Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
10
,
No.
4
,
A
ugus
t
2020
,
pp.
34
12
~
34
22
IS
S
N:
20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v
10
i
4
.
pp3412
-
34
22
3412
Journ
al h
om
e
page
:
http:
//
ij
ece.i
aesc
or
e.c
om/i
nd
ex
.ph
p/IJ
ECE
Activ
e pow
er oup
tut opti
mizati
on
for win
d farms
and the
rm
al
un
its by m
ini
mizin
g t
he
operatin
g cost
and emissi
on
s
Na
z
ha C
herk
aoui,
Ab
del
az
i
z
Bel
fq
ih, Fa
is
sa
l E
l M
aria
m
i
, Jam
al Bouk
heroua
a,
Abd
el
maj
id Be
r
dai
La
bora
tor
y
of
Elec
tr
ic
a
l
S
y
s
te
m
s
and
En
erg
y
,
Nat
i
onal
High
er
Sch
ool
of El
ec
tr
ic
i
t
y
and
Me
cha
n
ic
s
(ENSEM),
Morocc
o
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
J
ul
18
, 2
019
Re
vised
Jan
3
0
,
20
20
Accepte
d
Fe
b
1
0
, 202
0
In
recent
y
e
ars,
m
an
y
works
ha
ve
bee
n
done
in
orde
r
to
d
iscuss
ec
onom
ic
dispat
ch
in
whi
c
h
wind
far
m
s
ar
e
install
ed
in
elec
tr
ic
a
l
grids
in
addi
ti
on
to
conve
nt
iona
l
po
wer
pla
n
ts.
Nev
e
rthe
l
ess,
th
e
emi
ss
ions
ca
used
b
y
foss
il
fue
ls
have
not
bee
n
c
onsidere
d
in
m
ost
of
the
studie
s
done
bef
ore
.
In
f
ac
t
,
the
rm
al
power
pla
nts
produc
e
important
quant
ities
of
e
m
issions
for
inst
anc
e
,
ca
rbo
n
dioxi
de
(CO
2
)
a
nd
sulphur
dioxide
(SO
2
)
tha
t
ar
e
har
m
ful
to
the
e
nvironment.
Thi
s
pap
er
pre
s
e
nts
an
opt
imizati
on
al
gor
it
hm
wit
h
the
objecti
v
e
t
o
m
ini
m
iz
e
the
emiss
ion
l
e
vel
s
and
the
pr
oduct
ion
cost
.
A
compari
son
of
the
result
s
obta
in
ed
with
d
iffe
ren
t
opt
imiz
at
ion
m
et
hods
l
ea
ds
us
to
op
t
f
or
the
g
r
e
y
wolf
opti
m
izer
t
ec
hniqu
e
(GW
O)
to
use
for
solv
ing
the
propose
d
objecti
v
e
func
ti
on
.
First,
the
m
et
hod
use
d
to
esti
m
ate
th
e
wind
power
o
f
a
pla
n
t
is
pre
sente
d
.
Seco
nd,
the
ec
onom
ic
dispatch
m
odel
s
for
wind
and
the
rm
al
gene
ra
tors
are
pre
sente
d
fol
lo
wed
b
y
the
e
m
ission
dispat
ch
m
odel
for
the
the
rm
a
l
un
it
s.
Th
en,
th
e
p
roposed
obje
c
tive
func
ti
o
n
is
form
ula
te
d.
Final
l
y
,
th
e
sim
ula
ti
on
resul
ts
obta
in
ed
b
y
ap
pl
y
ing
the
GW
O
and
othe
r
known opt
imizat
ion
t
ec
hniqu
es
a
re
an
aly
sed
and
compare
d.
Ke
yw
or
d
s
:
Eco
no
m
ic
d
isp
at
ch
Em
issi
on
level
s
Pr
od
uctio
n
c
ost
Ther
m
al
p
ower
p
la
nts
W
i
nd
far
m
s
Copyright
©
202
0
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Nazh
a
Che
rk
a
ou
i,
Lab
or
at
ory
of
Ele
ct
rical
System
s an
d Ene
r
gy
,
Nati
on
al
Highe
r
Sc
hool
of Ele
ct
rici
ty
an
d
Me
chan
ic
s
,
El Jadida
Roa
d, km
7
, Casa
bl
anca,
M
orocc
o.
Em
a
il
:
nazh
a.c
herka
ou
i@e
nsem
.ac.
m
a
1.
INTROD
U
CTION
Re
centl
y,
the
i
nteg
rati
on
of
t
he
wind
e
nerg
y
into
el
ect
rica
l
gr
i
ds
has
i
ncrea
sed
si
gn
i
ficantl
y
beca
us
e
it
is
cl
ean
and
cheap
i
n
c
om
par
iso
n
to
c
onve
ntion
al
e
nerg
y
so
urces.
T
he
refor
e
,
in
case
of
i
ntegrat
ion
of
wi
nd
far
m
s
(
W
F
)
wi
th
an
e
xisti
ng
gr
i
d
with
c
onve
ntion
al
s
ource
s,
it
is
necessar
y
to
ta
ke
al
so
i
nto
acc
ount
the
wind
powe
r
pla
nts
(
WPP)
in
t
he
e
conom
ic
disp
at
ch
(E
D)
.
I
n
li
te
ratur
e,
m
any
works
ha
ve
be
en
do
ne
in
order
t
o
discuss di
verse
m
e
tho
ds
of
ec
onom
ic
d
ispatc
h
in
which
WFs are i
nteg
rated
into p
ow
e
r
sys
tem
s.
In
fact,
i
n
[1
]
,
an
ec
onom
ic
disp
at
c
h
f
or
c
om
bin
ed
wind
therm
al
syst
e
m
s
is
reali
zed
us
in
g
flo
wer
po
ll
inati
on
al
gorithm
(F
P
A).
Be
sides,
t
he
a
uthors
in
[
2],
pr
ese
nt
a
ne
w
appr
oach
f
or
E
D
pro
blem
s
in
w
hich
WFs
a
re
instal
le
d
in
the n
et
w
ork
us
i
ng
pa
rtic
le
swar
m
op
ti
m
iz
at
ion
(P
SO)
te
chn
i
que.
Al
so
,
the
a
uthor
s
in
[
3
]
,
discuss
a
n
eco
no
m
ic
load
disp
at
ch
(E
LD
)
in
w
hich
so
la
r
and
wind
unit
s
are
include
d
in
ad
diti
on
to
therm
al
un
it
s.
To res
ol
ve
the
EL
D,
t
he
f
ire
f
ly
algorit
hm
o
pti
m
iz
at
io
n
te
ch
nique is
us
e
d.
Nev
e
rtheless
,
al
tho
ug
h
the
f
act
t
hat
the
wind
ene
rg
y
i
s
cl
ean
,
the
therm
al
po
we
r
so
urces
are
consi
der
e
d
as
po
ll
utio
n
s
our
ces.
As
a
res
ult,
eve
n
the
e
m
issi
on
s
ha
ve
to
be
ta
ke
n
into
acco
unt
durin
g
the
plan
ning
sta
ge.
I
n
this
pa
per,
we
pro
pos
e
an
obj
ect
ive
functi
on
that
al
lows
getti
ng
th
e
op
ti
m
a
l
real
powe
r
gen
e
rati
on
of
t
he
un
it
s
w
hich
co
ns
ist
of
t
herm
al
gen
erat
or
s
an
d
WPP
s
.
T
he
pro
posed
ob
je
ct
ive
f
un
ct
io
n
aim
s
to
re
du
ce
both
the
pro
duct
ion
cost
an
d
em
issi
on
s
sim
ultaneou
sly
.
In
this
work,
the
pote
ntial
power
of
a
wind
far
m
is
con
sid
ered
a
s
a
co
ns
t
raint
of
the
pro
po
s
ed
obj
ect
iv
e
functi
on
s
o
that
to
no
t
e
xce
ed
the
a
vaila
bl
e
wi
nd
powe
r.
The
grey
wo
lf
op
ti
m
iz
er
(GWO
)
m
et
ho
d
is
util
iz
ed
in
order
to
so
lve
the
pro
posed
op
ti
m
iz
at
ion
al
gorithm
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Act
iv
e p
ower
oup
t
ut opti
miz
ation
f
or
wi
nd f
arms
and t
her
m
al unit
s
by min
imizi
ng
…
(
Na
zh
a C
her
ka
oui
)
3413
This
pap
e
r
is
orga
nized
as
f
ollows:
first,
t
he
prob
a
bi
li
ty
de
ns
it
y
functi
on
(pd
f)
of
t
he
w
ei
bull
distrib
ution
is
pr
ese
nted
f
ol
lowe
d
by
the
m
et
ho
d
us
e
d
to
est
i
m
at
e
t
he
wind
pow
er
of
a
sit
e.
Seco
nd,
the
eco
no
m
ic
disp
at
c
h
m
od
el
fo
r
the
rm
al
conve
ntion
al
a
nd
wind
unit
s
is
descr
ibe
d.
Thir
d,
the
em
i
ssio
n
disp
at
c
h
m
od
el
fo
r
t
her
m
al
un
it
s
is
pr
ese
nte
d.
T
he
n,
the
pr
opos
e
d
obj
ect
ive
f
unct
ion
is
form
ulate
d.
Finall
y,
the case st
ud
y
and the
sim
ulatio
n res
ults are
giv
e
n.
2.
WIN
D
P
OWE
R
EST
I
MA
TI
ON
The
probabil
it
y
den
sit
y
f
un
ct
ion
(pdf)
of
t
he
weib
ull
distri
bu
ti
on
is
us
e
d
to
es
tim
at
e
the
wind
s
peed
in an
y
place.
T
he pr
obabili
ty
d
en
sit
y functi
on
f
v
(
v)
of the
w
i
nd spee
d i
s exp
resse
d
as
f
ollo
ws
[4]
:
f
v
(
v
)
=
(
k
c
)
(
v
c
)
(
k
−
1
)
e
−
(
v
c
)
k
, 0 <
v
<
∞
(1)
wh
e
re:
c
: i
s the scale
pa
ram
et
er
k
: i
s the shape
param
et
er
v
: i
s the
wind s
pe
ed
The
m
et
ho
d
ci
te
d
in
[5
]
is
use
d
f
or
m
od
el
li
ng
the
wind
ge
ner
at
or
c
urve
,
as
it
is
show
n
in
Fig
ur
e
1.
This
m
et
ho
d
is
ch
os
en
bec
aus
e
i
t
is
consi
dered
to
be
the
m
os
t
sim
plifie
d
m
et
ho
d
t
o
sim
ulate
the p
owe
r
outp
ut
of a
wind
gen
e
rator [
6]. The
powe
r prov
i
de
d by a
wind tu
r
bin
e ca
n be
re
presente
d
as
[5]:
w
=
{
0
w
r
v
−
v
c
v
r
−
v
c
w
r
v
<
v
c
, v >
v
f
(2)
v
c
<
v
<
v
r
v
r
≤
v
≤
v
f
wh
e
re:
v
c
: i
s the c
ut
-
in
wind s
pee
d of
t
he win
d
tu
r
bine
v
f
: i
s the c
ut
-
off win
d
s
pee
d of
t
he win
d
tu
r
bine
v
r
: i
s the r
at
e
d w
ind
sp
ee
d of t
he
w
in
d
t
urbine
Figure
1. P
ow
e
r
c
urve
of a
wind tu
rb
i
ne
[
7]
The
tran
sf
or
m
at
ion
of
the
pr
ob
a
bili
ty
distribu
ti
on
f
unct
io
n
pdf
of
the
wi
nd
s
pee
d
to
th
e
wind
powe
r
can
be
e
xpress
ed
as
foll
ows [4]
:
f
w
(
w
)
=
{
1
−
e
−
(
v
c
c
)
k
+
e
−
(
v
f
c
)
k
kl
v
c
w
r
c
(
(
1
+
ρ
l
)
v
c
c
)
(
k
−
1
)
−
e
−
(
v
r
c
)
k
−
e
−
(
v
f
c
)
k
e
−
(
(
1
+
ρ
l
)
v
c
c
)
k
v
<
v
c
, v >
v
f
(3)
v
c
<
v
<
v
r
v
r
≤
v
≤
v
f
wh
e
re:
ρ
=
w
w
r
an
d
l
=
v
r
−
v
c
v
c
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
10
, No
.
4
,
A
ugus
t
2020
:
3
412
-
3
422
3414
3.
WIN
D
P
OWE
R
P
OTE
NTI
AL OF
A SIT
E
The win
d p
ower
po
te
ntial
is g
ive
n by [
8]:
P
(
v
)
=
1
2
ρ
Γ
(
1
+
3
k
)
c
3
A
(4)
wh
e
re
:
A
: Swe
pt ar
ea
of
the
ro
t
or
bla
de
s in
m
2
ρ
: Air
de
ns
it
y (kg/
m
3
)
an
d
is
calc
ul
at
ed
as
fo
ll
ows
:
ρ
=
ρ
0
-
1,1
94
x
10
−
4
x
H
m
(
5)
with:
ρ
0
= 1
,
225 k
g/
m
3
is t
he
air
de
ns
it
y value
at s
ea le
vel a
nd
H
m
is t
he
sit
e ele
vati
on in
m
.
I
n t
his
wor
k,
it
is co
ns
ide
red that
H
m
is eq
ual to 343m
.
Γ
: gam
m
a functi
on
The
sta
nd
a
r
d g
a
m
m
a fu
nctio
n i
s expr
e
ssed
by
[9]
:
Γ
(
x
)
=
∫
t
x
−
1
∞
0
exp
(
−
t
)
dt
(6)
4.
ECONO
MIC
DIS
P
ATC
H
The
go
al
of
th
e
eco
no
m
ic
disp
at
ch
is
t
o
m
i
nim
iz
e
the
ope
rati
ng
c
os
t
of
gen
e
rato
rs
c
ontribu
ti
ng
t
o
pro
vid
e
t
he
loa
d
dem
and
.
In
this
stu
dy,
t
he
valve
point
e
ffec
t
is
ta
ken
int
o
acc
ount
i
n
th
e
eco
no
m
ic
disp
at
c
h.
Hen
ce
, th
e
ope
rati
ng co
st
of e
ach c
onve
ntio
na
l gen
e
rato
r
ca
n be
giv
e
n by the
fo
ll
owin
g [
10
]
:
C
i
=
a
i
p
i
2
+
b
i
p
i
+
c
i
+
|
sin
(
f
i
(
p
i
min
−
p
i
)
|
(7)
wh
e
re:
p
i
: i
s the
gen
e
rati
on outp
ut
of g
e
ner
at
or
i
a
i
,
b
i
,
c
i
: are the
co
st
c
oeffici
ents
of
ge
ner
at
or
i
e
i
an
d
f
i
: are the
co
st
c
oeffici
ents
of
ge
ner
at
or
i
re
flect
ing
valve
poi
nt effect
s
The
ope
rati
ng
cost
of
the
WPP
is
the
su
m
of
three
com
pone
nts
w
hich
are
the
direct
co
st,
the
pen
al
ty
cost
and
the
r
eserv
e
c
os
t.
T
hese
three
c
ost
s
are
exp
la
ine
d
in
detai
l
belo
w
.
The
syst
em
op
erato
r
m
us
t
pay
a
wind
powe
r
gen
e
rati
on
c
ost
C
w
i
to
the
wind
pro
d
uce
r
wh
ic
h
m
ay
no
t
exi
st
if
the
wind
powe
r
pla
nts
a
re
owne
d by
the
powe
r o
per
at
or
[4
]
.
C
w
i
=
d
i
w
i
(8)
wh
e
re:
w
i
: i
s the sc
hedul
ed win
d powe
r
f
r
om
the w
in
d p
ow
e
r ge
ner
at
or i
d
i
: i
s the
direct c
os
t c
oeffici
ent
of the
wind
po
wer ge
ner
a
t
or i
If
t
he
sc
he
duli
ng
of
the
wind
po
wer
is
l
ess
tha
n
it
w
ou
l
d
be
due
t
o
a
n
unde
rest
i
m
ation
of
the av
ai
la
ble wi
nd
powe
r, a
pe
nalty
co
st
C
p
will
ap
pea
r
t
hat ca
n be e
xpresse
d as [
4]:
C
p
i
=
k
p
i
∫
(
w
−
w
i
)
f
w
(
w
)
dw
w
r
i
w
i
(9)
wh
e
re:
k
p
i
: i
s the
pen
al
ty
cost c
oeffici
ent for
t
he win
d p
ow
e
r ge
ner
at
or
i
f
w
(
w
)
: i
s the
weib
ull distrib
utio
n functi
on for wi
nd
powe
r
w
r
i
: i
s the r
at
e
d w
ind
powe
r fr
om
the w
in
d p
ower
g
e
ner
at
or i
The
pen
al
ty
cost
m
ay
be
e
qu
al
to
ze
r
o
if
the
wi
nd
f
ar
m
is
ow
ned
by
the
po
w
er
syst
em
.
If
t
he
sc
he
du
li
ng
of
t
he
wind
powe
r
is
m
or
e
than
it
w
ould
be
du
e
to
an
overesti
m
at
ion
of
the
a
vaila
bl
e
wi
nd
powe
r,
a
r
ese
rve cost
C
r
i
will
app
ear that ca
n be
giv
e
n by [
4]:
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Act
iv
e p
ower
oup
t
ut opti
miz
ation
f
or
wi
nd f
arms
and t
her
m
al unit
s
by min
imizi
ng
…
(
Na
zh
a C
her
ka
oui
)
3415
C
r
i
=
k
r
i
∫
(
w
i
−
w
)
f
w
w
i
0
(
w
)
dw
(10)
wh
e
re:
k
r
i
: i
s the r
e
ser
ve c
os
t c
oeffici
ent of the
w
i
nd po
wer ge
ner
at
or i
The
t
otal
opera
ti
ng
c
os
t i
s e
xpresse
d
as
f
ollo
ws:
C
(
X
)
=
∑
C
i
+
∑
C
w
i
n2
i
=
1
n1
i
=
1
+
∑
C
p
i
n2
i
=
1
+
∑
C
r
i
n2
i
=
1
(11)
wh
e
re:
X
:
th
e
posit
io
n o
f
eac
h partic
le
hav
i
ng the
dim
ensio
n (n
=
n1+
n2)
n1
:
the
num
ber
of the c
onve
ntio
nal g
e
ne
rato
rs
n2
:
the
num
ber
of w
in
d p
ow
e
r g
ener
at
or
s
5.
EMISSI
ON
D
ISPA
T
CH
The
em
issi
on
disp
at
c
h
ai
m
s
to
al
locat
e
the
op
ti
m
al
po
wer
ou
t
pu
ts
for
va
rio
us
ge
ne
rat
or
un
it
s
wi
t
h
the
ob
j
ect
ive
t
o
m
ini
m
iz
e
the
em
issi
on
s.
I
n
this
stu
dy,
the
e
m
issi
on
f
unct
ion
is
re
pr
ese
nt
ed
by
t
he
qu
a
dr
at
ic
functi
on [1
1]:
E
(
X
)
=
∑
α
i
+
β
i
p
i
+
γ
i
p
i
2
n1
i
=
1
(12)
wh
e
re:
α
i
,
β
i
,
γ
i
: The em
issi
on
coeffic
ie
nts
of
gen
e
rato
r
i
6.
PROBLE
M
F
ORMUL
ATI
ON
In
this
wor
k,
the
obj
ect
ive
functi
on
ai
m
s
to
fin
d
the
optim
al
allocati
on
of
powe
r
ou
t
pu
t
f
r
om
a
com
bin
at
ion
of
co
nventio
na
l
g
ene
rato
rs
a
nd
wind
power
plants
by
m
ini
m
iz
ing
both
t
he
operati
ng
c
ost
an
d
the em
issi
on
s. The
pro
posed
obj
ect
ive
fun
ct
ion
is
expre
sse
d
as
foll
ows:
F
(
X
)
=
w
1
C
(
X
)
+
w
2
h
T
E
(
X
)
(13)
wh
e
re
:
w
1
,
w
2
: are
weig
ht’s
f
act
or
s,
w
he
re
w
1
and
w
2
≥
0
a
nd
w
1
+
w
2
=1 [1
2]
h
T
: i
s the to
ta
l
pr
i
ce in
pen
al
ty
f
a
ct
or
PPF
in $/k
g
The
t
otal PPF
is ex
pr
e
ssed
as
the s
umm
at
ion
of P
P
F
of the
r
m
al
u
nits [
13
]
:
h
T
=
∑
h
i
n1
i
=
1
(14)
wh
e
re
:
h
i
: i
s the
pr
ic
e
pe
nalty
f
act
or
of
the g
e
ne
rato
r
i
In
this
p
a
per,
we
us
e
t
he
eq
uation
belo
w
t
o
cal
culat
e
the
PPF
of
the
i
-
th
ge
ne
rator
be
cause
it
wa
s
pro
ved that t
he
m
in/
m
ax
PPF i
s b
et
te
r
th
an
ot
her
PPF
ty
pes [13]
:
h
i
=
C
i
(
p
i
m
in
)
E
(
p
i
m
ax
)
(15)
The o
bj
ect
ive
fun
ct
io
n p
rop
ose
d
in
(1
3)
is
subj
ect
e
d
t
o
the
foll
ow
i
ng const
raints:
Op
e
rati
ng li
m
its
of the
co
nven
ti
on
al
and
wi
nd
powe
r gene
r
at
or
s:
p
i
min
≤
p
i
≤
p
i
max
(16)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
10
, No
.
4
,
A
ugus
t
2020
:
3
412
-
3
422
3416
0 ≤
w
i
≤
w
r
i
(17)
wh
e
re
:
p
i
max
: i
s the m
axi
m
um
lim
it
o
f
rea
l powe
r ou
t
pu
t
of the c
onve
ntion
al
ge
ner
at
or
i
p
i
min
: i
s the m
ini
m
u
m
lim
it
o
f
real
powe
r ou
t
pu
t
of the
con
ven
ti
onal
g
e
ne
rato
r
i
w
r
i
: i
s the r
at
e
d w
ind
powe
r of t
he
w
in
d p
ow
e
r gene
rato
r
i
The
est
im
at
ed
avail
able
wind
powe
r of
t
he g
ener
at
or
i
w
hic
h
is
obta
ined
usi
ng (4)
:
0 ≤
w
i
≤
P
(
v
)
(18)
Power bal
a
nce
The
total
po
w
er
ge
ner
at
e
d
f
r
om
the
con
ve
ntion
al
a
nd
wi
nd
powe
r
ge
ne
rators
sho
uld
be
eq
ual
to
the total
dem
a
nd
P
D
plu
s
the
net
work losse
s
P
L
.
∑
p
i
n1
i
=
1
+
∑
w
i
n2
i
=
1
=
P
D
+
P
L
(19)
wh
e
re
t
he pow
er lo
s
ses a
re ca
lc
u
la
te
d usin
g B
m
a
trix tech
ni
qu
e a
nd is e
xp
resse
d by the
[
14
]
:
P
L
=
∑
∑
p
i
n
j
=
1
n
i
=
1
B
ij
p
j
+
∑
B
0i
n
i
=
1
p
i
+
B
00
(20)
wh
e
re
B
ij
,
B
0i
an
d
B
00
are c
oeffici
ent of tra
ns
m
issi
on
loss.
In this
w
ork
, we
us
e the
B m
a
trix cit
ed i
n
[
15]
.
7.
OPTIMIZ
AT
ION
ALG
ORIT
HOMS
7.1.
Gre
y
w
ol
f opt
im
iz
er al
go
ri
th
m
f
or
s
ol
ving
th
e
eco
n
omic
an
d
emis
sion
dis
patch
In
t
his
w
ork,
the
G
WO
te
ch
ni
qu
e
w
hich
is
a
ne
w
m
et
aheu
risti
c
op
ti
m
iz
a
t
ion
m
et
ho
d
is
pro
po
se
d
t
o
so
lve
t
he
ec
onom
ic
and
em
i
ssion
dis
patch
pro
blem
du
e
to
it
s
m
any
a
dv
a
ntage
s
s
uc
h
as
bein
g
si
m
ple
in
pr
i
nciple,
ha
vin
g
a
fa
st
seek
ing
s
pee
d
a
nd
bein
g
easy
t
o
reali
ze
[
16
]
.
Be
sides,
i
n
[
17]
,
twe
nty
-
ni
ne
te
st
functi
ons
were
us
ed
to
be
nc
hm
ark
the
per
f
or
m
ance
of
the
G
W
O
in
te
r
m
s
of
expl
oitat
ion
,
ex
plo
rati
on
,
con
ve
rg
e
nce
and
local
optim
a
avo
ida
nc
e.
T
he
res
ults
il
lustrate
te
d
that
G
WO
cou
l
d
pro
vid
e
hi
gh
ly
com
petit
ive
resu
lt
s
com
par
e
d
to
well
know
n
he
ur
ist
ic
s
m
eth
ods.
T
he
G
WO
m
et
ho
d
is
inv
e
nted
by
S
ey
edal
i
et
.
al
.
in
2014
[
17
]
.
Grey
w
olve
s
m
os
tl
y
li
ve
in
a
gro
up
cal
le
d
a
pack.
T
hey
are
known
by
hav
i
ng
a
ve
ry
s
tric
t
so
ci
al
dom
inant
hie
rar
c
hy.
I
n
fact,
in
the
hi
erarch
y,
the
w
olv
es
withi
n
th
e
pac
k
a
re
div
i
ded
into
al
pha,
beta,
om
ega
and
del
ta
.
The
first
le
vel
of
hiera
rchy
of
grey
wo
l
ves
is
al
ph
a
.
T
he
al
pha
is
res
pons
i
bl
e
for
m
akin
g
decisi
ons
ab
ou
t
hunting
a
nd
it
s
decisi
on
s
are
dicta
te
d
to
the
pac
k.
Also
,
th
e
al
pha
is
con
si
der
e
d
to
be
the
dom
inant,
so
his
orde
rs
s
hould
be
fo
ll
owed
by
the
pa
ck.
T
he
sec
on
d
le
vel
of
hier
arch
y
is
beta
.
The
beta
wo
l
ves
hel
p
th
e
al
ph
as
in
de
ci
s
ion
m
aking
.
The
delta
w
olv
es
are
in
the
third
le
vel
of
hierar
c
hy.
T
he
delta
hav
e
to
obey
t
o
al
pha
a
nd
be
ta
;
however,
they
dom
inate
the
om
ega.
I
n
the
lo
west
le
vel,
the
re
a
re
om
ega
wo
l
ves
t
hat
ha
ve
to
obey
to
a
ll
the
othe
r
do
m
inant
w
olv
es
in
the
pac
k.
I
n
hun
ti
ng,
the
re
are
t
hr
ee
m
ai
n
ste
ps
fo
ll
owe
d
by
a
grey
w
olv
es:
a
)
Fin
ding,
c
hasin
g,
an
d
a
ppr
oach
i
ng
th
e
prey
.
b
)
En
ci
rcli
ng
a
nd
ha
rassin
g
the prey
un
ti
l i
t st
ops m
ov
in
g.
c
) Att
akin
g
the
prey
.
In
the
grey
wolf
al
go
rithm
,
it
is
con
sidere
d
that
the
al
ph
a
α
is
the
fitt
est
so
luti
on,
w
hile
beta
β
and
delta
δ
are
c
onside
red
res
pe
ct
ively
as
the
seco
nd
a
nd
th
e
third
best
s
ol
ution
s
.
Th
e
om
ega
wo
l
ves
fo
ll
ow
the o
t
her thr
ee
wo
l
ves.
T
he
e
qu
at
io
n
t
o upd
at
e
the posit
io
n o
f
the
p
ac
k
is
[17]:
D
⃗
⃗
=
|
C
⃗
.
X
⃗
⃗
p
−
X
⃗
⃗
(
t
)
|
(21)
X
⃗
⃗
(
t
+
1
)
=
X
⃗
⃗
p
−
A
⃗
⃗
.
D
⃗
⃗
(22)
wh
e
re
A
⃗
⃗
and
C
⃗
ar
e
coeffic
ie
nt
ve
ct
or
s,
t
is
the
current
it
erati
on,
X
⃗
⃗
p
is
the
posit
ion
vecto
r
of
t
he
pr
ey
,
a
nd
X
⃗
⃗
is
the posit
io
n ve
ct
or
of the
g
rey w
olf. The
v
ect
or
s
A
⃗
⃗
and
C
⃗
are ca
lc
ulate
d usin
g
t
he [1
7]:
A
⃗
⃗
=
2
a
⃗
.
r
1
−
a
⃗
(23)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Act
iv
e p
ower
oup
t
ut opti
miz
ation
f
or
wi
nd f
arms
and t
her
m
al unit
s
by min
imizi
ng
…
(
Na
zh
a C
her
ka
oui
)
3417
C
⃗
=
2
.
r
2
(24)
wh
e
re
r
1
a
nd
r
2
a
re
rand
om
s
ve
rctors
i
n
[0,1
]
,
an
d
com
pone
nets
of
are
li
near
ly
decr
ea
s
ed
from
2
t
o
0
durin
g
it
erati
ons.
The
posit
io
n
vector
of
the
gr
ey
w
olf
is
update
d
based
on
the
posit
ion
s
vecto
rs
of
t
he
first
three
best s
olu
t
ion
s
which
are α
, β
a
nd δ
.
In t
his r
e
ga
rd, the
fo
ll
owin
g
e
qua
ti
on
s a
re
us
e
d
[
17
]
:
D
⃗
⃗
α
=
|
C
⃗
1
.
X
⃗
⃗
α
−
X
⃗
⃗
|
,
D
⃗
⃗
β
=
|
C
⃗
2
.
X
⃗
⃗
β
−
X
⃗
⃗
|
,
D
⃗
⃗
δ
=
|
C
⃗
3
.
X
⃗
⃗
δ
−
X
⃗
⃗
|
(25)
X
⃗
⃗
1
=
X
⃗
⃗
α
−
A
⃗
⃗
1
.
D
⃗
⃗
α
,
X
⃗
⃗
2
=
X
⃗
⃗
β
−
A
⃗
⃗
2
.
D
⃗
⃗
β
,
X
⃗
⃗
3
=
X
⃗
⃗
δ
−
A
⃗
⃗
3
.
D
⃗
⃗
δ
(26)
X
⃗
⃗
(
t
+
1
)
=
X
⃗
⃗
1
+
X
⃗
⃗
2
+
X
⃗
⃗
3
3
(27)
The
ste
ps
for
s
olv
in
g
t
he
ec
onom
ic
an
d
em
issi
on problem
u
sin
g
t
he G
WO
alg
o
rithm
are
as
f
ollo
ws:
Step
1.
Ge
ner
a
te
r
an
dom
l
y t
he
grey
wolf
po
sit
ion
of
eac
h s
earch
ag
e
nt
x
i
k
.
Step
2.
Eval
uate the
obj
ect
ive
functi
on fo
r
ea
ch
sea
rch age
nt
(
13)
.
Step
3.
I
niti
al
i
ze
X
⃗
⃗
α
,
X
⃗
⃗
β
an
d
X
⃗
⃗
δ
.
X
⃗
⃗
α
is
the
posit
ion
of
the
fir
st
b
est
s
olu
ti
on
a
nd
X
⃗
⃗
β
and
X
⃗
⃗
δ
are
re
sp
ect
ively
the posit
io
ns
of the
seco
nd a
nd thi
rd b
est
so
l
utions.
Step
4.
U
pd
at
e
the
posit
ion
of each
searc
h
a
ge
nt (2
3)
,
(2
4)
,
(25),
(26),
and
(
27).
Step
5.
C
hec
k
t
hat the c
onstrai
nts ar
e
sati
sfie
d (16),
(17) an
d
(18).
Step
6.
Eval
uate the
obj
ect
ive
functi
on
of
ea
c
h
sea
rch age
nt
(13).
Step
7.
U
pd
at
e
X
⃗
⃗
α
,
X
⃗
⃗
β
an
d
X
⃗
⃗
δ
.
Step
8.
If the
m
axi
m
u
m
it
era
ti
on
is
not reac
hed,
return t
o
s
te
p4
.
O
t
herwis
e, sto
p
t
he
al
go
rithm
.
7.2.
Par
ticl
e s
w
arm
op
timi
z
at
i
on
techniq
u
e (PSO)
The
par
ti
cl
e
s
war
m
op
ti
m
isation
(
PS
O)
te
c
hn
i
qu
e
is
a
m
e
ta
heurist
ic
al
go
rithm
inv
e
nted
by
Ke
nned
y
and
Ebe
r
har
t
i
n
1995
[
18]
.
I
n
this
m
et
ho
d,
the
init
ia
li
zat
i
on
of
a
gro
up
of
pa
rtic
le
s
is
done
in
a
ra
ndom
m
ann
er
in
the
d
-
dim
ension
al
search
s
pace,
wh
e
re
d
is
the
siz
e
of
the
de
ci
sion
va
riable
s
in
the
op
ti
m
i
zat
in
pro
blem
.
To
e
ach
i
-
th
pa
rtic
le
a
posit
ion
ve
ct
or
x
i
,
a
vel
ocity
vecto
r
v
i
an
d
a
posit
io
n
Pbe
st
i
a
re
a
sso
ci
at
ed
.
The
par
ti
cl
es
exch
a
nge
ef
fect
ively
inform
at
i
on
dur
i
ng
a
n
it
erati
ve
pro
c
ess
so
that
to f
in
d
the
optim
al
so
luti
on.
In
eac
h
it
erati
on,
the
PS
O
a
lgorit
hm
searc
hes
f
or
the
op
tim
a
l
so
luti
on
by
updatin
g
th
e
velocit
y
(28
)
an
d
the
posit
ion
(
29)
of
each
i
-
th
par
ti
cl
e
ta
king
into
c
on
si
der
at
ion
it
s
pr
e
viou
s
best
po
sit
io
n
Pbe
st
i
an
d
the
b
est
po
sit
io
n
of
the
gro
up
gbest
.
A
t
each
it
erati
on
k,
t
he
e
qu
at
i
ons
al
lo
wing
to
update
the
vel
oc
it
y
and
the
po
sit
ion
of each
p
a
rtic
le
are give
n by
[19].
v
i
k
+
1
=
w
k
v
i
k
+
c
1
r
1
(
Pbe
st
i
k
−
x
i
k
)
+
c
2
r
2
(
g
be
st
k
−
x
i
k
)
(28)
x
i
k
+
1
=
x
i
k
+
v
i
k
+
1
(29)
wh
e
re:
r
1
and
r
2
:
Un
i
form
l
y dist
ribu
te
d ran
do
m
n
u
m
ber
s in
the
range
[0 1
]
.
w
:
In
e
rtia
w
ei
gh
t
.
c
1
a
nd
c
2
:
Accele
rati
on
coeffic
ie
nts.
The
fo
ll
owin
g equ
at
io
n
i
s
u
se
d
to
calc
ulate
t
he
ine
rtia
w
ei
ght [
19]
:
w
k
=
w
max
−
w
max
−
w
min
k
ma
x
x
k
(30)
wh
e
re:
k
: t
he
cu
rr
e
nt it
e
rati
on.
k
ma
x
: t
he
m
axi
m
u
m
num
ber
of ite
r
at
ion
s.
w
min
an
d
w
wa
x
: are the
lo
wer
and the
uppe
r bou
nd
s
of t
he
i
ner
ti
a
weig
htin
g fact
ors,
res
pe
ct
ively
.
7.3.
Ba
t alg
or
ithm
(BA)
Ba
t
al
go
rithm
(BA)
is
a
m
et
a
heurist
ic
op
ti
m
iz
at
ion
al
gori
th
m
inv
ented
in
2010
by
Ya
ng
[20].
I
n
this
op
ti
m
iz
ation
m
et
ho
d,
the
e
cho
l
ocati
on
be
hav
i
our
of
bat
s
is
us
e
d
[20].
In
orde
r
t
o
l
ook
for
pr
ey
,
bat
fly
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ol.
10
, No
.
4
,
A
ugus
t
2020
:
3
412
-
3
422
3418
rand
om
ely
with
a
velocit
y
v
i
and
a
posit
io
n
x
i
with
a
va
ryi
ng
l
oudness
A
and
f
re
qu
e
ncy
f.
T
he
eq
uatio
ns
belo
w
a
re
us
ed
to update
t
he po
sit
io
ns
of th
e b
at
s
[21]:
f
i
(
t
)
=
f
min
+
(
f
max
−
f
min
)
∗
u
(
0
,
1
)
(31)
v
i
(
t
+
1
)
=
v
i
(
t
)
+
(
x
i
(
t
)
−
x
Gbest
)
∗
f
i
(
t
)
(32)
x
i
(
t
+
1
)
=
x
i
(
t
)
+
v
i
(
t
+
1
)
(33)
wh
e
re:
u (
0,1
)
: i
s a unif
or
m
r
andom
n
um
ber ra
ng
i
ng fro
m
0
to
1
x
Gbest
: t
he
be
st sol
ution f
ound
by th
e sw
a
rm
A
r
an
dom
w
al
k
i
s
us
e
d for a l
ocal searc
h an
d
is e
xpresse
d by [
21]
:
x
i
(
t
)
=
x
Gbest
+
φ
A
i
(
t
)
N
(
0
,
σ
)
(34)
wh
e
re:
φ
: i
s a scali
ng f
a
ct
or
all
owin
g
t
o
li
m
it
the step
size o
f
the
r
a
ndom
w
al
k
A
i
: i
s the lou
dn
es
s
N
(
0,
σ
)
: i
s a nor
m
al
r
andom
n
um
ber
with a
sta
ndar
d de
viati
on
σ a
nd a m
ean equal
to
ze
ro
wh
e
n
the
bats
are
nea
r
their
t
arg
et
,
t
hey
dec
rease
the
lo
ud
ness
A
i
and
inc
re
ase
the
pulse
r
at
e
r
i
.
This
can
be
expresse
d by [
21
]
:
A
i
(
t
+
1
)
=
α
A
i
(
t
)
(35)
r
i
(
t
+
1
)
=
r
i
(
0
)
(
1
−
exp
(
−
γ
t
)
)
(36)
wh
e
r
e
α
a
nd γ
are c
on
sta
nts.
7.4.
Gr
av
i
tational se
arch al
go
ri
th
m
(G
SA)
The
GSA
is
a
heu
risti
c
opti
m
iz
at
ion
al
go
r
it
h
m
inv
ented
in
2009
by
Ra
sh
edi
et
al
.
[2
2].
GSA
te
chn
iq
ue
is
ba
sed
on
t
he
la
w
gr
a
vity
and
m
otion.
I
n
this
m
et
ho
d,
a
ge
nts
are
co
ns
ide
re
d
as
obj
ect
s
an
d
their
m
asses are
us
e
d
in
or
der
t
o
m
easur
e
their
p
e
rfor
m
ance.
T
he
posit
ion o
f
i
-
t
h
a
gen
t i
s
d
e
fin
ed by [
23]
:
X
i
=
(
x
i
,
…
x
i
d
,
…
,
x
i
n
)
,
i
=
1
,
2
,
…
m
(37)
wh
e
re:
x
i
d
: i
s the
po
sit
io
n o
f
it
h
m
ass in t
he
dt
h dim
ension
n
: i
s the
dim
ensi
on of
t
he
sea
rc
h
s
pace
At a s
pecific t
i
m
e t, the forc
e
act
ing
from
m
a
ss j to m
ass i is give
n by the
foll
ow
i
ng [2
3]:
F
ij
d
(
t
)
=
G
(
t
)
M
i
(
t
)
x
M
j
(
t
)
R
ij
(
t
)
+
ε
(
x
j
d
(
t
)
−
x
i
d
(
t
)
)
(38)
wh
e
re:
M
i
an
d
M
j
: are the
m
asse
s of the
ob
j
ect
s
i an
d j
R
ij
: i
s the e
uclidie
an dist
ance
bet
ween t
he o
bj
e
c
ts i
and
j
ε
: i
s a sm
all co
nst
ant
G
: i
s the
gr
a
vitat
ion
al
c
onsta
nt
at
tim
e t
First G
is init
ia
li
zed
with
G
0
a
nd the
n wil
l de
crease acc
ordi
ng to
t
he
ti
m
e
us
in
g
i
n
[
23]
:
G
(
t
)
=
G0
e
−
α
t
T
(39)
wh
e
re
α
is a
d
e
scen
ding c
oeffici
ent, t is the
c
urren
t i
te
rati
on
and T
is the m
axim
u
m
n
um
ber
of
it
erati
ons
.
The
t
otal f
or
ce
act
ing
on the
a
gen
t i
i
n
th
e
d dim
en
sion
is
giv
en
b
y t
he foll
ow
i
ng
in
[
23
]
:
F
i
d
(
t
)
=
∑
rand
j
F
ij
d
m
j
=
1
,
i
≠
j
(
t
)
(40)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
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88
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8708
Act
iv
e p
ower
oup
t
ut opti
miz
ation
f
or
wi
nd f
arms
and t
her
m
al unit
s
by min
imizi
ng
…
(
Na
zh
a C
her
ka
oui
)
3419
wh
e
re
rand
j
is a
rando
m
n
um
ber
i
n t
he
inte
rv
al
[
0
1].
The
acce
le
rati
on at ti
m
e t of
th
e age
nt i in
the
d dim
ension
is
expresse
d by [
23
]
:
a
i
d
(
t
)
=
F
i
d
(
t
)
M
ii
(
t
)
(41)
The
velocit
y a
nd the
posit
ion o
f
eac
h
a
gen
t i
s updat
ed
acc
ordi
ng to
t
he
[
23]
:
v
i
d
(
t
+
1
)
=
rand
i
×
v
i
d
(
t
)
+
a
i
d
(
t
)
(42)
x
i
d
(
t
+
1
)
=
x
i
d
(
t
)
+
v
i
d
(
t
+
1
)
(43)
wh
e
re
:
rand
i
: i
s a r
a
ndom
n
um
ber
fro
m
the inter
val [0,
1]
v
i
d
: i
s the
velocit
y o
f
the
ag
e
nt i i
n
the
d dim
ension
x
i
d
: i
s the
po
sit
io
n o
f
the
ag
e
nt i i
n
the
d dim
ension
8.
SIMULATI
O
N
AND RES
U
LT
S
In
orde
r
to
te
st
the
pr
opos
e
d
op
ti
m
isa
t
ion
al
gorithm
,
three
di
ff
er
ent
c
ases
are
sim
ul
at
ed
us
i
ng
the
IEEE
30
bu
s
syst
em
.
T
he
te
st
syst
e
m
is
con
sti
tuted
of
five
co
nve
nt
ion
al
pla
nts
and
on
e
wi
nd
far
m
.
The
fi
ve
co
nv
entional
th
erm
al
plants
are
at
bu
se
s
1,
2,
22
,
27
an
d
23.
Wh
il
e,
the
WF
is
at
bu
s
13.
Table
1
il
lustrate
s
the
cost
a
nd
em
issi
on
c
oe
ff
ic
i
ents
a
nd
the
m
axi
m
u
m
and
m
ini
m
u
m
power
outp
ut
of
each
conve
ntion
al
generat
or
i
n
t
he t
est
syst
e
m
[
13]
.
Table
1.
T
he
r
m
al
g
ener
at
or
s
d
at
a
Un
its
Bu
s
P
max
(M
W
)
P
min
(M
W
)
Co
st co
ef
f
icien
ts
E
m
iss
io
n
coef
f
icien
ts
a
($/
2
.
ℎ
)
b
($/
.
ℎ
)
c
($/h
)
e
($/
h)
f
(r
ad
/
)
γ
(kg
/
2
.
h)
β
(kg
/
.
ℎ
)
α
(kg
/h
)
1
1
200
50
0
2
0
.
0
0
3
7
5
15
0
.
063
0
.
0126
-
0
.
9
22
.
983
2
2
80
20
0
1
.
7
0
.
0175
14
0
.
084
0
.
02
-
0
.
1
25
.
313
3
22
50
15
0
1
0
.
0625
12
0
.
15
0
.
027
-
0
.
01
25
.
505
4
27
35
1
0
0
3
.
25
0
.
0
0
8
3
4
10
0
.
20
0
.
0291
-
0
.
005
24
.
9
5
23
30
10
0
3
0
.
025
10
0
.
25
0
.
029
-
0
.
004
24
.
7
The
wind f
a
rm
u
ti
li
zed in
this
p
a
per
has
a c
a
pacit
y of
120 M
W
. It
is co
nsi
der
e
d
that t
he
wind tu
rb
i
ne
te
chnolo
gy
ins
ta
ll
ed
in
the
WPP
is
V90/3000
(V
e
sta
s
)
[
24
]
.
Ther
e
f
or
e,
th
e
rated
powe
r
and
the
s
wep
t
area
of
the
r
otor
bla
de
s
of
the
wind
t
urbines
instal
le
d
in
t
he
WPP
are
re
sp
ect
ive
ly
3
M
W
a
nd
6361
.
7
m
2
.
Be
sid
es,
Table
2
s
hows
the
val
ues
of
t
he
wind
far
m
pro
duct
ion
lim
its
(
WF
mi
n
a
nd
WF
ma
x
),
the
direct
c
os
t
c
oeffici
ent,
the r
ese
r
ve
c
ost
co
ef
fici
ent a
nd the
p
e
nalty
c
os
t c
oeffici
ent
of the
WF i
n
t
he
test
syst
e
m
.
Table
2.
Win
d farm
s d
at
a
WF
Bu
s
WF
min
(M
W
)
WF
max
(M
W
)
k
r
($/M
W
.h)
k
p
($/M
W
.h)
d
(
$
/MW.h
)
1
13
0
120
1
1
1
.
25
In
the
three
cas
es,
th
e
loa
d
syst
e
m
is
con
si
dered
t
o
be
e
qual
t
o
300
M
W.
A
lso,
the
val
ue
of
the sh
a
pe
k
an
d
scal
e
pa
ram
et
er
c
are
consi
der
e
d
to
be
res
pecti
vel
y
equ
al
to
2
.
14
an
d
7
.
29
of
ta
ng
ie
r
reg
i
on
ci
te
d
in
[25].
Ca
se 1
: t
he
w
ei
gh
t
’s fact
ors ar
e co
ns
ide
red to
b
e
w
1
=1
a
nd
w
2
=0.
Ca
se 2
: t
he
w
ei
gh
t
’s fact
ors ar
e co
ns
ide
red to
b
e
w
1
=0
a
nd
w
2
=1.
Ca
se 3
: t
he
w
ei
gh
t
’s fact
ors ar
e co
ns
ide
red to
b
e
w
1
=0,5 a
nd
w
2
=0
.
5.
In
each
case
,
10
r
un
s
ar
e
done
us
in
g
the
G
WO
an
d
three
oth
e
r
m
et
aheu
risti
c
op
ti
m
iz
ation
al
gorithm
s:
the
PS
O,
t
he
BA
and
the
GSA
wh
ic
h
a
re
us
e
d
in
the
pur
po
se
of
c
om
par
ison.
T
he
optim
i
zat
ion
par
am
et
ers
are
sh
ow
n
in
Tab
le
3.
In
eac
h
c
ase,
the
ave
rage
values
of
the
ac
ti
ve
power
ou
t
pu
ts
,
the
lo
sses,
the
total
op
er
at
ing
cost
an
d
the
e
m
issi
on
s
ob
ta
ine
d
in
the
te
n
runs
fo
r
eac
h
opti
m
iz
at
ion
m
et
h
od
a
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
10
, No
.
4
,
A
ugus
t
2020
:
3
412
-
3
422
3420
cal
culat
ed
an
d
repor
te
d
in
Ta
ble
4.
As
we
c
an
noti
ce
from
Table
4,
wh
e
n
the
only
obje
ct
ive
to
m
inim
iz
e
is
the
total
c
os
t,
the
G
WO
m
eth
od
at
ta
ine
d
be
tt
er
res
ults
th
an
P
SO,
BA
a
nd
G
SA.
I
n
fa
ct
,
the
G
WO
m
et
ho
d
per
m
it
s
achieving the l
ow
e
st a
ver
a
ge value
of the
total
ope
r
at
ing
c
os
t.
In
the
sec
on
d
c
ase,
wh
e
n
t
he
on
ly
obj
ect
ive
to
m
ini
m
iz
e
is
the
em
issi
on
s,
the
G
WO
perf
or
m
s
bette
r
than
t
he
ot
he
r
opti
m
iz
at
ion
m
et
ho
ds
by
pro
du
ci
ng
t
he
best
res
ults
.
I
nd
ee
d,
t
he
aver
a
ge
valu
e
s
of
the
em
issi
on
s
ob
ta
ine
d
us
in
g
the
G
WO
is
280
.
60
20
kg
/
h,
wh
il
e
the
ave
r
age
val
ues
obta
ined
wit
h
PS
O,
BA
and
GSA
are
resp
ect
ively
280
.
7096
kg
/h
,
301
.
0234
kg
/h
and
299
.
90
55kg/h.
In
th
e
third
case,
whe
n
the
obj
ect
ive
is
to
re
du
ce
both
the
ope
rati
ng
c
os
t
a
nd
the
em
issi
on
s,
th
e
G
WO
per
m
i
ts
getti
ng
the
l
ow
es
t
value
of
the
op
erati
ng
c
os
t
in
com
par
ison
to
PSO,
BA
an
d
GSA.
Re
ga
rd
i
ng
the
em
issi
on
s,
the
PS
O
at
ta
ined
the
best
res
ults.
Ne
ver
thless
,
the
G
WO
pe
rm
i
ts
getti
ng
bette
r
res
ults
than
the
B
A
and
the
GSA.
I
n
fact,
the
ave
ra
ge
va
lues
of
t
he
em
i
ssion
s
obta
ine
d
with
the
G
W
O,
B
A,
a
nd
G
SA
a
re
resp
ect
ively
293
.
9747
kg/h,
314
.
7205
kg/h
and 30
1
.
7588
kg
/
h.
Accor
ding
to
the
sim
ulatio
n
r
esults,
the
m
axi
m
al
real
po
we
r
pro
vid
e
d
fro
m
the
W
F
is
72.
5881
M
W
wh
ic
h
represe
nts
th
e
wind
powe
r
pote
ntial
of
the
sit
e.
Ther
e
fore,
c
on
si
der
i
ng
the
wi
nd
powe
r
pote
nt
ia
l
of
a
sit
e
as
a
c
on
st
raint
of
the
m
ulti
ob
j
e
ct
ive
functi
on
propose
d
in
th
is
paper,
pe
rm
i
ts
no
t
exc
eedin
g
the av
ai
la
ble
w
ind
powe
r.
In a
dd
it
io
n,
the
G
WO
m
et
ho
d
ca
n
be use
d
to
s
ol
ve
su
c
h op
ti
m
iz
at
ion
proble
m
s
du
e
to
the
fact
th
at
it
a
ll
ow
s
ge
tt
ing
bette
r
r
esults
by
redu
ci
ng
both
t
he
op
e
rati
ng
c
ost
and
the
e
m
issi
on
le
vels
sim
ultan
eo
us
ly
in
co
m
par
ison
t
o
s
om
e
known
optim
iz
at
ion
al
gorithm
s,
as
we
ca
n
noti
ce
from
the sim
ulati
on
r
es
ults.
Table
3.
O
pti
m
iz
at
ion
param
e
te
rs
Alg
o
rith
m
Para
m
eter
Valu
e
GW
O
Po
p
u
latio
n
size
50
Maxi
m
u
m
nu
m
b
er
of
iter
atio
n
s
300
PSO
Inertia
weig
h
t [
w
min
,
w
max
]
[
0
,4 0
,9]
Acceler
atio
n
coef
ficients
c1 et c2
2
.
05
Po
p
u
latio
n
size
50
Maxi
m
u
m
nu
m
b
er
of
iteration
s
300
BA
Mini
m
al
f
requ
en
cy
f
min
0
Maxi
m
al
f
requ
en
cy
f
max
10
Initial lo
u
d
n
ess
A0
0
.
8
Initial p
u
lse rate
0
.
2
α
0
.
5
γ
0
.
99
Po
p
u
latio
n
size
50
Maxi
m
u
m
nu
m
b
er
of
iter
atio
n
s
300
GSA
G0
1
Alp
h
a
20
Po
p
u
latio
n
size
50
Maxi
m
u
m
n
u
m
b
er
of
iter
atio
n
s
300
Table
4.
Sim
ul
at
ion
resu
lt
s i
n ca
se
1,
2
a
nd 3
P
G1
(M
W
)
P
G2
(M
W
)
P
G3
(M
W
)
P
G4
(M
W
)
P
G5
(M
W
)
WF
(M
W
)
Los
ses
(M
W
)
Co
st
($/h
)
E
m
iss
io
n
s
(kg
/h
)
GW
O
Cas
e 1
97
.
2
8
2
7
68
.
1
0
2
4
49
.
9
8
3
6
15
.
4
7
9
1
11
.
5
0
2
8
71
.
3
6
6
3
13
.
7
1
2
6
591
.
7
0
4
5
332
.
2
4
9
0
Cas
e 2
93
.
9
3
5
0
49
.
8
9
1
9
35
.
1
9
0
5
30
.
9
8
4
3
29
.
2
4
0
3
72
.
5
8
7
5
11
.
8
2
6
8
652
.
9
3
2
5
280
.
6
0
2
0
Cas
e 3
98
.
2
9
8
8
56
.
9
4
0
0
43
.
6
1
8
5
22
.
2
0
4
8
19
.
1
4
3
1
72
.
5
8
0
1
12
.
7
8
7
6
602
.
5
2
2
4
293
.
9
7
4
7
PSO
Cas
e 1
1
0
4
.2088
5
7
.57
2
4
4
0
.23
8
8
2
0
.80
3
9
2
1
.29
8
3
7
0
.28
5
6
1
4
.40
7
0
6
0
1
.14
91
3
0
1
.6389
Cas
e 2
9
4
.03
8
8
4
9
.92
1
2
3
5
.44
5
4
3
1
.17
8
1
2
8
.67
8
4
7
2
.58
8
1
1
1
.84
9
9
6
5
2
.6833
2
8
0
.7096
Cas
e 3
9
8
.92
3
3
5
7
.18
2
7
3
6
.79
3
6
2
4
.69
1
6
2
2
.73
4
1
7
2
.58
8
1
1
2
.91
4
7
6
0
9
.2529
2
8
6
.4942
BA
Cas
e 1
1
1
3
.7615
6
4
.69
9
0
4
6
.79
8
3
1
9
.98
7
7
1
8
.77
5
8
5
4
.70
7
5
1
8
.73
1
1
6
2
4
.2498
3
7
2
.3040
Cas
e 2
9
8
.79
5
0
5
4
.15
4
7
3
8
.74
7
5
3
1
.03
5
0
2
7
.09
0
2
6
2
.77
8
7
1
2
.60
1
1
6
4
2
.6974
3
0
1
.0234
Cas
e 3
9
6
.49
9
8
6
3
.30
1
3
4
5
.11
1
2
2
5
.21
4
8
1
9
.76
9
2
6
2
.26
4
5
1
2
.16
5
7
6
1
6
.3462
3
1
4
.7205
GSA
Cas
e 1
7
9
.00
5
4
7
7
.43
5
9
4
9
.96
7
3
1
4
.34
7
1
2
2
.12
4
8
6
7
.44
0
5
1
0
.39
4
2
6
0
4
.1017
3
4
2
.4
5
4
9
Cas
e 2
9
8
.22
7
6
5
9
.11
9
6
3
3
.81
4
5
28
.
0
3
5
8
2
1
.76
4
0
7
2
.08
3
2
1
3
.08
7
8
6
4
6
.3965
2
9
9
.9055
Cas
e 3
8
8
.38
7
2
6
0
.89
3
8
4
3
.05
0
3
2
2
.00
4
4
2
4
.21
4
9
7
2
.43
4
3
1
0
.96
0
7
6
2
6
.9505
3
0
1
.7588
9.
CONCL
US
I
O
N
In
t
his
pa
pe
r,
we
pr
ese
nt
an
op
ti
m
iz
a
ti
on
al
gorit
hm
based
on
grey
w
olf
o
ptim
izer
(
G
WO).
The
pro
pose
d
al
gorithm
a
ll
ow
s
obta
inin
g
the
act
ive
powe
r
ou
t
put
of
the
r
m
al
and
wind
powe
r
plants
instal
le
d
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Act
iv
e p
ower
oup
t
ut opti
miz
ation
f
or
wi
nd f
arms
and t
her
m
al unit
s
by min
imizi
ng
…
(
Na
zh
a C
her
ka
oui
)
3421
in
the
gri
d
with
the
ob
j
e
ct
ive
to
redu
ce
the
cost
pro
du
ct
io
n
an
d
em
issi
on
le
vels
sim
ultan
eousl
y.
Thr
ee
di
ff
e
rent
cases
us
i
ng
the
G
WO
,
PS
O,
B
A
a
nd
G
SA
a
re
a
naly
sed
a
nd
com
par
ed
.
T
he
propos
e
d
op
ti
m
iz
ation
m
et
ho
d
al
lo
ws
m
ini
m
iz
ing
sign
i
ficantl
y
the
e
m
issi
on
s
an
d
the
o
per
at
in
g
cost
as
il
lustra
te
d
in
the sim
ulati
on
r
esults.
REFERE
NCE
S
[1]
Vela
m
ri,
S.
,
et
al
.
,
“
Stat
i
c
e
co
nom
ic
dispat
ch
inc
orp
ora
ti
ng
w
ind
far
m
using
Flower
poll
in
at
i
on
al
gori
thm
,”
Pe
rs
pec
t
iv
es
in Sci
en
ce
,
vol
.
8
,
pp.
260
-
262
,
20
16.
[2]
J.
Ans
ari
,
S.
Banda
ri,
M.
G.
Doze
in
and
M.
Kala
n
ta
r,
“
The
E
f
fec
t
of
W
ind
Pow
er
Plant
s
on
the
Tot
a
l
Cost
of
Producti
on
in
E
c
onom
ic
Dispatch
Problems
,
”
Res
earc
h
Journal
of
Appl
i
ed
Sc
ie
n
ce
s,
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ineering
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2013
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N.
Saxena
and
S.
Ganguli
,
“
So
la
r
and
W
ind
P
ower
Esti
m
at
io
n
and
Ec
onom
ic
Loa
d
Dispatch
Us
ing
Firef
l
y
Algorit
hm
,
”
4
th Inte
rnational
Co
nfe
renc
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on
Ec
o
-
frie
ndl
y
Co
mpu
ti
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Comm
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ati
on
Syst
ems,
201
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[4]
M.
Abuell
a
and
C.
Hat
zi
andon
i
u,
“
The
E
cono
m
ic
Dispatc
h
fo
r
Inte
gra
te
d
W
i
nd
Pow
er
S
y
ste
m
s
U
sing
Parti
c
le
Sw
arm Opti
m
iz
at
ion,
”
Version
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Sep.
5,
2015,
ar
Xiv:1509.
01693
v1
[cs.
CE]
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[5]
V.
Sohoni,
S.
C.
Gupta
and
R.
K.
Nem
a,
“
A
Crit
i
ca
l
Review
on
W
ind
Turbi
ne
Pow
er
Curve
Mo
del
li
ng
T
ec
hniq
ues
and
Th
ei
r
Appli
ca
t
ions i
n
W
ind
Based
En
erg
y
S
y
stems
,
”
Journa
l
of
Ene
rg
y,
vol
.
2016,
pp
.
1
-
18
,
2016.
[6]
S.
Diaf
,
M.
B
el
hamel
,
M.
Hadda
di
and
A.
Louc
he
,
“
T
ec
hni
ca
l
and
e
conomic
assess
m
ent
o
f
h
y
bri
d
photovol
taic
/win
d
s
y
st
em wit
h
b
a
tt
er
y
s
tora
ge
in
Corsica
isla
nd
,
”
Ene
rgy
Pol
i
cy
,
v
ol
.
36
,
no
.
2
,
pp
.
743
-
754,
2008
.
[7]
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