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Us
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telli
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tec
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rticle
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CC B
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p
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ail: a
s
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m
ea
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r
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ed
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r
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ly
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r
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m
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tim
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ized
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s
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o
s
itio
n
al
s
y
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tem
(
GPS)
to
tim
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s
tam
p
.
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h
u
s
,
u
s
in
g
PMU,
th
e
m
ea
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r
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en
ts
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e
c
o
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u
cted
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e
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te
p
o
in
ts
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a
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i
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a
t
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co
m
m
o
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tim
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[
1
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.
PMUs
ar
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lled
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ch
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m
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if
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am
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t
o
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ch
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s
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tial
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e
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atch
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ay
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tab
ilit
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[
2
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.
T
r
ad
itio
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ally
,
n
u
m
er
ic
m
ete
r
s
ar
e
u
s
ed
t
o
p
e
r
f
o
r
m
m
ea
s
u
r
e
m
en
ts
.
T
h
e
n
u
m
er
ic
m
ete
r
s
ar
e
in
s
talled
at
s
u
b
s
tatio
n
s
an
d
s
u
p
e
r
v
is
o
r
y
co
n
tr
o
l
an
d
d
ata
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q
u
is
itio
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(
SC
ADA)
ce
n
ter
s
f
o
r
m
o
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ito
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n
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a
n
d
co
n
tr
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llin
g
p
o
wer
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y
s
tem
s
.
Ho
wev
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s
ev
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al
ch
allen
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es
an
d
is
s
u
es
ca
n
ar
is
e
with
th
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in
s
tal
latio
n
s
.
Nu
m
er
ic
m
eter
s
d
o
n
o
t
p
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o
v
id
e
ac
cu
r
ate
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ata
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o
r
ef
f
ec
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ito
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c
o
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o
l.
T
h
u
s
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in
ac
cu
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ac
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ca
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lead
to
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co
r
r
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t
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m
ak
in
g
an
d
in
ef
f
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o
n
th
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p
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g
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Se
co
n
d
ly
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at
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ch
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p
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ates,
n
u
m
e
r
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m
eter
s
o
f
ten
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el
y
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n
co
m
m
u
n
icatio
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n
etwo
r
k
s
to
tr
a
n
s
m
it
d
ata
to
SC
ADA
s
y
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s
.
Failu
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Evaluation Warning : The document was created with Spire.PDF for Python.
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Ju
ly
20
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6
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ata
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e
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ef
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r
m
s
at
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o
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t
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les
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cy
cle.
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m
ea
s
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r
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e
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ase
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le
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d
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ag
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s
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m
s
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m
e
s
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n
ch
r
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izatio
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s
in
g
GPS,
en
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lin
g
p
r
ec
is
e
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m
p
a
r
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o
n
o
f
m
ea
s
u
r
e
m
en
ts
f
r
o
m
d
if
f
er
e
n
t
lo
ca
tio
n
s
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ab
les
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o
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ito
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d
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n
tr
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b
y
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ch
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ased
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ea
l
tim
e
an
d
o
f
f
lin
e
ap
p
licatio
n
s
o
f
PMU.
T
h
e
o
f
f
lin
e
a
p
p
licatio
n
s
a
r
e
p
o
wer
s
y
s
tem
m
o
d
el
v
er
if
icati
o
n
,
e
v
en
t
an
aly
s
is
an
d
r
ec
o
n
s
tr
u
ctio
n
,
b
ase
lin
in
g
p
o
wer
s
y
s
tem
p
er
f
o
r
m
a
n
ce
an
d
l
o
ad
c
h
ar
ac
ter
izatio
n
[
3
]
.
A
n
aly
s
is
o
f
th
e
ef
f
ec
tiv
en
ess
o
f
PM
U
b
ased
wid
e
ar
ea
m
o
n
ito
r
in
g
s
y
s
tem
in
th
e
I
n
d
ian
p
o
wer
g
r
id
h
as b
ee
n
cl
ea
r
ly
m
en
tio
n
e
d
b
y
Su
f
y
a
n
et
a
l.
[
4
]
,
[
5
]
.
2.
M
E
T
H
O
D
PMUs
p
r
o
v
id
e
r
ea
l
-
tim
e
d
ata
o
n
v
o
ltag
e
an
d
cu
r
r
en
t
p
h
aso
r
s
,
wh
ich
ar
e
ess
en
tial
f
o
r
m
ai
n
tain
in
g
th
e
r
eliab
ilit
y
,
s
tab
ilit
y
,
an
d
ef
f
ici
en
cy
o
f
p
o
wer
d
is
tr
ib
u
tio
n
.
H
o
wev
er
,
d
e
p
lo
y
in
g
PMUs a
cr
o
s
s
an
en
tire
g
r
id
ca
n
b
e
co
s
t
-
p
r
o
h
ib
itiv
e
d
u
e
to
th
eir
h
ig
h
in
s
tal
latio
n
an
d
m
ain
te
n
an
ce
co
s
ts
.
T
h
er
ef
o
r
e,
o
p
tim
izin
g
th
e
p
lace
m
en
t
an
d
u
tili
za
tio
n
o
f
PMUs
is
cr
u
cial
to
m
ax
im
ize
th
eir
b
en
ef
its
wh
ile
m
in
im
izin
g
co
s
ts
.
T
h
e
ch
allen
g
e
lies
in
d
eter
m
in
in
g
th
e
o
p
tim
al
p
lace
m
en
t
an
d
co
n
f
ig
u
r
atio
n
o
f
PMUs
with
in
a
s
m
ar
t
g
r
id
t
o
ac
h
i
ev
e
co
m
p
r
eh
e
n
s
iv
e
m
o
n
ito
r
in
g
an
d
f
au
lt
d
etec
tio
n
with
m
in
im
al
r
ed
u
n
d
an
c
y
an
d
ex
p
en
s
e.
T
r
a
d
itio
n
al
o
p
tim
izatio
n
m
eth
o
d
s
o
f
ten
f
ail
t
o
ca
p
tu
r
e
th
e
c
o
m
p
lex
,
n
o
n
-
lin
ea
r
r
elatio
n
s
h
i
p
s
b
etwe
en
v
ar
i
o
u
s
g
r
i
d
p
a
r
am
eter
s
an
d
PMU
p
lace
m
en
ts
,
lead
in
g
to
s
u
b
o
p
t
im
a
l
s
o
lu
tio
n
s
.
T
o
a
d
d
r
ess
th
i
s
is
s
u
e,
an
ar
tific
ial
n
eu
r
al
n
et
wo
r
k
(
ANN)
b
ased
ap
p
r
o
ac
h
f
o
r
PMU
o
p
tim
izatio
n
in
s
m
ar
t
g
r
id
s
is
p
r
o
p
o
s
ed
in
th
is
r
esear
ch
.
T
h
e
ANN
will
b
e
tr
ain
ed
to
p
r
ed
ict
th
e
o
p
tim
al
p
lace
m
e
n
t
an
d
n
u
m
b
er
o
f
PMUs
r
e
q
u
ir
ed
to
e
n
s
u
r
e
f
u
ll
o
b
s
e
r
v
ab
ilit
y
o
f
th
e
g
r
id
,
co
n
s
id
er
in
g
n
etwo
r
k
to
p
o
lo
g
y
,
lo
ad
d
is
tr
ib
u
tio
n
,
a
n
d
e
x
i
s
tin
g
in
f
r
astru
ctu
r
e
co
n
s
tr
ain
ts
.
T
h
e
g
o
als
ar
e
m
en
tio
n
ed
as
:
i)
.
Data
co
llectio
n
an
d
p
r
e
-
p
r
o
c
ess
in
g
:
g
ath
er
an
d
p
r
e
-
p
r
o
ce
s
s
d
ata
o
n
th
e
g
r
id
’
s
to
p
o
l
o
g
y
,
lo
ad
p
r
o
f
iles
,
ex
is
tin
g
PMU
p
lace
m
en
ts
an
d
h
is
to
r
ical
f
au
lt d
ata.
ii).
Mo
d
el
d
e
v
elo
p
m
e
n
t:
d
e
v
elo
p
an
ANN
m
o
d
el
ca
p
ab
le
o
f
lea
r
n
in
g
th
e
c
o
m
p
lex
r
elatio
n
s
h
i
p
s
b
etwe
en
g
r
id
p
ar
am
eter
s
an
d
t
h
e
ef
f
ec
tiv
e
n
e
s
s
o
f
PMU
p
lace
m
en
ts
.
iii).
T
r
ain
in
g
an
d
v
alid
atio
n
:
tr
ain
th
e
ANN
m
o
d
el
u
s
in
g
h
is
to
r
i
ca
l
d
ata
an
d
v
alid
ate
its
p
er
f
o
r
m
an
ce
u
s
in
g
a
s
ep
ar
ate
d
ataset
to
en
s
u
r
e
ac
cu
r
ac
y
an
d
g
en
e
r
aliza
b
ilit
y
.
iv
)
.
Op
tim
izatio
n
alg
o
r
ith
m
:
in
teg
r
ate
th
e
ANN
with
an
o
p
tim
i
za
tio
n
alg
o
r
ith
m
to
g
en
er
ate
th
e
m
o
s
t
co
s
t
-
ef
f
ec
tiv
e
PMU
p
lace
m
en
t stra
teg
y
th
at
en
s
u
r
es
co
m
p
lete
g
r
id
o
b
s
er
v
ab
ilit
y
.
v
)
.
I
m
p
lem
en
tatio
n
an
d
test
in
g
:
im
p
lem
en
t
th
e
p
r
o
p
o
s
ed
ANN
-
b
ased
o
p
tim
izatio
n
s
tr
ateg
y
in
a
s
im
u
lated
s
m
ar
t g
r
id
en
v
ir
o
n
m
en
t to
e
v
a
lu
ate
its
ef
f
ec
tiv
en
ess
an
d
p
r
ac
ticality
.
v
i)
.
Per
f
o
r
m
an
ce
m
et
r
ics:
d
ef
in
e
an
d
m
ea
s
u
r
e
k
e
y
p
er
f
o
r
m
a
n
c
e
in
d
icato
r
s
(
KPI
s
)
s
u
ch
as
co
s
t
s
av
in
g
s
,
g
r
id
o
b
s
er
v
ab
ilit
y
,
f
a
u
lt d
etec
tio
n
a
cc
u
r
ac
y
an
d
co
m
p
u
tatio
n
al
e
f
f
icien
cy
.
2
.
1
.
Wo
r
k
ing
o
f
P
M
U
Fig
u
r
e
1
s
h
o
ws
th
e
f
u
n
ctio
n
al
b
lo
ck
d
ia
g
r
am
o
f
PMU
[
6
]
.
A
n
alo
g
in
p
u
ts
ar
e
cu
r
r
en
t
s
ig
n
al
s
r
ec
eiv
ed
f
r
o
m
th
e
s
ec
o
n
d
a
r
y
o
f
c
u
r
r
en
t
tr
an
s
f
o
r
m
er
s
(
C
T
)
an
d
th
e
v
o
ltag
e
s
ig
n
als
r
ec
eiv
ed
f
r
o
m
t
h
e
s
ec
o
n
d
ar
y
o
f
a
p
o
ten
tial
tr
an
s
f
o
r
m
er
(
PT)
.
T
h
ese
s
ig
n
als
ar
e
s
en
s
ed
b
y
th
e
r
esp
ec
tiv
e
C
T
/PT
s
en
s
o
r
s
an
d
f
ed
to
a
n
ti
-
aliasin
g
f
ilter
wh
ich
r
estricts
th
e
b
a
n
d
wid
th
o
f
s
ig
n
al
with
r
esp
ec
t
to
th
e
s
am
p
lin
g
t
h
eo
r
em
.
GPS
c
o
n
s
is
ts
o
f
a
n
etwo
r
k
o
f
n
u
m
b
er
o
f
s
atellites
(
u
s
u
ally
2
4
)
wh
ich
w
o
r
k
i
n
g
eo
s
y
n
ch
r
o
n
o
u
s
o
r
b
its
,
p
r
o
v
id
i
n
g
lo
ca
ti
o
n
an
d
tim
e
at
an
y
in
s
tan
t
wh
ich
is
tak
en
as
a
r
e
f
er
e
n
ce
tim
e
[
7
]
.
T
h
e
p
h
ase
lo
ck
o
s
cillato
r
is
to
d
iv
i
d
e
th
e
p
u
ls
e
r
ec
eiv
e
d
.
T
o
in
p
u
t
to
t
h
e
m
icr
o
p
r
o
ce
s
s
o
r
,
th
e
p
u
ls
es
will
b
e
s
ep
ar
ated
a
n
d
f
ed
t
o
AD
co
n
v
er
ter
.
T
h
e
a
n
alo
g
in
p
u
t
s
ig
n
als
r
ec
eiv
ed
f
r
o
m
C
T
/PT
s
en
s
o
r
s
ar
e
tr
a
n
s
lated
in
to
d
ig
ital
f
o
r
m
to
b
e
ac
ce
p
tab
le
b
y
th
e
m
icr
o
p
r
o
ce
s
s
o
r
[
8
]
.
A
p
h
aso
r
m
icr
o
p
r
o
ce
s
s
o
r
is
a
1
6
-
b
it
p
r
o
ce
s
s
o
r
co
m
p
u
tes
p
o
s
itiv
e
s
eq
u
en
ce
p
h
aso
r
v
alu
es
(
m
ag
n
itu
d
e
an
d
an
g
le)
o
f
cu
r
r
en
t a
n
d
v
o
ltag
e
s
ig
n
als at
a
g
iv
en
s
y
n
ch
r
o
n
ized
p
u
ls
e
co
m
in
g
f
r
o
m
GPS r
ec
eiv
er
.
Acc
o
r
d
in
g
to
C
h
ar
les
Stei
n
m
etz,
th
e
p
u
r
e
s
in
u
s
o
id
al
wav
e
ca
n
b
e
ex
p
r
ess
ed
in
th
e
f
o
r
m
o
f
p
h
aso
r
[
9
]
,
[
1
0
]
.
T
h
e
s
in
u
s
o
id
al
s
ig
n
a
l is g
iv
en
b
y
t
h
e
(
1
)
.
(
)
=
(
c
os
+
)
(
1
)
W
h
er
e,
(
)
is
th
e
tim
e
-
b
ased
s
ig
n
al
with
r
esp
ec
t
to
tim
e
.
is
th
e
am
p
litu
d
e
o
f
th
e
s
ig
n
al.
T
h
e
v
a
r
iab
le
ω
is
an
an
g
u
lar
f
r
eq
u
en
cy
i
n
r
ad
ian
s
p
er
s
ec
o
n
d
an
d
is
th
e
p
h
ase
an
g
le
[
1
1
]
an
d
[
1
2
]
.
T
h
e
p
h
aso
r
r
ep
r
esen
tatio
n
o
f
th
ese
s
in
u
s
o
i
d
s
is
g
iv
en
b
y
t
h
e
(
2
)
in
ex
p
o
n
en
tial a
n
d
tr
ig
o
n
o
m
etr
ic
f
o
r
m
;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
P
h
a
s
o
r
mea
s
u
r
eme
n
t u
n
it o
p
timiz
a
tio
n
in
s
ma
r
t g
r
id
s
u
s
in
g
…
(
A
s
h
p
a
n
a
S
h
ir
a
lka
r
)
627
=
√
2
=
√
2
(
+
s
in
)
(
2
)
On
ce
th
e
m
ag
n
i
tu
d
e
an
d
an
g
le
ar
e
k
n
o
wn
it c
an
b
e
r
ep
r
esen
ted
in
f
o
r
m
o
f
a
p
h
aso
r
as (
3
)
a
n
d
(
4
)
,
=
|
|
=
|
|
∠
(
3
)
=
|
|
=
|
|
∠
(
4
)
As
s
h
o
wn
in
Fig
u
r
e
2
,
th
e
d
o
tted
lin
e
r
ep
r
esen
ts
a
r
ef
er
e
n
c
e
lin
e
with
r
esp
ec
t
to
wh
ich
t
h
e
lag
g
in
g
an
d
lead
in
g
p
h
aso
r
m
ea
s
u
r
em
en
t
is
co
n
d
u
cted
.
T
h
e
c
o
m
m
o
n
tim
e
r
ef
e
r
en
ce
is
r
eq
u
ir
ed
f
o
r
th
ese
m
ea
s
u
r
em
en
ts
.
T
o
o
b
tain
tim
e
r
ef
er
e
n
ce
s
,
GPS
is
u
s
ed
.
T
h
e
s
atellite
s
p
r
o
v
id
e
a
clo
c
k
p
u
ls
e
at
th
e
r
ate
o
f
o
n
e
p
u
ls
e
p
er
s
ec
o
n
d
.
T
h
e
PMU
r
ec
o
r
d
s
ab
o
u
t 3
0
s
am
p
les p
er
s
e
co
n
d
[
1
2
]
-
[
1
4
]
.
1
6
-
b
i
t
A
/
D
c
o
n
v
e
r
t
e
r
A
n
a
l
o
g
I
n
p
u
t
s
A
n
t
i
-
a
l
i
a
s
i
n
g
f
i
l
t
e
r
s
G
P
S
r
e
c
e
i
v
e
r
P
h
a
s
e
-
l
o
c
k
e
d
o
s
c
i
l
l
a
t
o
r
P
h
a
s
o
r
M
i
c
r
o
-
p
r
o
c
e
s
s
o
r
M
o
d
e
m
s
Fig
u
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e
1
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u
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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12
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1
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T
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d
ata
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r
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Fig
u
r
e
4
s
h
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cir
cu
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o
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-
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le
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1
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s
m
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at
s
en
d
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s
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x
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d
if
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m
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/2
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s
[
1
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]
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m
eth
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d
o
f
m
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eter
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ce
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ter
s
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t h
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t b
e
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Fig
u
r
e
4
.
C
ir
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it r
e
p
r
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tat
io
n
2
.
3
.
Art
if
i
ci
a
l
inte
llig
ence
a
pp
lica
t
io
n in po
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s
y
s
t
em
B
ef
o
r
e
d
ev
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p
in
g
th
e
ANN
b
ased
PMU
m
o
d
el,
it
is
r
eq
u
ir
ed
to
r
ev
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th
e
co
n
ce
p
ts
o
f
ar
tific
ial
in
tellig
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ce
(
AI
)
an
d
a
p
p
lica
tio
n
s
in
p
o
wer
s
y
s
tem
s
in
b
r
ief
.
AI
is
th
e
m
im
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r
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r
es
en
tatio
n
o
f
h
u
m
an
b
eh
av
io
r
.
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t
is
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e
r
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p
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en
t
o
f
a
h
u
m
an
b
y
a
co
m
p
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ter
.
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ch
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g
(
ML
)
is
th
e
s
tu
d
y
o
f
c
o
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ter
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o
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ith
m
s
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im
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o
v
em
en
t
u
s
in
g
ex
p
er
ien
ce
an
d
d
ata
[
1
6
]
.
T
h
e
f
am
o
u
s
p
r
o
d
u
cts
b
ased
o
n
ML
ar
e
T
esla,
Go
o
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le
C
ar
,
an
d
Al
ex
a.
ML
is
th
e
s
u
b
f
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f
AI
th
at
m
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ly
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ased
o
n
ex
p
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ce
wh
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is
d
ata
f
o
r
th
e
m
ac
h
in
e
[
1
7
]
.
Ob
s
er
v
atio
n
s
o
f
s
o
m
e
ex
p
er
i
m
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ts
ca
n
also
b
e
tr
ea
te
d
as
e
x
p
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ce
a
n
d
u
s
ed
as
d
ata.
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a
s
ed
o
n
th
e
b
lack
an
d
wh
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p
ix
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o
f
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im
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im
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g
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o
g
n
itio
n
ca
n
b
e
d
o
n
e
ef
f
ec
tiv
ely
u
s
in
g
ML
.
Py
th
o
n
la
n
g
u
ag
e
ca
n
b
e
u
s
ed
as
a
b
ac
k
-
en
d
to
o
l
f
o
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th
is
p
u
r
p
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s
e.
I
f
th
e
co
m
p
u
ter
is
g
iv
en
ac
ce
s
s
to
d
ata,
th
en
it
lear
n
s
f
r
o
m
th
e
d
ata
its
elf
.
AI
co
n
f
ir
m
s
wh
eth
e
r
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e
c
o
m
p
u
ter
th
in
k
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lik
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a
h
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m
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b
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n
g
o
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W
h
en
t
h
e
n
etwo
r
k
is
tr
ain
ed
th
e
m
o
d
el
f
in
d
s
th
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ex
p
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ted
o
u
tp
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t a
cc
u
r
ately
with
n
ev
er
-
s
ee
n
in
p
u
t [
1
8
]
-
[
2
0
]
.
I
n
p
o
wer
s
y
s
tem
s
b
o
th
d
is
tr
ib
u
tio
n
u
tili
ty
an
d
co
n
s
u
m
e
r
h
av
e
b
en
ef
ited
in
th
e
ad
v
e
n
t o
f
th
e
AI
b
ased
ap
p
licatio
n
s
.
So
m
e
o
f
th
ese
a
p
p
licatio
n
s
ar
e
c
o
n
d
u
cted
ef
f
ec
tiv
ely
u
s
in
g
lin
ea
r
r
eg
r
ess
io
n
an
d
ANNs
[
2
1
]
.
T
h
e
p
r
o
ac
tiv
e
m
ain
ten
a
n
ce
o
f
s
u
b
s
tatio
n
eq
u
ip
m
en
t
is
ca
r
r
ied
o
u
t
wh
er
ein
th
e
life
o
f
th
e
eq
u
ip
m
en
t
is
p
r
ed
icted
u
s
in
g
AI
-
b
ased
r
esid
u
al
life
ass
es
s
m
en
t
(
R
L
A)
te
ch
n
iq
u
es.
T
h
e
lo
a
d
f
r
eq
u
en
cy
co
n
tr
o
l
is
ac
h
iev
ed
ef
f
ec
tiv
ely
u
s
in
g
ANN.
T
h
e
e
lectr
ical
th
ef
t
co
m
m
itted
b
y
t
h
e
m
is
cr
ea
n
t
b
y
tam
p
er
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wi
th
th
e
e
n
er
g
y
m
eter
is
d
etec
ted
u
s
in
g
ANN
[
2
2
]
.
B
ased
o
n
th
e
ML
alg
o
r
ith
m
,
th
e
s
o
u
r
ce
co
d
e
is
wr
itten
.
Fo
r
th
is
p
u
r
p
o
s
e,
Py
th
o
n
is
th
e
m
o
s
t
ac
ce
p
ted
lan
g
u
ag
e,
s
im
p
le
an
d
ea
s
y
to
u
n
d
e
r
s
tan
d
.
Py
th
o
n
is
an
in
ter
p
r
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,
h
ig
h
le
v
el,
g
e
n
er
al
p
u
r
p
o
s
e,
o
b
ject
o
r
ien
ted
,
p
la
tf
o
r
m
in
d
ep
e
n
d
en
t;
web
en
a
b
led
d
y
n
am
ically
ty
p
ed
p
r
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g
r
am
m
in
g
lan
g
u
ag
e
d
ev
elo
p
e
d
b
y
Gu
id
o
Van
R
o
s
s
u
m
.
I
t
co
m
p
r
is
es
an
ex
ten
s
iv
e
s
et
o
f
lib
r
ar
ies
an
d
is
wid
ely
u
s
ed
i
n
d
ata
s
cien
ce
,
b
ig
d
ata,
ML
,
in
ter
n
et
o
f
th
i
n
g
s
(
I
o
T
)
,
clo
u
d
co
m
p
u
tin
g
,
an
d
AI
.
Go
o
g
le,
Y
o
u
T
u
b
e
,
I
n
s
tag
r
am
,
Dr
o
p
b
o
x
,
Q
u
o
r
a,
B
ig
T
o
r
r
en
t,
Delu
g
,
C
in
em
a
4
D,
an
d
Mo
z
illa
Fire
f
o
x
ar
e
s
o
m
e
o
f
th
e
w
ell
k
n
o
wn
,
f
am
o
u
s
an
d
g
l
o
b
ally
u
s
ed
ap
p
licatio
n
s
b
ased
o
n
Py
th
o
n
[
2
3
]
-
[
2
6
]
.
A
I
ap
p
r
o
ac
h
es
in
s
m
ar
t
g
r
id
ar
e
well
ex
p
lain
ed
b
y
J
u
d
g
e
et
a
l.
[
2
7
]
.
2
.
4
.
T
he
ANN
b
a
s
ed
P
M
U
m
o
del
T
h
e
h
u
m
an
b
r
ain
co
m
p
r
is
es
b
i
llio
n
s
o
f
n
er
v
e
ce
lls
ca
lled
n
e
u
r
o
n
s
.
T
h
e
n
eu
r
o
n
s
ar
e
co
n
n
e
cted
b
y
th
e
lin
k
s
ca
lled
d
en
d
r
ites
a
n
d
ax
o
n
s
.
T
h
e
n
eu
r
o
n
s
g
et
in
p
u
t
f
r
o
m
th
e
ey
es,
n
o
s
e,
to
u
ch
etc.
T
h
e
in
p
u
ts
r
ec
eiv
e
d
b
y
n
eu
r
o
n
s
ar
e
p
r
o
ce
s
s
ed
an
d
s
en
t
f
o
r
war
d
f
o
r
f
u
r
th
er
ac
tiv
at
io
n
.
T
h
u
s
,
th
e
n
etwo
r
k
f
o
r
m
ed
b
y
n
eu
r
o
n
s
an
d
d
en
d
r
ites
is
ca
lled
b
io
lo
g
ical
n
eu
r
al
n
etwo
r
k
(
B
NN)
.
T
h
e
B
NN
wo
r
k
s
o
n
p
ar
allel
p
r
o
ce
s
s
in
g
[
2
3
]
.
B
ased
o
n
th
is
an
alo
g
y
ANNs
ar
e
d
ev
el
o
p
ed
.
T
h
e
ANNs
ar
e
m
ass
iv
ely
p
ar
allel
c
o
m
p
u
tin
g
s
y
s
tem
s
co
m
p
r
is
in
g
o
f
lar
g
e
n
u
m
b
er
o
f
p
r
o
ce
s
s
o
r
s
h
av
i
n
g
i
n
ter
co
n
n
ec
tio
n
s
as in
s
p
ir
ed
b
y
th
e
B
NN
[
2
4
]
.
Fig
u
r
e
5
illu
s
tr
ates
an
ANN
m
o
d
el
f
o
r
th
e
f
t
d
etec
tio
n
.
T
h
e
ANN
m
o
d
el
b
asically
co
m
p
r
is
es
th
r
ee
lay
er
s
v
iz;
th
e
in
p
u
t
lay
er
,
th
e
h
id
d
en
lay
er
,
an
d
th
e
o
u
tp
u
t
l
ay
er
.
At
th
e
in
p
u
t
lay
er
,
th
e
in
p
u
t
s
ig
n
als
1
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
P
h
a
s
o
r
mea
s
u
r
eme
n
t u
n
it o
p
timiz
a
tio
n
in
s
ma
r
t g
r
id
s
u
s
in
g
…
(
A
s
h
p
a
n
a
S
h
ir
a
lka
r
)
629
2
ar
e
r
ec
eiv
e
d
b
y
ANN
as
p
h
as
e
an
g
les
o
f
v
o
ltag
es
at
th
e
s
en
d
in
g
en
d
an
d
r
ec
eiv
i
n
g
e
n
d
s
r
esp
ec
tiv
ely
.
T
h
e
b
ias
s
ig
n
al
b
is
g
i
v
en
ad
d
itio
n
to
in
p
u
t
s
ig
n
als.
I
t
is
p
o
s
s
ib
le
to
in
clu
d
e
b
ias at
th
e
in
p
u
t la
y
er
.
I
n
p
u
t
0
h
av
in
g
weig
h
t
w
0
ca
n
b
e
tak
en
in
th
e
in
p
u
t
lay
er
s
u
ch
th
at
0
=b
wh
ich
is
b
ias.
T
h
ese
in
p
u
ts
ar
e
f
ed
to
a
lin
ea
r
tr
an
s
f
er
f
u
n
ctio
n
at
a
h
id
d
en
l
ay
er
th
r
o
u
g
h
lin
k
s
f
o
r
m
ed
b
y
s
y
n
o
p
tic
weig
h
ts
-
0
,
1
an
d
2
.
All
in
p
u
ts
ar
e
m
o
d
if
ied
b
y
a
weig
h
t
(
e.
g
.
,
m
u
ltip
lied
b
y
weig
h
ts
)
a
n
d
th
en
ad
d
e
d
at
t
h
e
o
u
tp
u
t
lay
er
,
g
iv
in
g
o
u
tp
u
t,
y
[
1
1
]
.
T
h
is
ju
n
ctio
n
is
ca
lled
p
er
ce
p
tr
o
n
wh
ich
is
lik
e
a
n
eu
r
o
n
in
th
e
ca
s
e
o
f
B
NN.
T
h
e
ex
p
r
ess
io
n
f
o
r
o
u
tp
u
t
y
is
ex
p
r
ess
ed
in
th
e
f
o
r
m
o
f
th
e
(
6
)
.
Fig
u
r
e
5
.
ANN
m
o
d
el
f
o
r
th
ef
t
d
etec
tio
n
y=
0
0
+
1
1
+
2
2
=
0
2
(
6
)
I
n
o
r
d
e
r
to
o
b
tain
a
s
ca
lab
le
o
u
tp
u
t,
th
e
o
u
tp
u
t
y
is
f
u
r
th
e
r
p
r
o
ce
s
s
ed
u
s
in
g
an
ac
tiv
atio
n
f
u
n
ctio
n
.
T
h
er
e
a
r
e
a
n
u
m
b
er
o
f
ac
tiv
a
tio
n
f
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n
ctio
n
s
s
u
c
h
as
s
ig
m
o
i
d
,
r
ec
tifie
d
lin
ea
r
u
n
it
(
R
eL
U)
,
an
d
h
y
p
er
b
o
lic
tan
g
en
t.
T
h
e
s
ig
m
o
i
d
f
u
n
ctio
n
is
an
ac
tiv
atio
n
f
u
n
ctio
n
th
at
y
ield
s
o
u
tp
u
t
Y
b
etwe
en
0
to
1
.
T
h
e
s
ig
m
o
id
f
u
n
ctio
n
is
ex
p
r
ess
ed
as
(
7
)
[
2
5
]
.
Y
=
1
1
+
−
(
7
)
T
h
e
n
etwo
r
k
f
o
r
m
in
g
a
s
eq
u
e
n
ce
o
f
th
e
in
p
u
t
la
y
er
,
h
id
d
en
lay
er
an
d
o
u
tp
u
t
lay
er
is
ca
ll
ed
a
f
ee
d
f
o
r
war
d
n
etwo
r
k
.
T
h
e
o
u
tp
u
t
s
o
o
b
tain
ed
th
r
o
u
g
h
a
f
ee
d
f
o
r
war
d
n
etwo
r
k
is
ca
lled
as
p
r
ed
icted
o
u
t
p
u
t.
T
h
e
p
r
ed
icted
o
u
tp
u
t
(
Y)
is
c
o
m
p
ar
ed
with
th
e
tar
g
eted
o
u
tp
u
t
(
T
)
.
T
h
e
d
ev
iatio
n
b
etwe
en
p
r
ed
icted
o
u
tp
u
t
an
d
tar
g
eted
o
u
tp
u
t
is
ca
lled
an
er
r
o
r
,
d
en
o
te
d
b
y
e.
I
n
o
r
d
er
to
ac
h
iev
e
a
tar
g
eted
o
u
tp
u
t,
id
ea
lly
,
th
e
er
r
o
r
s
h
o
u
ld
b
e
o
b
liv
io
u
s
ly
ze
r
o
.
As
s
u
ch
th
e
n
eu
r
al
n
etwo
r
k
is
co
n
d
u
cted
o
n
ly
if
th
e
er
r
o
r
is
ze
r
o
o
r
with
in
a
s
p
ec
if
ied
p
er
m
is
s
ib
le
lim
it.
T
h
e
er
r
o
r
wo
u
ld
b
e
m
in
im
al
at
its
g
r
ad
ien
t
co
n
ce
r
n
in
g
weig
h
ts
.
T
h
e
g
r
ad
ien
t
is
th
e
r
ate
o
f
ch
a
n
g
e
o
f
er
r
o
r
with
r
esp
ec
t
to
weig
h
t
(
d
e/
d
w)
.
I
n
o
r
d
e
r
to
d
eter
m
i
n
e
th
e
g
r
a
d
i
en
t,
it
is
r
eq
u
ir
ed
to
tr
av
el
b
ac
k
f
r
o
m
er
r
o
r
to
wei
g
h
t.
T
h
is
p
r
o
ce
s
s
is
ca
lled
as
b
ac
k
p
r
o
p
ag
atio
n
.
T
h
er
e
ar
e
d
if
f
er
en
t
m
et
h
o
d
s
o
f
b
ac
k
p
r
o
p
ag
atio
n
s
u
ch
as c
h
ai
n
in
g
,
g
r
ad
ien
t
d
ec
en
t m
eth
o
d
an
d
s
o
f
o
r
th
[
2
8
]
-
[
3
0
]
.
T
h
e
f
o
llo
win
g
ANN
b
ased
a
lg
o
r
ith
m
is
d
ev
elo
p
ed
f
o
r
th
e
p
r
o
p
o
s
ed
m
eth
o
d
o
f
th
e
f
t
d
etec
tio
n
.
T
r
ain
in
g
a
n
d
test
d
ata
is
as sh
o
wn
in
T
ab
le
1
.
i)
.
C
r
ea
tio
n
o
f
a
n
e
u
r
al
n
etwo
r
k
.
T
h
e
s
y
n
o
p
tic
weig
h
ts
ar
e
in
itialized
r
an
d
o
m
ly
.
I
n
Py
t
h
o
n
,
th
e
r
an
d
o
m
lib
r
ar
y
is
im
p
o
r
ted
.
Alter
n
ati
v
ely
,
th
e
n
u
m
e
r
ic
Py
th
o
n
(
N
u
m
p
y
)
lib
r
ar
y
ca
n
also
b
e
im
p
o
r
ted
.
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n
th
e
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r
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p
o
s
ed
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,
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e
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m
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r
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en
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o
f
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n
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m
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e
r
s
.
ii).
T
h
e
in
p
u
t
d
atasets
ar
e
ap
p
lied
to
th
e
n
etwo
r
k
.
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n
th
e
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r
o
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ata
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o
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ts
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ap
p
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s
h
o
wn
in
T
ab
le
1
.
iii).
T
h
e
o
th
er
p
a
r
am
eter
s
o
f
th
e
n
etwo
r
k
ar
e
s
et
s
u
ch
as
b
ias,
th
r
esh
o
ld
an
d
ac
tiv
atio
n
f
u
n
ctio
n
.
T
h
e
o
u
t
p
u
t
is
ca
l
cu
lated
u
s
in
g
Py
th
o
n
s
o
u
r
ce
co
d
e.
iv
)
.
T
h
e
ca
lcu
lated
o
u
t
p
u
t
is
c
o
m
p
ar
ed
with
t
h
e
tar
g
eted
o
u
tp
u
t.
I
n
th
e
p
r
o
p
o
s
ed
m
eth
o
d
,
th
e
ta
r
g
eted
o
u
tp
u
t
is
o
b
tain
ed
th
e
an
g
le
at
wh
i
ch
th
e
m
ax
im
u
m
p
o
wer
tr
an
s
f
er
will
b
e
th
er
e.
T
h
e
d
if
f
e
r
en
ce
b
etwe
en
ca
lcu
lated
o
u
tp
u
t a
n
d
ta
r
g
eted
o
u
tp
u
t is ca
lled
an
e
r
r
o
r
.
v
)
.
T
o
m
in
im
ize
th
e
er
r
o
r
,
th
e
g
r
ad
ien
t
o
f
th
e
er
r
o
r
with
r
es
p
ec
t
to
weig
h
t
is
d
eter
m
in
ed
th
r
o
u
g
h
b
ac
k
p
r
o
p
a
g
atio
n
.
Fo
r
th
is
p
u
r
p
o
s
e,
th
e
tech
n
iq
u
es
n
am
ely
Gr
ad
i
en
t
Descen
t
an
d
c
h
ain
in
g
r
u
le
ar
e
ap
p
lied
in
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
.
v
i)
.
T
h
e
s
tep
s
d
an
d
e
ar
e
r
ep
ea
ted
th
r
o
u
g
h
th
e
n
u
m
b
e
r
o
f
iter
ati
o
n
s
till
th
e
er
r
o
r
is
r
ed
u
ce
d
to
th
e
ac
ce
p
tab
l
e
r
an
g
e.
T
h
is
p
h
en
o
m
en
o
n
is
ca
lled
tr
ain
in
g
o
f
th
e
n
etwo
r
k
.
v
ii).
On
ce
th
e
n
etwo
r
k
is
tr
ain
ed
,
it
is
v
alid
ated
b
y
a
p
p
ly
in
g
test
in
p
u
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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d
o
n
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J
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&
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20
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Py
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ased
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n
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ANN
m
o
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el
f
o
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tam
p
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h
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m
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ea
tu
r
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o
f
th
e
co
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e
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e
as f
o
llo
ws
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a)
T
h
e
lib
r
ar
y
Nu
m
p
y
is
im
p
o
r
ted
to
e
x
ec
u
te
m
ath
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atica
l
f
u
n
ctio
n
s
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ig
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o
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f
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n
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ticu
lar
.
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h
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ts
ar
e
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d
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ly
u
s
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g
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o
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f
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n
ct
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ailab
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m
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n
ativ
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e
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m
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e
im
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ted
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ep
ar
ately
.
b)
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h
e
d
atasets
ar
e
f
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m
e
d
u
s
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s
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ize
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iles
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C
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ig
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o
t
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b
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ilt
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s
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m
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Py
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ts
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w
2
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d
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ias
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in
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an
d
o
m
ly
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y
Py
th
o
n
.
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h
e
o
u
tp
u
t
y
is
d
eter
m
in
ed
as
p
er
(
1
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.
Usi
n
g
th
e
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ig
m
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n
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n
,
t
h
e
o
u
tp
u
t
Y
is
co
m
p
u
ted
as
s
h
o
wn
in
Fig
u
r
e
2
.
I
t
is
d
ef
in
ed
t
h
at
th
e
th
ef
t
ev
en
t
is
d
etec
ted
at
m
o
d
e
1
.
T
h
er
ef
o
r
e,
if
t
h
e
o
u
t
p
u
t
v
al
u
e
is
less
th
an
its
th
r
esh
o
ld
o
f
0
.
8
,
th
e
c
o
n
n
ec
tio
n
is
n
o
r
m
al;
o
th
er
wis
e,
th
e
th
ef
t
e
v
en
t
is
g
e
n
er
ated
b
y
th
e
n
eu
r
al
n
etwo
r
k
.
T
h
e
o
u
t
p
u
t
Y
is
co
m
p
ar
ed
with
th
e
tar
g
eted
o
u
t
p
u
t
T
.
T
h
en
e
r
r
o
r
e
is
co
m
p
u
ted
as
a
d
if
f
er
e
n
c
e
o
f
th
e
ca
lcu
late
d
o
r
p
r
ed
ict
ed
o
u
tp
u
t
(
Y)
a
n
d
t
ar
g
eted
o
u
tp
u
t
(
T
)
.
T
h
e
s
q
u
ar
e
o
f
er
r
o
r
is
co
m
p
u
te
d
an
d
is
d
if
f
er
en
tiated
with
r
e
s
p
ec
t
to
weig
h
ts
w
1
an
d
w
2
b
y
u
s
in
g
t
h
e
ch
ain
in
g
r
u
le
as
(
8
)
.
=
(
8
)
T
h
e
ch
ain
in
g
is
co
n
d
u
cted
th
r
o
u
g
h
a
n
u
m
b
e
r
o
f
s
u
cc
ess
iv
e
iter
atio
n
s
.
T
h
e
co
n
v
e
r
g
en
ce
is
s
aid
to
b
e
r
ea
ch
ed
wh
en
th
e
v
alu
es
o
f
weig
h
ts
d
o
n
o
t
c
h
an
g
e
with
r
esp
ec
t
to
iter
ativ
e
c
y
cles.
At
co
n
v
er
g
en
ce
th
e
er
r
o
r
is
m
in
im
u
m
.
As s
u
ch
th
e
p
r
ed
ict
iv
e
o
u
tp
u
t a
p
p
r
o
ac
h
es th
e
tar
g
eted
o
u
tp
u
t.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
m
o
d
el
h
as
b
ee
n
p
r
ep
ar
e
d
u
s
in
g
tr
ain
in
g
d
ata
an
d
test
d
ata
as
s
h
o
wn
in
T
ab
le
1
an
d
as
p
er
th
e
s
et
u
p
g
iv
en
in
Fig
u
r
e
3
.
T
h
e
o
b
s
er
v
atio
n
s
h
av
e
b
ee
n
u
n
d
er
g
o
n
e
in
a
d
etailed
m
an
n
e
r
an
d
r
esu
lts
ar
e
o
b
tain
ed
.
T
h
e
s
am
p
le
r
esu
lts
o
b
tain
ed
af
ter
g
iv
in
g
ad
e
q
u
ate
tr
ai
n
in
g
to
th
e
n
etwo
r
k
ar
e
f
u
r
n
is
h
ed
in
T
a
b
le
2
.
T
h
e
tam
p
er
ev
en
t
was
g
en
er
at
ed
b
y
co
n
n
ec
tin
g
a
lin
k
in
p
ar
allel
with
th
e
m
eter
in
th
e
ca
s
e
o
f
s
er
ial
n
u
m
b
er
s
1,
2,
5,
8
,
an
d
1
0
g
iv
en
in
T
ab
le
2
.
I
n
o
th
er
ca
s
es,
n
o
r
m
al
s
tatu
s
is
m
ain
tain
ed
.
T
h
e
r
esu
lts
f
u
r
n
is
h
ed
in
T
ab
le
2
ar
e
f
o
u
n
d
to
b
e
a
p
p
r
o
p
r
iate
as
co
m
p
ar
ed
with
th
e
co
r
r
esp
o
n
d
in
g
u
n
it
co
n
s
u
m
p
ti
o
n
d
is
p
lay
ed
o
n
th
e
ch
ec
k
m
eter
.
T
h
e
o
b
s
er
v
atio
n
s
f
r
o
m
th
e
ex
p
er
im
e
n
t a
ls
o
led
to
th
e
f
o
llo
win
g
r
esu
lts
o
r
f
in
d
in
g
s
.
a)
T
h
e
p
r
ed
ictio
n
o
f
o
u
tp
u
t
b
ec
o
m
es
m
o
r
e
ac
cu
r
ate
if
t
h
e
q
u
an
tu
m
o
f
th
e
tr
ain
in
g
d
ata
p
o
in
ts
is
g
r
ea
ter
.
T
h
e
p
r
e
d
icted
an
d
tar
g
eted
o
u
t
p
u
ts
c
o
m
e
clo
s
e
to
ea
c
h
o
th
er
in
th
e
ca
s
e
o
f
m
a
n
y
tr
ain
i
n
g
d
ata
p
o
in
ts
.
b)
T
h
e
s
u
cc
ess
o
f
th
e
n
e
u
r
al
n
etwo
r
k
d
ep
e
n
d
s
o
n
a
v
ar
iety
o
f
tr
ain
in
g
d
ata.
I
t
is
r
eq
u
ir
ed
to
co
v
er
all
co
n
d
itio
n
s
o
f
n
o
r
m
al
an
d
ab
n
o
r
m
al
d
ata.
Seco
n
d
ly
,
it
is
r
eq
u
ir
ed
to
co
v
e
r
d
if
f
er
e
n
t
lo
ad
i
n
g
co
n
d
itio
n
s
s
u
ch
as p
ar
tial lo
ad
an
d
f
u
ll lo
ad
.
c)
I
n
itially
,
th
e
p
r
o
g
r
a
m
ex
ec
u
ti
o
n
is
d
elay
ed
as
th
e
n
eu
r
al
n
etwo
r
k
is
n
o
t
tr
ain
ed
.
On
ce
th
e
n
etwo
r
k
g
ets
tr
ain
ed
,
th
e
p
r
o
g
r
am
ex
ec
u
tio
n
b
ec
o
m
es f
aster
.
d)
I
t
tak
es
a
lar
g
e
n
u
m
b
er
o
f
iter
ativ
e
cy
cles
th
r
o
u
g
h
a
r
a
n
g
e
s
u
ch
as
2
5
,
0
0
0
to
1
0
0
,
0
0
0
d
e
p
en
d
in
g
o
n
th
e
s
elec
tio
n
o
f
in
itial
v
alu
es
o
f
w
eig
h
ts
to
g
et
co
n
v
er
g
en
ce
.
I
n
t
h
is
co
n
tex
t,
th
e
Py
t
h
o
n
co
d
e
i
s
f
o
u
n
d
to
b
e
a
p
r
o
p
er
ch
o
ice
co
m
p
a
r
ed
to
co
n
v
en
tio
n
al
C
/C
++
an
d
J
av
a
p
l
atf
o
r
m
s
.
T
h
e
f
ast
co
n
v
e
r
g
en
ce
d
ep
en
d
s
o
n
th
e
s
elec
tio
n
o
f
in
itial v
alu
es o
f
w
eig
h
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
P
h
a
s
o
r
mea
s
u
r
eme
n
t u
n
it o
p
timiz
a
tio
n
in
s
ma
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t g
r
id
s
u
s
in
g
…
(
A
s
h
p
a
n
a
S
h
ir
a
lka
r
)
631
e)
T
h
e
Sig
m
o
id
f
u
n
ctio
n
is
f
o
u
n
d
to
b
e
a
p
r
o
p
er
ch
o
ice
o
u
t
o
f
av
ailab
le
ac
tiv
atio
n
f
u
n
ctio
n
s
as
co
m
p
ar
ed
to
th
e
o
th
er
ac
tiv
atio
n
f
u
n
ctio
n
s
s
u
ch
as T
an
h
,
R
am
p
,
an
d
R
eL
U.
f)
T
h
e
b
ac
k
p
r
o
p
a
g
atio
n
is
d
o
n
e
ef
f
ec
tiv
ely
u
s
in
g
th
e
g
r
ad
i
en
t
d
ec
en
t
m
eth
o
d
an
d
th
e
c
h
ain
in
g
r
u
le,
as
co
m
p
ar
ed
to
th
e
o
th
er
m
et
h
o
d
s
.
T
h
e
r
esu
lts
o
b
tain
ed
f
r
o
m
th
e
ANN
m
o
d
el
co
m
p
ar
e
d
with
th
e
o
u
tp
u
t
f
r
o
m
th
e
E
T
AP
s
i
m
u
latio
n
.
T
h
e
p
h
ase
d
if
f
er
en
ce
b
etwe
en
s
en
d
in
g
e
n
d
an
d
r
ec
eiv
in
g
en
d
v
o
ltag
es
is
co
m
p
u
ted
u
s
i
n
g
th
e
ANN
m
o
d
el
th
r
o
u
g
h
a
n
u
m
b
e
r
o
f
iter
atio
n
s
an
d
co
m
p
ar
ed
with
th
e
o
u
tp
u
t
o
b
tai
n
ed
f
r
o
m
E
T
AP
s
im
u
l
atio
n
.
T
h
e
r
esu
lts
o
f
b
o
th
m
eth
o
d
s
ar
e
n
ea
r
ly
th
e
s
a
m
e
as f
u
r
n
is
h
ed
i
n
T
ab
le
2
.
T
ab
le
2
.
Sam
p
le
r
esu
lts
f
r
o
m
ANN
an
d
s
im
u
latio
n
m
o
d
els u
s
in
g
E
T
AP
X
1
r
a
d
i
a
n
s
X2
r
a
d
i
a
n
s
ANN
o
u
t
p
u
t
Y
O
u
t
p
u
t
f
r
o
m ET
A
P
si
m
u
l
a
t
i
o
n
3
.
1
4
3
.
1
4
0
.
0
0
1
0
3
.
1
1
3
.
2
1
-
0
.
0
9
9
9
-
0
.
0
9
9
8
3
3
4
1
7
3
.
3
1
3
.
2
2
0
.
0
8
8
0
.
0
8
9
8
7
8
5
4
9
0
.
5
0
3
1
.
1
4
-
0
.
5
7
9
-
0
.
5
7
8
5
9
0
9
1
4
3
.
1
2
1
.
5
5
0
.
9
9
8
1
3
.
2
2
1
.
5
8
0
.
9
4
5
0
.
9
4
2
.
9
9
1
.
4
3
0
.
9
9
8
0
.
9
9
9
9
4
1
7
2
1
.
2
0
0
.
5
9
0
.
5
7
5
0
.
5
7
2
8
6
7
4
6
0
.
8
9
0
.
2
1
0
.
6
2
4
0
.
6
2
8
7
9
3
0
2
4
2
.
7
8
1
.
2
0
0
.
9
9
7
0
.
9
9
9
9
5
7
6
4
6
4.
CO
NCLU
SI
O
N
T
h
e
PMU
p
r
o
v
id
es
s
y
n
ch
r
o
n
ized
d
ata
as
r
eq
u
ir
ed
f
o
r
W
AM
S
an
d
p
lay
s
a
cr
itical
r
o
le
in
m
o
n
ito
r
in
g
an
d
co
n
tr
o
llin
g
m
o
d
er
n
p
o
wer
s
y
s
tem
s
w
ith
in
s
m
ar
t g
r
id
s
.
F
o
r
th
is
p
u
r
p
o
s
e,
th
e
PMUs a
r
e
in
s
talled
at
v
ar
io
u
s
lo
ca
tio
n
s
in
th
e
tr
an
s
m
is
s
io
n
n
etwo
r
k
.
Mo
s
t
o
f
th
e
ap
p
licatio
n
s
p
r
esen
ted
h
er
e
in
th
is
p
a
p
er
ar
e
cu
r
r
en
tly
in
p
r
ac
tice
in
th
e
p
o
wer
s
ec
to
r
.
Fo
r
in
s
tan
ce
,
in
Ma
h
ar
ash
tr
a
s
tate
in
I
n
d
ia,
th
e
PMUs
ar
e
p
r
o
v
i
d
ed
at
2
1
lo
ca
tio
n
s
co
v
er
in
g
5
s
u
b
s
tatio
n
s
.
T
h
e
co
n
d
itio
n
o
f
m
ax
im
u
m
p
o
wer
tr
an
s
f
er
is
m
et
wh
en
th
e
p
h
as
e
d
if
f
er
en
ce
b
etwe
en
th
e
p
h
aso
r
s
o
f
s
en
d
in
g
en
d
an
d
r
ec
ei
v
in
g
en
d
v
o
l
tag
es
is
π
/2
r
ad
ian
s
.
T
h
e
AN
N
is
d
ev
elo
p
ed
as
p
h
ase
an
g
les
o
f
s
en
d
i
n
g
e
n
d
an
d
r
ec
ei
v
in
g
e
n
d
v
o
ltag
es
a
s
in
p
u
ts
,
wh
ich
ar
e
r
ec
eiv
ed
f
r
o
m
t
h
e
o
u
tp
u
t
o
f
PMUs
an
d
π
/2
r
ad
ian
s
as
tar
g
eted
o
u
tp
u
t.
Af
ter
u
n
d
er
g
o
in
g
s
ev
er
al
s
u
cc
ess
iv
e
iter
at
io
n
s
,
th
e
n
eu
r
al
n
etwo
r
k
was
f
u
lly
tr
ain
ed
.
T
h
e
ANN
m
o
d
el
b
ased
o
n
PMUs
d
etec
ts
m
ax
im
u
m
p
o
wer
tr
an
s
f
er
b
etwe
en
th
e
s
en
d
in
g
en
d
an
d
th
e
r
ec
eiv
in
g
en
d
th
r
o
u
g
h
v
o
ltag
e
an
g
les.
T
h
e
m
eth
o
d
ca
n
b
e
ex
ten
d
e
d
to
m
u
ltip
l
e
b
u
s
s
y
s
tem
s
.
T
h
u
s
,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
is
f
o
u
n
d
to
b
e
n
o
v
ice,
ac
cu
r
ate,
c
o
s
t e
f
f
ec
tiv
e,
an
d
f
ea
s
ib
le
f
o
r
s
m
ar
t g
r
id
.
ACK
NO
WL
E
DG
M
E
N
T
S
T
h
e
au
th
o
r
e
x
p
r
ess
es g
r
atitu
d
e
to
AI
SS
MS
I
n
s
ti
tu
te
o
f
I
n
f
o
r
m
atio
n
T
ec
h
n
o
lo
g
y
,
Pu
n
e,
I
n
d
ia
f
o
r
th
eir
en
co
u
r
a
g
em
en
t a
n
d
s
u
p
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