Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
9
, No
.
6
,
Decem
ber
201
9
, p
p.
4573
~
4579
IS
S
N:
20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v
9
i
6
.
pp4573
-
45
79
4573
Journ
al h
om
e
page
:
http:
//
ia
es
core
.c
om/
journa
ls
/i
ndex.
ph
p/IJECE
Detectio
n of p
ar
t
ial disch
arge
acou
stic emission
in p
ower transf
ormer
Yo
m
na O
. S
h
ak
er
Depa
rt
m
ent
o
f
E
le
c
tri
c
al E
ngin
eering,
Fa
y
oum
U
nive
rsit
y
,
Eg
y
p
t
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Feb
26
, 201
9
Re
vised
A
pr
2
4
, 2
01
9
Accepte
d
J
un
26
, 201
9
Parti
al
disch
arg
e
is
one
the
m
ost
important
fac
to
r
tha
t
leads
to
det
ero
r
at
io
n
and
fa
il
ure
of
the
power
tr
ansform
er
tra
ns
form
er.
Acousti
c
emiss
ion
det
e
ct
ion
is
eff
ec
t
ive
m
et
hod
t
o
eva
lu
at
e
the
hea
l
th
inde
x
of
the
power
tra
nsform
er
u
sin
g
ac
ousti
c
emiss
ion
(A
E)
sensor
s
for
par
tial
d
isc
har
ge
(PD
)
m
ea
surem
ent
is
conside
red
as
on
e
of
th
e
m
ost
pr
om
ising
te
chni
q
ues
to
de
tect
and
loc
a
li
z
e
PD
ac
t
ivi
ties
inside
the
tra
nsform
er
t
ank.
On
the
oth
e
r
hand,
AE
wave
s
suffer
from
high
at
te
nuati
on
and
ref
lecti
o
ns
while
tra
veli
ng
from
the
PD
source
to
the
AE
sensor.
T
he
m
odel
ing
of
the
AE
wave
ca
n
he
lp
t
o
under
stand
the
b
eha
vior
of
th
e
AE
PD
signal
during
it
s
tra
ve
l.
In
thi
s
pape
r,
the
AE
PD
sig
nal
is
assum
ed
to
be
com
posed
of
diff
ere
n
t
fre
quencie
s.
Thi
s
work
ai
m
s
to
inve
stig
ate
t
he
infl
u
enc
e
of
the
fre
qu
ency
v
al
ue
on
the
at
t
enua
t
ion and arri
va
l
t
ime
of
th
e
a
cousti
c
wav
e.
Ke
yw
or
d
s
:
Acousti
c em
iss
ion
Finit
e ele
m
ents
techn
i
qu
e
Ma
them
a
ti
cal
m
od
el
Partia
l disc
harge
Copyright
©
201
9
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Yo
m
na
S
hak
e
r
,
Dep
a
rtem
ent o
f
Ele
ct
rical
E
nginee
rin
g,
Fayoum
U
ni
ve
rsity
,
Kim
an
Fared,
Al Fayo
um
, Egy
pt
.
Em
a
il
:
y.shak
e
r@gm
ail.co
m
1.
INTROD
U
CTION
Mon
it
ori
ng
of
PD
is
one
of
the
too
ls
to
i
den
ti
fy
the
he
al
th
conditi
on
of
tra
nsfo
rm
e
r
ins
ulati
on
syst
e
m
.
Wh
e
n
PD
act
ivit
ie
s
are
i
niti
at
ed,
the
resu
lt
in
g
ene
rg
y
is
t
ra
ns
f
or
m
ed
int
o
dif
fer
e
nt
f
or
m
s
a
s
m
echan
ic
al
,
el
ect
rical
,
an
d
c
hem
ic
al
ener
gy
.
Am
on
g
al
l
PD
detect
ion
te
chn
i
qu
e
s,
t
here
is
a
gr
ow
i
ng
interest
in
the
PD
aco
ust
ic
detect
ion
m
et
ho
d
beca
use
it
ov
e
rc
om
es
seve
ral
disa
dv
antages
of
us
in
g
el
ect
rical
m
e
thods
li
ke
low s
us
ce
ptibil
it
y t
o
el
ect
ro
m
agn
et
ic
no
ise
and c
os
t ef
f
ect
iveness .
A
sign
i
ficant
effor
t
has
bee
n
exe
rted
to
unde
rstan
d
the
beh
a
vior
of
th
e
PD
aco
us
ti
c
w
ave
w
hile
travell
ing
f
ro
m
it
s
so
urce
t
o
the
se
nsor.
A
m
at
hem
atical
m
od
el
was
i
ntr
oduce
d
i
n
[
1]
by
so
lvin
g
t
he
a
coust
ic
wav
e
go
vernin
g
e
qu
at
i
on
s
th
r
ough
finite
el
e
m
ents
te
chn
i
que.
T
he
pr
ese
nt
ed
m
od
el
descri
bes
the
pr
op
a
gatio
n
of
P
D
ac
ousti
c
wav
e
i
n
the
whol
e
m
edium
(o
il
and
ste
el
)
with
c
on
t
our
plo
ts
to
s
how
t
he
at
te
nuat
ion
at
diff
e
re
nt
locat
ion
s
.
Mo
reove
r,
it
exa
m
ined
th
e
prop
a
gatio
n
pro
per
ti
es
un
de
r
the
ef
fect
of
changin
g
oil
de
ns
ity
as
the
tem
per
at
ur
e
incr
ease
d.
T
he
eff
ect
of
f
reque
ncy
on
aco
us
ti
c
PD
at
te
n
uati
on
was
stu
died
in
[2
]
by
ap
plyi
ng
pulse
s
with
dif
f
eren
t
widt
hs
.
As
t
he
f
re
qu
e
ncy
of
PD
pul
se
incr
eases,
this
re
su
lt
ed
in
highe
r
at
te
nu
at
io
n.
Th
is
un
de
rsta
nd
i
ng
of
the
P
D
be
hav
i
or
ca
n
be
ver
y
hel
pful
to
pr
edict
the
act
ual
fr
e
qu
e
ncy
r
ang
e
s
of
the g
e
ne
rat
ed
PD
b
a
sed
on
the r
ecei
ve
d
one. A
n
ap
proac
h i
n
[3
]
p
rese
nted
the PD
as a m
ul
ti
ple o
f
differen
t
sine
wa
ves
with
di
ff
e
ren
t
fr
e
quencies
a
nd
at
tem
pted
to
unde
rstan
d
the
i
nteracti
on
betwee
n
them
as
it
hap
pe
ns
in
PD
pu
lse
.
T
his
ap
proac
h
c
on
si
ders
that
al
l
these
sine
wa
ves
will
travel
with
the
sam
e
velocit
y
wh
ic
h
is
no
t
accurate
because
each
f
reque
ncy
will
travel
with
dif
fer
e
nt
velocit
y
as
dis
cusse
d
by
re
fe
ren
ce
[4
]
.
It
ha
s
been
m
entioned
t
hat
each
f
reque
nc
y
com
po
nen
t
of
the
P
D
wa
ve
will
travel
with
di
ff
e
ren
t
vel
ocity
and
hen
c
e
will
arr
ive
t
o
the
ta
nk
wall
at
diff
e
ren
t
tim
e
wh
ic
h
will
le
ad
to
a
hig
he
r
de
gr
ee
of
distort
ion
of
the
rec
ei
ved
PD
wa
ve.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
9
, N
o.
6
,
Dece
m
ber
201
9
:
4573
-
4579
4574
The
a
uthor
co
ns
ide
r
tw
o
fac
tors
t
hat
will
infl
uen
ce
the
a
coust
ic
wa
ve
at
te
nu
at
io
n
a
nd
disp
e
rsion
.
The
at
te
nuat
io
n
will
be
m
uch
gr
eat
er
f
or
t
he
high
f
re
qu
e
nc
y
com
po
nen
t
t
han
t
he
lo
w
f
re
qu
e
ncy
com
ponen
ts
.
Also
,
t
he
velo
ci
ty
of
high
f
r
equ
e
ncy
will
be
higher
t
han
t
he
lo
wer
one
wh
ic
h
will
res
ult
in
m
or
e
disp
ersi
on.
These t
wo ef
fe
ct
s w
il
l be c
ombine
d
to
get
her
to full
y u
nd
e
rst
and the
be
hav
i
or of the
aco
ust
ic
PD
wav
e
[4
]
.
Fr
om
the
pr
evio
us
disc
us
si
on
it
is
app
ar
ent
that
there
are
seve
ral
f
act
or
s
that
wi
ll
influ
enc
e
the
acoust
ic
wav
e
sta
rtin
g
fr
om
the
instant
of
occ
urr
ence
ti
ll
it
re
a
ches
the
tra
ns
f
or
m
er
wall
ta
nk
.
These
fact
or
s
are:
changin
g
of
velocit
y
of
the
PD
ac
ousti
c
sign
al
due
to
the
fr
e
quen
cy
as
well
as
the
change
in
the
at
te
nu
at
ion
of
the
dif
f
eren
t
f
reque
nc
y
co
m
po
ne
nts
in
the
PD
wa
ve
.
In
this
pa
pe
r,
the
pro
pa
gation
of
acoust
ic
wav
e
in
the
tra
nsfo
rm
er
oil
insu
l
at
ion
syst
em
will
be
in
vestigat
ed
c
onside
r
ing
t
ho
se
fact
or
s
t
hat
influ
e
nce
it
s
pro
pag
at
io
n
by
pr
ese
nting
a
m
at
he
m
at
ic
a
l
m
et
ho
d
that
will
be
so
lv
ed
by
f
i
nite
el
e
m
ents
te
chn
iq
ue
t
o de
te
ct
the freque
ncies
of
t
he wa
ve
acc
op
m
pin
e
d wit
h
thei
r veloci
ti
es.
2.
MA
TE
RIA
L
S
AND MET
H
ODS
2.1.
Part
i
al
disch
ar
ge
m
od
el
in
g
The
P
D
si
gnal
can
be
c
onsid
ered
a
s
a
po
i
nt
source
of
ac
ousti
c
wa
v
e
with
a
ver
y
s
hort
durati
on
in
the
ultras
on
ic
range
f
r
om
20
kH
z
t
o
1M
H
z
[2
,
5].
T
he
exact
sh
a
pe
of
t
he
pressu
re
wav
e
res
ulti
ng
from
the P
D
is
not k
now
n,
but i
t i
s
us
ua
ll
y assum
e
d
to
b
e
a
pu
lse
as d
e
picte
d
i
n Fi
gure
1 [2,
6].
Figure
1. A
ty
pi
cal
w
ave
form
f
or the
P
D
s
our
ce
The
ac
ou
sti
c
wav
e
pro
pa
gation
is
eval
uate
d
by
s
olv
in
g
pa
rtia
l
diff
er
ent
ia
l
equ
at
ions
(
PD
E
)
us
i
ng
finite
el
e
m
ent
te
chn
iq
ue.
T
he
sta
ndar
d
pa
rtia
l
diff
ere
nt
ia
l
equ
at
ion
t
hat
gove
rns
the
pro
pa
gatio
n
of
an
ac
ousti
c w
a
ve wit
hin
2
-
D
ho
m
og
e
neous
m
edia is give
n by
[5
,
7]:
2
2
−
2
[
2
2
−
2
2
]
=
(
−
)
(
−
)
(
)
(1)
Wh
e
re
P
is
t
he
press
ur
e
wa
ve
fiel
d
i
n
Pa
,
t
i
s
the
ti
m
e
in
sec,
C
is
t
he
ac
ousti
c
wa
ve
vel
ocity
in
m
s
-
1
,
and
is
the
Di
rac
Delt
a
f
un
ct
io
n
a
ss
ociat
ed
with
t
he
posit
ion
of
t
he
P
D
source
.
In
this
pa
per
,
i
t
is
assum
ed
that
the
ste
el
ta
nk
dim
e
ns
io
n
is
100cm
×100cm
,
the
transfo
rm
er
oil
den
sit
y
is
89
9
kg/m
3
and
the
PD
source
is
ass
um
e
d
to b
e
25 cm
awa
y from
the w
a
ll
as sh
own
i
n Fi
gure
2.
The
ar
rive
d
ac
ou
sti
c
wa
ve
at
sensor
(
S1)
lo
cat
ion
ass
um
in
g
the
P
D
sour
ce,
as
show
n
i
n
Fig
ur
e
1,
is
de
picte
d
i
n
Figure
3.
T
he
m
axi
m
u
m
peak
value
of
t
he
wav
e
ca
n
be
c
on
si
der
e
d
as
a
resu
lt
of
the
di
rect
oil
path
for
the
r
ec
ei
ved
wav
e
a
nd
he
nc
e
the
a
rri
val
tim
e
of
the
peak
value
c
an
be
c
onside
r
ed
as
an
act
ual
arr
ival
tim
e
fr
om
the
sp
eci
fied
po
sit
i
on
of
P
D
sour
ce.
It
can
be
unde
rstoo
d
fro
m
Figu
re
1
an
d
Fig
ur
e
3
that
sever
al
changes
happe
ned
t
o
the
wa
ve
duri
ng
it
s
pro
pag
at
io
n
in
the
oil
li
ke
ref
l
ect
ion
,
at
te
nu
at
ion
an
d
cha
nge
of
fr
e
qu
e
ncy.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Detect
ion
of
parti
al
disch
arg
e a
c
ousti
c emis
si
on
in
powe
r t
ra
nsf
ormer
(
Y
omn
a O.
Sh
aker
)
4575
Figure
2. Sc
he
m
at
ic
v
ie
w
f
or
acoust
ic
w
a
ve pr
opagati
on
Figure
3.
Ty
pi
cal
r
ecei
ve
d
ac
ou
sti
c
wa
ve
2.
2
.
Frequency
spectrum o
f
pa
rtial discharg
e
The
m
easur
e
d
PD
is
com
posed
of
di
ff
e
rent
fr
e
qu
e
ncies.
A
ty
pi
cal
A
E
PD
si
gn
al
m
ea
su
re
d
us
i
ng
the
set
up
de
pic
te
d
i
n
Fig
ur
e
4
is
sh
own
i
n
Fi
gure
5
(
a
)
.
Det
ai
ls
about
the
s
et
up
ca
n
be
found
in
[8
]
.
T
he
input
wav
e
co
ns
ist
s
of
a
group
of
fr
e
qu
e
ncy
c
ompone
nts
wh
ic
h
decays
a
t
dif
f
eren
t
rates
[4
]
.
Fig
ur
e
5
(
b
)
s
hows
the
fr
e
qu
e
ncy
sp
ect
r
um
of
the
received
ac
ousti
c
wav
e
that
ran
ge
s
from
5
0
-
250
kHz.
I
nst
ead
of
in
vestigat
in
g
the
w
hole
pu
ls
e,
pu
re
si
ne
w
aves
with
50
kHz,
150
kHz
a
nd
25
0
kH
z
w
il
l
be
ap
plied
as
a
si
ng
le
s
ou
rce
of
acoust
ic
w
a
ve t
o
s
how h
ow
t
he
syst
e
m
w
il
l
respond
t
o
eac
h i
nd
i
vidual f
re
qu
e
ncy c
om
po
nen
t.
Figure
4.
O
veral
l sy
stem
setup
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S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
9
, N
o.
6
,
Dece
m
ber
201
9
:
4573
-
4579
4576
(a)
(b)
Figure
5.
AE
m
easur
ed
P
D
s
ign
al
,
(a) t
im
e
do
m
ai
n
sig
nal
m
easur
ed
at S
1,
(b) fre
qu
e
ncy s
pectr
um
o
f
the
m
easur
ed
AE
PD
si
gn
al
3.
RESU
LT
S
A
ND AN
ALYSIS
3.1.
Wave
attenu
ati
on w
ith indi
vidu
al f
re
que
ncy
c
om
ponen
ts
As
pr
e
viously
addresse
d,
t
he
input
press
ure
was
co
ns
id
ered
a
s
a
pul
se
that
co
ntains
a
lot
of
fr
e
qu
e
ncy
co
m
po
nen
ts.
H
e
nce,
to
un
der
s
ta
nd
the
be
ha
vior
of
the
w
ho
le
A
E
PD
pu
lse
,
the
be
ha
vior
of
ind
ivi
du
al
fr
e
quencies
(
50,
150
a
nd
250
kHz)
will
be
st
udie
d.
T
he
in
div
i
du
al
fr
e
quency
com
po
ne
nts
will
be
tracke
d
at
dif
f
eren
t
distances
from
the
P
D
s
ource
t
o
get
th
e
val
ue
of
thei
r
at
te
nuat
io
n.
I
t
is
ve
ry
im
po
r
ta
nt
to
no
ti
ce
t
hat
the
v
al
ue
of
t
he
s
ound v
el
ocity
w
il
l
be
cha
nged
accordin
g
t
o
t
he
freq
ue
ncy
[
4].
T
he
velocit
y varies
betwee
n
1000
m
/s
fo
r
50
kHz
a
nd
reac
he
s
2700
m
/s
fo
r
250
kHz.
This
var
ia
ti
on
in
ve
locit
y
oc
curred
as
a
resu
lt
of
the
cha
ng
e
i
n
the
ac
ou
sti
c
i
m
ped
ance
ac
cordin
g
to
the
fr
e
qu
e
ncy
of
the
pr
e
ssur
e
so
urce.
Figure
6
s
how
s
the
trace
of
a
50
kHz
f
reque
ncy
com
po
ne
nt
in
oil
at
the
or
igin
locat
io
n,
5cm
,
and
15
c
m
fr
om
the s
ource.
(a)
(b)
(c)
Figure
6
.
The
trace
of
t
he 50
kH
z
freq
ue
ncy com
po
ne
nt as
a f
un
ct
io
n of di
sta
nce
,
(a)
The
P
D
s
ource
(
pure
sine
50 kHz
wa
ve)
,
(b) 5 cm
f
ro
m
so
urce
,
(c
) 15
c
m
f
ro
m
the s
ource
Evaluation Warning : The document was created with Spire.PDF for Python.
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t J
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Detect
ion
of
parti
al
disch
arg
e a
c
ousti
c emis
si
on
in
powe
r t
ra
nsf
ormer
(
Y
omn
a O.
Sh
aker
)
4577
The
wa
ve
is
assum
ed
to
pro
pag
at
e
with
a
sp
ee
d
of
1000
m
/s
and
the
am
pl
it
ud
e
of
t
he
first
pea
k
of
the
wa
ve
dec
r
eased
to
a
bout
6%
at
15
c
m
fr
om
it
s
or
iginal
m
agn
it
ud
e
at
the
sou
r
ce.
Fig
ur
e
7
s
hows
the
relat
io
n
be
tween
t
he
pea
k
value
of
the
wa
ve
a
nd
the
travell
ed
dist
ance
from
the
source
at
di
fferent
fr
e
qu
e
ncies
(
50,
150,
250
kHz).
It
is
evi
den
t
that
the
cha
nge
in
the
wa
ve
a
tt
enu
at
io
n
due
to
fr
e
quency
c
hange
is
no
t
sig
nific
ant
at
s
hort
di
sta
nces
f
ro
m
the
s
ource
(up
to
5cm
).
H
ow
e
ve
r,
at
l
onge
r
distances
,
m
or
e
at
te
nu
at
io
n
is
evide
nt
in
the
higher
f
re
qu
e
ncy
com
po
ne
nt
s.
Su
c
h
cha
nge
in
the
at
te
nu
at
io
n
rate
be
tween
the d
i
ff
e
ren
t
frequ
e
ncy c
om
po
ne
nts
will
inf
l
uen
ce
the
final
sh
a
pe of
t
he re
cei
ved
wa
ve.
Figure
7. The
value o
f
at
te
nu
at
ion
at
dif
fer
e
nt freq
ue
ncies
(50, 1
50, 2
50 kHz)
w
it
h dist
a
nce
3.2.
Effect
of
th
e
d
ifferen
t AE fr
equenc
y
c
omponen
ts veloci
ties o
n
the P
D
l
oca
li
z
at
io
n
In
add
it
ion
and
as
a
resu
lt
of
the
chan
ge
in
the
velocit
y
du
e
to
the
var
ia
ti
on
of
the
fr
equ
ency,
the
ti
m
e
arr
ival
of
each
fr
equ
ency
com
po
nen
t
wil
l
be
diff
eren
t.
This
m
eans
that
the
hig
her
fr
equ
ency
com
po
nen
ts
will
reach
the
transf
or
m
er
ta
nk
wall
bef
or
e
the
low
fr
equ
ency
com
po
nen
ts
and
this
will
resu
lt
in
fu
rther
distor
ti
on
in
the
sh
ape
of
the
received
acou
sti
c
sign
al
.
To
dem
on
strat
e
the
eff
ect
of
fr
equ
ency
com
po
nen
t
sp
eed
on
ti
m
e
arr
ival,
a
new
inp
ut
fu
nction
will
be
inv
est
igate
d
thro
ug
h
the
pr
op
os
ed
m
od
el
with
a
new
locat
io
n
fo
r
the
senso
r
(at
80
cm
fr
om
the
so
ur
ce).
The
inp
ut
fu
nction
as
dep
ic
te
d
in
Figu
re
8
can
be
con
sidered
as
a
m
ulti
ple
of
sine
wav
es w
it
h
diff
eren
t am
plit
ud
es and
d
iffer
ent f
req
uen
ci
es as f
ollow
s:
30 sin
50 k
Hz +
50 s
i
n 150 k
Hz
+
20 si
n
250 kH
z
(2)
Figure
8.
I
nput
w
a
ve wit
h
m
ulti
ple f
re
qu
e
nci
es
It
is
im
po
rtant
to
stu
dy
the
e
ff
ect
of
velo
ci
ty
changin
g
on
the
ar
rival
ti
m
e
as
a
res
ult
of
fr
e
quen
cy
changin
g.
Fir
s
t,
it
will
be
as
su
m
ed
that
al
l
fr
e
quen
ci
es
will
travel
with
a
co
ns
ta
nt
ve
locit
y
of
14
00
m
/s.
As
a
res
ult
an
d
as
sho
wn
in
Fig
ur
e
9,
the
arr
i
val
ti
m
e
fo
r
the
pea
k
va
l
ue
of
t
he
rec
ei
ved
AE
P
D
sign
al
is 5
84 µs.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
9
, N
o.
6
,
Dece
m
ber
201
9
:
4573
-
4579
4578
On
t
he
oth
er
ha
nd,
by
us
in
g
t
he
sine
wa
ves
separ
at
el
y
wit
h
di
ff
e
ren
t
vel
ociti
es,
the
20
sin
25
0
kHz
com
po
ne
nt
in
(
2
)
will
travel
with
t
he
highe
st
velocit
y
(
27
00
m
/s).
T
his
m
eans
that
t
he
hi
gh
est
f
reque
ncy
will
arr
ive
first
c
om
par
ed
to
the
oth
e
r
f
reque
ncies
an
d
the
real
arr
ival
ti
m
e
of
the
input
wav
e
can
be
co
ns
id
ered
a
s
the arr
iv
al
tim
e
o
f
the h
i
gh
e
st fr
e
qu
e
ncy com
pone
nt in
th
is i
nput.
Fig
ure 1
0
sho
ws
the r
e
cei
ved
ac
ou
sti
c
w
ave
du
e
to
250
kH
z
com
po
ne
nt
a
nd
it
s
ar
rival
t
i
m
e
wh
ic
h
is
297µs
c
an
be
con
sidere
d
a
s
the
ar
rival
ti
m
e
f
or
the
w
ho
le
wa
ve
descr
i
bed
by
(
2
)
.
S
uc
h
cha
nge
in
the
a
rr
iva
l
tim
e
will
resu
lt
in
a
chan
ge
i
n
the
cal
c
ulate
d
P
D
locat
ion
an
d further
d
e
f
or
m
at
i
on of t
he
recei
ved AE
P
D
si
gnal
.
Figure
9.
The
re
cei
ved
aco
us
ti
c w
a
ve
at
80
c
m
f
ro
m
the s
ource
with
constant
veloc
it
y
Figure
10.
T
he
r
ecei
ve
d
ac
ou
sti
c w
ave
due t
o
250 k
Hz
c
om
po
ne
nt
on
ly
4.
CONC
ULSI
O
N
The
ou
t
pu
t
ac
ou
sti
c
wav
e
re
cei
ved
by
the
sens
or
ca
n
be
analy
zed
us
in
g
it
s
fr
e
qu
e
ncy
com
po
ne
nts
.
Each
fr
e
qu
e
nc
y
com
po
ne
nt
will
travel
wit
h
di
ff
e
ren
t
vel
ocity
and
he
nc
e
reach
the
s
ens
or
with
dif
fer
e
nt
arr
ival
ti
m
e.
More
ov
e
r,
the
at
te
nu
at
ion
of
each
c
om
po
nen
t
inc
reases
with
the
val
ue
of
f
reque
nc
y
an
d
travell
ed
distance.
By
rec
ollec
ti
ng
al
l
fr
e
quency
c
om
po
ne
nts,
the
disto
r
ti
on
of
the
rec
ei
ved
ac
ousti
c
wave
cou
l
d be c
om
plete
ly
u
nd
e
rstood an
d
t
he
lo
ca
ti
on
ca
n be
pr
e
ci
sel
y detec
te
d.
ACKN
OWLE
DGME
NT
This
work
wa
s
m
ade
po
ssi
bl
e
by
NP
R
P
grant
5
-
044
-
2
-
016
f
ro
m
Qatar
Nati
onal
Re
s
earch
Fun
d
(a m
e
m
ber
o
f
Qatar
Fou
nd
at
i
on). The
stat
em
ents m
ade h
erein a
re sole
ly
the r
es
ponsi
bili
ty
o
f
t
he
a
uthor
s.
REFERE
NCE
S
[1]
S.
A.
As
h
raf
,
e
t
al.
,
“
3
-
D
Sim
ula
ti
on
and
Model
i
ng
of
Acousti
c
Signal
s
from
Pa
rti
al
Discha
rg
e
Acti
vity
”
,
Annu
al
Re
port
Con
fe
ren
ce
o
f El
e
ct
rica
l
I
nsulati
on
and
Di
el
e
ct
ric
Ph
enome
na
,
2009
,
pp
.
6
19
-
622.
[2]
P.
Kundu,
et
a
l
.
,
”
Sim
ula
ti
on
a
nd
Anal
y
sis
of
Acoustic
W
ave
Propaga
ti
ng
du
e
to
Partial
Disc
har
ge
Act
ivi
t
y
”
,
Annual
Re
port
C
onfe
renc
e
of
E
lectric
al
Insulat
io
n
and
Die
lectric
Phe
nomena
,
200
6
,
pp
.
607
-
610
.
[3]
D.Wotzka
,
T. B
ocz
ar
,
and
P
.
Fra
cz
,
“
Mathe
m
at
i
c
al
Model
and
Nu
m
eri
ca
lAna
l
y
s
is
of
AE
W
ave
Ge
ner
ated
b
y
Part
ial
Discha
rge
,
”
Act
a
Phy
si
ca Pol
on
ic
a
A
,
v
ol.
120,
n
o.
4
,
pp
.
767
-
77
1.
[4]
L.
E.
Lundgaar
d,
“
Parti
a
l
d
isc
har
ge.
XIV
.
Ac
oustic
Part
ial
D
ischa
rge
Det
ec
t
i
on
-
Prac
tical
Applicati
on
,
”
IEEE
El
e
ct
rica
l
Insula
ti
on
Magazin
e
,
v
ol.
8
,
no
.
5
,
pp
.
3
4
-
42,
Sep
-
Oc
t
1992.
[5]
S.
M.
Marka
lo
us,
S.
Te
nb
ohl
en
and
K.
Feser,
“
Dete
c
ti
on
and
Loc
a
ti
on
o
f
Parti
al
Disch
arg
es
in
Pow
er
Tra
nsform
ers
using
Acoustic
an
d
El
e
ct
rom
agnetic
Sign
al
s,”
IE
EE
Tr
ansacti
on
s
on
Diel
ectric
s
and
El
e
ct
rica
l
Insulati
on
,
vol
.
15,
no
.
6
,
pp
.
15
76
-
1583,
2008
.
[6]
M.
Koza
ko,
K.
Yam
ada
,
A.
Morita,
S.
Ohtsuka,
M.
Hikit
a
,
K.
Ka
shine,
I.
Nak
amura,
H.
Koide
“
Fundam
ent
al
stu
d
y
on
Parti
al
Disch
arg
e
Induc
ed
Ac
oustic
W
ave
Propaga
t
ion
in
Sim
ula
t
ed
Tra
nsfor
m
er
Com
posite
Insulat
ion
S
y
st
e
m
,
”
Proce
ed
ings
of
t
he
9th
In
te
rnati
onal
Confe
ren
ce
on
Properties
and
Appl
i
cat
ions
of
Dielec
tri
c
Ma
te
rials
,
Ha
rbi
n
,
China
,
Jul
2009
.
[7]
L.
Tsang
and
D.
Rada
r
,
“
Num
eri
cal
Evalua
ti
on
of
Tra
nsien
t
Ac
oustic
W
ave
for
m
due
to
Point
Source
in
a
Flui
d
Fill
ed
Bor
e
Hol
e
,
”
G
eoph
y
si
cs,
v
ol.
44
,
no
.
10
,
pp
.
1706
-
1720
,
Oc
t
1979
.
[8]
Mus
ta
fa
Harba
j
i
,
Khale
d
Shab
an
and
A
y
m
an
El
-
Hag,
“
Cla
ss
ifi
c
a
ti
on
of
Com
m
on
Parti
al
Disch
ar
ge
T
y
pes
in
Oil
-
Paper
Insulat
ion
Sy
st
em
Us
ing
Acoustic
Signals
,
”
IEEE
Tr
ans
act
ions
on
Dielec
tri
cs
and
El
e
c
tric
al
Insulat
ion
,
vol.
22
,
no
.
3
,
pp
.
1674
-
1683
,
Jun
2015
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Detect
ion
of
parti
al
disch
arg
e a
c
ousti
c emis
si
on
in
powe
r t
ra
nsf
ormer
(
Y
omn
a O.
Sh
aker
)
4579
BIOGR
AP
HI
ES OF
A
UTH
ORS
Yomn
a
O.
Sh
a
ker
was
born
in
Fa
y
oum
,
Eg
ypt
,
in
1976
.
Sh
e
recei
ved
th
e
B.
Sc.
degr
e
e
with
Honors
from
Fay
oum
Uni
ver
sit
y
in
1998
and
the
M.Sc
.
a
nd
Ph.D.
deg
ree
from
Cai
ro
Univer
sit
y
,
C
ai
r
o
,
Eg
y
pt
,
in
20
03,
and
2010
r
espe
ctively
.
S
he
is
an
assistan
t
profe
ss
or
i
n
the
El
e
ct
r
ic
a
l
E
ngine
er
ing
Depa
rtment,
Fa
y
ou
m
nive
rsit
y
,
Eg
y
pt
and
a
visit
i
ng
schola
r
in
Am
eri
ca
n
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