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[
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[
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[
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[
4
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No
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I
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8
6
9
4
P
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947
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T
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tim
al
p
lace
m
en
t
an
d
s
izin
g
(
O
PS
)
o
f
PV
-
DG
a
n
d
STAT
C
OM
s
ar
e
cr
u
cial
to
o
p
t
im
izin
g
an
d
m
ax
im
izin
g
th
eir
ad
v
an
tag
es.
Su
b
o
p
tim
al
in
teg
r
atio
n
is
ca
p
ab
le
o
f
ca
u
s
in
g
a
r
is
e
in
en
er
g
y
lo
s
s
es,
v
o
ltag
e
v
i
o
latio
n
s
,
an
d
r
ed
u
c
ed
s
y
s
tem
ef
f
icien
cy
.
As
th
e
p
en
etr
atio
n
o
f
R
E
S
an
d
th
e
u
s
e
o
f
g
r
id
s
u
p
p
o
r
t
d
ev
ices
lik
e
STAT
C
OM
s
co
n
tin
u
e
to
g
r
o
w,
th
e
n
ee
d
f
o
r
r
o
b
u
s
t
o
p
tim
izatio
n
m
eth
o
d
s
h
as n
ev
er
b
ee
n
m
o
r
e
cr
itical
[
7
]
,
[
8
]
.
Ad
ap
tiv
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
wo
r
k
s
b
etter
t
h
an
s
tatic
alg
o
r
ith
m
s
lik
e
DE
,
NSGA
-
I
I
,
an
d
GSO
b
ec
au
s
e
it
r
ed
u
ce
s
lo
s
s
es
m
o
r
e
(
u
p
to
5
7
.
8
9
%)
an
d
m
ak
es
v
o
ltag
e
m
o
r
e
s
tab
le
[
9
]
,
[
1
0
]
.
B
ec
au
s
e
it
ca
n
o
p
tim
ize
s
ev
er
al
o
b
jectiv
e
f
u
n
ctio
n
s
s
im
u
ltan
eo
u
s
ly
,
it
ca
n
s
im
u
ltan
eo
u
s
ly
r
ed
u
ce
h
ar
m
o
n
ic
d
is
to
r
tio
n
,
v
o
ltag
e
d
ev
iatio
n
(
VD)
,
a
n
d
p
o
wer
lo
s
s
es
(
f
o
r
ex
am
p
le,
T
HD
was
lo
wer
ed
to
3
.
9
8
%)
[
9
]
,
[
1
1
]
.
T
h
e
m
eth
o
d
h
as b
ee
n
ex
am
in
e
d
an
d
d
e
m
o
n
s
tr
ated
ef
f
icac
y
to
wo
r
k
o
n
c
o
n
v
en
tio
n
al
I
E
E
E
3
3
/6
9
-
b
u
s
test
s
y
s
tem
s
an
d
r
ea
l
-
wo
r
ld
n
etwo
r
k
s
lik
e
So
u
t
h
Ker
m
an
DSSK
[
1
1
]
,
[
1
2
]
.
A
d
a
p
tiv
e
PS
O
is
a
s
tr
o
n
g
an
d
s
c
alab
le
s
o
lu
tio
n
f
o
r
d
is
tr
ib
u
tio
n
s
y
s
tem
s
with
a
l
o
t
o
f
PVs
b
ec
au
s
e
it
ca
n
h
a
n
d
le
th
e
co
m
p
r
o
m
is
e
b
etwe
e
n
ex
p
l
o
r
atio
n
an
d
ex
p
lo
itatio
n
an
d
wo
r
k
ar
o
u
n
d
o
p
er
atio
n
al
lim
its
lik
e
2
4
-
h
o
u
r
lo
ad
p
r
o
f
iles
[
9
]
.
OPS
o
f
p
h
o
to
v
o
ltaic
s
y
s
tem
s
an
d
STAT
C
OM
s
s
ig
n
if
ican
tly
en
h
a
n
ce
r
ad
ial
d
is
tr
ib
u
tio
n
n
e
two
r
k
(
R
DN)
p
er
f
o
r
m
an
ce
th
r
o
u
g
h
th
e
r
ed
u
ctio
n
o
f
p
o
wer
l
o
s
s
es,
en
h
an
cin
g
V
Ps
,
an
d
b
o
o
s
tin
g
s
tab
ilit
y
.
A
r
ec
en
t
r
ev
iew
o
f
t
h
e
ap
p
licati
o
n
o
f
th
e
a
d
ap
tiv
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
APSO)
ap
p
r
o
ac
h
es
,
in
clu
d
in
g
v
ar
ian
ts
with
ac
ce
ler
atio
n
co
ef
f
icien
ts
,
m
u
lti
-
o
b
jectiv
e
f
r
a
m
ewo
r
k
s
,
a
n
d
d
y
n
am
ic
m
o
m
e
n
tu
m
,
d
em
o
n
s
tr
a
ted
o
n
th
is
to
p
ic
f
o
u
n
d
th
at
s
u
p
er
io
r
ef
f
icac
y
in
s
o
lv
in
g
th
ese
c
o
m
p
lex
o
p
tim
izatio
n
p
r
o
b
lem
s
.
Sh
a
h
ee
n
et
a
l.
[
9
]
p
r
o
p
o
s
ed
a
h
u
n
te
r
–
p
r
e
y
o
p
tim
izatio
n
(
HPO)
alg
o
r
ith
m
f
o
r
th
e
o
p
tim
al
allo
ca
tio
n
o
f
PV
-
STAT
C
OM
u
n
it
s
in
R
DN,
aim
in
g
to
m
in
im
iz
e
th
e
ac
tiv
e
en
er
g
y
lo
s
s
es
an
d
VDs
in
1
d
ay
.
T
h
e
s
u
g
g
ested
ap
p
r
o
ac
h
h
as
b
ee
n
im
p
lem
en
ted
in
th
e
I
E
E
E
3
3
-
an
d
6
9
-
b
u
s
test
s
y
s
tem
s
.
W
h
er
e
th
e
p
r
o
p
o
s
ed
m
eth
o
d
was
ap
p
lied
to
two
well
-
k
n
o
wn
b
e
n
ch
m
a
r
k
test
s
y
s
tem
s
,
n
am
ely
th
e
I
E
E
E
3
3
-
b
u
s
an
d
I
E
E
E
6
9
-
b
u
s
R
DN.
T
h
e
HPO
o
u
tco
m
es
o
u
tp
er
f
o
r
m
tr
ad
itio
n
al
alg
o
r
ith
m
s
lik
e
DE
(
d
if
f
er
e
n
tial
ev
o
lu
tio
n
)
,
tr
a
d
itio
n
al
PS
O
alg
o
r
ith
m
s
,
ar
tific
i
al
r
ab
b
its
’
alg
o
r
ith
m
(
AR
A
)
,
an
d
g
o
ld
e
n
s
ea
r
ch
o
p
tim
izer
(
GSO
)
in
ter
m
s
o
f
co
n
v
er
g
en
ce
an
d
ac
c
u
r
ac
y
wh
ile
ac
h
iev
in
g
n
o
tab
le
g
ain
s
in
p
o
wer
q
u
ality
an
d
ef
f
icien
cy
.
I
n
s
o
m
e
ca
s
es,
lo
w
er
in
g
c
o
m
b
in
e
d
o
b
jectiv
e
m
et
r
ics
b
y
o
v
er
8
5
%.
H
o
wev
er
,
th
e
m
ar
g
in
al
b
e
n
ef
it
d
ec
r
ea
s
es
af
ter
th
r
ee
u
n
its
ar
e
d
ep
lo
y
e
d
,
an
d
th
e
m
eth
o
d
'
s
p
er
f
o
r
m
a
n
ce
is
co
n
s
tr
ain
ed
wh
en
o
n
ly
o
n
e
d
ev
ice
is
in
s
talled
,
as
it
is
u
n
ab
le
to
ad
eq
u
ately
a
d
d
r
ess
v
o
ltag
e
co
n
s
tr
ain
ts
.
L
ab
ed
et
a
l
.
in
[
1
3
]
ap
p
lied
an
ad
a
p
tiv
e
ac
ce
ler
atio
n
co
e
f
f
icien
ts
PS
O
(
AAC
-
PS
O)
alg
o
r
ith
m
to
d
e
ter
m
in
e
th
e
OPS
o
f
PV
-
DG
an
d
DSTA
T
C
OM
u
n
its
in
an
I
E
E
E
3
3
-
b
u
s
R
DN.
T
h
e
r
esu
lts
d
em
o
n
s
tr
ated
s
ig
n
if
ican
t
m
in
im
izatio
n
o
f
APL
an
d
e
n
h
an
ce
m
en
t
of
VPs
,
ac
h
iev
in
g
a
p
p
r
o
x
im
at
ely
a
2
7
%
r
ed
u
ctio
n
in
p
o
we
r
lo
s
s
es
co
m
p
ar
ed
to
o
th
er
PS
O
v
ar
ian
ts
,
wh
ile
th
eir
ap
p
r
o
ac
h
,
th
o
u
g
h
s
u
p
er
i
o
r
in
co
n
v
er
g
en
ce
an
d
s
o
lu
ti
o
n
q
u
ality
,
r
em
ain
s
s
p
ec
if
ically
tailo
r
ed
to
r
ad
ial
n
etwo
r
k
s
an
d
m
ay
n
o
t g
en
er
al
ize
well
to
m
esh
ed
g
r
id
s
with
o
u
t r
ec
o
n
f
ig
u
r
atio
n
o
f
co
n
s
tr
ain
t h
an
d
lin
g
.
Ad
v
an
ce
d
PS
O
m
eth
o
d
s
h
a
v
e
b
ee
n
v
e
r
y
p
o
p
u
lar
in
th
e
last
s
ev
er
al
y
ea
r
s
f
o
r
tack
lin
g
m
u
lti
-
o
b
jectiv
e
p
r
o
b
lem
s
in
p
o
wer
d
is
tr
ib
u
ti
o
n
n
etwo
r
k
s
.
I
m
p
r
o
v
ed
v
er
s
io
n
s
o
f
m
u
lti
-
o
b
jectiv
e
PS
O
(
MO
PS
O)
th
at
u
s
e
ad
ap
tiv
e
g
r
id
s
tr
u
ctu
r
es
an
d
r
o
u
lette
wh
ee
l
s
elec
tio
n
m
ec
h
an
is
m
s
h
av
e
p
r
o
v
en
to
b
e
v
er
y
g
o
o
d
at
b
alan
cin
g
co
n
f
lictin
g
g
o
als
lik
e
r
ed
u
cin
g
n
etwo
r
k
lo
s
s
es,
co
n
tr
o
llin
g
v
o
ltag
e
f
l
u
ctu
atio
n
s
,
a
n
d
lim
itin
g
th
e
ca
p
ac
ity
o
f
s
tatic
v
ar
g
en
er
ato
r
s
(
SVGs
)
.
T
h
ese
m
eth
o
d
s
h
a
v
e
s
h
o
wn
b
e
tter
r
esu
lts
th
an
tr
ad
itio
n
al
e
v
o
lu
tio
n
ar
y
m
eth
o
d
s
,
s
u
ch
as
th
e
non
-
d
o
m
in
ated
s
o
r
tin
g
g
en
etic
alg
o
r
it
h
m
I
I
(
NS
GA
-
I
I
)
,
esp
ec
ially
wh
en
it
co
m
es
to
k
ee
p
in
g
th
e
v
ar
iety
o
f
th
e
Par
eto
f
r
o
n
t
in
s
to
ch
asti
c
d
is
tr
ib
u
ted
p
h
o
to
v
o
ltaic
(
PV)
s
ettin
g
s
[
1
4
]
.
T
o
m
ak
e
s
ca
lab
ilit
y
an
d
co
n
v
er
g
en
ce
ev
en
b
etter
,
a
M
o
d
if
ied
PS
O
with
d
y
n
am
ic
m
o
m
en
tu
m
(
MPSO
-
DM
)
was
s
u
g
g
ested
t
o
h
an
d
le
h
ig
h
-
d
im
e
n
s
io
n
al
o
p
tim
izatio
n
p
r
o
b
lem
s
in
lar
g
e
-
s
ca
le
s
y
s
tem
s
,
lik
e
th
e
I
E
E
E
7
9
-
b
u
s
n
et
wo
r
k
.
T
h
is
wo
r
k
ed
b
etter
th
an
tr
ad
itio
n
al
PS
O
v
ar
ian
ts
at
r
ed
u
ci
n
g
lo
s
s
es
an
d
im
p
r
o
v
in
g
ec
o
n
o
m
ic
p
er
f
o
r
m
an
ce
[
1
5
]
.
E
x
p
er
im
en
tal
s
tu
d
ies
o
n
I
E
E
E
33
-
,
6
9
-
,
an
d
7
9
-
b
u
s
test
s
y
s
t
em
s
s
h
o
w
th
at
ad
ap
tiv
e
PS
O
tech
n
iq
u
es
ca
n
cu
t
APL
f
r
o
m
2
5
to
7
6
.
3
%
[
9
]
,
[
1
3
]
,
[
1
5
]
,
[
1
6
]
,
s
tab
ilize
VPs
b
etwe
en
0
.
9
5
an
d
1
.
0
5
p
.
u
.
with
d
ev
iatio
n
s
r
ed
u
ce
d
to
4
2
.
8
4
%
[
9
]
,
[
1
7
]
,
an
d
m
a
k
e
th
e
s
y
s
tem
m
o
r
e
ec
o
n
o
m
ica
lly
v
iab
le
b
y
u
s
in
g
D
-
STAT
C
OM
s
with
p
ay
b
ac
k
p
er
io
d
s
as sh
o
r
t a
s
1
.
8
y
ea
r
s
a
n
d
co
s
t
-
s
av
in
g
b
en
ef
its
f
r
o
m
h
y
b
r
id
PV
-
STAT
C
OM
co
n
f
ig
u
r
atio
n
s
[
1
7
]
,
[
1
8
]
.
Ad
ap
tiv
e
PS
O
alg
o
r
ith
m
s
p
r
o
v
e
h
i
g
h
ly
e
f
f
ec
tiv
e
f
o
r
o
p
tim
izin
g
PV
-
STAT
C
OM
d
ep
lo
y
m
en
t,
o
f
f
er
in
g
d
y
n
am
ic
p
ar
am
eter
a
d
ju
s
tm
en
ts
th
at
o
u
tp
e
r
f
o
r
m
s
tatic
m
eth
o
d
s
.
Key
r
esu
lts
in
clu
d
e
s
u
b
s
tan
tial
lo
s
s
r
ed
u
ctio
n
s
(
2
5
–
7
6
.
3
%),
v
o
lta
g
e
s
tab
ilit
y
with
in
r
eg
u
lato
r
y
lim
its
,
an
d
co
s
t
-
ef
f
icien
t
s
o
lu
tio
n
s
with
r
ap
id
p
ay
b
ac
k
p
e
r
io
d
s
.
W
h
ile
H
u
n
t
er
-
p
r
ey
o
p
tim
izatio
n
(
HPO
)
an
d
a
r
tific
ial
r
ab
b
its
’
o
p
tim
iz
atio
n
(
AR
O
)
s
h
o
w
co
m
p
etitiv
e
r
esu
lts
in
s
p
ec
if
i
c
s
ce
n
ar
io
s
,
a
d
ap
tiv
e
PS
O’
s
f
lex
ib
ilit
y
in
h
an
d
lin
g
m
u
lti
-
o
b
jectiv
e
co
n
s
tr
ain
ts
p
ar
ticu
lar
ly
in
lar
g
e
-
s
ca
le
n
et
wo
r
k
s
s
o
lid
if
ies
its
u
tili
ty
f
o
r
m
o
d
er
n
d
is
tr
ib
u
tio
n
s
y
s
tem
s
.
So
m
e
o
p
tim
izatio
n
m
eth
o
d
s
ar
e
p
r
esen
ted
in
T
a
b
le
1
.
Fu
tu
r
e
w
o
r
k
c
o
u
ld
e
x
p
lo
r
e
h
y
b
r
id
f
r
am
ewo
r
k
s
co
m
b
in
in
g
PS
O
with
m
ac
h
in
e
lear
n
in
g
f
o
r
r
ea
l
-
tim
e
g
r
id
ad
a
p
tab
ilit
y
[
1
4
]
,
[
1
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
2
,
J
u
n
e
20
2
6
:
9
4
6
-
95
7
948
T
h
is
s
tu
d
y
a
d
d
r
ess
es
th
ese
ch
allen
g
es
b
y
em
p
lo
y
in
g
ad
v
a
n
ce
d
o
p
tim
izatio
n
alg
o
r
ith
m
s
t
o
o
p
tim
ize
th
e
p
lace
m
en
t a
n
d
s
izin
g
o
f
P
V
-
DG
an
d
STAT
C
OM
u
n
its
i
n
a
s
tan
d
ar
d
I
E
E
E
3
3
-
b
u
s
d
is
tr
ib
u
tio
n
s
y
s
tem
.
T
h
e
p
r
im
ar
y
o
b
jectiv
es
ar
e
th
e
m
in
im
izatio
n
o
f
APL
an
d
th
e
en
h
an
ce
m
en
t
o
f
v
o
ltag
e
s
tab
ilit
y
.
B
y
co
m
p
ar
in
g
th
e
p
er
f
o
r
m
an
ce
o
f
v
ar
io
u
s
o
p
tim
izatio
n
tech
n
iq
u
es,
th
is
wo
r
k
s
ee
k
s
to
ascer
tain
th
e
m
o
s
t
ef
f
ec
tiv
e
ap
p
r
o
ac
h
f
o
r
ac
h
iev
in
g
o
p
tim
al
s
y
s
tem
p
er
f
o
r
m
a
n
ce
.
T
h
e
im
p
o
r
tan
ce
o
f
th
is
s
tu
d
y
lies
in
its
ca
p
ac
ity
to
im
p
r
o
v
e
th
e
ef
f
icien
cy
an
d
r
eliab
ilit
y
o
f
elec
tr
ical
d
is
tr
ib
u
tio
n
s
y
s
tem
s
,
p
av
in
g
th
e
way
f
o
r
m
o
r
e
s
u
s
tain
ab
le
en
er
g
y
m
an
ag
em
en
t
p
r
ac
tices.
T
h
e
f
in
d
in
g
s
ar
e
ex
p
ec
ted
to
p
r
o
v
id
e
v
alu
a
b
le
in
s
ig
h
ts
f
o
r
u
tili
ty
o
p
er
ato
r
s
,
p
o
licy
m
ak
er
s
,
a
n
d
r
esear
ch
e
r
s
,
s
u
p
p
o
r
tin
g
th
e
g
l
o
b
al
tr
an
s
itio
n
to
war
d
r
en
ewa
b
le
en
e
r
g
y
i
n
teg
r
atio
n
a
n
d
th
e
d
ev
elo
p
m
e
n
t o
f
s
m
ar
te
r
,
m
o
r
e
r
esil
ien
t p
o
wer
g
r
i
d
s
.
T
ab
le
1
.
C
o
m
p
a
r
ativ
e
an
aly
s
is
o
f
d
if
f
er
en
t
o
p
tim
izatio
n
m
et
h
o
d
s
A
l
g
o
r
i
t
h
m
Lo
ss r
e
d
u
c
t
i
o
n
V
o
l
t
a
g
e
i
m
p
r
o
v
e
m
e
n
t
K
e
y
a
d
v
a
n
t
a
g
e
s
A
d
a
p
t
i
v
e
P
S
O
7
6
.
3
%
4
2
.
8
4
%
r
e
d
u
c
t
i
o
n
i
n
d
e
v
i
a
t
i
o
n
s
D
y
n
a
mi
c
c
o
e
f
f
i
c
i
e
n
t
t
u
n
i
n
g
f
o
r
e
x
p
l
o
r
a
t
i
o
n
-
e
x
p
l
o
i
t
a
t
i
o
n
b
a
l
a
n
c
e
[
1
3
]
,
[
1
4
]
H
u
n
t
e
r
-
P
r
e
y
(
H
P
O
)
5
7
.
8
9
%
4
4
.
6
9
%
r
e
d
u
c
t
i
o
n
i
n
d
e
v
i
a
t
i
o
n
s
S
u
p
e
r
i
o
r
c
o
n
si
s
t
e
n
c
y
i
n
v
a
r
i
a
b
l
e
l
o
a
d
c
o
n
d
i
t
i
o
n
s
[
9
]
A
r
t
i
f
i
c
i
a
l
R
a
b
b
i
t
s
(
A
R
O
)
6
5
.
4
%
(
r
e
a
c
t
i
v
e
l
o
s
s)
TH
D
r
e
d
u
c
e
d
t
o
3
.
9
8
%
Ex
c
e
l
s
i
n
h
a
r
m
o
n
i
c
mi
t
i
g
a
t
i
o
n
a
n
d
g
l
o
b
a
l
o
p
t
i
m
a
[
1
9
]
S
i
n
e
-
C
o
si
n
e
(
S
C
A
)
3
5
.
6
3
%
Ef
f
i
c
i
e
n
t
c
o
m
p
u
t
a
t
i
o
n
F
a
st
e
r
c
o
n
v
e
r
g
e
n
c
e
t
h
a
n
V
o
r
t
e
x
S
e
a
r
c
h
[
2
0
]
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
AND
CO
NST
RAIN
T
S
T
h
e
two
m
ain
o
b
jectiv
e
f
u
n
c
tio
n
s
in
th
is
r
esear
c
h
to
o
p
ti
m
ize
ar
e
th
e
m
in
im
izatio
n
o
f
APL
b
y
in
cr
ea
s
in
g
th
e
ac
tiv
e
p
o
wer
l
o
s
s
es
in
d
ex
(
APLI
)
,
w
h
er
e
h
ig
h
er
v
al
u
es
tr
an
s
late
to
h
ig
h
e
r
p
er
ce
n
tag
es
o
f
lo
s
s
r
ed
u
ctio
n
.
T
h
e
s
ec
o
n
d
o
b
jecti
v
e
co
n
s
is
ts
o
f
im
p
r
o
v
in
g
v
o
lt
ag
e
p
r
o
f
iles
an
d
m
ax
im
izin
g
t
h
e
v
o
ltag
e
s
tab
ilit
y
in
d
ex
to
e
n
h
an
ce
s
y
s
tem
r
eliab
ilit
y
u
n
d
er
v
ar
io
u
s
lo
ad
s
an
d
g
en
er
atio
n
c
o
n
d
itio
n
s
.
2
.
1
.
O
bje
c
t
iv
e
f
un
ct
io
ns
f
o
r
m
ula
t
io
n
First,
th
e
m
in
im
izatio
n
o
f
AP
L
b
y
m
a
x
im
izin
g
APLI
,
wh
ic
h
is
eq
u
iv
alen
t to
(
1
)
a
n
d
(
2
)
.
1
=
∑
∑
(
,
)
=
2
=
1
(
1
)
(
,
)
=
−
/
−
/
+
−
/
×
100
(
2
)
W
h
er
e
−
/
an
d
−
/
r
ep
r
esen
t
th
e
p
o
wer
lo
s
s
es
b
ef
o
r
e
an
d
af
ter
th
e
im
p
lem
en
tatio
n
o
f
th
e
PV
-
DG
an
d
DSTA
T
C
OM
.
T
h
e
eq
u
ati
o
n
b
elo
w
illu
s
tr
ates th
e
ac
tiv
e
p
o
wer
lo
s
s
[
2
1
]
:
=
(
+
)
+
(
+
)
(
3
)
{
=
(
−
)
=
(
+
)
(
4
)
W
h
er
e
an
d
ar
e
lo
s
s
co
ef
f
icien
ts
,
,
d
en
o
tes
th
e
lin
e'
s
r
esis
ta
n
ce
,
(
,
)
an
d
(
,
)
ar
e
th
e
v
o
ltag
e
s
an
d
a
n
g
les
at
t
h
e
b
u
s
es,
r
esp
e
ctiv
ely
.
(
,
)
d
e
n
o
tes
ac
tiv
e
p
o
wer
,
wh
ile
(
,
)
s
ig
n
if
ies
r
ea
ctiv
e
p
o
wer
.
Seco
n
d
,
th
e
e
n
h
an
ce
m
en
t o
f
th
e
VP th
r
o
u
g
h
th
e
r
ed
u
ctio
n
o
f
th
e
as d
etailed
in
(
5
)
.
2
=
=
|
1
−
|
(
5
)
W
h
er
e
d
en
o
te
th
e
v
o
ltag
e
m
a
g
n
itu
d
e
at
b
u
s
j.
2
.
2
.
Co
ns
t
ra
ints o
f
equa
lity
T
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
o
f
ea
c
h
b
u
s
m
u
s
t
b
e
eq
u
al
to
th
e
p
o
wer
l
o
ad
s
co
n
n
ec
ted
to
th
at
s
am
e
b
u
s
,
as in
d
icate
d
in
(
6
)
a
n
d
(
7
)
.
+
=
+
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
P
erfo
r
ma
n
ce
a
s
s
ess
men
t o
f P
S
O
va
r
ia
n
ts
fo
r
o
p
tima
l p
h
o
to
vo
lta
ic
a
n
d
DS
TATC
OM
…
(
Mo
h
a
med
K
h
erch
i
)
949
+
=
+
(
7
)
P
G
an
d
Q
G
r
ep
r
esen
t
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
o
f
th
e
g
e
n
er
ato
r
;
−
is
th
e
t
o
tal
ac
tiv
e
p
o
wer
in
jecte
d
f
r
o
m
th
e
PV
-
DG
s
o
u
r
ce
a
n
d
is
th
e
r
ea
ctiv
e
p
o
wer
in
jecte
d
f
r
o
m
th
e
DSTA
T
C
OM
.
,
ar
e
t
h
e
to
tal
lo
ad
d
em
an
d
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
,
r
esp
ec
tiv
ely
.
APLs
ar
e
d
en
o
ted
b
y
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
es
(
R
PL)
ar
e
d
en
o
ted
b
y
Q
L
o
s
s
,
r
esp
ec
tiv
ely
.
2
.
3
.
Dis
t
ributio
n line c
o
ns
t
ra
ints
T
h
e
d
is
tr
ib
u
tio
n
lin
e
r
estrictio
n
s
ar
e
ar
ticu
lated
u
s
in
g
(
8
)
to
(
1
0
)
.
≤
|
|
≤
(
8
)
|
1
−
|
≤
(
9
)
|
|
≤
(
1
0
)
a
n
d
s
i
g
n
if
y
t
h
e
m
a
x
i
m
u
m
a
n
d
m
in
im
u
m
v
o
lt
a
g
e
li
m
i
t
s
,
r
esp
ec
t
iv
el
y
.
r
e
p
r
es
en
ts
t
h
e
m
a
x
i
m
u
m
v
o
l
ta
g
e
d
r
o
p
.
a
n
d
,
r
ep
r
es
en
t
th
e
m
a
x
i
m
u
m
a
n
d
a
p
p
a
r
e
n
t
p
o
we
r
w
it
h
i
n
th
e
d
is
tr
ib
u
ti
o
n
li
n
e
.
2
.
4
.
P
V
-
DG
co
ns
t
ra
ints
T
h
e
lim
its
o
f
th
e
PV
-
DG
u
n
its
ar
e
f
o
r
m
u
lated
as
(
1
1
)
to
(
1
6
)
.
−
≤
−
≤
−
(
1
1
)
≤
≤
(
1
2
)
∑
−
≤
∑
=
1
=
1
(
1
3
)
2
≤
−
≤
(
1
4
)
≤
−
.
(
1
5
)
,
/
≤
1
(
1
6
)
W
h
er
e
,
−
an
d
−
d
en
o
te
t
h
e
m
in
i
m
u
m
an
d
m
ax
im
u
m
o
u
tp
u
t
p
o
wer
o
f
th
e
PV
-
DG,
r
esp
ec
tiv
ely
.
,
th
e
m
in
im
u
m
a
n
d
m
ax
im
u
m
r
ea
ctiv
e
p
o
wer
o
u
tp
u
ts
o
f
th
e
DSTA
T
C
OM
,
r
esp
ec
tiv
ely
.
−
s
ig
n
if
ies
th
e
PV
-
DG
u
n
it’s n
u
m
b
er
.
−
,
d
en
o
tes
th
e
lo
ca
tio
n
o
f
PV
-
DG
u
n
its
at
b
u
s
i
.
3.
O
VE
RVI
E
W
O
F
VAR
I
O
US
AL
G
O
RIT
H
M
S
I
n
th
is
p
ap
e
r
,
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asic
an
d
n
o
v
el
PS
O
alg
o
r
ith
m
s
ar
e
ap
p
lied
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o
r
th
e
p
u
r
p
o
s
e
o
f
th
e
OPS
o
f
th
r
ee
PV
-
DG
u
n
its
an
d
th
r
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DSTA
T
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OM
s
in
th
e
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tan
d
ar
d
I
E
E
E
3
3
-
b
u
s
R
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T
h
e
b
asic
PS
O
alg
o
r
ith
m
is
r
ep
r
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ted
b
y
m
ea
n
s
o
f
(
1
7
)
an
d
(
1
8
)
.
+
1
=
.
+
1
1
[
−
]
+
2
2
[
−
]
(
1
7
)
+
1
=
+
+
1
(
1
8
)
T
h
e
v
elo
city
o
f
th
e
p
a
r
ticle
is
d
en
o
ted
b
y
,
th
e
weig
h
t
o
f
in
er
tia
is
d
en
o
ted
b
y
,
an
d
t
h
e
ac
ce
ler
atio
n
co
ef
f
icien
ts
ar
e
d
en
o
te
d
b
y
1
,
2
.
1
,
2
ar
e
in
d
e
p
en
d
e
n
t
r
a
n
d
o
m
n
u
m
b
er
s
.
T
h
e
b
est
-
k
n
o
wn
p
o
s
itio
n
o
f
t
h
e
p
ar
ticle
is
d
en
o
ted
b
y
,
wh
ile
th
e
b
est
-
k
n
o
wn
p
o
s
itio
n
o
f
th
e
en
tire
s
war
m
is
d
en
o
ted
b
y
,
an
d
is
th
e
p
o
s
itio
n
o
f
th
e
p
ar
ticle.
T
ab
le
2
g
iv
es
a
s
u
m
m
a
r
y
o
f
s
o
m
e
ty
p
es
o
f
PS
O
v
ar
ian
ts
an
d
p
r
esen
ts
th
eir
m
ath
em
atica
l
f
o
r
m
u
latio
n
s
u
s
ed
to
a
d
ap
t
th
e
ac
ce
ler
atio
n
c
o
ef
f
icien
ts
d
u
r
in
g
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
.
T
h
e
tab
le
also
h
ig
h
lig
h
ts
th
e
c
o
r
r
e
s
p
o
n
d
in
g
co
n
tr
o
l
p
ar
a
m
eter
s
an
d
co
n
s
tan
ts
u
s
ed
in
ea
ch
te
ch
n
iq
u
e,
r
ef
lectin
g
d
is
tin
ct
ad
ap
tiv
e
s
tr
ateg
ies
p
r
o
p
o
s
ed
to
b
ala
n
ce
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
in
PS
O
alg
o
r
ith
m
s
.
Fig
u
r
e
1
d
is
p
lay
s
th
e
v
a
r
iatio
n
p
r
o
f
iles
o
f
t
h
e
ac
ce
ler
atio
n
co
e
f
f
icien
ts
1
an
d
2
o
f
th
e
s
tu
d
ied
PS
O
al
g
o
r
ith
m
s
with
r
esp
ec
t
to
th
e
iter
ativ
e
p
r
o
ce
d
u
r
e.
T
h
e
latter
clea
r
ly
s
h
o
ws
th
e
d
if
f
er
e
n
t
ad
ap
tatio
n
tactics
ad
o
p
ted
b
y
ea
ch
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
2
0
8
8
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4
I
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&
Dr
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No
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2
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u
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20
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v
ar
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d
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h
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g
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le
2
.
PS
O
v
ar
ian
ts
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d
th
ei
r
r
esp
ec
tiv
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ac
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A
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m
R
e
f
s
F
o
r
mu
l
a
s f
o
r
a
c
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e
l
e
r
a
t
i
o
n
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o
e
f
f
i
c
i
e
n
t
s
C
o
n
st
a
n
t
s
AAC
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PSO
[
2
2
]
1
=
+
(
−
)
(
−
(
4
×
)
2
)
a
n
d
2
=
−
(
−
)
(
−
(
4
×
)
2
)
c
m
i
n
=
0
.
5
,
c
m
a
x
=
2
.
5
A
P
G
-
PSO
[
2
3
]
1
=
1
.
95
−
(
2
×
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a
n
d
2
=
0
.
05
−
(
2
×
)
α
=
1
/
3
NDAC
-
PSO
[
2
4
]
1
=
−
(
−
)
(
)
2
+
a
n
d
2
=
(
1
−
)
2
+
(
)
c
i
=
0
.
5
,
c
f
=
2
.
5
S
C
A
C
-
PSO
[
2
5
]
1
=
.
[
(
1
−
)
×
2
]
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a
n
d
2
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.
[
(
1
−
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×
2
]
+
=
2
,
=
0
.
5
TV
A
-
PSO
[
2
6
]
1
=
1
+
(
1
−
1
)
a
n
d
2
=
2
+
(
2
−
2
)
.
c
1i
=
2
.
5
,
c
1f
=
0
.
5
c
2i
=
0
.
5
,
c
2f
=
2
.
5
Fig
u
r
e
1
.
Acc
eler
atio
n
co
ef
f
icien
t v
ar
iatio
n
c
u
r
v
es f
o
r
PS
O
alg
o
r
ith
m
s
4.
AP
P
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I
CA
T
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O
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A
ND
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h
e
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i
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s
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r
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e
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y
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f
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b
u
s
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d
3
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d
i
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u
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s
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c
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e
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f
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1
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r
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l
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s
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e
n
t
e
d
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n
F
i
g
u
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3
an
d
i
n
T
a
b
l
e
3
.
T
h
e
s
e
o
u
t
c
o
m
e
s
o
f
t
h
e
o
b
t
a
i
n
e
d
s
i
m
u
l
a
t
i
o
n
p
r
o
v
i
d
e
c
o
n
v
i
n
c
i
n
g
e
v
i
d
e
n
c
e
t
h
a
t
t
h
e
o
p
t
i
m
a
l
(
m
a
x
i
m
u
m
)
A
P
L
I
i
s
a
c
h
i
e
v
e
d
u
s
i
n
g
t
h
e
t
i
m
e
-
v
a
r
y
i
n
g
a
c
c
e
l
e
r
at
i
o
n
PS
O
(
T
V
A
-
PS
O
)
a
l
g
o
r
i
t
h
m
at
9
2
.
5
2
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,
wi
t
h
1
7
.
0
6
k
W
a
n
d
1
3
.
8
2
k
V
a
r
a
c
t
i
v
e
a
n
d
r
e
a
c
ti
v
e
l
o
s
s
es,
r
e
s
p
e
c
t
i
v
el
y
.
T
h
e
b
u
s
v
o
l
t
a
g
e
m
a
g
n
i
t
u
d
e
s
w
e
r
e
al
s
o
i
n
d
i
ca
t
ed
i
n
T
a
b
l
e
3
s
h
o
w
s
t
h
e
O
PS
o
f
t
h
e
t
h
r
e
e
P
V
-
DG
an
d
t
h
r
e
e
D
S
T
A
T
C
O
M
t
h
a
t
r
e
s
u
l
t
e
d
a
f
t
e
r
t
h
e
a
p
p
li
c
a
ti
o
n
o
f
e
a
c
h
P
S
O
a
l
g
o
r
i
t
h
m
.
Fig
u
r
e
3
illu
s
tr
ates
th
e
co
n
v
er
g
en
ce
cu
r
v
es
o
f
m
u
ltip
le
PS
O
v
ar
ian
ts
ap
p
lied
to
th
e
OPS
o
f
PV
an
d
STAT
C
OM
u
n
its
in
th
e
IEEE
33
-
b
u
s
R
DN.
Acc
o
r
d
in
g
to
t
h
e
f
in
d
in
g
s
,
th
e
T
VA
-
PS
O
alg
o
r
ith
m
ac
h
iev
ed
th
e
b
est
p
er
f
o
r
m
an
ce
o
u
t
o
f
all
t
h
e
ex
am
in
e
d
m
et
h
o
d
s
i
n
ter
m
s
o
f
th
e
h
ig
h
est
APLI
,
wh
e
r
e
it
r
ea
ch
es
9
2
.
5
%
af
ter
2
2
5
iter
atio
n
s
.
Oth
er
alg
o
r
ith
m
s
,
s
u
ch
as
APG
-
PS
O
an
d
N
DAC
-
PS
O
,
o
b
tain
ed
r
elativ
el
y
s
tab
le
APLI
v
alu
es
ea
r
lier
b
u
t
with
lo
wer
m
ax
i
m
u
m
p
er
f
o
r
m
an
ce
co
m
p
a
r
ed
to
th
e
T
VA
-
PS
O
alg
o
r
ith
m
.
T
h
e
B
ASI
C
-
PS
O
alg
o
r
ith
m
tak
es
lo
n
g
e
r
to
co
v
er
,
alm
o
s
t
s
im
ilar
ly
to
th
e
T
VA
-
PS
O
m
eth
o
d
.
Ho
wev
er
,
th
e
B
ASI
C
-
P
SO
alg
o
r
ith
m
g
ets
th
e
lo
west
APLI
(
8
4
%)
c
o
m
p
ar
e
d
t
o
T
VA
-
PS
O,
wh
ich
m
ea
n
s
th
at
it
is
th
e
wo
r
s
t
i
n
ter
m
s
o
f
b
o
th
s
p
ee
d
an
d
ef
f
icie
n
cy
.
T
h
ese
r
esu
lts
h
ig
h
lig
h
t
th
e
s
u
p
er
io
r
ity
o
f
T
VA
-
PS
O
in
ter
m
s
o
f
co
n
v
er
g
e
n
ce
ef
f
icien
cy
an
d
r
o
b
u
s
tn
ess
.
Acc
o
r
d
in
g
to
th
is
f
in
d
in
g
,
th
e
T
VA
-
PS
O
tech
n
iq
u
es
d
e
m
o
n
s
tr
ate
th
at
th
ey
o
u
tp
er
f
o
r
m
th
e
r
esu
lts
o
f
o
t
h
er
ad
a
p
tiv
e
PS
O
ap
p
r
o
ac
h
e
s
.
E
x
am
in
in
g
th
e
d
ata
p
r
ese
n
ted
in
T
ab
le
3
,
it
b
ec
o
m
es
ev
id
en
t
t
h
at
th
e
co
n
cu
r
r
en
t
in
te
g
r
atio
n
o
f
DG
an
d
DSTA
T
C
OM
u
n
its
ef
f
ec
tiv
ely
d
ec
r
ea
s
es
to
tal
p
o
wer
lo
s
s
to
ac
ce
p
tab
le
lev
els
ac
r
o
s
s
all
alg
o
r
ith
m
s
.
T
h
e
T
VA
-
PS
O
alg
o
r
ith
m
y
ield
s
th
e
b
est
APLI
o
u
tco
m
e,
d
esig
n
atin
g
b
u
s
es
2
5
,
2
8
,
a
n
d
1
3
as
o
p
tim
al
em
p
l
ac
em
en
ts
f
o
r
in
teg
r
atin
g
DG
u
n
its
,
to
talin
g
2
.
8
0
4
MW.
L
ik
ewise,
th
e
b
est
lo
ca
tio
n
f
o
r
DSTA
T
C
OM
u
n
it
in
te
g
r
atio
n
is
d
eter
m
in
ed
t
o
b
e
b
u
s
es
2
6
,
3
0
,
an
d
1
4
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
P
erfo
r
ma
n
ce
a
s
s
ess
men
t o
f P
S
O
va
r
ia
n
ts
fo
r
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p
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l p
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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4
I
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&
Dr
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,
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Po
w
E
lec
&
Dr
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s
t
I
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N:
2088
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8
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
2
,
J
u
n
e
20
2
6
:
9
4
6
-
95
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954
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er
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ith
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r
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r
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ltag
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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P
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h
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tically
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as
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ll a
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Hig
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Scien
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r
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g
h
th
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PR
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r
o
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wh
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was f
u
n
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y
Gr
an
t N
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ity
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o
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ir
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Pro
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.
AUTHO
R
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h
is
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u
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al
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s
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C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
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ec
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g
n
ize
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d
iv
id
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al
au
th
o
r
co
n
tr
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tio
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s
,
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ed
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ce
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th
o
r
s
h
ip
d
is
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tes,
an
d
f
ac
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ate
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llab
o
r
atio
n
.
Na
m
e
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Aut
ho
r
C
M
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Va
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Vi
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h
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ed
k
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✓
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Hac
en
e
Me
llah
✓
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So
u
h
il M
o
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✓
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An
war
Fellah
i
✓
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✓
C
:
C
o
n
c
e
p
t
u
a
l
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t
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:
M
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t
h
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So
f
t
w
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:
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l
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a
t
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r
mal
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n
v
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t
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g
a
t
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:
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so
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r
c
e
s
D
:
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a
t
a
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a
t
i
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:
W
r
i
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g
-
O
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l
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d
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p
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v
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s
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r
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t
a
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mi
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r
a
t
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Fu
:
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n
d
i
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g
a
c
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si
t
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CO
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C
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NT
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h
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th
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r
s
claim
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o
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o
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lict
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f
in
ter
est
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NF
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NS
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N
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All stu
d
y
p
ar
ticip
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ts
g
av
e
i
n
f
o
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m
ed
c
o
n
s
en
t
.
DATA AV
AI
L
AB
I
L
I
T
Y
T
h
e
co
r
r
esp
o
n
d
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g
au
t
h
o
r
ca
n
p
r
o
v
id
e
th
e
d
ata
u
s
ed
in
th
is
s
tu
d
y
u
p
o
n
r
eq
u
est.
RE
F
E
R
E
NC
E
S
[
1
]
M
.
D
a
n
e
sh
v
a
r
,
B
.
M
o
h
a
m
ma
d
i
-
I
v
a
t
l
o
o
,
a
n
d
K
.
Za
r
e
,
“
A
n
i
n
n
o
v
a
t
i
v
e
t
r
a
n
sa
c
t
i
v
e
e
n
e
r
g
y
a
r
c
h
i
t
e
c
t
u
r
e
f
o
r
c
o
m
mu
n
i
t
y
m
i
c
r
o
g
r
i
d
s
i
n
mo
d
e
r
n
mu
l
t
i
-
c
a
r
r
i
e
r
e
n
e
r
g
y
n
e
t
w
o
r
k
s:
a
C
h
i
c
a
g
o
c
a
se
st
u
d
y
,
”
S
c
i
e
n
t
i
f
i
c
Re
p
o
r
t
s
,
v
o
l
.
1
3
,
n
o
.
1
,
p
.
1
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,
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2
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:
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9
8
-
023
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-
7.
[
2
]
S
.
A
d
a
k
,
“
C
o
n
t
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o
l
s
t
r
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t
e
g
y
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a
l
u
a
t
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o
r
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p
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man
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men
t
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,
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c
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f
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.
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y.
[
3
]
D
.
S
i
n
g
h
,
N
.
El
g
e
b
e
r
i
,
M
.
A
l
j
a
i
d
i
,
R
.
K
u
ma
r
,
R
.
E.
A
l
M
a
ml
o
o
k
,
a
n
d
M
.
K
.
S
i
n
g
l
a
,
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O
p
t
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ma
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l
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c
a
t
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o
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o
f
r
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w
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n
e
r
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e
r
a
t
o
r
s
i
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t
r
a
n
sm
i
s
s
i
o
n
a
n
d
d
i
s
t
r
i
b
u
t
i
o
n
sy
st
e
m
o
f
d
e
r
e
g
u
l
a
t
e
d
p
o
w
e
r
s
e
c
t
o
r
:
a
r
e
v
i
e
w
,
”
En
e
rg
y
En
g
i
n
e
e
r
i
n
g
,
v
o
l
.
1
2
2
,
n
o
.
3
,
p
p
.
8
2
3
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5
9
,
2
0
2
5
,
d
o
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:
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0
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3
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6
0
4
/
e
e
.
2
0
2
5
.
0
5
9
3
0
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.