Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
s
(
IJ
PEDS
)
Vo
l.
12
,
No.
1
,
M
a
r
2021
, p
p.
130
~
138
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v12.i
1
.
pp130
-
138
130
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Allocati
ng acti
ve power l
oss wit
h netw
or
k
reconfig
uratio
n in
electric
al p
ower
distribut
ion syst
em
s
Ambik
a
Pr
asa
d H
ota
1
,
Sivk
uma
r
M
ishr
a
2
,
De
bani
Pr
asad
Mishr
a
3
,
S
urender
Red
d
y Salku
ti
4
1,3
Depa
rtm
en
t
of
Elec
tr
ical Engi
n
ee
ring
,
In
te
rn
at
i
onal
Inst
it
ut
e
of
Inform
ation
T
echnology
Bhuban
eswar,
Odisha
,
I
ndia
2
Depa
rtment of
El
e
ct
ri
ca
l
Eng
in
ee
ring
,
CAP
GS
,
BP
UT,
Odisha, I
ndia
4
Depa
rtment of
Rai
lro
ad
and
E
lectr
i
ca
l
Eng
ine
er
i
ng,
Woosong
Univer
sity
,
Da
ej
eo
n
,
Repub
li
c
of
Korea
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
A
ug
27
, 202
0
Re
vised
Jan
4
,
2021
Accepte
d
Fe
b 1, 2
021
Thi
s
pape
r
p
re
sents
a
bra
n
ch
exc
hang
e
(BE
)
base
d
heur
ist
ic
ne
twork
rec
onfigur
at
ion
te
chn
ique
wher
e,
the
proposed
bus
cl
assifi
cati
on
strat
egy
rem
ode
ls
dyna
mi
c
al
ly
as
per
t
he
modi
f
ie
d
top
ology
in
ord
er
t
o
provide
a
rec
onfigur
ed
n
etw
ork
with
mi
ni
mum
loss.
Furth
er,
for
fai
r
al
lo
c
at
ion
of
the
ac
t
ive
pow
er
los
ses,
i
t
d
evelops
a
n
ew
ac
t
ive
po
wer
loss
al
lo
cati
on
(AP
LA)
te
chn
ique
which
er
adi
c
at
es
th
e
i
nflue
nc
e
of
c
ross
-
te
rm
analytica
l
ly
from
loss
formul
a
ti
on
with
out
any
assumpt
ions
and
appr
oxi
ma
ti
ons
.
The
eff
ec
t
ive
nes
s
of
the
proposed
proc
edu
re
h
as
bee
n
inve
stig
ate
d
against
o
the
r
esta
bli
sh
ed
me
thods
using
a
69
-
bus
rad
ia
l
distri
buti
on
netw
ork
(RDN
).
T
he
resul
ts
of
AP
LA
ac
hi
eve
d
for
or
igi
n
al
and
re
conf
igure
d
6
9
-
bus
RDN
are
found
to
be
promi
sing
and
j
udic
ious
as
reg
a
rd
to
th
ei
r
loa
d
dem
ands
and
ge
ogra
phica
l
loc
a
ti
ons.
The
i
mpl
ement
at
ion
o
f
pre
sen
t
r
ec
onfi
gura
ti
on
proc
ed
ure
provid
es
a
total
loss
red
u
ct
ion
b
ene
fi
t
of
55.
73%
to
the
u
ti
lity
which
h
ig
hli
ghts
th
e
signifi
c
anc
e
of t
he
dev
el
op
ed
pr
oce
dure
ag
ai
nst
othe
r established
technique
s
.
Ke
yw
or
d
s
:
Acti
ve powe
r
Distr
ib
ution ne
twork
Loa
d
fl
ow
Loss
al
locat
ion
Netw
ork reco
nfi
gurati
on
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Su
r
en
der Re
dd
y
Sal
ku
ti
Dep
a
rtme
nt of
Ra
il
ro
ad
a
nd E
le
ct
rical
En
gi
ne
erin
g
Woos
ong U
nive
rsity
17
-
2,
Ja
ya
ng
-
Don
g,
D
ong
-
G
u,
Daejeo
n
-
3460
6,
Re
public
of Ko
rea
Emai
l:
su
re
nde
r@wsu.ac
.
kr
1.
INTROD
U
CTION
Ele
ct
rical
pow
er
distrib
utio
n
s
ys
te
m
(E
P
DS
)
is
c
urrent
ly
faci
ng
nu
mer
ou
s
c
halle
ng
e
s
due
t
o
pen
et
rati
on
of
distrib
uted
ene
rgy
res
ources
(D
ERs
)
s
uc
h
a
s:
ene
rgy
st
or
i
ng
de
vices,
distribu
te
d
ge
nerat
or
s
(DGs)
an
d
po
wer
facto
r
c
orrecti
on
eq
uipm
ents
at
the
co
nsum
e
r
pr
e
mises
[
1
]
-
[
3].
T
he
pen
et
rati
on
of
DER
s
mainly
ca
us
es
rev
e
rse
c
urren
t
in
the
net
wor
k
an
d
th
us
,
a
ffec
ts
power
l
oss
of
t
he
EP
DS.
If
powe
r
loss
of
a
sy
ste
m
in
creas
es,
it
s
eff
ic
ie
nc
y
dec
reases
.
O
ne
of
the
so
l
ution
s
to
get
rid
out
of
this
diff
ic
ulty
is
to
c
ha
nge
the
netw
ork
to
pology
i.e.
,
im
plementat
io
n
of
pro
per
netw
ork
recon
fig
ur
a
ti
on
(
NR)
te
c
hn
i
qu
e
t
o
ac
hieve
an
op
ti
mal
los
s
pro
vid
i
ng
netw
ork.
B
ut,
e
xec
ution
of
NR
a
lt
ers
the
entire
struct
ur
e
of
the
EP
DS
fro
m
th
e
el
ect
rical
po
int
of
vie
w
an
d
s
imult
ane
ou
sl
y,
br
i
ngs
an
oth
e
r
possibil
it
y
to
inv
est
igate
t
he
influ
e
nce
of
NR
on
loss all
ocati
ons
(
L
As) of
netw
ork partic
ipa
nt
s in
t
his m
od
e
r
n
sce
nar
i
o of p
ow
e
r dist
rib
ution net
wor
k.
Keep
i
ng
this
i
n
view
,
a
t
hrough
li
te
ratu
re
re
view
ha
s
bee
n
carried
out
on
the
est
a
bli
sh
e
d
te
ch
niques
relat
ing
to
network
rec
onfig
ur
at
io
n
an
d
power
los
s
al
l
oca
ti
on
.
It
is
ve
rifi
ed,
in
m
os
t
of
the
li
te
ratu
re,
NR
[4
]
-
[
6]
a
nd
LA
[7]
are
co
ns
i
der
e
d
broa
dly
as
t
wo
ind
e
pe
nd
e
nt
a
rea
of r
esearc
h
sti
ll
;
ver
y
few
w
ork
s
are
ide
nt
ifie
d
wh
e
re
both
of
th
ese
ha
ve
ta
ken
to
gethe
r.
Oliveira
et
al
.
[
8]
we
re
the
first
to
exec
ut
e
rec
onfig
ur
at
i
on
an
d
AP
L
A
to
gethe
r
f
or
EP
DS
s
with
dist
rib
uted
ge
ne
rato
rs,
wh
e
re
r
eco
nf
i
gurati
on
is
ca
rr
ie
d
out
th
rough
a
heurist
ic
pr
inci
ple
a
nd
powe
r
loss
al
locat
io
ns
with
the
im
plement
at
io
n
of
a
Z
-
bus
te
ch
nique.
H
owev
er,
thi
s
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
All
oca
ti
ng
activ
e power l
oss
wi
th n
et
work
r
econ
fi
gur
atio
n i
n
el
ect
ric
al po
we
r
…
(
A
m
bika
Pr
asad H
ot
a
)
131
te
chn
iq
ue
ca
n
no
t
be
s
uggest
ed
f
or
pract
ic
al
implementa
ti
on
as
it
suffe
r
s
from
the
de
merit
s
of
the
Z
-
bus
scheme
of
al
lo
cat
ion
.
T
his
drawb
ac
k
is
not
fou
nd
in
[
9
]
,
[
10]
w
her
e
a
B
E
based
NR
te
chn
i
qu
e
with
quad
rati
c
LA
met
hod
\
is
util
ise
d
to
aw
ard
l
os
ses
to
t
he
rad
ia
l
distri
buti
on
netw
ork
par
ti
ci
pa
nts
at
bo
t
h
sce
nar
io
s
of
th
e
RDN
(i.e.
,
be
f
or
e
a
nd
a
fter
NR).
I
n
[
11]
,
a
br
a
nc
h
c
urre
nt
dec
omp
os
it
ion
meth
od
as
discusse
d
i
n
[
12]
is
employe
d
for
al
locat
ion
of
powe
r
l
os
ses
w
her
e
a
group
s
earch
o
ptimi
zat
ion
te
c
hn
i
qu
e
is
util
ise
d
to
a
chieve
the
op
ti
m
um
s
olu
ti
ons.
Simi
l
arly,
a
minim
um
br
a
nc
h
c
urr
ent
base
d
ci
r
cu
la
r
-
up
dating
m
echan
is
m
is
us
ed
f
or
ob
ta
ini
ng
a
re
config
ur
e
d
R
DN
in
the
propose
d
meth
od
[13
].
To
al
locat
e
lo
sses
j
ud
ic
io
us
l
y
a
m
ong
the
consu
me
rs
of
the
R
DN,
a
c
urren
t
summat
io
n
a
ppr
oach
of
LA
has
be
en
di
scusse
d
in
[14
]
wh
e
re
t
he
m
utu
al
te
rms
of
po
we
r
loss
e
qu
at
io
n
are
distrib
uted
am
ong
the
con
s
um
e
rs
a
nd
D
G
ow
ner
s
us
in
g
a
lo
gari
thmic
scheme
of
LA
.
Howe
ver,
this
te
chn
iq
ue
is
only
a
pp
li
ca
ble
wh
e
n
p
arti
ci
pa
ti
on
fact
or
s
li
e
within
{
0
-
2
}
.
The
auth
or
s
of
[
15
]
-
[
19]
ha
ve
rec
om
me
nded
ga
me
the
ory
-
ba
s
ed
proce
dures
for
AP
L
A
of
E
PD
Ss
by
util
iz
ing
the
con
ce
pt
of
S
ha
pley
value
f
or
sh
ari
ng
losse
s
amo
ng
the
net
work
use
rs
.
Bu
t
LA
proce
dur
e
ge
ner
al
ly
s
olv
ed
by
Sh
a
pl
ey
value
te
chn
iq
ue
face
s
dif
ficult
ie
s
of
mem
ory
bur
den
a
nd
ti
me
com
plexcit
y
w
hen
a
ppli
ed
to
la
rg
er
RDNs.
This
draw
bac
k
is
not
f
ound
i
n
t
he
disc
us
se
d
in
[20]
a
nd
[21
]
as
the
y
assig
n
losse
s
acc
ord
ing
t
o
pro
portion
al
s
har
i
ng
a
nd
power
s
ummat
io
n
pr
inci
ples,
r
e
sp
ect
ively
.
St
il
l,
these
meth
od
s
are
not
a
wardin
g
exact
al
locat
io
ns
a
s
t
hey
are
dev
el
op
e
d
wit
h
ce
rtai
n
ass
umpti
ons.
T
o
over
w
helm
t
his
pro
blem
t
he
a
ut
hors
of
[22]
hav
e
intr
oduce
d
a
n
e
xa
ct
schem
e
of
LA
by
anal
yz
ing
the
i
nter
r
el
at
ion
sh
i
p
preent
betwee
n
br
a
nc
h
currents
an
d
t
heir
s
ubse
qu
e
nt
node
volt
age
s.
T
he
c
ro
s
s
-
te
rm
dec
ompo
sit
ion
meth
od
(C
TD
M
)
de
velo
pe
d
in
[23]
distrib
ute
s
the
mu
t
ual
powe
rs
us
in
g
lo
ss
al
locat
ion
f
act
or
s
with
a
minimu
m
er
ror
of
4%
betwe
en
th
e
cal
culat
ed
a
nd
true
value
of
D
G
re
mune
rati
on.
T
he
node
vo
lt
age
-
base
d
al
gorith
m
dev
el
oped
in
[
24]
pro
vi
des
exact
al
locat
io
ns
to
the
RD
N
s
wit
h/with
ou
t
D
Gs
bu
t,
it
sa
ys
nothi
ng
a
bout
DG
rem
un
e
rati
on.
This
iss
ue
is
so
lve
d
by
im
plementat
io
n
of
a
par
ti
ci
patio
n
-
base
d
D
G
re
m
un
e
rati
on
sche
me
in
[
25]
w
he
re
the
enti
re
be
nef
it
s
of RD
N
los
s r
e
du
ct
io
n d
ue
t
o dist
rib
uted ge
ne
rati
on unit
s are
provide
d
t
o
t
he DG
ow
ner
s
.
Keep
i
ng
a
bove
disc
us
se
d
points
in
view,
thi
s
pa
pe
r
int
rod
uc
es
a
node
vo
lt
age
base
d
AP
L
A
meth
od
\
in
Sect
io
n
2
w
her
e
the
impa
c
t
of
c
ro
ss
-
te
r
m
has
been
wipe
d
out
em
piric
al
ly
f
rom
t
he
powe
r
lo
ss
e
quat
ion
with
proper
m
at
hemati
cal
for
mu
la
ti
on.
T
he
resu
lt
s
of
A
PL
A
are
f
ound
t
o
be
pro
per
as
pe
r
loa
d
dema
nds
a
nd
phys
ic
al
l
ocati
on
s
of
the
en
d
-
us
e
rs.
T
he
de
ta
il
discuss
i
on
on
t
he
al
gorithm
of
BE
bas
ed
NR
te
c
hn
i
que
is
p
er
forme
d
i
n
Sect
ion
3.
I
n
Sect
ion
4,
the
loss
al
locat
io
n
res
ults
as
ob
t
ai
ned
f
or
both
base
a
nd
rec
on
fig
ur
e
d
69
-
bu
s
RD
N
a
re
c
ompare
d
w
it
h
that
of
t
he
oth
e
r
oth
er
exi
sti
ng
meth
od
s
to
sho
w
s
uperi
or
it
y
of
the
pr
esent
proce
dure
i
n
c
on
t
rast
to
disc
us
se
d
e
sta
blis
hed
met
hods.
Finall
y,
the
c
on
cl
us
ive
r
em
ark
s
a
re
pro
vi
ded
in
Sect
ion
5.
2.
LOSS
ALLO
CA
TI
ON ME
THOD
This
sect
io
n
c
on
ta
in
s
tw
o
s
ubsect
io
ns
.
First
par
t
i
ntr
oduce
s
the
bu
s
ide
ntific
at
ion
te
ch
ni
qu
e
us
e
d
i
n
the
entire
for
mu
la
ti
on
proce
dure
wh
il
e
the
seco
nd
par
t
di
scusses
reg
a
rdi
ng
the
de
rivat
ion
of
t
he
de
ve
lop
e
d
loss
al
locat
io
n
proce
dure
.
T
he
e
ntire
form
ulati
on
is
car
ri
ed
out
by
util
iz
ing
opti
mal
volt
ages
a
s
ob
t
ai
ned
thr
ough
a
for
w
ard
-
bac
kwar
d
swee
p
(F
BS
)
ba
sed
po
wer
flo
w
a
ppr
oac
h
[
26]
.
I
n
i
rd
e
r
to
inco
r
porate
D
G
s
int
o
the
evaluati
on
proce
dure,
th
e
neg
at
ive
l
oa
d
m
od
el
li
ng
of
ge
ner
at
or
s
a
s
discusse
d
i
n
[27
]
,
[
28]
ca
n
be
impleme
nted
to
get
the
net
powe
r
injec
ti
on
s,
an
d
with
the
se
values
the
l
oad
flo
w
can
be
carried
out
f
ur
t
her
to
get d
e
sired
s
olu
ti
ons.
2.1.
Pro
po
se
d
bus
iden
tific
ati
on
sch
eme
In
present
stra
te
gy
,
the
r
oo
t
node
is
i
ndexe
d
as
‘
1’
a
nd
t
he
s
uccessi
ve
bu
s
es
al
on
g
th
e
main
a
nd
la
te
ral
feed
e
rs
are
numb
e
re
d
i
n
the
inc
reasin
g
order
as
s
ho
wn
in
Fig
ur
e
1.
He
re,
thre
e
ar
ray
s
(
s
b[]
,
mfs[
]
an
d
mts[
]
)
are
pro
pose
d
f
o
r
keep
i
ng
the
e
ntire
i
nformat
ion
rel
at
ing
to
s
ub
se
quent
buses
of
t
he
R
DN
as
dis
cusse
d
in
[
29].
T
he
ar
ray
s
b[]
is
us
e
d
f
or
kee
ping
the
subse
quent
nodes
of
al
l
th
e
br
a
nc
hes
of
t
he
ra
dial
distri
bu
ti
on
netw
ork.
Tw
o
po
i
nter
ar
ray
s
mfs[
]
an
d
mts[
]
are
util
ise
d
t
o
st
or
e
the
init
ia
l
and
fi
na
l
mem
ory
posit
ion
s
of
t
he
su
ccessi
ve
node
s
releva
nt
t
o
each
br
a
nc
h
of
the
R
DN,
re
s
pecti
vely
.
T
he
formati
on
s
of
t
hese
a
rr
a
ys
are
done
by u
ti
li
sing i
np
ut d
at
a
of the
RDN
i
n M
AT
LAB
-
R
2018b
env
i
ronme
nt.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
130
–
138
132
Figure
1. A
sa
mp
le
69
-
node
t
est
d
ist
rib
utio
n system
b
e
f
or
e
NR
2.1.
Form
ula
tion
of the pr
oposed
APL
A M
eth
od
The
loa
d
cu
rr
e
nt (
LC)
at
an
y node
-
i
with
net
c
omplex
po
we
r
i
nject
ion
S
Li
=P
Li
+jQ
Li
an
d n
od
e
volt
age
V
i
can
be
e
valu
at
ed
as
(1)
:
=
[
+
]
∗
=
−
(
)
∗
,
=
2
,
3
,
…
…
.
(1)
The
c
urre
nt of
any bra
nch
-
jj
c
an be esti
mate
d by ad
diti
on of the
LCs
of th
e su
cces
sive c
onsume
r
s
(2)
(
)
=
[
∑
(
(
)
)
=
(
(
)
)
]
(2)
The
c
urre
nt in a b
ran
c
h
-
jj
ca
n be
f
ur
the
r
e
xpla
ined us
i
ng equati
ons (1
)
a
nd (2)
a
s
(3)
,
(
)
=
∑
−
(
)
∗
(
(
)
)
=
(
(
)
)
(3)
Acti
ve
po
wer
l
os
s
(
AP
L
)
of
a
ny
br
a
nc
h
-
jj
ca
n
be
est
imat
ed
with
branc
h
im
ped
a
nce
Z
(jj)
a
nd
br
a
nc
h
current
I(
jj
)
as
(4)
:
(
)
=
[
{
|
(
)
|
2
}
{
(
)
}
]
=
[
[
{
(
)
}
{
(
)
}
∗
]
{
(
)
}
]
(4)
The
APL
of
t
he
branc
h
-
jj
c
an
be
prese
nted
i
n
te
rms
of
sen
ding
e
nd
volt
age
(
Vs
),
re
cei
vin
g
e
nd
vo
lt
age
(
Vr
)
a
nd the
bra
nch cu
rr
e
nt
I
(
jj
)
as:
(
)
=
[
{
(
)
−
(
)
(
)
}
∗
{
(
)
}
{
(
)
}
]
(5)
(
)
=
[
[
(
)
−
(
)
]
∗
[
(
)
(
)
∗
]
[
(
)
]
]
(6)
Substi
tuti
ng th
e v
al
ue
of
br
a
nc
h
c
urren
t
I(
jj
)
from (
3)
i
n (6),
(
)
=
[
[
(
)
−
(
)
]
∗
[
(
)
(
)
∗
]
[
∑
−
{
}
∗
(
(
)
)
=
(
(
)
)
]
]
(7)
Re
arr
a
ng
i
ng,
(
)
=
[
∑
[
{
(
)
−
(
)
}
∗
{
(
)
(
)
∗
}
]
[
−
]
(
(
)
)
=
(
(
)
)
]
(8)
Since,
al
l
par
a
mete
rs
prese
nt
in
the
first
pa
rt
of
(
8)
a
re
c
omplex
quantit
ie
s,
t
heir
s
olu
ti
on
will
be
a
com
plex q
ua
ntit
y.
T
hu
s
,
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
All
oca
ti
ng
activ
e power l
oss
wi
th n
et
work
r
econ
fi
gur
atio
n i
n
el
ect
ric
al po
we
r
…
(
A
m
bika
Pr
asad H
ot
a
)
133
[
{
(
)
−
(
)
}
∗
{
(
)
(
)
∗
}
]
=
(
,
)
+
(
,
)
(9)
The
value
of
(
9)
mainl
y
de
pe
nds
on
,
as
oth
er
quantit
ie
s
are
co
ns
ta
nt
f
o
r
bra
nch
-
.
He
nc
e,
this
expressi
on
is
e
xclusi
vely
rela
te
d
to
the
subs
equ
e
nt
node
-
of
br
a
nc
h
-
.
Her
e
,
A
(jj,i
)
a
nd
B(j
j,i
)
re
pr
e
sent
t
he
real
and
ima
gi
nary
pa
rt
ass
ociat
ed
with
t
he
subse
quent
node
-
i
of
br
a
nch
-
jj
,
res
pect
ively.
T
her
e
f
ore,
the
equ
at
io
n o
f AP
L for
the
br
a
nc
h
-
jj
ca
n be stat
ed
as:
(
)
=
∑
(
,
)
=
(
(
)
)
=
(
(
)
)
∑
{
(
,
)
+
(
,
)
}
(
(
)
)
=
(
(
)
)
(10)
It
is
reali
sed
from
(10)
that,
t
he
co
nsume
rs
beyo
nd
branc
h
-
jj
of
t
he
RD
N
are
li
able
f
or
AP
L
of
t
he
br
a
nc
h
-
jj
,
an
d
the
refor
e
,
it
s
hould
be
distri
bu
te
d
am
ong
these
cust
om
e
r
s.
T
hus,
AP
L
A
at
eac
h
bus
‘
i
’
is
evaluate
d
as:
(
)
=
∑
(
,
)
−
1
=
1
(11)
Th
us
, t
he
e
ntir
e loss o
f
the
E
PD
S
is esti
mate
d
as
[28],
=
∑
(
)
=
1
(12)
3.
POWER
DIS
TRIBUTIO
N NET
WO
RK RECO
NFI
GURATI
ON
The
B
E
base
d
NR
te
ch
ni
qu
e
mainly
ai
ms
to
pro
vid
e
a
n
op
ti
mu
m
netw
or
k
with
ou
t
distu
rb
i
ng
ra
dial
natu
re
of
the
s
ys
te
m.
I
t
is
ge
ner
al
ly
perf
ormed
th
r
ough
two
ste
ps
.
In
first
ste
p,
a
cl
ose
d
lo
op
is
ma
de
b
y
cl
os
in
g
an
op
e
n
switc
h
(
i.e.
,
ti
e
li
ne
‘
tl
’)
,
and
t
hen
i
n
the
nex
t
ste
p,
the
rev
ival
of
radi
al
it
y
of
the
R
DN
i
s
execu
te
d
by
op
enin
g
a b
ra
nch
(
i.e.,
sect
ion
al
iz
ing
s
witc
h
‘
s
s
’)
w
it
hin
t
he
c
losed
l
oop.
The
sel
ect
ion
o
f
t
ie
-
li
ne
is
per
f
orme
d
by
cal
culat
ing
volt
age
acr
os
s
a
ll
the
ti
e
li
nes.
The
‘tl
’
with
maxim
um
po
te
ntial
diff
e
ren
ce
(P
D
)
is
identifie
d
as
the
first
ti
e
li
ne
to
be
cl
ose
d.
Simult
ane
ously,
on
e
branc
h
i
s
to
be
m
ade
open
i
n
or
der
to
retai
n
rad
ia
li
ty
of
the
po
wer
net
wor
k.
F
or
this
pur
po
s
e,
t
he
volt
ages
of
t
he
t
wo
no
de
points
c
orres
pondin
g
t
o
t
he
sel
ect
ed
ti
e
li
ne
are
fi
rst
mea
su
re
d.
The
n,
th
e
br
a
nc
h
li
nke
d
to
t
he
node
point
with
lo
w
vo
lt
age
is
ma
de
open
and
total
A
PL
of
the
netw
ork
is
c
omp
uted.
If
total
AP
L
of
t
he
ne
wly
ob
ta
ined
RD
N
is
obse
rv
e
d
to
be
le
ss
than
that
of
th
e
basic
RD
N
then
,
th
e
nex
t
branc
h
is
mar
ke
d
to
be
ope
ned.
The
sa
me
pro
cedure
is
car
ried
ou
t
ti
ll
the
power
loss
of
t
he
ne
wly
obta
ined
RDN
remai
ns
equ
al
t
o
that
of
the
previ
ou
s
on
e
.
Af
te
r
gett
ing
t
he
sect
ion
al
iz
ing
switc
h
‘
ss
’
f
or
the
co
ns
ide
re
d
ti
e
li
ne
‘tl’,
the
entire
proce
ss
is
con
ti
nue
d
ti
ll
the
final
opti
mal
RDN
is
ob
ta
in
ed.
Th
us,
NR
is
pe
rformed
f
rom
a
set
of
s
witc
hing
data
wh
ic
h
is
prese
nted
as
(
tl
,
ss
)
pair
s
.
Af
te
r
eac
h
s
witc
hin
g
process,
a
new
RD
N
is
achie
ved.
T
he
refor
e
,
the
pr
opose
d
ar
ray
s
a
re
to
be
m
odifie
d
as
per
t
he
ne
wly
ob
ta
ine
d
R
D
N
f
or
ve
rificat
ion
of
furthe
r
switc
hing
op
e
r
at
ion
.
T
he
detai
l
al
go
rithm
of
t
he
pro
po
se
d
he
ur
i
sti
c
‘bran
c
h
e
xch
a
nge’
te
ch
nique
[30]
is
discusse
d
th
oroug
hly
i
n
s
ub
sect
ion
-
3.1
f
or
pro
per
impleme
ntati
on
a
nd test
ed us
ing
a
69
-
bus te
st distri
buti
on
sy
ste
m i
n
s
ubs
ect
ion
4.1.
3.1.
Algori
t
h
m of
th
e p
ro
p
os
ed
branch
e
xc
ha
n
ge
b
as
e
d NR techni
q
ue
The det
ai
l p
ro
c
edure
of the
N
R met
hod i
s pr
esented
b
el
ow.
Step
1
∶
Com
pute
of the
R
D
N
us
in
g
e
quat
ion (
12).
Step
2
∶
T
he
volt
age
ac
ross
a
ll
ti
e
li
nes
(
)
ar
e
com
pute
d
(
.
.
∆
(
)
)
,
wh
e
re
=
1
,
2
,
…
.
,
,
a
nd
=
total
n
umb
er
of ti
e li
nes pr
e
se
nt.
Step
3
∶
I
den
t
ify
the
′
′
whos
e
volt
age
is
t
he
maxim
um,
the
n
a
ssig
n
a
co
de
′
′
to
it
(
.
.
∆
,
=
∆
(
)
)
.
P
oin
t
ou
t
t
he
t
wo ends
of the
‘n
th
’
ti
e li
ne
as
‘k’
a
nd ‘w’
ob
eyin
g
the
r
el
at
ion
|V
k
| < |
V
w
|.
Step
4
∶
T
he
ne
w
′
′
is
fixe
d
to
′
=
[
,
]
′
,
and the a
dj
ace
nt
bra
nch of
ℎ
node
is
ma
rk
e
d
as
′
′
.
Step
5
∶
Eval
ua
te
total
pow
e
r
l
os
s
of the
n
e
wl
y ob
ta
ine
d net
work (
i.e
.,
T
PL
os
s
new
)
us
in
g e
qu
at
io
n (
12)
Step
6
∶
Per
f
orm
ste
p
8 i
f
T
P
Lo
ss
new
<
T
PL
os
s
,
o
t
herwise
go
to
ste
p 7
.
Step
7
∶
Per
f
orm
11
after
rem
oving
t
he
s
witc
hi
ng.
Step
8
∶
Set
T
P
Lo
ss
=
TPL
os
s
new
Step
9
∶
Per
f
orm
11
w
he
n
it
is c
he
cked f
or entir
e
branc
he
s
of t
he
lo
op;
el
se
proceed
to
10
.
Step
10
∶
Proce
ed
to
5
after
assi
gnment
of
bo
t
h
′
to
[
,
]
′
,
a
nd
′
′
as
ad
ja
cent branc
h o
f
′
′
.
Step
11
∶
Set
=
−
1
, th
en
pr
oceed
to
2
if
>
0
oth
e
rw
ise
,
perform
12
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
130
–
138
134
4.
RESU
LT
S
AND DI
SCUS
S
ION
This
sect
io
n
com
pr
ise
s
of
two
s
ubsect
io
ns
.
T
he
first
par
t
e
xp
la
in
s
about
the
e
ntire
so
l
ution
proce
dure
f
or
ob
ta
ini
ng
the
minimu
m
lo
ss
pro
vid
in
g
reconfi
gured
RD
N
us
in
g
a
12.
66
kV,
69
-
bus
EP
DS
with
73
branc
hes
a
nd
5
ti
e
li
nes
as
represe
nted
i
n
Figure
1.
T
he
corres
pondin
g
li
ne
an
d
loa
d
da
ta
of
t
he
sai
d
EPD
S
are
c
ollec
te
d
f
rom
t
he
discusse
d
meth
od
[9].
The
sec
ond
par
t
in
vestigat
es
the
ef
fecti
ve
ness
of
t
he
presen
t
AP
L
A
sc
hem
e
by
a
nalyzi
ng
loss
al
locat
io
n
res
ults
of
t
he
co
ns
ide
re
d
R
DN
with
oth
er
est
ablishe
d
m
et
ho
ds
(Qua
dr
at
ic
met
hod
[
9],
E
xact
method
[22],
and
CT
D
M
[
23]
)
at
two
scen
arios
(i.e.,
ea
rl
ie
r
an
d
ne
xt
to
NR).
The
AP
L
A
re
su
lt
s
of
the
ori
gin
al
a
nd
re
config
ur
e
d
net
work
are
pres
ented
i
n
Ta
bl
e
1
a
nd
Ta
bl
e
2,
resp
ect
ivel
y.
Table
1: L
os
s
a
ll
ocati
on
of 69
-
bus
te
st s
ys
te
m b
e
f
or
e
rec
onfig
ur
at
io
n
No
d
e
No
.
Prop
o
sed
Metho
d
Exact
Metho
d
Qu
ad
ratic
Metho
d
CTDM
No
d
e
No
.
Prop
o
sed
Metho
d
Exact
Metho
d
Qu
ad
ratic
Metho
d
CTDM
6
0
.03
1
3
0
.02
7
9
0
.00
0
3
0
.02
2
5
37
0
.00
3
8
0
.00
3
5
0
.00
2
6
0
.00
3
4
7
0
.88
8
5
0
.85
5
8
0
.26
8
1
0
.66
9
9
39
0
.00
7
6
0
.00
7
3
0
.00
5
4
0
.00
7
8
1
.81
3
2
1
.77
5
1
0
.88
3
1
1
.39
8
2
40
0
.00
7
6
0
.00
7
3
0
.00
5
4
0
.00
7
9
0
.77
3
3
0
.75
0
1
0
.17
4
4
0
.58
0
4
41
0
.00
1
3
0
.00
1
0
.00
0
0
2
3
0
.00
0
8
10
0
.86
4
7
0
.87
2
4
0
.22
3
0
.68
7
8
43
0
.00
7
2
0
.00
6
8
0
.00
0
9
0
.00
4
9
11
4
.82
4
2
4
.74
5
5
4
.22
7
4
.14
1
6
45
0
.04
7
7
0
.04
8
5
0
.05
2
0
.04
9
5
12
5
.41
7
7
5
.33
2
9
5
.10
5
7
4
.79
6
46
0
.04
7
7
0
.04
8
5
0
.05
2
0
.04
9
5
13
0
.32
2
0
.32
2
6
0
.02
0
8
0
.25
7
1
48
0
.06
3
3
0
.06
3
4
0
.01
2
6
0
.04
4
14
0
.35
1
8
0
.35
2
3
0
.02
6
0
.28
1
7
49
1
.12
7
3
1
.12
5
2
1
.15
1
5
1
.13
3
2
16
2
.15
3
4
2
.19
2
4
1
.16
3
1
1
.84
1
7
50
1
.24
4
7
1
.24
0
7
1
.26
8
7
1
.25
17
2
.73
5
2
.92
0
3
1
.85
4
2
.45
1
3
51
0
.96
3
9
0
.95
8
1
0
.29
1
2
0
.73
7
2
18
2
.73
5
6
2
.92
1
1
.85
4
6
2
.45
1
9
52
0
.08
9
3
0
.08
5
7
0
.00
1
2
0
.06
5
9
20
0
.04
7
2
0
.04
9
8
0
.00
0
2
0
.03
8
3
53
0
.13
3
7
0
.12
3
7
0
.00
2
3
0
.09
2
8
21
5
.93
2
5
.86
2
1
6
.00
4
1
5
.58
3
7
54
0
.86
0
2
0
.84
3
2
0
.14
6
1
0
.59
3
7
22
0
.26
5
5
0
.27
0
2
0
.01
0
7
0
.21
1
9
55
0
.90
7
3
0
.89
1
9
0
.12
5
7
0
.59
5
4
24
1
.46
9
8
1
.44
9
6
0
.53
4
4
1
.20
5
1
59
9
.45
6
9
9
.40
6
1
3
.01
7
8
5
.34
9
26
0
.73
9
3
0
.72
9
3
0
.12
9
1
0
.59
1
3
61
1
3
8
.2015
1
3
8
.2765
1
8
0
.0178
1
6
2
.7689
27
0
.73
9
7
0
.72
9
6
0
.12
9
5
0
.59
1
7
62
3
.58
0
6
3
.57
2
8
0
.37
7
7
1
.81
5
28
0
.00
1
1
0
.00
1
0
.00
0
3
0
.00
0
9
64
2
5
.99
4
1
2
6
.01
9
1
1
3
.56
3
2
1
6
.36
9
2
29
0
.00
2
1
0
.00
2
1
0
.00
1
6
0
.00
2
1
65
6
.79
2
2
6
.80
6
1
1
.38
1
7
3
.57
5
1
33
0
.00
9
8
0
.00
9
7
0
.00
8
7
0
.00
9
3
66
0
.60
2
5
0
.59
0
9
0
.1
0
.47
2
6
34
0
.02
1
7
0
.02
1
5
0
.02
5
4
0
.02
3
7
67
0
.60
2
6
0
.59
0
9
0
.1
0
.47
2
6
35
0
.00
6
9
0
.00
7
1
0
.00
2
6
0
.00
5
68
1
.05
5
8
1
.04
1
4
0
.31
4
4
0
.84
9
9
36
0
.00
1
2
0
.00
1
1
0
.00
0
4
0
.00
1
69
1
.05
5
8
1
.04
1
5
0
.31
4
4
0
.84
9
9
Table
2: L
os
s a
ll
ocati
on
of 69
-
bus test
s
ys
te
m af
te
r
r
ec
onfi
gurati
on
No
d
e
No
.
Prop
o
sed
Metho
d
Exact
Metho
d
Qu
ad
ratic
Metho
d
CTDM
No
d
e
No
.
Prop
o
sed
Metho
d
Exact
Metho
d
Qu
ad
ratic
Metho
d
CTDM
6
0
.00
7
5
0
.00
6
8
0
.00
0
2
0
.00
6
3
37
0
.69
3
4
0
.01
3
8
0
.00
5
6
0
.52
6
6
7
0
.20
8
1
0
.20
4
1
0
.14
9
8
0
.19
2
1
39
0
.65
1
4
0
.03
6
0
.01
2
9
0
.49
1
1
8
0
.42
1
1
0
.41
9
9
0
.45
1
3
0
.41
2
9
40
0
.65
1
6
0
.03
6
3
0
.01
3
0
.49
1
2
9
0
.17
7
7
0
.17
5
5
0
.09
9
8
0
.16
1
4
41
0
.03
9
4
0
.00
7
3
0
.00
0
1
0
.02
6
4
10
0
.25
0
1
0
.25
6
1
0
.12
2
8
0
.22
1
6
43
0
.18
8
7
0
.05
2
4
0
.00
2
8
0
.12
9
9
11
1
.44
0
1
1
.43
9
4
2
.00
8
1
1
.56
6
2
45
1
.20
4
6
0
.38
0
.19
7
9
0
.90
5
3
12
1
.65
7
2
1
.65
6
7
2
.29
3
9
1
.82
4
46
1
.24
9
6
0
.38
0
3
0
.19
8
0
.96
5
7
13
0
.09
0
6
0
.09
2
2
0
.01
0
3
0
.07
3
48
0
.15
8
8
0
.16
0
7
0
.02
1
5
0
.07
1
14
0
.09
1
2
0
.09
2
8
0
.01
1
6
0
.07
3
7
49
3
.20
8
6
3
.14
4
2
1
.82
8
6
1
.73
4
3
16
0
.41
7
8
0
.77
5
0
.43
3
0
.35
9
1
50
3
.37
6
4
3
.69
1
7
2
.10
1
2
.11
3
17
0
.67
2
3
1
.16
9
3
0
.75
9
9
0
.60
2
4
51
0
.22
4
9
0
.22
7
8
0
.16
2
6
0
.21
0
8
18
0
.67
4
1
1
.17
0
8
0
.76
0
6
0
.60
4
52
0
.02
0
9
0
.02
0
4
0
.00
0
8
0
.01
8
20
0
.01
4
6
0
.02
1
9
0
.00
0
1
0
.01
1
7
53
0
.02
7
7
0
.02
6
0
.00
1
4
0
.02
3
5
21
2
.06
5
2
.63
1
9
2
.90
1
8
1
.90
2
8
54
0
.15
9
6
0
.15
9
2
0
.08
2
3
0
.14
5
4
22
0
.09
2
8
0
.12
3
5
0
.00
4
1
0
.07
3
55
0
.14
6
3
0
.14
6
3
0
.06
9
4
0
.13
2
9
24
0
.58
5
9
0
.69
7
0
.23
3
9
0
.46
4
7
59
3
.77
3
5
3
.83
7
7
0
.49
9
1
1
.07
3
9
26
0
.36
7
9
0
.39
6
3
0
.05
6
7
0
.27
5
6
61
6
1
.45
6
1
6
3
.25
7
4
7
1
.26
2
5
6
4
.08
5
2
27
0
.38
2
1
0
.40
3
8
0
.05
7
3
0
.28
7
6
62
1
.19
0
1
1
.62
7
5
0
.05
7
4
0
.32
1
4
28
0
.00
1
1
0
.00
1
1
0
.00
0
3
0
.00
0
8
64
8
.14
6
2
7
.77
8
7
1
1
.06
7
5
8
.80
0
5
29
0
.00
2
1
0
.00
2
1
0
.00
1
6
0
.00
1
9
65
1
.66
1
1
.87
6
8
1
.17
2
6
1
.64
5
8
33
0
.00
9
8
0
.00
9
7
0
.00
8
7
0
.00
9
2
66
0
.18
0
7
0
.18
0
1
0
.05
6
8
0
.15
3
8
34
0
.02
1
7
0
.02
1
6
0
.02
5
4
0
.02
3
6
67
0
.18
0
7
0
.18
0
1
0
.05
6
8
0
.15
3
8
35
0
.00
6
9
0
.00
7
1
0
.00
2
6
0
.00
5
68
0
.33
0
5
0
.33
1
0
.16
4
7
0
.27
9
9
36
0
.68
5
6
0
.00
1
8
0
.00
0
6
0
.52
1
7
69
0
.33
0
6
0
.33
1
1
0
.16
4
7
0
.27
9
9
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
All
oca
ti
ng
activ
e power l
oss
wi
th n
et
work
r
econ
fi
gur
atio
n i
n
el
ect
ric
al po
we
r
…
(
A
m
bika
Pr
asad H
ot
a
)
135
4.1.
So
lu
tio
n Steps
for
ob
t
ai
ning
r
ec
onfig
ur
ed
op
tim
um
69
-
b
us
R
DN
It
can
be
view
ed
f
r
om
Fig
ure
1
t
hat
the
fiv
e
ti
e
li
nes
i.e.,
50
-
59,
27
-
65,
15
-
46,
13
-
21
a
nd
11
-
43
of
the
c
on
si
der
e
d
69
-
node
RD
N
are
pri
maril
y
pr
ese
nt
i
n
t
he
op
e
n
sta
te
co
ndit
ion
.
At
this
scenari
o,
the
present
LA
pr
ocedure
awards
a
total
loss
of
22
5.0
016
kW
wh
ic
h
is
al
mo
st
ne
ar
to
the
resu
l
t
of
ot
her
est
a
blishe
d
methods
(i.e
.,
225.0
015
kW
by
ex
act
meth
od,
224.9
517
kW
by
Q
ua
drat
ic
method,
a
nd
22
4.150
7
kW
by
CTDM
meth
od)
.
T
he
P
D
ac
ro
ss
al
l
t
he
5
-
t
ie
li
nes
are
cal
culat
ed,
a
nd
m
aximum
am
ount
is
obse
rved
acro
s
s
5
0
-
59
si
nce
th
e
diff
e
re
nce
in
vo
lt
age
is
fou
nd
t
o
be
|
V
50
-
V
59
|=
0.069
4
p.
u.
T
her
e
f
or
e,
a
loop
is
made
with
the
help
of
′
=
[
50
,
59
]
′
.
B
ut,
in
orde
r
t
o
mak
e
the
net
wor
k
rad
ia
l,
one
bra
nch
of
this
lo
op
is
to
be
op
e
ne
d.
As
vo
lt
age
of
node
-
59
(
V
59
=
0.9
248pu)
is
le
ss
than
that
of
bu
s
-
50
(
V
50
=
0.9
942pu)
i.
e.,
V
59
(
0.924
8
p.u.)
<
V
50
(0.99
42 p.u.),
the
′
=
[
58
,
59
]
′
is i
de
ntifie
d
to
b
e
ma
de o
pen b
e
f
or
e
f
unct
ion
in
g of t
he
′
50
−
59′
.
But,
at
this
co
nd
it
io
n,
the
t
otal
AP
LA
of
t
he
restru
ct
ur
e
d
netw
ork
is
obs
erv
e
d
to
be
13
2.158
3
kW.
Scie
nce
the
re
i
s
a
re
duct
ion
in
total
AP
L
A,
so
in
vestigat
io
n
is
ca
rr
ie
d
out
for
br
a
nc
h
57
-
58.
Howe
ver
,
powe
r
loss
f
or
t
he
RDN
with
ope
ni
ng
of
t
he
bran
c
h
57
-
58
is
eval
uated
to
be
132.158
3
kW
(
no
dev
ia
ti
on)
.
Th
us
,
the
′
=
50
−
59′
is
finall
y
ide
nt
ifie
d
f
or
the
′
=
58
−
59′
.
The
simi
la
r
pr
ocedu
re
is
fo
ll
ow
e
d
f
ur
the
r
f
or
rest
of
the
ti
e
li
ne
s
to
get
the
opti
mu
m
RD
N.
The
P
D
a
cr
oss
the
re
maini
ng
f
our
ti
e
li
ne
s
are
co
m
pu
t
ed
a
nd
maxim
um
dif
f
eren
ce
is
obse
rv
e
d
at
′
=
27
−
65′
i.e.,
|
V
27
-
V
65
|=
0.0
362.
Si
nce
V
65
(0.93
49
p.u.)
<V
27
(0.97
11
p.u
.),
t
he
br
a
nc
h
64
−
65
is
f
irst
ma
de
op
e
n
by
cl
os
in
g
t
he
t
ie
li
ne
27
−
65
.
It
is
noti
ced,
the
t
otal
AP
L
A
of
the
sy
ste
m
a
gai
n
decr
ease
s
to
128.7
273
kW
with
this
rest
r
uctu
red
net
work.
It
is
note
w
or
t
hy
to
ob
s
er
ve
that
t
ot
al
loss
f
ur
the
r
decr
ease
s
to
127.5
2
kW
as
t
he
br
a
nch
′6
3
−
64′
is
made
open
by
cl
os
in
g
′6
4
−
65′
.
H
ow
e
ve
r,
it
r
et
ai
ns
previ
ou
s
value
of
12
7.52
kW
as
is
e
sti
mate
d
f
or
′6
2
−
63′
.
Ther
e
f
or
e,
the
br
a
nc
h
′2
7
−
65′
is i
de
ntifie
d
as
the tie
li
ne w
hi
le
the bran
c
h
′6
3
−
64′
is desig
nated
a
s the secti
onal
i
zi
ng
switc
h.
Since,
pote
ntial
diff
e
re
nce
of
br
a
nc
h
′1
5
−
46′
(i.e.
,
|V
15
-
V
46
|
=
0.038
3
p.u.)
is
f
ound
ma
xim
um
against
th
e
rest
3
-
li
ne
s,
the
br
anc
h
co
nnect
in
g
node
po
i
nts
15
an
d
46
is
se
le
ct
ed
to
be
cl
os
e
d.
As
po
te
nt
ia
l
of
node
-
15
(V
15
=
0.960
1pu)
is
no
ti
ce
d
to
be
le
ss
than
t
hat
of
no
de
-
46
(
V
46
=
0.9
984
p.u.)
,
the
br
a
nc
h
14
-
15
is
consi
der
e
d
to
be
opene
d.
T
hi
s
le
ads
t
o
a
drop
in
t
otal
A
P
LA
to
99.
66
k
W.
F
rom
a
bove
obse
rv
at
i
on,
the
lo
op
br
a
nc
h
′1
4
−
15′
is
ide
nt
ifie
d
to
be
op
ened
with
res
pe
ct
to
the
ti
e
li
ne
′1
5
−
46′
beca
us
e,
th
e
ope
ning
of
th
e
br
a
nc
h
′1
3
−
14′
en
han
c
es RD
N
los
s to
99.739
0 kW.
Figure
2:
A
sa
mp
le
69
-
bu
s
test
d
ist
rib
utio
n system
a
fter
N
R
Figure
3:
Vo
lt
a
ge
prof
i
le
of th
e 69
-
bus R
DN
befor
e
and a
fte
r
rec
onfi
gurati
on
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
130
–
138
136
Likewise,
the
r
esp
on
ses
of
ot
her
2
-
ti
e
li
nes
are
al
so
ve
rifie
d
in
the
simi
la
r
ma
nner
a
nd
i
n
eac
h
case
,
the
total
AP
L
A
is
ob
se
rv
e
d
to
be
hi
gh
e
r
tha
n
that
of
99.
66
kW
an
d
th
us,
ex
cl
ud
e
d
f
rom
f
urt
her
c
onside
ra
ti
on
.
Fo
r
chec
king
of
t
hese
2
-
ti
e
li
nes
two
l
oa
d
fl
ow
s
are
t
o
be
car
ried
ou
t.
He
nce,
t
ot
al
‘1
0’
powe
r
flo
w
cal
culat
ion
s
ar
e
to
b
e p
e
rformed
to
g
et
t
he
op
ti
mal
restr
uc
ture
d
R
DN
as
sh
oe
n
in
Fi
gur
e
2.
The
t
otal APL
A
o
f
the
modifie
d
69
-
bus
Fig
ur
e
2
is
fo
un
d
to
be
99.59
46
kW
by
the
prese
nt
AP
L
A
sch
eme
wh
ic
h
is
very
cl
os
e
to
the r
es
ults
of
ot
her
e
xisti
ng m
et
hods
.
4.2.
Analy
sis o
n l
os
s
a
ll
oc
ati
on
r
e
sults
The
total
A
PL
As
of
t
he
ori
gi
nal
an
d
reconfi
gure
d
69
-
bus RDN
a
re
f
oun
d
to b
e v
er
y
cl
os
e
to
22
5
k
W
and
99.
59
kW
resp
ect
ivel
y
by
al
l
the
discu
ssed
m
et
hods.
Hen
ce
,
propos
ed
a
ppro
ac
h
of
LA
is
c
on
te
m
porary
and
c
ompara
bl
e
to
oth
er
e
xisti
ng
met
hods
.
As
sy
ste
m
l
os
s
ha
s
dec
reased
f
rom
22
5
kW
to
99.59
kW,
a
total
prof
it
of
125.4
1
kW
has
bee
n
pro
vid
e
d
t
o
the
util
it
y
by
t
he
present
sc
he
me
du
e
to
N
R.
It
can
be
obser
ve
d
from
Fig
ur
e 3
, b
ef
or
e
NR,
mi
nimum vo
lt
age
is
assig
ned
at
n
ode
-
65 (
i.e. V
min
=V
65
=0.
90
92 p
.
u.
)
w
her
ea
s
three
nodes
(
V
min
=V
61
=V
62
=V
63
=0.948
3
p.u.)
are
al
locat
ed
wit
h
minimu
m
vo
lt
ages
of
0.9
483
pu
afte
r
NR.
Also
,
it
can
be
ide
ntifie
d
the
im
pro
ve
ment
in
volt
age
prof
il
e
is
be
tt
er
after
reconfi
gurati
on
tha
n
that
of
be
for
e
NR
.
CTDM
a
nd
Q
uadrati
c
met
hod
al
locat
e
la
r
ge
am
ount
of
l
os
s
to
t
he
c
us
t
om
e
r
at
bus
61
w
hile
an
a
de
qu
at
e
amo
un
t
of los
s
is assi
gned
by t
he pr
opos
e
d p
r
ocedu
re
Exact
meth
od
awards
e
qual
amo
un
t
of
l
os
s
t
o
the
highly
de
man
ded
cust
ome
r
at
bus
61
as
that
of
the
pro
po
se
d
meth
od.
T
o
te
st
c
ompete
nc
e
of
t
he
de
velo
pe
d
te
chn
i
qu
e
as
re
ga
rd
to
t
heir
ph
ys
ic
al
locat
io
ns,
tw
o
typ
es
of
cust
ome
rs
with
e
qual
dema
nd
s
bu
t
sit
uated
at
dif
fer
e
nt
posit
ion
in
the
netw
ork
are
i
den
ti
fie
d.
It
ca
n
be
viewe
d
fro
m
Fig
ure
4(
a
)
t
hat
be
f
or
e
NR,
the
discre
pa
nc
y
of
A
PLA
bet
ween
tw
o
cl
ose
node
s
36
an
d
37
of
equ
al
dem
an
ds i
s the
highest
by the
pro
pose
d
m
et
hod
a
s c
ompa
red to
oth
e
r discusse
d me
thods.
Af
te
r
NR
,
E
xa
ct
meth
od
s
hows
bette
r
re
s
ult
agai
ns
t
othe
r
te
ch
niques
bu
t
a
m
oderat
e
APLA
is
no
ti
ced
by
the
pr
ese
nt
proce
dure
.
F
urt
her,
it
can
be
reali
sed
f
rom
Fi
gure
4(b
)
w
hich
re
presents
t
he
dif
fe
ren
ce
in
AP
L
A
betw
een
tw
o
dista
nc
e
nodes
10
(c
lose
to
the
s
ub
sta
ti
on
bus
)
an
d
28
(
far
a
wa
y
from
the
s
ubs
ta
ti
on
bu
s
)
t
hat
the
pe
rformance
of
the
propose
d
a
nd
ex
act
pr
oce
dure
a
re
ve
ry
cl
os
e
to
eac
h
ot
her
at
al
l
co
ndit
ion
s
of
t
he
netw
ork.
These
t
wo
pro
cedures
s
how
bette
r
res
ult
as
com
par
e
d
t
o
ot
her
t
wo
meth
ods.
O
ut
of
oth
e
r
tw
o
te
chn
iq
ues
,
C
TD
M
prov
i
des
bette
r
L
A
a
ga
inst
Q
ua
dr
at
ic
sche
me.
H
oweve
r,
LA
by
pro
posed
ap
proac
h
is
fou
nd
t
o
be
pr
om
ine
nt
in
co
nt
rast
to
oth
er
di
scusse
d
meth
ods
at
bo
t
h
be
fore
a
nd
a
fter
re
config
ur
at
io
n
of
the
netw
ork.
He
nc
e,
it
can
be
s
uggested
in
pract
ic
al
fiel
d
of
a
ppli
cat
ion
for
e
f
fici
ent
an
d
reli
able
ma
na
gem
ent
o
f
smart
powe
r
s
yst
ems.
(a)
(b)
Figure
4. (a
) D
iffer
e
nce i
n AP
LA betwee
n n
od
e
s
36 and
37
; (b)
Diff
e
re
nc
e in
AP
L
A
betwee
n nodes
10 a
nd 28
5.
CONCL
US
I
O
NS
This
pa
pe
r
pr
esents
a
co
m
par
at
ive
a
naly
sis
on
R
DN
l
os
s
al
locat
io
n
with
res
pect
to
netw
ork
reconfi
gurati
on.
The
br
a
nch
exch
a
nge
base
d
he
u
risti
c
ap
proac
h
of
NR
prov
i
des
e
ff
ic
ie
nt
res
ults
as
c
ompa
red
to
othe
r
te
c
hn
i
qu
e
s
disc
us
se
d.
The
de
velo
pe
d
A
PL
A
sche
me
is
f
ound
to
be
f
ree
from
t
he
in
flue
nce
of
cro
s
s
-
te
rm
of
powe
r
loss
e
quat
ion.
He
nce,
l
os
s
a
ll
ocati
on
s
are
promisin
g
as
r
egard
to
their
load
de
ma
nd
s
and
geog
raphical
l
ocati
ons.
T
he
pro
po
se
d
loss
al
locat
ion
(L
A
)
meth
od
is
de
velo
ped
with
out
a
ny
ass
umpt
ion
s
a
nd
appr
ox
imat
io
ns
w
hich
ca
n
be
treat
ed
as
major
a
dvanta
ge
of
the
pr
e
sent
procedu
re
f
or
fai
r
loss
al
locat
io
n.
T
he
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
All
oca
ti
ng
activ
e power l
oss
wi
th n
et
work
r
econ
fi
gur
atio
n i
n
el
ect
ric
al po
we
r
…
(
A
m
bika
Pr
asad H
ot
a
)
137
eff
ic
ie
nc
y
of
the
pr
ese
nt
p
r
oc
edure
has
bee
n
ver
ifie
d
a
gai
ns
t
oth
er
existi
ng
te
ch
niques
us
in
g
a
69
-
bus
RDN
.
The
res
ults
of
AP
L
A
a
re
f
ound
to
be
prop
e
r
as
pe
r
l
oad
de
man
ds
a
nd
phys
ic
al
l
ocati
ons
of
the
e
nd
-
us
ers
.
Fu
rt
her,
t
o
te
st
ef
fici
ency
of
t
he
de
velo
ped
proce
dure
i
n
a
restr
uctu
re
d
powe
r
e
nvir
onment,
a
BE
ba
sed
NR
te
chn
iq
ue
is
impli
mente
d
he
re
f
or
ac
hiev
ing
a
mi
nimum
po
wer
loss
pro
vid
i
ng
RDN
.
As
a
ju
diciou
s
distrib
ution
of
act
ive
powe
r
loss
is
noti
ced
at
al
l
the
lo
ad
points
he
nc
e,
ca
n
be
co
ns
ide
red
for
pract
ic
al
impleme
ntati
on
.
A
C
KNOWL
E
DGE
MENTS
This
resea
rch
work
was
s
upport
e
d
by
“
W
ooso
ng
U
ni
ver
sit
y’
s
Acad
e
mic
Re
search
F
undi
ng
-
(
2020
-
2021)
”
.
REFERE
NCE
S
[1]
M.
Khos
rav
i,
H.
Mons
ef,
M.
H
Alia
bad
i,
“L
oss
allocation
in
d
istri
buti
on
ne
twork
including
d
i
stribut
ed
ene
rgy
resourc
es
(DE
Rs),”
Int
ernational
Tr
ansactions
on
Elec
tr
ic
al
Ene
rgy
S
yste
ms
,
v
ol
.
28,
2018
,
doi
:
10.
1002/etep
.
25
48
.
[2]
P.
Kumar
,
N
.
G
upta
,
K.
R
.
Ni
az
i
,
and
A.
Sw
arn
k
ar
,
“A
Cross
-
ter
m
De
com
positi
o
n
Method
for
L
oss
Alloc
ation
i
n
Distribut
ion
Sys
te
ms
Consider
in
g
Loa
d
Pow
er
F
ac
tor
,
”
Elec
tri
c
Powe
r
Compone
nts
and
Syste
ms
,
v
ol.
46
,
pp
.
218
-
229,
2018
,
doi
:
1
0.
1080/1532500
8.
2018.
1434840
.
[3]
S.R.
Salkuti,
Y
.
H.
Lho
,
“
Opt
i
mum
Lo
ca
t
i
on
of
Volta
ge
R
egul
a
tors
in
th
e
Radial
Distri
buti
on
Sys
te
ms
”,
Inte
rnational
Jo
urnal
of
Eme
rgi
ng
Elec
tri
c
Pow
er
Syste
ms
,
vol
.
17,
no
.
3
,
pp
.
35
1
-
361,
2016
,
do
i
:
10.
1515
/i
j
ee
ps
-
2015
-
0197
.
[4]
Y.
Merz
oug,
B
.
Abdelkr
im,
B.
L
arb
i,
“Distri
but
i
on
net
work
re
co
nfigura
t
ion
for
l
oss
red
uct
ionusi
ng
PS
O
me
thod,”
Inte
rnational
Jo
urnal
of El
e
ct
ri
c
al
and
Comput
er
Engi
n
ee
ring
(IJ
ECE
)
,
vol
.
10
,
n
o.
5
,
pp
.
5009
-
5
015,
2020
.
[5]
T.
T
.
Nguy
en,
“
El
e
ct
ri
c
d
istri
bu
ti
on
n
et
work
re
conf
iguration
fo
r
power
loss
r
educ
t
ion
b
ase
d
on
runne
r
roo
t
a
lgori
th
m,”
Inte
r
nati
onal
Journal
of
E
le
c
tric
al
an
d
Computer
Eng
ine
ering
(IJ
ECE)
,
vo
l.
10,
no
.
5
,
pp.
5016
-
5024
,
2020
,
doi
:
10
.
11
591/i
jece
.
v10i5
.
pp5016
-
5024
.
[6]
S.
Mishra
,
D.
Das,
S.
Pau
l,
“
A
com
pr
ehe
nsiv
e
r
eview
on
po
wer
distr
ibut
ion
ne
twork
r
ec
onf
igura
ti
on
,
”
Ene
r
gy
Syste
ms
, v
ol
.
6
,
n
o.
2
,
pp
.
1
-
5
,
2
017
,
doi
:
10
.
100
7/s12667
-
016
-
0195
-
7
.
[7]
A.P.
Hota
,
S.
Mi
shra,
D.P.
Mishra,
“L
oss
Allocation Stra
te
g
ie
s
in A
ct
ive Pow
er
Di
stribut
ion
Ne
tworks:
A Re
vi
ew,
”
In:
AE
CSS
.
Lec
t
ur
e
Note
s
in
E
lectric
al
Eng
ine
er
ing
,
vo
l
.
665
,
pp
.
889
-
902,
2020
,
doi:
10
.
1007/97
8
-
981
-
15
-
5262
-
5
_
68
.
[8]
M.
E.
de
Ol
ivei
ra,
L
.
F.
Ochoa
,
A.
Pad
il
ha
-
Fe
ltrin
and
J.
R.
S.
Mantov
ani,
"N
et
work
rec
onf
ig
ura
ti
on
and
loss
al
lo
ca
t
ion
for
d
i
stribut
ion
sys
tems
with
distri
b
ute
d
gene
r
at
ion
,
"
2004
I
EE
E
/PES
Tr
ansm
ision
and
Distributi
o
n
Confe
renc
e
and
Ex
positi
on:
Lati
n
Ame
rica
(IE
E
E
Cat
.
No.
04E
X956)
,
Sao
Paul
o,
Bra
zi
l
,
2004
,
pp.
206
-
211,
doi
:
10.
1109/T
DC.20
04.
1432379.
[9]
J.
S.
Sav
ie
r
and
D.
Das,
"Impa
ct
of
Ne
twork
Re
c
onfigura
t
ion
on
Loss
Alloc
a
ti
on
of
Radial
Distri
buti
on
Sys
tems,
"
in
IE
EE
Tr
ansacti
ons
on
Powe
r
Delive
ry
,
vol
.
2
2
,
no
.
4
,
pp
.
2473
-
2480,
Oct.
2007,
d
oi:
10.
1109/T
PWR
D.2007.
905370.
[10]
J.
S.
Savier,
D.
Das,
“
Loss
All
oca
t
ion
to
Con
sumers
bef
or
e
and
af
te
r
re
con
figura
t
ion
of
R
adi
a
l
Distribu
ti
o
n
Networks,”
in
E
l
ec
tri
cal
Powe
r a
nd
Ene
rgy
Syst
e
ms
,
vol. 33,
pp.
540
-
549,
2011
,
doi:
10
.
1016/j.ijepe
s.2010.
1
1.
00
7
.
[11]
M.
Heida
r
i
-
Kap
ourc
hali
and
V.
Aravi
ntha
n
,
"Lo
ss
al
locati
on
co
ntrol
in
power
d
istri
buti
on
sys
tem
re
conf
iguratio
n
in
th
e
pr
ese
nce
of
distri
bu
te
d
g
e
ner
at
ors,"
2014
IEE
E
PE
S
Gene
ral
Me
e
ti
ng
|
C
onfe
renc
e
&
E
x
positi
on,
Nati
on
al
Harbor,
MD
,
US
A,
2014,
pp.
1
-
5,
doi: 10.
1109
/PESG
M.2014.
6939508.
[12]
E.
C
arp
an
et
o,
G.
Chi
cc
o
and
J.
S.
Akili
m
al
i
,
"B
ran
ch
cur
ren
t
de
com
positi
on
met
hod
for
loss
allo
ca
t
ion
in
rad
i
al
distri
buti
on
sys
t
em
s
with
dist
rib
ute
d
g
ene
r
at
ion
,
"
in
IEEE
Tr
ansacti
ons
on
Power
Syste
ms
,
vol
.
2
1,
no
.
3
,
pp.
117
0
-
1179,
Aug.
2006
,
doi
:
10
.
1109/TP
WRS.2006
.
876
68
4.
[13]
A.
A.
Mohd
Z
i
n,
A
.
K.
Ferda
v
ani
,
A.
B
.
Khai
ruddin
and
M.
M.
Na
ei
ni
,
"Re
conf
iguration
of
Rad
ia
l
Elec
tr
ical
Distribut
ion
Ne
t
work
Through
Minim
um
-
Curre
nt
Circ
u
la
r
-
Upd
at
ing
-
Me
cha
nis
m
Method,
"
in
I
EE
E
Tr
ansacti
o
ns
on
Powe
r S
ystem
s
,
vol. 27, no.
2,
pp
.
968
-
97
4
,
May
2012,
doi:
10.
1109/T
PWR
S.2011.
2174258
.
[14]
K.
M.
Jagta
p
,
D.
K.
Khatod,
“Nove
l
appr
o
ac
h
for
loss
al
locati
on
o
f
distri
buti
on
netw
orks
with
DG
s
,
”
E
lectric
Power
Syste
ms
Re
sear
c
h
,
vol
.
143
,
pp
.
3
03
-
311,
2017
,
d
oi:
10
.
1016/j.e
ps
r.
2016.
10
.
032
.
[15]
S.
Sharm
a
and
A.
R.
Abhyank
ar,
"Loss
Allo
c
at
ion
for
W
ea
kl
y
Meshed
Distr
ibut
ion
Sys
te
m
Us
ing
Analyt
i
cal
Formula
ti
on
of
Shaple
y
Value,"
in
IE
EE
Tr
ansacti
ons
on
Pow
er
Syst
ems
,
vo
l.
32,
no
.
2
,
pp.
1369
-
1377,
Mar
ch
2017,
doi
:
10
.
11
09/T
PWRS
.
201
6.
2571980.
[16]
Q.
Yu,
J.
Xi
e,
X.
Chen,
K.
Yu
,
L
.
Gan
,
L
.
Ch
en,
“L
oss
allocation
for
r
adi
a
l
d
istri
buti
on
net
w
ork
inc
lud
ing
D
Gs
using
Shapl
ey
v
al
ue
samp
li
ng
es
ti
mate
,
”
IE
E
Pr
oc.
o
f
Gene
rat
io
n,
Tr
ansm
ission,
and
Distributi
o
n
,
v
o
l.
13
,
no
.
8,
pp.
1382
-
1390
,
2019
,
doi
:
10
.
10
49/i
et
-
g
td.
2018
.
6486
.
[17]
H.
Amar
is
,
Y.
P
.
Molina,
M.
Alo
nso
and
J.
E.
Lu
yo,
"Loss
Alloca
ti
on
in
Distributi
on
Networks
Ba
sed
on
Aumann
–
Shaple
y,
"
in
I
EE
E
Tr
ansactions
on
Powe
r
Syste
ms
,
vol
.
33,
no.
6
,
p
p.
6655
-
6666,
Nov.
2018,
do
i:
10.
1109/T
PWR
S.2018.
28447
40.
[18]
Y.
P.
Molin
a,
R
.
B.
Prada
and
O.
R.
Saave
dr
a,
"Comple
x
Losses
Allocati
on
to
Gene
ra
tors
and
Loa
ds
B
ase
d
o
n
Circ
uit
The
ory
a
nd
Aumann
-
Sha
ple
y
Method
,
"
i
n
IE
EE
Tr
ansacti
ons
on
Pow
er
Syste
ms
,
vol.
25
,
no.
4
,
pp.
1928
-
1936,
Nov.
2010
,
doi
:
10
.
1109/TP
WRS.201
0.
204
4425.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
130
–
138
138
[19]
S.
Sharm
a,
A.
R
.
Abhyank
ar,
“
Loss
al
lo
cation
of
rad
ia
l
distr
ib
uti
on
sys
tem
us
ing
Shapl
ey
v
alue:
A
seque
n
ti
a
l
appr
oac
h
,
”
Int
e
rnational
Journal
of
E
le
c
tric
a
l
Pow
er
En
ergy
Syst
ems
,
v
o
l
.
88
,
pp
.
33
-
4
1,
2017
,
do
i:
10.
1016/j.ijepe
s.
2016.
11.
015
.
[20]
S.S.
Ka
shyap,
M.
De,
“
Loss
a
ll
oc
at
ion
and
lo
ss
mi
nim
i
za
t
ion
for
rad
i
al
d
istr
ibut
ion
sys
tem
inc
ludi
ng
DG
s
,”
IET
Re
n
ewabl
e
Powe
r Gene
rat
i
on
,
vol
.
11
,
pp
.
8
06
-
818,
2017
,
d
oi:
10
.
1049/iet
-
r
pg.
2016.
0506
.
[21]
M.
Atana
sovs
ki
and
R.
Ta
l
eski,
"P
ower
Summa
t
ion
Method
for
Loss
Alloc
ation
in
Radial
Distri
buti
on
Networks
Wi
th
DG
,
"
in
IEE
E
Tr
ansacti
ons
on
Power
Syste
ms
,
vol.
26,
no.
4
,
p
p.
2491
-
2499,
Nov.
2011,
do
i:
10.
1109/T
PWR
S.2011.
2153216.
[22]
J.
S.
Savie
r
,
D.
Das,
“An
Exact
Method
for
Loss
Alloc
a
ti
on
in
R
adi
a
l
Distributio
n
Sys
te
ms
,”
E
lectric
al
Powe
r
an
d
Ene
rgy
S
yste
ms
,
vol.
36
,
pp
.
100
-
106,
2012
,
doi
:
1
0.
1016/j.ijepe
s.2
011.
10.
030
.
[23]
P.
Kumar
,
N.
G
upta
,
K.
R
.
Nia
z
i
and
A.
Sw
arn
k
ar
,
"A
Circ
u
it
T
heor
y
-
Based
Lo
ss
Alloc
at
ion
M
et
hod
for
Act
ive
Distribut
ion
Sys
te
ms,"
in
IEEE
Tr
ansacti
ons
o
n
Smar
t
Gr
id
,
vol.
10
,
no.
1,
pp.
1005
-
1012
,
Jan.
2019,
doi
:
10.
1109/T
SG
.
20
17.
2757059.
[24]
A.P
.
Hota
,
S.
Mishra,
D.P
.
M
ishra,
“
A
New
Acti
ve
Pow
er
Loss
Allo
c
at
ion
Method
for
R
adi
a
l
Distr
ibut
io
n
Networks
with
DG
s
,”
In
:
AE
C
SS.
Lect
ure
No
t
es
in
Elec
tri
cal
Engi
ne
ering
,
v
ol
665.
,
pp
.
50
1
-
514,
2020
,
do
i:
10.
1007/978
-
98
1
-
15
-
5262
-
5_37
.
[25]
A.
P.
Hota
,
S.
Mi
shra,
“A
br
anc
h
orie
nt
ed
a
ct
iv
e
p
ower
loss
allocat
ion
method
for
r
adi
a
l
distr
ibut
io
n
net
works
with
distri
bute
d
gen
e
r
at
ors,”
Sc
ie
nt
ia
I
ranica
,
2020
.
[26]
S.R.
Salkuti,
“O
pti
mal
locat
ion
a
nd
siz
ing
of
DG
and
D
-
STATCO
M
in
distr
ibut
io
n
ne
tworks”,
Ind
onesian
Journal
of
Elec
tric
al
Engi
ne
ering
a
nd
Computer
Scienc
e
,
vo
l
.
16,
no.
3,
pp.
1107
-
11
14,
2019
,
do
i:
10.
11591/ijeecs.
v16.
i3.
pp1107
-
1
114
.
[27]
S.
Ghos
h,
D.
Da
s,
“Me
thod
for
l
oad
-
flow
soluti
o
n
of
rad
i
al
distr
i
buti
on
ne
tworks,”
IEE
Proceedi
n
gs
-
Gene
ration,
Tr
ansm
i
ss
ion
and
Distributi
on
, v
ol.
146
,
pp
.
641
-
648,
1999
,
doi
:
10.
1049/i
p
-
g
td:
1
9990464
.
[28]
A.P.
Hota
,
S.
Mishra,
D.P
.
M
ishra,
“
A
New
Acti
ve
Pow
er
Loss
Allocati
on
Method
for
R
adi
a
l
Distr
ibut
io
n
Networks
with
DG
s
,”
In
:
Prad
han
G.
,
Morris
S.,
Nay
ak
N.
(
eds)
Adv
an
ce
s
i
n
Elec
tri
cal
Co
ntrol
and
S
igna
l
Syste
ms
.
Lec
ture
Note
s
in
E
lect
rical
Eng
ineerin
g
,
vol
.
665,
pp.
501
-
514
,
2020
,
doi:
10
.
1007/9
78
-
981
-
15
-
5262
-
5_37
.
[29]
A.
P.
Hota
,
S.
Mishra,
“
A
For
ward
-
Bac
kward
Sw
ee
p
base
d
nu
me
ri
ca
l
appr
o
ach
for
a
ct
iv
e
pow
er
loss
alloc
at
io
n
of
rad
ial
distri
bu
ti
o
n
ne
twork
wi
th
distri
bute
d
g
ene
r
at
ions,
”
Inte
rnat
ional
Journal
of
Numerical
Mode
ll
ing:
E
lectronic
Net
works,
De
vic
es
and
F
ields
,
W
il
ey
,
2020
,
doi
:
10.
1002/j
n
m.
27
88
.
[30]
A.P.
Hot
a,
S.
Mishra,
“L
oss
a
ll
oc
at
ion
in
d
ist
ribut
ion
ne
tworks
with
distri
bu
t
ed
g
ene
r
at
ors
u
nder
going
net
w
ork
rec
onfigur
at
ion
,
”
In
te
rnationa
l
Journal
o
f
Elec
tri
cal
and
C
omputer
Eng
ineering
(I
JE
C
E)
,
vol
.
10,
no
.
4,
pp.
3375
-
3383
,
2020
,
doi
:
10.
1
1591/i
jece
.
v10i4
.
pp3375
-
3383
.
Evaluation Warning : The document was created with Spire.PDF for Python.