In
d
o
n
e
sian
Jou
r
n
al of
Ele
c
tr
i
c
a
l
En
g
in
e
erin
g
a
n
d
C
om
pu
t
er S
c
ien
ce
Vol.
14, No.
1, April 2019,
pp.
219~229
ISSN: 2502-
4752,
DOI
:
10.115
91/ijeecs.
v
14.
i
1
.
pp219-229
219
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/
i
j
eec
s
Frequency response of transform
er winding to investig
ate the
influe
nce of RL
C
S.
A
l
-
A
m
er
i
1
,
M. F. M
.
Yousof
2
,
N
o
rh
a
f
i
z
A
z
i
s
3
,
S.
A
v
i
n
a
s
h
4
,
M. A
. Tali
b
5
,
A
li. A
.
Sa
lem
6
1,
2
,
6
Dep
a
rt
m
e
nt
o
f
Elect
rical
a
nd Elect
ronic
E
nginee
r
i
n
g
,
U
niv
e
rsity
Tun
Hu
ssein
O
n
n
Ma
l
a
y
s
ia, M
al
ay
sia
3,
4
Centre of
E
l
ect
rom
a
gnet
i
c
and
L
i
ghtnin
g
P
ro
tecti
on
Research
(
CE
LP
),
M
a
l
aysia
3
In
stit
u
t
e o
f
A
dvanced
T
echn
o
l
o
g
y
(ITMA
), U
n
i
versi
t
i
P
u
t
r
a M
a
lay
sia,
M
alay
sia
5
T
N
B Research
, K
a
j
ang
,
S
elan
go
r, M
a
l
ay
si
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Sep
2
7
,
2
018
Re
vise
d N
ov
26,
201
8
A
c
c
e
pte
d
D
ec 7,
201
8
F
r
equ
e
ncy
resp
o
n
s
e
m
easu
r
emen
ts
a
re
u
sed
f
o
r
pow
er
t
ran
s
f
o
rme
r
wi
ndi
ng
f
a
il
ures
d
etectio
n.
T
h
e
v
ari
a
ti
on
b
e
tw
een
f
re
qu
ency
r
es
po
nses
i
n
d
i
cate
m
echan
ical
c
han
g
e
s
in
t
h
e
t
ran
s
fo
rm
er
w
in
d
i
ng
.
O
n
e
m
e
t
hod
t
o
i
n
v
e
stigat
e
wi
ndin
g
f
ail
u
res
in
t
ran
s
f
o
rm
er
i
s
t
o
d
evelo
p
a
r
el
iab
l
e
circu
i
t
model
which
can
s
im
ulate
t
h
e
f
r
equ
e
ncy
resp
o
n
s
e
o
f
an
a
ct
ual
w
i
ndi
ng.
T
h
e
m
ain
rea
s
on
to
u
se
t
h
e
m
od
e
l
i
s
be
c
a
use
it
is
e
x
p
e
n
sive
t
o
c
r
e
a
t
e
da
ma
g
e
s
o
n
an
a
ctual
wi
ndin
g
.
This
p
aper
p
ro
pos
es
n
-s
tag
e
s
circuit
lad
d
er
n
et
wo
rk
t
o
s
im
u
l
ate
th
e
resp
on
se
o
f
a
windi
ng
w
h
i
ch
h
as
u
n
i
qu
e
design
.
It
p
res
e
nts
a
ne
w
t
echn
i
qu
e
to
calcu
lat
e
t
h
e
r
esi
s
t
a
nce,
i
nduct
a
nce
and
c
a
p
aci
tan
ce
of
t
he
win
d
i
ng.
Th
en,
the
relation
sh
ip
b
e
t
ween
t
he
R
LC
p
a
r
am
et
ers
an
d
t
h
e
f
r
eq
u
ency
resp
on
se i
s s
t
u
d
ied.
T
he w
in
di
ng cho
s
en
i
n
th
is
inves
tig
a
t
i
o
n
i
s
a
sin
g
le
p
h
a
se
3
3
k
V
t
r
a
ns
form
e
r
w
in
ding
.
The
simu
la
te
d
fre
q
ue
n
c
y
re
spo
n
se
w
as
com
p
a
r
ed
with
t
he
m
easured
r
es
po
ns
e
t
o
v
erif
y
t
h
e
pro
p
o
s
ed
m
od
el.
T
h
e
m
o
del
can
g
i
v
e
a
c
o
m
p
r
e
h
e
n
s
i
v
e
u
n
d
e
r
s
t
a
n
d
i
n
g
a
b
o
u
t
t
h
e
e
f
f
e
c
t
o
f
R
L
C
p
a
r
a
me
te
r
s
o
n
th
e f
r
equ
e
ncy
re
spo
n
s
e
.
K
eyw
ord
s
:
FRA
La
dd
er n
et
wo
r
k
Tra
n
sf
orme
r
mode
l
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
Scien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Sal
e
m
Mg
amm
a
l
Awad
h
N
asser
Al
-
A
meri
,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
and
Ele
c
t
ron
i
c E
n
g
i
nee
r
in
g,
U
n
i
v
ersi
ti
T
un
H
u
ssei
n
O
nn
Ma
lays
ia,
86
4
00 Pa
rit Ra
ja,
Joh
o
r,
M
alays
i
a.
Em
ail:
mga
m
m
a
l10
@
gm
ail.
com
1.
I
N
TR
OD
U
C
TI
O
N
P
o
w
e
r
tra
n
sfor
me
rs
a
re
d
e
s
ig
ne
d
t
o
p
r
o
v
i
de
s
a
f
e,
r
eli
a
b
l
e
del
i
v
e
r
y
o
f
e
le
ctric
i
t
y
t
o
t
h
e
p
u
b
lic
a
n
d
con
s
um
ers.
H
ow
eve
r
,
ope
rat
i
n
g
t
he
t
rans
fo
r
m
er
a
t
ve
ry
h
i
g
h
l
o
a
d
i
ng
con
d
iti
on
t
o
m
e
e
t
t
h
e
de
ma
n
d
s
ca
n
ac
cele
r
ate
t
h
e
de
t
e
r
i
ora
t
i
o
n
o
f
t
he
u
n
it.
T
h
i
s
i
s
d
ue
t
o
t
h
e
i
n
c
r
ea
se
o
f
mec
h
a
n
ic
al
,
e
l
ec
t
r
i
c
,
and
th
erma
l
st
re
sse
s
du
ri
ng
t
h
e
o
p
e
ra
t
i
on
.
If
t
h
e
t
ran
s
fo
rmer
i
n
s
ul
a
t
i
o
n
c
o
n
d
i
t
i
on
s
deg
r
aded,
the
c
l
a
m
pin
g
p
r
e
ss
ure
c
o
ul
d
b
e
co
me
l
oo
s
e
t
hu
s
oth
e
r
f
a
i
l
u
r
e
s
a
c
c
ru
ed
.
Thi
s
w
oul
d
re
d
u
c
e
th
e
a
b
ili
t
y
o
f
a
tra
n
sfor
m
e
r
to
w
i
t
hst
a
nd
h
igh
curr
ent
fr
om
s
hor
t
circu
i
t
fa
u
lt.
I
n
a
d
d
i
t
i
on,
t
her
e
a
r
e
o
t
h
er
f
a
i
l
u
res
t
h
a
t
c
o
u
l
d
o
ccu
r
su
ch
a
s
mi
sh
and
l
in
g
th
e
un
it d
u
ri
ng transp
orta
t
i
o
n
, ear
t
h
qua
kes a
n
d eve
n
c
o
m
bu
st
ible
g
a
s ex
p
l
o
s
i
on [1]. F
or his re
a
son, it
is im
por
ta
nt
to co
n
duc
t
stu
d
i
es
t
o
i
n
ve
st
iga
t
e
the tra
n
sform
e
r
fail
ure
s
.
To
da
y,
t
he
F
RA
h
as
b
ec
ome
a
c
o
mple
me
nta
r
y
tec
h
ni
q
u
e
in
o
rde
r
t
o
i
n
v
es
tiga
t
e
t
h
e
t
r
a
n
sf
orme
r
fa
il
ure
s
.
The
F
R
A
m
e
a
s
ur
em
ent
ty
p
i
cal
l
y
p
e
r
form
s
at
a
f
r
e
que
nc
y
r
a
n
ge
(50H
z to 5MH
z)
[
1]
.
Ba
se
d
o
n
I
EEE
[2]
s
t
a
n
dar
d
a
n
d
CI
G
RE [
3]
i
t is ap
p
r
o
x
i
m
a
t
e
ly i
n the
r
a
n
g
e
of
20H
z
to 2MH
z
.
The F
R
A
t
est i
s
used t
o
de
t
ec
t
me
cha
n
ic
al
d
e
f
orm
a
ti
o
n
i
n
a
tra
n
s
f
orm
e
r.
I
t
is
a
ppl
ied
a
f
te
r
s
o
m
e
i
nc
i
d
en
ts
t
ha
t
ha
v
e
t
he
p
oss
i
bi
li
t
y
o
f
ca
usin
g
th
is
m
ec
han
i
ca
l
or
e
l
ectr
i
c
a
l
d
a
m
a
g
e
t
o
t
he
p
ow
e
r
t
r
a
ns
form
er
.
P
hysi
cal
c
han
g
e
s
in
t
he
r
e
s
is
t
a
nce
,
in
duc
ta
nce
a
n
d
ca
paci
ta
nc
e ne
tw
ork
of
t
he
t
r
a
nsfor
m
e
r
w
i
ndi
n
g
s
can
a
lt
er
t
h
e
m
a
t
h
e
ma
tic
al
t
ran
s
fe
r
func
t
i
on
.
The
tr
ans
f
er
f
u
n
ct
i
o
n
be
ha
vio
r
c
a
n
d
e
t
ec
t
a
wide
r
a
nge
o
f
me
cha
ni
ca
l
or
e
l
e
ctr
i
ca
l
cha
n
ge
s
i
n
t
he
e
le
c
t
rica
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2502-
4752
I
n
do
n
e
si
an
J
E
l
e
c
E
n
g
&
C
o
m
p
S
ci
, V
o
l
.
1
4
,
No. 1, April 2019 :
219 –
2
29
22
0
circ
u
i
t
r
e
prese
n
t
a
tio
n
o
f
t
he
t
rans
for
m
e
r
.
Besi
des
m
e
c
h
a
n
ica
l
d
amag
e
.
F
R
A
i
s
al
so
s
e
n
si
t
i
v
e
t
o
d
i
e
l
ec
t
r
i
c
cha
nge
s suc
h
a
s due
t
o a
g
i
n
g
w
h
i
c
h is n
ot c
a
t
eg
orize
d
as
a me
ch
anical f
a
u
l
t
[
4].
In
o
rd
er
t
o
i
nve
s
t
i
g
at
e
t
h
e
ef
f
e
c
t
o
f
w
i
n
d
in
g
f
a
il
u
r
e
s
o
n
F
R
A
m
easur
em
ent,
f
a
u
l
t
s
ne
e
d
t
o
be
a
pp
l
i
e
d
in
t
he
a
c
t
ua
l
w
i
n
d
i
n
g
.
H
o
w
e
v
e
r
,
t
his
i
s
d
i
f
f
i
c
u
lt
a
n
d
c
o
st
ly
b
e
cause
o
f
th
e
tra
n
sform
e
r
wi
nd
ing
st
re
ngt
h
an
d
the
pr
ice
of
t
r
a
nsfor
m
e
r
.
F
o
r
this
r
ea
so
n,
i
t
i
s
m
ore
prac
t
i
c
a
l
t
o
p
e
rfo
r
m
wi
ndi
ng
f
a
ilu
re
s
i
n
a
t
ran
s
fo
rmer
mode
l
re
prese
n
t
e
d
usi
n
g
su
i
t
a
b
l
e
s
oftw
a
r
e.
I
t
is
k
n
o
w
n
t
hat
tra
n
s
f
o
rme
r
w
i
n
di
ng
can
b
e
re
p
r
es
ent
e
d
by
elec
tr
ical
c
irc
u
it
w
ith
p
ar
am
et
ers
of
r
e
s
i
s
tanc
e,
i
nd
uc
tanc
e,
a
nd
c
a
p
ac
it
a
n
c
e
(
RLC).
Ther
efor
e,
it
is
i
mp
ort
a
n
t
t
o
b
e
a
ccu
rat
e
i
n
cal
cu
l
a
tin
g
wi
ndi
ng
p
a
r
amet
e
r
s.
T
h
e
re
a
re
v
a
r
io
u
s
t
ec
hn
i
ques
use
d
t
o
s
i
mul
a
t
e
t
h
e
trans
f
or
me
r
RLC
mo
de
l
s
u
c
h
a
s
fin
i
t
e
e
l
e
me
nt
m
et
ho
d
(
F
EM)
a
n
d
s
ta
te
s
pa
ce
m
o
de
l
.
A
s
tu
dy
c
o
n
duc
te
d
in
[
5]
u
se
d
fi
n
i
te
e
lem
e
nt
a
n
a
ly
si
s
to
c
a
l
c
u
la
t
e
t
he
i
n
d
u
ct
a
n
c
e
a
n
d
c
a
p
a
c
i
t
a
n
c
e
o
f
t
h
e
w
i
n
d
i
n
g
i
n
o
r
d
e
r
t
o
in
ves
tiga
t
e
t
h
e
w
i
nd
i
ng
de
fo
rm
atio
n.
I
t
w
a
s
fo
un
de
d
t
h
a
t
F
EM
g
i
ve
s
a
n
a
cc
urac
y
i
n
acc
ep
tab
l
e
l
i
mit
s
.
Also,
a
st
u
d
y
con
d
u
cte
d
i
n
[6]
t
o
s
tu
dy
a
r
adia
l
de
form
at
io
n
i
n
t
h
e
w
i
n
d
i
n
g
u
s
i
n
g
F
E
M
.
I
t
w
a
s
s
h
o
w
n
t
h
a
t
F
E
M
ca
n
prov
i
d
es
a
s
ig
nif
i
c
a
n
t
i
n
for
m
a
t
i
on
abo
u
t
t
he
c
ha
n
g
es
o
f
c
ap
ac
it
an
c
e
a
nd
i
ndu
c
t
a
n
ce
o
f
t
h
e
wi
n
d
in
g.
The
w
e
a
knes
s
i
n
F
E
M
is
t
hat
it
ob
ta
ins
o
n
l
y
ap
prox
im
ate
s
o
lu
ti
o
n.
I
n
a
d
d
i
t
i
on,
it
w
a
s
s
t
ated
i
n
[7]
t
h
at
F
EM
has
a
n
i
nhe
ren
t
e
rror.
O
n
t
h
e
o
t
her
ha
nd,
a
s
ta
te
s
pa
ce
mo
del
i
n
g
w
a
s
pr
esen
ted
i
n
[
8]
t
o
s
i
m
u
late
t
he
actu
a
l
me
asure
m
e
n
t
distri
b
u
t
i
on
t
ra
nsform
er.
It
w
a
s
f
o
u
nde
d
tha
t
it
is
e
a
s
y
t
o
r
ea
l
i
z
e
t
h
e
i
m
p
ac
t
of
v
ar
i
o
us
me
cha
n
ic
al de
f
orm
a
ti
o
n
s
o
n
t
he
t
r
a
ns
form
er F
RA
s
igna
t
u
re
.
I
n
t
h
i
s
pa
p
e
r,
a
l
um
pe
d
l
a
dder
netw
ork
m
o
d
e
l
is
p
r
e
se
nte
d
.
The
adv
a
n
t
ag
es
o
f
th
e
mo
d
e
l
a
r
e
t
h
at
t
h
e
p
h
y
s
i
cal
m
e
a
n
i
n
g
o
f
t
h
e
m
od
el
p
a
r
amet
ers
i
s
e
asy
t
o
i
den
tif
y
.
T
hi
s
mo
d
e
l
can
b
e
use
d
l
at
e
r
t
o
si
mu
l
a
t
e
vari
ous
w
i
n
ding
da
ma
ges.
F
or
e
xam
p
l
e
,
it
is
easy
to
i
den
t
i
f
y
th
e
d
i
sc
r
equire
d
t
o
a
pp
ly
t
he
f
a
u
l
t
i
n.
In
a
d
d
i
t
i
on,
i
t
is
m
o
r
e
p
hys
ic
al
t
o
m
a
ke
t
he
c
ha
nge
s.
T
he
n
o
v
e
l
t
y
i
n
t
h
i
s
s
t
u
dy
i
s
tha
t
t
h
e
w
i
n
di
ng
str
u
c
t
u
r
e
i
t
s
e
l
f
i
s
e
n
t
i
r
e
l
y
n
e
w
t
h
u
s
p
o
s
e
s
n
e
w
c
h
a
l
l
e
n
g
e
s
t
h
a
t
r
e
q
u
i
r
e
s
d
i
ffe
r
ent
ap
proa
ch
t
o
simu
la
t
e
t
he
fre
que
nc
y
respons
e.
Th
is
s
t
u
d
y
p
r
e
se
n
t
s
a
l
u
m
p
ed
p
a
r
am
eter
e
qu
i
v
ale
n
t
c
i
r
c
ui
t
m
ode
l
w
h
i
c
h
r
e
p
r
e
s
e
n
t
a
c
t
u
a
l
H
V
w
i
n
d
in
g.
T
he
w
in
d
i
n
g
g
e
o
me
try
w
a
s
ta
ken
from
a
n
ac
tua
l
t
ra
nsf
o
r
mer
H
V
w
i
n
di
ng
.
Th
en
,
t
h
e
RLC
p
a
ramet
e
rs we
r
e
ca
l
c
u
l
at
ed
u
si
ng
a
n
ew
m
e
t
ho
d
fo
r
th
e
n
e
w wi
n
d
i
n
g
s
truc
tur
e
. The sim
ul
ated
resp
ons
e show
s
an
a
p
p
rox
i
m
a
t
e
ly
s
im
i
l
a
r
w
hen
com
p
are
d
w
i
t
h
the
me
asu
r
ed
r
e
s
po
n
se.
Th
en
,
ch
a
n
g
e
s
i
n
t
h
e
R
LC
p
a
r
amet
e
r
s
are
app
lie
d
to
i
nve
st
i
g
ate
t
h
e
effe
c
t
on
the
r
e
sp
onse.
T
his
mod
el
can
a
l
s
o
b
e
u
sed
t
o
i
n
v
e
st
i
g
at
e
t
h
e
ef
fec
t
o
f
numbe
r
of
d
i
s
cs
o
n
the
re
sponse
.
N
ever
t
h
e
l
e
ss,
t
he
m
ain
p
u
rp
ose
o
f
t
h
is
s
t
u
dy
i
s
t
o
i
nve
st
iga
t
e
t
h
e
rela
tio
ns
hip
b
e
tw
e
e
n
the
le
vel
o
f
f
a
u
lt
-based
o
n
th
e
c
h
an
ge
o
f
wi
nd
in
g
resi
st
a
n
ce
,
ca
p
a
c
i
t
a
n
ce
and
in
duc
ta
nce
.
2.
HI
GH-FREQUENCY MODEL
I
NG OF
TRANS
FO
RMERS
Mo
de
l
i
n
g
t
he
h
i
g
h
fre
que
nc
y
re
sponse
of
t
r
a
nsform
er
w
in
din
g
h
a
s
a
c
erta
i
n
d
eg
re
e
of
c
o
m
p
l
exit
y
.
Th
is
i
s
d
u
e
t
o
t
he
a
rrange
me
nt
o
f
tra
n
sform
e
r
w
i
nd
ing
e
l
e
c
tr
ica
l
c
i
r
c
u
i
t
.
I
t
i
s
i
m
p
o
s
s
i
b
l
e
t
o
u
s
e
a
s
i
m
p
l
e
equ
i
vale
n
t
c
irc
u
i
t
t
o presen
t
the
tra
n
s
f
orm
e
r
w
i
n
d
in
g.
T
hi
s
is
beca
use
a
t
h
i
gher
fr
eq
ue
nc
ie
s
w
a
vele
ng
t
h
o
f
th
e
signa
l
s
a
re
c
ompar
e
d
w
i
th
t
h
e
transf
o
r
m
e
r
w
i
n
di
n
g
ge
o
m
e
t
r
y [9]
.
The
s
t
ep
s
sh
o
w
n
i
n
F
i
g
ur
e
1
a
r
e
fol
l
ow
ed
f
or
calc
u
la
t
i
n
g
t
he
h
i
gh
fr
eq
ue
nc
y
re
s
p
o
n
se
o
f
tra
n
sf
o
r
me
r
w
i
n
d
in
g.
T
he
f
irs
t
s
t
e
p
i
s
t
o
m
easure
t
h
e
w
i
n
d
in
g
ge
o
m
etry.
T
h
e
s
e
c
o
n
d
s
t
e
p
i
s
t
o
c
a
l
c
u
l
a
t
e
t
h
e
w
i
n
d
i
n
g
resista
n
ce
,
ca
pa
cita
nce
,
s
e
l
f
and
mut
u
a
l
i
n
duc
ta
nce
us
i
n
g
ce
rta
i
n
f
o
r
mu
las.
T
he
n,
t
he
c
alcu
la
te
d
re
si
sta
n
ce
,
se
ri
e
s
c
ap
ac
it
an
c
e
, s
e
l
f
an
d
mu
t
u
a
l
i
ndu
ct
a
n
ce a
r
e
e
n
t
e
red
in M
A
TLA
B to
c
alcu
la
te
t
he freque
nc
y r
e
spo
n
se.
M
o
de
l
i
n
g
F
r
e
que
nc
y
R
e
s
p
o
n
s
e
o
f
t
r
ans
f
o
r
m
e
r
w
i
n
d
i
n
g
Wi
n
d
i
n
g
g
e
o
m
e
t
r
y
RL
C
ca
l
c
u
l
a
t
i
o
n
Mo
d
e
l
s
i
m
u
l
a
t
i
o
n
W
:
c
o
n
d
u
c
t
o
r
w
i
d
t
h
h
:
c
on
d
u
c
t
or
h
e
i
gh
t
d
i
:
W
i
n
di
ng
i
n
n
e
r
r
a
d
i
u
s
d
o
:
W
i
n
di
ng
o
u
t
e
r
r
a
d
i
u
s
T
p:
I
n
s
u
l
a
t
io
n
t
h
ic
k
n
e
s
s
R
:
W
i
n
d
i
ng
r
e
s
i
s
t
a
n
c
e
L
:
S
el
f
a
n
d
m
u
t
u
al
i
n
d
u
c
t
a
n
c
e
C
:
S
e
r
i
e
s
C
ap
a
c
i
t
an
ce
s
i
m
u
l
a
t
e
d
/
c
a
lc
u
l
a
t
e
d
f
r
e
q
ue
nc
y
r
e
s
p
o
n
s
e
o
f
t
h
e
tr
a
n
s
f
o
r
m
e
r
w
i
n
d
in
g
F
i
gure
1. T
h
e
m
odel
i
ng s
t
eps
to c
alcu
la
te
t
he
freque
nc
y re
spo
n
s
e of
t
ra
n
s
fo
rmer
wi
n
di
ng
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesia
n
J
Elec Eng
&
C
o
m
p
S
ci
ISSN:
2502-
4752
Fr
equ
e
n
c
y resp
on
se
of
t
r
a
n
sfo
r
me
r
w
i
ndi
ng
t
o
i
n
v
e
stig
at
e th
e
i
n
fl
u
e
n
c
e of
RL
C
(S
.
Al
-Am
e
ri
)
22
1
2
.
1
. N-La
d
d
e
r Net
w
o
r
k
A
s
s
how
n
in
F
ig
ur
e
2
(
a
)
n-
st
a
g
e
of
l
a
dder
netw
or
k
me
t
h
o
d
i
s
a
w
e
ll-
k
n
o
w
n
m
e
t
ho
d
to
m
ode
l
the
tr
a
n
sf
or
m
e
r
w
i
nd
i
ng.
E
a
c
h
di
sc
o
f
t
h
e
w
i
nd
in
g
is
r
epr
e
sen
t
ed
b
y
r
esista
n
c
e,
c
a
p
a
c
ita
nce
,
a
nd
in
d
u
cta
n
ce
.
I
n
e
v
ery
dis
c
,
for
exa
m
p
l
e
D1
show
n
in
F
i
g
u
r
e
2(
a
)
c
ons
ists
o
f
se
r
i
es
i
n
duc
ta
nce
Ls
,
se
ries
c
a
p
ac
i
t
anc
e
Cs
,
se
ri
es resi
s
t
a
n
c
e
Rs
a
nd
gr
ou
nd
ca
paci
ta
nc
e
Cg
.
F
i
r
s
t
step
t
he
w
in
d
i
n
g
g
e
o
m
e
tr
y
w
a
s
m
e
a
s
ur
e
d
m
anua
l
l
y
suc
h
a
s
c
on
duc
t
o
r
geom
etr
y
a
nd
w
i
n
d
i
n
g
in
ner
and
o
u
t
e
r
r
adiu
s.
T
he
t
r
a
nsfor
m
er
w
as
a
ppr
o
x
im
ate
l
y
l
o
o
k
e
d
l
i
k
e
F
ig
ur
e2(
b
)
.
A
cc
or
di
ng
t
o
[
1
0
]
,
t
he
r
e
a
re
sever
a
l
t
ype
s
o
f
t
r
a
nsf
o
r
m
e
r
w
i
n
di
n
g
a
nd
h
a
ve
d
i
ffe
r
e
nt
w
ays
of
c
a
l
c
u
la
tion.
T
he
m
ain
t
ype
s
of
t
he
w
indi
n
g
ar
e
he
li
c
a
l
w
in
di
n
g
,
l
a
yer
w
i
n
d
i
n
g,
a
nd
disc
w
in
din
g
.
The
tr
ans
fo
r
m
er
s
el
e
c
t
e
d
in
th
i
s
s
t
u
d
y
i
s
d
i
s
c
w
i
n
d
i
n
g
.
Th
e e
q
u
i
v
a
l
e
nt
c
i
r
c
u
it
o
f th
e
di
sc
w
i
ndi
ng
t
r
a
n
s
fo
rme
r
f
o
r
n
-
s
t
ag
e l
a
dd
er n
et
wo
rk
i
s sh
o
w
n i
n
Fi
g
u
r
e
2
Fig
u
r
e
2
(
a).
I
n
o
rd
er
t
o
s
i
mu
l
a
te
t
h
e
t
ra
n
s
f
o
rmer
w
in
di
ng
f
requ
e
n
cy
r
espo
nse,
i
t
i
s
r
equ
i
re
d
t
o
ca
l
c
ul
at
e
t
h
e
to
t
a
l
se
ri
es
capa
c
i
t
an
ce
Cs
.
Thi
s
r
equ
i
re
d
t
o
c
alcu
la
te
t
h
e
c
apac
i
t
a
n
ce
i
n
b
etwee
n
t
urns
Ct
for
e
v
ery
disc.
In
t
he
m
e
a
n
t
ime
,
it
i
s
e
sse
nt
ia
l
t
o
c
a
l
c
u
la
te
t
he
c
a
p
ac
i
t
anc
e
in
b
e
t
we
en
d
i
s
cs
Cd
.
Afte
r
tha
t
,
ca
l
c
ul
at
e
th
e
se
ri
es
r
e
s
i
s
t
a
n
c
e
Rs
,
c
a
pa
cita
nc
e
to
t
he
g
r
o
un
d
Cg
,
c
o
ndu
ct
an
ce
Gs
,
self
a
n
d
m
ut
ua
l
i
n
d
u
c
t
anc
e
M
L
.
T
h
o
s
e
el
e
c
t
r
i
c
a
l
p
ara
m
e
t
ers
mu
st
b
e
ob
ta
i
n
ed
a
s
a
s
econ
d
s
t
e
p
t
o
s
i
m
u
l
a
t
e
t
he
f
r
e
q
u
e
n
cy
r
e
s
pon
se
o
f
th
e
tr
a
n
sf
or
m
e
r
w
i
n
d
i
ng.
(a)
(b
)
F
i
gur
e
2.
(
a)
N
-
s
tage
e
qui
va
le
n
t
l
um
pe
d
cir
c
u
i
t
f
o
r
the
sing
l
e
w
i
nd
i
n
g,
(
b)
the
3
D
o
f
s
i
n
g
l
e-
phase
w
i
n
d
i
n
g
[1
1]
2
.
2
. Series
Ca
pa
cita
n
c
e Ca
lcu
l
a
t
io
n
B
a
se
d
o
n
t
h
e
t
r
a
nsf
o
r
m
er
w
ind
i
ng
s
t
r
u
c
t
ur
e
as
s
h
o
w
n
i
n
F
i
gur
e
2
(b
),
t
he
c
a
p
ac
it
an
c
e
b
et
ween
t
h
e
c
ond
uc
tor
s
i
n
the
sam
e
d
isc
C
t
n
ee
ds
t
o
be
c
a
l
c
u
late
d
in
o
r
d
er
t
o
f
i
n
d
t
he
s
er
ie
s
ca
pa
cita
nc
e
.
At
t
h
e
s
ame
time
,
t
he
c
a
p
a
c
ita
nce
be
tw
ee
n
c
o
nd
uc
t
o
r
s
i
n
t
h
e
a
d
jac
e
nt
d
isc
C
d
(
c
a
pac
i
t
a
nce
be
tween
d
i
s
c
s
)
i
s
a
ls
o
c
a
lcu
l
a
t
e
d
.
The
ca
paci
tanc
e
betwe
e
n
t
wo
c
on
d
u
ct
ors
re
p
r
esen
ts
C
t
i
s
s
h
o
w
n
in
F
i
g
ur
e
3.
T
he
capa
c
i
t
anc
e
be
t
w
e
e
n
t
w
o
t
ur
ns
i
s
gi
ve
n
by
(
1
)
.
F
i
gur
e
3.
T
he
t
w
o
c
on
duc
t
o
r
s
d
i
a
gr
am
s
oi
led
line
t
h
e
f
i
r
s
t
con
d
uct
o
r
dote
d
l
i
n
e
t
h
e
seco
n
d
c
on
d
u
ct
or
[
1
2
]
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e
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E
l
e
c
E
n
g
&
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o
m
p
S
ci
, V
o
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.
1
4
,
No. 1, April 2019 :
219 –
2
29
22
2
(1)
Whe
r
e
the
L
i
s
the
le
ng
t
h
o
f
t
h
e
c
o
n
d
uc
tor
w
h
ic
h
re
prese
n
t
t
h
e
he
i
ght.
b
a
n
d
a
a
r
e
t
h
e
i
n
n
e
r
r
a
d
i
u
s
and
ou
ter
radi
us
o
f
the
o
u
t
e
r
a
nd
in
ne
r
c
onduc
tor
s
r
espe
ct
i
v
e
l
y
.
ε
o
i
s
per
m
itt
iv
it
y
o
f
t
h
e
f
ree
spac
e
whic
h
is
8.85
4
×
10
-12
a
n
d
ε
r
i
s
3.85
w
h
i
ch
i
s
t
h
e
r
e
la
t
i
v
e
p
erm
itti
v
ity
o
f
t
h
e
ins
u
l
a
tion
p
ap
er
l
o
c
ate
d
b
e
t
ween
t
h
e
o
ut
er
and
i
n
ner
co
n
duc
tors.
O
n
t
h
e
o
ther
h
a
nd,
t
he
c
a
p
aci
ta
nc
e
be
t
w
e
e
n
ad
j
ace
nt
d
i
s
c
s
a
s
i
n
F
i
gure
4
c
a
n
b
e
ca
l
c
u
l
a
t
e
d
by
(5)
w
h
i
c
h de
riv
e
d a
s
s
how
n i
n
(2), (3)
a
nd (
4
)
.
F
i
gur
e 4.
The
ca
p
aci
ta
nc
e i
n
b
e
t
ween
t
wo d
is
cs
(2)
(
3
)
(
4
)
W
h
ere:
(
5
)
W
h
ere:
d
i
s
th
e
d
i
st
ance
b
et
we
en
t
u
r
n
s
(
ac
c
ount
in
g
fo
r
fring
i
n
g
eff
e
c
t
)
.
d
i
a
n
d
d
o
a
r
e
t
h
e
i
n
n
e
r
a
n
d
o
u
t
e
r
diam
et
er
i
f
th
e
w
i
n
d
i
n
g.
F
igure
5
is
a
n
e
x
am
ple
o
f
a
n
e
q
u
i
va
l
e
n
t
ne
t
w
ork
o
f
t
w
o
d
i
s
cs
i
n
the
w
i
n
d
i
n
g
.
The
c
i
rc
uit
s
h
o
w
s
tha
t
C
t
i
s
co
nt
a
c
t
e
d
in
s
eri
e
s
wh
e
r
ea
s
t
h
e
C
d
a
re
i
n
par
a
ll
e
l
.
S
i
nce
C
t
f
or
e
ver
y
b
e
t
w
e
e
n
t
w
o
con
d
u
ct
ors
are
di
ffe
re
nt
d
ue
t
o
d
i
ffe
r
en
t
c
o
n
d
u
ct
or
l
e
ngt
h,
t
he
re
f
o
re
w
e
cal
c
ulate
a
l
l
C
t
a
nd
t
h
e
t
o
tal
is
con
s
i
d
ere
d
i
n ser
i
e
s
as
(6).
(
6
)
On the
o
ther
h
and,
t
h
e
t
o
t
a
l
c
apac
ita
nce
be
t
w
ee
n discs i
s
g
ive
n
a
s
(
7
).
1
2
(
7
)
S
i
nce
t
h
e
ca
pa
cita
nc
e
i
n
b
e
t
we
en
d
i
s
c
s
i
s
i
n
p
ar
al
le
l
a
s
s
how
n
i
n
t
he
e
qu
iva
l
e
n
t
c
i
r
c
ui
t
F
i
gur
e
5.
The
to
t
a
l
se
rie
s
capa
c
ita
nce
of
w
ho
le
w
i
n
d
i
n
g
c
a
n
b
e
ca
lc
ul
a
t
e
d
a
s
(8
).
H
o
w
ev
e
r
,
f
o
r
a
on
e
di
sc
t
he
t
otal
series
c
a
p
ac
ita
nce
c
a
n
b
e
ob
t
a
in
b
y
C
d
+ C
t
.
Rega
rd
i
n
g
to
t
h
i
s
pa
rt
i
c
ula
r
w
in
di
ng
in
t
h
i
s
st
ud
y
t
h
e
in
(
8)
c
an
gi
ve t
he
m
ost sim
i
l
a
r r
e
spo
n
se
c
ompa
red
w
ith
t
he
m
ea
sur
e
d
r
e
spo
nse [
13],
[14].
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
IS
S
N
: 2502-
47
52
Fre
que
ncy
res
p
o
n
se o
f
t
r
an
sf
orm
e
r wi
nd
in
g
to
i
n
v
e
s
t
i
ga
te
the
in
f
l
ue
nce
o
f
RL
C
(S.
Al
-
A
meri)
22
3
F
i
gur
e 5.
La
yout
o
f t
h
e
equ
i
v
a
len
t
c
apac
ita
n
ce
di
a
g
ram
n
e
t
w
ork
of t
he
w
i
n
d
i
ng
4
(
8
)
W
h
ere
t
h
e
C
dt
i
s
t
he
r
e
s
u
l
ta
nt
i
n
t
e
r-disc
c
a
pac
ita
nce.
I
n
add
i
tio
n,
t
he
re
i
s
al
so
c
ap
ac
it
a
n
c
e
t
o
the
g
r
ou
nd
C
g
.
In
t
h
i
s
st
udy
,
th
e
me
a
s
u
r
ed
t
ra
n
s
fo
rme
r
w
i
n
d
i
ng
d
o
not
h
av
e
c
apa
c
i
t
a
n
ce
t
o
the
gr
ou
n
d
s
in
ce
t
her
e
is
n
o
gro
u
nde
d ta
nk d
u
r
i
ng
th
e
m
ea
sur
e
m
e
nt
. There
ar
e
oth
e
r
e
le
ctrica
l pa
r
a
m
e
ters t
o
be
calc
u
la
t
e
d i
n
o
rde
r
to
si
m
u
late
t
he r
espons
e such
s
eries
resist
a
n
ce
R
s
, sel
f, a
n
d
mu
tu
al
i
ndu
ct
a
n
c
e
.
2
.
3
.
T
h
e
Se
ri
e
s
R
es
i
s
t
a
nc
e
C
a
l
c
ul
a
t
i
o
n
To
c
a
l
cu
la
te th
e
se
r
ies resis
t
a
n
ce o
f
t
he
w
in
di
n
g
, i
t
i
s re
qu
i
r
e
d
t
o
k
n
o
w
t
h
e
to
ta
l c
i
rcum
fer
e
nce
of
t
he
con
d
u
ct
or
.
Th
e
t
o
tal
circum
ference is given
i
n
2
.
(9)
Ω
/
m
(
1
0
)
F
r
om
(
10)
,
h
,
w
,
a
r
e
t
h
e
h
e
i
g
h
t
a
nd
w
id
th
o
f
t
h
e
co
ndu
ct
o
r
r
es
p
e
c
tiv
el
y
.
W
h
e
re
f
i
s
the
signal
fre
que
nc
y,
a
nd
a
re
t
he
p
erm
e
a
b
ili
t
y
a
nd
co
n
duc
t
i
v
i
t
y
o
f
t
h
e
con
duc
t
o
r.
O
n
t
h
e
o
t
h
e
r
h
a
n
d
,
t
h
e
con
d
u
cta
n
c
e
G
is a
m
a
trix w
hic
h
c
a
n
be
o
b
t
a
i
ne
d from
(11) w
here
is
t
h
e
i
n
sula
ti
on d
i
ss
ip
a
tio
n
fac
t
or
.
2
(
1
1
)
2
.
4
.
T
h
e
sel
f
a
n
d
Mu
t
ua
l Inducta
n
ce Ca
lcula
t
io
n
The
sel
f
a
nd
mut
u
a
l
in
d
u
c
t
anc
e
b
etw
e
e
n
t
urn
s
w
e
r
e
obt
a
i
ne
d fr
om
(
12), (13)
.
1
(
1
2
)
(
1
3
)
Where
L
km
i
s
the
mut
u
a
l
i
nd
u
c
tanc
e
be
tw
e
e
n
d
i
sc
k
a
n
d
d
i
s
c
m
.
r
i
s
t
h
e
a
v
era
g
e
ra
di
u
s
o
f
t
h
e
di
scs
and
z
i
s
t
h
e
ax
i
a
l
d
i
s
t
a
n
ce
be
twe
e
n
the
two
di
scs.
N
k
a
nd
N
m
a
r
e
t
he
n
u
m
be
r
of
t
urn
s
i
n
k
-
t
h
sec
tio
n
and
m
-th
sect
io
n
as
s
h
o
w
n
i
n
F
i
g
ure
6.
K
a
n
d
E
a
r
e
t
he
e
lli
pt
ic
i
nte
g
ra
l
s
o
f
the
fi
r
s
t
a
nd
sec
o
nd
kin
d
s.
F
or
se
lf-
in
duc
ta
nce
w
h
ere
:
k
=
m
,
z
i
s
ca
lcu
l
a
t
ed
b
y
z =
0
.
22
35×
(
h+w
).
A
ls
o,
h
1
a
n
d
w
1
a
r
e
a
l
i
k
e
t
o
h
2
a
nd
w
2
.
The
sel
f
i
n
duc
t
a
nc
e
for
t
h
e
L
km
m
a
t
r
i
x
is
r
ep
r
e
sent
in
g
the
dia
g
ona
l
e
l
em
en
ts
w
h
i
le
o
f
f
-di
a
go
na
l
el
ement
s
a
re
the
mut
u
a
l
i
nd
uc
t
a
nce
be
tw
e
e
n
disc
s.
I
n
this
s
t
u
d
y
,
the
v
a
lue
o
f
a
r
e
e
qua
le
d.
T
hi
s
is
b
e
cause
t
he
ave
r
age
ra
diu
s
o
f
t
h
e
se
ct
io
ns
a
re
t
he
s
a
m
e
.
T
he
v
a
l
ue
o
f
m
a
gne
tic
p
e
r
m
eabi
l
i
t
y
of
t
he
m
edi
u
m
is
4
1
0
.
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c
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&
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o
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o
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.
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,
No. 1, April 2019 :
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22
4
F
i
gure
6. The
ge
n
e
r
a
l
d
i
m
en
s
i
o
n
s o
f
t
he
w
i
n
di
n
g
di
s
c
s
3.
RESULT
S
A
N
D
ANALY
S
IS
3.1.
Measu
rem
en
t of th
e
Ac
t
u
a
l
Tr
an
sfo
r
mer
The
m
easure
m
e
n
t
w
a
s
c
ond
u
c
t
e
d
o
n
a
n
a
c
t
u
al
t
ra
nsf
o
rme
r
i
n
orde
r
t
o
v
e
r
i
f
y
a
n
d
c
o
m
p
a
r
e
w
i
t
h
t
h
e
deve
l
ope
d
m
o
del.
F
RA
m
eas
ure
m
e
n
t
w
a
s
p
e
rform
e
d
o
n
t
he
H
V
w
i
ndi
n
g.
A
ls
o,
i
t
is
p
erfor
m
e
d
from
20
H
z
t
o
2MH
z
.
The
tr
ansfer
f
unc
ti
on
o
b
ta
i
n
ed
b
y
the
ra
t
i
o
/
b
ase
d
on
CIG
R
E
re
porte
d
in
[
3]
.
The
m
e
a
s
urem
ent
co
nf
igur
a
tio
n
is
t
a
k
e
n
i
n
si
n
g
l
e
p
h
a
se
H
V
w
i
nd
i
n
g
a
s
sh
ow
n
in
F
igur
e
7.
T
his
me
asure
m
e
n
t
c
o
n
f
igur
at
ion
is
m
os
t
l
y
use
d
b
e
cause
i
t
pro
v
i
d
e
e
n
o
ug
h
infor
m
a
tion
t
o
a
na
lys
i
s
t
h
e
trans
f
or
me
r c
ondi
ti
o
n
.
F
i
gure
7.
F
RA
m
ea
sur
e
m
e
nt t
est c
o
nfig
urat
i
on
3.2.
Paramet
ers
C
alculati
on
on th
e M
e
asur
ed
Transf
o
rme
r
The
F
R
A
m
e
a
s
ur
em
ent
is
c
o
n
d
u
c
t
ed
on
a
s
i
ng
le
pha
se
3
3
k
V
H
V
w
i
n
d
i
ng.
T
o
c
a
l
c
u
la
te
e
le
ctr
i
cal
p
a
ramet
e
rs
o
f
th
e
t
e
st
ed
t
ra
n
s
fo
rme
r
,
t
h
e
sp
eci
fi
cat
ion
s
o
f
t
h
e
g
e
o
me
t
r
i
c
a
l
s
uc
h
a
s
d
i
m
en
si
on of t
he co
n
duc
t
o
r
and
th
ic
k
n
ess
of
t
he
i
n
s
u
l
a
tio
n
a
r
e
c
a
lcu
l
a
t
e
d
.
The
f
u
ll
w
i
n
d
i
n
g
c
o
n
s
i
s
t
s
o
f
9
6
d
i
s
c
s
.
I
n
e
v
e
r
y
d
i
s
c
,
t
h
e
r
e
a
r
e
fi
ve
t
urns.
In
e
very
t
ur
ns
t
he
re
a
re
s
i
x
c
o
n
d
u
ct
ors
c
o
n
n
ec
t
e
d
t
o
g
e
t
h
e
r
a
t
t
he
t
erm
i
nal.
T
his
is
t
he
n
o
v
e
lty
i
n
t
h
i
s
p
a
p
e
r
w
h
e
r
e
a
n
e
w
w
i
n
d
i
n
g
d
e
s
i
g
n
i
s
s
t
u
d
i
e
d
t
o
c
a
l
c
u
l
a
t
e
i
ts
e
le
ct
rical
p
a
r
am
ete
r
s
and
sim
u
l
a
te
t
he
fre
que
nc
y
respons
e.
The
ful
l
w
ind
i
ng
s
t
ruc
t
ure
is
s
how
n
i
n
F
i
g
ure
8.
T
he
c
on
duc
t
o
r
has
2.
4
mm
w
i
dt
h
an
d
11.
5mm
in
hei
g
ht
a
s
s
h
o
w
n
i
n
F
i
gure
9(b).
Base
d
on
T
ab
le
1
t
he
t
r
a
nsform
e
r
dim
e
ns
io
n
s
s
uc
h
inne
r
a
n
d
o
u
t
er
r
a
d
ius
w
e
r
e
c
alcu
late
d.
T
he
t
ota
l
c
i
r
c
u
mfere
n
ce
of
t
he
c
o
nduc
tor
is
g
i
ve
n
by
2
.
The
winding
parameters
a
re
pro
v
i
d
e
d
i
n
Table
1.
T
he
i
n
s
ula
t
io
n
t
h
ick
n
e
ss
betw
ee
n
c
o
nduc
to
r
s
is
0
.
5
mm.
H
owe
v
er,
ther
e
i
s
a
n
a
i
r
gap
betw
ee
n tur
n
3
a
nd
t
u
r
n
4.
The
5mm a
i
r
gap is sh
o
w
n
i
n F
i
gur
e
9
(
a)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesia
n
J
Elec Eng
&
C
o
m
p
S
ci
ISSN:
2502-
4752
Fr
equ
e
n
c
y resp
on
se
of
t
r
a
n
sfo
r
me
r
w
i
ndi
ng
t
o
i
n
v
e
stig
at
e th
e
i
n
fl
u
e
n
c
e of
RL
C
(S
.
Al
-Am
e
ri
)
22
5
F
i
gur
e
8.
T
he
2
D
for
the
f
u
l
l
w
in
din
g
s
tr
uc
tur
e
t
e
s
t
e
d
tr
ans
f
or
mer
(a)
(b
)
F
i
gur
e
9.
(
a)
t
he
t
r
a
nsf
o
r
m
er
w
in
din
g
s
t
r
i
c
tur
e
w
i
t
h
5mm
o
f
a
ir
g
ap
b
etw
e
e
n
p
ar
ticu
l
a
r
t
u
r
ns
(
b)
t
he
c
on
duc
t
o
r
m
easur
e
m
e
n
t
d
i
me
nsio
ns
A
s
g
i
v
e
n
i
n
Tab
l
e
1
the
w
i
n
d
i
n
g
d
i
m
e
ns
io
ns
s
uc
h
a
s
i
n
n
e
r
a
n
d
o
u
t
e
r
radi
u
s
w
ere
ca
l
c
ul
a
t
ed
.
The
t
o
t
a
l
cir
c
u
m
fe
r
e
nc
e
of
t
h
e
c
on
duc
t
o
r
is
g
i
v
e
n
b
y
2
π
r
.
B
a
se
d
o
n
w
in
d
i
n
g
p
a
r
am
e
t
e
r
s
pr
ov
i
d
e
d
i
n
T
a
ble
1,
c
a
pac
ita
nc
e,
r
esi
s
tanc
e
a
n
d
i
n
duc
ta
nc
es
a
r
e
c
alc
u
l
a
t
e
d.
Tab
l
e
1. The
Tra
nsform
er
P
aram
ete
r
s S
p
ecific
a
t
i
on
s
Wi
nding
Ge
o
m
et
r
y
i
n m
m
C
onduc
t
o
r
w
i
dth
(W)
2
.
4
C
onduc
t
o
r
high
(h
)
11.
5
Insula
ti
on thic
kne
s
s
t
p
0.
5
Nu
m
b
e
r
o
f
t
u
rns
p
e
r
dis
c
(mt
)
30
Air ga
p insula
tion thic
kne
ss
5
Pre
s
sboa
rd
t
hic
k
n
e
ss
be
t
w
e
e
n
disc
s
d
3
Wi
nd
i
ng
inne
r
r
a
dius
r
374.
5
Ou
ter d
i
ame
t
e
r
do
933
Inne
r
diam
e
t
e
r
di
749
T
h
e
tota
l c
i
r
c
u
m
f
e
re
nc
e
of
t
he
c
ondu
c
t
or
C
ir
9423
8.
64
3
.
3
. Co
m
p
a
riso
n
b
e
t
w
een
the Mea
suremen
t
a
nd Simu
la
tio
n
The
m
o
del
i
s
a
pp
lied
t
o
s
imu
l
ate
the
fr
e
q
u
e
n
c
y
r
e
sponse
o
f
t
he
c
o
nt
i
nuo
u
s
d
i
s
c
w
i
nd
i
ng.
F
igur
e
1
0
show
s
t
h
e
me
asur
e
d
a
n
d
t
he
s
im
ula
t
e
d
r
e
s
po
nse
s
o
f
the
H
V
w
i
n
d
i
n
g.
T
he
d
as
hed
l
i
ne
p
r
e
sen
t
s
t
h
e
m
easur
e
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2502-
4752
I
n
do
n
e
si
an
J
E
l
e
c
E
n
g
&
C
o
m
p
S
ci
, V
o
l
.
1
4
,
No. 1, April 2019 :
219 –
2
29
22
6
r
e
s
p
o
n
s
e
w
h
i
l
e
t
h
e
s
o
l
i
d
l
i
n
e
i
s
t
h
e
s
i
m
u
l
a
t
e
d
r
e
s
p
o
n
s
e
.
T
h
e
t
w
o
re
spo
n
se
s
sh
ow
t
he
s
a
m
e
path
o
f
ne
gat
i
v
e
and
p
o
sit
i
v
e
sl
ope
.
N
o
net
h
e
l
ess,
t
here
a
re
s
ome
d
i
ffere
nc
es
i
n
the
res
onance
at
t
he
h
igh-freque
ncy
region.
These
re
so
na
n
ces
a
re
not
s
h
o
wn
i
n
the
ca
lc
ula
t
e
d
r
espo
n
s
e.
i
t
i
s
b
e
l
i
e
ve
d
t
h
at
t
hi
s
i
s
b
e
c
a
use
5
mm
a
i
r
g
a
p
on
ly
i
nc
lu
de
d
in
s
er
i
e
s
c
a
pa
c
i
t
a
nce
a
nd
s
e
l
f
i
n
d
u
cta
n
ce
c
a
l
cu
la
t
i
o
n
.
H
o
w
e
ve
r,
it
i
s
r
equ
i
re
d
to
i
n
c
l
ude
d
i
n
mutua
l
i
n
d
u
ct
anc
e
c
a
l
c
u
la
tion.
T
he
s
am
e
tra
n
sform
e
r
is
r
e
c
om
me
n
d
e
d
to
b
e
stud
i
e
d
i
n
t
h
e
f
ut
ure
a
nd
ca
l
c
u
l
a
t
e t
h
e
mutua
l
i
nd
uc
t
a
nc
e
with t
he a
ir ga
p
effec
t
.
H
o
w
e
ver,
F
i
g
ur
e
11
sh
ow
s
the
m
e
a
s
ur
ed
a
nd
sim
u
l
a
te
d
re
spo
n
se
s
o
f
t
h
e
sa
me
w
i
ndi
ng
a
ft
er
impro
v
e
m
e
n
t.
T
h
e
s
im
u
l
a
t
e
d
r
espo
nse
s
how
s
mor
e
s
im
i
l
a
r
t
o t
h
e
m
e
a
sure
d
re
sp
on
se.
Th
is i
s beca
use
of
s
om
e
cha
nge
s
i
n
t
he
w
i
n
din
g
r
e
s
i
s
tanc
e
R
s
,
con
d
u
cta
n
c
e
,
G
s
,
a
n
d
se
lf-i
n
d
uc
t
a
nce
.
T
h
i
s
im
pro
v
em
ent
is
implem
e
n
te
d
us
in
g
tria
l
an
d
er
ror
m
e
th
o
d
.
The
c
h
a
n
g
e
s
a
r
e
a
p
p
l
i
e
d
b
y
d
e
c
r
ea
si
ng
w
i
n
ding
r
es
i
s
t
a
n
c
e
,
con
d
u
cta
n
c
e
,
a
nd
sel
f
-
i
nd
uc
t
a
nce.
T
he
t
o
t
al
r
esu
l
ts
o
f
t
h
e
tra
n
sform
e
r
w
i
nding
e
l
ectrical
param
e
ter
s
a
re
pro
v
i
d
e
d
i
n
Table
2.
I
t
also
i
nc
lu
de
s
para
me
ters
o
f
the
im
pr
ove
d
s
i
mula
t
e
d
r
e
spo
n
se.
To
f
ur
ther
u
nde
rsta
n
d
t
h
e
resu
lt
s
shown
in
T
ab
l
e
2
,
mo
re
i
nv
e
s
ti
gat
i
on
i
s
n
e
e
d
ed
o
n
t
he
c
hose
n
t
r
a
ns
form
er
w
in
din
g
s
truc
tur
e
a
nd
t
h
e
c
a
l
c
ul
at
io
n
o
f
i
t
s
e
l
ect
ri
cal
p
ara
m
e
t
e
r
s.
T
hi
s
fut
u
re
r
e
c
o
m
me
n
d
a
t
i
on
i
s
t
o
e
xpl
a
i
n
t
h
e
re
ason
o
f
mi
n
o
r
di
ffe
re
nt
b
etw
e
e
n
s
im
u
l
a
tio
n
a
nd
me
asured
r
e
s
po
nse
s
.
Eve
n
t
ho
u
g
h,
t
he
a
ssum
e
d
spac
in
g
a
r
e
a
i
r
g
a
p.
B
ut
i
n
a
c
t
u
a
l
t
r
a
n
s
f
o
r
m
e
r
i
t
i
n
c
l
u
d
e
s
p
r
e
s
s
b
o
a
r
d
a
n
d
o
i
l
p
a
r
t
i
a
l
s
w
h
i
c
h
i
s
b
e
l
i
e
v
e
d
m
a
k
e
s
t
h
e
d
i
f
f
e
r
e
n
c
e
s
i
n
si
m
u
late
d
an
d m
e
a
s
ured
r
espons
es.
F
i
gure
1
0
.
The
calcul
a
t
e
d vs.
me
asure
d
r
e
s
pons
es
f
or
t
he
H
V
w
i
n
d
i
ng
o
f
96
d
i
s
cs wi
n
d
i
ng
(a
)
(b)
F
i
gure
1
1
. The
A
djus
te
d c
a
lc
ula
t
e
d
v
s. m
ea
sured
respo
n
se
(
a)
pr
e
s
e
n
ts
f
irs
t
im
p
ro
ved r
e
sul
t
s
(b)
present
s
the
se
co
nd im
pro
v
e
d
resul
t
s
Ta
b
l
e
2:
The
T
o
ta
l Res
u
lts
o
f the
Trans
f
o
r
me
r Mode
l
Elec
tri
c
a
l
P
ara
m
e
t
ers
C
a
l
c
ul
at
ion
Pa
r
a
m
e
te
rs
C
a
l
c
u
l
a
t
e
d
r
e
sponse
R
e
sponse
in
Figure
11
(a
)
R
e
sponse
in
F
i
gure
11
(b
)
Ct
3.
18×
10
-1
1
F
-
-
Cd
2.
79×
10
-9
F
-
-
Cs
h
v
2.
82×
10
-9
F
-
-
Gs
h
v
3.
55×
10
-9
Ω
3.
55×
10
-12
Ω,
-
Rs
h
v
0.
8806Ω
0
.
88×
10
-9
Ω
1×
10
-3
Ω
MR
Ma
trix96×
96
-
-
ML
Ma
trix96×
96
M
L
/100
M
L
/
3
Cg
0F
-
-
10
2
10
3
10
4
10
5
10
6
Frequency
(Hz)
-100
-80
-60
-40
-20
0
Magnitude
(dB)
si
mu
l
a
t
e
d
m
eas
ur
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
IS
S
N
: 2502-
47
52
Fre
que
ncy
res
p
o
n
se o
f
t
r
an
sf
orm
e
r wi
nd
in
g
to
i
n
v
e
s
t
i
ga
te
the
in
f
l
ue
nce
o
f
RL
C
(S.
Al
-
A
meri)
22
7
3.4.
R
LC
A
n
a
ly
sis
Base
d
on
t
h
e
ob
ta
ine
d
r
es
ul
ts,
it
ca
n
be
r
ea
l
i
ze
d
t
h
at
t
he
freq
ue
nc
y
re
s
p
o
n
se
i
s
a
f
fec
t
e
d
b
y
th
e
cha
nge
o
f
w
i
n
d
i
n
g
R
,
L
a
nd
C
v
a
l
ues.
T
he
c
ha
n
g
es
i
n
e
l
e
c
t
r
i
c
a
l
p
ar
am
et
ers
c
a
use
the
f
r
eque
n
cy
r
e
s
p
ons
e
to
sh
i
f
t
tow
a
r
d
s
l
o
w
e
r
or
h
i
gher
fr
eq
uenc
y
.
T
o
i
nves
t
i
g
ate
th
e
se
n
si
ti
v
i
t
y
o
f
the
m
o
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an
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t
h
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fol
l
o
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g cha
n
ges
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r
e
appl
i
e
d
:
a)
Incr
ease
of
s
eries
capa
c
i
t
ance
C
s
a
s show
n
in
F
igure
12.
b)
Incr
ease
of
s
eries
resistance
R
s
as
sh
ow
n in F
igur
e 1
3
.
c)
Incr
ease
of
s
elf-in
duc
ta
nc
e
L
s
as
show
n
i
n
F
igure
1
4
.
By
i
n
c
re
asi
ng
th
e
wi
nd
ing
c
a
p
aci
t
a
n
c
e,
t
h
e
r
e
s
pon
se
i
s
shi
f
t
e
d
tow
a
rds
l
o
w
fr
eque
nc
y.
The
sim
u
l
a
t
e
d
respo
n
se
i
n
F
i
gure
1
2
r
epre
se
nt
t
he
w
i
n
din
g
w
he
n
i
t
h
a
s
h
ig
h
capa
c
i
t
a
n
ce
whi
c
h
is
t
e
n
t
i
m
es
hi
ghe
r
tha
n
t
h
e
nor
ma
l
w
i
n
d
in
g
respo
n
se.
By
r
e
f
er
rin
g
t
o
Ta
b
l
e
3
w
h
ic
h
is
t
a
k
e
n
f
rom
ot
her
li
t
e
r
a
ture
,
the
i
n
c
r
ea
se
o
f
se
ries
capa
c
i
t
a
nce
is
m
a
i
n
l
y
due
t
o
t
h
e
ag
in
g
o
f
tra
n
sf
orme
r
insula
t
i
o
n
.
Table
3
s
how
s
the
in
ves
tiga
t
e
d
pa
r
am
eters
t
h
a
t
i
nfl
u
ence
t
he
f
re
q
u
e
n
c
y
r
espo
nse.
On
t
he
o
t
h
er
h
an
d,
t
he
i
ncr
ease
o
f
s
e
r
ies
resist
a
n
ce
is
a
ffe
c
t
i
n
g
t
he
r
e
s
ponse
a
t
l
ow
f
re
que
nc
y
a
s
show
n
in
F
igu
r
e
13.
I
n
t
h
e
f
i
g
u
r
e
,
the
s
i
m
u
l
a
te
d
resp
on
s
e
a
t
fr
e
q
u
e
n
c
ie
s
b
e
l
o
w
10kHz
sh
o
w
e
d
a
d
rop
i
n
ma
gni
tude
.
T
h
e
i
n
cre
a
se
o
f
resis
t
a
n
ce
i
s
us
ual
l
y
due
t
o
d
a
ma
ges
s
uc
h
a
s
i
n
the
t
a
p
c
h
an
ger
acc
ordi
ng
t
o
Tab
l
e 3. Ba
s
e
d
on a stu
d
y
o
n tap c
h
a
nger
da
m
a
ge
in [1
5], fin
d
i
n
gs
i
n
t
h
e
r
e
fe
renc
e also s
how
s a s
i
m
ilar
effec
t
on t
h
e
me
asure
d
re
s
po
nse
w
h
i
c
h r
e
fe
rs to
a cok
i
ng
in
t
he ta
p
c
h
a
nge
r.
The
i
n
cr
ease
o
f
s
e
l
f-i
n
d
u
c
ta
n
c
e
b
y
t
en
tim
es
o
f
t
h
e
or
ig
in
al
v
a
l
u
e
has
a
sign
i
f
ica
n
t
c
h
a
nge
i
n
t
h
e
si
m
u
late
d
re
s
p
on
s
e
.
The
a
n
ti-r
e
sona
nce
w
h
ic
h
w
a
s
ori
g
ina
l
ly
a
t
20
0k
H
z
h
as
b
een
s
h
i
fted
t
ow
ar
ds
l
ow
fre
que
nc
y
a
t
3
0kH
z
a
nd
s
h
o
w
ed
a
d
r
o
p
i
n
m
agni
tude
o
n
t
h
e
ne
ga
t
i
ve
s
lo
pe.
S
u
ch
c
ha
n
g
es
on
the
re
sp
onse
i
s
bel
i
e
v
ed
t
o
be
due t
o sh
ort
cir
c
ui
t a
n
d cor
e
de
f
orm
a
ti
o
n
as
me
n
t
i
o
n
ed
i
n T
a
ble
3.
F
i
gur
e 1
2
.
Inc
r
ea
sing
o
f
se
r
ies c
a
pac
ita
nce
b
y
10
t
i
m
e
s (
C
shv×10)
F
i
gur
e 1
3
.
Inc
r
ea
sing
the
ser
i
e
s
re
s
i
s
tanc
e
by
10
3
Figure
1
4
.
The
change
s in sel
f-
i
n
d
u
c
t
a
n
ce
whic
h i
n
cr
ease
d
10 t
i
m
e
s (ML×
10)
Table
3.
Mo
de
l
P
a
ra
me
ters
a
nd the
Tra
n
sfor
me
r
F
a
ults Whic
h
Infl
u
e
n
c
e
[
16
]
Mode
l p
a
r
a
me
t
e
r
T
y
p
e
of fa
ult
S
e
r
i
es
cap
ac
i
t
a
n
ce,
Cs
A
g
ing
of
i
ns
ula
t
i
o
n,
m
o
ist
u
r
e
c
ont
e
n
t
i
ngre
ss
a
nd
d
i
sk m
ovem
e
nt
(
d
i
splac
e
m
e
nt)
Re
sist
a
n
ce
,
Rs
Short
o
r
b
roke
n
disk,
f
a
ilure
o
f ca
ulk
i
ng
c
ont
act
s,
ta
p c
h
a
n
g
e
r
dam
a
g
e
.
Ind
u
c
t
a
n
ce
,
Ls
D
i
sk
d
e
f
orm
a
ti
on
,
l
o
ca
l
br
e
a
kdow
n,
core
de
f
o
r
m
a
tion
w
i
nding
sho
r
t
c
i
rcui
t.
Magni
tude (dB)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2502-
4752
I
n
do
n
e
si
an
J
E
l
e
c
E
n
g
&
C
o
m
p
S
ci
, V
o
l
.
1
4
,
No. 1, April 2019 :
219 –
2
29
22
8
4.
CONCL
U
S
ION
It
h
a
s
b
ee
n
no
t
e
d
t
h
a
t
F
RA
i
s
a
re
li
ab
le
m
e
t
hod
t
o
i
n
v
e
sti
g
at
e
t
h
e
me
c
h
ani
cal
c
o
n
d
i
tio
n
of
trans
f
or
me
r
w
i
nd
ing.
T
h
i
s
pa
per
prese
n
t
s
a
s
tud
y
on
a
un
i
que
t
r
a
n
sform
e
r
w
i
nd
in
g
s
t
ru
cture
t
o
s
im
u
l
a
t
e
t
h
e
fre
que
nc
y resp
ons
e.
This w
i
n
d
i
n
g has 5mm
air ga
p i
n
be
t
w
een w
in
d
i
n
g
tu
r
ns 2 a
nd 3 th
u
s
pr
e
sent a
c
ha
lle
n
g
e
t
o
s
i
m
ul
at
e
th
e
re
sp
on
se
a
s
t
h
e
wi
nd
i
n
g
tu
rns
are
n
o
t
uni
forml
y
d
ist
r
i
b
u
t
e
d
.
In
t
h
i
s
s
t
ud
y,
w
e
pr
esent
a
new
tech
n
i
q
u
e
w
h
ic
h
is
t
o
cal
cu
l
a
te
t
he
capa
c
i
ta
nce
in
b
e
t
we
en
t
ur
n
s
Ct
s
e
p
ara
t
e
l
y.
S
imi
l
a
rly
goe
s
w
i
t
h
t
he
ca
l
c
u
l
a
tio
n
of
c
a
pac
ita
nce
be
t
w
ee
n d
i
scs,
Cd
.
In
a
d
d
it
i
o
n
,
t
he
s
el
f-i
ndu
ct
a
n
c
e
p
er
d
i
s
c
consi
d
ere
d
i
n
thi
s
stud
y
is
t
ha
t
ther
e
a
r
e
a
c
tua
l
l
y
t
wo
d
i
f
fere
n
t
s
e
l
f-in
d
u
cta
n
ce
s
whic
h
a
r
e
c
o
n
n
e
c
te
d
in
s
erie
s.
T
his
is
due
t
o
t
h
e
in
su
la
ti
o
n
g
a
p
i
n
be
tw
e
e
n
tur
n
s
2
a
n
d
3.
I
t
has
be
e
n
o
b
s
er
ved
t
hat
inc
r
ea
sing
t
h
e
ser
i
e
s
c
a
p
aci
ta
nc
e
c
a
uses
shi
f
t
i
ng
i
n
t
h
e
re
sp
on
se
t
o
w
ard
s
l
o
w
fre
qu
enci
e
s
.
Whi
l
s
t
inc
r
ea
si
ng
t
h
e
w
i
ndi
ng
resi
st
a
n
ce
s
ho
ws
a
d
ro
p
i
n
ma
gni
tude
a
t
t
h
e
low
-
fre
que
ncy
re
gi
o
n
.
In
f
ac
t,
t
he
c
ha
n
g
e
i
n
s
elf
-
in
duc
t
a
n
ce
sho
w
s
a
ma
j
o
r
e
ffe
c
t
o
n
th
e
response.
The
response
s
how
s
a
dr
o
p
in
t
he
a
n
t
i
-
re
so
na
nc
e
o
f
t
h
e
resp
ons
e.
I
n
t
h
e
me
ant
i
m
e
,
t
h
e
dr
op
in
respo
n
se
i
s
c
l
e
a
rly
s
how
n
a
t
l
ow
f
re
que
n
c
ie
s.
I
n
th
is
p
a
p
er,
RL
C
a
n
a
l
ysis
o
n
l
y
in
ves
t
i
g
a
t
e
the
i
n
cr
easi
ng
o
f
se
ri
e
s
cap
ac
it
a
n
c
e
,
s
e
r
i
e
s
re
si
st
an
c
e
,
an
d
sel
f-ind
u
c
t
a
n
c
e.
T
hi
s
i
s
b
e
c
a
u
s
e
w
e
b
e
l
i
e
v
e
d
t
h
a
t
t
h
e
s
e
t
h
r
e
e
para
me
ters
h
a
v
e
m
a
j
o
r
effec
t
o
n
the
fre
q
u
e
ncy
res
p
onse.
F
urther
s
t
u
d
y
i
s
r
e
c
o
m
m
e
n
d
e
d
t
o
d
e
v
e
l
o
p
s
t
a
t
e
space
m
o
d
e
l
f
or
t
h
i
s
par
tic
u
l
ar
t
r
a
nsform
er
w
hic
h
c
ou
l
d
b
e
com
p
are
w
ith
t
he
p
r
o
p
o
s
e
d
m
o
d
e
l.
T
hi
s
is
t
o
conc
l
ude
w
hic
h
a
pproac
h
es
c
a
n
g
ive
sim
i
la
r
to
t
he
m
e
a
sure
d
resp
o
n
se.
But,
i
t
is
b
e
l
i
e
ve
d
tha
t
t
he
m
inor
cha
nge
s
betw
e
e
n
sim
u
l
a
tio
n
and
m
e
a
s
ure
d
r
espo
nses
i
s
b
eca
use
o
f
t
he
a
ssump
ti
o
n
s
o
f
t
he
w
i
n
di
ng
spac
es.
The
spa
c
e
s
i
nc
lu
des a
w
o
o
d
e
n
p
ress boa
rd a
nd o
i
l
part
ial
s
w
hic
h
h
as
a
n e
ffe
c
t
on
the
fr
e
que
nc
y
re
spo
n
s
e.
S
YMB
O
LS
Nd
Nu
mb
er
o
f
d
i
scs
mt
N
u
m
b
er
o
f tur
n
s
per
di
sc
d
Th
e
di
s
t
an
ce
be
t
we
en
t
wo
di
s
c
s
h
H
e
i
g
ht o
f t
h
e
turns
w
ith
ou
t i
n
su
l
a
t
i
on.
w
W
i
dt
h
of
th
e
t
urn
s
wi
t
hou
t
th
e i
n
su
l
a
ti
on
.
C
i
r
The
t
o
t
a
l
circ
u
m
fe
renc
e
of th
e
c
ond
uc
tor.
The
perm
it
tiv
i
t
y
of
f
ree
spac
e
Re
lat
i
v
e pe
rm
i
t
t
i
v
it
y of t
he
i
n
s
u
l
at
i
on pa
pe
r
Ct
Th
e
c
a
p
a
ci
t
a
n
ce i
n
b
et
we
en
t
urn
s
Cd
Ca
pac
ita
n
c
e
i
n
b
etw
e
e
n
t
he
d
isc
s
ACKNOW
LEDG
E
MEN
T
S
Th
is
w
or
k
is
s
up
por
t
e
d
fi
na
nc
i
a
l
l
y
by
t
h
e
U
n
i
v
er
sit
y
T
un
H
u
sse
i
n
O
nn
Mala
ys
ia
u
nde
r
S
p
ec
ia
l
Co
nt
rac
t
G
rant
v
ot
U
425
a
nd
G
P
P
S
Ph
D
stu
d
e
nt
g
ra
nt
p
roj
e
ct
v
o
t
U
7
08.
T
his
pro
j
e
c
t
a
l
s
o
s
u
pp
or
ted
b
y
R
e
sear
ch F
un
d
,
R
MC, U
THM"
REFE
RENCES
[1]
N.
A
beywick
r
ama,
Y
.
V.
S
erdyuk
,
and
S
.
M
.
Gub
a
nsk
i
,
“
H
igh
-
f
requ
ency
m
o
d
eli
n
g
o
f
pow
er
t
ra
ns
f
o
rm
ers
f
o
r
u
s
e
in
f
requ
ency
r
espo
ns
e anal
ys
is
(
F
R
A),”
I
E
EE
Tr
ans.
Power Del
i
v.
,
v
o
l
.
2
3
,
n
o.
4
,
p
p
.
20
42–
20
49,
2
008
.
[2]
T.
C
o
m
mittee,
I
.
P
o
wer,
a
nd
E
.
Soc
i
ety,
IEEE
Guid
e f
o
r th
e A
pplica
t
i
o
n
an
d
Int
e
rpr
e
ta
ti
on
of
F
r
e
q
uency
Resp
on
s
e
Anal
y
s
is f
o
r Oil-
Immersed T
r
ansf
o
rm
ers IEE
E
P
o
wer
and
E
n
erg
y
So
ciet
y
, n
o
. Mar
ch. 2
01
3.
[3]
Cigre
W
G
A
2.26,
“
M
echani
cal
C
ondition
Asses
s
m
e
n
t
o
f
Tr
ansf
o
rm
er
W
i
nding
s
Us
in
g
F
r
e
q
u
e
ncy
Res
pon
s
e
An
alysis
(F
r
a),”
Ci
gre
, n
o.
Ap
r
il,
pp
.
3
0–
3
4
, 20
0
8
.
[4]
O. Särnerot
h
, “I
n
sulation
Mat
e
rials
,
”
libra
ry.e.ab
b
.
c
o
m
,
v
o
l
.
2
,
p
p
.
1
–2
1,
2
01
4.
[5]
S
.
G
.
S
a
hoo
,
S
a
ro
ja
K
an
ti,
“W
in
d
i
n
g
D
ef
orm
a
tion
Anal
ys
is
i
n
P
o
w
er
T
ran
s
f
o
rm
ers
u
s
in
g
Finit
e
E
lem
e
nt
M
et
hod
,”
pp
.
3
41–
34
6,
2014.
[
6
]
Z
.
W
.
Z
h
a
n
g
,
W
.
H
.
T
a
n
g
,
T
.
Y
.
J
i
,
a
n
d
Q
.
H
.
W
u
,
“
F
i
n
i
t
e
-
e
l
e
m
en
t
m
o
deli
ng
f
or
a
n
a
lys
i
s
o
f
r
a
d
ial
d
e
f
o
rm
ati
ons
within
t
ransf
o
r
m
er wind
i
ngs,”
IEEE Trans.
Power D
e
liv.
,
v
o
l
.
2
9
,
n
o.
5
,
p
p
.
229
7–23
05
,
2
0
1
4
.
[7]
O.
d
e W
eck an
d
I.
Y
.
K
im
, “
F
inite
Ele
m
e
n
t
M
et
h
o
d,”
En
g
.
De
s. Ra
pid Pro
t
oty
p
.
,
v
o
l
.
81
0,
p
. 2
6,
20
0
4
.
[8
]
A.
A
b
u
-S
ia
d
a
,
“
H
igh
Fre
q
ue
n
c
y
Tra
n
sfor
me
r
M
o
d
e
ll
in
g
usin
g
S
t
a
te
S
p
a
ce
Rep
r
es
ent
a
tio
n
f
o
r
F
R
A
st
ud
i
e
s,
”
11
th
Int
.
S
y
mp.
Di
agnos
ti
cs
E
l
ectr. M
a
ch
.
P
o
wer
Elect
ro
n.
Dri
ves
,
20
17
.
[
9
]
M
.
F
.
M
.
Y
o
u
s
o
f
,
C
.
E
k
a
n
a
y
a
k
e
,
T
.
K
.
S
a
h
a
,
a
n
d
H
.
M
a
,
“
A
s
t
udy
o
n
s
u
i
t
a
bili
ty
o
f
d
i
ff
eren
t
transf
orm
e
r
wi
ndin
g
m
o
d
e
ls
f
or f
req
u
ency
resp
o
n
s
e an
alys
is
,”
IE
EE Po
wer
En
erg
y
Soc.
G
e
n.
M
eet.
, p
p. 1–
8
, 2
01
2.
[1
0]
E
. Bjerk
an,
H
i
gh F
r
equ
e
ncy M
odelin
g Of Power
T
r
a
n
sfo
r
m
e
r
s
, n
o. 19
5
. 2
01
2.
[11]
B
. J.
Van Jaarsv
el
d, “Wide
band
modelling
o
f
an
air-core
p
o
w
er tran
s
f
o
rm
er
w
i
nding
,” n
o. D
ecem
ber, 2
01
3.
[
1
2
]
D
.
B
.
K
a
n
d
i
ć
,
B
.
D
.
R
e
l
j
i
n
,
a
n
d
I
.
S
.
R
e
l
j
i
n
,
“
O
n
m
o
d
e
l
l
i
n
g
of
t
wo-wi
r
e
transmis
si
on
li
nes
wit
h
u
nif
o
rm
p
assi
ve
lad
d
ers,
”
M
a
t
h.
Pr
obl.
Eng.
,
vol.
2
0
1
2
,
201
2
.
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