In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
1, Mar
ch 20
19,
p
p.
486~
5
0
3
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
1.pp
4
86-
50
3
486
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Solution for optim
al pow
er flow
p
roblem in wind energy system
using hybrid m
ulti objectiv
e artific
i
al physi
cal
optimization algorithm
P.
N
agalesh
m
i
P
a
naco
rp S
o
f
t
w
a
r
e S
o
luti
on
s
,
N
a
g
erco
il,
India
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Dec
1
6
,
2
017
Re
vise
d A
p
r
13,
201
8
Ac
ce
p
t
ed
Oc
t
3
, 2
0
18
No
rm
ally
,
the
character
o
f
the
wi
nd
e
nerg
y
as
a
r
enew
ab
le
e
ne
rg
y
so
urc
e
s
has
un
c
e
rt
ain
t
y
i
n
g
enerati
o
n
.
T
o
resol
v
e
t
h
e
O
p
tim
al
P
ow
er
F
lo
w
(O
PF)
draw
back,
thi
s
p
aper
p
ro
po
sed
a
rep
l
acem
e
n
t
Hyb
r
id
M
u
l
t
i
O
b
j
ec
t
ive
Arti
f
i
cia
l
P
hysical
O
ptimizat
ion
(HMOAP
O)
a
lgor
i
t
hmic
r
ul
e,
w
hi
ch
d
oes
no
t
re
q
u
i
r
e
any
m
a
n
a
gem
e
nt
p
aram
et
ers
co
m
p
ared
t
o
diff
erent
m
e
t
a-h
e
uris
ti
c
algorithms
w
ithin
t
he
literat
u
re
.
Arti
fi
cial
P
hysi
cal
O
ptimi
z
at
ion
(AP
O
),
a
moderately
n
e
w
p
opul
a
t
ion-b
a
sed
inte
lligen
ce
algorit
h
m,
s
hows
f
ine
p
e
rform
a
nc
e
on
i
mpro
ve
m
e
nt
i
ssue
s.
M
o
r
e
o
v
e
r,
t
h
i
s
pa
p
e
r
p
r
e
s
e
n
t
s
hyb
rid
vari
ety
of
A
n
i
mal M
i
grati
o
n
Opti
mizati
o
n
(AM
O
) alg
o
ri
th
mi
c rul
e
to
ex
press
th
e
con
v
erg
e
nc
e
chara
c
t
e
ristic
o
f
APO.
T
he
O
P
F
d
rawb
ack
i
s
take
n
into
accou
n
t
wi
th
s
ix
t
ot
ally
d
iff
e
rent
c
heck
case
s
,
th
e
eff
ecti
v
ene
ss
o
f
the
p
r
op
ose
d
H
MO
APO
te
c
h
niqu
e
i
s
t
e
s
te
d
on
I
E
E
E
30
-b
us
,
I
E
EE
1
1
8
-b
u
s
and
IEEE
3
00
-bus
c
h
e
ck
s
y
s
t
e
m
.
T
h
e
o
b
t
ai
ned
resul
t
s
f
r
om
t
he
H
M
O
AP
O
a
l
go
rith
m
is
c
omp
a
re
d
wi
th
t
h
e
o
the
r
i
mp
rov
e
me
nt
t
e
c
hn
iq
ue
s
wi
t
hin
th
e
literat
u
re.
T
h
e
o
b
tai
n
ed
c
ompariso
n
resul
t
s
i
ndic
a
te
t
hat
propo
s
e
d
t
echn
i
qu
e
is eff
ecti
v
e t
o
s
u
cce
ed
in
best resol
uti
on f
o
r th
e
O
P
F
d
r
a
w
back
.
K
eyw
ord
s
:
A
n
ima
l
m
i
g
r
a
t
i
on
o
p
t
im
iz
at
i
o
n
(AMO)
Me
ta-he
u
r
i
stic
a
lg
ori
t
h
ms
artific
ia
l
ph
ysi
c
a
l
op
t
i
m
iza
t
i
o
n
(A
P
O
)
Re
new
a
b
l
e
ene
r
gy so
urc
e
s
op
tim
al pow
e
r
f
l
o
w
(O
P
F
)
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
P. Na
g
alashm
i
,
Pa
nacor
p
Softw
are
Solu
ti
o
n
s,
N
a
ge
rcoi
l –
6
290
0
1
,
India.
Em
ail:
naga
les
h
m
i
p1
7@
gm
ai
l.c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
To
da
y’s
t
e
c
h
n
o
l
o
g
i
c
a
l
w
ord
fu
l
l
y
de
pe
nds
o
n
e
l
e
c
t
ric
i
ty
;
bu
t
th
e
av
a
i
l
a
b
ili
ty
o
f
e
l
ec
t
r
i
c
s
o
u
r
c
e
i
s
l
o
w.
T
h
e
d
ef
ic
ien
c
y
of
e
l
e
c
t
ric
i
ty
b
eco
me
s
t
h
e
b
r
ea
k
i
ng
p
oi
nt
f
or
e
m
e
rgi
n
g
c
o
u
n
t
r
i
e
s
.
Th
ere
f
ore
,
t
he
r
es
ea
rch
orga
niza
t
i
o
n
s
t
e
nd
i
n
t
o
r
ese
a
rc
h
to
d
isc
o
ve
r
an
a
p
p
ro
pria
te
s
o
l
uti
o
n
fo
r
giv
i
ng
u
ni
nt
e
r
rup
t
a
b
l
e
e
l
e
c
t
ri
cit
y
.
In
th
i
s
s
i
t
ua
ti
on
t
h
e
usage
o
f
r
enew
a
b
l
e
e
ner
g
y
s
ourc
e
s
ar
e
the
su
peri
or
s
ol
uti
o
n,
s
o
t
h
e
s
e
re
new
a
b
l
e
e
n
erg
y
sy
st
ems
a
r
e
e
n
co
u
r
ag
ed
f
o
r
e
l
e
ct
r
i
cit
y
p
rodu
ct
io
n
[1
],
[
2
]
.
Th
e
m
ost
a
v
a
ila
ble
renew
a
b
l
e
so
urce
i
n
the
w
o
r
l
d
i
s
w
i
n
d
a
n
d
s
o
l
a
r
,
t
h
e
r
e
s
e
a
r
c
h
e
s
o
n
t
h
e
s
e
t
o
a
r
e
a
a
r
e
u
n
d
e
r
p
r
og
re
ssing
b
u
t
w
in
d
en
e
r
gy
c
o
n
v
e
rsi
o
n
i
s
m
o
s
t
prom
i
s
in
g
rese
arc
h
a
re
a
bec
a
use
o
f
i
ts
l
ow
c
omple
x
i
t
y
i
n
i
n
s
ta
l
lat
i
on
a
n
d
m
a
i
n
tena
nce
[3].
T
he
w
i
n
d
e
n
ergy
syste
m
s are
dir
e
c
tly
i
n
t
e
g
r
a
te
d in
to t
he p
ow
er
syst
e
m for p
o
w
e
r
syst
e
m u
s
age.
The
in
t
e
g
rati
on of w
in
d e
n
erg
y
i
n
t
o
e
xi
s
ting
po
we
r
sy
st
em
p
re
se
nt
s
a
t
e
ch
ni
c
a
l
p
r
obl
ems
a
n
d
t
h
a
t
n
e
e
ds
a
t
t
en
t
i
o
n
of
v
ol
ta
ge
r
egu
l
a
t
i
o
n,
st
a
b
il
it
y,
p
ow
e
r
qual
i
t
y
i
ss
ues
[4].
The
p
o
w
e
r
qu
ali
t
y
is
a
n
im
p
o
rta
n
t
cus
t
om
er
f
oc
used
m
easure
an
d
i
s
s
i
g
n
i
fi
ca
ntl
y
a
ff
ect
ed
b
y
th
e
opera
tio
n
o
f
a
d
istri
b
ut
ion
an
d
tra
n
sm
i
s
s
i
o
n
n
e
t
w
o
r
k
.
The
issue
o
f
p
o
w
e
r
qua
l
i
t
y
i
s
of
g
r
eat
i
m
porta
nc
e
to
t
he
wi
nd
t
u
r
bi
n
e
[
6
]
.
By
a
gg
re
g
a
t
i
ng
m
u
l
ti
pl
e
wi
nd
t
u
r
bi
n
e
s
as
w
i
n
d
f
a
r
m
or
p
a
r
k,
g
rea
t
e
r
a
mount
o
f
e
l
ec
trica
l
pow
er
c
an
b
e
ge
n
e
ra
te
d
from
it.
T
o
i
n
terc
o
nne
ct
w
in
d
p
o
w
e
r
to
t
he
u
ti
l
ity
g
ri
d,
t
her
e
m
u
s
t
be
a
n
a
p
pro
p
ria
t
e
g
r
id
i
n
t
erc
onne
ct
ion
,
c
o
n
t
r
ol
s
y
s
t
e
m
a
n
d
reg
u
l
a
t
i
on
t
o
e
n
su
re
h
i
gh
po
w
e
r
qua
lit
y,
r
e
lia
b
ili
t
y
a
n
d
s
ta
bi
lit
y.
H
o
w
e
v
e
r
,
t
h
e
o
n
e
o
f
t
h
e
m
o
s
t
c
r
i
t
i
c
a
l
p
r
o
b
l
e
m
s
a
s
s
o
c
i
a
t
e
d
w
i
t
h
wi
nd
pow
er
i
s
th
at,
t
h
e
a
m
o
u
n
t
o
f
p
o
w
e
r
gene
ra
ted
b
y
t
he
s
a
m
e
i
s
a
ffe
c
ted
b
y
t
he
i
n
t
erm
itte
nt
n
a
t
u
r
e
of
w
i
nd
flo
w
w
hich
i
s
d
i
ffic
u
lt
t
o
p
re
dic
t
[
7]
.
It
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
So
l
u
t
i
on
f
o
r
o
p
t
im
al p
o
w
er f
l
o
w
pr
ob
l
e
m
in
w
i
n
d
ene
r
g
y
sy
ste
m
usi
n
g
hyb
r
i
d
..
. (P.
Nag
a
l
eshm
i)
48
7
fo
l
l
ow
s
tha
t
,
the
gri
d
i
n
t
e
g
ra
ted
w
i
nd
p
o
w
e
red
u
n
i
ts,
m
a
y
i
n
t
r
o
du
c
e
s
ever
e
cha
lle
n
g
e
s
t
o
t
r
a
d
i
tio
na
l
gene
ra
ti
o
n
sc
h
edu
l
in
g
m
e
t
h
o
d
o
l
og
ie
s a
n
d ope
rat
i
o
n
of p
o
w
er
s
yst
em
[
8]
. F
o
r satisfac
t
o
r
y gri
d
in
t
e
g
ra
tio
n,
t
he
w
i
n
d
pow
er
f
luc
t
ua
tio
n
m
a
y
ha
ve
t
o
be
b
a
l
a
n
ced
b
y
o
t
her
t
y
pe
s
o
f
ge
ne
r
a
ti
o
n
.
A
l
terna
t
ive
l
y,
t
o
com
p
e
n
sa
te
for
t
h
e
p
o
w
e
r
i
m
bala
nc
e
due
t
o
uncer
t
a
in
ty
o
f
w
i
n
d
,
add
i
tio
na
l
c
o
st
m
ay
h
a
v
e
t
o
b
e
a
dde
d
w
i
t
h
t
he
t
o
t
a
l
power
gene
r
at
i
on co
st o
f the
sys
t
em
[9].
T
h
e
m
a
j
o
r
g
o
a
l
o
f
O
p
t
i
m
a
l
P
o
w
e
r
F
l
o
w
(
O
P
F
)
i
s
t
o
i
m
p
r
o
v
e
a
t
a
r
g
e
t
c
a
p
a
c
i
t
y
s
uc
h
a
s
c
o
s
t of
f
ue
l
b
y
me
ans
of
i
de
a
l
c
han
g
e
o
f
t
he
c
on
t
r
ol
v
ar
iab
l
es
s
i
m
ul
t
a
neo
u
s
l
y
d
i
ffe
re
nt
e
qua
l
i
t
y
a
nd
i
n
equa
l
i
t
y
c
on
str
a
in
ts.
Fo
r
t
h
e
ma
i
n
i
n
t
e
n
d
of
e
c
onomi
c
al
a
nd
s
ecure
o
p
e
ra
ti
on
a
nd
p
l
a
n
n
i
ng
of
pow
er
s
ys
tem
s
,
optim
al
p
ow
e
r
f
low
(OP
F
)
is
e
m
p
l
oye
d
[1
0]
.
The
ob
ject
i
v
e
o
f
O
P
F
i
s
t
o
r
e
d
u
ce
t
he
c
ost
of
f
ue
l,
e
nviro
nm
ent
a
l
p
o
l
l
ut
i
o
n
a
n
d
a
l
s
o
the
pow
er
l
os
t
by
t
h
e
ne
tw
or
k.
I
n
p
o
w
e
r
sy
st
e
m
e
c
o
n
o
mic
l
o
ad
d
i
s
p
atc
h
(
ELD
)
is
c
om
m
onl
y
use
d
t
o
fin
d
gene
ra
ti
o
n
o
r
fue
l
c
o
s
t.
T
h
e
m
ajor
goa
l
o
f
E
c
o
n
o
m
i
c
D
i
s
p
atc
h
(
E
D
)
i
s
t
o
m
i
n
im
ize
the
a
m
o
u
n
t
o
f
tot
a
l
po
llu
t
i
o
n
c
a
u
se
d
b
y
the
e
n
v
i
r
o
n
me
nt
.
T
h
is
c
a
n
be d
one
by a
v
o
i
di
n
g
the
bur
ni
n
g
of
f
u
e
l
s [11].
Ec
o
nomic
Lo
a
d
D
i
spa
t
c
h
(
ELD
)
is
d
eter
mi
ned
as
t
he
t
ec
hn
i
q
ue
i
n
w
h
i
c
h
th
e
ge
ne
rat
i
on
l
ev
e
l
s
a
r
e
a
l
lo
cate
d
t
o
t
h
e
g
e
n
e
rat
i
n
g
un
its. A
s a
r
e
s
u
lt
the
loa
d
o
f t
h
e s
y
stem
i
s
to
tal
l
y a
n
d
ec
o
n
o
m
ica
lly
s
u
p
p
l
i
e
d
. The
ELD
i
s a
lar
g
e-sc
a
l
e, h
igh
l
y
no
n-l
i
ne
ar,
cons
traine
d
o
p
ti
m
i
z
a
t
i
o
n
p
ro
b
l
e
m
[
12].
The
m
a
in
a
im
o
f
ELD
i
s
c
o
n
f
lic
tin
g
i
n
n
a
t
ur
e
and
t
o
ac
hi
e
v
e
a
n
a
c
c
e
pta
b
le
s
trate
g
y
of
p
ow
er
d
is
patc
h
w
ith
in
d
iffer
e
nt
s
y
s
t
e
m
co
nst
r
a
i
nt
s
an
d
a
l
so
i
t
h
e
lp
s
to
k
e
e
p
the p
o
l
l
u
tio
n w
i
t
h
in t
he
lim
its
a
nd i
t
re
duce
s
t
he
fue
l cos
t
[1
3].
A
p
p
lica
tio
n
w
i
t
h
r
e
n
ew
a
b
le
e
ne
rg
y
so
ur
ces
s
uc
h
as
s
o
l
ar
c
ell
a
r
ra
y,
w
i
n
d
tur
b
i
n
es,
or
f
ue
l
ce
lls
h
a
v
e
incre
a
se
d sig
n
i
fica
ntl
y
dur
i
n
g
t
h
e
pa
st deca
d
e
. To obta
i
n the
c
lea
n
ener
gy,
w
e are
usi
ng t
h
e h
ybr
id s
ol
a
r
-w
ind
pow
er
g
e
n
e
r
a
t
i
on.
C
on
sum
e
r
s
p
re
fer
qua
l
i
t
y
pow
er
f
r
o
m
su
pp
lier
s
.
The
qu
ali
t
y
o
f
p
ower
c
an
b
e
me
asure
d
b
y
us
i
n
g
par
a
m
e
ters
s
uch
as
v
ol
ta
ge
s
a
g
,
har
m
onic
a
nd
p
o
w
e
r
fac
t
or
.
To
o
bt
ai
n
qu
a
lit
y
po
w
e
r
w
e
h
a
v
e
dif
f
ere
n
t
to
pol
o
g
ie
s.
I
n o
u
r
pa
pe
r w
e
pr
e
sent a
ne
w
poss
i
b
l
e
t
o
p
o
lo
g
y
w
hi
c
h
impr
o
ves p
o
w
e
r qua
lit
y [14]
.
The
h
y
b
rid
po
w
e
r
syst
e
m
i
s
norm
a
l
l
y
e
q
u
i
ppe
d
w
i
th
c
on
t
r
ol
s
ys
te
m
w
h
i
c
h
fu
nc
t
i
o
n
s
to
r
educe
t
h
e
syste
m
f
re
que
ncy
osc
i
ll
a
tio
n
s
a
nd
ma
ke
s
t
h
e
w
i
nd
turbi
n
e
gene
ra
tor
p
o
w
er
out
pu
t
fol
l
ow
t
he
p
e
rform
anc
e
curve
w
h
en
t
h
e
s
ystem
is
s
u
b
j
e
c
t
e
d
t
o
w
i
n
d
/
l
oa
d
dist
urba
nces.
U
sual
ly
P
I
contr
o
lle
rs
a
r
e
e
m
p
l
oye
d
i
n
t
hes
e
syste
m
s.
U
nfo
r
tuna
te
l
y
s
ince
t
he
o
per
a
t
i
ng
p
oi
n
t
c
ha
n
g
e
s
d
e
p
en
d
i
n
g
on
t
h
e
d
e
m
a
nd
o
f
c
on
su
mers,
t
h
i
s
con
s
ta
n
t
g
a
i
n
P
I
c
ont
r
o
l
l
er
a
re
unsui
ta
ble
t
o
o
the
r
oper
a
ting
p
oi
n
t
s.
T
he
re
fore
,
it
de
scribe
s
t
h
e
a
p
pli
c
a
t
i
o
n
o
f
f
u
zzy
g
a
i
n
sc
hed
u
l
i
n
g
of
P
I
c
o
nt
roll
e
r
f
o
r
a
n
i
s
ol
at
e
d
w
ind
-
d
i
e
sel
hy
bri
d
p
ow
e
r
s
ystem
w
ith
s
uperc
o
n
duc
tin
g
ma
gnet
i
c e
n
erg
y
s
tor
a
ge
[
1
5
].
Re
duc
tio
n
o
f
ope
ra
ti
n
g
c
os
t
s
i
n
p
o
w
e
r
system
i
n
orde
r
to
r
e
t
ur
n
t
he
i
nve
stme
n
t
c
os
t
s
a
n
d
m
o
r
e
profi
t
ab
i
l
i
t
y
h
as
v
it
al
i
m
p
orta
nc
e
in
p
o
w
er
i
nd
us
try.
E
c
o
nomic
L
o
ad
D
is
patc
h
(
ELD
)
is
o
ne
o
f
t
h
e
m
o
st
impor
ta
nt
i
ssu
e
s
in
r
ed
uc
in
g
ope
rat
i
ng
c
o
st
s.
ELD
i
s
for
m
ulate
d
a
s
a
no
nl
i
n
e
a
r
opt
i
m
i
z
a
tio
n
p
r
ob
l
e
m
wi
th
con
t
in
uou
s var
i
ab
les w
i
th
in the
p
ow
e
r
p
la
n
t
s. The ma
i
n
p
u
r
pose
of t
h
i
s pr
ob
l
e
m is op
t
i
m
al p
l
a
nn
ing of pow
er
gene
ra
ti
o
n
i
n
p
o
w
e
r
pl
a
n
t
s
w
i
t
h
mi
nim
u
m
c
o
s
t
by
t
o
ta
l
u
n
i
ts,
re
g
a
rded
t
o
equa
lit
y
an
d
in
equa
l
ity
c
o
n
str
a
ints
i
n
clu
d
i
n
g
lo
a
d
d
e
m
a
n
d
a
n
d
th
e
ra
ng
e
o
f
uni
ts'
p
o
w
e
r
p
rodu
c
t
i
v
it
y.
I
n
th
is
a
rtic
le,
Ec
onom
ic
L
o
a
d
D
i
s
p
at
c
h
pro
b
lem
ha
s
b
e
en
m
o
d
e
l
e
d
b
y
c
o
n
s
i
d
eri
n
g
t
h
e
va
l
v
e
-
p
o
i
nt
l
oa
d
i
ng
e
f
f
ec
ts
w
it
h
p
o
w
e
r
p
l
a
n
ts
'
c
ons
trai
n
t
s
suc
h
as:
t
h
e
bala
nc
e
o
f
p
rod
u
c
t
i
o
n
an
d
c
o
ns
u
m
pti
o
n
in
s
ys
tem
,
t
he
f
o
rb
i
dde
n
z
o
nes,
r
a
nge
o
f
pro
d
u
ct
i
on,
incre
a
s
i
ng
an
d
decr
easi
ng ra
te
s, reliab
i
l
i
t
y
c
o
n
s
t
r
a
in
t
s
a
n
d
n
e
t
w
ork sec
u
r
ity
[
1
6
].
I
n
r
ec
ent
year
s
w
i
n
d
t
ur
bi
ne
t
ec
hn
olo
g
y
h
as
u
nder
g
one
r
api
d
d
e
v
e
l
o
p
m
ents,
gr
ow
t
h
i
n
size.
T
he
w
i
n
d
e
nerg
y
b
ecom
e
i
ncre
as
i
ngl
y
com
p
e
t
iti
ve
w
it
h
c
o
n
v
e
n
ti
o
n
al
e
ner
gy
s
ource
s
ba
se
d
o
n
t
he
o
p
timiz
a
t
i
o
n
o
f
w
i
n
d
turb
i
nes. The pene
t
ra
t
i
o
n
of
w
i
n
d
e
ner
g
y
i
n
the
gr
i
d
r
a
ise
s
qu
e
s
tio
ns
a
bo
ut
t
he
c
o
m
p
a
tib
i
lit
y
of
t
he
w
i
n
d
tur
b
ine
p
o
w
e
r
pro
duc
t
i
o
n
w
ith
t
h
e
g
rid.
I
n
par
tic
ula
r
,
t
h
e
con
t
ribu
ti
o
n
t
o
g
r
i
d
s
t
a
bi
li
t
y
,
po
wer
qu
a
l
i
t
y
a
n
d
beha
v
i
or
d
uri
n
g
fa
u
l
t
s
i
t
u
a
tio
ns
p
la
ys
t
he
ref
o
re
a
s
im
porta
nt
a
r
o
l
e
as
t
h
e
r
eliab
i
lit
y.
I
n
th
is
p
a
p
e
r
,
a
vect
or
con
t
ro
l sche
me
is de
ve
lo
pe
d t
o
c
on
t
r
o
l
t
h
e
r
ot
or
si
d
e
vo
l
t
a
g
e
s
ou
r
c
e
con
v
e
r
ter
[17].
A
new
con
t
rol
m
e
t
h
od
fo
r
qua
si
-
Z
-so
u
r
c
e
casc
a
ded
m
u
lti
le
ve
l
in
v
er
t
e
r-ba
s
ed
g
r
i
d-c
onne
c
t
ed
ph
o
t
o
v
o
l
t
a
i
c
(P
V)
s
yste
m
is
p
ro
pose
d
.
The
pro
pose
d
m
e
t
h
od
is
c
a
pab
l
e
o
f
b
oo
st
i
ng
the
P
V
a
rra
y
volta
ge
t
o
a
hi
ghe
r
le
ve
l
a
n
d
s
o
lve
s
t
he
i
mba
l
a
n
ce
p
ro
b
l
e
m
o
f
D
C
-lin
k
vo
l
t
a
g
e
i
n
t
ra
d
iti
o
n
al
casca
de
d
H
-
bri
dge
i
n
v
e
rter
s.
Th
is
s
ys
tem
adj
u
sts
the
gri
d
i
n
j
ec
t
e
d
c
u
rre
nt
i
n
phase
w
it
h
the
g
r
i
d
vo
l
t
age
a
n
d
a
c
hie
v
es
i
n
d
e
p
ende
n
t
ma
ximum
p
o
w
e
r
poin
t
t
rac
k
i
ng
(
M
P
P
T)
f
or
t
he
s
e
p
ara
t
e
P
V
a
r
r
ays.
T
o
a
c
hi
e
v
e
t
h
e
s
e
goa
l
s
,
the
prop
o
r
ti
ona
l
-
int
e
gral
(
PI
)
c
o
ntrollers
a
re
e
m
p
lo
ye
d
for
eac
h
m
o
d
u
l
e.
F
or
a
ch
iev
i
ng
t
he
b
es
t
perfor
m
a
n
ce,
t
h
i
s
pa
p
e
r
prese
n
t
s
a
n
op
t
i
mum
appr
oac
h
t
o
des
i
gn
t
h
e
con
t
ro
ll
e
r
p
ar
a
m
e
t
er
s
usi
ng
pa
rt
icle
s
w
a
r
m
o
p
tim
iza
t
ion
(P
SO
).
The
pr
i
m
ar
y
design
goa
l
i
s
t
o
obtain
g
ood
response
by
m
i
ni
m
i
zin
g
the
in
t
e
gra
l
a
bsol
u
t
e
e
rror.
A
lso,
t
he
trans
i
en
t
re
sp
o
n
se
i
s
g
u
ar
an
t
eed
b
y
m
i
n
i
m
i
zi
n
g
t
he
o
ve
rsho
ot,
s
ett
l
i
n
g
t
i
m
e
a
nd
rise
t
i
m
e
of
t
he
s
ystem
re
sp
on
se
.
Th
e
ef
f
ect
iv
en
e
ss
o
f
t
h
e
n
e
w
p
ropo
sed
c
ont
rol
met
hod
has
bee
n
v
eri
f
ie
d
t
h
ro
u
g
h
sim
u
l
a
tio
n
stud
ies
b
a
sed
o
n
a
se
ve
n
l
e
v
e
l
qu
asi
-
Z-So
u
r
c
e
c
a
s
ca
d
e
d
mu
ltil
ev
el
i
nv
e
r
t
e
r [18].
Em
bel
lishe
d
P
a
rti
c
le
S
w
a
rm
O
pt
imiza
t
i
o
n
i
s
t
o
e
x
ten
d
t
he
s
in
gle
p
o
pula
tio
n
P
S
O
to
t
he
i
n
t
e
r
ac
t
i
ng
mult
i-sw
ar
m
m
odel.
T
hro
u
gh
th
i
s
m
ul
ti
-sw
a
rm
c
oope
r
a
ti
v
e
a
p
p
r
o
a
c
h,
d
ive
r
si
t
y
i
n
t
h
e
w
hole
sw
arm
com
m
uni
t
y
c
a
n
b
e
u
phe
ld.
C
onc
urre
nt
ly,
the
sw
arm
-
to-sw
a
rm
m
echa
nism
d
r
a
sti
c
ally
s
pee
d
s
up
t
he
s
warm
com
m
uni
t
y
t
o
con
v
erge
t
o
th
e
g
l
o
b
a
l
n
e
a
r
op
t
i
m
u
m
.
I
n
o
r
der
to
e
va
l
u
a
t
e
the
per
f
orm
a
nc
e
o
f
t
he
p
ro
pos
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
48
6 –
50
3
48
8
algorithm,
it
has
been
t
es
t
e
d
in
s
ta
ndar
d
I
EEE
57,118
bus
s
yste
ms
a
nd
r
e
su
lts
s
h
o
w
th
a
t
E
m
b
e
l
l
i
s
h
ed
P
a
r
ticle
S
w
arm
O
p
tim
iz
ati
o
n
(EP
S
O)
i
s
more
e
ffic
ie
nt
i
n
r
e
duc
i
n
g
t
h
e
Rea
l
po
w
e
r
losse
s
w
h
e
n
c
o
mpa
r
ed
t
o
o
t
her
st
a
ndard
r
ep
or
te
d alg
o
ri
t
h
ms
[
19].
The
pro
b
lem
of
O
pt
im
al
P
o
w
er
F
low
ca
n
be
s
olve
d
by
u
ti
l
i
zi
n
g
v
a
r
i
ous
t
e
c
h
ni
q
u
es
l
i
k
e
line
a
r
p
r
og
rammi
n
g
,
n
on
-li
n
e
a
r
p
r
og
rammi
n
g
,
i
nt
erio
r-p
oin
t
t
e
c
hni
qu
e,
qua
dra
tic
p
r
ogr
am
ming,
s
eque
n
t
i
a
l
u
n
c
on
st
ra
i
n
ed
m
i
n
i
m
iz
a
tio
n
an
d
Ne
wto
n
b
a
s
e
d
t
e
c
h
n
iq
ues
a
nd
al
so
i
t
c
a
n
b
e
s
olv
e
d
b
y
t
h
e
i
nt
e
g
ra
t
i
on
of
op
tim
iza
t
i
o
n
t
e
c
h
n
i
que
s
like
e
v
olu
t
io
nary
p
ro
gram
m
i
ng
(
EP
),
p
ar
t
i
c
l
e
swar
m
op
t
i
m
i
zat
io
n
(
PSO),
a
n
d
seq
u
en
t
i
al
q
ua
dra
tic
p
r
o
g
r
am
ming
(
S
Q
P
)
[20].
The
r
e
a
r
e
t
w
o
ste
p
s
i
nv
o
l
ved.
I
n
th
e
f
i
r
s
t
s
t
e
p
,
the
so
l
u
t
i
on
space
i
s
i
n
ve
st
iga
t
e
d
b
y
b
o
t
h
E
P
and
PS
O
tec
h
n
i
q
u
e
s
.
In
t
he
s
ec
o
nd
s
t
e
p
,
S
Q
P
is
u
t
ili
ze
d
w
h
e
n
t
her
e
i
s
a
d
e
v
e
l
o
p
m
e
n
t
i
n
t
h
e
r
e
s
u
l
t
o
f
f
i
r
s
t
p
h
a
s
e
[
2
1
]
.
E
P
i
s
a
k
i
n
d
o
f
g
l
ob
al
s
e
a
rc
hing
tec
h
niq
u
e.
I
t
beg
i
n
s
a
t
the
p
opu
l
a
t
i
on
of
c
a
n
did
a
te
s
o
l
uti
o
n
a
n
d
a
t
l
ast
ev
a
l
u
a
ti
on
p
roc
e
s
s
i
s
ut
il
i
z
e
d
t
o
fi
nd
t
h
e
n
e
a
r
g
l
ob
al
s
o
l
uti
on
in
para
l
l
e
l
.
G
A
i
s
a
s
ea
rch
a
l
g
o
r
ithm
ba
sed
on
t
he
m
ec
ha
nic
s
o
f
na
tu
ral
g
e
n
e
ti
c
s
a
nd
n
a
t
u
r
al
s
el
ectio
n
.
T
he
evo
l
ut
ion
proc
edure
of
o
rga
n
s
w
ith
f
u
n
c
t
i
o
n
a
l
op
t
i
miza
t
i
o
n
s
i
s
i
n
te
gr
ate
d
h
e
r
e.
R
e
p
rod
u
c
ti
o
n
,
cr
oss
ove
r
an
d
muta
ti
on
ar
e
t
h
e
t
h
ree
bas
i
c
prim
e
ope
ra
tor
s
a
ssoc
i
ate
d
w
ith
G
A
.
B
a
sed
on
the
chrom
o
somes,
G
A
wor
k
s.
A
set
o
f
b
i
n
ar
y
di
gits
w
h
i
c
h
d
e
s
c
r
ibes t
he
c
o
n
tr
o
l
p
ara
m
e
t
er
c
od
i
ng
is
c
on
t
a
i
n
e
d
i
n
the
s
e
c
h
rom
o
som
e
s
w
h
ich i
s
com
p
o
s
ed t
he
m
s
elves
with
g
enes
[
2
2
],
[
23].
I
t
is nec
e
ssary
t
o
c
o
ntro
l the
p
o
w
e
r fl
ow
at t
h
e op
tim
al r
ang
e
whi
l
e
t
h
e ren
e
wable e
n
er
g
y
source
s a
r
e
use
d
i
n
pow
e
r
s
ystem
s
.
T
h
e
m
a
in
c
on
t
r
ib
ut
i
on
of
t
h
i
s
pa
per
i
s
i
)
To
f
o
r
mula
te
t
he
o
p
tima
l
pow
e
r
f
low
pro
b
lem
as
a
m
ult
i
o
b
j
ec
t
i
v
e
o
p
t
imiz
at
ion
pr
oble
m
i
i)
A
nd
to
u
t
il
i
ze
t
h
e
Arti
fi
cia
l
P
h
y
s
ic
a
l
O
ptimi
z
ati
on
(AP
O
)
algori
t
h
m
w
i
t
h
A
n
i
m
a
l
m
igra
t
i
o
n
o
p
timiz
at
ion
as
a
s
o
l
u
tio
n
t
o
t
h
e
O
P
F
prob
le
m
.
T
he
r
em
ainder
of
th
i
s
p
a
p
er
i
s
or
gan
i
ze
d
as
f
ol
l
o
ws:
Som
e
o
f
t
h
e
rec
e
n
t
r
ela
t
ed
rese
arc
h
es
t
o
our
p
ro
pose
d
m
eth
o
d
i
s
e
x
p
l
ai
ne
d
i
n
s
e
c
t
i
on
2
.
Th
e
p
r
o
p
o
s
ed
m
e
t
ho
dol
o
g
y
wi
th
p
robl
em
f
o
r
mu
l
a
ti
on
i
s
e
xpl
ai
n
e
d
in
s
ect
io
n
3.
T
h
e
Ex
perim
e
n
t
al
r
e
s
u
lts
o
f
t
h
e
p
r
op
osed
m
et
h
o
d
a
n
d
t
he
c
ompa
rison
w
i
t
h
e
xi
sti
ng
m
e
t
h
o
d
s
a
re
p
resente
d
i
n
sect
io
n 4
fo
l
l
o
w
e
d
by t
h
e
con
c
l
u
si
o
n
in se
c
tion
5.
2.
REL
A
TE
D
WORK
S
S
o
me
o
f
the
r
ece
nt
r
e
s
e
a
rc
h
work
r
ela
t
e
d
t
o
t
h
e
OPF
prob
lem
i
n
w
i
nd
e
ner
g
y
syst
e
m
i
s
li
s
t
ed
a
s
fo
l
lo
ws:
S
h
anhe
J
i
a
n
g
e
t.a
l
[
2
4
]
i
n
tr
oduc
e
d
“
A
hy
brid
p
a
r
t
i
c
l
e
sw
a
r
m
opt
i
m
izat
i
o
n
a
nd
grav
ita
t
i
ona
l
sea
r
ch
a
l
go
rith
m f
o
r so
l
v
i
n
g
ec
ono
mi
c
e
m
i
ssi
on
l
o
a
d
di
sp
at
ch
p
rob
l
ems
w
ith var
io
us pr
a
c
tica
l
c
ons
trai
n
t
s”. To
sol
v
e
ec
onom
ic
e
m
i
ssion
l
o
a
d
d
i
s
pa
t
c
h
pr
o
b
l
e
m,
i
n
t
h
is
p
a
p
er
P
S
O
w
as
inte
grate
d
w
i
t
h
G
S
A.
B
o
t
h
t
h
e
uti
l
i
z
e
d
appr
oa
ch
w
as
b
a
s
e
d
on
p
o
p
u
l
at
i
on.
I
n
P
S
O
tec
h
n
i
q
u
e
,
t
he
a
ge
nts
w
e
r
e
t
a
k
e
n
a
s
p
a
r
t
i
c
l
e
.
H
e
r
e
t
h
e
m
o
v
e
m
e
n
t
of
e
a
c
h
p
art
i
cl
e
w
a
s
base
d
o
n
bo
t
h
t
he
p
a
s
t
bes
t
s
o
l
ut
ion
o
f
i
t
s
ow
n
a
n
d
t
h
e
pa
st
b
e
s
t
s
o
lut
i
o
n
o
f
its
g
rou
p
.
In
G
S
A
,
t
he
a
ge
nt
s
w
e
re
t
a
k
e
n
a
s
o
b
jec
t
s.
H
er
e
the
one
obje
c
t
w
as
fa
sci
n
ate
d
b
y
ot
her
ob
jec
t
s
thr
o
u
g
h
grav
ita
t
i
o
n
a
l
f
or
ce.
T
he
a
ge
n
t
i
n
G
S
A
w
a
s
descri
be
d
thro
ug
h
fou
r
t
y
p
e
s
of
p
a
r
amet
ers.
T
h
e
f
i
r
st
p
a
r
amet
e
r
wa
s
t
h
e
po
sit
i
o
n
o
f
t
h
e
ma
ss
in
w
hi
ch
s
ol
u
tio
n
t
o
t
h
e
p
ro
b
l
em
w
as
s
t
a
t
e
d
a
t
s
p
e
c
i
f
i
ed
s
ea
rch
spac
e.
T
h
e
seco
nd
par
a
m
e
ter
w
a
s
t
h
e
ine
r
ti
a
l
m
ass
w
h
ich
dec
e
l
era
t
e
s
i
t
s
m
o
ti
on
b
y
r
eflec
tio
n
o
f
i
t
s
r
e
s
i
s
tanc
e.
T
he
t
h
i
r
d
and
fo
urt
h
p
ar
am
eter
w
a
s
t
he
a
ct
i
v
e
a
n
d
pas
s
i
v
e
grav
ita
t
i
o
n
al
m
a
s
s.
T
he
e
st
i
m
ati
o
n
of
b
oth
gra
v
ita
ti
o
n
a
l
a
n
d
iner
tia
l
m
a
ss
w
a
s
do
ne
t
hr
o
ugh
fitne
s
s
fun
c
ti
on.
B
o
t
h
t
h
e
al
gor
ithm
s
w
er
e
in
te
gra
t
e
d
b
y
a
n
y
o
n
e
of
t
he
t
w
o
proce
dures.
(i.e
.)
one
w
or
k
starts
a
fter
t
he
c
omp
l
e
t
e
n
es
s
o
f
t
h
e
pre
v
i
o
us
w
or
k
a
n
d
t
h
e
o
t
her
w
a
y
w
a
s
t
o
em
plo
y
c
o-e
v
olu
t
i
o
nary
m
e
t
ho
d
to
c
ons
i
d
er
t
he
s
w
a
r
m
c
om
po
ne
n
t
s
as
t
he
c
om
po
ne
nt
s
intr
od
uc
ed
b
y
PSO-
G
SA.
A
n
iru
d
dha
B
ha
tt
a
c
h
ar
ya
a
nd
P
r
a
nab
K
u
m
a
r
Cha
t
t
opa
d
h
y
a
y
[2
5]
d
e
v
e
l
ope
d
“
H
ybrid
D
iffere
nti
a
l
Ev
olu
t
i
o
n
w
i
th
B
i
o
ge
ogra
p
h
y
-
Base
d
O
p
t
i
m
i
z
a
ti
on
f
o
r
S
o
l
u
tio
n
of
Ec
on
omi
c
L
o
a
d
Di
spat
ch
”
.
H
e
r
e
th
e
i
s
su
e
of
b
o
t
h
c
o
n
v
e
x
a
nd
no
n-c
o
n
v
e
x
e
co
n
o
m
i
c
loa
d
d
ispa
tc
h
w
a
s
sol
v
e
d
by
t
h
e
c
o
mbi
n
at
i
on
of
d
i
f
f
e
re
ntia
l
evo
l
ut
ion
(D
E)
a
l
g
ori
t
hm
a
n
d
b
io
ge
ogra
p
hy-
based
o
p
ti
m
i
z
a
t
i
o
n
a
l
g
o
rit
h
m
.
T
he
a
b
ove
c
om
b
i
nat
i
on
o
f
alg
o
ri
t
h
ms
a
l
s
o
so
l
v
es
p
r
o
bl
e
m
s
like
de
gra
d
a
t
i
on
of
s
olu
t
io
n
q
u
a
l
i
t
y
a
n
d
l
o
w
spee
d.
T
he
D
E
a
l
g
o
ri
t
h
m
w
a
s
base
d
o
n
p
op
ula
t
i
o
n.
H
er
e
fu
nc
ti
ons
l
i
k
e
no
n-d
i
ffe
r
en
ti
a
b
le,
n
o
nli
n
ea
r
a
nd
m
u
lti-m
o
d
a
l
o
b
j
ec
ti
ve
c
an
b
e
han
d
l
ed a
nd
a
t
r
ia
l
vec
t
or w
a
s
cons
truc
ted by
e
ac
h
par
e
n
t
i
n
d
i
v
i
d
ua
l
i
n
o
rd
e
r
t
o pro
duce
n
e
w
offspr
ing.
T
he
re
w
e
r
e
t
hree
t
yp
es
o
f
ba
sic
o
p
e
r
ators
w
a
s
i
n
v
o
l
v
e
d
t
o
e
n
h
a
n
c
e
t
h
e
p
o
p
u
l
a
t
i
on
na
me
l
y
m
u
t
ati
on,
c
rosso
ve
r,
a
nd
selec
t
i
o
n.
I
n
B
i
o
g
e
ogra
p
h
y
acti
v
i
ties
li
k
e
t
he
m
ovem
e
nt
o
f
o
n
e
i
s
l
a
nd
t
o
a
not
he
r,
a
p
p
e
a
r
an
ce
a
n
d
di
sa
p
p
ear
ance
o
f
new
specie
s
w
e
r
e
e
x
p
r
essed.
T
he
q
ual
ity
o
f
the
s
o
l
uti
on
w
i
l
l
b
e
d
eg
rade
d
in
l
at
er
s
t
a
ge
d
u
e
t
o
t
h
e
e
x
i
s
t
e
n
c
e
o
f
c
r
o
s
s
-
o
v
e
r
o
p
e
r
a
t
i
o
n
i
n
e
v
o
l
u
t
i
o
n
a
r
y
b
a
s
e
d
al
g
o
rit
h
m
where
a
s
i
n
B
B
O
,
cr
oss-
over
opera
tio
n
w
a
s no
t r
e
stric
t
ed.
I
e
jinCa
i
e
t
.al
[26]
p
r
e
se
nte
d
“
A
hybrid
C
P
S
O
–
S
Q
P
m
e
th
od
for
ec
o
no
mi
c
di
sp
a
t
ch
c
on
si
d
e
ring
t
h
e
val
v
e-
po
in
t
ef
fec
t
s”
.
I
n
t
his
pa
per,
c
ha
ot
ic
p
a
r
ti
cle
sw
a
r
m
opt
im
iza
t
io
n
(CP
S
O
)
a
l
gori
t
hm
a
n
d
s
e
que
n
t
i
a
l
qua
dra
tic
p
ro
g
r
amm
i
ng
(
S
Q
P
)
w
e
r
e
i
ncor
por
a
t
ed
t
o
ret
r
ieve
t
h
e
s
ol
ut
ion
fo
r
ec
on
omi
c
p
o
w
e
r
d
isp
a
t
c
h
pro
b
lem
.
H
ere
t
h
e
ce
ntra
l
op
t
i
m
i
z
e
r
w
a
s
th
e
CP
S
O
a
nd
to
e
nha
nc
e
q
ua
li
t
y
o
f
the
s
o
l
u
ti
o
n
,
the
re
su
l
t
s
w
e
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
So
l
u
t
i
on
f
o
r
o
p
t
im
al p
o
w
er f
l
o
w
pr
ob
l
e
m
in
w
i
n
d
ene
r
g
y
sy
ste
m
usi
n
g
hyb
r
i
d
..
. (P.
Nag
a
l
eshm
i)
48
9
adj
u
s
t
e
d
b
y
S
Q
P
.
T
he
C
P
S
O
w
a
s
de
si
gne
d
base
d
on
t
e
n
t
e
q
ua
ti
on.
C
P
S
O
w
a
s
a
c
o
m
b
i
n
a
t
i
o
n
o
f
P
S
O
a
n
d
CL
S
.
W
he
re g
loba
l
e
x
pl
ora
t
i
o
n
w
a
s
car
rie
d
o
ut
i
n
P
S
O
a
n
d
loca
l
sea
r
ch
w
as
d
o
n
e
to
t
he
s
o
l
u
t
i
o
ns of
th
e
PS
O
t
h
r
o
u
g
h
C
L
S
.
I
N
S
Q
P
,
t
h
e
r
e
w
e
r
e
t
h
r
e
e
s
t
a
g
e
s
.
I
n
t
h
e
f
i
r
s
t
s
t
a
g
e,
t
h
e
H
e
ssi
a
n
m
at
rix
c
o
nta
i
ned
in
t
h
e
lagra
ngia
n
f
u
n
c
ti
o
n
w
as
u
p
d
a
t
ed.
Estim
at
io
n
of
l
i
n
e
sear
ch
a
nd
m
e
r
i
t
fu
nc
tio
n
w
a
s
do
ne
a
t
the
se
c
o
n
d
s
ta
ge
and
fina
lly
s
o
l
ut
i
on
w
a
s
a
c
q
u
i
red
f
o
r
t
h
e
prob
lem
o
f
q
ua
d
r
atic
progra
m
m
i
ng.
T
he
o
p
t
i
m
al
pow
er
g
e
n
era
tion
of
eac
h u
n
i
t
w
h
ic
h w
a
s subm
i
t
te
d
t
o
o
pera
ti
on
w
a
s foun
d
b
y
the
h
ybr
idiz
a
tio
n
of CP
S
O
-
S
Q
P
techni
q
u
e
.
Be
hna
m
M
o
ha
m
m
a
d
i-Ivatl
o
o
et.a
l
[
2
7]
d
isc
u
sse
d
“
N
onco
n
v
ex
D
ynam
i
c
Eco
nom
ic
P
ow
e
r
D
ispatc
h
P
r
ob
le
ms
S
ol
u
t
i
o
n
U
s
i
ng
H
y
bri
d
I
m
m
u
ne
-G
e
n
et
i
c
A
l
gor
i
t
hm”
.
T
he
c
o
s
t
nee
d
e
d
f
or
o
p
e
rati
on
w
a
s
re
d
u
c
e
d
and
a
l
s
o
t
he
s
o
l
u
t
i
o
n
f
o
r
t
h
e
pr
oble
m
o
f
d
yna
mic
ec
on
om
ic
d
is
pa
tc
h
(
D
ED
)
in
a
non-
con
v
e
x
s
o
l
ut
ion
spac
e
w
a
s
foun
d
by
t
he
c
o
n
sol
i
d
at
i
on
o
f
i
mm
une
a
l
g
or
it
hm
(IA)
and
gen
e
tic
a
lg
ori
t
hm
(
G
A
)
.
I
n
I
A
,
w
hen
the
extra
n
eo
us
m
o
l
ec
u
l
e
s
w
as
a
rr
i
v
e
d
i
n
t
h
e
imm
une
s
ys
tem
o
f
huma
n
bo
d
y
a
r
e
a
c
t
i
o
n
o
ccu
rs.
Ev
e
n
t
houg
h
thi
s
alg
o
ri
t
h
m
do
e
s
n
o
t
c
o
n
t
ai
n
a
ny
kn
ow
l
e
d
g
e
abo
u
t
t
ha
t
m
o
l
ecule,
t
he
y
w
e
re
a
na
lyze
d
b
y
t
his
a
l
gor
ithm
after
some
time
a
n
d
als
o
so
l
u
t
i
o
n for t
h
e
r
e
m
o
va
l of
t
he
se mo
l
ec
ul
e
s
was fo
un
d
. He
r
e
the extr
a
n
eo
us m
o
l
ecu
le was
kn
ow
n a
s
a
nt
i
g
ens a
n
d t
h
e rea
c
tio
n o
f
the
im
m
une syste
m w
a
s kno
w
n
a
s a
n
ti
b
odi
e
s
.
The
a
n
tib
odi
es
s
ho
ul
d
b
e
bala
nc
e
d
w
i
t
h
th
e
un
k
now
n
ant
i
g
ens.
T
he
a
nt
i
bod
ies
w
e
re
g
i
v
e
n
b
y
th
e
ob
jec
t
i
v
e
f
u
nct
i
on,
i
t
s
c
o
m
bin
e
d
c
o
nst
r
a
i
nt
s
f
r
om
t
h
e
a
n
t
ig
e
n
s
an
d
t
h
e
sol
u
tio
n
s
w
hi
ch
e
nhan
c
e
t
he
m.
S
om
e
a
n
t
i
bo
d
i
es
w
a
s
g
ener
ate
d
by
th
e
h
u
m
an
b
ody
a
t
t
h
e
in
iti
al
s
t
a
g
e
a
n
d
th
ose
an
t
i
bod
i
e
s
wa
s
co
mp
ar
ed
w
it
h
the
new
c
o
m
e
r
a
ntige
n
s
and
the
ide
n
ti
c
a
l pr
ope
rties be
tw
e
e
n
the
m
w
as e
st
imated.
Th
is e
st
i
m
ati
o
n
w
a
s
k
n
ow
n
as
a
ffin
i
t
y
fa
ctor.
K
.
V
a
i
sa
kh
e
t
.
a
l
[2
8]
d
e
s
ig
ned
“
S
ol
v
i
n
g
d
y
n
a
m
ic
e
c
o
nom
ic
d
i
s
pa
t
c
h
d
rawb
a
c
k
w
it
h
se
cu
r
i
ty
con
s
trai
n
t
s
e
x
plo
ita
t
i
on
ba
c
t
erial
for
a
ge
P
S
O
-D
E
a
l
gor
it
hm
”.
H
e
re
p
ro
blem
s
l
i
ke
n
o
n
-sm
o
o
t
h,
n
on
-
c
on
vex
nat
u
re
a
t
t
ri
b
u
t
a
ble
to
v
a
l
ve-p
oi
n
t
l
oa
din
g
e
ffe
c
ts,
ra
mp
r
ate
l
im
its,
sp
in
n
i
ng
rese
rve
c
a
p
abi
l
ity,
pro
h
i
b
ited
i
n
opera
tio
n
zo
ne
s
and
se
cur
i
t
y
c
on
st
r
a
i
n
t
s
w
a
s
s
how
n
i
n
D
ED
d
ra
w
b
ac
k.
T
he
o
n
to
p
of
m
enti
one
d
iss
u
es
i
s
ofte
n
de
fe
at
ed
by
t
h
e
mix
i
n
g
o
f
bac
t
e
r
ia
l
forage
P
art
i
cl
e
Swarm
i
m
p
rovem
e
n
t
(
B
P
SO
)
w
ith
d
i
f
fer
e
ntia
l
evo
l
ut
ion
(D
E)
a
l
gor
it
hmic
r
u
l
e
.
T
he
B
P
S
O
w
a
s
a
m
i
x
t
ure
of
m
i
c
r
o
o
rga
n
i
s
m
forage
o
p
t
i
m
iza
tio
n
a
l
gor
i
t
hm
ic
r
u
l
e
a
n
d
P
S
O
.
T
h
e
b
a
c
t
e
r
i
u
m
w
i
t
h
p
o
s
i
t
i
v
e
f
o
r
a
g
i
n
g
m
e
t
h
o
d
s
w
a
s
c
hos
e
n
b
y
t
h
e
P
S
O
ope
rat
o
r
w
i
t
h
i
n
t
he
cha
nge
m
et
ho
d
of
e
ach
c
he
mo-ta
c
t
i
c
ste
p
,
so
a
s
to
g
e
t
r
educe
d
p
r
i
ce
.
In
o
ur
n
e
w
B
P
S
O-D
E
a
ppr
oa
ch,
th
e
prima
r
y st
e
p
w
a
s
the su
b
s
t
i
t
ut
io
n of vel
oc
i
t
y in p
la
ce o
f
de
l
ta
. Wit
h
in the
s
e
c
on
d
s
t
e
p
,
thr
o
u
g
h
t
he ca
l
c
u
la
tio
n
of
f
i
t
ne
s
s
o
pera
te
t
he
p
op
u
l
a
t
i
o
n
o
f
b
e
s
t
fit
n
ess
w
i
th
in
t
he
c
u
rre
nt
g
e
n
e
r
ati
o
n
a
nd
al
so
t
he
w
ort
h
f
or
w
orld
bes
t
f
i
t
ne
ss
w
a
s
o
b
t
a
i
n
e
d.
W
i
t
h
i
n
t
h
e
third
ste
p
,
the
p
o
si
t
i
on
of
g
en
era
tio
n
w
a
s
modi
fie
d
t
o
a
repl
ace
me
n
t
pos
it
io
n.
W
ith
in
t
he
f
ourt
h
s
t
e
p,
t
o
r
e
trie
v
e
t
he
l
o
sses
fr
om
p
ow
er,
appa
ren
t
pow
e
r
w
it
hin
the
l
i
n
e
s
an
d
vo
lta
ge
s
o
f
l
oa
d
w
a
s
retr
i
e
ve
d
b
y
t
he
l
oa
d
f
l
ow
ope
ra
ti
o
n
t
ha
t
w
a
s
do
ne
w
i
t
h
t
h
ose
ne
w
po
pu
l
a
tio
ns
m
a
d
e
at
the
prev
i
o
us
s
te
p.
W
it
h
i
n
t
h
e
fifth
s
t
e
p
t
he
v
io
la
tio
ns
w
a
s
v
e
r
ifie
d
for
t
h
e
li
ne
f
low
s
a
n
d
c
a
r
go
vo
l
t
a
g
es.
If
it
con
t
a
i
n
s
v
i
o
la
t
i
o
n
s
the
n
p
ena
l
t
y
t
er
ms
w
er
e
add
i
t
i
o
n
al
t
o
the
f
i
t
ness
ope
rate
o
f
ea
c
h
B
P
S
O
and
D
e
la
w
a
re
.
Eac
h
t
he
f
itne
s
s
fu
nct
i
ons
w
e
r
e
com
p
ar
ed
f
or
e
ac
h
bacter
ia
l
p
o
p
u
l
at
i
on
a
nd
a
l
so
t
he
b
es
t
w
o
rth
w
a
s
ke
e
p
in
g
in
a
n
exce
e
d
in
gly
se
pa
rate
v
a
r
iab
l
e.
T
he
s
im
ple
s
t
va
lue
of
f
itn
e
s
s,
r
ea
l
p
o
w
e
r
g
ener
ati
o
n
pric
e,
v
o
lta
ge
s,
lin
e
fl
ow
s,
pow
er
l
osse
s
for
the
give
n
i
n
t
e
rva
l
w
ere
upda
te
d
for
al
l
t
he
m
i
c
roorga
ni
sm
p
o
p
u
l
a
t
i
on
as
p
be
st
a
n
d
gl
oba
l be
st (
gb
est).
Then the
p
roce
dure
for
nex
t
c
hem
o
-tac
tic
s
te
p w
a
s
cont
inua
l.
3.
PROPOS
E
D
OPTIMI
Z
ATI
O
N
SOL
U
TI
ON TO
OP
F PROBL
E
M
I
n
a
w
i
n
d
e
n
e
r
g
y
s
y
s
t
e
m
,
O
p
t
i
m
a
l
P
o
w
e
r
F
l
o
w
(
O
P
F
)
i
s
a
M
u
l
t
i
-
o
b
j
ecti
v
e
o
p
ti
mi
za
ti
o
n
p
r
ob
l
e
m
th
at
seeks
t
o
f
ind
ou
t
a
com
p
rom
i
se
s
olu
t
io
n
to
m
inim
i
z
e
t
h
e
fue
l
c
o
st,
power
l
o
ss,
e
m
i
ss
ion
and
ma
int
a
in
in
g v
o
lta
ge
s
ta
b
ili
ty. The
So
l
u
t
i
on
o
f
o
p
t
i
m
a
l
pow
e
r
f
l
ow
(
O
P
F
)
p
r
oble
m
a
im
s
t
o
o
pt
imiz
e
a
se
le
cted
ob
jec
t
i
v
e
fu
nc
tio
n
t
h
ro
u
gh
op
t
i
m
a
l
a
d
jus
t
m
e
nt
o
f
the
p
o
w
e
r
syst
em
c
on
tr
ol
v
aria
ble
s
w
hi
le
a
t
t
h
e
sa
me
t
im
e
sat
i
sf
y
i
n
g
t
he
v
ari
ous
e
q
u
a
l
i
t
y
a
n
d
i
n
e
qua
lit
y
c
ons
trai
n
t
s.
A
cc
ordin
g
t
o
the
resu
l
t
s
of
p
r
e
vio
u
s
in
ves
tig
a
t
i
o
ns,
An
i
m
al
M
ig
ra
ti
on
O
p
t
i
m
i
zati
o
n
(AM
O
)
and
Art
i
fi
ci
a
l
P
hysi
c
a
l
O
pt
imiza
tio
n
(A
P
O
)
hav
e
b
e
t
ter
pe
rform
anc
e
for
s
o
lv
in
g
op
t
i
miz
a
tio
ns
p
r
o
blem
s.
I
n
t
h
is
w
ork,
w
e
in
te
nd
to
prop
ose
a
H
ybr
id
M
ult
i
o
b
j
ec
t
i
ve
A
rt
ific
ial
P
hysi
c
a
l
O
pt
i
m
iza
t
i
o
n
(H
M
O
A
P
O
)
i
s
t
o
s
ol
vin
g
t
he
O
P
F
(
O
p
tima
l
P
owe
r
F
l
o
w)
p
ro
b
l
em
i
n
win
d
en
e
r
gy
syste
m
.
The
a
r
chi
t
ec
t
u
re
of
o
u
r prop
ose
d
w
ork
i
s
s
h
o
w
n
i
n
F
i
gur
e 1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
48
6 –
50
3
49
0
cv
A
n
im
a
l
m
i
g
r
a
ti
o
n
w
i
th
a
r
t
if
i
c
i
a
l
ph
ys
i
c
a
l
opt
i
m
iz
at
i
o
n
A
d
apt
i
ve
p
ena
l
t
y
func
t
i
on
Hybr
i
d
opt
i
m
i
z
at
i
on for opt
i
m
a
l
p
ow
e
r
fl
o
w
c
o
n
t
r
o
l
F
i
gure
1.
A
rc
hi
te
ct
ure
of o
ur
prop
o
sed
w
o
rk
T
o
e
n
h
a
n
c
e
t
h
e
p
e
r
f
o
r
m
a
n
c
e
o
f
A
P
O
,
t
h
i
s
w
o
r
k
a
p
p
l
i
e
s
a
n
A
n
i
m
a
l
Migra
t
ion
algorithm
(AMO)
w
h
i
c
h
f
o
l
l
o
w
s
t
h
r
e
e
m
a
i
n
r
u
l
e
s
f
o
r
e
a
c
h
i
n
d
i
v
i
d
u
a
l
a
n
d
a
l
s
o
t
o
ove
rcom
e
the
d
r
aw
ba
ck
o
f
pre
m
a
t
ure
con
v
er
ge
nce
.
I
n
ad
di
t
i
on,
t
he
M
O
A
P
O
is
c
ombi
ne
d
w
ith
A
da
p
tive
P
en
al
t
y
F
u
n
c
tio
n
t
o
h
a
n
d
l
e
equ
a
lity
a
nd
ine
q
ual
i
t
y
c
o
n
s
t
r
ai
ns
a
s
s
oc
ia
t
e
d
w
i
th
O
P
F
p
rob
l
em
s.
T
he
a
da
p
tiv
e
pena
l
t
y
fu
nc
ti
o
n
(
A
P
F
)
,
w
h
i
c
h
co
n
v
e
r
t
a
con
s
trai
ne
d
pr
ob
lem
in
to
a
n
unc
o
n
stra
ine
d
one
w
he
re
t
he
‘
P
e
nalt
y
F
unc
t
i
on’
p
e
n
a
l
i
z
e
t
h
e
in
feasi
b
le
s
ol
u
tio
ns
to m
ove t
ow
a
r
ds des
ira
b
l
e
fe
a
si
bl
e
so
l
u
ti
o
n
s
.
3.1.
O
P
F
pr
o
b
l
e
m
d
e
fi
ni
t
i
o
n
The
O
P
F
prob
lem
is
c
o
n
s
i
de
re
d
as
a
g
e
n
era
l
o
p
t
imiza
tio
n
prob
lem
.
Th
e
O
P
F
proble
m
e
xpec
t
s
t
o
reduc
e
the
w
h
ole
f
u
el
c
os
t
pe
rform
w
h
ere
a
s
fu
l
f
i
l
lin
g
t
h
e
w
h
o
l
e
l
oa
d,
c
omp
l
ete
l
y
di
ffere
n
t
e
qua
l
i
t
y
a
n
d
d
i
f
f
e
ren
c
e
co
nst
r
ai
n
t
s.
L
i
k
ewi
s
e,
t
h
e
b
e
s
t
va
l
u
e
s
o
f
t
h
e
man
a
g
e
me
nt
v
ari
a
bl
e
s
w
ith
i
n
t
h
e
po
we
r
g
r
i
d
a
re
resol
v
ed
w
i
t
h
i
n the
O
P
F
pr
ob
l
e
m.
Mathem
a
t
i
ca
l ex
pre
ssio
n
b
e
lo
ng
i
n
g to
t
he
m
atter
i
s
d
el
inea
t
i
n
g
as
fo
l
l
ow
s.
T
OF
OF
OF
OF
OF
OF
Min
)
,
,
,
,
,
(
6
5
4
3
2
1
(
1
)
Su
b
j
ect
to
:
,
sin
cos
|
|
|
|
1
ij
ij
ij
ij
N
j
j
i
Di
Gi
B
G
V
V
P
P
,
N
i
(
2)
,
cos
sin
|
|
|
|
1
N
j
ij
ij
ij
ij
j
i
Di
Ci
Gi
B
G
V
V
Q
Q
Q
,
N
i
(
3
)
,
,
max
min
g
Gi
Gi
Gi
N
i
P
P
P
(
4
)
,
,
max
min
g
Gi
Gi
Gi
N
i
Q
Q
Q
(
5)
,
|,
|
|
|
|
|
max
min
N
i
V
V
V
i
i
i
(
6)
,
,
max
min
t
k
k
k
N
k
t
t
t
(
7
)
,
,
nbr
i
S
S
rated
li
li
(
8)
,
,
max
min
c
ci
ci
ci
N
i
Q
Q
Q
(
9)
1
sin
|
|
4
2
j
i
i
j
ij
ij
V
Q
X
LSI
(
10)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
So
l
u
t
i
on
f
o
r
o
p
t
im
al p
o
w
er f
l
o
w
pr
ob
l
e
m
in
w
i
n
d
ene
r
g
y
sy
ste
m
usi
n
g
hyb
r
i
d
..
. (P.
Nag
a
l
eshm
i)
49
1
,
tan
1
ij
ij
R
X
(
11)
.
sin
|
|
|
|
sin
|
|
|
||
|
2
ij
j
j
i
ij
j
i
j
Z
V
Z
V
V
Q
(
1
2
)
I
n
t
h
i
s
w
o
rk,
the
targ
et
p
erform
o
f
the
OP
F
pr
obl
e
m
is
p
roposed
b
ec
au
se
t
h
e
t
ot
a
l
g
e
n
era
t
io
n
v
a
lu
e
as
w
e
ll
as
v
a
l
ve
-p
oi
nt
i
m
p
a
c
t,
l
oss
m
i
n
i
m
i
z
a
t
i
o
n
a
nd
p
ro
hi
bite
d
z
on
es.
Th
e
p
o
w
er
f
lo
w
equ
a
t
i
o
n
s
a
re
th
oug
h
t
-a
b
out
b
e
cau
se
t
he
e
qua
l
ity
c
o
n
stra
in
t
s
.
The
tra
n
s
m
issi
o
n
li
m
i
ts
a
nd
al
terna
tiv
e
se
curit
y
lim
i
t
s
a
r
e
u
s
ed
a
s
dif
f
e
r
en
c
e
con
s
t
r
ain
t
s.
T
h
e
v
e
c
t
o
r
s
a
re
o
ut
lin
ed
a
s
st
a
t
e
v
ari
a
bl
e
and
con
t
rol
v
a
ri
ab
l
e
v
ecto
r
s
a
r
e
ou
tli
ne
d
as fo
l
l
o
w
s
:
.
........
,
........
,
.......
,
......
1
1
1
1
Nc
c
c
Nt
Ng
g
g
Ng
g
g
Q
Q
T
T
V
V
P
P
(
1
3
)
Where
g
P
,
g
V
,
Nt
T
,
c
Q
a
re
d
esc
r
ibe
d
a
s
the
a
c
tive
p
o
w
e
r
of
t
he
s
lac
k
b
u
s
,
the
v
o
lta
g
e
ma
gnit
ude
o
f
the
l
o
ad
b
uses
,
ac
t
i
ve
p
ower
o
u
t
pu
t
of
t
he
g
enera
t
ors
ex
c
e
pt
a
t
t
h
e
s
l
ack
b
u
s
,
th
e
re
ac
t
i
v
e
p
o
w
e
r
o
f
the
gene
ra
tors r
esp
e
c
t
i
v
e
l
y.
.
......
,
.......
,
......
1
1
1
nbr
PQ
l
l
N
PQ
PQ
Ng
g
g
S
S
V
V
Q
Q
(
1
4
)
Where
g
Q
,
PQ
V
and
l
S
a
re
define
d
as
t
h
e
re
ac
t
i
ve
p
ower
gene
r
ati
o
n at
b
u
s
,
the
vo
lta
g
e
of load bus
and
the
l
i
ne
flo
w, r
especti
v
el
y
.
O
b
jec
tiv
e
fu
nc
t
i
on
I
n
t
h
i
s
pa
per,
t
h
e
o
bj
e
c
t
ive
fu
nct
i
on
of
t
he
O
P
F
pr
o
b
le
m
i
s
d
e
f
ine
d
a
s
m
i
n
i
m
i
za
t
i
o
n
o
f
t
h
e
to
ta
l
fue
l
cos
t
of
t
h
e pow
e
r
ge
n
era
tio
n
sys
t
em
.
The
t
o
t
a
l
fue
l
c
os
t
ca
n
be
m
a
t
he
ma
ti
c
a
ll
y de
fine
d as
f
o
l
l
o
w
s
:
Ng
i
i
Gi
i
Gi
i
c
P
b
P
a
OF
1
2
1
(
1
5
)
Where
i
PG
a
re r
epre
se
nt
e
d
a
s
the a
c
ti
ve p
ow
e
r
out
p
u
t o
f
t
he
th
i
ge
n
era
t
or
, respec
tive
l
y.
i
a
,
i
b
and
i
c
a
re the
f
u
e
l
cos
t
coe
ffic
i
e
nts
o
f
t
he
th
i
g
en
er
ator.
3.2.
Th
e
gen
eratio
n
cost min
i
mi
z
a
tion
wit
h
valve
p
oin
t
lo
a
d
i
n
g
(
V
P
L)
e
f
f
e
c
t
The
ge
ne
rat
i
o
n
c
o
st
w
i
t
h
va
lv
e-po
i
n
t
e
f
f
e
c
t
is
p
r
es
en
t
e
d
as
f
o
l
lo
ws
:
Gi
Gi
i
i
Ng
i
i
Gi
i
Gi
i
P
P
e
d
c
P
b
P
a
OF
min
1
2
2
sin
(
1
6
)
Where
i
d
a
n
d
i
e
a
re
c
o
e
ffi
c
i
e
n
t
s
o
f
t
h
e
va
lv
e-p
o
i
n
t
e
f
f
ect
o
f
t
h
e
th
i
g
ene
r
a
t
or.
Typ
i
ca
l
c
u
rve
rela
t
e
d to f
ue
l cos
t
w
it
h a
nd
w
i
t
h
o
u
t
val
v
e-
po
i
n
t e
f
fec
t
of
t
h
e
ge
n
e
r
a
t
i
on
un
i
t
s
is sh
o
w
n
i
n F
i
gur
e2.
Un
i
t
Co
s
t
W
i
t
h
val
ve
p
o
i
n
t
e
f
f
e
c
t
W
i
th
o
u
t
v
a
l
v
e
p
o
i
n
t
e
f
fe
c
t
F
i
gur
e 2.
Typ
i
c
a
l
c
urve
re
l
ate
d
t
o
fue
l
c
ost
w
ith
a
nd w
ith
o
u
t v
a
l
ve-
p
oin
t
e
ffe
c
t
of t
h
e
ge
nera
t
i
o
n
u
nits
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
48
6 –
50
3
49
2
Let
k
j
W
k
j
P
W
,
,
be
t
he
e
l
e
ctrica
l
e
n
erg
y
c
ost
of
w
i
nd
pow
er
o
f
t
h
e
th
j
win
d
f
arm
and
t
h
e
th
k
w
i
nd
pow
er
gene
r
at
or.
Ther
efor
e,
t
he c
os
t
of
t
he
w
in
d un
i
t
ca
n
be
de
f
i
ne
d b
y
:
k
j
k
j
k
j
z
k
j
k
j
k
j
z
k
j
k
j
k
j
W
k
j
P
P
P
P
P
P
W
,
,
,
,
,
,
,
,
,
,
,
,
~
ˆ
~
2
1
(
17)
Whi
c
h,
k
j
k
j
P
P
,
,
~
,
a
r
e
e
xpe
cted
a
nd
a
v
ai
l
a
ble
gene
ra
ti
o
n
o
utp
u
t
of
t
he
u
n
i
t
j
in
t
h
e
w
i
n
d
f
a
r
m
k
(
M
W
)
.
k
j
,
,
k
j
z
,
,
1
a
nd
k
j
z
,
,
2
are
na
m
e
ly
d
irec
t
,
o
vere
stim
at
io
n
and
u
n
d
ere
s
t
i
m
a
tion
e
l
ec
tri
c
a
l
wi
nd
e
n
e
rg
y
cost
c
o
eff
i
ci
ent
o
f
th
e
u
ni
t
j
i
n
t
he
w
in
d
farm
k
($
/
M
W
h
).
3.3.
Generatin
g
un
its with p
rohi
b
i
ted
op
erat
i
n
g
z
ones (POZ
s
)
The
p
h
y
si
c
a
l
l
imita
t
i
ons
o
f
t
h
e
p
o
w
e
r
pla
n
t
c
o
mp
one
nts,
p
roh
i
bi
te
d
o
p
e
r
ati
ng
z
one
s
(P
O
Z
s)
a
re
occ
u
rred in
a
h
ydr
o-ge
nera
t
i
n
g
un
it. T
his co
ns
train
t
di
c
ta
t
e
s s
e
v
era
l
f
e
a
si
bl
e
su
b
-
re
gi
on
s
fo
r
hyd
ro
-g
en
erat
i
ng
un
its a
s show
n in
F
ig
ure
3
and
ca
n be
e
xpre
sse
d by
:
Va
l
v
e
po
i
n
t
ef
f
ect
Pr
o
h
i
b
i
t
e
d
zo
n
e
Co
s
t
T
h
e
u
ni
t
th
i
k
LB
i
P
1
k
UB
i
P
F
i
gure
3.
Top
o
l
o
gy
of
c
os
t
fu
nct
i
on w
i
th pr
o
hi
b
i
t
zo
ne
co
n
s
t
rai
n
t
and
v
al
ve
p
o
i
nt
e
f
f
e
c
t
k
g
i
i
UB
i
LB
i
i
UB
i
LB
i
i
i
N
k
N
i
P
P
P
P
P
P
P
P
P
k
k
k
,.....,
2
,
1
,
,......,
2
,
1
,
max
min
1
1
(
1
8
)
Whi
c
h,
1
k
UB
i
P
a
n
d
k
LB
i
P
a
r
e
u
p
p
e
r
a
n
d
lo
w
e
r
li
m
i
ts
o
f
t
h
e
th
k
su
b-
regi
o
n
s
of
t
he
th
i
u
n
i
t
,
re
spe
c
ti
ve
ly.
g
N
and
k
N
a
r
e
the nu
m
b
er
o
f
t
h
e
r
m
a
l un
i
t
s
an
d
su
b-r
e
gi
on
s.
Pow
e
r L
o
ss
Mini
m
i
z
a
tion
The
t
o
ta
l re
al p
ow
e
r
loss in power syste
ms i
s
re
p
r
es
en
t
e
d
by
N
i
N
j
j
i
j
i
ij
j
i
j
i
ij
Q
P
P
Q
Q
Q
P
P
OF
11
3
(
19)
Whi
c
h
j
i
j
i
ij
ij
j
i
j
i
ij
ij
V
V
r
V
V
r
sin
,
cos
,
i
i
V
i
s
t
h
e
com
p
le
x
vo
l
t
a
g
e
at
t
he
bus
th
i
.
ij
ij
ij
jx
r
Z
is
t
h
e
th
ij
ele
m
e
n
t
of
[
Z
bus]
i
m
pe
da
nc
e
m
a
trix.
i
P
an
d
j
P
a
r
e
t
h
e
ac
t
i
ve
p
ower
i
nj
e
c
t
i
o
n
s
a
t
th
e
th
i
and
th
j
buses,
re
sp
ec
ti
v
e
ly
.
i
Q
an
d
j
Q
a
r
e
the
rea
c
t
i
v
e
power
i
n
j
e
c
ti
ons
a
t
the
th
i
and
th
j
buses,
r
espective
l
y.
N
is
t
he
numbe
r of b
us
es.
L-i
n
d
e
x
m
i
ni
mizat
i
on
The
v
o
l
t
a
g
e
sta
b
il
ity
i
nde
x (
V
S
I
)
w
h
ich
en
su
res
secur
e
ope
rati
o
n
s
a
nd
i
s
w
r
i
t
t
e
n
a
s
f
oll
o
ws
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
So
l
u
t
i
on
f
o
r
o
p
t
im
al p
o
w
er f
l
o
w
pr
ob
l
e
m
in
w
i
n
d
ene
r
g
y
sy
ste
m
usi
n
g
hyb
r
i
d
..
. (P.
Nag
a
l
eshm
i)
49
3
and
V
V
V
dV
V
V
OF
avg
N
i
avg
i
2
|
|
|
|
,
|
|
min
max
1
4
(
2
0
)
,
2
|
|
min
max
V
V
dV
(
21)
Where
n
i
s
s
e
l
e
c
ted
t
o
be
eq
ua
l
1
.
F
i
nal
l
y,
w
ind pow
er
ca
n
be
expr
essed
by
t
h
e
p
i
e
ce
wi
s
e
l
in
e
a
r
as foll
o
ws:
f
w
k
j
co
k
j
k
j
h
k
j
h
k
j
k
j
k
j
k
j
k
j
k
j
k
j
k
j
k
j
ci
k
j
k
j
k
j
k
j
k
j
k
j
k
j
k
j
k
j
ci
k
j
k
j
k
j
k
j
k
j
ci
k
j
k
j
k
j
h
k
i
N
k
N
j
otherwise
T
T
T
T
T
T
T
T
D
T
T
D
T
T
D
T
T
T
T
T
D
T
T
D
T
T
T
T
D
P
P
,...
2
,
1
,
,...
2
,
1
,
0
,
1
),
(
)
(
)
(
),
(
)
(
,
,
,
,
,
,
,
,
,
2
,
,
2
,
,
,
3
,
,
1
,
,
2
,
,
2
,
,
,
,
1
,
,
1
,
,
2
,
,
,
1
,
,
1
,
,
,
2
,
,
,
,
1
,
,
1
,
,
1
,
,
,
,
,
,
1
,
,
,
(22)
Whi
c
h,
Di,j,k
is
s
l
o
pe
o
f
se
ct
ion
j
of
t
he
w
i
n
d
u
n
it
w
in
w
in
d
fa
rm
f
(MW
s
/m)
.
Tc
i,j,k
,
Tco
,
j,k
,
Ti,j,
k
and
T
h
,j,k
ar
e
c
u
t
-
i
n
w
i
n
d
sp
e
e
d,
c
u
t
-ou
t
w
i
nd
spee
d,
b
re
a
k
p
o
i
nt
o
f
seg
m
en
t
i
an
d
rat
e
d
w
i
n
d
s
p
e
ed,
for
a
l
l
the w
i
nd
un
it
s
w
in the wind farm (
m
/
s),
res
p
ectively.
Artif
ic
i
a
l Phy
s
i
c
al O
p
tim
iz
ati
o
n
AP
O i
s
a nat
ure-
i
n
s
p
ire
d
m
et
aheur
i
st
ic me
t
ho
d i
n
sp
ire
d
b
y
na
tur
al ph
y
s
i
cal forc
e
s
ba
se
d
o
n
art
ific
ia
l
ph
ysic
s
(A
P
)
fram
e
w
o
r
k
[
2
9
]w
hic
h
i
s
de
vel
o
ped
by
S
p
ea
r
e
t
a
l.
B
ase
d
o
n
th
e
si
mi
l
a
ri
ty
a
mo
ng
t
h
e
A
P
met
h
od
a
n
d
po
pul
a
tio
n
-
b
a
sed
opt
i
m
i
zati
o
n
a
l
go
rith
m,
r
e
c
e
n
tly
s
o
m
e
a
uth
o
rs
p
ro
p
o
se
d
A
P
O
and
te
ste
d
i
t
s
op
tim
iza
t
i
o
n p
e
r
f
orm
a
nc
e [30
–
3
2
]
.
A
P
O
c
a
n
be
descr
i
be
d b
r
iefly
as fo
l
l
o
w
s
A
ssum
e
t
he
op
timiz
a
t
i
on pr
o
b
l
e
m
can
b
e
exp
r
e
s
se
d as
D
d
x
x
x
t
s
x
f
d
d
d
d
,........,
2
,
1
,
.
.
)
(
min
max
min
Where
D
i
s
t
h
e
d
ime
n
si
on
of
t
he
p
r
o
b
l
e
m
,
d
x
min
an
d
d
x
max
a
r
e
t
h
e
mini
mu
m
a
n
d
m
a
x
i
m
u
m
li
m
i
t
s
o
f
varia
b
l
e
d
x
.
The
pa
rtic
l
e
’s pos
i
tio
n
si
gn
i
f
i
e
s the
so
l
u
t
i
o
n
to t
h
e
o
p
tim
iza
t
i
o
n pro
b
lem
. The
p
osit
io
n o
f
p
artic
le
i
is
d
efi
n
e
d
as
.
,.........
2
,
1
,
,.......,
,.......,
,
2
1
NP
i
x
x
x
x
X
D
i
d
i
i
i
i
Where
N
P
is the
numbe
r of in
d
iv
id
ua
ls i
n A
P
O
;
d
i
x
i
s
t
h
e posit
i
on
o
f the
th
i
i
ndi
vid
u
a
l
in
th
d
dime
n
s
i
o
n.
Step
1
: Pop
u
l
at
io
n Ini
t
i
al
iza
t
io
n.
T
he
N
P
i
ndi
v
i
dua
l’s po
si
tio
n
s
a
re
r
andom
l
y
for
me
d in th
e
n
-d
im
e
n
si
o
n
a
l
d
eci
si
on
space
.
The
N
P
i
ndi
v
i
dua
l’s ve
loc
itie
s a
r
e set to
b
e z
e
ro.
Step
2
: Fit
n
ess
c
a
lcu
l
a
t
io
n.
C
om
pu
te t
he
fi
t
ne
ss of
e
a
c
h i
n
d
i
vid
u
a
l
a
c
c
o
rdi
ng t
o
t
he
o
b
j
e
c
t
i
v
e f
unc
t
i
o
n
.
Step
3
: For
ce
ca
l
c
u
l
a
t
i
o
n.
I
n
t
he
A
P
O
,
the
proce
s
s
of
o
p
t
im
iz
at
i
on
i
s
c
on
t
i
n
u
o
u
s
l
y
p
e
r
form
ed
by
mo
vi
n
g
t
he
i
nd
ivi
dua
l
t
o
w
a
r
d
t
h
e
p
r
o
m
i
s
i
ng
re
g
i
on
unt
il
t
h
e
o
p
t
i
m
al
s
o
l
u
t
io
ns
i
s
fo
und
.
An
d
t
h
e
r
u
l
e
s
for
m
ovin
g
t
he
i
nd
ivi
d
u
a
ls
a
re
dec
i
de
d by t
h
e
forc
es a
ct o
n
eac
h ot
her.
The
rules
c
a
n
b
e
ex
pre
sse
d
b
y t
h
e
fo
l
l
ow
i
n
g
eq
ua
ti
o
n
s:
4.
SIMU
L
A
TION
R
ESULT
S
AN
D
COMP
A
R
I
S
O
NS
The
pro
p
o
s
ed
a
lg
ori
t
hm
i
s
d
e
vel
o
ped
u
s
i
n
g
MA
TLA
B
ve
r
s
i
o
n
6.5
pr
ogr
am
ming
la
ng
u
a
ge
a
nd
t
he
pro
pose
d
m
et
h
o
d
o
l
o
gy
is
t
es
te
d
i
n
I
EE
E
3
0
-
bus
s
yst
e
m
and
the
sa
m
p
les
ar
e
te
st
e
d
o
n
2
.
6-Ghz
Penti
u
m-IV
P
C
.
The
gener
a
tors da
t
a
and
cos
t
coe
ffic
i
e
nts
are gathe
r
e
d
f
rom
[
25]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
48
6 –
50
3
49
4
4.1.
Case stu
d
ie
s
on
t
he
IEEE 30-b
us Syste
m
4.1.
1. Comp
a
ris
o
n wi
t
h
g
l
o
b
a
l
optimiz
a
tion
I
n
itia
l
l
y
t
h
e
sa
mple
i
s
t
e
s
t
e
d
i
n
IEEE
30-bus,
41-
bra
n
c
h
s
ys
tem
w
i
t
h
th
e
vo
lt
a
g
e
con
s
t
r
a
i
nt
o
f
l
o
wer
and
u
p
p
er
lim
i
t
s
a
r
e
0.
9
p.u
a
n
d
1.
1
p.u.
,
re
spect
i
v
e
l
y.
T
he
A
P
O
pop
ula
t
io
n
siz
e
i
s
t
a
ken
equa
l
3
0
,
t
h
e
m
o
st
range
o
f
ge
nera
t
i
o
n
i
s
10
0,
a
nd
cros
so
ver
a
nd
m
u
ta
tio
n
ar
e
app
l
i
e
d
w
i
t
h
i
n
i
t
i
a
l
l
i
k
el
i
h
o
od
ze
ro.9
a
nd
0.0
1
sever
a
l
l
y. F
igur
e
4 show
s the
t
o
p
o
l
o
gy o
f
n
o
r
m
a
l IE
EE 30 bus
s
y
stem
.
Figure
4.
I
EEE 30
bus s
ystem
F
o
r
the
aim
o
f
s
up
p
o
rt
i
v
e
the
effic
i
e
n
c
y
o
f
t
h
e
pro
p
o
se
d
a
p
pr
oa
ch,
we
h
ave
a
te
n
d
enc
y
t
o
c
r
ea
t
e
d
a
com
p
aris
on of our ef
f
ic
ie
ncy w
ith
o
t
h
ers co
m
p
etit
i
v
e OPF
e
f
fici
e
n
c
y
.
I
n
[25]
,
the
y
c
on
fe
r
r
ed a typic
a
l
G
A
,
i
n
[
3
]
th
e
au
tho
r
s
co
nfe
r
re
d
asso
ci
at
e
enh
a
n
ced
G
A,
a
n
d
so
i
n
[2
6
]
,
the
y
p
rop
o
sed
a
n
I
mpr
o
ved
e
v
olu
t
i
onar
y
pro
g
ra
mm
ing
(IEP
)
.
In
[
27]
t
he
y
presen
te
d
a
n
o
pt
i
m
um
p
ow
er
f
l
o
w
s
o
l
u
t
ion
usi
n
g
G
A
-
F
u
zz
y
s
y
ste
m
appr
oa
ch
(
F
G
A
)
,
a
nd
i
n
[
1
1
]
a
c
han
g
e
d
d
iffer
e
n
t
ial
ev
o
l
ut
ion
i
s
p
r
o
p
o
se
d
(MD
E
)
.
T
h
e
b
ud
ge
t
item
s
i
n
o
u
r
pro
pose
d
a
p
p
roa
c
h
is
800.
8
3
3
6
a
n
d
the
r
ef
o
r
e
the
pow
e
r
l
oss
is
8
.92
t
h
a
t
a
re
a
un
i
t
high
e
r
t
h
a
n
th
e
ot
h
e
rs
st
r
a
te
gie
s
r
ep
o
r
ted
w
i
t
h
in
t
he
liter
a
t
u
re.
R
e
s
u
lt
i
n
T
a
b
le
1
s
h
ow
c
lear
ly
t
ha
t
t
h
e
pro
pose
d
a
pproa
c
h
p
rov
i
des
hi
ghe
r r
e
sult
s.
Ta
b
l
e 1.
Resu
lts
o
f the
m
i
n
i
m
u
m
cost an
d
p
o
w
er
g
ener
atio
n
com
p
a
red
wi
th
:
SG
A
,
E
G
A, IEP
, FGA
and MDE
for
IEEE
30-bus
Var
i
a
b
l
e
s
O
u
r
a
ppr
oa
c
h
E
PGA
Globa
l
opti
m
iza
tion m
e
t
hods
NP
=
1
NP
=2
NP=
3
SG
A
[19]
EGA
[
3
]
IEP
[
20]
FG
A
[21]
MDE
[1
1
]
P1
(
M
W)
180.
12
175
.
1
2
174.
63
179.
367
176.
20
176.
23
58
175.
13
7
175.
97
4
P2
(
M
W)
44.
18
48
.
1
8
47.
70
44.
24
48.
75
49.
009
3
50.
353
48.
884
P5
(
M
W)
19.
64
20
.
1
2
21.
64
24.
61
21.
44
21.
502
3
21.
451
21.
510
P8M
W
)
20.
96
22
.
7
0
20.
24
19.
90
21.
95
21.
811
5
21.
176
22.
240
P
11(
M
W
)
14.
90
12
.
9
6
15.
04
10.
71
12.
42
12.
338
7
12.
667
12.
251
P
13(
M
W
)
12.
72
13
.
2
4
12.
98
14.
09
12.
02
12.
012
9
12.
11
12.
000
Q
1
(Mva
r)
-4
.
5
0
-2.11
-2.
03
-
3
.1
56
-
-
-
6
.5
62
-
Q
2
(Mva
r)
30.
71
32
.
5
7
32.
42
42.
543
-
-
22.
356
-
Q
5
(Mva
r)
22.
59
24
.
3
1
23.
67
26.
292
-
-
30.
372
-
Q
8
(Mva
r)
37.
85
27
.
8
2
28.
22
22.
768
-
-
18.
89
-
Q
11(M
v
a
r)
-2
.
5
2
0
.
490
0.
48
29.
923
-
-
21.
737
-
Q
13(M
v
a
r)
-
13.
0
8
-11.
4
3
-11.
4
3
32.
346
-
-
22.
635
-
1(de
g)
0.
00
0.
0
0
0.
00
0.
000
-
-
0.
00
-
2(de
g)
-
3
.4
48
-
3
.3
24
-3.31
3
-
3
.6
74
-
-
-
3
.6
08
-
5(de
g)
-
9
.8
58
-
9
.7
25
-9.62
3
-10.
1
4
-
-
-
1
0
.
50
9
-
8(de
g)
-
7
.6
38
-
7
.3
81
-7.42
1
-10.
0
0
-
-
-
8
.1
54
-
11(de
g)
-
7
.5
07
-
7
.6
80
-7.32
2
-
8
.8
51
-
-
-
8
.7
83
-
13(de
g)
-
9
.1
02
-
8
.9
42
-8.92
6
-10.
1
3
-
-
-
1
0
.
22
8
-
C
o
st
(
$/hr
)
801.
34
800
.
8
3
800.
92
803.
699
802.
06
802.
46
5
802.
00
03
802.
37
6
P
l
oss (MW)
9.
120
8
.
920
8.
833
9.
5177
9.
3900
9.
494
9.
459
C
P
U
t
i
m
e
(s
)
~0.
954
-
-
594.
08
-
23.
07
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
So
l
u
t
i
on
f
o
r
o
p
t
im
al p
o
w
er f
l
o
w
pr
ob
l
e
m
in
w
i
n
d
ene
r
g
y
sy
ste
m
usi
n
g
hyb
r
i
d
..
. (P.
Nag
a
l
eshm
i)
49
5
Ta
b
l
e
1
de
no
t
e
s
t
h
e
c
o
st
c
o
n
sum
p
t
i
on
o
f
t
he
p
ro
p
o
se
d
and
pre
v
a
i
l
i
ng
g
l
ob
al
m
e
t
hod
o
l
o
g
i
e
s.It
i
s
clea
rl
y
se
en
t
ha
t
t
h
e
c
o
st
c
o
n
sum
p
ti
on
of
t
he
p
reva
i
l
i
n
g
m
e
tho
d
ologies
such
a
s
S
ga
,
tg
a,I
ep
,F
ga
and
M
de
.
ar
e
com
p
ara
t
i
v
e
l
y
hi
g
h
er
t
ha
n
t
h
at
o
f
t
h
e
co
st
c
ons
um
p
tio
n
o
f
our
p
r
o
p
o
se
d
m
e
tho
d
o
l
ogy
i
m
p
ly
ing
EP
G
A
.
T
h
is
clea
rl
y dep
i
c
t
s
t
h
e
co
st e
ffic
ie
ncy o
f
o
ur
f
rame
w
o
rk from ot
her
s.
Tabl
e
2
sho
w
s
t
h
e
be
st
s
olu
t
io
n
of
s
h
u
n
t
c
o
mp
en
sa
tio
n
o
bt
ain
e
d
a
t
t
he
s
tan
d
ard
l
o
ad
d
em
and
(P
d=
2
8
3
.4
M
W)
u
s
i
ng
rea
c
tive
pow
er
p
la
nn
i
ng.
T
hi
s
de
sc
ribes
the
s
hu
nt
r
e
act
iv
e
po
we
r
co
mp
ensat
i
on
o
f
Ep
ga
a
nd
E
ga
w
here
c
ompa
rati
vel
y
b
e
tte
rme
n
t
is
s
h
o
w
n
i
n
fa
vo
ur
of
E
p
g
a
.
T
he
t
r
a
nsmiss
i
on
l
i
n
e
loa
d
in
g
aft
e
r op
t
i
miz
a
tion
com
p
are
d
t
o a
c
o a
nd fga
for
iee
e
30-
bus
a
s s
h
o
w
n
i
n
T
ab
l
e
3
.
Tabl
e 2.
Comp
a
r
ati
v
e r
e
sul
t
s
of t
he
s
h
u
n
t
r
ea
cti
v
e p
o
we
r compe
n
sat
i
on
b
e
tw
ee
n
EP
G
A
and EG
A
[7]
for
ieee
30-
bus
S
hun
t
N°
1
2
3
4
6
7
8
9
Bu
s
N°
1
0
1
2
1
5
1
7
2
1
2
3
2
4
2
9
Be
st Q
svc
[pu]
0
.
1517
0
.
0781
0
.
029
0
.
0485
0
.
0602
0
.
0376
0
.
0448
0.
0245
B
e
st c
as
e
bsh
[p
u]
[
7]
0
.
0
5
0.
05
0
.
0
3
0.
05
0
.
0
5
0.
04
0
.
0
5
0.
03
Table
3.
Transm
i
ssi
on l
i
ne l
o
a
di
n
g
a
fter
op
t
im
iza
tio
n c
o
mp
a
r
ed
t
o
A
C
O
an
d
F
G
A
for
iee
e
30-b
u
s
E
P
G
A
:
P
D=
283.
4
M
W
A
C
O
[
22]
F
GA
[
2
1
]
Li
n
e
R
at
in
g
(MV
A
)
From
B
us
P(
MW)
To
Bu
s
P(M
W
)
To
Bu
s
P(
MW)
To
Bu
s
+(
P
(
M
W
)
)
1-2
130
113.
9
2
00
-
7.
73
00
-
11
9.
5488
117.
211
1-3
130
60.
71
0
0
5.
7000
-
58.
3
682
58.
3995
2-4
65
32.
06
0
0
4.
3000
-
34.
2
334
34.
0758
3-4
130
56.
86
0
0
3.
7900
-
55.
5
742
54.
5622
2-5
130
62.
42
0
0
4.
9000
-
62.
4
522
63.
7783
2-6
65
43.
30
0
0
2.
4400
-
44.
5
805
45.
3399
4-6
90
49.
17
0
0
-8.
0
1
0
0
-49.
0
123
50.
2703
5-7
70
-
11.
7
900
7
.
2300
1
1.
293
9
14.
1355
6-7
130
34.
98
0
0
0.
8800
-
34.
0
939
33.
9924
6-8
32
11.
85
0
0
-1.
3
2
0
0
-11.
0
638
13.
6882
6-9
65
16.
57
0
0
-3.
3
4
0
0
-19.
7
631
22.
4033
6-1
0
32
12.
54
0
0
0.
0700
-
13.
1
277
14.
6187
9-1
1
65
-
15.
0
400
-
0.
07
00
1
0.
433
0
24.
1764
9-1
0
65
31.
61
0
0
-3.
8
0
0
0
-30.
1
961
32.
7929
4-1
2
65
31.
22
0
0
16.
720
0
-33.
1
670
30.
5889
12-
13
6
5
-12.
9
800
11.
800
0
1
2
.
173
0
24.
9376
12-
14
3
2
7.
6
600
1
.
0500
-
8.
04
53
7.
6911
12-
15
3
2
18.
10
0
0
1.
4900
-
18.
1
566
17.
4525
12-
16
3
2
7.
2
400
1
.
3600
-
7.
49
61
6.
34027
14-
15
1
6
1.
4
000
-
0.
68
00
-
1.
83
40
1.
2313
16-
17
1
6
3.
6
900
-
0.
54
00
-
3.
97
15
3.
2983
15-
18
1
6
5.
8
900
1
.
9700
-
6.
22
24
5.
4066
18-
19
1
6
2.
6
500
1
.
0000
-
3.
01
40
2.
3627
19-
20
3
2
-6.
8
5
0
0
-2.
4
1
0
0
6.
5015
8
.
5117
10-
20
3
2
9.
1
500
3
.
3200
-
8.
70
15
11.
0315
10-
17
3
2
5.
3
200
0
.
8600
-
5.
02
85
9.
861616
10-
21
3
2
16.
10
0
0
3.
9800
-
15.
8
419
18.
96153
10-
22
3
2
7.
7
800
1
.
7400
-
7.
67
78
9.
0741
21-
22
3
2
-1.
4
8
0
0
-0.
6
1
0
0
1.
6585
2
.
0887
15-
23
1
6
5.
2
100
-
0.
70
00
-
5.
46
13
4.
5343
22-
24
1
6
6.
2
600
1
.
0400
-
5.
95
93
6.
9397
23-
24
1
6
1.
9
900
1
.
8800
-
2.
23
88
1.
14447
24-
25
1
6
-0.
5
0
0
0
1.
1200
0
.
5027
1
.
3934
25-
26
1
6
3.
5
400
2
.
3600
-
3.
50
00
4.
2647
25-
27
1
6
-4.
0
5
0
0
-1.
2
4
0
0
4.
0748
5
.
633
27-
28
6
5
17.
32
0
0
2.
9500
-
17.
3
814
19.
7428
27-
29
1
6
6.
1
900
-
0.
29
00
-
6.
10
70
6.
4154
27-
30
1
6
7.
0
600
0
.
8900
-
6.
92
95
7.
2897
29-
30
1
6
3.
7
200
1
.
3500
-
3.
67
05
3.
7542
8-2
8
32
2
.
0
700
-
2.
19
00
-
2.
20
67
3.
3685
6-2
8
32
15.
29
0
0
-0.
6
8
0
0
-15.
1
747
16.
5409
P
l
oss
(M
W)
8.
8836
9
.
8520
9
.
494
Evaluation Warning : The document was created with Spire.PDF for Python.