Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
6, N
o
. 1
,
Mar
c
h
20
15
,
pp
. 56
~64
I
S
SN
: 208
8-8
6
9
4
56
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Multiphase Transformer Mode
lling using Finite Element
Meth
od
Nor
Az
iz
ah Mohd
Yusoff*,
Kasr
ul
Abdul Karim
*
, Sh
ar
in
Ab
Gh
ani
*
,
Tole
S
u
tikn
o**, Auz
a
ni Jid
i
n*
*
Facu
lty
of El
e
c
tri
cal
Eng
i
neer
i
ng, Un
iversi
ti
Te
knikal
Mala
ysi
a
Mela
ka (UTe
M),
Ma
la
cc
a,
Ma
lay
s
ia
** Departement
of Electr
i
cal
En
g
i
neer
ing, Univer
sitas Ahmad Dahlan, Yog
y
akar
ta, Indon
esia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 10, 2014
Rev
i
sed
D
ec 22
, 20
14
Accepte
d Ja
n
5, 2015
In the
y
e
ar
of 1
970 saw the star
ting inv
e
ntion
of
the f
i
ve-ph
a
se
motor as the
milestone in
ad
vanced
electr
ic
motor. Through
the
y
e
ars, th
er
e are man
y
res
earch
ers
,
whi
c
h pas
s
i
onat
e
l
y
work
ed towards develop
i
ng for
multiphas
e
drive s
y
stem
.
T
h
e
y
dev
e
lop
e
d
a sta
tic
tr
ansformation s
y
stem to obtain
a
multiphase supp
ly
from the av
ailable th
r
ee-ph
ase supply
.
Th
is idea g
i
ves
an
influen
ce
for fu
rther d
e
ve
lopm
ent in
el
ec
tric
m
achin
es
as
an
e
x
am
ple;
an
efficient solu
tio
n for bulk power transfer
. This
paper high
li
ght
e
d
the de
ta
il
descriptions that lead
to five-ph
a
se
supply
with
f
i
xed voltage
and
frequen
c
y
b
y
using
Finite-
E
lement Method
(FEM).
Iden
tif
ying of specification on a r
e
al
transformer had
been don
e b
e
for
e
app
lied
into
so
ftware modeling
. Th
erefor
e,
Finite-Element Method
provi
d
e
s clearly
understandable
in
terms of visualize
the g
e
ometr
y
mo
deling
,
connecti
on scheme
and o
u
tput wav
e
form.
Keyword:
Finite elem
ent
Fi
ve-
p
hase m
o
t
o
r
Mu
ltip
h
a
se
Three
-
phase
s
u
ppl
y
Transform
e
r
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
No
r Azizah
M
o
h
d
Y
u
so
ff
,
Facu
lty of Electri
cal Engineering,
Un
i
v
ersiti Tekn
ik
al Malaysia Melak
a
(UTeM),
76100 Duria
n
Tunggal, Mala
cca, Malaysia.
Em
a
il: k
a
sru
l
@u
tem
.
ed
u
.
m
y
1.
INTRODUCTION
Multiphase (more
t
h
an
t
h
ree
-
phase
)
system has bee
n
the foc
u
s
of
res
earch
recently
due t
o
their
intrinsic adva
ntages c
o
m
p
ared to
three-pha
se syste
m
s
.
The applica
tions of m
u
ltiphase system
s are
in
v
e
stig
ated
to
b
e
in
electric po
wer g
e
n
e
ration
,
tran
sm
issio
n
,
and
u
tilizatio
n
.
Si
x
ph
ase tran
sm
issio
n
lin
es can
provide t
h
e sa
me power capacity with a l
o
we
r
phase-t
o
-pha
se
voltage
and sm
aller, m
o
re com
p
act towe
rs
co
m
p
ared
to
a stan
d
a
rd
d
oub
le-circu
it th
ree-p
h
a
se lin
e.
Th
e geom
et
ry
of t
h
e si
x-
pha
se com
p
act
t
o
wers
m
a
y
al
so ai
d i
n
t
h
e
red
u
ct
i
o
n o
f
m
a
gnet
i
c
fi
el
ds
as wel
l
[1]
-
[
4]
.
The m
u
l
t
i
phase
m
o
t
o
rs are t
y
pi
cal
l
y
suppl
i
e
d b
y
ac/dc/ac conve
rters.
He
nce, t
h
e foc
u
s
of t
h
e researc
h
on th
e m
u
ltip
h
a
se electric d
r
i
v
e is li
m
i
ted
to th
e
m
odel
i
ng a
n
d
cont
rol
of
t
h
e
s
u
p
p
l
y
sy
st
em
s. As
t
h
ree
-
phas
e
supp
ly is d
i
rectly av
aila
ble from
the grid, t
h
ere
’
s
n
eed to
d
e
v
e
lop
a
fix
e
d
ph
ase tran
sfo
r
m
a
tio
n
system
to
o
b
t
ain
a m
u
lti-p
h
a
se supp
ly fro
m
ex
isting
three-p
h
a
se
su
pp
ly [5
].
Th
is
p
a
p
e
r literally p
r
o
p
o
s
ed
a con
tin
uou
s st
u
d
y
o
f
th
e
ph
ase tran
sfo
r
m
a
ti
o
n
system
wh
ereb
y
u
s
ing
available three
-
phase s
u
pply
tran
sform
in
to
m
u
l
ti-p
h
a
se sup
p
l
y d
e
v
e
lo
p
fro
m
th
e static
p
h
a
se tran
sformatio
n
sy
st
em
. Transf
orm
e
r i
s
beco
m
i
ng a key
i
n
st
rum
e
nt
i
n
t
h
e devel
opm
ent
of fi
ve-
p
hase
sup
p
l
y
vi
a sp
eci
al
trans
f
orm
e
r connection tec
hni
que
. T
h
is
conce
p
t
has
recently been
challenged
by
trans
f
orm
e
r studies
dem
onst
r
at
i
n
g t
h
ei
r w
o
r
k
i
n
g m
echani
s
m
an
d i
t
s
di
ffere
nt
vari
an
ts. Part of th
e ai
m
o
f
th
is p
r
o
j
ect is to
d
e
v
e
l
op
a fi
ve-
pha
se t
r
ansf
o
r
m
e
r operat
i
ng sy
st
em
that
i
s
com
p
at
ibl
e
usi
n
g Fi
ni
t
e
-El
e
m
e
nt
M
e
tho
d
t
h
ro
u
gh
A
N
S
Y
S
MAXWELL
3D softwa
re. B
a
sic bloc
k dia
g
ram
for the sys
t
e
m
is shown i
n
Fi
gure 1. By using Fi
nite-Ele
m
e
nt
tools, t
h
ree si
ngle-phase
transform
e
rs
m
ode
l have
bee
n
de
veloped according to act
ual
specification.
These
m
odel
s
t
h
en ca
n
be
dri
v
en
by
va
ri
o
u
s c
o
n
n
e
c
t
i
on sc
hem
e
s of t
h
e ci
rc
ui
t
(
S
t
a
r-St
a
r,
St
ar-
P
ol
y
g
o
n
,
Del
t
a
-St
a
r
or
Del
t
a
-P
ol
y
g
o
n
)
. M
i
ni
m
i
ze
t
h
e sco
p
e, t
h
i
s
pape
r f
o
c
u
sed
on t
h
e st
ar-st
a
r
con
n
ect
i
o
n sc
hem
e
. Fi
ni
t
e
-el
e
m
e
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Mu
ltip
ha
se
Tra
n
s
f
o
rmer Mod
e
llin
g
u
s
i
n
g Fin
ite Elemen
t
Meth
o
d
(No
r
Aziza
h
Mohd
Yuso
ff)
57
m
e
thod,
(FEM
) techni
que
s are useful to obtain an accu
rate
characterization
of th
e elect
rom
a
gnetic be
havi
or
of t
h
e m
a
gnet
i
c
com
pone
nt
s,
suc
h
as t
r
a
n
s
f
o
r
m
e
r. The
n
,
t
h
e m
a
i
n
adva
nt
ages
of
t
h
e
FEM
o
v
er t
h
e
ot
he
r
m
e
thods
beca
use its a
b
ility to s
k
etch m
odel
of t
r
an
sform
e
r in
ge
om
etrically
and s
o
lve c
o
m
positionall
y
com
p
lex probl
e
m
s [6]. In fa
ct, it
is capable to ta
ke into account the
non-lin
ea
rity and inhom
ogeneous
ch
ar
acter
istic
o
f
th
e m
o
d
e
l [
7
]. H
e
n
c
e, it r
e
su
ltin
g
a good
app
r
o
x
i
m
a
ti
o
n
to
th
e actual tr
an
sfo
r
m
e
r
m
o
d
e
l.
M
o
re
ove
r, t
h
e
t
r
ansi
ent
m
odel
coupl
e
d
wi
t
h
ext
e
r
n
al
ci
rcui
t
,
al
l
o
ws use
r
t
o
sim
u
l
a
t
e
t
h
e dy
nam
i
c behavi
or o
f
th
e tran
sform
e
r with
th
e
real p
o
wer
s
u
ppl
y
and e
x
t
e
r
n
al
l
o
ad c
o
nnect
i
o
n.
Th
is p
a
p
e
r
starts with
a detailed
descri
ption of Multiphase
concept
and
connection schem
e
in section 2. T
h
e
num
b
er of turn for each core was
estim
a
ted
accordi
ngly. In sec
tion 3
de
scri
be
d
the desi
gn
data based on t
h
e actual tra
n
s
f
orm
e
r. All this data
will b
e
e
m
p
l
o
y
ed
to
create th
e
m
o
d
e
l o
f
tran
sform
e
r u
s
i
n
g
FEM in
sectio
n
4
.
In
FEM, th
e m
o
d
e
l h
a
s typ
i
cally
been c
o
upled t
o
circuit sim
u
lation using ANSYS Circ
uit
Editor. This approac
h
can
be
very accurate, but with
lo
ng
duratio
n of ti
m
e
tak
i
n
g
fo
r sim
u
latio
n
.
Th
e
resu
lt fro
m FEM will b
e
sho
w
n
in th
is
sectio
n
.
It was
clearly
seen t
h
at
t
h
e
o
u
t
p
ut
i
s
a
bal
a
n
ced
fi
ve-
p
hase
su
ppl
y
c
o
nve
r
t
i
ng
fr
om
a bal
a
nced
t
h
ree-
p
h
a
se i
n
put
.
Fi
gu
re
1.
B
l
oc
k
rep
r
ese
n
t
a
t
i
on
of
t
h
e M
u
l
t
i
phase sy
st
em
2.
R
E
SEARC
H M
ETHOD
Th
is section
presen
ted
th
e tech
n
i
q
u
e
to
o
b
t
ain
of fi
v
e
p
h
ase as illu
strated
in
Figu
re
3, Figu
re
4,
Tabl
e 1
,
an
d
Tabl
e 2
.
T
h
e
pha
se v
o
l
t
a
ges
are al
l
eq
ual
i
n
m
a
gni
t
ude
but
onl
y
di
ffe
r
i
n
t
h
ei
r
out
p
u
t
phase
angl
e,
whi
c
h r
e
qui
red
f
o
r
ph
ase
an
gl
e 7
2
o
b
e
tw
een
each
p
h
a
se.
Th
e con
s
tru
c
tio
n for
o
u
t
p
u
t
ph
ase is found
u
s
ing
ap
pro
p
riate tu
rns ratio fro
m
th
e p
r
incip
a
l o
f
ph
asor d
i
ag
ram
.
The tu
rn
ratios of a tran
sfo
r
m
e
r are
defi
ned
as t
h
e
num
ber
of
t
u
r
n
s
on
i
t
s
p
r
i
m
ary
de
vi
de
d
b
y
t
h
e n
u
m
b
er
of t
u
r
n
s
o
n
i
t
s
seco
nda
ry
. T
h
e t
u
r
n
s
ratio of a tra
n
sform
e
r therefore
defi
nes t
h
e trans
f
orm
e
r as step-up or
step-down. Howeve
r,
alm
o
st
every
p
a
p
e
r th
at
h
a
s
b
een written
on
m
u
ltip
h
a
se tran
sfo
r
m
e
r in
clu
d
e
s a section relatin
g
t
o
turn
s
ratio
used
1:1
of
t
u
r
n
s
rat
i
o
.
U
n
der
t
h
i
s
c
o
ndi
t
i
on,
t
h
e
rat
i
o
o
f
t
h
e
i
n
put
t
o
out
put
v
o
l
t
a
ge
s w
o
ul
d
be e
q
ual
as i
n
e
quat
i
on
(
1
)
whe
r
e
is
d
e
fi
ned
the turn rati
o
o
f
th
e t
r
ansfo
r
m
e
r. By ex
amin
in
g
t
h
e simu
latio
n graph in
Fi
g
u
re
11
and
1
2
,
the output of t
h
e three phas
e
tran
sform
e
r in
2
0
V after tr
a
n
s
f
orm
i
ng from
three
phase to
five phase t
h
e output
is
also
rem
a
in
i
n
g
as 20
V.
(1)
Figure
2
below summ
arizes all necessa
ry steps
fo
r c
r
eat
i
n
g
a M
u
l
t
i
phase
o
f
po
wer
Tra
n
s
f
orm
e
r:
Fig
u
re
2
.
Modelin
g
p
r
o
cess of Mu
ltiph
a
se Tran
sfo
r
m
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
5
6
– 64
58
The phas
or diagram
for
multiphase is drawn
m
a
nually from
AutoCAD. T
h
e correct use of
Aut
o
C
A
Ds
di
m
e
nsi
on i
s
t
h
e key
t
o
p
r
o
d
u
ci
n
g
c
onsi
c
e
m
easured
dra
w
i
n
gs.
To
m
e
asure
t
u
r
n
s
rat
i
o, t
h
e
m
easurem
ent
of di
m
e
nsi
o
n
l
i
n
es phas
o
r
was use
d
.T
h
e
di
agram
i
n
Fi
gure
4 re
prese
n
t
s
t
h
e wi
n
d
i
n
g
arra
ngem
e
nt
i
n
o
r
de
r t
o
de
vel
o
p
a M
u
l
t
i
phas
e
sy
st
em
.
2.
1.
P
h
as
or Di
a
g
ra
m Co
n
s
truc
ti
on
In t
h
e t
r
a
n
sf
o
r
m
e
r
m
odel
i
n
g
t
h
e i
nput
p
h
a
s
es are i
ndi
cat
ed wi
t
h
l
e
t
t
e
rs “X”, “Y”, a
n
d “Z” refe
r
sp
ecifically to
th
e red
,
yellow and
b
l
u
e
co
lor wh
ile th
e ou
tput phases a
r
e i
ndicated w
ith letters “A”, “B”, “C”,
“D” an
d “E” co
rresp
ond
to the green co
l
o
r
as
illu
strated
i
n
Fig
u
re 2
o
f
ph
aso
r
d
i
ag
ram
.
Fi
gu
re
3.
P
h
as
or
re
prese
n
t
a
t
i
o
n
o
f
t
h
e M
u
l
t
i
pha
se t
r
a
n
sf
o
r
m
e
r co
nnect
i
o
n
Th
e turn
ratio
s will b
e
d
e
termin
ed
throug
h
ph
aso
r
s
caling
.
Th
is pro
c
ess can
b
e
d
o
n
e
m
a
th
em
a
ticall
y
b
y
ru
ling
th
e len
g
t
h
of th
e d
i
ag
on
al lin
e o
r
th
eir
m
a
gni
t
u
d
e
from
zero p
o
i
nt
. Fo
r exam
ple output phas
e “A”
(V
A
) is alon
g
with
inpu
t ph
ase “X”
(V
X
).
Next, t
h
e
out
put phase
for “
B
” (V
B
) will be d
e
term
in
ed
th
rou
gh
vect
o
r
a
ddi
t
i
o
n
o
f
t
w
o
v
o
l
t
a
g
e
s w
h
i
c
h
i
n
vol
ves
by
f
o
rm
i
n
g a
t
r
i
a
n
g
l
e
.
S
o
, t
h
e c
o
m
pon
ent
s
f
o
r
out
put
p
h
ase
“B” can be
formed by
ad
di
n
g
t
w
o
vect
o
r
s (
-
V
Z
+ V
Y
). Similarly, “C” (V
C
) is ob
tain
ed
fro
m
v
ecto
r
(-V
X
+
V
Y
). T
h
e
out
put of phase “
D
”
(V
D
) is
o
b
t
ai
n
e
d
b
y
th
e
v
ector ad
d
ition
of voltag
e
in
(-V
X
+ V
Z
) an
d
last bu
t no
t
least the output phase “E” (V
E
) is fro
m
th
e
v
ector su
m
o
f
v
o
ltag
e
(-V
Y
+ V
Z
). In
th
is way th
e fiv
e
p
h
a
ses are
obtaine
d from
three phase to
five phase.
Yet, it
may pr
oduc
e an error if not draw
n phas
or diagram
accurately
or c
o
rrect
l
y
t
o
scal
e. S
o
, t
h
e
n
u
m
b
er o
f
t
u
r
n
ca
n
be cal
cu
l
a
t
e
d by
a
ppl
y
i
ng t
h
e f
o
rm
ula pr
o
p
o
s
ed
gi
v
e
n i
n
Equ
a
tio
n (3
) with
in
itial n
u
m
b
e
r of turn
for
p
r
im
ary win
d
i
n
g
are acqu
i
re
fro
m
Farad
a
y’s law eq
u
a
tion in
(2).
Np
.
(2)
Whe
r
e:
V = RM
S
val
u
e
= fre
que
ncy
of
t
h
e fl
u
x
= Nu
m
b
er
o
f
t
u
rn
s
on
th
e pr
i
m
ar
y w
i
nd
ing
= Peak val
u
e
of the
flux
A = a
r
ea
of
b
o
bbi
n
4.
44
= a c
o
nst
a
nt
[e
xact
val
u
e
=
2
/
√2
]
Tab
l
e
1
an
d 2 sh
ow
s t
h
e
nu
m
b
er
o
f
t
u
rn
f
o
r
pr
im
ar
y an
d
seco
nd
ar
y of
tr
an
sf
or
m
e
r
u
s
ing
i
n
m
o
d
e
lin
g
by
f
o
l
l
o
wi
n
g
t
h
e
pr
o
pose
d
e
q
uat
i
o
n
bel
o
w
.
(3)
V
C
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I
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S
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:
208
8-8
6
9
4
Mu
ltip
ha
se
Tra
n
s
f
o
rmer Mod
e
llin
g
u
s
i
n
g Fin
ite Elemen
t
Meth
o
d
(No
r
Aziza
h
Mohd
Yuso
ff)
59
Table 1
.
Turn ratio
fo
r
Prim
ary tu
rn
s.
Prima
r
y
L
e
ngth
(V
oltage M
agnitude,
V
)
Turns, N
X
10
200
Y
10
200
Z
10
200
Tab
l
e
2
.
Tur
n
ratio
fo
r
Secondar
y
tu
rn
s.
Secondary
Length(V
oltage
M
agnitude,
V
)
Turns, N
X
10
200
4.
7508
95
Y
2.
4008
48
6.
7872
136
8.
5811
172
Z
2.
4008
48
6.
7872
136
8.
5811
172
2.
2.
Winding Con
n
ection Sc
he
me; s
t
ar
-s
tar
In
lin
e wit
h
Tab
l
e 1
and
Tab
l
e 2
can
b
e
seen
fo
r Mu
ltiph
a
se syste
m
, th
ree sin
g
l
e ph
ase
tran
sform
e
rs
are nee
d
e
d
(X, Y, and Z
)
. In each core carrying
one
pr
imary and thre
e seconda
r
y co
ils, exce
pt in core
‘x’
wh
ich
on
ly two
secon
d
a
ry co
ils are u
s
ed. Thu
s
, th
is en
tir
e tran
sform
e
r
co
nsists o
f
six ter
m
in
al o
f
p
r
i
m
aries
(V
X
, V
Y
and
V
Z
) and 16 te
rm
inals of seconda
r
y (V
A
, V
B
, V
C
, V
D
and
V
E
). T
h
e term
inal from
entire
tran
sform
e
r will b
e
conn
ected in
star-star con
n
ection
.
Fi
gu
re 4.
W
i
nd
i
ng
a
rra
n
g
em
ent
o
f
fi
ve p
h
as
e
t
r
ans
f
orm
e
r
3
.
MODEL
DETAIL
Sim
u
l
a
t
i
ons f
r
o
m
FEM
were carri
ed
o
u
t
based
o
n
cu
st
om
bui
l
d
of
si
ngl
e p
h
ase
,
shel
l
-
t
y
pe
trans
f
orm
e
r. Shell form
is
charact
e
r
i
zed
by
t
h
e wi
ndi
n
g
w
r
ap
pe
d ce
nt
ra
l to
th
e three-legg
ed
of
E an
d
I
l
a
m
i
nat
e
d core
. Fi
g
u
r
e
5 s
h
o
w
s t
h
e
phy
si
ca
l
sket
ch
di
m
e
nsi
o
n
o
f
m
a
gnet
i
c
core:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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-86
94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
5
6
– 64
60
Fi
gu
re
5.
C
o
re
Di
m
e
nsi
o
n
The wi
ndow
of c
o
re
will determ
ine the am
ount of
c
o
pper that a
ppea
r
s in the
window a
r
ea of
trans
f
orm
e
r. These e
n
tire fact
ors a
r
e a
dde
d t
oget
h
er; to
tal ab
ou
t 80
p
e
rcent fro
m
th
e whole window core area
(Figu
r
e 6). Th
e windo
w u
tilizatio
n
will b
e
i
n
flu
e
n
ced b
y
five factors
wh
ich is:
a)
In
su
latio
n of
wire
b)
Fill facto
r
c)
Effectiv
e wi
n
d
o
w
area (o
r when
u
s
ing
a to
ro
id
, th
e clearan
ce ho
le fo
r p
a
ssag
e shu
ttle)
d)
In
su
latio
n required
for m
u
ltip
layer wi
n
d
i
n
g
s
,
o
r
b
e
t
w
een wi
n
d
i
n
g
s
e)
Work
m
a
n
s
h
i
p
,
(q
u
a
lity)
Fi
gu
re 6.
W
i
nd
ow
ar
eas
fo
r
co
pp
er
B
y
em
pl
oy
i
ng t
h
e Equat
i
o
n
(2
) an
d (
3
),
d
a
t
a
were gat
h
e
r
ed a
nd
gi
ve
n as i
n
Tabl
e 3.
Hence, t
h
e
diam
e
t
er of the
wire is then be determ
ined by tran
sform
e
r
window size accordingl
y to the highest num
ber of
wind
ing
s
. By referring
to th
e
tab
l
e, core
‘y’
an
d cor
e
‘
z
’ h
a
s th
e
h
i
gh
est
valu
e of
55
6 tu
rn
s.
Tabl
e 3.
T
o
t
a
l
num
ber of
wi
n
d
i
n
g fo
r
eac
h
c
o
re
Co
re
Wind
ing
X
Y
Z
Pri
m
a
r
y 1
200
200
200
Secondar
y
1
200
48
48
Secondar
y
2
95
136
136
Secondar
y
3
-
172
172
Total
495
556
556
Di
am
et
er of
wi
re ca
n
be
det
e
r
m
i
n
ed u
s
i
n
g t
h
e Eq
uat
i
o
n (
4
):
(4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Mu
ltip
ha
se
Tra
n
s
f
o
rmer Mod
e
llin
g
u
s
i
n
g Fin
ite Elemen
t
Meth
o
d
(No
r
Aziza
h
Mohd
Yuso
ff)
61
= 6
7
m
m
x 20
m
m
=
134 m
m
2
d
2
=
0
.8
=
0.
241m
m
2
d =
√
0.024
1
=
0.
49m
m
/ 24
gauge
(
A
WG
)
4.
FEM SIMUL
A
TION RESULT
Multiphase sys
t
e
m
s of tra
n
sform
e
r in FEM
worki
n
g und
er
transient a
n
alysis can
be devi
ded
i
n
t
o
t
w
o
main
p
a
rts: Geo
m
etrical
ly
m
o
d
e
l an
d
exp
o
rt th
e ex
tern
al circu
it co
nn
ectio
n in
Max
w
ell
3
D
. Fu
rth
e
r
d
a
ta
co
llectio
n
is req
u
i
red
to
analyze th
e
m
o
d
e
l with
th
e electro
m
a
g
n
e
tic b
e
h
a
v
i
or im
p
l
e
m
en
ted
within
th
e
Mag
n
e
t
o
static so
lv
er.
4.
1.
Transformer
Model using F
E
M
Th
e
first stag
e o
f
th
e
sim
u
la
tio
n
is starts
with
sk
etch the g
e
o
m
etry
mo
d
e
l
fo
r t
h
ree
sin
g
l
e
ph
ase
tr
an
sf
or
m
e
r
b
y
Fin
ite Ele
m
e
n
t Meth
od
(
F
EM)
.
Figu
r
e
7 an
d
Figu
r
e
8 sh
ow
n
th
e
n
o
r
m
al
tr
an
sf
or
mer
w
a
s
m
odel
l
e
d bot
h
i
n
3D an
d 2
D
FEM
.
The p
r
i
m
ary
wi
ndi
n
g
and sec
o
n
d
a
r
y
wi
n
d
i
n
gs are r
e
prese
n
t
by
rec
t
angl
es
of co
rr
esp
o
ndi
ng m
a
t
e
ri
al
i
n
Tabl
e 4. T
h
e i
n
sul
a
t
i
o
n bet
w
een t
u
r
n
s an
d l
a
y
e
rs can be i
g
no
re
d com
p
l
e
tel
y
. To
enabl
e
t
h
e
fi
ve
-p
hase
out
put
c
a
n be see
n
cl
ea
rl
y
,
t
h
e so
ftware was carried
out with
certain analysis
setup. The
sh
eet
wind
ing
s
were assi
g
n
i
ng
with
co
il termin
al u
s
ing
the d
a
ta
fro
m
Tab
l
e 3.
Fin
a
lly,
th
e so
lu
tion
setu
p
fo
r
t
h
e param
e
t
e
rs used f
o
r s
o
l
v
i
ng t
h
e si
m
u
l
a
t
i
on
has t
o
be s
p
eci
fi
ed
.T
he t
r
ansf
o
r
m
e
r assem
b
ly
i
s
com
posed o
f
m
u
l
tip
le
m
a
teri
als and
th
eir mo
d
e
l
d
e
tails are listed
in
Tab
l
e 4
.
Tabl
e 4.
Detai
l
s o
f
Tran
sformer Mo
d
e
l
Specificatio
n
Classification
Specification
Voltage [V]
20
Fr
equency
[Hz]
50
Co
re Mate
rial
Steel 1008
W
i
nding M
a
ter
i
al
Copper
Fi
gu
re
7.
3D
m
odel
of t
r
a
n
s
f
orm
e
r i
n
F
E
M
Fi
gu
re
8.
2
D
m
odel
o
f
t
r
a
n
sf
o
r
m
e
r i
n
FEM
4.
2.
Circuit-c
oupled Connecti
o
n
Th
e tran
sien
t
m
o
d
e
l co
up
led
with ex
ternal circu
it b
a
sed
on
Fi
gu
re
4 co
nn
ection
sch
e
m
e
. Th
e
wind
ing
s
fro
m
fin
ite elem
en
t
m
o
d
e
l are driven
b
y
th
is
ex
tern
al circu
it (Fi
g
u
r
e 10
)
in star-star
circ
um
stance.
0.49mm
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-86
94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
5
6
– 64
62
Fi
gu
re
9.
T
r
an
sfo
r
m
e
r con
n
e
c
t
i
on sc
hem
e
from
ANS
YS
M
a
xweel
C
i
rc
ui
t
Edi
t
o
r
4.
3.
Mag
n
etic Flux
Density
The di
st
ri
b
u
t
i
on
of m
a
gnet
i
c
fl
ux de
nsi
t
y
sho
w
n i
n
Fi
gu
re 9 ge
ner
a
t
e
d by
t
h
e FEM
wi
t
h
t
h
e
tran
sform
e
r is
in
n
o
-lo
a
d
con
d
ition
b
y
Mag
n
e
t
o
static so
lv
er. As seen
in
th
e Figu
re
9
,
m
a
g
n
e
tic field
is
uni
fo
rm
ly
di
st
ri
but
ed
o
v
e
r
t
h
e
st
eel
core
. T
h
us, t
h
r
o
ug
h
t
h
e
color s
h
a
d
ed
(magnetic fi
eld, B), it clearly reveals
t
h
at
t
h
e
m
a
gn
et
i
c
fi
el
d di
st
ri
but
i
o
n
has a h
o
ri
z
ont
al
sy
m
m
e
t
r
y
axi
s
t
h
at
passes t
h
r
o
u
gh t
h
e m
i
ddl
e
of t
h
e
tran
sform
e
r core lim
b
s
.
Fi
gu
re 1
0
.
M
a
gnet
i
c
fi
el
d di
s
t
ri
but
i
o
n of
t
r
a
n
sf
orm
e
r
m
odel
by
FEM
.
0
0
0
L
W
i
ndi
ng
_A
+
20
V
Labe
l
I
D
=
V
3
L
abe
l
I
D
=
I
V
o
l
t
m
et
er
6
LW
i
n
d
i
n
g_B
LW
i
n
d
i
n
g_C
LW
i
n
d
i
n
g_F
LW
i
n
d
i
n
g_E
L
abe
l
I
D
=
I
V
o
l
t
m
et
er
5
6
+
20V
Labe
l
I
D
=
V
5
8
LW
i
ndi
ng_
D
LW
i
n
d
i
n
g_J
LW
i
n
d
i
n
g_I
Lab
el
I
D
=
I
V
o
l
t
m
e
t
e
r
6
8
+
20
V
L
abel
I
D
=
V
70
LW
i
ndi
ng_
H
LW
i
n
d
i
n
g_G
LW
i
ndi
ng_
K
L
abel
I
D
=
I
V
o
l
t
m
e
t
e
r
1
2
2
0
La
bel
I
D
=
I
V
o
l
t
m
e
t
e
r
1
2
8
La
bel
I
D
=
I
V
o
l
t
m
e
t
e
r
129
Labe
l
I
D
=
I
V
ol
t
m
et
er
1
3
0
Labe
l
I
D
=
I
V
ol
t
m
et
er
1
3
1
0
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Mu
ltip
ha
se
Tra
n
s
f
o
rmer Mod
e
llin
g
u
s
i
n
g Fin
ite Elemen
t
Meth
o
d
(No
r
Aziza
h
Mohd
Yuso
ff)
63
4.
4.
Result
Ou
tpu
t
Wa
ve
form
Fi
gu
re
11 a
n
d
Fi
gu
re
12
re
prese
n
t
t
h
e
re
sul
t
s
i
n
p
u
t
a
n
d o
u
t
p
ut
vol
t
a
ge wa
ve
fo
rm
s fr
om
Fi
ni
t
e
Ele
m
en
t Meth
o
d
(
F
EM)
.
I
t
is clear
ly seen
t
h
at th
e
o
u
t
p
u
t
is a b
a
lan
c
ed
fiv
e
-p
h
a
se supply f
r
o
m
a th
r
e
e-
ph
ase
in
pu
t.
I
n
d
i
v
i
d
u
al o
u
t
p
u
t
ph
ases ar
e
sho
w
n alo
n
g
w
ith
t
h
eir
r
e
sp
ectiv
e input v
o
ltag
e
s.
Figure 11.
Three
phase
i
n
p
u
t fr
om
ANS
YS M
a
xweel
Fi
gu
re
1
2
.
B
a
l
a
nced
o
u
t
p
ut
o
f
fi
ve
pha
se t
r
a
n
sf
orm
e
r f
r
om
AN
SY
S M
a
x
w
eel
5.
CO
N
C
LUS
I
ON
Thi
s
pa
pe
r de
al
s wi
t
h
t
h
e c
ont
ri
b
u
t
i
on t
o
devel
op a t
r
an
si
ent
m
odel
of
t
r
ans
f
o
r
m
e
r cou
p
l
e
d
wi
t
h
ext
e
r
n
al
ci
rcui
t
.
Th
us
, i
n
vol
vi
ng
o
f
i
d
e
n
t
i
cal
act
ual
t
r
an
sfo
r
mer sp
ecificatio
n to
tran
sform
th
e th
ree-phase to
a
fiv
e
-ph
a
se ou
tp
u
t
supp
ly u
s
in
g
FEM. Ex
ten
s
iv
e sim
u
la
tio
n
clarify th
e ab
ility o
f
FEM
to
clearly v
i
su
alize th
e
m
odel and pat
t
ern of electromagnetic characteristic of
t
h
e t
r
an
sf
orm
e
r. The c
o
n
n
ect
i
on sc
hem
e
and t
h
e
p
h
a
sor
d
i
agram
a
l
o
n
g
with t
h
e turn
ratios
were d
i
stin
ctly illu
strated
.
ACKNOWLE
DGE
M
ENT
Th
e au
t
h
ors wo
u
l
d
lik
e to
th
an
k
Un
i
v
ersiti Tek
n
i
k
a
l Mal
a
ysia Melak
a
(UTeM
)
and
Min
i
stry of
Edu
catio
n
(KPM)
f
o
r
sponso
r
i
n
g
th
is r
e
sear
ch
w
o
r
k
s u
n
d
e
r
gr
an
t
(
F
RG
S/
2
/
20
13
/TK02
/
U
T
EM/0
2
/
7)
.
Co
rrespon
d
i
n
g
ly to
ANSYS
Max
w
ell so
ft
ware for th
e
capab
ilities requ
ired
toward
s th
e co
m
p
letio
n
o
f
th
is
wo
rk
s.
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r J, Sha
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0.
00
2.
50
5
.
00
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50
10.
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Ti
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m
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[
m
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1
2.
50
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00
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5
0
25
.
0
0
Y1
[
V
]
M
a
xw
e
l
l
3
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D
e
si
g
n
2
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Y
P
l
ot
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r
v
e
In
f
o
N
o
deV
o
l
ta
ge
(
I
V
o
l
t
m
e
te
r
122
)
S
e
tu
p1
: T
r
a
n
s
i
e
n
t
N
o
deV
o
l
ta
ge
(
I
V
o
l
t
m
e
te
r
123
)
S
e
tu
p1
: T
r
a
n
s
i
e
n
t
N
o
deV
o
l
ta
ge
(
I
V
o
l
t
m
e
te
r
124
)
S
e
tu
p1
: T
r
a
n
s
i
e
n
t
N
o
deV
o
l
ta
ge
(
I
V
o
l
t
m
e
te
r
125
)
S
e
tu
p1
: T
r
a
n
s
i
e
n
t
N
o
deV
o
l
ta
ge
(
I
V
o
l
t
m
e
te
r
126
)
S
e
tu
p1
: T
r
a
n
s
i
e
n
t
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