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Appl
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I
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,
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.
4
,
Dec
em
b
er
20
24
,
p
p
.
8
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3
I
SS
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DOI
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tec
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ACTS
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e
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n
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e
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th
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ti
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S
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n
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e
sy
ste
m
l
o
a
d
a
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ty
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d
e
x
a
n
d
to
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i
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re
a
c
ti
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e
p
o
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g
e
n
e
ra
ti
o
n
b
y
g
e
n
e
ra
to
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i
n
c
e
DSS
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is
o
f
l
o
w
p
o
we
r.
a
sm
a
ll
v
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lu
e
o
f
re
a
c
tan
c
e
is
e
m
u
late
d
i
n
t
h
e
l
in
e
.
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e
n
u
m
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e
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re
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u
t
e
d
a
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n
g
th
e
tran
sm
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li
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e
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t
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g
u
la
r
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terv
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ls
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e
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o
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sid
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ra
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le
c
h
a
n
g
e
i
n
th
e
c
u
r
re
n
t.
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p
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rti
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le
sw
a
rm
o
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ti
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iza
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o
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imp
lem
e
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ted
t
o
d
e
term
in
e
DSS
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e
m
u
late
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re
a
c
tan
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e
o
p
ti
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a
ll
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n
t
h
is
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o
n
d
it
io
n
,
a
ll
t
h
e
li
n
e
s
fl
o
win
g
p
o
we
r
i
n
t
h
e
ir
l
imits
with
in
c
re
a
se
d
lo
a
d
in
g
c
o
n
d
it
i
o
n
.
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a
x
imu
m
sy
ste
m
lo
a
d
a
b
il
it
y
in
d
e
x
is ev
a
lu
a
ted
b
y
e
m
p
lo
y
in
g
o
p
ti
m
a
l
n
u
m
b
e
r
o
f
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S
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o
n
t
h
e
li
n
e
.
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m
u
l
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jec
ti
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ro
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lem
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fo
rm
u
late
d
.
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n
e
o
b
je
c
ti
v
e
fu
n
c
ti
o
n
is
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o
rm
e
d
s
u
c
h
t
h
a
t
n
o
li
n
e
wo
u
ld
b
e
c
o
m
e
o
v
e
rlo
a
d
e
d
e
v
e
n
wh
e
n
lo
a
d
i
n
g
is
i
n
c
re
a
se
d
.
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e
r
o
b
jec
ti
v
e
is
fo
rm
u
late
d
t
o
m
i
n
imiz
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re
a
c
ti
v
e
p
o
we
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g
e
n
e
ra
ti
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b
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e
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e
ra
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A
c
o
m
p
ro
m
ise
so
l
u
ti
o
n
is
in
v
e
sti
g
a
ted
f
o
r
o
p
ti
m
a
ll
y
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o
n
n
e
c
ted
o
f
DS
S
C
d
e
v
ice
s
to
a
c
h
iev
e
b
o
th
t
h
e
o
b
jec
t
iv
e
f
u
n
c
ti
o
n
s.
IEE
E
1
4
b
u
s
s
y
ste
m
is
tak
e
n
fo
r
M
ATLAB
sim
u
latio
n
o
f
DSS
C
c
o
m
p
e
n
sa
ted
sy
ste
m
.
K
ey
w
o
r
d
s
:
Dis
tr
ib
u
ted
s
tatic
s
er
ies
co
m
p
en
s
ato
r
Flex
ib
le
AC
tr
an
s
m
is
s
io
n
s
y
s
tem
L
o
ad
ab
ilit
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Par
ticle
s
war
m
o
p
tim
izatio
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R
ea
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atio
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Static sy
n
ch
r
o
n
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s
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er
ies
co
m
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en
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atio
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T
h
is i
s
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n
o
p
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n
a
c
c
e
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rticle
u
n
d
e
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CC B
Y
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li
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se
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C
o
r
r
e
s
p
o
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A
uth
o
r
:
San
d
ee
p
R
.
Gaig
o
wal
Yesh
wan
tr
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C
h
av
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o
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o
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E
n
g
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R
T
M
Nag
p
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p
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r
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d
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m
ail:
s
an
d
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p
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m
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co
m
1.
I
NT
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D
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I
O
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Po
wer
s
y
s
tem
o
p
er
atio
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an
d
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tr
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in
a
s
ec
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e
m
an
n
e
r
is
a
m
ajo
r
co
n
ce
r
n
n
o
wad
ay
s
.
Nu
m
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s
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ew
g
en
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ate
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allelly
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with
a
g
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s
t
o
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er
w
o
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ld
wid
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t
a
ls
o
in
jects
p
o
wer
in
th
e
ex
itin
g
p
o
wer
g
r
i
d
.
T
h
is
to
tal
g
en
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ated
p
o
wer
is
d
is
tr
ib
u
ted
to
lo
ad
b
y
tr
an
s
m
i
s
s
io
n
n
etwo
r
k
an
d
d
is
tr
ib
u
ted
n
etwo
r
k
.
B
ec
au
s
e
o
f
in
c
r
ea
s
ed
p
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in
s
er
tio
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th
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g
r
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,
s
o
m
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m
a
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b
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v
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an
d
at
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e
s
am
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tim
e,
s
o
m
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lin
es
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ay
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p
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atin
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elo
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its
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al
lim
it.
T
h
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r
e,
n
e
w
lin
es
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ee
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to
b
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er
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ted
to
av
o
id
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g
esti
o
n
i
n
th
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ex
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g
g
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id
.
B
u
t
d
u
e
t
o
th
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h
ig
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t
o
f
in
s
tallatio
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alo
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g
with
o
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s
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v
ir
o
n
m
e
n
tal
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s
u
es,
lo
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lo
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s
,
an
d
lan
d
ac
q
u
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r
o
b
lem
s
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it
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n
o
t
a
f
ea
s
ib
le
s
o
lu
tio
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to
av
o
id
tr
a
n
s
m
is
s
io
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o
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er
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s
.
Flex
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AC
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s
m
is
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s
y
s
te
m
(
FAC
T
S)
o
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a
n
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p
tio
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to
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v
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p
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[
1
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.
I
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I
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2
2
5
2
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8
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9
2
I
n
t J Ap
p
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wer
E
n
g
,
Vo
l.
13
,
No
.
4
,
Dec
em
b
er
20
24
:
8
3
5
-
843
836
co
n
tr
o
l,
p
o
wer
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s
cillatio
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d
am
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in
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ed
r
eliab
ilit
y
[
2
]
.
Dis
tr
ib
u
ted
s
er
ies
r
ea
cto
r
s
(
DSR
)
,
d
is
tr
ib
u
ted
s
er
ies
im
p
ed
an
ce
s
(
DSI
)
,
an
d
d
is
tr
ib
u
ted
s
tatic
s
er
ies
co
m
p
en
s
ato
r
(
DSSC
)
ar
e
s
o
m
e
o
f
th
e
d
is
tr
ib
u
ted
FAC
T
S
d
ev
ices
t
o
co
n
tr
o
l
p
o
wer
f
lo
w
s
ig
n
if
i
ca
n
tly
[
3
]
.
A
d
is
tr
ib
u
ted
p
o
wer
f
lo
w
co
n
tr
o
ller
(
DPFC
)
i
s
o
n
e
o
f
th
e
ty
p
es
o
f
d
is
tr
ib
u
ted
s
er
ies
FA
C
T
S
co
n
tr
o
ller
[
4
]
.
I
t
is
th
e
d
ev
ice
s
im
ilar
to
u
n
if
ied
p
o
wer
f
lo
w
co
n
tr
o
ller
(
UPFC
)
b
u
t
it
is
w
ith
o
u
t
co
m
m
o
n
DC
lin
k
f
o
r
s
er
ies
an
d
s
h
u
n
t
co
m
p
en
s
atin
g
co
n
tr
o
ller
s
.
I
t
co
n
s
is
ts
o
f
m
u
ltip
le
lo
w
p
o
wer
DSSC
d
ev
ices
o
n
th
e
lin
e
with
s
in
g
le
s
tatic
co
m
p
en
s
ato
r
(
STAT
C
OM
)
.
Activ
e
p
o
wer
r
eq
u
ir
ed
f
o
r
s
er
ies
co
m
p
en
s
a
to
r
at
t
h
e
DC
ter
m
in
als
is
p
r
o
v
id
ed
b
y
th
e
lin
e
cu
r
r
en
t
with
its
th
ir
d
h
ar
m
o
n
i
c
cu
r
r
en
t
in
jectio
n
.
Similar
ly
,
a
d
is
tr
ib
u
ted
p
o
wer
f
lo
w
co
n
t
r
o
ller
u
s
in
g
e
m
itter
tu
r
n
o
f
f
(
E
T
O)
d
e
v
ice
is
p
r
esen
ted
in
[
5
]
.
I
t
c
o
n
s
is
ts
o
f
m
o
d
u
lar
s
elf
-
p
o
wer
ed
co
n
v
er
ter
co
n
n
ec
ted
with
th
e
lin
e
with
o
u
t
co
u
p
lin
g
tr
a
n
s
f
o
r
m
er
.
DSSC
is
em
p
lo
y
ed
f
o
r
a
lter
in
g
lin
e
r
ea
ctan
ce
t
o
co
n
tr
o
l
lin
e
cu
r
r
e
n
t
[
6
]
.
T
h
e
u
s
e
o
f
DSSC
ca
n
b
e
em
p
lo
y
ed
to
lim
it
th
e
f
a
u
lt
cu
r
r
e
n
t
in
th
e
lin
e.
DSSC
o
p
er
atio
n
in
in
d
u
ctiv
e
m
o
d
e
will
in
cr
ea
s
e
ef
f
ec
tiv
e
lin
e
r
ea
ctan
ce
an
d
r
ed
u
ce
th
e
f
au
l
t
cu
r
r
en
t
[
7
]
.
A
lin
ea
r
ize
d
DSSC
m
o
d
elin
g
is
p
r
esen
ted
in
[
8
]
.
Dis
tr
ib
u
ted
p
o
wer
f
lo
w
co
n
tr
o
ller
u
s
in
g
DSC
is
d
escr
ib
ed
f
o
r
ac
tiv
e
p
o
wer
in
th
e
lin
e
a
n
d
p
er
f
o
r
m
an
ce
an
aly
s
is
is
in
v
esti
g
ated
[
9
]
,
[
1
0
]
.
Vo
ltag
e
s
tab
ilit
y
in
DSSC
co
m
p
en
s
ated
s
y
s
t
em
is
p
u
t
u
p
in
th
e
r
ef
er
en
ce
[
1
1
]
.
Ma
n
y
m
o
r
e
r
esear
ch
p
ap
e
r
s
wer
e
p
u
b
lis
h
ed
o
n
th
e
s
er
ies co
m
p
en
s
atio
n
u
s
in
g
DSSC
[
1
2
]
-
[
1
6
]
.
Pro
b
lem
with
th
e
DSS
C
ap
p
li
ca
tio
n
is
th
at
lar
g
e
n
u
m
b
er
o
f
d
ev
ices
n
ee
d
to
b
e
co
n
n
ec
te
d
in
s
er
ies
with
th
e
lin
e
at
r
e
g
u
lar
in
ter
v
als.
W
ith
th
e
ap
p
licatio
n
o
f
o
p
tim
izatio
n
tech
n
iq
u
e,
n
u
m
b
e
r
o
f
DSSC
d
ev
ices
ca
n
b
e
c
h
o
s
en
o
p
tim
ally
to
a
ch
iev
e
ac
tiv
e
p
o
wer
c
o
n
tr
o
l.
Var
io
u
s
liter
atu
r
e
is
cited
o
n
o
p
tim
al
lo
ca
tio
n
o
f
FAC
T
S
co
n
tr
o
ller
s
s
o
lv
in
g
m
u
ltio
b
jectiv
e
p
r
o
b
lem
[
1
7
]
,
[
1
8
]
.
Op
tim
al
c
o
o
r
d
in
ated
o
p
er
atio
n
o
f
d
is
tr
ib
u
ted
s
tatic
s
er
ies
co
m
p
en
s
ato
r
s
f
o
r
wid
e
-
ar
ea
n
etwo
r
k
co
n
g
esti
o
n
r
elief
is
p
r
esen
ted
in
[
1
9
]
.
B
io
g
eo
g
r
ap
h
y
b
ased
o
p
tim
izatio
n
is
u
s
ed
to
f
in
d
o
p
tim
al
lo
ca
tio
n
o
f
d
is
tr
ib
u
ted
s
tatic
s
er
ies
co
m
p
en
s
ato
r
s
[
2
0
]
.
Dif
f
er
e
n
t
o
b
jectiv
es
ar
e
f
o
r
m
u
lated
s
u
ch
as
m
in
im
izin
g
c
o
s
t
o
f
in
s
t
allatio
n
,
im
p
r
o
v
in
g
l
o
ad
in
g
m
ar
g
in
,
m
in
im
izin
g
v
o
ltag
e
d
ev
iatio
n
co
n
s
id
er
i
n
g
d
if
f
er
e
n
t
c
o
n
s
tr
ain
ts
.
Op
tim
al
lo
ca
tio
n
o
f
s
h
u
n
t
-
s
er
ies
F
AC
T
S
co
n
tr
o
ller
is
o
b
tain
ed
b
y
a
p
p
ly
in
g
m
u
ltio
b
jectiv
e
o
p
tim
izatio
n
m
eth
o
d
.
A
m
ath
em
atica
l
o
p
tim
izatio
n
p
r
o
g
r
a
m
m
in
g
is
f
o
r
m
u
lated
u
s
in
g
Ɛ
-
co
n
s
tr
ain
t.
Op
tim
al
lo
ca
tio
n
o
f
p
h
ase
s
h
if
tin
g
tr
an
s
f
o
r
m
e
r
(
PS
T
)
,
h
y
b
r
id
f
lo
w
co
n
tr
o
lle
r
(
HFC
)
,
an
d
UPFC
is
o
b
tain
e
d
alo
n
g
with
th
eir
s
ettin
g
to
attain
m
u
ltio
b
jectiv
e
f
u
n
ctio
n
[
2
1
]
.
Op
tim
izatio
n
asp
ec
t
in
DSSC
co
m
p
en
s
ated
s
y
s
tem
to
g
et
m
ax
im
u
m
lo
ad
a
b
ilit
y
an
d
m
in
im
u
m
r
ea
ctiv
e
p
o
wer
g
e
n
er
atio
n
is
n
o
t a
d
d
r
ess
ed
in
th
e
liter
atu
r
e.
I
n
th
e
p
r
o
p
o
s
ed
wo
r
k
,
DSSC
is
d
em
o
n
s
tr
ated
f
o
r
c
u
r
r
en
t
co
n
tr
o
l
i
n
th
e
lin
e.
Ma
n
y
n
u
m
b
er
s
o
f
DSSC
’
s
ar
e
o
p
tim
ally
p
lace
d
i
n
th
e
lin
e
to
ac
h
iev
e
two
ta
r
g
e
ts
;
f
ir
s
t
is
to
g
et
m
ax
im
u
m
lo
a
d
ab
ilit
y
in
d
e
x
with
o
p
tim
u
m
em
u
lated
r
ea
ctan
ce
o
f
DSSC
’
s
an
d
s
ec
o
n
d
is
to
m
in
im
ize
r
ea
ctiv
e
p
o
wer
g
en
e
r
atio
n
.
I
n
t
h
is
wo
r
k
,
two
o
b
jectiv
e
f
u
n
ctio
n
s
ar
e
o
p
tim
ally
s
o
lv
ed
o
n
DSSC
co
m
p
en
s
ated
s
y
s
tem
.
W
h
en
DS
SC
d
ev
ices
in
lar
g
e
n
u
m
b
er
a
r
e
co
n
n
ec
ted
in
th
e
l
in
e,
a
s
u
b
s
tan
tial
alter
atio
n
in
th
e
lin
e
cu
r
r
en
t
is
f
o
u
n
d
.
Op
ti
m
izatio
n
tech
n
iq
u
e
is
em
p
lo
y
ed
to
f
in
d
o
p
tim
u
m
u
s
ag
e
o
f
DSSC
d
ev
ices
o
n
o
p
tim
al
lo
ca
tio
n
o
f
th
e
d
e
v
ic
e.
A
m
u
ltio
b
jectiv
e
o
p
tim
izatio
n
p
r
o
b
lem
is
f
o
r
m
u
lated
to
m
ax
im
ize
s
y
s
tem
l
o
ad
ab
ilit
y
in
d
ex
an
d
m
in
im
iz
in
g
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
.
A
p
ar
ticle
s
war
m
o
p
tim
izatio
n
m
eth
o
d
is
ap
p
lie
d
to
s
o
lv
e
th
e
o
p
tim
izatio
n
.
Pap
er
is
o
r
g
a
n
ized
as
f
o
llo
ws:
i)
Sectio
n
1
g
iv
es
in
tr
o
d
u
ctio
n
ab
o
u
t
th
e
r
esear
ch
ca
r
r
ied
o
u
t;
ii)
Sectio
n
2
is
p
r
esen
ted
o
n
DSSC
co
n
s
tr
u
ctio
n
an
d
o
p
er
atio
n
;
iii)
Sectio
n
3
c
o
v
er
s
f
lo
wch
ar
t
an
d
m
et
h
o
d
o
f
th
e
p
r
o
p
o
s
ed
wo
r
k
i
n
th
is
p
ap
er
;
an
d
iv
)
Sectio
n
4
p
r
esen
ts
s
y
s
tem
s
tu
d
ies
f
o
llo
wed
b
y
r
es
u
lt
an
d
c
o
n
clu
s
io
n
.
I
E
E
E
1
4
b
u
s
test
s
y
s
tem
is
co
n
s
id
er
ed
f
o
r
s
tu
d
ies.
MA
T
L
AB
s
o
f
twar
e
is
u
s
ed
to
v
alid
ate
th
e
s
y
s
tem
s
tu
d
ies.
2.
DIS
T
RI
B
U
T
E
D
S
T
A
T
I
C
S
E
RI
E
S CO
M
P
E
N
SAT
O
R
(
DSSC)
DSSC
is
s
er
ies
co
n
n
ec
ted
lo
w
p
o
wer
d
ev
ice
co
n
n
ec
te
d
o
n
ea
ch
p
h
ase
(
~2
0
k
VA)
as
s
h
o
wn
in
Fig
u
r
es
1
(
a)
an
d
1
(
b
)
.
W
ith
t
h
e
h
elp
o
f
DSSC
,
a
s
er
ies
co
m
p
en
s
atio
n
is
r
ea
lized
.
an
d
it
ca
n
b
e
im
p
lem
en
ted
o
n
th
e
lin
e
co
n
d
u
cto
r
d
ir
ec
tly
.
DSS
C
m
ain
ly
co
n
s
titu
tes
a
s
i
n
g
le
-
p
h
ase
in
v
er
te
r
.
I
n
p
u
t
to
in
v
er
ter
is
g
iv
en
b
y
v
o
ltag
e
ac
r
o
s
s
DC
lin
k
ca
p
ac
ito
r
.
Hig
h
tu
r
n
s
r
atio
STT
is
u
s
ed
to
co
n
n
ec
t
DSSC
d
ev
ice
in
th
e
ex
is
tin
g
lin
e.
STT
co
r
e
is
wo
u
n
d
o
n
th
e
tr
a
n
s
m
is
s
io
n
lin
e
co
n
d
u
cto
r
an
d
it
ac
ts
a
s
win
d
in
g
o
f
s
in
g
le
tu
r
n
tr
an
s
f
o
r
m
e
r
.
On
th
e
o
th
er
s
id
e
o
f
tr
an
s
f
o
r
m
e
r
,
it
co
n
s
is
ts
o
f
n
u
m
b
er
o
f
tu
r
n
s
wh
ich
s
tep
s
d
o
wn
cu
r
r
en
t
in
th
e
in
v
er
ter
cir
cu
it.
T
h
is
d
r
o
p
s
d
o
wn
i
n
v
er
ter
c
o
s
t.
DSSC
is
a
s
er
ie
s
co
n
n
ec
ted
co
m
p
en
s
ato
r
an
d
it
in
jects
v
o
ltag
e
in
s
er
ies
with
th
e
lin
e.
I
n
jecte
d
v
o
ltag
e
at
9
0
°
lead
in
g
o
r
lag
g
in
g
to
lin
e
c
u
r
r
en
t
em
u
lates
in
d
u
ctiv
e
o
r
c
ap
ac
itiv
e
r
ea
ctan
ce
in
s
er
ies with
th
e
lin
e
r
ea
ctan
c
e.
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
Op
tima
l D
S
S
C
’
s
d
ep
lo
yme
n
t i
n
p
o
w
er sys
tem
u
s
in
g
P
S
O
(
S
a
n
d
ee
p
R
.
Ga
ig
o
w
a
l
)
837
(
a)
(
b
)
Fig
u
r
e
1
.
DSC
C
: (
a)
s
u
s
p
en
d
e
d
o
n
lin
e
an
d
(
b
)
s
tr
u
ct
u
r
e
2
.
1
.
P
o
wer
f
lo
w
equa
t
io
ns
inco
rpo
ra
t
ing
DSSC
Ser
ies
FAC
T
S
d
ev
ice
SS
SC
m
o
d
elin
g
is
g
iv
e
n
in
[
2
2
]
,
[
2
3
]
.
On
s
im
ilar
lin
es,
th
e
m
o
d
ellin
g
o
f
DSSC
i
s
p
r
esen
ted
as
a
v
o
ltag
e
s
o
u
r
ce
∠
.
C
o
n
s
id
er
in
g
DSSC
co
n
n
ec
ted
o
n
th
e
lin
e
b
etwe
en
b
u
s
i
an
d
j
as g
iv
en
in
Fig
u
r
e
2
.
P
ij
a
n
d
Q
ij
p
o
wer
(
with
DSSC
co
m
p
en
s
atio
n
)
is
g
iv
en
b
y
:
=
2
−
[
(
−
)
+
(
−
)
]
−
[
(
−
)
+
(
−
)
]
(
1
)
=
−
2
−
[
(
−
)
−
(
−
)
]
−
[
(
−
)
−
(
−
)
]
(2
)
DC
lin
k
v
o
ltag
e
is
r
eg
u
lated
th
r
o
u
g
h
lin
e
its
elf
.
A
s
m
all
ac
tiv
e
p
o
wer
is
tak
en
f
r
o
m
t
h
e
lin
e
an
d
it
also
p
r
o
v
id
e
co
n
v
er
ter
lo
s
s
es.
(
∗
)
=
−
(
(
−
)
−
(
−
)
+
(
(
−
)
−
(
−
)
(
3
)
W
h
er
e
=
+
.
Fig
u
r
e
2
.
DSSC
o
n
th
e
lin
e
b
e
twee
n
I
an
d
j
b
u
s
2
.
2
.
P
r
o
blem
f
o
rm
ula
t
io
n
Sin
g
le
u
n
it
o
f
DSSC
is
a
lo
w
p
o
wer
an
d
lig
h
t
weig
h
t
d
e
v
ice.
Du
e
to
lo
w
p
o
wer
,
it
will
n
o
t
g
iv
e
an
y
s
ig
n
if
ican
t
ch
a
n
g
e
in
ac
tiv
e
p
o
wer
.
T
h
er
ef
o
r
e,
m
u
lti
p
le
n
u
m
b
e
r
o
f
DSSC
’
s
ar
e
r
eq
u
ir
ed
t
o
g
et
a
n
o
ticea
b
le
ch
an
g
e
in
t
h
e
lin
e
cu
r
r
en
t
is
o
b
tain
ed
.
A
wo
r
k
is
p
r
o
p
o
s
ed
to
f
in
d
th
e
lo
ca
tio
n
o
f
DSSC
d
ev
ice
o
n
th
e
lin
e
o
p
tim
ally
alo
n
g
with
th
e
en
h
an
ce
d
lo
ad
a
b
ilit
y
in
d
ex
.
Min
im
u
m
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
with
o
p
tim
u
m
u
s
e
o
f
DSSC
co
m
p
en
s
atio
n
d
ev
ices is also
p
r
o
p
o
s
ed
.
T
wo
o
b
jectiv
e
f
u
n
ctio
n
s
ar
e
co
n
s
id
er
ed
; o
n
e
is
to
lo
ca
te
DSS
C
d
ev
ices
o
p
tim
ally
with
o
p
tim
u
m
u
s
e
o
f
t
h
e
d
ev
ices
an
d
s
ec
o
n
d
o
b
jectiv
e
is
to
m
in
im
ize
r
ea
ctiv
e
p
o
wer
g
en
er
atio
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.
13
,
No
.
4
,
Dec
em
b
er
20
24
:
8
3
5
-
843
838
2
.
2
.
1
.
O
bje
ct
iv
e
f
un
ct
io
n
Ob
jectiv
e
f
u
n
ctio
n
F
1
is
f
r
am
ed
to
f
in
d
m
ax
im
u
m
lo
ad
a
b
ilit
y
in
d
ex
s
u
ch
th
at
n
o
lin
e
wo
u
ld
b
e
o
v
er
lo
ad
e
d
.
Ov
er
lo
a
d
f
ac
to
r
i
s
ch
ar
ac
ter
ized
as
/
.
Ob
jectiv
e
f
u
n
ctio
n
F
1
is
wr
itten
in
(
4
)
.
an
d
m
ax
im
u
m
allo
wab
le
c
u
r
r
en
t
lim
it
is
r
ep
r
esen
ted
b
y
I
L
a
n
d
th
e
ac
tu
al
cu
r
r
en
t
f
lo
w
o
f
i
th
tr
an
s
m
is
s
io
n
.
n
l
r
ep
r
esen
ts
n
u
m
b
er
t
r
an
s
m
is
s
io
n
lin
es.
W
h
en
t
h
e
cu
r
r
en
t
ex
c
ee
d
s
th
an
its
th
er
m
al
lim
it,
f
ac
to
r
F
1
will
b
ec
o
m
e
m
o
r
e
th
an
1
.
T
o
av
o
id
o
v
er
lo
a
d
in
g
o
f
an
y
o
f
th
e
lin
e,
F
1
s
h
o
u
ld
b
e
less
th
an
1
o
r
e
q
u
al
to
1
.
1
=
1
∑
(
)
∑
=
1
(
4
)
T
h
e
Ob
jectiv
e
f
u
n
ctio
n
F
2
is
f
r
am
ed
t
o
g
et
m
in
im
u
m
r
ea
ct
iv
e
p
o
wer
g
en
e
r
atio
n
.
I
t
is
f
o
r
m
u
lated
as
g
i
v
en
in
(
5
)
wh
e
r
e
Q
Gi
is
th
e
g
en
er
ated
r
ea
ctiv
e
p
o
wer
o
f
i
th
g
en
er
a
to
r
.
2
=
(
5
)
2
.
2
.
2
.
Co
ns
t
ra
ints
a)
E
q
u
ality
co
n
s
tr
ain
t
T
h
e
eq
u
ality
c
o
n
s
tr
ain
t is g
iv
e
n
as
(
6
)
.
∑
−
−
=
0
=
1
(
6
)
P
Gi
:
p
o
wer
g
en
e
r
atio
n
b
y
i
th
g
en
er
ato
r
;
P
D
:
to
tal
p
o
wer
d
e
m
an
d
;
P
loss
:
tr
an
s
m
is
s
io
n
p
o
wer
lo
s
s
es
;
an
d
ng
:
n
u
m
b
er
o
f
g
en
er
ato
r
s
.
(
6
)
s
h
o
ws p
o
wer
b
alan
ce
eq
u
atio
n
.
B
u
s
i p
o
wer
is
ex
p
r
ess
ed
as
(
7
)
an
d
(
8
)
.
−
−
∑
(
=
1
[
(
−
)
+
(
−
)
=
0
(
7
)
−
−
∑
(
=
1
[
(
−
)
+
(
−
)
=
0
(
8
)
N
-
R
p
o
wer
f
lo
w
eq
u
atio
n
s
ar
e
s
o
lv
ed
.
(
9
)
s
h
o
ws
pow
er
lo
s
s
wh
er
e
g
k
is
th
e
co
n
d
u
ctan
ce
o
f
k
th
lin
e,
it
is
b
etwe
en
b
u
s
es i
an
d
j.
=
∑
(
=
1
[
(
−
)
+
(
−
)
(
9
)
b)
I
n
eq
u
ality
c
o
n
s
tr
ain
ts
T
h
e
(
1
0
)
a
n
d
(
1
1
)
s
h
o
w
in
eq
u
ality
co
n
s
tr
ain
ts
.
Activ
e
p
o
wer
f
lo
w
in
th
e
lin
es
s
h
o
u
ld
n
o
t
ex
ce
e
d
s
lin
e
th
er
m
al
lim
it.
m
i
n
≤
≤
i =
1
,
2
….
.
n
(
1
0
)
≤
≤
i =
1
,
2
….
ng
(
1
1
)
I
n
eq
u
ality
co
n
s
tr
ain
t
d
is
p
lay
i
n
(
1
0
)
wh
ich
s
h
o
ws
g
e
n
er
ato
r
b
u
s
v
o
ltag
es
s
h
o
u
ld
b
e
with
in
ac
ce
p
ta
b
le
r
a
n
g
es.
Similar
ly
,
(
1
1
)
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
ac
ce
p
tab
le
lim
its
.
c)
FAC
T
S
c
o
n
s
tr
ain
ts
R
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
b
y
DSSC
d
ev
ices
s
h
o
u
ld
b
e
b
o
u
n
d
e
d
.
C
o
m
p
en
s
atio
n
lim
i
t
is
f
ix
ed
.
Fo
r
th
ese
s
tu
d
ies,
DSSC
d
ev
ices
ar
e
b
o
u
n
d
to
p
r
o
v
i
d
e
r
ea
c
tan
ce
em
u
latio
n
u
p
to
5
0
%
o
f
lin
e
r
ea
ctan
ce
.
I
n
(
1
2
)
,
X
DSSC
is
th
e
DSSC
’
s
em
u
lated
r
ea
ctan
ce
a
n
d
X
Line
is
th
e
lin
e
r
ea
ctan
ce
.
≤
0
.
5
(
1
2
)
3.
F
L
O
WCH
AR
T
AND
M
E
T
H
O
D
Flo
wch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
w
ay
to
f
in
d
o
p
tim
al
lo
ca
tio
n
o
f
th
e
DSSC
d
ev
ices
to
m
ax
im
ize
s
y
s
tem
lo
ad
ab
ilit
y
in
d
ex
is
s
h
o
wn
in
Fig
u
r
e
3
.
DSSC
d
ev
ices
ar
e
i
m
p
lem
en
ted
o
n
ea
ch
lin
e
an
d
o
p
tim
u
m
em
u
lated
r
ea
ctan
ce
is
d
eter
m
in
ed
b
y
u
s
i
n
g
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PSO
)
s
o
th
at
all
co
n
s
tr
ain
ts
ar
e
s
atis
f
ied
.
Step
b
y
s
tep
lo
ad
in
g
is
in
cr
ea
s
ed
t
ill
m
ax
im
u
m
lo
ad
ab
ilit
y
in
d
e
x
is
r
ea
ch
ed
.
Pro
ce
d
u
r
e
is
co
n
tin
u
ed
f
o
r
all
th
e
lin
es.
Sy
s
tem
lo
ad
ab
ilit
y
in
d
e
x
is
tab
u
lated
an
d
m
ax
im
u
m
lo
ad
ab
ilit
y
in
d
ex
is
n
o
ted
with
th
e
co
r
r
esp
o
n
d
in
g
lin
e
with
DSSC
.
T
h
is
is
th
e
o
p
tim
al
lo
ca
tio
n
o
f
DSSC
d
ev
i
ce
to
ac
h
ie
v
e
m
ax
im
ize
s
y
s
tem
lo
ad
ab
ilit
y
in
d
ex
.
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
Op
tima
l D
S
S
C
’
s
d
ep
lo
yme
n
t i
n
p
o
w
er sys
tem
u
s
in
g
P
S
O
(
S
a
n
d
ee
p
R
.
Ga
ig
o
w
a
l
)
839
Similar
ly
,
Fig
u
r
e
4
s
h
o
ws
f
lo
wch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
p
r
o
ce
d
u
r
e
to
m
in
im
ize
r
ea
ctiv
e
p
o
wer
g
e
n
er
atio
n
.
I
n
th
i
s
alg
o
r
ith
m
,
DSSC
is
p
lace
d
o
n
ea
ch
lin
e
an
d
em
u
lated
r
ea
ctan
ce
o
n
co
n
ce
r
n
ed
lin
e
is
c
alcu
lated
u
s
in
g
PS
O
with
th
e
m
ain
co
n
s
tr
ain
t
th
at
n
o
t
a
s
in
g
le
lin
e
wo
u
ld
cr
o
s
s
its
th
er
m
al
lim
it.
Pro
ce
s
s
r
e
p
e
ats
f
o
r
all
th
e
lin
es
an
d
r
esu
lts
ar
e
tab
u
lated
in
d
i
ca
tin
g
r
ea
ctiv
e
p
o
wer
g
e
n
er
at
io
n
an
d
co
n
ce
r
n
e
d
lin
e
with
o
p
tim
u
m
em
u
lated
r
ea
ctan
ce
b
y
DSSC
.
Fro
m
th
e
tab
le
m
in
im
u
m
r
ea
ctiv
e
g
e
n
er
atio
n
is
n
o
ted
alo
n
g
with
c
o
r
r
e
s
p
o
n
d
in
g
lin
e
with
em
u
lated
r
ea
ctan
ce
.
C
o
n
s
id
er
i
n
g
b
o
th
o
b
jectiv
e
f
u
n
ctio
n
s
,
a
co
m
p
r
o
m
is
e
s
o
lu
tio
n
is
d
eter
m
in
ed
wh
ich
g
iv
es
o
p
tim
al
lo
ca
tio
n
o
f
DSSC
d
ev
ices
with
o
p
tim
u
m
em
u
lated
r
ea
ctan
ce
with
m
ax
im
u
m
s
y
s
tem
lo
ad
ab
ilit
y
in
d
ex
an
d
m
in
im
u
m
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
.
B
y
co
n
s
id
er
i
n
g
r
esu
lts
o
f
b
o
th
o
b
jectiv
e
f
u
n
cti
o
n
s
,
a
co
m
p
r
o
m
is
e
s
o
lu
tio
n
is
d
eter
m
i
n
ed
w
h
ich
g
iv
es
o
p
tim
al
l
o
ca
tio
n
o
f
DSSC
d
ev
ices
with
o
p
tim
u
m
e
m
u
l
ated
r
ea
ctan
ce
with
m
ax
im
u
m
s
y
s
tem
lo
ad
a
b
ilit
y
in
d
ex
a
n
d
m
in
im
u
m
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
.
R
u
n
N
-
R
p
o
w
e
r
f
l
o
w
f
o
r
d
i
f
f
e
r
e
n
t
l
o
a
d
i
n
g
a
n
d
f
i
n
d
i
n
g
m
a
x
.
s
y
s
t
e
m
l
o
a
d
a
b
i
l
i
t
y
i
n
d
e
x
w
i
t
h
o
u
t
D
S
S
C
d
e
v
i
c
e
s
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Fig
u
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3
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Flo
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th
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s
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ize
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Fig
u
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4
.
Flo
wch
ar
t
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p
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m
to
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in
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ize
r
ea
ctiv
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p
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r
atio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
5
2
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2
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13
,
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4
,
Dec
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b
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20
24
:
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3
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840
4.
SYST
E
M
ST
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E
S
I
n
th
e
p
r
esen
t
wo
r
k
,
I
E
E
E
-
1
4
b
u
s
s
y
s
tem
is
co
n
s
id
er
ed
t
o
s
tu
d
y
DSSC
o
n
th
e
p
o
wer
s
y
s
tem
in
s
ec
u
r
ed
m
an
n
e
r
.
MA
T
POW
E
R
is
u
s
ed
f
o
r
an
aly
s
is
[
2
4
]
.
I
E
E
E
s
y
s
tem
d
ata
is
p
u
lled
f
r
o
m
r
ef
er
e
n
ce
[
2
5
]
.
Fiv
e
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
es
ar
e
s
h
o
wn
.
T
h
r
ee
m
ac
h
in
es
ar
e
ex
clu
s
iv
ely
f
o
r
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
.
B
u
s
1
is
co
n
s
id
er
ed
as
s
lack
b
u
s
.
Gen
er
ally
,
p
o
wer
tr
a
n
s
f
er
lim
it
o
f
tr
an
s
m
is
s
io
n
lin
e
is
co
n
s
id
er
ed
with
r
esp
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t
to
th
er
m
al
lim
it
o
f
tr
an
s
m
is
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io
n
co
n
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u
cto
r
.
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n
ew
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o
r
m
u
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o
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o
s
ed
to
f
in
d
p
o
we
r
tr
an
s
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er
lim
it
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y
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em
o
n
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tr
atin
g
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tr
o
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th
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m
al
co
u
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g
e
f
f
ec
t
o
f
tr
a
n
s
m
is
s
i
o
n
lin
e
in
[
2
6
]
.
T
a
b
le
1
s
h
o
w
s
lin
e
th
er
m
al
lim
it.
C
u
r
r
en
t
f
lo
win
g
th
r
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g
h
th
e
t
r
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s
m
is
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io
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lin
e
s
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o
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ld
n
o
t
c
r
o
s
s
th
er
m
al
lim
it.
T
o
g
et
m
a
x
im
u
m
lo
ad
a
b
ilit
y
in
d
ex
,
lo
ca
tio
n
o
f
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p
lace
m
en
t
is
d
eter
m
in
ed
o
p
tim
ally
.
T
wo
r
eg
io
n
s
ar
e
f
o
r
m
ed
in
I
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E
E
-
1
4
b
u
s
s
y
s
tem
.
B
u
s
es 1
to
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ar
e
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s
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d
in
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an
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it is
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r
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lace
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en
t.
T
ab
le
1
.
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ep
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le
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r
r
e
n
t (
t
h
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al
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atin
g
)
o
f
lin
es [
2
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r
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t
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r
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3
3
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1
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B
a
s
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s
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re
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ults
New
to
n
-
R
h
ap
s
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n
p
o
wer
f
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w
eq
u
atio
n
is
s
o
lv
ed
o
n
test
s
y
s
tem
with
o
u
t
co
n
s
id
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in
g
an
y
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m
p
en
s
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n
o
n
t
h
e
lin
e.
R
e
ac
tiv
e
p
o
wer
g
en
er
atio
n
is
s
h
o
wn
in
T
a
b
le
2
.
Activ
e
p
o
wer
lo
s
s
is
1
3
.
5
9
MW
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
is
5
6
.
9
0
MV
AR
.
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s
tem
lo
ad
ab
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in
d
ex
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ca
lcu
lated
an
d
it is
eq
u
al
to
1
.
0
8
with
o
u
t
an
y
c
o
m
p
e
n
s
atio
n
.
Po
wer
f
lo
w
s
h
o
ws
th
at
lin
es
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etwe
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b
u
s
1
-
2
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d
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g
m
o
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d
th
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m
al
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its
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r
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Similar
ly
,
lin
es
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n
n
ec
tin
g
b
u
s
es
1
-
5
,
2
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3
,
2
-
4
,
3
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4
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an
d
4
-
5
ar
e
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o
u
n
d
v
er
y
v
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r
a
n
t
to
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ad
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ar
iatio
n
.
T
ab
le
2.
R
ea
ctiv
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p
o
wer
g
en
e
r
atio
n
G
e
n
B
u
s
Q
g
mi
n
(
M
V
A
R
)
Q
g
ma
x
(
M
V
A
R
)
Q
g
(
M
V
A
R
)
1
S
l
a
c
k
b
u
s
S
l
a
c
k
b
u
s
-
1
5
.
2
2
3
2
-
40
50
4
7
.
9
2
8
3
0
40
2
7
.
7
5
8
6
-
6
24
2
3
.
0
2
6
8
-
6
24
2
1
.
0
3
4
.
2
.
DSSC e
m
plo
y
ed
t
o
ma
x
im
ize
s
y
s
t
em
lo
a
da
bil
it
y
ind
ex
T
h
e
m
ain
p
u
r
p
o
s
e
o
f
th
is
ca
s
e
is
to
ac
h
iev
e
t
h
e
h
ig
h
est
s
y
s
tem
lo
ad
ab
ilit
y
in
d
ex
.
T
o
ac
h
ie
v
e
th
is
,
th
e
o
p
tim
izatio
n
p
r
o
b
lem
is
s
o
lv
e
d
b
y
f
i
n
d
in
g
t
h
e
o
p
tim
al
u
s
e
o
f
DSSC
with
th
e
h
ig
h
est
lo
ad
in
g
.
Ob
jectiv
e
is
f
r
am
ed
s
u
ch
th
at
n
o
n
e
o
f
th
e
lin
e
o
v
er
lo
ad
s
.
Fo
r
s
ec
u
r
e
p
o
wer
tr
an
s
f
er
,
lin
e
wo
u
ld
ca
r
r
y
cu
r
r
en
t
well
b
elo
w
its
th
er
m
al
r
atin
g
.
T
o
en
s
u
r
e
t
h
at
all
lin
es
o
p
er
ate
well
b
el
o
w
th
eir
t
h
er
m
al
lim
it,
th
e
o
v
e
r
lo
ad
f
ac
to
r
in
(
4
)
m
u
s
t
b
e
eit
h
er
less
th
an
o
r
e
q
u
al
to
1
.
T
h
e
al
g
o
r
ith
m
s
h
o
wn
i
n
Fig
u
r
e
3
is
ap
p
lied
to
f
in
d
o
p
tim
al
lo
ca
tio
n
f
o
r
DSSC
p
lace
m
en
t.
DSSC
i
s
p
lace
d
o
n
an
y
p
ar
ticu
lar
tr
an
s
m
is
s
io
n
lin
e.
Po
wer
f
lo
w
is
r
u
n
an
d
o
p
tim
izatio
n
p
r
o
b
lem
is
s
o
lv
ed
to
f
in
d
o
p
ti
m
u
m
r
ea
ctan
ce
wh
ic
h
is
em
u
l
ated
b
y
DSSC
s
o
th
at
p
o
wer
tr
an
s
f
er
is
with
in
its
lim
its
.
I
f
n
o
lin
e
is
o
v
er
lo
ad
in
g
,
F1
is
le
s
s
th
an
o
r
eq
u
al
to
1
.
I
n
th
is
co
n
d
itio
n
,
lo
ad
a
b
ilit
y
in
d
ex
is
in
cr
ea
s
ed
s
tep
wis
e
an
d
ab
o
v
e
s
tep
s
ar
e
r
ep
ea
ted
.
I
t
is
co
n
tin
u
ed
till
m
ax
im
u
m
lo
a
d
ab
ilit
y
in
d
e
x
i
s
o
b
tain
ed
.
At
th
is
in
d
ex
,
all
t
h
e
lin
es
ar
e
eith
er
b
elo
w
o
r
eq
u
al
t
o
its
r
atin
g
.
Op
tim
u
m
em
u
lated
r
ea
ctan
ce
b
y
DSSC
p
lace
m
en
t
o
n
p
ar
ticu
lar
lin
e
with
p
ar
ticu
lar
m
ax
im
u
m
lo
ad
a
b
ilit
y
in
d
ex
is
g
ain
ed
.
Pro
ce
d
u
r
e
r
ep
ea
ted
f
o
r
DSSC
co
m
p
en
s
atio
n
o
n
all
th
e
lin
es.
L
o
ad
ab
ilit
y
i
n
d
ices
alo
n
g
with
o
p
tim
u
m
MV
A
b
y
DSSC
ar
e
ca
lcu
lated
f
o
r
all
th
e
lin
es.
T
h
e
o
p
tim
al
n
u
m
b
er
o
f
DSSC
s
ar
e
co
n
n
ec
ted
to
ea
ch
lin
e
an
d
th
e
m
a
x
im
u
m
lo
ad
a
b
ilit
y
in
d
e
x
is
o
b
s
e
r
v
ed
.
W
h
en
DSSC
s
ar
e
o
n
a
s
p
ec
if
ic
lin
e,
T
ab
le
3
d
is
p
lay
s
th
e
m
ax
im
u
m
s
y
s
t
em
lo
ad
ab
ilit
y
in
d
e
x
ac
h
iev
e
d
an
d
th
e
o
p
tim
al
r
ea
ctan
ce
em
u
lated
b
y
DSSC
.
Acc
o
r
d
in
g
to
b
ase
ca
s
e
N
-
R
p
o
wer
f
lo
w
s
tati
s
tics
,
cu
r
r
en
t
in
lin
es
1
-
2
is
in
cr
ea
s
in
g
an
d
it
is
g
ettin
g
cl
o
s
e
to
its
th
er
m
al
lim
it.
W
ith
o
u
t
DSS
C
co
m
p
en
s
atio
n
,
s
y
s
te
m
lo
ad
ab
ilit
y
in
d
ex
is
f
o
u
n
d
1
.
0
8
.
Fr
o
m
T
ab
le
3
s
y
s
tem
lo
ad
ab
ilit
y
is
o
b
tain
ed
m
ax
im
u
m
wh
en
DSSC
is
im
p
lem
en
ted
o
n
lin
e
1
-
5.
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
Op
tima
l D
S
S
C
’
s
d
ep
lo
yme
n
t i
n
p
o
w
er sys
tem
u
s
in
g
P
S
O
(
S
a
n
d
ee
p
R
.
Ga
ig
o
w
a
l
)
841
T
ab
le
3
.
R
esu
lts
o
f
o
p
tim
izati
o
n
p
r
o
b
lem
F
1
Lo
c
a
t
i
o
n
o
f
D
S
S
C
Emu
l
a
t
e
d
r
e
a
c
t
a
n
c
e
(
p
u
)
M
a
x
l
o
a
d
a
b
i
l
i
t
y
i
n
d
e
x
Q
G2
(
M
V
A
R
)
P
L
os
s
(
M
W
)
Q
L
os
s
(
M
V
A
R
)
1
-
2
0
.
0
2
9
6
1
.
0
8
3
8
.
7
8
6
1
1
6
.
3
0
0
7
6
7
.
7
0
9
8
1
-
5
0
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0
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3
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2
5
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4
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1
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5
.
6
4
1
5
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1
.
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1
4
3
2
-
4
0
.
0
3
3
6
1
.
0
7
3
6
.
8
7
3
7
1
6
.
1
4
6
9
6
5
.
0
9
3
6
2
-
5
0
.
0
3
3
4
1
.
0
7
3
7
.
7
2
7
6
1
6
.
0
8
1
1
6
5
.
6
3
6
7
3
-
4
0
.
0
5
1
8
1
.
0
8
3
6
.
6
9
3
7
1
6
.
4
3
1
9
6
7
.
2
5
1
6
4
-
5
0
.
0
3
8
7
1
.
1
3
8
.
7
1
6
1
1
7
.
1
4
9
3
6
8
.
3
2
8
5
4
.
3
.
DSSC f
o
r
re
a
ct
iv
e
po
we
r
g
ener
a
t
io
n o
ptim
iz
a
t
io
n
I
n
I
E
E
E
-
1
4
b
u
s
s
y
s
tem
,
o
u
t
o
f
5
r
ea
ctiv
e
p
o
wer
g
en
e
r
atio
n
s
o
u
r
ce
s
,
r
ea
ctiv
e
p
o
wer
g
e
n
er
atio
n
is
m
ax
im
u
m
f
o
r
th
e
g
en
er
at
o
r
at
b
u
s
2
.
T
h
er
ef
o
r
e,
th
e
g
o
al
is
to
r
ed
u
ce
th
e
am
o
u
n
t
o
f
r
ea
cti
v
e
p
o
wer
g
en
e
r
ated
at
b
u
s
2
.
W
h
ile
g
ettin
g
m
in
im
u
m
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
,
n
o
tr
a
n
s
m
is
s
io
n
lin
e
wo
u
ld
ca
r
r
y
cu
r
r
en
t
m
o
r
e
th
a
n
its
th
er
m
al
lim
its
.
DSSC
’
s
ar
e
p
lace
d
o
n
ea
ch
lin
e
in
r
eg
io
n
I
as
g
i
v
en
in
f
lo
w
ch
a
r
t.
Acc
o
r
d
in
g
to
T
a
b
le
4
r
esu
lt,
th
e
least
r
ea
ctiv
e
p
o
wer
g
e
n
er
atio
n
at
b
u
s
2
will
co
m
e
f
r
o
m
th
e
DSSC
s
co
n
n
ec
ted
t
o
b
u
s
es 1
-
2.
T
ab
le
4
.
R
esu
lts
o
f
o
p
tim
izati
o
n
p
r
o
b
lem
F
2
D
S
S
C
l
o
c
a
t
i
o
n
D
S
S
C
e
m
u
l
a
t
e
d
r
e
a
c
t
a
n
c
e
(
p
u
)
Q
G2
(
M
V
A
R
)
P
L
os
s
(
M
W
)
Q
L
os
s
(
M
V
A
R
)
1
-
2
0
.
0
2
9
5
3
4
.
8
6
1
4
.
2
6
4
9
.
0
7
1
-
5
0
.
1
1
1
5
4
3
.
2
2
1
3
.
8
4
4
9
.
0
7
2
-
3
0
.
0
9
8
9
4
4
.
1
2
1
3
.
6
1
5
0
.
6
7
2
-
4
0
.
0
8
7
7
4
2
.
9
2
1
4
.
4
4
5
3
.
7
7
2
-
5
0
.
0
8
4
8
1
4
6
.
3
0
1
4
.
0
9
5
5
.
1
8
3
-
4
0
.
0
8
3
4
4
3
.
9
0
1
3
.
7
3
5
6
.
4
8
4
-
5
0
.
0
8
3
0
4
3
.
9
2
1
3
.
7
3
5
6
.
4
9
4
.
4
.
B
est
co
m
pro
m
is
e
s
o
lutio
n
W
h
en
DSS
C
’
s
ar
e
p
lace
d
o
n
th
e
lin
e
f
r
o
m
1
-
5
,
it
s
h
o
ws
m
ax
im
u
m
lo
ad
a
b
ilit
y
in
d
ex
1
.
1
9
an
d
m
in
im
u
m
r
ea
ctiv
e
p
o
wer
g
e
n
er
atio
n
o
f
g
en
e
r
ato
r
at
b
u
s
2
is
m
in
im
u
m
wh
en
DSSC
is
p
lace
d
o
n
lin
e
f
r
o
m
1
-
2
.
Fig
u
r
e
5
s
h
o
ws
o
v
er
lo
ad
f
ac
to
r
wh
en
DSSC
’
s
ar
e
p
lace
d
o
n
lin
e
1
-
5
.
Fig
u
r
e
6
s
h
o
ws
r
ea
ctiv
e
p
o
wer
g
en
e
r
atio
n
o
p
tim
izatio
n
r
esu
lts
at
b
u
s
2
wh
en
DSS
C
i
s
p
lace
d
o
n
lin
e
1
-
5
.
B
est co
m
p
r
o
m
is
e
s
o
lu
tio
n
is
DSSC
p
lace
m
en
t
o
n
th
e
lin
e
c
o
n
n
ec
tin
g
b
u
s
es
1
-
5
.
I
t
g
iv
es
m
ax
im
u
m
l
o
ad
ab
ilit
y
i
n
d
ex
a
n
d
co
m
p
ar
ativ
e
less
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
.
Fig
u
r
e
5
.
Ov
e
r
lo
ad
f
ac
to
r
(
ta
k
in
g
in
to
ac
c
o
u
n
t D
SS
C
o
n
lin
es 1
–
5
)
with
m
a
x
im
u
m
l
o
ad
in
g
f
ac
to
r
1
.
1
9
Fig
u
r
e
6
.
R
ea
ctiv
e
p
o
wer
g
en
e
r
atio
n
at
g
en
e
r
ato
r
at
b
u
s
2
with
DSSC
o
n
lin
e
1
-
5
5.
CO
NCLU
SI
O
N
I
n
th
is
p
a
p
er
,
m
u
ltio
b
jectiv
e
m
ath
em
atica
l
p
r
o
g
r
am
m
i
n
g
f
o
r
o
p
tim
al
lo
ca
tio
n
o
f
DSSC
d
ev
ices
is
d
ev
elo
p
e
d
u
s
in
g
PS
O
tech
n
iq
u
e.
DSSC
i
s
lo
w
p
o
wer
in
v
er
t
er
wh
ich
is
h
an
g
ed
o
n
th
e
ex
is
tin
g
lin
e
to
ac
h
iev
e
ac
tiv
e
p
o
wer
f
lo
w
co
n
tr
o
l
th
r
o
u
g
h
lin
e.
T
w
o
o
b
jectiv
e
f
u
n
ctio
n
s
ar
e
co
n
s
id
er
ed
t
o
d
e
m
o
n
s
tr
ate
o
p
tim
a
l
lo
ca
tio
n
o
f
DSSC
.
First
o
b
jec
tiv
e
is
f
o
r
m
u
lated
to
i
n
cr
ea
s
e
lo
ad
in
g
m
ar
g
i
n
a
n
d
o
th
er
o
b
jectiv
e
is
f
r
am
e
d
t
o
r
ed
u
ce
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
.
A
co
m
p
r
o
m
is
e
s
o
lu
ti
o
n
is
f
o
u
n
d
o
u
t
f
u
lf
illi
n
g
b
o
th
o
b
jectiv
es
an
d
s
atis
f
y
in
g
all
th
e
co
n
s
tr
ain
ts
.
W
h
en
DSSC
s
ar
e
p
lace
d
o
n
t
h
e
lin
e
f
r
o
m
b
u
s
1
to
b
u
s
2
,
th
e
m
in
im
u
m
r
ea
ctiv
e
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.
13
,
No
.
4
,
Dec
em
b
er
20
24
:
8
3
5
-
843
842
p
o
wer
is
p
r
o
d
u
ce
d
b
y
th
e
g
en
er
ato
r
at
b
u
s
2
,
an
d
m
a
x
i
m
u
m
s
y
s
tem
lo
ad
ab
ilit
y
is
a
ttain
ed
with
DSS
C
co
m
p
en
s
atio
n
wh
e
n
DSSC
s
ar
e
p
lace
d
o
n
th
e
lin
e
f
r
o
m
b
u
s
1
to
b
u
s
2
.
I
t
is
f
ea
s
ib
le
to
s
elec
t
lin
e
f
r
o
m
b
u
s
1
to
5
f
o
r
DSSC
p
lace
m
en
t
to
g
et
m
a
x
im
u
m
lo
ad
a
b
i
lity
in
d
ex
as
well
as
m
in
im
u
m
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
.
R
esu
lts
co
n
clu
d
e
th
at
o
p
tim
al
lo
ca
tio
n
o
f
DSSC
d
ev
ices
wit
h
o
p
tim
al
em
u
lated
r
ea
ctan
ce
in
cr
ea
s
ed
th
e
s
y
s
tem
lo
a
d
in
g
m
ar
g
in
as
well
as
r
e
d
u
ce
s
g
e
n
er
ato
r
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
.
RE
F
E
R
E
NC
E
S
[
1
]
N
.
G
.
,
H
i
n
g
o
r
a
n
i
,
a
n
d
L
.
G
y
u
g
y
i
,
U
n
d
e
rs
t
a
n
d
i
n
g
F
AC
T
S
:
c
o
n
c
e
p
t
s
a
n
d
t
e
c
h
n
o
l
o
g
y
o
f
f
l
e
x
i
b
l
e
AC
t
ra
n
sm
i
ss
i
o
n
sys
t
e
m
s
.
W
i
l
e
y
-
I
EEE
P
r
e
ss,
2
0
0
0
.
[
2
]
D
.
M
.
D
i
v
a
n
e
t
a
l
.
,
“
A
d
i
st
r
i
b
u
t
e
d
st
a
t
i
c
ser
i
e
s
c
o
m
p
e
n
sa
t
o
r
sy
s
t
e
m
f
o
r
r
e
a
l
i
z
i
n
g
a
c
t
i
v
e
p
o
w
e
r
f
l
o
w
c
o
n
t
r
o
l
o
n
e
x
i
s
t
i
n
g
p
o
w
e
r
l
i
n
e
s,
”
i
n
I
EEE
T
ra
n
s
a
c
t
i
o
n
s
o
n
Po
w
e
r Del
i
v
e
r
y
,
Ja
n
.
2
0
0
4
,
p
p
.
6
5
4
–
6
6
1
.
d
o
i
:
1
0
.
1
1
0
9
/
TPW
R
D
.
2
0
0
6
.
8
8
7
1
0
3
.
[
3
]
H
.
J
o
h
a
l
a
n
d
D
.
D
i
v
a
n
,
“
D
e
si
g
n
c
o
n
si
d
e
r
a
t
i
o
n
s
f
o
r
seri
e
s
-
c
o
n
n
e
c
t
e
d
d
i
s
t
r
i
b
u
t
e
d
F
A
C
TS
c
o
n
v
e
r
t
e
r
s,
”
I
EEE
T
ra
n
s
a
c
t
i
o
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