s
hows
the
p.
u.
the
volt
a
ge
leve
l
of
th
bus
.
3.
4.
M
in
i
m
izat
ion
of
ac
t
ive
p
owe
r
los
s
e
s
wit
h
r
e
n
e
wabl
e
e
n
e
r
gy
r
e
s
ou
r
c
e
s
T
he
opti
mi
z
a
ti
on
of
r
e
a
l
powe
r
los
s
e
s
(
M
W
)
may
be
c
omput
e
d
by;
Obje
c
ti
ve
4:
m
ini
mi
z
e
-
4
=
=
∑
−
=
1
∑
=
1
(
17)
whe
r
e
a
nd
r
e
pr
e
s
e
nt
the
outpu
t
a
nd
dis
pa
tch
a
t
th
bus
;
s
hows
the
number
o
f
bus
e
s
.
3.
5.
E
n
h
an
c
e
m
e
n
t
of
volt
age
s
t
ab
il
it
y
in
d
e
x
c
on
t
ain
in
g
r
e
n
e
wabl
e
e
n
e
r
gy
r
e
s
ou
r
c
e
s
T
he
mos
t
s
igni
f
ica
nt
index,
whic
h
indi
c
a
tes
the
v
olt
a
ge
c
ons
tanc
y
mar
gin
of
e
a
c
h
bus
,
is
the
index
to
pr
e
s
e
r
ve
the
c
ons
tant
volt
a
ge
with
in
s
uit
a
ble
leve
l
unde
r
nor
mal
op
e
r
a
ti
ng
c
ondit
ions
.
L
-
inde
x
pr
ovides
a
s
c
a
lar
number
f
or
e
ve
r
y
P
Q
bus
.
index
l
ies
in
a
s
pa
n
of
‘
0
’
(
no
load)
a
nd
‘
1’
(
volt
a
ge
c
oll
a
p
s
e
)
.
T
he
a
mount
o
f
volt
a
ge
c
oll
a
ps
e
indi
c
a
tor
f
o
r
th
bus
is
obtaine
d
a
s
:
=
|
1
−
∑
=
1
|
∀
=
1
,
2
,
…
…
,
(
18)
=
−
[
1
]
−
1
[
2
]
(
19)
whe
r
e
1
a
nd
2
we
r
e
the
s
ub
-
matr
ice
s
of
.
T
he
obj
e
c
ti
ve
f
unc
ti
on
o
f
volt
a
ge
s
tabili
ty
e
nha
nc
e
ment
is
wr
it
ten
by
:
5
=
=
(
)
∀
=
1
,
2
,
…
…
,
(
20)
3.
6.
E
q
u
ali
t
y
c
on
s
t
r
ain
t
s
E
qua
li
ty
bounds
a
r
e
given
by
powe
r
f
low
e
qua
ti
on
s
whic
h
s
hows
that
both
r
e
a
l
a
nd
im
a
ginar
y
powe
r
pr
oduc
e
d
in
a
s
ys
tem
s
hould
ha
ve
s
a
ti
s
f
ied
the
load
de
mand
a
nd
los
s
e
s
in
the
s
ys
tem.
−
−
∑
[
(
)
+
(
)
]
=
0
∀
∈
=
1
(
21)
−
−
∑
[
(
)
−
(
)
]
=
0
∀
∈
=
1
(
22)
whe
r
e
=
−
,
is
the
v
a
r
ianc
e
in
pha
s
e
a
ngles
of
volt
a
ge
a
mong
bus
a
nd
bus
,
s
hows
ove
r
a
ll
bus
e
s
,
a
nd
a
r
e
r
e
a
l
a
nd
VA
R
powe
r
de
mand
r
e
s
pe
c
ti
ve
ly
a
t
th
bus
.
a
nd
a
r
e
r
e
a
l
a
nd
VA
R
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
Stochas
ti
c
r
e
ne
w
able
e
ne
r
gy
r
e
s
ou
r
c
e
s
int
e
gr
ated
multi
-
objec
ti
v
e
…
(
S
undar
am
B
.
P
andy
a
)
1589
output
s
r
e
s
pe
c
ti
ve
ly
of
th
bus
by
e
it
he
r
unit
(
ther
m
a
l
or
non
-
c
onve
nti
ona
l)
a
s
a
ppli
c
a
ble.
s
hows
the
c
onduc
tanc
e
a
nd
s
hows
the
s
us
c
e
ptanc
e
be
twe
e
n
bus
a
nd
bus
,
r
e
s
pe
c
ti
ve
ly.
3.
7.
I
n
e
q
u
ali
t
y
c
on
s
t
r
ain
t
s
I
ne
qua
li
ty
bounds
we
r
e
the
ope
r
a
ti
ona
l
bounda
r
ie
s
of
de
vice
s
a
nd
s
e
c
ur
it
y
boun
ds
of
li
ne
s
a
nd
P
Q
bus
e
s
.
I
n
(
23)
to
(
25)
s
igni
f
ies
the
r
e
a
l
powe
r
ou
tpu
t
bounds
of
ther
mal
,
wind
unit
s
a
nd
s
olar
unit
s
r
e
s
pe
c
ti
ve
ly.
Af
ter
wa
r
d,
(
26)
to
(
28
)
s
igni
f
ies
the
VA
R
powe
r
c
a
pa
c
it
y
of
ge
ne
r
a
ti
ng
unit
s
.
s
hows
the
ove
r
a
ll
volt
a
ge
c
ontr
ol
bus
e
s
.
In
(
29)
s
hows
bounds
on
the
volt
a
g
e
of
P
V
bus
e
s
,
whe
r
e
a
s
,
(
30)
s
hows
the
volt
a
ge
bounds
on
P
Q
bus
e
s
whe
r
e
is
the
number
o
f
P
Q
bus
e
s
.
L
ine
loading
bounda
r
ies
a
r
e
de
f
ined
us
ing
(
31
)
f
o
r
tot
a
l
number
of
li
ne
s
in
a
s
ys
tem.
G
e
ne
r
a
to
r
b
o
u
nd
s
:
⩽
⩽
,
=
1
,
…
.
.
,
(
23
)
ws
,
j
⩽
,
⩽
ws
,
j
,
=
1
,
…
.
.
,
(
24
)
ss,
k
⩽
,
⩽
ss,
k
,
=
1
,
…
.
.
,
(
25)
⩽
⩽
,
=
1
,
…
.
.
,
(
26)
ws
,
j
⩽
,
⩽
ws
,
j
,
=
1
,
…
.
.
,
(
27)
ss,
k
⩽
,
⩽
ss,
k
,
=
1
,
…
.
.
,
(
28
)
⩽
⩽
,
=
1
,
…
.
.
,
(
29)
S
e
cu
r
it
y
b
o
u
nd
s
:
⩽
⩽
,
=
1
,
…
.
.
,
(
30)
⩽
,
=
1
,
…
.
.
,
(
31)
4.
M
UL
T
I
-
OB
J
E
CT
I
VE
M
OT
H
F
L
AM
E
OP
T
I
M
I
Z
E
R
He
r
e
,
the
M
oth
F
lame
Optim
iza
ti
on
(
M
F
O)
a
lgo
r
it
hm
is
a
dopted
to
s
olve
the
mul
ti
-
objec
ti
ve
opti
mal
powe
r
f
low
p
r
oblem.
4.
1.
I
n
s
p
irat
ion
I
t
is
ba
s
ica
ll
y
ins
pir
e
d
f
r
om
the
mot
hs
in
na
tu
r
e
.
T
he
na
vigation
of
the
mot
hs
a
t
night
is
a
li
t
tl
e
bit
int
e
r
e
s
ti
ng
by
us
ing
the
moonl
ight
.
T
he
tr
a
ns
ve
r
s
e
or
ienta
ti
on
of
mec
ha
nis
m
is
uti
li
z
e
d
by
the
mot
hs
f
or
na
vigation
a
s
s
hown
in
F
igu
r
e
3
.
T
he
mot
h
f
li
e
s
by
ke
e
ping
up
s
ome
po
int
c
onc
e
r
ning
the
moon
,
the
vit
a
l
a
nd
viable
mec
ha
nics
of
long
tr
a
ve
li
ng
long
s
e
pa
r
a
ti
ons
.
B
e
that
a
s
it
may,
r
e
ga
r
dles
s
of
the
tr
a
ns
ve
r
s
e
or
ienta
ti
on,
mot
hs
f
ly
s
pir
a
ll
y
a
r
ound
the
l
ight
s
.
T
his
is
a
dir
e
c
t
r
e
s
ult
of
the
inade
qua
c
y
of
the
t
r
a
ns
ve
r
s
e
int
r
oduc
ti
on,
in
whic
h
i
t
is
va
luable
f
or
s
uf
f
e
r
ing
i
n
a
l
inea
r
wa
y
a
t
the
ti
me
of
r
e
mot
e
loca
ti
on
li
ght
s
o
ur
c
e
.
E
xa
c
tl
y
whe
n
mot
hs
ge
t
a
n
a
r
ti
f
icia
l
li
ght
s
our
c
e
,
th
e
y
do
e
f
f
or
ts
to
ke
e
p
up
a
c
ompar
a
ti
ve
e
dge
to
a
li
g
ht
s
our
c
e
to
s
oa
r
in
a
li
ne
a
r
wa
y.
M
e
a
nwhile,
thi
s
li
ght
is
to
a
n
e
xtr
a
or
dinar
y
de
gr
e
e
c
los
e
s
tood
out
f
r
om
th
e
moon,
ne
ve
r
thele
s
s
,
ke
e
ping
up
th
e
s
a
me
point
a
t
a
li
ght
s
our
c
e
c
r
e
a
tes
a
va
in
or
letha
l
winding
to
s
a
il
r
oute
f
or
mot
hs
.
F
igur
e
3.
T
r
a
ns
ve
r
s
e
o
r
ienta
ti
on
[
24
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1582
-
1599
1590
4.
2.
M
F
O
algorit
h
m
I
n
M
F
O
a
l
g
o
r
i
t
h
m
,
t
h
e
s
o
l
u
t
i
o
n
s
o
f
p
r
o
b
l
e
m
s
a
r
e
g
i
v
e
n
b
y
m
o
t
h
s
a
n
d
t
h
e
v
a
r
i
a
b
l
e
s
a
r
e
r
e
p
r
e
s
e
n
t
e
d
b
y
t
h
e
p
o
s
i
t
i
o
n
s
o
f
m
o
t
h
s
i
n
a
s
p
a
c
e
,
f
l
y
i
n
g
i
n
1
D
,
2
D
,
3
D
o
r
a
n
y
o
t
h
e
r
d
i
m
e
n
s
i
o
n
a
l
s
p
a
c
e
b
y
v
a
r
y
i
n
g
i
t
s
p
o
s
i
t
i
o
n
v
e
c
t
o
r
s
.
a.
I
nit
ialize
pos
it
ion
ve
c
tor
of
mot
hs
W
it
h
‘
’
s
hows
the
ove
r
a
ll
va
r
iable
s
a
nd‘
’
s
hows
th
e
dim
e
ns
ions
,
the
pos
it
ion
mat
r
ix
is
g
iven
by;
=
[
1
,
1
1
,
2
2
,
1
2
,
2
⋯
1
,
⋯
2
,
⋮
⋮
,
1
1
,
1
⋮
⋮
⋯
,
]
(3
2
)
b.
I
nit
ialize
pos
it
ion
ve
c
tor
of
f
lame
s
A
nother
va
luable
matr
ix
is
the
pos
it
ion
ve
c
tor
mat
r
ix
of
f
lame
s
whic
h
is
given
by;
=
[
1
,
1
1
,
2
2
,
1
2
,
2
⋯
1
,
⋯
2
,
⋮
⋮
,
1
1
,
1
⋮
⋮
⋯
,
]
(
33)
whe
r
e
the
‘
’
s
hows
ove
r
a
ll
va
r
iable
s
a
nd
the
‘
’
s
ho
ws
ove
r
a
ll
dim
e
ns
ions
.
c.
F
it
ne
s
s
e
va
luation
F
or
the
f
indi
ng
the
f
i
tnes
s
ther
e
is
a
n
a
r
r
a
y
of
the
mot
hs
whic
h
is
given
by
:
=
[
1
2
⋮
]
(
34)
whe
r
e
‘
’
g
ives
the
ove
r
a
ll
va
lue
o
f
mot
hs
.
I
t
m
a
y
be
s
e
e
n
that
the
d
im
e
ns
ions
of
the
pos
it
ion
ve
c
tor
s
of
mot
hs
a
nd
f
lame
s
a
r
e
the
s
a
me.
S
o
the
ve
c
tor
f
o
r
s
a
ving
the
e
quiv
a
lent
f
it
ne
s
s
va
lue
is
given
by
:
=
[
1
2
⋮
]
(
35)
T
he
M
F
O
a
ppr
oa
c
h
is
ha
ving
the
th
r
e
e
main
f
unc
ti
ons
f
or
f
indi
ng
the
global
r
e
s
ult
s
a
s
:
=
(
,
,
)
(3
6
)
s
how
the
f
unc
ti
on
f
or
ge
ne
r
a
ti
ng
the
c
us
tom
popu
l
a
ti
ons
with
the
c
or
r
e
s
po
nding
f
it
ne
s
s
whic
h
is
give
n
by
:
:
∅
→
{
,
}
(3
7
)
s
im
il
a
r
ly,
f
unc
ti
on
is
a
ls
o
the
main
f
unc
ti
on
,
a
nd
g
e
tt
ing
f
r
om
the
mat
r
ix
o
f
e
ve
ntually
upda
ted
a
s
:
:
→
(3
8
)
a
ls
o,
ther
e
is
a
nother
ter
mi
na
ti
on
c
r
it
e
r
ion
f
or
f
unc
ti
on
f
or
the
c
ondit
ion
,
s
a
ti
s
f
a
c
ti
on
mea
ns
if
s
a
ti
s
f
ied
than
tr
ue
other
wis
e
f
a
ls
e
.
:
→
{
,
}
(3
9
)
F
ir
s
tl
y,
the
in
it
ializa
ti
on
o
f
the
f
unc
ti
o
ns
,
the
‘
’
f
un
c
ti
on
is
e
va
luate
d
un
ti
l
the
s
a
ti
s
f
a
c
ti
on
s
tanda
r
ds
of
the
‘
’
f
unc
ti
on
a
r
e
not
f
u
lf
il
led
.
Now
t
he
mot
h
is
modi
f
ied
a
c
c
or
ding
to
the
f
la
me,
s
o
the
mathe
matica
l
model
of
the
tr
a
ns
ve
r
s
e
or
ienta
ti
ons
of
thi
s
be
ha
vior
is
given
by
the
e
qua
ti
on
given
:
=
(
,
)
(
40
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
Stochas
ti
c
r
e
ne
w
able
e
ne
r
gy
r
e
s
ou
r
c
e
s
int
e
gr
ated
multi
-
objec
ti
v
e
…
(
S
undar
am
B
.
P
andy
a
)
1591
whe
r
e
indi
c
a
te
the
ℎ
mot
h,
indi
c
a
tes
the
ℎ
mot
h
o
f
th
e
s
pir
a
l
f
unc
ti
on
.
He
r
e
,
the
mot
ion
of
mot
h
is
logar
it
hmi
c
s
pir
a
l
whos
e
s
tar
t
ing
po
int
s
hould
be
t
he
mot
h,
the
f
inal
point
s
h
ould
be
f
lame
a
nd
a
r
a
n
ge
doe
s
not
s
ur
pa
s
s
the
e
xplor
a
ti
on
a
r
e
a
.
S
o
,
the
po
int
o
f
th
e
M
F
O
a
ppr
o
a
c
h
in
loga
r
it
hmi
c
s
c
a
le
given
a
s
:
(
,
)
=
.
.
(
2
)
+
(
41
)
w
he
r
e
is
the
r
e
mo
tene
s
s
of
ℎ
mot
h
f
r
om
ℎ
f
lame
.
“
"
is
t
he
c
ons
tant
indi
c
a
ti
ng
the
pr
o
f
il
e
of
the
log
s
pir
a
l
a
nd
is
the
r
a
ndom
number
in
the
r
a
nge
o
f
[
-
1,
1]
.
T
he
c
a
lcula
ti
on
of
dis
tanc
e
c
a
n
be
given
a
s
:
=
|
−
|
(
42
)
w
he
r
e
is
the
r
e
mot
e
ne
s
s
of
ℎ
mot
h
f
r
om
the
ℎ
mot
h
,
s
how
s
the
ℎ
f
lame
a
nd
s
hows
the
ℎ
mot
h.
d.
Ada
pti
ve
na
tur
e
of
r
e
duc
ing
the
number
o
f
f
lame
s
F
ur
ther
,
the
number
s
of
f
lame
s
a
r
e
r
e
duc
e
d
while
the
number
of
i
ter
a
ti
ons
is
incr
e
a
s
ing
whic
h
is
given
b
y
:
=
(
−
∗
−
1
)
(
43
)
4.
3.
F
or
m
u
lat
io
n
of
m
u
lt
i
-
o
b
j
e
c
t
ive
f
u
n
c
t
ion
wit
h
t
h
e
n
on
-
s
or
t
in
g
M
F
O
a
lgorit
h
m
T
he
mul
ti
-
objec
ti
ve
opti
mi
z
a
ti
on
is
s
ue
s
c
ompr
is
ing
the
a
mount
of
c
las
hing
ob
jec
ti
ve
f
unc
ti
ons
a
r
e
opti
mi
z
e
d
s
i
mul
tane
ous
ly
while
a
t
the
s
a
me
ti
me
f
ul
f
il
li
ng
a
ll
the
c
ons
tr
a
int
s
.
T
he
r
e
a
r
e
the
number
of
opti
mi
z
a
ti
on
methods
that
a
r
e
uti
li
z
e
d
pr
ior
t
o
the
a
r
ti
c
le
to
e
xplain
the
mul
ti
-
objec
ti
ve
OPF
pr
oblem.
S
tar
ti
ng
with
thos
e
wor
ks
o
f
li
ter
a
tu
r
e
,
it
is
s
e
e
n
that
nu
mer
ous
r
e
s
e
a
r
c
he
r
s
ha
ve
c
ha
nge
d
o
ve
r
that
mul
ti
-
objec
ti
ve
is
s
ue
unde
r
a
s
ingl
e
objec
ti
ve
is
s
ue
uti
li
z
ing
the
s
tr
a
ight
mi
xtu
r
e
of
the
two
c
las
hin
g
objec
ti
ve
wor
ks
towa
r
d
a
pplyi
ng
the
we
ight
ing
c
omponents
a
ppr
oa
c
h.
F
ur
ther
mo
r
e
,
the
f
iner
r
oute
f
or
f
indi
ng
the
r
e
s
ult
of
the
mul
ti
-
objec
ti
ve
is
s
ue
may
be
to
e
s
ti
mate
the
s
e
t
of
idea
l
tr
a
de
of
f
s
wha
t's
mo
r
e
dis
c
ove
r
ing
the
be
s
t
c
ompr
omi
s
ing
s
olut
ions
a
r
ound
e
ve
r
y
la
s
t
one
of
pa
r
e
to
f
r
onts
.
T
he
mul
ti
-
objec
ti
ve
opti
mi
z
a
ti
on
pr
oblem
ne
e
ds
to
be
f
igur
e
d
a
s
:
(
)
,
=
1
,
2
,
3
…
…
…
…
.
,
(
44)
(
)
=
0
,
=
1
,
2
,
3
…
…
…
.
.
(
45)
ℎ
(
)
≤
0
,
=
1
,
2
,
3
…
…
…
…
.
(
46)
w
he
r
e
s
hows
the
ℎ
objec
ti
ve
f
unc
ti
on;
r
e
pr
e
s
e
nts
the
de
c
is
ion
ve
c
tor
s
;
s
tands
f
or
tot
a
l
obje
c
ti
ve
f
unc
ti
on;
s
tands
f
or
the
tot
a
l
powe
r
f
low
boun
ds
a
nd
s
tands
f
or
tot
a
l
phys
ica
l
bounds
on
de
v
ice
s
.
I
n
the
mul
t
i
-
objec
ti
ve
opti
mi
z
a
ti
on,
the
non
-
dom
inate
d
s
or
ti
ng
tec
hnique
c
a
n
ha
ve
two
p
r
o
ba
bil
it
ies
,
one
domi
na
ti
ng
the
othe
r
objec
ti
ve
s
o
r
no
o
ne
do
mi
na
ted
the
o
ther
.
I
n
other
wor
ds
,
without
los
ing
g
e
ne
r
a
li
ty;
1
domi
na
tes
the
2
only
if
the
given
two
c
r
it
e
r
ia
a
r
e
f
u
lf
il
led
:
∀
∈
{
1
,
2
,
3
…
…
}
∶
(
1
)
≤
(
2
)
(
47)
∃
∈
{
1
,
2
,
3
…
…
}
∶
(
1
)
≤
(
2
)
(
48)
I
n
the
e
ve
nt
that
a
ny
of
the
a
bove
c
ondit
ions
is
dis
r
e
ga
r
de
d,
a
t
that
point
,
a
r
r
a
nge
ment
1
doe
s
not
r
u
le
2
.
T
he
a
r
r
a
nge
ment
1
is
known
a
s
the
non
-
c
omm
a
nde
d
a
r
r
a
nge
ment,
i
f
1
ove
r
whe
lm
s
the
2
a
r
r
a
nge
m
e
nts
.
F
lowc
ha
r
t
of
given
M
F
O
a
ppr
oa
c
h
f
or
r
e
s
olv
ing
O
P
F
is
s
ue
is
s
hown
in
F
igu
r
e
4.
T
he
method
o
f
the
s
ugge
s
ted
non
-
s
or
ti
ng
M
F
O
a
ppr
oa
c
h
ha
s
a
ppe
a
r
e
d
in
a
lgor
it
hm
-
1.
I
ni
ti
a
ll
y,
int
r
oduc
e
pa
r
a
mete
r
s
,
f
or
e
xa
mpl
e
,
population
s
ize
,
a
nd
s
toppi
ng
v
a
lue
,
he
r
e
it
is
the
mos
t
e
xtr
e
me
no
.
of
ge
ne
r
a
ti
on
to
pr
oc
e
e
ds
the
method.
B
e
s
ides
,
a
r
a
ndom
pa
r
e
nt
population
in
pos
s
ibl
e
s
pa
c
e
S
is
pr
oduc
e
d
a
nd
e
ve
r
y
objec
ti
ve
f
unc
ti
on
of
the
objec
ti
ve
ve
c
tor
F
f
or
is
a
s
s
e
s
s
e
d.
Af
ter
wa
r
d,
non
-
domi
na
ted
s
or
ti
ng
a
long
with
c
r
owding
dis
tanc
e
c
a
lcula
ti
on
a
s
c
lar
i
f
ied
in
t
a
ble
[
25]
a
nd
is
im
pleme
nted
on
.
S
ubs
e
que
ntl
y,
th
e
M
F
O
a
ppr
oa
c
h
is
uti
li
z
e
d
to
make
the
f
r
e
s
h
population
,
a
nd
then
it
is
c
onve
r
ge
d
with
to
s
ha
pe
the
blende
d
population
.
T
his
is
a
r
r
a
nge
d
in
view
of
e
li
ti
s
m
no
n
-
domi
na
ti
on,
a
nd
in
l
ight
of
the
f
igur
e
d
e
s
ti
matio
ns
of
c
r
owding
dis
tanc
e
(
C
D)
a
nd
non
-
domi
na
ti
on
r
a
nk
(
ND
R
)
,
the
be
s
t
a
r
r
a
nge
ments
a
r
e
r
e
f
r
e
s
he
d
to
f
r
a
me
a
nother
pa
r
e
nt
population
.
T
his
p
r
oc
e
dur
e
is
r
e
pe
a
t
e
d
unti
l
the
highes
t
no
.
of
ge
ne
r
a
ti
ons
(
c
yc
les
)
a
r
e
c
ome
to.
I
t
mus
t
be
not
ice
d
that
a
s
im
il
a
r
a
ppr
oa
c
h
c
a
n
be
uti
li
z
e
d
a
long
with
e
nd
c
r
it
e
r
ia
s
e
t
a
c
c
or
ding
to
the
tot
a
l
e
va
luations
of
the
f
unc
ti
on
.
Algor
it
hm
1
.
Non
-
domi
na
ted
mot
h
f
lam
e
opti
mi
z
a
ti
on
[
25]
Evaluation Warning : The document was created with Spire.PDF for Python.