I
nte
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l J
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f
Adv
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nces in Applie
d Science
s
(
I
J
AAS)
Vo
l.
10
,
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188
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t
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s
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n
d
e
d
g
re
a
tl
y
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o
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ra
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tt
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K
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:
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CC B
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li
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C
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p
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A
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d
z
1.
I
NT
RO
D
UCT
I
O
N
Dis
tr
ib
u
ted
r
en
ewa
b
le
e
n
er
g
y
g
en
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r
atio
n
is
s
m
all
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g
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n
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clu
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wit
h
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tech
n
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d
p
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d
iv
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s
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ch
allen
g
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wh
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in
teg
r
atin
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with
u
tili
ty
g
r
id
Mo
s
t
o
f
th
e
d
is
tr
ib
u
ted
r
en
ewa
b
le
en
er
g
y
s
o
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ce
s
(
D
-
R
E
Ss
)
s
h
all
b
e
lo
ca
ted
n
ea
r
lo
ad
ce
n
tr
e
o
n
d
is
tr
ib
u
tio
n
g
r
id
.
D
-
R
E
S
in
tr
o
d
u
ce
s
n
eg
ativ
e
ef
f
ec
ts
o
n
s
y
s
tem
o
p
e
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n
.
On
e
o
f
th
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n
e
g
ativ
e
im
p
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ts
is
r
elay
co
o
r
d
in
atio
n
[
1
]
.
T
h
e
in
teg
r
atio
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o
f
d
is
tr
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ted
r
en
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D
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n
t
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elec
tr
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ca
l n
etwo
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k
co
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tain
s
m
an
y
ad
v
an
tag
es
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Ho
wev
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,
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lt
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f
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tr
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d
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t
h
ese
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t
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Sev
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ef
f
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ts
o
f
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p
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an
d
th
e
p
o
s
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in
th
e
n
etwo
r
k
[
2
]
.
B
o
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f
f
a
an
d
C
h
ag
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i
[
3
]
p
r
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p
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ed
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d
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s
im
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lex
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eth
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d
to
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th
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f
tim
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d
ial
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T
DS
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wh
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s
tan
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v
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I
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d
I
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3
3
-
b
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s
with
in
s
t
allin
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e
D
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R
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S.
I
n
t
h
e
p
r
esen
t
ar
ticle,
a
p
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s
war
m
o
p
ti
m
izatio
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is
p
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p
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ed
to
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th
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f
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b
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th
T
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an
d
I
P
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f
r
elay
s
with
r
esp
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t to
v
ar
io
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s
co
n
s
tr
a
in
ts
in
th
e
p
r
esen
ce
o
f
two
D
-
R
E
S.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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Ap
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A
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189
2.
DIRE
CT
I
O
NAL
O
V
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R
-
CU
RREN
T
RE
L
AY
S
Fo
r
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p
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in
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f
d
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v
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cu
r
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en
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(
DOC
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r
elay
s
,
it
is
n
ec
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ar
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to
d
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r
m
in
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th
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o
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d
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DOC
r
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b
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(
1
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[
4
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,
[
5
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.
=
×
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14
(
×
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02
−
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1
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itatio
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[
6
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,
[
7
]
.
−
−
≤
(
4
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−
≤
(
5
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W
h
er
e
:
Tj
F1
is
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p
in
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b
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p
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T
I
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e
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m
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2
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0
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5
s
[
4
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[7
]
,
[
8
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T
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e
C
T
I
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s
et
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d
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o
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0
.
3
s
ec
.
3.
I
M
P
L
E
M
E
NT
A
T
I
O
N
O
F
P
RO
P
O
SE
D
P
SO
AL
G
O
R
I
T
H
M
O
N
T
H
E
CO
O
RD
I
NA
T
I
O
N
P
RO
B
L
E
M
T
h
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
,
wh
ich
h
as
g
a
in
ed
r
ap
id
p
o
p
u
lar
ity
as
an
ef
f
icien
t
o
p
tim
izatio
n
tech
n
iq
u
e,
is
r
ela
tiv
ely
a
r
ec
e
n
t
h
e
u
r
is
tic
in
tr
o
d
u
ce
d
b
y
E
b
er
h
a
r
t
an
d
Ken
n
ed
y
[
9
]
.
T
h
e
v
ar
io
u
s
s
tep
s
in
v
o
lv
ed
in
t
h
e
im
p
lem
e
n
tatio
n
o
f
PS
O
to
th
e
DOCR
s
p
r
o
b
lem
with
6
4
d
ec
is
io
n
s
v
ar
iab
les ar
e:
Step
1
.
I
n
p
u
t th
e
d
ata
o
f
3
3
I
E
E
E
d
is
tr
ib
u
tio
n
test
s
y
s
tem
f
o
r
ca
lcu
late
th
e
p
o
wer
f
lo
w
an
d
cu
r
r
en
t
Step
2
.
Def
in
e
p
o
p
u
latio
n
s
ize
(
5
0
)
,
n
o
o
f
iter
at
io
n
(
=5
0
0
)
,
as
s
u
m
e
s
u
itab
le
v
alu
es o
f
PS
O
p
ar
am
eter
s
Step
3
.
I
n
itial
s
ea
r
ch
in
g
p
o
in
ts
an
d
v
elo
cities
ar
e
r
a
n
d
o
m
ly
g
en
er
ated
with
in
t
h
eir
lim
its
.
Pb
est
is
s
et
to
ea
c
h
in
itial
s
ea
r
ch
in
g
p
o
in
t.
T
h
e
b
est
-
ev
alu
ated
v
alu
es
a
m
o
n
g
i
n
d
iv
id
u
al
b
est
(
P
best
)
ar
e
s
et
t
o
g
lo
b
al
b
est
(g
best
)
.
Step
4
.
New
v
elo
cities ar
e
ca
lcu
lated
u
s
in
g
th
e
e
q
u
atio
n
(
9
)
.
Step
5
.
E
v
alu
ate
th
e
f
itn
ess
v
a
lu
es
f
o
r
n
ew
s
ea
r
c
h
in
g
p
o
in
t.
I
f
ev
alu
ated
v
alu
es
o
f
ea
ch
ag
en
t
is
b
etter
th
an
p
r
ev
io
u
s
Pb
est th
en
s
et
to
Pb
e
s
t.
I
f
th
e
b
est Pb
est is
b
etter
th
an
b
est g
b
est th
en
s
et
to
g
b
est.
Step
6
.
I
f
th
e
m
ax
im
u
m
iter
atio
n
is
r
ea
ch
ed
s
to
p
th
e
p
r
o
ce
s
s
o
th
er
wis
e
g
o
to
s
tep
3
.
T
h
e
s
u
m
m
atio
n
o
f
tr
ip
p
in
g
tim
es
o
f
all
p
r
im
ar
y
r
elay
s
is
k
n
o
wn
as
o
b
jectiv
e
f
u
n
ct
io
n
(
OF)
.
C
o
n
v
en
tio
n
ally
,
th
e
o
p
tim
al
co
o
r
d
in
atio
n
p
r
o
b
le
m
d
eter
m
in
es
two
p
ar
am
eter
s
,
th
at
is
,
th
e
p
ick
u
p
cu
r
r
en
t
s
ettin
g
I
P
an
d
th
e
tim
e
d
ial
s
ettin
g
T
DS.
T
h
e
OF is g
iv
en
b
y
(
6
)
.
=
∑
=
1
(
6
)
W
h
er
e:
OF is th
e
o
b
jectiv
e
f
u
n
ctio
n
in
s
ec
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
10
,
No
.
2
,
J
u
n
e
2
0
2
1
:
1
8
8
–
1
9
2
190
t
il
is
th
e
o
p
er
atin
g
tim
e
o
f
th
e
i
th
r
elay
,
N
is
th
e
to
tal
DOC
R
s
in
th
e
s
y
s
tem
.
T
h
e
two
v
ar
ia
b
les
in
th
e
o
b
je
ctiv
e
f
u
n
ctio
n
ar
e
T
DS
an
d
I
p
.
B
y
m
in
im
izin
g
b
o
th
th
e
T
DS
an
d
I
p
we
ca
n
b
e
ab
le
to
m
in
im
ize
th
e
t
r
ip
p
in
g
t
im
e
o
f
th
e
p
r
im
ar
y
r
elay
s
an
d
s
atis
f
y
in
g
th
e
C
T
I
.
3
.
1
.
G
o
a
l o
f
Study
T
h
is
wo
r
k
p
r
esen
ted
th
e
PS
O
alg
o
r
ith
m
to
f
in
d
th
e
o
p
ti
m
al
C
T
I
o
f
DOC
R
elay
s
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
was
ev
alu
ated
u
s
in
g
I
E
E
E
3
3
-
b
u
s
s
y
s
tem
in
p
r
esen
ce
o
f
two
D
-
R
E
Ss
.
T
h
e
m
ain
co
n
tr
ib
u
ti
o
n
s
o
f
th
is
p
ap
er
ar
e
u
s
in
g
th
e
o
p
tim
izatio
n
tech
n
iq
u
e
to
f
i
n
d
o
p
tim
al
r
ela
y
s
et
tin
g
s
,
s
o
lv
e
th
e
n
o
n
-
lin
ea
r
co
o
r
d
in
atio
n
p
r
o
b
lem
o
f
DOC R
elay
s
with
th
e
s
y
s
tem
ch
an
g
ed
to
p
o
l
o
g
y
.
4.
CASE
S
T
UD
I
E
S
I
n
th
is
p
ap
e
r
I
E
E
E
3
3
-
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
f
ee
d
er
is
co
n
s
id
er
ed
to
o
p
tim
al
p
air
o
f
DOC
R
elay
s
in
p
r
esen
ce
o
f
two
em
p
lace
m
e
n
t
s
o
f
D
-
R
E
S.
T
h
e
o
p
er
atin
g
v
o
ltag
e
is
1
2
.
6
6
k
V.
DOC
R
el
ay
s
ar
e
u
s
ed
in
th
e
s
y
s
tem
to
p
r
o
tect
th
e
f
ee
d
e
r
in
ca
s
e
o
f
th
r
ee
p
h
ase
f
a
u
lts
.
T
h
e
I
E
E
E
3
3
-
b
u
s
s
y
s
te
m
is
p
r
esen
ted
in
Fig
u
r
e
1
[
1
0
]
,
[
1
1
]
.
T
h
e
m
o
d
el
is
s
im
u
lated
in
MA
T
L
A
B
s
o
f
twar
e
with
o
u
t
an
d
with
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
to
ca
lcu
late
t
h
e
o
p
tim
al
s
ettin
g
o
f
DOCR
s
u
s
in
g
PS
O
m
eth
o
d
u
n
d
er
s
y
s
tem
c
h
an
g
es.
T
h
e
p
r
o
g
r
am
is
im
p
lem
en
ted
f
o
r
two
em
p
lace
m
en
ts
o
f
r
e
n
ewa
b
le
en
e
r
g
y
s
o
u
r
ce
s
.
T
h
r
ee
p
h
ase
f
a
u
lts
ar
e
g
en
er
ated
o
n
ea
c
h
b
u
s
.
Fig
u
r
e
1
.
Po
wer
d
is
tr
ib
u
tio
n
s
y
s
tem
o
f
th
e
I
E
E
E
3
3
-
b
u
s
s
y
s
tem
u
n
d
e
r
s
tu
d
y
4
.
1
.
I
m
pa
ct
o
f
t
he
D
-
RE
S o
n t
he
s
ho
rt
circ
uit
lev
el
Fro
m
a
p
o
wer
p
er
s
p
ec
tiv
e,
t
h
e
in
teg
r
atio
n
o
f
a
n
ew
D
-
R
E
S
in
to
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
will
in
c
r
ea
s
e
th
e
p
o
wer
o
f
th
e
n
et
wo
r
k
.
T
h
u
s
,
th
e
n
ew
s
o
u
r
ce
will
b
e
m
o
d
ele
d
in
s
u
ch
a
way
as
to
tak
e
o
n
ly
its
cu
r
r
en
t
co
n
tr
ib
u
tio
n
in
t
h
e
ev
en
t
o
f
a
s
h
o
r
t
cir
c
u
it.
T
h
e
ele
ctr
ical
n
etwo
r
k
,
o
f
wh
ich
we
will
d
eter
m
in
e
th
e
d
if
f
er
en
t
s
h
o
r
t
cir
cu
it
c
u
r
r
e
n
ts
with
o
u
t
(
an
d
with
)
D
-
R
E
S,
h
as
a
r
a
d
ial
ar
c
h
itectu
r
e
Fig
u
r
e
1
,
an
d
we
tak
e
a
p
ar
t o
f
t
h
is
n
etwo
r
k
f
o
r
th
e
ca
lcu
la
tio
n
s
o
f
s
h
o
r
t
cir
cu
it c
u
r
r
e
n
ts
,
as sh
o
w
in
Fig
u
r
e
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2
2
5
2
-
8
8
1
4
A
p
p
lica
tio
n
o
f P
S
O
fo
r
o
p
tima
l c
o
o
r
d
in
a
tio
n
o
f d
ir
ec
tio
n
a
l
o
ve
r
-
cu
r
r
en
t
r
ela
ys
…
(
La
z
h
a
r
B
o
u
g
o
u
ffa
)
191
Fig
u
r
e.
2
.
Simp
le
d
is
tr
ib
u
tio
n
n
etwo
r
k
with
R
E
S
T
h
e
cu
r
r
en
t
in
th
e
f
a
u
lt
p
o
i
n
t
will
b
e
th
e
s
u
m
o
f
t
h
e
s
h
o
r
t
cir
cu
it
cu
r
r
en
t
with
o
u
t
D
-
R
E
S
an
d
th
e
s
h
o
r
t c
ir
cu
it c
u
r
r
en
t in
jecte
d
i
n
to
th
e
n
etwo
r
k
o
n
ly
b
y
th
e
D
-
R
E
S,
is
g
iv
en
b
y
(
7
)
.
=
+
−
(
7
)
T
h
e
d
ir
ec
t im
p
e
d
an
ce
s
ee
n
b
et
wee
n
th
e
b
ar
(
1
1
)
an
d
th
e
ea
r
t
h
is
(
8
)
.
−
=
−
−
+
−
+
−
2
(
8
)
I
m
p
lies
th
at
(
9
)
,
(
1
0
)
,
(
1
1
)
.
−
=
−
−
+
−
+
−
2
(
9
)
−
=
2
.
−
−
+
−
+
−
2
(
1
0
)
−
=
.
−
−
+
−
+
−
2
(
1
1
)
W
e
f
in
d
th
e
f
au
lt c
u
r
r
en
t is
(
1
2
)
,
(
1
3
)
,
a
n
d
(
1
4
)
.
=
−
+
−
1
+
−
2
+
−
−
+
−
+
−
2
(
1
2
)
=
2
.
[
−
+
−
1
+
−
2
+
−
−
+
−
+
−
2
]
(
1
3
)
=
.
[
−
+
−
1
+
−
2
+
−
−
+
−
+
−
2
]
(
1
4
)
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
wo
lo
ca
tio
n
s
ar
e
ch
o
s
en
f
o
r
i
n
s
tallin
g
th
e
D
-
R
E
S
in
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
;
to
illu
s
tr
ate
th
e
ef
f
ec
ts
o
f
D
-
R
E
S
in
s
er
tio
n
s
o
n
th
e
s
ettin
g
o
f
R
elay
s
.
A
m
in
im
u
m
r
elay
tr
ip
p
in
g
tim
e
is
th
e
m
ain
g
o
al
o
f
s
ettin
g
o
f
r
elay
s
.
Als
o
,
th
e
C
T
I
is
s
atis
f
i
ed
(
i.e
.
,
C
T
I
≥
0
.
3
)
.
T
a
b
le
1
s
h
o
ws
th
e
o
p
tim
al
r
esu
lts
o
f
T
DS
s
in
p
r
esen
ce
o
f
D
-
R
E
S
in
s
tallat
io
n
in
th
e
3
3
-
b
u
s
d
is
tr
ib
u
tio
n
s
y
s
tem
.
T
ab
le
2
s
h
o
ws
th
e
o
p
tim
al
r
esu
lts
o
f
I
p
s
in
p
r
esen
ce
o
f
D
-
R
E
S
.
T
ab
le
1
.
S
ettin
g
v
al
u
es o
f
r
elai
s
T
DS
S
e
t
t
i
n
g
o
f
TD
S
R
e
l
a
y
s
W
i
t
h
o
u
t
D
-
R
ES
W
i
t
h
D
-
R
ES
TD
S
1
0
.
5
0
0
0
0
.
5
0
0
0
TD
S
2
0
.
3
5
0
0
0
.
3
5
0
0
TD
S
3
0
.
3
4
0
0
0
.
3
4
0
0
TD
S
4
0
.
3
3
0
0
0
.
3
3
0
0
TD
S
5
0
.
3
4
0
0
0
.
3
0
0
0
TD
S
6
0
.
3
5
0
0
0
.
3
5
0
0
TD
S
7
0
.
2
7
0
0
0
.
2
7
0
0
TD
S
8
0
.
2
4
0
0
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CO
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elay
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in
th
e
test
s
y
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tem
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h
e
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lt
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s
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alg
o
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ith
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3
3
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is
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tem
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s
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ee
f
a
u
lt c
u
r
r
e
n
ts
.
RE
F
E
R
E
NC
E
S
[1
]
A.
S
h
riv
a
sta
v
a
,
D.
K
u
m
a
r
S
a
i
n
i,
M
.
P
a
n
d
it
,
“
Re
lay
c
o
-
o
r
d
in
a
ti
o
n
o
p
ti
m
iza
ti
o
n
f
o
r
in
teg
ra
te
d
s
o
lar
p
h
o
t
o
-
v
o
lt
a
i
c
p
o
we
r
d
istr
ib
u
ti
o
n
g
rid
,”
Co
g
e
n
t
En
g
i
n
e
e
rin
g
,
v
o
l.
6
,
n
o
.
1
,
p
p
.
1
-
1
9
,
2
0
1
9
.
[2
]
R.
M
.
Ch
a
b
a
n
l
o
o
,
H.
A.
Ab
y
a
n
e
h
,
A.
Ag
h
e
li
,
H.
Ra
ste
g
a
r,
“
Ov
e
rc
u
rre
n
t
re
lay
s
c
o
o
rd
i
n
a
ti
o
n
c
o
n
si
d
e
rin
g
tra
n
sie
n
t
b
e
h
a
v
i
o
u
r
o
f
fa
u
lt
c
u
rre
n
t
li
m
it
e
r
a
n
d
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
i
n
d
istri
b
u
ti
o
n
p
o
we
r
n
e
two
r
k
,
”
I
ET
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
&
Distrib
u
ti
o
n
,
v
o
l.
5
,
n
o
.
9
,
p
p
.
9
0
3
-
9
1
1
,
2
0
1
1
.
[3
]
L.
B
o
u
g
o
u
ffa
,
A.
Ch
a
g
h
i,
“
Eff
e
c
t
o
f
re
n
e
wa
b
le
e
n
e
rg
y
s
o
u
rc
e
s
in
teg
ra
ti
o
n
o
n
th
e
o
p
ti
m
a
l
c
o
o
rd
i
n
a
ti
o
n
o
f
d
irec
ti
o
n
a
l
o
v
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r
-
c
u
rre
n
t
re
lay
s
in
d
istri
b
u
ti
o
n
s
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Ap
p
li
e
d
Po
we
r
E
n
g
i
n
e
e
rin
g
IJ
AP
E
,
v
o
l.
9
,
n
o
.
3
,
p
p
.
2
5
0
-
2
5
5
,
2
0
2
0
.
[4
]
P
.
M
.
An
d
e
rso
n
, “
P
o
we
r
S
y
ste
m
P
ro
tec
ti
o
n
,
”
M
c
G
ra
w
-
Hill
,
Ne
w Yo
rk
.
1
9
9
9
.
[5
]
A.
S
.
No
g
h
a
b
i
,
H.
R.
M
a
sh
h
a
d
i
,
J.
S
a
d
e
h
,
“
Op
t
ima
l
Co
o
r
d
in
a
ti
o
n
o
f
Dire
c
ti
o
n
a
l
O
v
e
r
-
c
u
rre
n
t
Re
la
y
s
Co
n
si
d
e
rin
g
Diffe
re
n
t
Ne
two
rk
To
p
o
l
o
g
ies
u
sin
g
In
terv
a
l
Li
n
e
a
r
P
r
o
g
ra
m
m
in
g
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
De
li
v
e
ry
,
v
o
l.
2
5
.
p
p
.
1
3
4
8
-
1
3
5
4
.
2
0
1
0
.
[6
]
Qu
a
n
m
in
g
Yu
e
,
F
e
i
p
e
n
g
Lu
,
Wei
y
o
n
g
Yu
,
Jie
Wan
g
,
“
A n
o
v
e
l
a
lg
o
rit
h
m
to
d
e
term
in
e
m
in
imu
m
b
re
a
k
p
o
i
n
t
se
t
fo
r
o
p
ti
m
u
m
c
o
o
p
e
ra
ti
o
n
o
f
d
irec
ti
o
n
a
l
p
ro
tec
ti
o
n
re
lay
s
i
n
m
u
lt
i
lo
o
p
n
e
two
rk
s,”
i
n
IE
EE
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
De
li
v
e
ry
,
v
o
l.
2
1
,
n
o
.
3
,
p
p
.
1
1
1
4
-
1
1
1
9
,
J
u
ly
2
0
0
6
.
[7
]
T.
Am
ra
e
e
,
“
Co
o
rd
i
n
a
ti
o
n
o
f
Dir
e
c
ti
o
n
a
l
Ov
e
rc
u
rre
n
t
Re
lay
s
Us
i
n
g
S
e
e
k
e
r
Al
g
o
ri
th
m
,
”
i
n
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r De
li
v
e
ry
,
v
o
l.
2
7
,
n
o
.
3
,
p
p
.
1
4
1
5
-
1
4
2
2
,
Ju
l
y
2
0
1
2
.
[8
]
P
a
n
ig
ra
h
i
B.
K,
M
a
n
o
h
a
r
S
in
g
h
,
A.R.
A
b
h
y
a
n
k
ar
,
“
Op
ti
m
a
l
c
o
o
r
d
in
a
ti
o
n
o
f
d
irec
ti
o
n
a
l
o
v
e
r
-
c
u
rre
n
t
re
lay
s
u
si
n
g
Tea
c
h
in
g
Lea
rn
i
n
g
-
Ba
se
d
Op
ti
m
i
z
a
ti
o
n
(TL
BO)
a
lg
o
r
it
h
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
Po
w
e
r
a
n
d
En
e
rg
y
S
y
ste
ms
,
v
o
l.
5
0
,
p
p
.
3
3
-
4
1
,
2
0
1
3
.
[9
]
R.
E
b
e
rh
a
rt,
J.
Ke
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