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R
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ize
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(TVD).
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th
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ial
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d
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re
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wo
rld
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b
u
s
RDS.
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lati
o
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t
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e
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fter
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p
ti
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ize
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t.
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ize
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m
s
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K
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w
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d
s
:
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Dis
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p
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etwo
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Po
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ev
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T
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CC B
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C
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Vel
T
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R
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Dr
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&
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titu
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Av
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in
1.
I
NT
RO
D
UCT
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N
D
is
tr
ib
u
tio
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p
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etwo
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k
s
(
DPNs
)
h
av
e
en
d
u
r
ed
h
ig
h
e
r
p
o
wer
d
em
a
n
d
i
n
r
ec
e
n
t
tim
es
d
u
e
to
r
ap
id
ad
v
an
ce
m
e
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ts
in
tech
n
o
lo
g
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an
d
g
lo
b
aliza
tio
n
.
T
h
e
in
cr
ea
s
ed
p
o
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d
em
an
d
ca
n
c
r
ea
te
s
ev
er
al
p
r
o
b
lem
s
,
in
clu
d
in
g
p
o
wer
q
u
ality
,
r
elia
b
ilit
y
,
p
o
wer
lo
s
s
es
,
an
d
en
v
ir
o
n
m
en
tal
d
e
g
r
ad
atio
n
[
1
]
.
Dis
tr
ib
u
ted
g
e
n
er
atio
n
(
DG)
in
teg
r
atio
n
is
o
n
e
o
f
th
e
p
r
o
m
is
in
g
m
et
h
o
d
s
f
o
r
n
u
llify
in
g
th
e
is
s
u
es
in
DPN
[
2
]
.
A
ty
p
ical
DG
em
p
lo
y
s
s
m
all
-
s
ca
le
p
o
wer
-
g
en
er
atin
g
u
n
its
(
esp
ec
ially
r
en
ewa
b
le
en
er
g
y
DGs)
to
p
r
o
d
u
ce
elec
tr
icity
lo
ca
lly
in
to
th
e
DPN.
DG
allo
ca
tio
n
s
im
p
r
o
v
e
p
o
wer
q
u
ality
,
r
e
d
u
ce
p
o
w
er
lo
s
s
es
(
PL)
,
en
h
an
ce
r
eliab
ilit
y
,
an
d
r
ed
u
ce
en
v
ir
o
n
m
en
tal
p
o
llu
tio
n
[
3
]
.
H
o
wev
er
,
DG
allo
ca
tio
n
is
a
d
if
f
icu
lt
an
d
n
o
n
-
lin
ea
r
p
r
o
b
lem
.
Hen
ce
,
an
ef
f
icien
t
m
eth
o
d
o
l
o
g
y
is
ess
en
tial
to
o
p
t
im
ize
th
e
DG
in
DPN
f
o
r
s
ec
u
r
in
g
m
a
x
im
u
m
b
en
ef
its
.
Ma
n
y
m
eta
-
h
e
u
r
is
tics
(
MH
)
an
d
b
i
o
-
in
s
p
ir
ed
(
B
I
)
a
lg
o
r
ith
m
s
wer
e
in
tr
o
d
u
ce
d
to
f
in
d
th
e
o
p
tim
al
s
o
lu
tio
n
f
o
r
th
is
co
m
p
lex
a
n
d
d
y
n
am
ic
DG
allo
ca
tio
n
p
r
o
b
le
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Mu
lti
-
o
b
jective
h
u
n
ter p
r
ey
o
p
timiz
e
r
tech
n
iq
u
e
fo
r
d
is
tr
ib
u
ted
g
en
era
tio
n
p
la
ce
men
t
(
K
esa
va
n
Du
r
a
is
a
my
)
147
Dif
f
er
en
tial e
v
o
lu
tio
n
(
DE
)
[
4
]
,
g
en
etic
alg
o
r
ith
m
(
GA)
[
5
]
,
an
d
cu
c
k
o
o
s
ea
r
c
h
alg
o
r
ith
m
s
(
C
SA)
[
6
]
wer
e
ap
p
lied
to
o
p
tim
ize
DG
f
o
r
PL
r
e
d
u
ctio
n
an
d
v
o
ltag
e
d
ev
iatio
n
(
VD)
m
in
im
izatio
n
.
Dif
f
er
en
t
ty
p
es
o
f
DGs
wer
e
o
p
tim
ized
u
s
in
g
wh
ale
o
p
tim
izatio
n
alg
o
r
ith
m
(
W
OA)
[
7
]
,
m
an
ta
r
ay
f
o
r
ag
in
g
o
p
tim
izatio
n
(
MR
FO)
alg
o
r
ith
m
[
8
]
,
B
AT
alg
o
r
ith
m
[
9
]
,
s
alp
s
war
m
alg
o
r
ith
m
(
SS
A)
[
1
0
]
,
s
in
e
co
s
in
e
alg
o
r
ith
m
(
SC
A)
[
1
1
]
,
ad
ap
tiv
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
APSO)
[
1
2
]
,
m
o
d
if
ied
g
r
av
itatio
n
al
s
ea
r
ch
alg
o
r
ith
m
(
MG
SA)
[
1
2
]
,
g
r
ey
wo
lf
alg
o
r
ith
m
(
GW
A)
[
1
3
]
,
AL
O
alg
o
r
ith
m
[
1
4
]
,
Har
r
is
h
awk
o
p
tim
izatio
n
(
HHO)
[
1
5
]
an
d
tu
r
b
u
le
n
t
wate
r
f
lo
w
o
p
tim
izatio
n
(
T
W
FO)
[
1
6
]
to
en
h
a
n
ce
th
e
p
er
f
o
r
m
an
c
e
o
f
DPN.
T
h
e
au
t
h
o
r
s
[
1
7
]
u
tili
ze
d
a
teac
h
in
g
-
lear
n
in
g
alg
o
r
ith
m
to
o
p
tim
ize
o
f
f
s
h
o
r
e
W
T
in
th
e
3
3
-
b
u
s
s
y
s
tem
.
Mu
lti
-
o
b
jectiv
e
P
SO
wa
s
u
s
ed
to
o
p
tim
ize
in
v
er
ter
-
b
ased
DG
allo
ca
tio
n
i
n
Un
it
La
ya
n
a
n
P
ela
ksa
n
a
(
U
L
P)
W
ay
Halim
8
8
-
b
u
s
DPN
[
1
8
]
.
An
in
teg
r
ated
o
p
tim
izatio
n
ap
p
r
o
ac
h
u
s
in
g
a
teac
h
in
g
-
lear
n
in
g
alg
o
r
ith
m
an
d
PS
O
alg
o
r
ith
m
was
p
r
o
p
o
s
ed
a
n
d
s
im
u
ltan
eo
u
s
ly
o
p
tim
ized
th
e
DGs
an
d
STAT
C
OM
s
[
1
9
]
.
A
m
u
lti
-
o
b
jectiv
e
f
ir
ef
ly
a
n
aly
tical
h
ier
ar
ch
y
alg
o
r
ith
m
was
a
p
p
lied
t
o
o
p
tim
ally
allo
ca
te
ty
p
e
-
1
DG
u
n
it
s
f
o
r
PL
r
ed
u
ctio
n
,
VP
e
n
h
an
c
em
en
t
,
an
d
s
tab
ilit
y
im
p
r
o
v
em
e
n
t
[
2
0
]
.
A
m
u
lti
-
o
b
jectiv
e
en
er
g
y
m
a
n
ag
em
en
t
p
r
o
b
lem
was
s
o
lv
ed
u
s
in
g
th
e
gol
d
e
n
jack
al
o
p
tim
izatio
n
(
GJO)
alg
o
r
ith
m
in
a
m
icr
o
g
r
id
s
y
s
tem
p
o
wer
e
d
by
h
y
b
r
id
en
er
g
y
s
o
u
r
ce
s
[
2
1
]
.
Sev
er
al
alg
o
r
ith
m
s
ar
e
o
f
ten
tr
ap
p
ed
in
lo
ca
l
o
p
tim
a
s
o
lu
tio
n
s
an
d
o
f
f
er
p
o
o
r
co
n
v
e
r
g
en
ce
(
L
OS)
d
u
e
to
th
e
co
m
p
lex
ity
o
f
t
h
e
DG
al
lo
ca
tio
n
p
r
o
b
lem
.
Fo
r
in
s
tan
ce
,
GA
an
d
C
SA
o
f
f
er
s
lo
w
co
n
v
er
g
en
ce
a
n
d
h
en
ce
r
eq
u
ir
e
r
eg
u
lar
p
ar
am
eter
tu
n
i
n
g
.
B
AT
alg
o
r
ith
m
o
f
te
n
p
r
o
d
u
ce
s
u
n
s
tab
le
r
esu
lts
b
ec
au
s
e
o
f
its
p
o
o
r
e
x
p
lo
r
atio
n
ca
p
ab
ilit
y
.
GW
O
an
d
AL
O
al
g
o
r
ith
m
s
g
r
iev
e
f
r
o
m
in
ac
cu
r
ac
y
an
d
s
lo
w
co
n
v
er
g
en
ce
.
T
h
e
s
h
o
r
tco
m
i
n
g
s
o
f
th
ese
p
o
p
u
lar
al
g
o
r
ith
m
s
h
a
v
e
led
to
an
o
p
p
o
r
tu
n
ity
f
o
r
th
e
d
e
v
elo
p
m
en
t
o
f
n
ew
B
I
an
d
MH
alg
o
r
ith
m
s
.
Hu
n
ter
p
r
ey
o
p
tim
izer
(
HPO)
is
a
n
o
v
el
b
io
-
in
s
p
ir
ed
alg
o
r
ith
m
th
at
ch
ar
ac
ter
izes
th
e
h
u
n
tin
g
b
eh
a
v
io
r
o
f
a
n
an
im
al
to
s
o
lv
e
a
wid
e
r
an
g
e
o
f
o
p
tim
iz
atio
n
p
r
o
b
lem
s
[
2
2
]
.
T
h
e
HPO
alg
o
r
ith
m
h
as
a
d
i
v
er
s
e
ex
p
lo
r
atio
n
ca
p
ab
ilit
y
to
co
v
er
th
e
en
tire
s
ea
r
ch
s
p
ac
e
o
f
th
e
o
p
tim
izatio
n
p
r
o
b
lem
a
n
d
ca
n
ev
a
d
e
lo
ca
l
o
p
tim
a
s
tag
n
atio
n
is
s
u
es.
Als
o
,
it
ca
n
p
r
o
p
o
r
tio
n
ately
t
u
n
e
its
p
ar
am
eter
s
ac
co
r
d
in
g
to
th
e
p
r
o
b
lem
d
ef
in
itio
n
.
I
m
p
o
r
tan
tly
,
t
h
e
d
y
n
a
m
ic
h
u
n
tin
g
b
eh
av
io
r
b
etwe
en
th
e
h
u
n
ter
an
d
p
r
ey
o
f
f
er
s
f
aster
co
n
v
er
g
en
ce
[
2
3
]
.
Hen
ce
,
t
h
is
s
t
u
d
y
im
p
lem
e
n
ts
an
o
p
tim
izatio
n
tec
h
n
iq
u
e
u
s
in
g
t
h
e
HPO
alg
o
r
ith
m
t
o
o
p
tim
ize
th
e
s
ite
an
d
s
ize
o
f
PV
an
d
W
T
in
t
h
e
r
a
d
ia
l
DPN.
T
h
e
p
r
o
p
o
s
ed
s
tu
d
y
is
p
r
ese
n
ted
in
d
if
f
e
r
en
t
s
ec
tio
n
s
as
f
o
llo
ws.
Sectio
n
2
p
r
esen
ts
th
e
m
ath
e
m
atica
l
f
r
am
ewo
r
k
o
f
th
e
m
u
lti
-
o
b
je
ctiv
e
DG
p
lace
m
en
t
p
r
o
b
le
m
.
Sectio
n
3
d
escr
ib
es
th
e
p
r
o
p
o
s
ed
HPO
-
DG
o
p
tim
izatio
n
tech
n
iq
u
e.
Sectio
n
4
d
is
cu
s
s
es
th
e
s
im
u
latio
n
f
in
d
in
g
s
f
o
r
o
p
tim
ized
s
in
g
le
an
d
two
DG
p
lace
m
en
ts
.
Sectio
n
5
s
u
m
m
a
r
izes th
e
s
ig
n
if
ican
t c
o
n
tr
ib
u
tio
n
o
f
th
e
r
esear
ch
s
tu
d
y
as a
co
n
clu
s
io
n
.
2.
O
B
J
E
CT
I
V
E
F
UNC
T
I
O
N
F
RAM
E
WO
RK
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
o
b
je
ctiv
es
o
f
t
h
e
DG
all
o
ca
tio
n
p
r
o
b
lem
,
p
o
wer
f
lo
w
co
n
s
tr
ain
t
s
an
d
DG
m
o
d
ellin
g
.
T
h
e
HPO
alg
o
r
ith
m
is
im
p
lem
en
ted
to
o
p
tim
ize
th
e
b
u
s
lo
ca
tio
n
(
s
)
an
d
s
ize(
s
)
o
f
PV
an
d
W
T
DG
u
n
it(s)
to
m
in
im
ize
to
tal
R
PL
an
d
im
p
r
o
v
e
VP o
f
DPN.
T
h
e
p
r
im
ar
y
o
b
jectiv
e
(
f
1
)
is
th
e
m
in
im
izatio
n
o
f
t
o
tal
r
ea
l p
o
wer
lo
s
s
(
P
Tlos
s
)
.
(
1
)
ex
p
r
ess
es th
e
o
b
jectiv
e
f
u
n
ctio
n
f
o
r
f
1
.
1
=
m
in
(
T
lo
s
s
)
(
1
)
P
Tloss
in
a
D
PN
i
s
co
m
p
u
ted
th
r
o
u
g
h
p
o
wer
f
l
o
w
ex
ec
u
tio
n
u
s
in
g
a
b
ac
k
war
d
/f
o
r
war
d
s
wee
p
(
B
FS
)
alg
o
r
ith
m
[
2
4
]
.
Fo
r
a
DPN
with
‘
n
’
n
u
m
b
er
o
f
n
o
d
es,
th
e
r
e
al
p
o
wer
lo
s
s
‘
P
loss,
k
’
alo
n
g
a
b
r
an
ch
‘
k
’
is
g
i
v
e
n
in
(
2
)
.
W
h
er
e
,
R
k
d
e
n
o
tes to
p
.
u
.
r
esis
tan
ce
.
los
s
,
k
=
2
(
2
)
P
Tloss
o
f
a
R
DS w
ith
‘
n
b
’
n
u
m
b
er
o
f
b
r
an
c
h
es c
an
b
e
ex
p
r
ess
ed
as in
(
3
)
.
T
l
os
s
=
∑
los
s
,
k
nb
=
1
(
3
)
T
h
e
v
o
ltag
e
p
r
o
f
ile
(
VP)
im
p
r
o
v
em
en
t
is
th
e
s
ec
o
n
d
a
r
y
o
b
jectiv
e
(
f
2
)
an
d
ca
n
b
e
ac
h
iev
ed
b
y
m
in
im
iz
in
g
t
h
e
to
tal
v
o
ltag
e
d
e
v
iatio
n
(
T
VD)
o
f
R
DS.
T
h
e
(
4
)
ex
p
r
ess
es th
e
o
b
jectiv
e
f
u
n
ctio
n
o
f
T
VD
m
i
n
im
izatio
n
.
2
=
m
in
(
∑
|
1
−
|
|
|
=
1
)
(
4
)
W
h
er
e,
‘
N
’
r
ef
er
s
a
to
tal
n
o
.
o
f
b
u
s
es in
R
DS.
2
.
1
.
DG
o
ptim
iza
t
io
n
:
Weig
hte
d
s
um
m
et
ho
d
T
h
e
o
p
tim
al
s
o
lu
tio
n
f
o
r
th
e
m
u
lti
-
o
b
jectiv
e
(
f
1
an
d
f
2
)
DG
allo
ca
tio
n
p
r
o
b
lem
is
o
b
tain
e
d
u
s
in
g
th
e
weig
h
ted
s
u
m
m
eth
o
d
(
W
SM)
.
(
5
)
p
r
esen
ts
t
h
e
o
b
jectiv
e
f
u
n
c
tio
n
(
MO
F)
f
o
r
a
DG
o
p
tim
iza
tio
n
p
r
o
b
lem
u
s
in
g
weig
h
tag
e
f
ac
to
r
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
1
,
Ma
r
ch
20
25
:
1
46
-
1
54
148
obj
=
1
1
+
2
2
(
5
)
W
h
er
e
ω
1
an
d
ω
2
r
ef
er
r
ed
to
weig
h
tag
e
f
ac
to
r
s
.
An
d
,
ω
1
+ω
2
=1
.
T
h
e
v
alu
es
o
f
f
1
an
d
f
2
s
h
o
u
ld
b
e
n
o
r
m
alize
d
ac
co
r
d
in
g
to
th
eir
c
o
r
r
esp
o
n
d
i
n
g
b
ase
v
alu
es d
u
r
in
g
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
.
2
.
2
.
Co
ns
t
ra
ints
T
h
e
o
p
tim
al
s
o
lu
tio
n
f
o
r
th
e
m
u
lti
-
o
b
jectiv
e
DG
p
lace
m
en
t
p
r
o
b
lem
m
u
s
t
s
atis
f
y
s
ev
er
al
o
p
er
atio
n
al
lim
its
o
r
co
n
s
tr
ain
ts
o
f
R
DS.
T
h
e
lis
t
o
f
eq
u
ality
an
d
i
n
eq
u
alit
y
o
p
er
atio
n
al
co
n
s
tr
ain
ts
c
o
n
s
id
er
ed
in
t
h
e
p
r
esen
t
s
tu
d
y
is
p
r
esen
ted
b
el
o
w
.
2
.
2
.
1
.
P
o
wer
ba
la
nce
co
ns
t
ra
ints
T
h
is
is
an
eq
u
ality
co
n
s
tr
ain
t
th
at
r
elate
s
to
th
e
in
co
m
in
g
an
d
o
u
tg
o
in
g
p
o
wer
f
lo
w
o
f
R
DS.
T
h
e
o
p
tim
ized
s
o
lu
tio
n
m
u
s
t
en
s
u
r
e
th
at
th
e
to
tal
in
co
m
in
g
p
o
w
er
f
lo
w
is
eq
u
al
to
th
e
to
tal
o
u
tg
o
in
g
p
o
wer
.
T
h
e
m
ath
em
atica
l e
x
p
r
ess
io
n
s
f
o
r
p
o
wer
b
alan
ce
co
n
s
tr
ain
ts
[
2
5
]
ar
e
p
r
esen
te
d
in
(
6
)
an
d
(
7
)
.
+
DG
=
∑
(
)
=
1
+
∑
l
o
ss
(
)
nb
=
1
(
6
)
+
DG
=
∑
(
)
=
1
+
∑
l
o
ss
(
)
nb
=
1
(
7
)
W
h
er
e,
‘
P
DG
’
an
d
‘
Q
DG
’
co
r
r
e
s
p
o
n
d
to
o
p
tim
al
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
r
atin
g
o
f
DG
u
n
it(s)
,
r
esp
ec
tiv
ely
;
‘
P
L
’
an
d
‘
Q
L
’
p
o
in
t t
o
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
d
em
an
d
r
esp
ec
tiv
ely
.
2
.
2
.
2
.
B
us
v
o
lt
a
g
e
co
ns
t
ra
int
T
h
e
o
p
tim
al
o
u
tco
m
e
f
o
r
DG
p
lace
m
en
t
s
h
o
u
ld
n
o
t
v
i
o
late
th
e
v
o
ltag
e
co
n
s
tr
ain
t
ex
p
r
ess
ed
in
(
8
)
.
Fo
r
en
s
u
r
in
g
a
s
ec
u
r
e
an
d
r
eliab
le
o
p
e
r
atio
n
o
f
R
DS,
b
u
s
v
o
ltag
e
(
V
i
)
v
ar
iatio
n
m
u
s
t
b
e
k
ep
t
with
in
±
5
%
o
f
th
e
s
u
b
s
tatio
n
v
o
ltag
e
(
s
lack
b
u
s
)
.
m
in
≤
≤
m
a
x
(
8
)
W
h
er
e,
‘
V
max
’
an
d
‘
V
min
’
ar
e
th
e
m
ax
im
u
m
a
n
d
m
i
n
im
u
m
b
u
s
v
o
ltag
es,
r
esp
ec
tiv
ely
.
2
.
2
.
3
.
DG
ca
pa
cit
y
lim
it
T
h
e
o
p
tim
ize
d
ca
p
ac
ity
o
f
DG
u
n
its
(
s
in
g
le
o
r
m
u
ltip
le)
m
u
s
t
b
e
less
th
an
th
e
to
tal
p
o
wer
d
em
an
d
o
f
R
DS to
av
o
id
s
ec
u
r
ity
is
s
u
es [
2
5
]
.
DG
≤
(
9
)
DG
≤
(
1
0
)
2
.
3
DG
m
o
dellin
g
I
n
th
is
s
tu
d
y
,
s
o
lar
PV
an
d
W
T
ar
e
r
ep
r
esen
te
d
as
P
ty
p
e
an
d
P
-
Q
ty
p
e
m
o
d
els,
r
esp
ec
tiv
ely
.
(
1
1
)
m
ath
em
atica
lly
d
escr
ib
es th
e
ch
ar
ac
ter
is
tics
o
f
a
s
o
lar
PV [
2
5
]
.
Her
e,
Q
DG
is
as
s
u
m
ed
ze
r
o
.
DG
=
{
×
(
)
,
0
≤
≤
r,
≤
}
(
1
1
)
T
h
e
o
u
tp
u
t c
h
ar
ac
ter
is
tic
eq
u
a
tio
n
f
o
r
W
T
is
p
r
esen
ted
in
(
1
2
)
an
d
(
1
3
)
[
2
3
]
,
[
2
2
]
.
DG
=
{
0,
×
(
−
cin
−
cin
)
,
,
0
≤
≤
c
in
c
in
≤
≤
≤
≤
c
o
ut
}
(
1
2
)
DG
=
×
ta
n
(
co
s
−
1
(
p.f
.
DG
)
)
(
1
3
)
W
h
er
e
‘
P
r
’
is
th
e
r
ated
o
u
tp
u
t
p
o
wer
o
f
a
s
o
lar
PV,
‘
G’
is
a
s
o
lar
ir
r
ad
ian
ce
at
th
e
o
p
tim
al
s
ite(
s
)
,
‘
Gr
’
is
th
e
r
ated
s
o
lar
ir
r
ad
ian
ce
at
ea
r
th
'
s
s
u
r
f
ac
e,
‘
P
r
’
is
th
e
r
ated
o
u
t
p
u
t
p
o
wer
o
f
W
T
,
‘
V
r
’
,
an
d
‘
V
’
is
th
e
r
ated
an
d
ac
tu
al
win
d
v
elo
city
(
W
V)
in
m
eter
/s
ec
at
th
e
o
p
tim
al
s
ites
.
‘
V
cin
’
an
d
‘
V
cout
’
ar
e
th
e
c
u
t
-
in
an
d
cu
t
-
o
u
t WV in
m
eter
/s
ec
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Mu
lti
-
o
b
jective
h
u
n
ter p
r
ey
o
p
timiz
e
r
tech
n
iq
u
e
fo
r
d
is
tr
ib
u
ted
g
en
era
tio
n
p
la
ce
men
t
(
K
esa
va
n
Du
r
a
is
a
my
)
149
3.
H
P
O
AL
G
O
RIT
H
M
:
SO
L
U
T
I
O
N
T
E
CH
N
I
Q
UE
F
O
R
D
G
AL
L
O
CA
T
I
O
N
T
h
is
s
ec
tio
n
o
u
tlin
es th
e
m
ath
em
atica
l
m
o
d
elin
g
o
f
th
e
HPO
alg
o
r
ith
m
an
d
its
ap
p
licatio
n
in
o
p
tim
al
DG
allo
ca
tio
n
.
HPO
is
a
n
o
v
el
b
io
-
in
s
p
ir
ed
alg
o
r
ith
m
an
d
is
m
o
d
eled
to
ch
ar
ac
ter
ize
th
e
h
u
n
tin
g
b
eh
a
v
io
r
o
f
an
an
im
al
.
3
.
1
.
M
a
t
hema
t
ica
l
m
o
dellin
g
HPO
i
s
a
b
io
-
in
s
p
ir
ed
an
d
p
o
p
u
latio
n
-
b
ased
o
p
tim
izatio
n
a
lg
o
r
ith
m
th
at
ch
ar
ac
ter
izes
th
e
h
u
n
tin
g
b
eh
av
io
r
o
f
a
n
an
im
al.
T
h
e
p
o
p
u
latio
n
p
o
s
itio
n
is
r
an
d
o
m
ly
s
et
in
s
ea
r
ch
s
p
ac
e
an
d
is
ex
p
r
ess
ed
in
(
1
4
)
.
=
r
a
n
d
(
1,d
)
×
(
−
)
+
(
1
4
)
W
h
er
e,
i
=
1
,
2
,
…
n
p
o
p
an
d
d
=
1
,
2
,
…
M.
Her
e,
x
i
r
e
f
er
s
th
e
h
u
n
ter
p
o
s
itio
n
,
‘
n
p
o
p
’
p
o
in
t’
s
th
e
p
o
p
u
latio
n
s
ize,
M
p
o
in
ts
th
e
s
ea
r
ch
s
p
ac
e
s
ize,
‘
l’
an
d
‘
u
’
d
en
o
tes th
e
lo
wer
an
d
u
p
p
e
r
lim
it
o
f
s
ea
r
ch
s
p
ac
e.
T
h
e
p
o
s
itio
n
o
f
h
u
n
ter
is
u
p
d
a
ted
u
s
in
g
(
1
5
)
.
i,j
(
+
1
)
=
i,j
(
)
+
1
2
⁄
{
(
2
∗
∗
∗
p
o
s
(
)
−
i,j
(
)
)
+
(
2
(
1
−
)
∗
∗
−
i,j
(
)
)
}
(
1
5
)
W
h
er
e,
x
(t)
a
n
d
x
(t+
1)
r
ep
r
esen
t
th
e
p
r
esen
t
an
d
f
u
t
u
r
e
p
o
s
itio
n
o
f
th
e
h
u
n
ter
,
r
esp
ec
tiv
el
y
.
P
p
os(j)
p
o
in
ts
th
e
p
r
e
y
p
o
s
itio
n
.
µ
j
is
th
e
av
er
a
g
e
o
f
th
e
lo
ca
tio
n
s
an
d
is
ex
p
r
ess
ed
as
(
1
6
)
.
=
1
⁄
∑
n
p
o
p
=
1
(
1
6
)
Ad
ap
tiv
e
p
ar
am
ete
r
(
Z
)
is
co
m
p
u
ted
u
s
in
g
(
1
7
)
an
d
(
1
8
)
.
=
1
<
C
;ID
X
=
(
=
=
0
)
(
1
7
)
=
2
⊗
IDX
+
3
⊗
(
≈
IDX
)
(
1
8
)
W
h
er
e,
r
1
an
d
r
2
ar
e
th
e
v
ec
to
r
s
r
ep
r
esen
t
a
r
an
d
o
m
v
al
u
e
b
et
wee
n
[
0
,
1
]
;
I
DX
co
r
r
esp
o
n
d
s
to
an
in
d
ex
n
u
m
b
er
o
f
r
1
th
at
s
atis
f
ies
th
e
co
n
d
itio
n
(
P==0
)
;
C
is
a
f
a
cto
r
th
at
h
elp
s
to
b
alan
ce
ex
p
lo
itatio
n
an
d
ex
p
lo
r
atio
n
.
T
y
p
ically
,
th
e
v
al
u
e
o
f
C
is
r
e
d
u
ce
d
f
r
o
m
1
to
0
.
0
2
d
u
r
in
g
th
e
co
u
r
s
e
o
f
t
h
e
iter
ativ
e
p
r
o
ce
s
s
an
d
it
is
ex
p
r
ess
ed
in
(
1
9
)
.
=
1
−
it
∗
(
0.98
i
t
m
a
x
)
(
1
9
)
W
h
er
e
‘
it
max
’
an
d
‘
it’
p
o
in
ts
to
m
ax
im
u
m
iter
atio
n
an
d
p
r
esen
t iter
atio
n
n
u
m
b
er
r
esp
ec
tiv
ely
.
T
h
e
p
r
e
y
(
P
pos
)
is
ch
o
s
en
r
ef
e
r
r
in
g
t
o
a
s
ea
r
ch
a
g
en
t
lo
ca
ted
f
ar
f
r
o
m
µ.
p
o
s
=
|
i
is
in
de
x
of
M
a
x
(
e
n
d
)
s
or
t
(
De
uc
)
(
2
0
)
T
h
e
E
u
clid
ea
n
d
is
tan
ce
is
co
m
p
u
ted
f
r
o
m
a
n
av
er
a
g
e
lo
ca
tio
n
o
f
s
ea
r
ch
s
p
ac
e
u
s
in
g
(
2
1
)
.
e
uc
(
)
=
(
∑
(
i,j
−
)
2
=
1
)
1
2
⁄
(
2
1
)
T
h
e
c
o
n
v
e
r
g
e
n
c
e
o
f
H
PO
is
a
c
o
n
c
e
r
n
w
h
e
n
t
h
e
d
i
s
t
a
n
c
e
b
e
t
w
e
e
n
t
h
e
s
e
a
r
c
h
a
g
e
n
t
a
n
d
μ
b
e
tw
e
e
n
c
o
n
s
e
c
u
t
i
v
e
i
t
e
r
at
i
o
n
s
is
l
ar
g
e
.
T
h
e
r
e
f
o
r
e
,
o
n
c
e
t
h
e
p
r
e
y
i
s
c
a
u
g
h
t
i
n
a
h
u
n
t
i
n
g
s
c
e
n
e
t
h
e
h
u
n
t
er
s
h
o
u
l
d
l
o
o
k
f
o
r
w
a
r
d
t
o
t
h
e
n
e
x
t
p
r
e
y
.
T
h
i
s
s
c
e
n
a
r
i
o
is
e
x
p
r
e
s
s
e
d
i
n
(
2
2
)
a
n
d
(
2
3
)
.
W
h
e
r
e
,
‘
n
’
p
o
i
n
t
s
t
o
n
u
m
b
e
r
o
f
s
ea
r
c
h
a
g
e
n
t
s
.
k
b
e
s
t
=
r
ound
(
×
n
pop
)
(
2
2
)
p
o
s
=
|
i
is s
or
te
d
D
e
uc
(
k
b
e
s
t
)
(
2
3
)
At
th
e
b
eg
in
n
in
g
o
f
th
e
alg
o
r
i
th
m
,
‘
k
b
est’
is
s
et
eq
u
al
to
‘
n
p
o
p
’
.
T
h
e
‘
k
b
est’
v
alu
e
is
p
r
o
g
r
ess
iv
ely
d
ec
r
ea
s
ed
af
ter
th
e
h
u
n
ter
p
ick
s
a
f
ar
th
est
s
ea
r
ch
ag
en
t
(
p
r
ey
)
an
d
ca
p
tu
r
es
it.
At
th
e
en
d
o
f
th
e
alg
o
r
ith
m
,
‘
k
b
est’
v
alu
e
p
o
in
ts
to
th
e
f
ir
s
t
s
ea
r
ch
ag
en
t
(
least
d
is
tan
ce
f
r
o
m
µ)
.
T
h
er
ef
o
r
e,
(
1
5
)
is
r
ep
la
ce
d
b
y
(
2
4
)
in
o
r
d
er
to
lo
ca
te
th
e
p
o
s
itio
n
o
f
p
r
ey
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
1
,
Ma
r
ch
20
25
:
1
46
-
1
54
150
i,j
(
+
1
)
=
po
s
(
)
+
∗
∗
c
os
(
4
2
π
)
×
(
p
o
s
(
)
(
)
−
i,j
(
)
)
(
2
4
)
W
h
er
e,
x
(t+
1)
is
u
p
d
ated
lo
ca
tio
n
o
f
n
ex
t
p
r
ey
,
T
pos(j)
is
th
e
o
p
tim
al
p
o
s
itio
n
o
f
p
r
ey
(
g
lo
b
a
l)
an
d
r
4
is
a
r
an
d
o
m
v
ar
iab
le
b
etwe
en
[
0
,
1
]
.
T
h
e
p
o
s
itio
n
s
o
f
h
u
n
ter
an
d
p
r
ey
a
f
te
r
th
e
u
p
d
ate
ar
e
e
x
p
r
ess
ed
in
(
2
5
)
an
d
(
2
6
)
:
i,j
(
+
1
)
=
i,j
(
)
+
1
2
⁄
{
(
2
∗
∗
∗
p
o
s
(
)
−
i,j
(
)
)
+
(
2
(
1
−
)
∗
∗
−
i,j
(
)
)
}
if
5
<
(
2
5
)
e
ls
e
i,j
(
+
1
)
=
p
o
s
(
)
+
∗
∗
c
os
(
4
2
π
)
×
(
p
o
s
(
)
(
)
−
i,j
(
)
)
(
2
6
)
I
f
r
5
<ꞵ,
th
en
th
e
s
ea
r
c
h
ag
en
t
i
s
tr
ea
ted
as
a
h
u
n
ter
(
25
)
,
else th
e
s
ea
r
ch
ag
en
t
is
a
p
r
e
y
(
26
)
.
Her
e
r
5
r
ef
er
s
to
a
r
an
d
o
m
n
u
m
b
er
b
etwe
en
0
a
n
d
1
; ꞵ is a
r
eg
u
latin
g
f
ac
to
r
eq
u
al
to
0
.
1
.
3
.
2
.
I
m
ple
m
ent
a
t
io
n
T
h
e
p
r
o
p
o
s
ed
HPO
alg
o
r
ith
m
f
in
d
s
th
e
b
est
s
o
lu
tio
n
(
DG
l
o
ca
tio
n
an
d
s
ize)
f
o
r
th
e
DG
allo
ca
tio
n
p
r
o
b
lem
b
y
e
x
ec
u
tin
g
t
h
e
f
o
ll
o
win
g
s
tep
s
.
˗
Step
1
:
Def
in
e
th
e
o
p
tim
izatio
n
p
r
o
b
lem
p
ar
am
ete
r
s
in
clu
d
i
n
g
th
e
s
ite,
s
ize
,
an
d
ty
p
e
(
PV
an
d
W
T
)
o
f
th
e
DG.
Als
o
,
in
itial
ize
th
e
HPO
alg
o
r
ith
m
o
p
er
atio
n
al
p
ar
am
eter
s
s
u
ch
as
p
o
p
u
latio
n
s
ize
an
d
m
a
x
im
u
m
iter
atio
n
s
.
˗
Step
2
:
At
f
ir
s
t,
p
er
f
o
r
m
a
r
an
d
o
m
walk
to
g
en
er
ate
t
h
e
in
iti
al
s
o
lu
tio
n
o
f
t
h
e
DG
p
lace
m
e
n
t p
r
o
b
lem
.
˗
Step
3
:
R
u
n
p
o
wer
f
lo
w
f
o
r
th
e
test
s
y
s
tem
f
o
r
th
e
r
an
d
o
m
s
o
l
u
tio
n
an
d
d
eter
m
i
n
e
th
e
f
itn
ess
lev
el
o
f
MO
F
ex
p
r
ess
ed
in
(
5
)
.
Ass
ig
n
th
e
co
m
p
u
ted
f
itn
ess
lev
el
as ‘
k
b
est’.
˗
Step
4
:
Up
d
ate
th
e
lo
ca
tio
n
s
o
f
th
e
h
u
n
ter
(
DG
s
ize)
ac
co
r
d
in
g
t
o
th
e
p
r
esen
t
lo
ca
tio
n
a
n
d
th
e
o
p
tim
al
lo
ca
tio
n
(
DG
s
ite)
ex
p
lo
r
ed
s
o
f
ar
.
T
h
e
u
p
d
a
te
d
p
o
s
itio
n
d
en
o
tes
a
p
o
s
s
ib
le
b
est
s
o
lu
t
io
n
f
o
r
th
e
DG
p
lace
m
en
t p
r
o
b
lem
.
˗
Step
5
:
Up
d
ate
th
e
a
d
ap
tiv
e
(
Z
)
an
d
b
alan
ce
(
C
)
p
a
r
am
eter
s
e
x
p
r
ess
ed
in
(
1
8
)
a
n
d
(
1
9
)
.
˗
Step
6
:
C
o
m
p
ar
e
r
5
with
r
eg
u
l
atin
g
p
ar
am
eter
ꞵ
.
I
f
r
5
<
ꞵ,
th
e
n
co
m
p
u
te
th
e
n
ew
p
o
s
itio
n
o
f
th
e
h
u
n
ter
(
DG
s
ize)
u
s
in
g
(
25
).
Oth
er
wis
e,
u
p
d
ate
th
e
p
o
s
itio
n
o
f
p
r
ey
(
DG
s
ite)
u
s
in
g
(
26
).
˗
Step
7
:
R
u
n
p
o
wer
f
lo
w
f
o
r
th
e
u
p
d
ated
h
u
n
ter
p
o
s
itio
n
a
n
d
co
m
p
u
te
th
e
f
itn
ess
lev
el
f
o
r
t
h
e
MO
F
.
˗
Step
8
:
R
ep
lace
‘
k
b
est’
if
th
e
f
itn
ess
lev
el
co
m
p
u
ted
in
Step
7
is
less
th
an
th
e
p
r
ev
io
u
s
b
est v
alu
e.
˗
Step
9
:
I
n
cr
ea
s
e
th
e
iter
atio
n
c
o
u
n
t a
n
d
r
ep
ea
t t
h
e
ab
o
v
e
s
tep
s
u
n
til th
e
s
to
p
p
in
g
cr
iter
ia
is
r
ea
ch
ed
.
˗
Step
1
0
:
Prin
t th
e
o
p
tim
al
s
o
lu
tio
n
.
4.
T
E
ST
R
E
SU
L
T
S AN
D
D
I
S
CUSS
I
O
N
T
h
e
s
im
u
latio
n
o
u
tco
m
es
f
o
r
th
e
test
s
y
s
tem
s
u
n
d
er
s
tu
d
y
ar
e
in
v
esti
g
ated
f
o
r
a
s
in
g
le
an
d
m
u
ltip
le
(
two
)
DG
p
lace
m
en
t.
T
h
e
n
ec
ess
ar
y
p
r
o
g
r
am
m
in
g
was
co
d
ed
in
MA
T
L
AB
s
o
f
twar
e
v
er
s
io
n
-
2
0
2
2
b
an
d
ex
ec
u
ted
u
s
in
g
a
n
I
n
tel
i3
,
4
.
1
0
GHz
p
r
o
ce
s
s
o
r
p
er
s
o
n
al
co
m
p
u
te
r
.
Sin
ce
,
t
h
e
o
b
jectiv
e
f
u
n
ctio
n
is
p
r
o
p
o
s
ed
to
s
o
lv
e
u
s
in
g
th
e
weig
h
tag
e
f
ac
to
r
s
ap
p
r
o
ac
h
,
ap
p
r
o
x
im
atio
n
o
f
ω
1
an
d
ω
2
is
v
ital
f
o
r
ac
h
iev
in
g
a
b
etter
s
o
lu
tio
n
.
T
h
e
co
m
b
in
atio
n
s
o
f
weig
h
t
ag
e
f
ac
to
r
s
th
at
g
iv
e
m
i
n
im
u
m
f
itn
ess
v
alu
e
f
o
r
t
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
ar
e
co
n
s
id
er
ed
as
ap
p
r
o
p
r
iate
v
al
u
es
[
2
6
]
.
I
n
t
h
is
s
tu
d
y
,
weig
h
tag
e
f
ac
to
r
s
a
r
e
ap
p
r
o
x
im
at
ed
f
o
r
a
s
in
g
le
PV
-
o
p
tim
ized
allo
ca
tio
n
.
T
h
e
co
m
b
i
n
a
t
i
o
n
ω
1
=
0
.
6
an
d
ω
2
=
0
.
4
ar
e
ch
o
s
en
a
s
a
p
p
r
o
p
r
ia
te
w
e
i
g
h
t
ag
e
f
a
c
t
o
r
s
s
i
n
c
e
t
h
e
y
p
r
o
v
id
ed
t
h
e
l
e
a
s
t
f
i
t
n
e
s
s
v
a
lu
e
f
o
r
t
h
e
o
p
t
i
m
i
ze
d
s
i
n
g
l
e
P
V
a
l
l
o
c
a
t
i
o
n
.
4
.
1
.
I
E
E
E
6
9
-
bu
s
RDS:
S
im
ula
t
io
n
re
s
ults
T
h
e
6
9
-
b
u
s
DPN
d
eliv
er
s
3
.
8
MW
o
f
r
ea
l
p
o
wer
an
d
2
.
6
9
MV
Ar
o
f
r
ea
ctiv
e
p
o
wer
[
2
7
]
.
T
h
e
s
im
u
latio
n
r
u
n
r
esu
lts
o
f
th
e
t
est
s
y
s
tem
with
o
u
t
an
d
with
DG
in
s
er
tio
n
ar
e
p
r
esen
ted
in
T
ab
le
1
.
Po
wer
f
l
o
w
(
PF
)
r
esu
lts
f
o
r
th
e
test
s
y
s
tem
h
av
e
b
ee
n
o
b
tain
e
d
v
ia
B
FS
a
lg
o
r
ith
m
.
T
h
e
test
s
y
s
tem
with
n
o
DG
p
lace
m
en
t
ac
co
u
n
ted
f
o
r
2
2
5
k
W
to
tal
r
e
al
PL
an
d
0
.
9
0
9
2
p
.
u
m
in
im
u
m
v
o
ltag
e
(
V
min
)
.
B
esid
es,
a
t
o
tal
o
f
9
b
u
s
es
h
av
e
v
io
l
ated
V
min
c
o
n
s
tr
ain
t
(
<
0
.
9
5
p
.
u
.
)
.
T
h
e
o
p
tim
ize
d
s
in
g
le
PV
an
d
W
T
p
lace
m
en
t
h
as
r
e
d
u
ce
d
th
e
to
tal
r
ea
l
PL
to
7
1
.
1
2
k
W
an
d
1
3
.
6
7
k
W
an
d
in
cr
ea
s
ed
V
min
to
0
.
9
7
7
5
p
.
u
an
d
0
.
9
8
4
2
p
.
u
,
r
esp
ec
tiv
ely
.
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n
th
e
ca
s
e
o
f
two
PVs
an
d
W
T
s
p
lace
m
en
ts
,
th
e
PL
h
as
b
ee
n
c
u
t
d
o
wn
to
7
0
.
4
5
k
W
an
d
7
.
6
8
k
W
,
r
esp
ec
tiv
ely
.
Simu
ltan
eo
u
s
ly
,
V
min
h
as
b
ee
n
en
h
a
n
ce
d
to
0
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9
7
9
8
p
.
u
an
d
0
.
9
9
5
1
p
.
u
,
r
esp
ec
tiv
ely
.
Fig
u
r
e
1
(
a
)
illu
s
tr
ates
th
e
VP
o
f
th
e
69
-
b
u
s
test
s
y
s
tem
a
f
ter
th
e
allo
ca
tio
n
o
f
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u
n
its
.
I
t
is
o
b
v
io
u
s
ev
id
en
t
f
r
o
m
th
e
illu
s
tr
atio
n
th
at
n
o
b
u
s
es in
th
e
test
s
y
s
tem
r
ec
o
r
d
a
v
o
ltag
e
b
elo
w
0
.
9
5
p
.
u
af
ter
th
e
DG
allo
ca
tio
n
s
.
T
h
e
o
p
t
i
m
i
z
e
d
i
n
t
e
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r
a
t
i
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m
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t
.
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u
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b
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p
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
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E
n
g
I
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N:
2252
-
8
7
9
2
Mu
lti
-
o
b
jective
h
u
n
ter p
r
ey
o
p
timiz
e
r
tech
n
iq
u
e
fo
r
d
is
tr
ib
u
ted
g
en
era
tio
n
p
la
ce
men
t
(
K
esa
va
n
Du
r
a
is
a
my
)
151
w
i
t
h
W
T
p
l
a
c
e
m
e
n
t
.
M
o
r
e
o
v
e
r
,
t
h
e
H
P
O
al
g
o
r
i
t
h
m
r
e
a
c
h
e
d
t
h
e
o
p
t
i
m
a
l
s
o
l
u
ti
o
n
i
n
1
0
.
2
3
a
n
d
1
1
.
8
s
e
c
o
n
d
s
a
t
1
6
th
a
n
d
1
9
th
it
e
r
a
t
i
o
n
s
f
o
r
a
s
i
n
g
l
e
PV
a
n
d
W
T
p
l
a
c
e
m
e
n
t
,
r
es
p
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c
t
iv
e
l
y
.
W
h
e
r
e
a
s
,
f
o
r
tw
o
PV
a
n
d
W
T
a
l
l
o
c
at
i
o
n
s
,
t
h
e
H
P
O
a
l
g
o
r
it
h
m
c
o
n
v
e
r
g
e
d
i
n
1
3
.
4
a
n
d
1
4
.
1
s
e
c
o
n
d
s
a
n
d
t
o
o
k
2
0
a
n
d
2
2
i
t
e
r
a
t
i
o
n
s
,
r
e
s
p
ec
t
i
v
e
l
y
.
F
i
g
u
r
e
1
(
b
)
i
l
l
u
s
t
r
a
t
es
t
h
e
c
o
n
v
e
r
g
e
n
c
e
p
l
o
t
f
o
r
t
h
e
HP
O
a
l
g
o
r
i
t
h
m
f
o
r
s
i
n
g
l
e
a
n
d
tw
o
DG
p
l
a
ce
m
e
n
t
s
.
F
u
r
t
h
e
r
m
o
r
e
,
t
h
e
HPO
a
l
g
o
r
i
t
h
m
h
a
s
n
o
t
s
h
o
w
n
a
n
y
s
ig
n
o
f
l
o
c
a
l
o
p
t
i
m
a
l
s
t
a
g
n
a
ti
o
n
ti
l
l
t
h
e
c
o
n
v
e
r
g
e
n
c
e
.
T
ab
le
1
.
I
E
E
E
6
9
-
b
u
s
R
DS: T
est
r
esu
lts
with
an
d
with
o
u
t D
G
ac
co
m
m
o
d
atio
n
s
O
u
t
c
o
m
e
N
o
D
G
W
i
t
h
s
i
n
g
l
e
D
G
W
i
t
h
t
w
o
D
G
s
PV
WT
P
V
s
W
Ts
O
p
t
i
mal
si
t
e
-
57
57
17
61
17
61
O
p
t
i
mal
si
z
e
(
k
W
/
k
V
A
)
/
p
.
f
.
-
1
7
7
6
.
5
4
/
1
1
8
7
8
.
9
/
0
.
8
2
1
1
6
2
1
.
5
4
/
1
1
4
9
2
.
6
5
/
1
6
2
3
.
1
6
/
0
.
8
2
9
3
2
0
0
5
.
7
6
/
0
.
8
2
3
4
R
P
L
T
(
k
W
)
2
2
5
7
1
.
1
2
1
3
.
6
7
7
0
.
4
5
7
.
6
8
V
min
(
p
.
u
.
)
0
.
9
0
9
2
0
.
9
7
7
5
0
.
9
8
4
2
0
.
9
7
9
8
0
.
9
9
5
1
S
i
mu
l
a
t
i
o
n
r
u
n
t
i
m
e
(
se
c
)
-
1
0
.
2
3
1
1
.
8
1
3
.
4
1
4
.
1
N
o
.
o
f
i
t
e
r
a
t
i
o
n
s
-
16
19
20
22
(
a)
(
b
)
Fig
u
r
e
1
.
Simu
latio
n
r
esu
lts
: (
a)
VP o
f
6
9
-
b
u
s
r
a
d
ial
DPN
an
d
(
b
)
co
n
v
er
g
e
n
ce
cu
r
v
e
o
f
H
PO
alg
o
r
ith
m
f
o
r
6
9
-
b
u
s
DPN
4
.
2
.
Co
m
pa
ra
t
iv
e
s
t
ud
y
A
co
m
p
ar
ativ
e
ass
ess
m
en
t
b
etwe
en
th
e
s
im
u
latio
n
f
in
d
in
g
s
o
f
HPO
an
d
o
th
e
r
alg
o
r
it
h
m
s
is
cited
in
th
e
liter
atu
r
e
an
d
is
g
r
a
p
h
icall
y
illu
s
tr
ated
in
Fig
u
r
e
2
.
T
h
e
c
o
m
p
ar
is
o
n
is
d
em
o
n
s
tr
ated
in
ter
m
s
o
f
p
er
ce
n
ta
g
e
PL
r
ed
u
ctio
n
an
d
V
min
.
Fo
r
a
s
in
g
le
PV
o
p
tim
iz
ed
allo
ca
tio
n
,
th
e
HPO
alg
o
r
ith
m
r
ed
u
ce
d
PL
o
f
th
e
test
s
y
s
tem
b
y
6
8
.
3
9
%
wh
ich
is
5
.
3
8
%,
5
.
3
9
%,
5
.
3
7
%
,
an
d
4
1
.
0
9
%
m
o
r
e
th
an
DE
[
4
]
,
MRF
O
[
8
]
,
W
OA
[
7
]
,
an
d
SS
A
[
1
0
]
,
r
esp
ec
tiv
ely
.
L
ik
ewise,
HPO
-
o
p
tim
ized
s
in
g
le
W
T
p
lace
m
en
t
cu
t
d
o
w
n
th
e
PL
b
y
9
3
.
9
2
%
wh
ic
h
i
s
1
1
.
0
2
%,
1
7
.
3
2
%,
4
.
2
2
%
,
an
d
4
.
2
1
%
m
o
r
e
th
an
GA
[
5
]
,
C
SA
[
6
]
,
AL
O
[
1
4
]
,
an
d
W
OA
[
7
]
,
r
esp
ec
tiv
ely
.
Similar
ly
,
f
o
r
two
PV
an
d
W
T
p
lace
m
en
ts
,
th
e
HPO
alg
o
r
ith
m
ac
h
iev
ed
b
etter
PL
r
e
d
u
ct
io
n
th
an
SC
A
[
1
1
]
,
APSO
[
1
2
]
,
an
d
MG
SA
[
1
2
]
.
I
n
th
e
ca
s
e
o
f
VP
en
h
an
ce
m
en
t,
HPO
alg
o
r
ith
m
-
o
p
tim
ized
DG
in
teg
r
atio
n
r
esu
lted
in
b
etter
V
min
th
a
n
W
OA,
S
C
A
,
AL
O,
APSO
,
a
n
d
MG
SA.
T
h
e
HPO
alg
o
r
it
h
m
-
o
p
tim
ized
DG
in
teg
r
atio
n
p
r
o
v
i
d
es su
p
er
io
r
r
esu
lts
th
an
th
e
o
th
er
alg
o
r
ith
m
s
with
a
s
ig
n
if
ican
t r
ate
o
f
c
o
n
v
er
g
en
ce
.
4
.
3
Ca
iro
-
5
9
bu
s
RDS:
Sim
ula
t
io
n r
esu
lt
s
C
air
o
-
5
9
b
u
s
R
DS
is
a
r
ea
l
-
w
o
r
ld
p
o
wer
n
etwo
r
k
m
o
d
el
th
at
o
p
er
ates
at
1
1
k
V
an
d
s
u
p
p
lies
5
0
.
3
4
8
MW
an
d
2
1
.
4
4
8
MV
Ar
o
f
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
,
r
esp
ec
tiv
ely
.
T
h
e
s
im
u
latio
n
r
u
n
o
u
tco
m
es
o
f
C
air
o
-
5
9
b
u
s
R
DS
with
an
d
with
o
u
t
DG
ac
co
m
m
o
d
atio
n
a
r
e
p
r
esen
ted
in
T
ab
le
2
.
T
h
e
test
s
y
s
tem
r
ec
o
r
d
ed
2
1
8
.
9
9
k
W
o
f
R
PL
T
an
d
0
.
9
8
6
4
p
.
u
o
f
V
min
b
ef
o
r
e
DG
o
p
tim
izatio
n
.
Fo
r
a
s
i
n
g
le
o
p
t
im
ize
d
PV
an
d
W
T
p
lac
e
m
e
n
t
,
th
e
HPO
a
l
g
o
r
i
th
m
c
o
n
v
e
r
g
es
t
o
a
n
o
p
ti
m
al
s
o
l
u
ti
o
n
wit
h
1
4
3
2
8
.
2
k
W
a
n
d
1
3
4
8
2
.
5
k
VA
ca
p
a
cit
y
,
r
esp
ec
t
iv
el
y
,
a
n
d
m
in
im
i
ze
s
t
h
e
R
PL
T
to
7
1
.
1
2
k
W
a
n
d
1
3
.
6
7
k
W
,
r
es
p
e
cti
v
e
ly
.
At
th
e
s
am
e
tim
e,
V
mi
n
o
f
t
h
e
t
est
s
y
s
t
em
i
m
p
r
o
v
e
d
t
o
0
.
9
9
0
1
p
.
u
a
n
d
0
.
9
9
2
5
p
.
u
,
r
esp
ec
ti
v
el
y
.
L
i
k
ewis
e,
f
o
r
t
h
e
o
p
ti
m
iz
e
d
all
o
c
ati
o
n
o
f
tw
o
PVs
a
n
d
W
T
s
,
PL
h
as
b
e
e
n
r
e
d
u
c
ed
t
o
7
0
.
4
5
k
W
a
n
d
7
.
6
8
k
W
a
n
d
V
min
e
n
h
an
ce
d
t
o
0
.
9
9
2
3
p
.
u
a
n
d
0
.
9
9
5
2
p
.
u
,
r
es
p
e
cti
v
e
ly
.
Fi
g
u
r
e
3
il
lu
s
tr
ates
t
h
e
VP
a
n
d
c
o
n
v
e
r
g
e
n
ce
c
u
r
v
e
o
f
th
e
HP
O
al
g
o
r
i
th
m
f
o
r
C
a
ir
o
-
5
9
b
u
s
R
D
S w
it
h
o
p
ti
m
iz
e
d
D
G
s
i
n
te
g
r
at
io
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
1
,
Ma
r
ch
20
25
:
1
46
-
1
54
152
T
ab
le
2
.
C
air
o
-
5
9
b
u
s
R
DS: T
est
r
esu
lts
with
an
d
with
o
u
t D
G
ac
co
m
m
o
d
atio
n
s
O
u
t
c
o
m
e
N
o
D
G
O
n
e
P
V
O
n
e
W
T
Tw
o
P
V
s
Tw
o
W
T
s
O
p
t
i
mal
si
t
e
s
-
3
3
25
41
25
41
O
p
t
i
mal
si
z
e
s
(
k
W
/
k
V
A
)
/
p
.
f
.
-
1
4
3
2
8
.
2
/
1
1
3
4
8
2
.
5
/
0
.
8
3
0
3
1
0
0
3
4
.
3
/
1
7
8
9
4
.
8
/
1
8
9
8
0
.
5
/
0
.
8
1
3
4
9
0
0
1
.
8
/
0
.
8
2
1
8
RPL
T
(
k
W
)
2
1
8
.
9
9
7
1
.
1
2
1
3
.
6
7
7
0
.
4
5
7
.
6
8
V
m
i
n
(
p
.
u
.
)
0
.
9
8
6
4
0
.
9
9
0
1
0
.
9
9
2
5
0
.
9
9
2
3
0
.
9
9
5
2
(
a)
(
b
)
Fig
u
r
e
2
.
Simu
latio
n
r
esu
lts
co
m
p
ar
is
o
n
f
o
r
(
a)
s
in
g
le
an
d
(
b
)
two
DG
p
lace
m
en
t
(
a)
(
b
)
Fig
u
r
e
3
.
Simu
latio
n
r
esu
lts
:
(
a)
VP o
f
C
ai
r
o
-
5
9
b
u
s
R
DS
an
d
(
b
)
c
o
n
v
e
r
g
en
ce
c
u
r
v
e
o
f
H
PO
alg
o
r
ith
m
f
o
r
C
a
ir
o
-
5
9
b
u
s
R
DS
5.
CO
NCLU
SI
O
N
I
n
th
is
wo
r
k
,
th
e
HPO
alg
o
r
ith
m
was im
p
lem
en
ted
to
s
o
lv
e
a
m
u
lti
-
o
b
jectiv
e
DG
p
lace
m
en
t p
r
o
b
lem
in
a
DPN.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
HPO
alg
o
r
ith
m
was
ev
alu
ated
o
n
a
s
tan
d
ar
d
I
E
E
E
6
9
-
b
u
s
b
en
ch
m
ar
k
r
a
d
ial
DPN
an
d
a
r
ea
l
-
wo
r
ld
C
air
o
-
5
9
b
u
s
R
DS
.
T
h
e
PL
in
6
9
-
b
u
s
R
DS
was r
ed
u
ce
d
b
y
6
8
.
3
9
%
an
d
9
3
.
9
2
% f
o
r
th
e
o
p
tim
ized
s
in
g
le
PV
an
d
W
T
p
lace
m
en
t
an
d
6
8
.
6
8
%
an
d
9
6
.
5
9
%
f
o
r
two
PVs
an
d
W
T
s
allo
ca
tio
n
s
,
r
esp
ec
tiv
ely
.
T
h
e
m
in
im
u
m
v
o
ltag
e
(
V
min
)
o
f
t
h
e
6
9
-
b
u
s
R
DS
was
s
ig
n
if
ican
tly
in
cr
ea
s
ed
to
0
.
9
7
7
5
p
.
u
an
d
0
.
9
7
9
8
p
.
u
a
f
ter
a
s
in
g
le
an
d
two
PV
allo
ca
tio
n
s
,
r
esp
ec
tiv
ely
,
an
d
s
im
ilar
ly
,
af
ter
s
in
g
le
an
d
two
W
T
in
teg
r
atio
n
s
V
min
was in
cr
ea
s
ed
to
0
.
9
8
4
2
p
.
u
a
n
d
0
.
9
9
5
1
p
.
u
,
r
esp
ec
tiv
ely
.
L
ik
ewise,
th
e
o
p
t
im
ized
allo
ca
tio
n
o
f
s
in
g
le
an
d
two
DG
in
C
air
o
-
5
9
b
u
s
R
DS
h
as
s
ig
n
if
ican
tl
y
r
e
d
u
ce
d
th
e
PL
an
d
c
o
n
s
id
e
r
ab
ly
im
p
r
o
v
ed
th
e
VP.
No
tab
ly
,
th
e
HPO
alg
o
r
it
h
m
ef
f
ec
tiv
ely
ev
ad
e
d
th
e
lo
c
al
o
p
tim
al
s
tag
n
atio
n
an
d
co
n
v
er
g
ed
to
an
o
p
tim
al
s
o
lu
tio
n
.
Fu
r
th
er
m
o
r
e,
th
e
co
m
p
ar
ativ
e
s
tu
d
y
b
etwe
en
th
e
s
im
u
latio
n
f
in
d
in
g
s
o
f
HPO
an
d
o
th
er
alg
o
r
ith
m
s
s
ig
n
if
ied
its
s
u
p
er
io
r
ity
in
h
an
d
lin
g
co
m
p
lex
an
d
n
o
n
lin
ea
r
o
p
tim
izatio
n
p
r
o
b
lem
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Mu
lti
-
o
b
jective
h
u
n
ter p
r
ey
o
p
timiz
e
r
tech
n
iq
u
e
fo
r
d
is
tr
ib
u
ted
g
en
era
tio
n
p
la
ce
men
t
(
K
esa
va
n
Du
r
a
is
a
my
)
153
RE
F
E
R
E
NC
E
S
[
1
]
N
.
K
a
n
w
a
r
,
N
.
G
u
p
t
a
,
K
.
R
.
N
i
a
z
i
,
a
n
d
A
.
S
w
a
r
n
k
a
r
,
“
I
mp
r
o
v
e
d
m
e
t
a
-
h
e
u
r
i
st
i
c
t
e
c
h
n
i
q
u
e
s
f
o
r
si
mu
l
t
a
n
e
o
u
s
c
a
p
a
c
i
t
o
r
a
n
d
D
G
a
l
l
o
c
a
t
i
o
n
i
n
r
a
d
i
a
l
d
i
s
t
r
i
b
u
t
i
o
n
n
e
t
w
o
r
k
s,”
I
n
t
e
rn
a
t
i
o
n
a
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Evaluation Warning : The document was created with Spire.PDF for Python.