Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 2, No. 2,
May 2016, pp
. 248 ~ 258
DOI: 10.115
9
1
/ijeecs.v2.i2.pp24
8-2
5
8
248
Re
cei
v
ed
Jan
uary 15, 201
6
;
Revi
sed Fe
brua
ry 29, 20
16; Accepted
March 13, 20
16
Investigating Ferroresonance Phenomenon in a Single-
Phase T
r
ansformer with the Effect of Magnetic
Hysteresis
Behro
o
z
Re
zaeealam*, Behza
d
Nor
o
u
z
i
Dep
a
rtement o
f
Electrical Eng
i
ne
erin
g, Lores
tan Univ
ersit
y
,
681
37-1
7
1
33, Khorram
aba
d, Loresta
n, Iran
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: rezaee.b
h
@l
u.ac.ir
A
b
st
r
a
ct
F
e
rroreso
nanc
e is a non-
lin
e
a
r phe
no
me
no
n and very dy
na
mic in th
e p
o
w
e
r qual
ity probl
e
m
s
.
T
h
is phe
no
me
non sh
ou
ld be
carefully a
nal
y
z
e
d
so t
hat p
r
eventiv
e mea
s
ures cou
l
d b
e
taken b
e
fore
its
app
eara
n
ce
an
d prev
ent in
jur
y
and
da
ma
ge
to electric
al p
o
w
er appl
ianc
es
. F
e
rroreson
a
n
c
e is see
n
mor
e
in the mid
d
le-
v
oltag
e
netw
o
r
ks w
i
th supplyi
ng un
loa
d
e
d
o
r
slightly lo
ad
e
d
transfor
m
ers
by cables. T
h
e
mater
i
als
use
d
in the
ma
nufa
c
ture of transfo
rmer c
o
res
ar
e
creates a
ma
j
o
r role
in the
i
r
dyna
mic be
hav
ior.
In this article
a
r
e use
d
from t
w
o types ma
g
netic
materi
al
GOES and N
GOES in the transfor
m
er cor
e
of
singl
e phas
e. T
he
p
h
ysica
l beh
avior
of
th
ese mat
e
ria
l
s
is cons
id
ered
duri
ng th
e cor
e
hyster
esis.
F
o
r
mo
de
lin
g the hysteresis l
o
o
p
has be
en u
s
ed from Ji
les
-
Atherton
met
hod. By usin
g
the finite ele
m
e
n
t
meth
od
an
d w
i
th hel
p COMS
OL Multip
hysic
s
Softw
are,
tra
n
sformer is si
mu
late
d in tw
o
space
di
me
nsi
ons
.
Lab
oratory tes
t
the transformer c
o
re hyst
eresis
l
oop
is descri
bed
and
show
s w
h
ich the Jiles-Ath
e
r
to
n
mo
de
l is one o
f
the best know
n mode
ls
of hysteresis. T
he results show
s w
h
ich use of GOES materi
als
i
n
the transfor
m
e
r
core
is c
aus
e Si
gnific
ant r
educti
on
the c
o
re
losses
i
n
comparis
on
w
i
th the
NGOE
S
mater
i
als. A
l
so
chan
ge
of ferroreso
nanc
e
mode
an
d the s
e
verity its occurr
ence
are th
e re
sults of cha
n
g
i
ng
the materia
l
us
ed in the tra
n
sformer core.
Ke
y
w
ords
: F
e
rroreso
nanc
e, F
i
nite Ele
m
ent Method (F
EM),
Hysteresis los
s
, Single Ph
as
e T
r
ansformer
Copy
right
©
2016 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
A transfo
rme
r
is a devi
c
e u
s
ed to tran
sfer ele
c
tri
c
al e
nergy from o
ne ci
rcuit to anothe
r.
In
o
t
h
e
r
wo
rd
s
,
tr
an
s
f
or
me
r
s
ar
e
de
vice
s
u
s
ed
in
e
l
ectri
c
al
circu
i
ts to chan
ge
the voltage
of
electri
c
ity flo
w
ing
in th
e
circuit. T
h
e
r
efo
r
e, tra
n
sf
o
r
m
e
rs a
r
e
one
o
f
the mo
st im
portant
ele
c
tri
c
al
equipm
ent. F
e
rrore
s
o
nan
ce is a
nonli
n
ear phe
nom
e
non,
whi
c
h
o
c
curs
betwee
n
the
network
cap
a
cito
r a
n
d
nonlin
ear in
ducta
nce the
equip
m
ent
su
ch
as tran
sf
orme
rs re
act
o
r. In
conditi
ons
unloa
ded
or slightly loade
d
,
with the
inci
den
ce
of
dist
urba
nces, t
r
a
n
sformer wi
n
d
ing th
rou
gh
the
cap
a
cito
r of
line
s
a
nd t
r
an
sform
e
r
windi
ng
s
co
nstitute the
resona
nt ci
rcuit and
with
the
transfo
rme
r
core
saturatio
n
, ferroreson
ance i
s
cr
eat
ed [1]. Althou
gh
re
sona
nt i
s
al
so
in
clud
es
a
cap
a
cito
r an
d an in
du
cto
r
, but certai
nly doe
s not
exist re
so
n
ant freq
uen
cy whe
r
e in t
he
ferro
re
son
a
n
c
e o
c
curs. So that in the ferro
re
son
a
n
c
e ph
enom
e
non, there are more tha
n
one
respon
se
for a set of ide
n
tical p
a
ram
e
ters [2]. In ferrore
s
o
nan
ce mod
e
, rel
a
tionshi
p bet
ween
voltage an
d
current in
addi
tion to the
fre
quen
cy is rel
a
ted to oth
e
r
fa
ctors su
ch as
voltag
e,
in
itial
con
d
ition
s
an
d circuit losses [3]. Nowa
days, from soft magnetic material
s are
used st
rongl
y in
the structu
r
e
of elect
r
ical
equipm
ent. Silicon
steel
i
s
use
d
a
s
a
soft magneti
c
material i
n
th
e
manufa
c
ture
of tran
sform
e
rs, moto
rs an
d gen
erato
r
s
[6-4]. This ty
pe of mate
ria
l
s is
co
nsi
dered
as th
e b
e
st
combinatio
n fo
r tra
n
smissio
n
an
d di
strib
u
t
ion of el
ect
r
i
c
al
ene
rgy a
n
d
u
s
ing
them
is
more economical. Silicon steel used i
n
core of
electri
c
al machi
nes has a
si
gnificant impact on
the magn
etic field [7]. In the event that t
hese m
a
terial
s have
placed u
n
d
e
r an
alterna
t
ing
curre
n
t, are
causes l
o
sse
s
and he
at in the ci
rcui
t. Silicon
used in t
h
is mate
rial h
a
s rang
e of 0
.
5
to 5%. By increa
sing th
e amo
unt of
silicon d
e
creases th
e a
m
ount of lo
sse
s
. In term
s of
Electri
c
al pro
c
e
ssi
ng, these material
s can be divide
d
into two cate
gorie
s:
1) Grain O
r
ie
nted Electri
c
a
l
Steel (GOE
S)
2) NON-G
r
ai
n Oriente
d
Electri
c
al Steel
(NGOES).
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 2, May 2016 : 248 –
258
249
Silicon rang
e
use
d
in NGO
ES materials
is
between
0-3% and in th
e GOES mat
e
rial
s is
betwe
en 3
-
3.
8% [8]. The b
a
si
c differen
c
e bet
ween
th
ese
two
types of
steel i
s
d
i
fferences in t
he
dire
ction of magneti
z
atio
n.
St
udies of
magn
etic
be
havior
ar
e
sh
ows o
p
timal
state G
O
ES
only
one directio
n
.
So magnetic dipole
s
a
r
e
conver
ge
s in one directi
on. While NGOES is sh
ows
magneti
c
p
r
o
pertie
s
a
s
an
isotro
pic fe
ature. Ba
s
ed
o
n
the sta
nda
rds a
pplied i
n
the manufa
c
t
u
re
of pro
d
u
c
ts,
type of ste
e
l used in
manufa
c
turi
n
g
equi
pment
is different. At the co
re of
transfo
rme
r
s are
u
s
ed
u
s
ually of
GO
ES catego
rie
s
an
d fo
r th
e produ
ction
of motors
and
gene
rato
rs from NG
OES categ
o
ry. Fro
m
pro
perti
e
s
of these m
a
terial
s can b
e
mentione
d the
high Permea
bility and ind
u
ction a
nd lo
w mag
netic l
o
sse
s
. Perm
eability and
high ind
u
cta
n
ce
redu
ce
s the
size a
nd
weig
ht of the equi
pment. Also l
o
w m
agneti
c
losse
s
re
du
ces g
ene
rate
heat
and in
crea
se
s its effici
en
cy. In gene
ral, the pr
ope
rties
of mag
netic m
a
teria
l
s a
r
e evalu
a
t
ed
according to
the magn
etic field
stren
g
th and
m
a
g
netic flux de
nsity. Although the n
eed
to
accurate de
scriptio
ns m
a
gnetic p
r
o
c
e
s
ses h
a
s b
e
en increa
se
d
in these ma
terials
with their
developm
ent, but is co
ntin
ues
ca
reful a
nalysi
s
of ma
gnetic b
ehavi
o
r.
Physical behavio
r these
material
s a
r
e
refle
c
ted
as magn
etic hy
stere
s
i
s
.
On
e
of the imp
o
rtant facto
r
s
is the
effect
of
hystere
s
i
s
lo
sse
s
which creates
an im
p
o
rtant role
in
the beh
avior
of ferro
re
so
n
ance [9-10]. The
con
d
u
c
ted re
sea
r
che
s
ab
out ferro
re
so
nan
ce have
sho
w
n that the simul
a
tion
results are very
sen
s
itive to magneti
c
sat
u
ration
cha
r
a
c
teri
stic me
th
od and core l
o
sse
s
[11]. The co
re hyste
r
esi
s
losse
s
are d
epen
dent to
freque
ncy a
n
d
en
closed l
e
vel in the h
y
stere
s
is
cu
rve and the
r
e
f
ore
depe
ndent to
the hystere
s
i
s
model. The
r
efore for
mo
deling ma
gne
tic cha
r
a
c
teri
stic an
d the core
hystere
s
i
s
are use
d
from
more a
c
curate model
s.
No
wad
a
ys calcul
ation th
e hysteresi
s
losse
s
with
finite eleme
n
t method h
a
s b
een
notice
d
in
cre
a
sin
g
ly by co
mputer
scien
c
e [12
].
Refe
ren
c
e [1
3] ferroresona
nce
phen
omen
on
is
examined
on
a tran
sform
e
r to th
e finite
eleme
n
t met
hod, b
u
t do
e
s
n
o
t p
r
ovide
exact
mod
e
l
of
hystere
s
i
s
. Variou
s m
e
tho
d
s i
s
p
r
ovide
d
for m
odelin
g of hyste
r
e
s
is, whi
c
h i
n
t
h
is b
e
twe
en t
he
Jile
s-Athe
rton
model [17-14] and prei
sa
ch mo
d
e
l
[18] are provides a
c
curate model
s of
hystere
s
i
s
losse
s
. In refere
nce [19] ferro
r
esona
nc
e da
mping control
is studied wit
h
rega
rd to the
effect of the non-lin
ea
r losses. In refe
ren
c
e [20]
a ne
w model of hysteresi
s
i
s
pro
v
ided ba
sed
on
the prei
sa
ch
theory with
the new fo
rmulat
io
n in
the ATP software
whi
c
h the nonlin
ear
cha
r
a
c
teri
ze
s of materials is not modele
d
well.
In this pape
r, a new
approa
ch is p
r
esented of the
ferro
re
son
a
n
c
e p
hen
ome
non. By sim
u
lating the t
r
an
sform
e
rs
core ma
de
of soft mag
netic
material i
n
th
e two-dime
nsional
spa
c
e
b
y
finite
eleme
n
t method, th
e effect of u
s
e these mate
rial
in ferrore
s
o
n
ance problem
has b
een
stu
d
ied. Fo
r mo
deling the
ma
gnet
ic
hysteresi
s
is u
s
e
d
from
Jile
s-Athe
rton
method. Mo
deling
of Tra
n
sformer i
s
d
one in the co
msol
softwa
r
e whi
c
h si
mul
a
tes
Non
-
line
a
r el
ements
with very high p
r
e
c
i
s
ion.
In Section 2,
the ba
sics of
Ferroresona
nce
phe
nom
enon
ha
s be
en stu
d
ied i
n
orde
r to
unde
rsta
nd b
e
tter of these
pheno
men
o
n
. In Section
3, a brief ex
planatio
n is
provide
d
of h
o
w
taking i
n
to a
c
cou
n
t the hy
steresi
s
model
and
cal
c
ul
ation meth
od of
the core lo
sses. In Se
ction
4
the simulatio
n
results a
r
e
pre
s
ente
d
.
2. The Basic
s
of Ferro
res
onanc
e Phe
nomenon
Whe
n
the
ferroma
gneti
c
core
s
of hig
h
pre
s
sure e
qui
pment
satu
ra
ted an
d
are
p
l
ace
d
in
circuit as
se
ries
with ca
pacitive prop
erty,
the co
ndition
s are
provided fo
r ferrore
s
o
n
a
n
ce
phen
omen
on.
In power
sy
stem
s, transf
o
rme
r
s a
r
e f
ed mainly by cable
s
. The
cabl
es h
a
ve the
highe
r
cap
a
ci
tive prop
ertie
s
a
nd a
s
se
ri
es
are
pla
c
e
d
with th
e tra
n
sformers
coi
l
equip
ped
wi
th
ferrom
agn
etic co
re [2
1]. F
e
rrore
s
o
nan
ce is
a
ki
nd
o
f
temporary
overvoltage
a
nd h
a
s
different
types. Thi
s
p
henom
eno
n i
s
reviews a
s
pect
s
of the
domain
and
duratio
n a
nd
its ha
rmoni
cs. If
a
wave
with
hig
h
amplitu
de
a
nd the
mo
re
harm
oni
cs ex
ists i
n
the
lon
g
du
ration
on
the e
quipm
e
n
t,
lead to d
a
ma
ge an
d even
destructio
n
of
it. For ex
am
ple, the exist
ence of ha
rm
onic volta
ge
on
the tran
sform
e
r cau
s
e
s
overhe
ating an
d dama
ge
to
the transfo
rmer wi
ndin
g
s. So should
be
avoided f
r
om
the existe
nce of this fa
ct
or that
i
s
u
n
d
e
r imp
a
ct th
e
ferro
re
so
nan
ce p
hen
ome
non
on the tran
sf
orme
r. Figu
re 1 sho
w
s the equival
e
n
t
circuit the ferro
re
son
a
n
c
e ph
enom
e
non
whe
r
e ind
u
ct
ors h
a
ve no
nlinea
r ch
ara
c
teri
stics. Wit
h
curre
n
t pa
ssi
ng thro
ug
h the circuit, the
cap
a
cito
r is
charg
ed. Th
e voltage sto
r
e
d
in a
capa
cit
o
r could
be a
s
sumed
DC
voltage whi
c
h
is
locate
d in two end
s of the magnetizatio
n rea
c
tan
c
e
of transfo
rme
r
, and ca
use
s
the co
re to
be
saturated. T
he m
agn
etization
rea
c
ta
nce
redu
ced
and
ferro
r
eso
nan
ce
o
c
curs. Th
ere
f
ore
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Inve
stigating
Ferroresona
n
c
e Phen
om
enon in
a Singl
e-Pha
s
e … (Behro
o
z
Re
zaeeal
am
)
250
Ferroresona
n
c
e is a n
o
n
-
linear p
hen
o
m
enon
whi
c
h is functio
n
of paramete
r
s in
cludi
ng the
indu
ced volta
ge, magneti
z
ation ch
ara
c
t
e
ri
sti
c
, losse
s
and the circu
i
t capa
citor.
Figure 1. The
equivalent ci
rcuit ferro
r
e
s
onan
ce
3. The H
y
steresis Model
With the adv
ancement
of
technology
has be
en
created the possi
bilit
y of to consi
der
more
co
mplet
e
mod
e
l of th
e ferroma
gne
tic mate
rial. T
he mo
st p
r
o
m
inent b
ehav
ior
whi
c
h
sho
w
s
ferrom
agn
etic materials fro
m
themselve
s
is the hy
ste
r
esi
s
be
havio
r, which in the simple
st ca
se
cau
s
e
s
th
e di
rectio
n
witho
u
t the m
agn
e
t
ization i
s
different
from
direction
with
its magn
etizatio
n.
The
Jile
s-Ath
e
rton m
e
thod
is u
s
e
d
du
e
to high
ac
cu
racy in
estima
ting the hy
stere
s
is loop
a
nd
also e
a
sy i
m
pleme
n
t in the softwa
r
e. This mo
d
e
l is ba
se
d
on the en
ergy bal
an
ce in
ferrom
agn
etic material
s. So that the to
tal ener
gy d
u
ring a p
e
rio
d
is saved a
s
the magn
e
t
ic
energy
(
Wm
)
and
/or is wasted
as the hyste
r
esi
s
losse
s
(
h
W
).
Whe
n
the
n
e
twork is protected
with
dista
n
ce
rel
a
ys, ea
ch
lin
e is p
r
ote
c
te
d by
the
main
and ba
ckup relay
of
its
line.
By
placi
ng
ove
r
current
rel
a
ys
along with distan
ce rela
ys,
prote
c
tive territory of the tran
smi
ssi
on
netwo
rk
will expand. If a disturban
ce
occurre
d
, initiall
y
main di
stance relay will
operates
and i
f
it fails to clear fault,
overcurrent rel
a
y
will operates.
If
main relay f
a
ils to
ope
ra
te, the ba
ckup di
stan
ce
relay
will op
erate
and if
it fails to o
p
e
rate
ultimately ba
ckup ove
r
current relay mu
st isol
ate
the
faulted
se
ction. As
sho
w
n in Fig
u
re 2
in
orde
r to
e
s
ta
blish
the m
e
n
t
ioned
se
que
nce
protectio
n
, two
other
con
s
trai
nt sh
ould
be a
dde
d to
the con
s
trai
nts of coo
r
din
a
tion pro
b
lem
s
:
h
m
W
W
W
(1)
Based
on thi
s
a
s
sumption
and refere
n
c
e [16] obtai
ned the follo
wing e
quatio
n for all
ferrom
agn
etic material
s:
irr
rev
M
M
M
(2)
Whe
r
e
M
is the
material
s m
a
gnetization,
rev
M
is
the
mate
rial
s reversibl
e
magneti
z
atio
n
and
irr
M
is the material
s irreve
rsibl
e
mag
net
ization.
))
(coth(
)
(
e
e
s
e
an
H
a
a
H
M
H
M
(3)
Acco
rdi
ng to
the modifie
d
langevin fu
nction t
hat is
e
x
presse
d to
descri
be b
e
h
a
vior of
ferrom
agn
etic material
s, fo
r
the ide
a
l m
agneti
z
ation
curve,
s
M
is th
e
magneti
c
saturation,
a
is
a co
efficient
to describe t
he tempe
r
atu
r
e an
d
e
H
is th
e effect of th
e magn
etic fi
eld which is
achi
eved a
s
the followi
ng e
quation:
M
H
H
e
(4)
By changin
g
the magn
etic field the equ
ation der
ive
d
from ren
e
wabl
e field is as fo
llows:
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251
)
)
(
(
)
(
irr
e
an
irr
e
an
irr
M
H
M
k
M
H
M
dH
dM
(5)
In the equati
on (5
)
k
is the
material ha
rdne
ss
coefficient,
is coeffi
cient to de
scribe
con
n
e
c
tion
of the ma
gneti
c
fields and
indicate
s th
e di
rectio
n of th
e
magn
etic fiel
d chan
ge.
is a dire
ction
a
l param
eter which h
a
s t
he value of +1 if
0
dt
dH
and has the value
of -1 if
0
dt
dH
.
1
.
0
)
(coth
1
.
0
3
e
e
e
e
e
s
e
e
s
an
H
H
H
H
a
a
H
M
H
a
H
M
M
(6)
The reve
rsi
b
l
e
equatio
n of the magneti
c
fields a
s
follo
ws:
)
)
(
(
)
(
irr
e
an
e
rev
M
H
M
c
H
M
(7)
W
h
er
e
c
is th
e mate
rial
re
versibl
e
coef
ficient. Usin
g
of eq
uation
s
(2),
(3
) a
n
d (7),
equatio
n the magneti
z
atio
n material i
s
obtaine
d as f
o
llows:
dH
H
dM
c
M
H
M
k
M
H
M
c
dH
dM
e
an
irr
e
an
irr
e
an
)
(
)
)
(
(
)
)
(
(
)
1
(
(8)
The pa
ramet
e
rs of thi
s
me
thod co
uld be
obse
r
ved su
mmari
zed In t
he Table 1.
Table 1. De
scrib
e
s of the
para
m
eters J-A method
the unit
Descr
iption
paramete
r
[
1
Am
]
the magnetic saturation
s
M
[
1
Am
]
Temper
ature coe
fficient
a
[
1
Am
]
the material hard
ness
k
-
Connection mag
netic field
-
The reve
rsible coefficient
c
3.1. Calculati
ng H
y
steresi
s Losse
s
As was
ment
ioned
many
method
s h
a
ve bee
n p
r
op
o
s
ed i
n
the lit
eratu
r
e a
nd
boo
ks fo
r
cal
c
ulatin
g h
y
stere
s
is lo
sse
s
. In this
article,
fo
r calcul
ating hy
stere
s
i
s
lo
sses a
r
e
used
the
followin
g
equ
ation:
T
Loss
HdB
T
P
0
1
(9)
3.2. Calculati
on of Edd
y
Curre
nt Lo
s
ses
Most ferroma
gnetic mate
ri
als
are con
d
u
ctors of ele
c
tri
c
al cu
rren
t. This cau
s
e
s
whi
c
h
with pla
c
e
d
i
n
a time
-vary
i
ng ma
gneti
c
field,
the ph
enome
non
of
eddy
curre
n
ts a
r
e
created
in
the op
po
site
dire
ction
of th
e external fiel
d.
Incid
e
n
c
e
of eddy
curre
n
t phe
nom
en
a is
cau
s
ed
t
he
cre
a
tion of
a losse
s
co
mpone
nt at the core
o
f
electrom
ag
netic sy
stem
s. For la
min
a
te
ferrom
agn
etic materi
als,
whi
c
h it
s sh
eet thickn
ess
i
s
smalle
r
in comp
ari
s
on
to
its o
t
her
dimen
s
ion
s
, power Lo
sse
s
ca
used by eddy cu
rrents can be exp
r
e
s
sed a
s
follo
ws [22]:
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Inve
stigating
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e Phen
om
enon in
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e … (Behro
o
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Re
zaeeal
am
)
252
T
edd
t
B
d
P
0
2
2
)
(
12
(10
)
W
h
er
e
is the sheet
ele
c
trical
cond
ucti
vity,
d
is sh
eet
t
h
ic
kne
s
s a
n
d
B
is
the flux
den
sity passi
ng throug
h th
e sheet. Th
e
thickne
ss
of
a sheet of i
n
the internatio
nal sta
nda
rd
s is
betwe
en 0.35
to 0.5 mm.
Also cal
c
ul
ation of eddy
current losse
s
is done in a
c
cord
an
ce to
the
state befo
r
e.
4. Labora
t
or
y
Sample Sp
ecifica
tion
For i
n
vestiga
t
e the ele
c
tromagn
etic
b
ehavior the
s
e mate
rials i
s
u
s
ed
from
a si
ngle
-
pha
se tran
sfo
r
mer. T
he tra
n
sformer u
s
e
d
with
voltag
e 220 volt
an
d freq
uen
cy
60 Hz h
a
s be
en
locate
d in th
e ci
rcuit. Th
e tran
sforme
r spe
c
ific
atio
n is p
r
e
s
ent
ed in the ta
ble 2. Also
the
transfo
rme
r
geomet
rical dimen
s
ion
s
are sho
w
n i
n
figure 2. The J-A mo
del paramet
ers i
s
pre
s
ente
d
for the iron co
re
of transfo
rme
r
with mag
net
ic materi
als G
O
ES in the table 3.
Table 2. sp
ecification of the studie
d
tran
sform
e
r
the a
m
o
unt
of
Parameter
20 W
Nominal po
w
e
r
220 V
T
he initial voltag
e
12 V
Secondar
y
volta
g
e
50 Hz
Freque
nc
y
1600
Number
of prima
r
y
w
i
ndings
90
Number of S
e
condar
y
w
i
ndings
Figure 2. Tra
n
sformer
Geo
m
et
rical Dimensions (x
=11mm)
Table 3. The
J-A mo
del pa
ramete
rs fo
r tran
sform
e
r
core with
GOE
S materials
the a
m
o
unt
of
parame
ter
1350000
s
M
62.15
a
94.52
k
0.05
0.000108
c
4.1. Modeling of b
y
Finite Element M
e
thod
In mathem
atics finite el
e
m
ent meth
o
d
(FEM
) i
s
a num
eri
c
al
techni
que
for finding
approximate
solutio
n
s to
boun
dary
value p
r
o
b
lem
s
. Thi
s
m
e
tho
d
is
similar t
o
the
idea
t
hat
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253
con
n
e
c
ting m
any tiny strai
ght line
s
ca
n
approx
imate
a larg
er
circl
e
. FEM enco
m
passe
s all t
h
e
method
s fo
r
con
n
e
c
ting m
any sim
p
le
el
ement
e
quati
ons over ma
ny small
Sub
d
omain,
nam
ed
finite eleme
n
t
s, to ap
prox
imate a
more complex
e
q
uation
over a la
rge
r
d
o
m
ain [24
-
2
3
]. By
applying
relat
i
ons th
e J-A
model to th
e
finite element
method
co
ul
d be a
c
hi
eve
d
the hyst
ere
s
is
curve fo
r different pa
rts o
f
the transformer core
. From the Finite
element met
h
od an
d to help
COMSO
L
Mu
ltiphysics software is
used
for com
put
er s
i
mulation [25]. Th
is
software
s
o
lves
the
nonlin
ear
system
s equati
ons by the
partial differe
ntial equatio
n and in the
presen
ce of
an
electroma
gne
tic field and so on. Also, it there is
po
ssi
ble to define elect
r
ical circuits
su
ch
as
load, resi
stan
ce, ind
u
cta
n
ce, cap
a
cita
nce and
so
on
with the m
a
g
n
etic field. Fi
gure
3
sho
w
s a
two-di
men
s
io
nal mo
del of
tran
sform
e
r.
Co
nsid
er
i
n
g
the hyste
r
e
s
is curve
by the J-A m
e
thod
coul
d b
e
a
c
hi
eved the
ma
gnetic path
e
a
ch
poi
nt
of t
r
an
sform
e
r core. Fi
gu
re
4
sh
ows
mag
n
e
tic
flux path to a desired
point from the tran
sfor
m
e
r co
re. Fig
u
re 5 sho
w
s the flux density
distrib
u
tion t
he tran
sform
e
r core. Th
e
Primary
an
d
second
ary tran
sform
e
r
current cu
rve
s
is
pre
s
ente
d
in the normal op
erating m
ode
in figure 6.
Figure 3. Two
-
dime
nsi
onal
model of tran
sform
e
r
Figure 4. Hysteresi
s
curve
for desi
re
d po
int
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Inve
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c
e Phen
om
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e-Pha
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o
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Re
zaeeal
am
)
254
Figure 5. The
flux density distributio
n the
transfo
rme
r
core with G
O
ES core
Figure 6. Current cu
rve
s
in
the normal o
peratin
g mod
e
In Figu
re 7
the hy
stere
s
i
s
loop
obtain
e
d
from
the
s
e
state i
s
sho
w
n with
the hy
stere
s
i
s
loop
by expe
rimental
resul
t
s. As i
s
exp
e
cted,
co
nsi
d
ering
the
dyn
a
mic ph
enom
e
na
ha
s le
d t
o
the co
rrect
re
sults f
r
om th
e hyste
r
e
s
is l
oop. Th
er
efo
r
e, taking
into
accou
n
t the
hystere
s
i
s
in
a
transfo
rme
r
model cau
s
e whe
r
e
it
mod
e
l
more
a
c
cu
rate phy
sically. It is noteworthy that outputs
analysi
s
was
carrie
d are
re
lated to no-lo
ad state of tra
n
sformer.
Figure 7. The
hystere
s
is
cu
rve
By using the mentione
d method
the value of core losse
s
cal
c
ulate
d
at normal o
peratin
g
point of transf
o
rme
r
is
sho
w
n in the Tab
l
e 4.
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255
Table 4. Tran
sform
e
r
core losse
s
with G
O
ES material
s
v
a
l
u
e o
f
los
ses
(
w
)
losses
0.4552 W
hy
ster
esis losses
0.1298 W
Eddy
curr
ent losses
Therefore th
e Jile
s-Athe
rton method
with
good accura
cy model
s the hystere
s
is loop.
Corre
c
tne
s
s
of re
sults is expre
s
sed
based
on th
e corre
c
t ch
oice
of p
a
ra
meters the
Jiles-
Atherton m
e
thod, so that changi
ng a
n
y para
m
eter
wi
l
l
create a
gre
a
t impa
ct on
hystere
s
i
s
lo
op.
Therefore
fro
m
this
mode
l co
uld b
e
u
s
ed
to
simul
a
te tran
sfo
r
mer
with
co
re from
NGO
E
S
material
s. In the event that the lines ca
pa
ci
tance, transfo
rm
er win
d
ing
s
and/or O
r
lo
ad
con
n
e
c
ted to
the tran
sformer i
s
neutralize
s
T
he
effect of in
du
ctive of tran
sf
orme
r
windi
n
g
s,
ferro
re
son
a
n
c
e o
c
curred
and
cau
s
e
s
the creatio
n o
f
unbalan
ce
d
curre
n
ts a
nd
large volta
g
e
s
in
the tran
sfo
r
m
e
r.
When
o
c
curren
ce
of ferrores
ona
nce
the tran
sfo
r
m
e
r
co
re i
s
e
n
tered
ma
gneti
c
saturation. T
h
is i
s
sue i
s
shown in fig
u
re 8. Fig
u
re
s
9 and
10
sh
o
w
s tran
sfo
r
m
e
r p
r
ima
r
y cu
rre
nt
curve
and
ca
pacito
r
voltag
e duri
ng the
occurre
n
ce
o
f
ferroresona
nce i
n
tran
sf
orme
r with i
r
on
core m
ade
of
the m
a
terial
GOES, re
sp
e
c
tively. In
this state,
cu
rre
n
t
and volta
g
e
cu
rve
s
g
e
t o
u
t
from si
nu
soid
al mode. Am
plitude of the
voltage an
d
curre
n
t is g
r
e
a
tly incre
a
se
d. Voltage a
nd
curre
n
t harm
onics are ca
u
s
ing
warming
and tran
sformer in
sulatio
n
damag
e.
Figure 8. The
hystere
s
is lo
op cu
rve du
ri
ng the occu
rrence
of Ferro
r
esona
nce
Figure 9. Tra
n
sformer
cu
rrent waveform
during
the o
c
curre
n
ce of Ferrore
s
o
nan
ce at the
trans
former core of GOES
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Inve
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c
e Phen
om
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e-Pha
s
e … (Behro
o
z
Re
zaeeal
am
)
256
Figure 10. Transfo
rme
r
voltage wavefo
rm durin
g
the occurre
n
ce of ferro
re
sona
n
c
e at the
trans
former core of GOES
By obtaining the hyste
r
e
s
is
loop when th
e occu
rre
nce
of fe
rro
re
son
ance and
by usin
g of
mentione
d m
e
thod, the va
lues
of
hysteresi
s
an
d ed
d
y
current lo
sses g
ene
rated
are
cal
c
ulate
d
in the transfo
rmer core. Lo
sse
s
cal
c
ul
ate
d
are sho
w
n i
n
the table 5.
Table 5. The
core losse
s
d
u
ring the o
ccurren
ce of Fe
rro
re
son
a
n
c
e
v
a
l
u
e o
f
los
ses
(
w
)
The t
y
p
e
of l
o
ss
es
15.7229 W
hy
ster
esis losses
0.1666 W
Eddy
curr
ent losses
The
results
of the si
mul
a
tion sho
w
t
hat du
ring t
he o
c
curren
ce of ferro
r
e
s
onan
ce
increa
se
s th
e core
lo
sses. In th
e
event that
f
e
rrore
s
o
nan
ce not
stop,
with
contin
uing
f
e
rro
re
son
a
n
c
e al
so in
cre
a
se
s t
he c
o
re
loss
es.
In the n
e
xt p
hase, tran
sfo
r
mer was test
ed Simila
r to
the tran
sfo
r
m
e
r p
r
evio
us.
With thi
s
differen
c
e
tha
t
only the
ma
gnetic core th
ese
tra
n
sfo
r
mer i
s
mad
e
up of
NGOE
S. Table
6
sh
ows
J-A
procedu
re pa
ram
e
ters for
co
re th
e
s
e type
of
tra
n
sformer.
Th
e voltage
an
d current
cu
rves
are sho
w
n in
the ferrore
sonan
ce mo
d
e
in Figure
s
11 and 12, resp
ectively. As can be
seen,
ferro
re
son
a
n
c
e
occu
rred i
n
the mil
der
mode. Al
so
, f
e
rrore
s
o
nan
ce mod
e
cha
n
ge i
s
du
e to t
h
e
cha
nge the iron co
re. Co
m
pare the
re
sul
t
s sho
w
s that
the material
s
use
d
in the transfo
rme
r
co
re
have creat an
essential rol
e
in the
occurren
ce of the ferrore
s
o
nan
ce.
Table 6. The
J-A meth
od p
a
ram
e
ters for t
he transfo
rmer core
with
NGOES mat
e
rial
s
va
l
u
e
parame
ters
1159000
s
M
177.69
a
359.99
k
0.1396
0.00035
c
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ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 2, May 2016 : 248 –
258
257
Figure 11. Transfo
rme
r
voltage wavefo
rm durin
g
the occurre
n
ce of ferro
re
sona
n
c
e at the
trans
former core of NGOE
S
Figure 12. Transfo
rme
r
cu
rre
nt waveform durin
g the occurre
n
ce of ferro
re
sona
n
c
e at the
trans
former core of NGOE
S
5. Conclusio
n
In this pape
r, using the finite element
method is been inve
stigated ferrore
s
on
an
ce
phen
omen
on
in transform
ers. Contra
ry
to previ
ous rese
arch, a new app
ro
ach
is provided f
r
om
review ferrom
agneti
c
m
a
terials
used i
n
t
he m
anufa
c
tu
re
of tra
n
sfo
r
mer
co
re
s. F
r
om two type
s of
magneti
c
m
a
terials G
O
ES and
NGOE
S is
used i
n
the
singl
e-p
hase tra
n
sfo
r
mer
co
re. T
he
followin
g
re
su
lts were obtai
ned by anal
y
z
ing the ferro
r
esona
nce ph
enome
non:
1.
Duri
ng o
c
cu
rrence of Fe
rro
r
es
ona
nce th
e tran
sformer co
re e
n
tere
d
to the inten
s
i
t
y magnetic
saturation. Current and vo
ltage get out of thei
r norm
a
l operating
mode an
d increa
se
s theirs
amplitude. T
h
is in
crea
sin
g
amplitud
e i
n
t
he
po
we
r transfo
rme
r
s are cau
s
e
s
creating
th
e
insul
a
tion failure an
d gettin
g
warmer of t
r
an
sform
e
rs.
2.
Con
s
id
erin
g t
he ma
gneti
c
hystere
s
i
s
in
the
si
mulati
ons is ve
ry
necessa
ry an
d impo
rtant.
Becau
s
e
the
behavio
r of f
e
rromag
netic material
s
used at the
equ
ipment
core i
s
reflecte
d i
n
magneti
c
hysteresi
s
curren
t.
3.
The
use of
G
O
ES materi
al
in the
tra
n
sf
orme
rs
core,
unlike the
lo
wer
core lo
sses
co
mpa
r
ed
to NGOS mat
e
rial, the more deleteri
o
u
s
effe
cts sho
w
durin
g occu
rrenc
e of Ferro
r
esona
nce.
Ferroresona
n
c
e in the tran
sform
e
rs mad
e
of
GOES material oc
curs with more int
ens
ity.
Referen
ces
[1]
Khan
SA, Bak
a
r AHA,
Rah
i
m NA a
n
d
T
an C.Ana
l
ysis
of
ferroreso
nanc
e
sup
p
ressi
on
a
nd tra
n
sie
n
t
respo
n
se p
e
rformanc
es for various ferr
o
r
eson
ance s
u
ppress
i
on c
i
rcuits in ca
paci
t
ive volta
g
e
transformers. In
3rd IET
Inter
natio
nal
Co
nfe
r
ence
on C
l
e
a
n
Ener
gy a
nd
T
e
chno
logy
(C
EAT
)
. 2014:
1-6.
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