Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol.
5, No. 6, Decem
ber
2015, pp. 1262~
1
274
I
S
SN
: 208
8-8
7
0
8
1
262
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
/
IJECE
Numerical and Experimental Inves
tigation of Bridge Currents
of an Induction Machine Equipp
ed with Bridge Confi
g
ured
Winding
Si
var
am
akri
s
hna
n Na
tes
a
n
*
, Kar
u
n
a
K
a
l
i
ta
*, Ven
k
a
t
es
u
S
a
mal
a
**
* Departm
e
nt
of
Mechani
cal
Eng
i
neering
,
Ind
i
an
I
n
stitute
of
Te
chn
o
log
y
Guwahat
i
,
India
** ICON Design and Automation
,
Bangalore, Ind
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 25, 2015
Rev
i
sed
Ju
l 14
,
20
15
Accepte
d Aug 3, 2015
An e
c
c
e
n
t
r
ic
rotor mot
i
on i
m
ba
la
nc
e
s
t
h
e magn
etic field distr
i
b
u
tion in
the
air-gap reg
i
on.
Due to this uneven flux de
nsity
d
i
stribution
,
a net radial force
called Unbalanced Magnetic Pull (UMP) is
in act
ion towards the
shortest air-
gap. This
UM
P can degrade t
h
e m
achine’s
perform
ance
. UM
P
can be
controlled b
y
a
special kind of wi
nding called Bridge Configur
ed Winding
(BCW). The BCW winding is a single set of
winding which is used to
produce th
e torq
ue as well as th
e
controll
able for
ce.
The main co
ntribution of
this paper is to
inspect th
e flow
of bridge curre
nts in the bridg
e
s when the
machine is having rotor ecc
entricity
or unbalance. Th
e bridge cu
rrents in th
e
presence of roto
r eccentr
icity
with th
e stator of
an Induction
machine model
has
been
ana
l
yz
ed b
y
us
ing
an
Ele
c
tr
om
agnet
i
c
Finite
El
em
ent
(FE) solve
r
cal
led Oper
a 2D
/RM
s
o
lver (Rot
ation M
o
t
i
on An
al
y
s
is
).
The br
id
ge curr
ents
have been meas
ured for two differe
nt
cases, (i) Induction machine model
with zero e
cce
ntrici
t
y
, (i
i) In
ducti
on machin
e model with 10% static
ecc
entri
c
it
y
of
the a
i
r gap
.
E
xperim
e
nta
l
res
u
lts
are
pres
en
t
e
d for th
e
valid
ation
of Op
era 2D/RM
results. A
modified 3
7kW Induction
machine h
a
s
been used fo
r this stud
y
.
A kn
own mass unbalance is in
trodu
ced in
the
perforat
e
d dis
c
i
n
order to cr
eat
e the unb
alan
ce
in the s
y
s
t
em
purpos
efu
l
l
y
.
The bridge cur
r
e
nts have been
measur
ed and compared with and without
unbalan
ce pr
esent in
the s
y
stem. Th
e
comparison of measu
r
ed bridg
e
currents
fo
r a
l
l
t
h
e c
a
s
e
s
ar
e g
i
ven in
the frequ
ency
domain.
Keyword:
B
r
i
dge
C
o
nfi
g
ure
d
Wi
n
d
i
n
g
Fin
ite Elem
en
t
Sim
u
lat
i
o
n
I
ndu
ctio
n m
a
c
h
in
e
Un
bal
a
nce
d
M
a
gnet
i
c
P
u
l
l
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
:
Karun
a
Kalita,
Dep
a
rtm
e
n
t
o
f
Mech
an
ical
Eng
i
n
e
ering
,
Ind
i
an
In
stitu
te o
f
Techn
o
l
o
g
y
,
Gu
wah
a
ti,
A
ssam
-
7
810
39, Ind
i
a, +9
1-
361
-25
826
80
.
Em
a
il: k
a
run
a
.k
alita@iitg
.ernet.in
1
.
IN
TR
OD
UC
TI
ON
In electrical machines
UMP
occurs
due
to t
h
e rotor ecce
ntricity present i
n
the system
a
nd it tends t
o
furth
e
r in
crease th
e ro
tor eccen
tricity. Th
is
may lead
to
t
h
e excessi
ve vi
b
r
at
i
o
n
,
st
at
or
a
nd
r
o
t
o
r r
u
bbi
n
g
, a
n
d
wear of bea
r
ing. It m
a
y reduce the
m
achine’s perform
ance, if they are
not
sufficien
tl
y co
n
t
ro
lled
.
So
, it is
very
i
m
port
a
nt
t
o
kn
o
w
ab
ou
t
t
h
e dy
nam
i
c
beha
vi
o
r
o
f
U
M
P act
i
ng o
n
t
h
e rot
o
r
du
ri
n
g
t
h
e desi
gn
p
r
oces
s
and c
o
nst
r
uct
i
on
of a
hi
g
h
s
p
eed
rot
a
t
i
n
g
m
achi
n
es. O
v
e
r
h
u
n
d
r
ed y
ear
s ago
,
m
a
ny
researche
r
s
have
st
udi
e
d
abo
u
t
t
h
e
so
u
r
ce an
d t
h
e
nat
u
re
o
f
t
h
e
UM
P an
d
ho
w i
t
c
a
n
be m
i
nim
i
zed. T
h
e
UM
P
can
be c
ont
r
o
l
l
ed
by
som
e
speci
al
k
i
nd
of
wi
ndi
ng
schem
e
s such
as d
u
al
set
of
s
t
at
or
wi
n
d
i
n
g,
si
ngl
e set
of
st
at
or
wi
n
d
i
n
g,
d
a
m
p
er
wi
n
d
i
n
g, seri
es
and pa
ral
l
e
l
wi
ndi
n
g
, e
qual
i
z
i
ng co
n
n
ec
tions in
p
a
rallel win
d
i
n
g
wh
ich
are p
r
esen
ted
in
[1
].
BCW is a single set o
f
wind
i
n
g wh
ich can
b
e
u
s
ed as a
bu
ilt-in
force actu
ato
r
. Th
e imp
o
rtan
t
feature o
f
th
is
typ
e
o
f
wi
n
d
i
ng
con
n
e
ctio
n
i
s
th
at it req
u
i
res a relativ
ely
lo
w curren
t
and
lo
w
vo
ltag
e
for th
e lateral force
pr
o
duct
i
o
n.
It
can el
i
m
i
n
at
e t
h
e d
r
aw
bac
k
s by
usi
ng
d
u
a
l
set
of
wi
n
d
i
ng c
o
n
n
ect
i
o
n. T
h
e l
a
t
e
ral
fo
rce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Nu
m
e
rica
l and Exp
e
ri
m
e
n
t
a
l
I
n
vestiga
tion
of Brid
g
e
Cu
rren
ts
o
f
an
I
ndu
ctio
n
…
(S
ivaram
a
k
rishn
a
n
N
a
tesa
n
)
1
263
pr
o
duct
i
o
n
has
bee
n
e
x
pl
ai
ne
d i
n
[
2
]
,
[3]
by
t
h
e B
C
W i
n
a
pol
y
pha
se i
n
d
u
ct
i
o
n
m
achi
n
e f
o
r a
c
t
i
v
e
vi
b
r
at
i
o
n
co
n
t
ro
l. Th
e dyn
amics o
f
th
e b
r
idg
e
con
f
i
g
u
r
ed
bu
ilt-in
fo
rce is p
r
esen
t
e
d
in
[4
]. An
an
alytical
m
o
d
e
l h
a
s
b
een
u
s
ed
to
co
n
t
ro
l th
e flexu
r
al v
i
b
r
ation
in
BC
W
b
a
sed
cag
e ind
u
c
tion
m
ach
in
e b
y
th
is lateral fo
rce. Th
e
prese
n
t
pa
per d
e
scri
bes t
h
e m
odel
i
n
g an
d si
m
u
l
a
t
i
on of a b
r
i
d
ge co
nfi
g
u
r
e
d
wi
n
d
i
n
g base
d i
n
d
u
ct
i
o
n m
a
chi
n
e
by
usi
n
g
Ope
r
a
2
D
/
R
M
sol
v
er
.
The real
t
i
m
e
engi
neeri
ng
pr
obl
em
s have b
een suc
cessf
ul
l
y
appl
i
e
d i
n
n
u
m
e
ri
cal
m
e
t
hods
wi
t
h
t
h
e
hel
p
of m
ode
r
n
hi
gh
spee
d
di
gi
t
a
l
com
put
ers. Fi
ni
t
e
El
em
ent
M
e
t
hod
i
s
one
of t
h
e
im
port
a
nt
num
eri
cal
m
e
t
hods w
h
i
c
h pr
o
v
i
d
e co
m
put
at
i
onal
t
e
chni
que
s fo
r t
h
e anal
y
s
i
s
an
d t
h
e sol
u
t
i
o
n
of t
h
e m
a
t
h
em
at
i
cal
pr
o
b
l
e
m
s
. Duri
ng
rece
nt
deca
des, t
h
e u
s
e o
f
FEM
t
ool
fo
r t
h
e n
u
m
e
ri
cal
sim
u
l
a
t
i
on has
b
ecom
e
m
o
re p
o
p
u
l
a
r
because of
its wide range of appli
cations. The
utilization of c
o
mm
ercial
software
is now available
for t
h
e
im
pl
em
ent
a
t
i
o
n o
f
Fi
ni
t
e
El
e
m
ent
t
echni
q
u
e
s. O
p
era
FE
M
soft
wa
re i
s
one
of t
h
e fi
ne
st
t
ool
s f
o
r t
h
e
2D a
n
d
3D electrom
a
gnetic analysis. Most of th
e fi
n
i
t
e
el
em
ent
pro
b
l
e
m
s
have been sol
v
ed
by
2D sol
v
e
r
i
n
o
r
der t
o
av
o
i
d
th
e co
mp
lex
ity in
n
a
ture as
well as t
h
e tim
e
an
d
the co
st. Co
m
p
arativ
ely few literatu
res h
a
v
e
b
een
st
udi
e
d
ab
out
t
h
e ne
w wi
ndi
ng sc
hem
e
call
e
d B
C
W
as
wel
l
as t
h
e ut
i
l
i
zat
i
on of O
p
era
2D a
n
d
3D
FE
Soft
ware
for an electrom
a
gnetic anal
ysis.
An effect of di
scretization of
th
e 2
D
indu
ctio
n
m
ach
in
e mo
d
e
l and
th
e sim
u
latio
n
o
f
3D
Op
era
FE Mod
e
l has
been
p
r
esen
ted
in
[5
],
[6
]. It
uses th
e m
u
lti-slice
m
o
d
e
l wit
h
th
e
st
rai
ght
r
o
t
o
r
b
a
r f
o
r t
h
e
di
sc
r
e
t
i
zat
i
on o
f
2D
m
odel
whi
c
h
can
pr
o
v
i
d
es
t
h
e
3D
en
vi
r
o
n
m
ent
.
The
res
u
l
t
s
of
2D
m
odel
ha
v
e
bee
n
c
o
m
p
ar
ed
wi
t
h
t
h
e
re
sul
t
s
o
f
3
D
skewed ro
tor
b
a
r m
o
d
e
l. Th
e resu
lt shows t
h
at th
e
skew
ed
r
o
to
r
b
a
r re
d
u
ces t
h
e
rot
o
r
ba
r c
u
r
r
e
n
ts. T
h
e
ve
ri
fi
cat
i
on
of
fi
el
d
-
ci
rcui
t
FM
m
odel
s
of a
n
i
n
du
ct
i
on
m
o
t
o
r i
s
descri
bed i
n
[
7
]
by
usi
n
g
Ope
r
a 2
D
st
eady
st
ate
(AC) sol
v
er a
n
d Tra
n
sie
n
t analysis (RM analysis)
m
e
t
hods
wi
t
h
t
h
e ex
pe
ri
m
e
ntal
resul
t
s
. T
h
e
m
achi
n
e pe
rf
o
r
m
a
nce was al
so st
u
d
i
e
d
by
DC
i
m
pul
se t
e
st
. The
charact
e
r
i
zat
i
on
of
m
achi
n
e be
havi
or
ha
s
bee
n
pre
s
en
t
e
d in [8]-[10]. T
h
e m
achine pa
ram
e
ters suc
h
as
effi
ci
ency
, t
o
r
que
, p
o
we
r l
o
s
s
and wi
ndi
ng
curre
nt
s ha
ve
been m
easured and com
p
ar
ed at various slip for
diffe
re
nt rot
o
r
bar m
a
terials
and
diffe
re
nt rot
o
r steel sheet thick
n
ess.
A
n
al
ysis h
a
s b
een
do
n
e
f
o
r
0.35
mm an
d
0.
50m
m
non o
r
i
e
nt
ed st
eel
sh
eet
t
h
i
c
kness o
f
rot
o
r co
re l
a
m
i
nat
i
ons are sho
w
e
d
i
n
[9]
.
I
t
can be not
i
c
e
d
t
h
at
t
h
e re
sul
t
s
of
0.
35m
m
t
h
i
c
kness
r
o
t
o
r
c
o
re
l
a
m
i
nat
i
on m
odel
has
g
o
o
d
ag
reem
ent
s
t
h
an
0.
50m
m
t
h
i
c
kne
s
s
rot
o
r c
o
r
e
l
a
m
i
nat
i
o
n
m
odel
.
Sim
u
l
a
t
i
on ha
s
bee
n
do
ne
fo
r
al
um
i
n
i
u
m
and co
ppe
r
rot
o
r
b
a
r m
a
t
e
ri
al
i
nduct
i
o
n
mach
in
e m
o
d
e
ls are p
r
esen
ted
in
[1
0
]
. Th
e
resu
lts show th
e cop
p
e
r ro
tor b
a
r is b
e
tter t
h
an
alu
m
in
iu
m ro
tor
bar
.
M
odel
i
n
g
and si
m
u
l
a
t
i
on of a sy
nch
r
o
n
ous
gene
rat
o
r,
In
d
u
ct
i
on m
a
chi
n
e an
d a reci
pr
ocat
i
n
g act
u
a
t
o
r by
Ope
r
a 2D for
the m
achine c
h
aracterization
have been presented
in
[11]. Opera
2D/R
M analysis has bee
n
in
clu
d
e
d fo
r the effect of
ro
t
o
r,
ro
t
o
r sk
ewn
e
ss, an
d ro
tor sl
o
ttin
g
.
Th
e
u
tilizatio
n
o
f
i
n
bu
ilt ro
t
o
r b
a
r
m
o
d
e
ls
in
th
e lib
rary of Op
era
2D so
ftware
h
a
s b
e
en u
s
ed
in
[12
]
fo
r
th
e In
du
ction
m
ach
in
e ana
l
ysis. Torque
,
stator
current and ohmic
losses ha
ve been
calcula
ted for all the
m
odels and c
o
m
p
ared with
each othe
r.
A time
st
eppi
ng
fi
ni
t
e
el
em
ent
m
e
t
h
o
d
has
bee
n
use
d
i
n
[
1
3]
fo
r t
h
e el
ect
rom
a
gnet
i
c
anal
y
s
i
s
of a bri
d
ge c
o
n
f
i
g
ur
e
d
base
d Induction m
achine. It
can
be
obse
r
ve
d that t
h
e frequency c
o
m
ponent of
UMP due
to eccentric
ity
has
good agreem
e
n
ts with t
h
e a
n
alytical
and ex
peri
m
e
nt
al
resul
t
s
. A
n
e
xpe
ri
m
e
nt
al
set
up
h
a
s bee
n
dem
o
n
s
t
r
at
ed
i
n
[
1
]
fo
r t
h
e
un
bal
a
nce
det
e
ct
i
on i
n
a
bri
d
ge co
n
f
i
g
u
r
ed
in
du
ctio
n m
a
c
h
in
es. Th
e equ
a
lizin
g
cu
rren
ts or
bri
dge c
u
r
r
ent
s
fl
ows i
n
t
h
e s
y
st
em
due t
o
unbal
a
nce p
r
ese
n
t
i
n
t
h
e sy
st
em
. The equal
i
z
i
ng cu
rre
nt
o
r
bri
dge
current ca
n
be
use
d
as a
m
eas
ure
of
unbalance present i
n
t
h
e syste
m
.
The cha
r
acteri
zation of a
n
induction m
achine and
the m
a
chine
’
s
performance
has bee
n
analyzed by
usi
n
g di
f
f
ere
n
t
con
duct
o
r m
a
t
e
ri
al
, di
ffer
e
nt
rot
o
r core l
a
m
i
nat
i
on
m
a
t
e
ri
al
, di
ffe
rent
cross sect
i
o
n o
f
rot
o
r
bars a
nd m
u
l
t
i
sl
i
ce
m
e
t
hod i
n
O
p
era FE s
o
ft
ware ar
e con
s
i
d
ere
d
i
n
t
h
e exi
s
t
i
ng w
o
rk
. Ho
we
ver
,
t
h
er
e i
s
no
im
pl
em
ent
a
t
i
o
n
of t
h
e
bri
dge
co
nfi
g
u
r
ed
wi
ndi
ng
sc
hem
e
al
on
g
wi
t
h
t
h
e
do
u
b
l
e
l
a
y
e
red
st
at
or
wi
n
d
i
n
g
.
T
h
e
main cont
ribution
of the
pres
ent work is
that to analy
ze t
h
e e
ffect
of
rotor ecce
ntri
city or unbalance
in the
sy
st
em
on t
h
e bri
dge c
u
r
r
ent
s
i
n
a B
C
W
ba
sed I
n
d
u
ction m
o
tor. The numerical
results from
Opera
2
D
/RM
have
bee
n
val
i
dat
e
d
wi
t
h
t
h
e ex
peri
m
e
nt
al
resul
t
s
.
Thi
s
pa
per
has
be
en
di
vi
de
d i
n
t
o
si
x
sect
i
o
ns.
The
literatu
re rev
i
ew to
t
h
e cu
rren
t
wo
rk
h
a
s
b
een pres
en
ted
in
Section
1
.
Sectio
n
2
ex
p
l
ains
th
e work
i
ng
p
r
i
n
cip
l
e
o
f
B
r
idg
e
Con
f
i
gured
Wi
n
d
i
n
g
sch
e
m
e
. Sectio
n
3
illu
strates th
e m
o
d
e
lin
g and
an
alysis o
f
an
Induction m
achine i
n
Opera
2D
which
ela
b
orates t
h
e tra
n
s
i
ent analysis (R
M An
alysis). Also, th
e m
o
delin
g
o
f
an
air
g
a
p
r
e
gio
n
and
w
i
nd
in
g
conn
ectio
n
in
O
p
er
a 2
D
ex
tern
al circu
it ed
ito
r h
a
s b
e
en
p
r
esen
ted in
thi
s
section. The induction m
achine
has
bee
n
modele
d
for two
diffe
re
nt
cases
suc
h
as, (i) Zero ecce
ntricity m
odel
,
(ii) 10% static eccentricity
m
odel.
The
10%
rot
o
r ecce
ntric
ity is given in
t
h
e ne
gative
Y- direction. Sect
ion
4.
dem
onstrates the experim
e
ntal rig set up.
The com
p
ar
ison
of ob
tain
ed
Op
era 2D/RM resu
lts, v
a
lid
atio
n
of
Op
era
2D results with
th
e exp
e
rim
e
n
t
al resu
lts and
con
c
l
u
si
o
n
a
r
e
pres
ent
e
d i
n
Se
ct
i
o
n
5. a
n
d Sect
i
o
n
5
.
5
.
respectively.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1262 –
1274
1
264
2
.
BR
ID
GE
CON
F
IGUR
ED WIND
IN
G
Th
e BC
W can b
e
u
s
ed as a b
u
ilt-in fo
rce actu
a
to
r. BC
W can
pro
d
u
c
e b
o
t
h
torq
u
e
as well as a
co
n
t
r
o
llab
l
e t
r
an
sv
er
se fo
r
c
e. Figu
r
e
1 show
s the
d
oub
le
layer
e
d
d
i
str
i
bu
ted
t
h
r
e
e ph
ase, fou
r
po
le
w
i
nd
ing
.
The stator
winding connecti
o
n has been
done accordi
ng t
o
the circuit
connection as shown in Figure 2. An
ad
d
ition
a
l 2-pole field
h
a
s
b
e
en
in
trod
u
c
ed
pu
rpo
s
efu
lly with
th
e
4
-
p
o
l
e
fun
d
a
m
e
n
t
al field
b
y
sh
ort circu
itin
g
t
h
e bri
dges
.
B
y
, supe
ri
m
posi
t
i
on of t
h
i
s
2
-
pol
e fi
el
d a
nd
4-
p
o
l
e
fi
el
d can pr
o
duce a f
o
rce cal
l
e
d l
e
vi
t
a
t
i
on
fo
rce w
h
i
c
h
ca
n be
use
d
t
o
c
o
u
n
t
e
ract the
UMP whic
h is already pres
en
t in
th
e system
. B
C
W
can
p
r
ov
ide
b
o
t
h
th
e t
h
ree p
h
a
se m
o
to
r supp
ly
and
three iso
l
at
ed
lev
itatio
n
p
o
wer supp
ly
. The fact that
it can be pos
sible to gene
ra
te th
e rad
i
al fo
rces
b
y
sho
t
-circu
itin
g
the
bri
dges
S
1
, S2
and
S
3
.
Fi
gu
re
1.
A
wi
ndi
ng
sc
hem
e
of
a
di
st
ri
b
u
t
e
d
d
o
u
b
l
e
layer
e
d
w
i
nd
ing
Fi
gu
re
2.
A
b
r
i
dge
co
n
f
i
g
ure
d
wi
n
d
i
n
g ci
rcui
t
The curre
nt re
sponsi
ble for the torque production a
r
e di
vided i
n
to two parallel paths in each phas
e
.
Consi
d
er t
h
e Phase-A
winding connec
tio
n
of th
e indu
ctio
n
m
o
to
r,
with
t
w
o
p
a
rallel b
r
an
ch
es co
m
p
risin
g
ten
series-c
onnect
ed coils each,
shown in
Figure 2. T
h
e currents flowing in
the arm
AB and CD are s
a
m
e
in
direction and m
a
gnitude
but bot
h the ar
m
s
were c
o
nnecte
d
in diam
etrically
opposite to each ot
her at a spa
n
of
18
0
o
.
Similarly, AC a
nd B
D
arm
s
were connected i
n
th
e s
a
m
e
fashion.
The
bra
n
c
h
es
AB and CD
have the
sam
e
p
o
l
arity wh
ile bo
th
bran
ch
es AC and
BD h
a
v
e
th
e op
po
site po
larity with
resp
ect to
AB and
CD. Th
e
bra
n
c
h
es AB
and C
D
have si
m
i
l
a
r feat
ure and t
h
ey
can
be
gro
u
p
ed t
o
get
h
er
. Li
kewi
se
, bra
n
c
h
es AC
and B
D
are set to be an another
group. Th
e
s
e two c
o
il groups are
placed diam
etri
cally opposite
to each other
in th
e
st
at
or sl
ot
s
.
T
h
e cur
r
e
n
t
fl
o
w
i
n
g
acr
oss B
C
i
s
cal
l
e
d l
e
vi
t
a
t
i
on c
u
r
r
e
n
t
o
r
bri
dge c
u
rre
nt
and
i
t
i
s
very
s
m
all
w
h
en
co
mp
a
r
ed
to th
e
cur
r
e
n
t
f
l
ow
ing
a
c
r
o
ss AD i.e., called m
a
in
supp
ly cu
rren
t.
2.1. Wor
k
ing Principle
of
B
r
idge Confi
g
ured
Winding
An
une
ve
n flux de
nsity distributio
n due to rotor eccentricity or unba
la
nce
prese
n
t in the syste
m
can
pr
o
duce a
n
ad
d
i
t
i
onal
fl
ux
of
pol
e pai
r
(w
he
re, p i
s
t
h
e n
u
m
ber of fu
n
d
a
m
ent
a
l
pol
e pa
i
r
s).
Any
o
n
e o
f
th
is add
itio
n
a
l
flu
x
po
le p
a
ir can
in
teract
with
th
e
f
und
amen
tal p
o
l
e pair flux
, a si
gn
ifican
t
n
e
t tran
sverse
fo
rce (
U
M
P
) c
a
n be
p
r
o
d
u
ce
d. B
C
W
sche
m
e
wor
k
s
on t
h
i
s
p
r
i
n
ci
pl
e
.
An a
d
di
t
i
onal
2-
p
o
l
e
fi
el
d
ha
s bee
n
i
n
t
r
o
d
u
ced
pu
r
pos
ef
ul
l
y
wi
t
h
t
h
e 4-
p
o
l
e
fu
n
d
am
ent
a
l
fi
el
d
by
sh
ort
ci
rcui
t
i
ng t
h
e b
r
i
d
ge
s. B
y
superi
m
posi
n
g
t
h
i
s
2-
pol
e fi
el
d an
d 4
-
p
o
l
e
fi
el
d, a l
e
vi
t
a
t
i
on f
o
rce ca
n be
pr
o
duce
d
t
o
c
o
unt
e
r
act
t
h
e U
M
P whi
c
h i
s
al
ready
prese
n
t in the system
. The induce
d
bridge currents ha
ve the capability of produci
ng a
n
additional 2-pole and
6-
p
o
l
e
m
a
gnet
i
c fl
u
x
de
nsi
t
y
com
pone
nt
s. T
h
ese
2-
pol
e a
n
d 6
-
pol
e fi
el
ds
can i
n
t
e
ract
w
i
t
h
t
h
e 4
-
p
o
l
e
m
a
i
n
fi
el
d a
n
d
t
h
us
a ra
di
al
m
a
gnet
i
c
fl
ux
de
nsi
t
y
can
be
p
r
o
d
u
c
e
d i
n
t
h
e
ai
r
ga
p.
The
ra
di
al
m
a
gnet
i
c
fl
u
x
den
s
i
t
y
by
t
h
e 2
-
p
o
l
e
, 4-
p
o
l
e
an
d 6-
p
o
l
e
fi
el
ds
ha
s b
een gi
ve
n by
e
quat
i
o
n (
1
) w
h
i
c
h
i
s
prese
n
t
e
d
i
n
[
4
]
.
(1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Nu
m
e
rica
l and Exp
e
ri
m
e
n
t
a
l
I
n
vestiga
tion
of Brid
g
e
Cu
rren
ts
o
f
an
I
ndu
ctio
n
…
(S
ivaram
a
k
rishn
a
n
N
a
tesa
n
)
1
265
Whe
r
e,
t
is t
h
e ti
m
e
,
d
e
no
tes th
e angu
lar co
-ordinate al
ong t
h
e
rot
o
r
pe
riphery,
are the
s
p
ace
vectors
of the
2-pole, 4-pol
e
and
6-pole
magnetic fl
ux
de
nsity distri
bution in t
h
e
air ga
p
respectively.
Consi
d
er the Phase A
winding conne
ction
of the In
du
ction
m
ach
in
e sh
ow
n
in
Fi
gu
r
e
1
.
W
h
en
th
e
Indu
ctio
n m
a
c
h
in
e is supp
lied
with
th
e m
a
i
n
sup
p
l
y, t
h
e cu
rren
t
will flow thro
ugh
th
e
arm
AB an
d B
D
in on
e
path as
well as
AC a
n
d CD i
n
a
n
a
not
her
path.
A four
pol
e
field has bee
n
form
ed accordi
ng t
o
the
wi
ndi
ng
pattern as s
hown i
n
Figure
3. It has
been
realized th
at the prese
n
ce
of
unbalance
i
n
the system
, the
current
will flo
w
t
h
rou
g
h
th
e arm
B
C
[2
] as so
on
as it is b
e
i
n
g
sh
ort circu
ited
an
d
it is
called as lev
itatio
n
cu
rren
t
i
Alev
. Th
e lev
itatio
n
curren
t
i
Alev
will flo
w
in
th
e arm
AB th
roug
h
th
e ar
m
CA in
ord
e
r to
m
a
k
e
a clo
s
ed lo
op
p
a
th
. Sim
ilarly
,
th
e lev
itatio
n
cu
rren
t
i
Alev
will flo
w
in
th
e
arm DB th
roug
h
CD. It h
a
s b
een
o
b
s
erv
e
d in
th
e
arm
s
AC an
d
BD th
at th
e levitatio
n
cu
rren
t
i
Alev
flo
w
s in
the o
ppo
site d
i
rectio
n
to
th
e
d
i
rectio
n
of m
a
in
su
pp
ly
current
i
Aph
sh
o
w
n i
n
Fi
g
u
re
2.
The
pol
ari
t
y
o
f
t
h
e c
u
r
r
ent
fl
owi
ng i
n
t
h
e a
r
m
s
AC
and B
D
ha
ve
been
re
verse
d
d
u
e
th
e opp
osite d
i
r
ection
of
f
l
ow
o
f
lev
itatio
n cu
rren
t
wh
ich
is shown in Fi
gu
r
e
4
,
and
th
u
s
th
e 2-
po
le f
i
el
d
has
bee
n
f
o
rm
ed.
The
su
pe
r i
m
posed l
e
vi
t
a
t
i
on
fi
el
d i
s
a
p
o
l
e
pai
r
di
ffe
re
nt
wi
t
h
t
h
e m
a
i
n
pol
e
pai
r
fi
el
d.
As a
resu
lt, a
n
e
t tran
sverse
force called
lev
itatio
n force is ex
ert
e
d o
n
t
h
e
rot
o
r
as sh
ow
n i
n
Fi
gu
re 5
.
T
h
ere
f
ore
,
a
lev
itatio
n
fo
rce can
b
e
p
r
od
uced
in
a
n
y arbi
trary direction
w
ith
th
e co
m
b
in
atio
n
o
f
b
r
i
d
g
e
conn
ectio
ns. Th
e
l
e
vi
t
a
t
i
on f
o
rc
e pr
o
duct
i
on
b
y
t
h
e i
n
t
e
ract
i
o
n
o
f
a
di
f
f
ere
n
ce
of
o
n
e
pol
e pai
r
bet
w
e
e
n
t
h
e fi
el
d
s
has
bee
n
p
r
ov
ed m
a
th
e
m
atical
ly in
[2].
Fi
gu
re
3.
M
a
i
n
4
-
Pol
e
fi
el
d
f
o
rm
ati
o
n
Figu
re
4.
2
-
P
o
le field
fo
rm
ation
Fi
gu
re
5.
S
upe
ri
m
posi
t
i
on o
f
4-P
o
l
e
a
n
d
2-P
o
l
e
fi
el
ds
3
.
OPERA 2D
FINITE
ELE
MENT MODELING
3.
1. Tr
ansien
t An
alysis
of
th
e Induc
tion
Machine
Ro
tatin
g
m
o
tio
n
an
alysis (RM) is u
s
ed
for
th
e transi
ent a
n
alysis of the i
n
duction m
achine. Fi
gure
6
sh
ow
s th
e inductio
n
m
ach
in
e m
o
d
e
l w
ith
B
C
W
sch
e
m
e
. Th
e m
ach
in
e p
a
r
a
m
e
ter
s
ar
e g
i
v
e
n
in
Tab
l
e 1. Th
e
cross
sect
i
o
ns
of
st
at
or
sl
ot
and
r
o
t
o
r
bar
are
gi
ve
n i
n
F
i
gu
re
7 a
n
d
Fi
gu
re
8
res
p
ect
i
v
el
y
.
The
i
n
d
u
ct
i
o
n
m
achi
n
e m
odel
has
60
st
at
or
sl
ot
s an
d
4
8
r
o
t
o
r sl
ot
s.
A
n
o
n
l
i
n
ear m
a
t
e
ri
al
pr
o
p
ert
y
h
a
s bee
n
gi
ve
n
t
o
t
h
e
stato
r
an
d ro
tor cor
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1262 –
1274
1
266
Fig
u
r
e
6
.
Op
era 2D
I
ndu
c
tio
n m
ach
in
e m
o
d
e
l with
BC
W
Tabl
e
1. M
a
c
h
i
n
e Pa
ram
e
t
e
rs
Sl No
Para
m
e
ter
Value
1
Stator
outer
dia
m
eter
350.
0
m
m
2
Stator
inner
dia
m
eter
221.
0
m
m
3
Stator
cor
e
length
212.
0
m
m
4
Rotor
outer
diam
eter
218.
5
m
m
5
Rotor
inner
diam
eter
75.
0
m
m
6 Rotor
skew
5o
7 Air
g
ap
1.
25
m
m
Fi
gu
re
7.
A
st
at
or sl
ot
di
m
e
nsi
o
n
Fi
gu
re
8.
A
r
o
t
o
r
ba
r
di
m
e
nsion
Th
e ro
tating
p
a
rts
are ro
tatin
g
relativ
ely
with
th
e
sta
t
i
ona
ry
part
s.
T
h
e i
m
port
a
nt
feat
u
r
e
o
f
t
h
i
s
FEM
to
o
l
is th
at it
c
a
n
rearrang
e th
e m
e
sh
in
th
e
air-g
ap
reg
i
o
n
in
o
r
d
e
r to
rejo
in
th
e ro
tatin
g
ele
m
en
ts wit
h
t
h
e
st
at
i
onary
el
e
m
ent
s
aft
e
r e
v
ery
rot
a
t
i
o
n
wi
t
h
an a
d
joi
n
i
n
g m
e
sh. The
F
E
M
m
odel
has
one
ai
r-
ga
p re
gi
o
n
t
o
separat
e
t
h
e st
at
or a
n
d
r
o
t
o
r
part
s i
n
o
r
der t
o
f
o
rm
t
h
e st
ator ai
r ga
p
re
gi
on
an
d
rot
o
r ai
r ga
p
regi
on
as
sh
ow
n
i
n
Fi
g
u
r
e
9. T
h
e ai
r
-
ga
p
o
f
t
h
e i
n
duct
i
o
n
m
achi
n
e i
s
”
1
.
25m
m
”
. The a
i
r-ga
p
i
s
di
vi
d
e
d i
n
t
o
t
h
ree
equa
l
regi
ons i
n
order to create the annular air-gap re
gion
of
”0
.4
266
67
mm
”
f
o
r
stato
r
air-
gap
and
ro
tor
air
-
g
ap
r
e
g
i
o
n
. I
t
is i
m
p
o
r
t
an
t to
g
i
v
e
m
i
d
a
ir
-
g
ap
r
a
d
i
u
s
so
th
at Op
er
a
2
D
/RM can
cr
eate th
e air
p
o
l
ygon
in
betw
een
st
at
or ai
r-
gap
regi
o
n
an
d r
o
t
o
r ai
r-
gap r
e
gi
o
n
. T
h
e m
i
dai
r
-
g
ap
radi
us o
f
t
h
e m
o
del
i
s
”10
9
.
8
75m
m
”
.
Triangula
r
element has bee
n
chosen
for the
mesh. Th
e com
p
le
te
m
o
d
e
l co
m
p
r
i
ses o
f
19
808
nod
es and
393
84
ele
m
ents. Figure
10 shows t
h
e close
view
of the m
e
sh in t
h
e air-gap re
gion.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Nu
m
e
rica
l and Exp
e
ri
m
e
n
t
a
l
I
n
vestiga
tion
of Brid
g
e
Cu
rren
ts
o
f
an
I
ndu
ctio
n
…
(S
ivaram
a
k
rishn
a
n
N
a
tesa
n
)
1
267
Fi
gu
re
9.
A
cl
o
s
e vi
e
w
of
st
at
or
an
d
rot
o
r
ai
r
ga
p
regi
on
Fi
gu
re
1
0
.
A cl
ose m
e
sh vi
e
w
of
t
h
e st
at
o
r
a
n
d
rot
o
r ai
r
gap
regi
on
An
ex
ternal circu
it h
a
s b
e
en
co
up
led
with
th
e in
du
ction
mach
in
e
m
o
d
e
l fo
r th
e transien
t an
alysis.
Fig
u
re
1
1
sh
ows th
e ex
tern
al circu
it ed
itor
in
Op
era
2
D
.
The
GO
an
d t
h
e R
ETUR
N
c
o
nd
uct
o
rs
of
t
h
e
st
at
or
wi
n
d
i
n
g ha
ve
been
defi
ned i
n
t
h
e ext
e
rnal
ci
rcui
t
edi
t
o
r
a
s
sho
w
n i
n
Ta
bl
e 2. T
h
e ex
tern
al circu
it co
nsists o
f
wi
n
d
i
n
g coi
l
s
,
resi
st
or
, i
n
d
u
ct
or a
nd a f
u
nct
i
onal
v
o
l
t
a
ge s
o
u
r
ces.
A
comi
file is a set o
f
fun
c
tio
n
s
wh
ich
h
a
s
been
use
d
t
o
dri
v
e t
h
e
fu
nc
t
i
onal
v
o
l
t
a
ge
so
urces
wi
t
h
t
h
e p
h
ase
di
f
f
ere
n
ce i
n
st
ea
d o
f
gi
vi
n
g
c
onst
a
nt
am
pl
i
t
ude v
o
l
t
a
ge at
5
0
Hz
. T
h
e r
o
t
o
r ba
rs ar
e sho
r
t
ci
rcui
t
e
d an
d t
h
e e
ffec
t
of r
o
t
o
r sk
ew
ness i
s
al
so i
n
c
l
ude
d
i
n
t
h
e
R
M
A
n
al
y
s
i
s
.
Si
m
u
lat
i
ons ha
ve b
een do
ne f
o
r t
w
o di
f
f
ere
n
t
cases
o
f
i
n
d
u
c
t
i
on
m
achi
n
e m
odel
.
Initially, the induction m
achine ha
s bee
n
modele
d wit
h
out
any eccentrici
t
y in
the Opera
2D m
odel. Lat
e
r, the
machine
was
m
odeled with
10% ecce
ntricity of t
h
e air
gap
le
ngt
h. The
rotor has bee
n
displace
d wi
th
10%
eccentricity of air gap le
ngt
h ie., ”0.1
25mm” with the stator. The ecce
nt
ric
ity was give
n in the
negati
ve Y-
di
rect
i
o
n i
n
t
h
e m
odel
.
The
r
o
t
o
r ba
rs a
n
d
t
h
e r
o
t
o
r c
o
re
were
gr
o
u
p
e
d
t
oget
h
e
r
as
o
n
e
regi
on i
n
t
h
e
Ope
r
a
m
odel
and t
h
a
t
regi
o
n
was
m
oved t
o
”
-
0
.
12
5m
m
”
i
n
Y-di
rect
i
o
n.
T
h
e
FFT
of
b
r
i
d
g
e
cur
r
e
n
t
s
an
d
m
a
i
n
su
pp
ly cu
rren
ts h
a
v
e
b
een
p
l
o
tted
in
M
A
TLABTM by u
s
in
g
Op
era 2
D
log
resu
lts file fo
r
bo
th
zero
eccentricity and
10% ecce
ntri
city induction
m
achin
e m
odels and c
o
m
p
ared
with eac
h
other.
Fig
u
re
11
.
Wind
ing
co
nn
ection
in Ex
tern
al
circu
it ed
ito
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1262 –
1274
1
268
Tab
l
e
2
.
Assi
gn
ing
o
f
Con
ducto
r
Nu
m
b
ers in
th
e ex
tern
al circu
it ed
itor
Phase W
i
nding
W
i
nding
GO Conductor
s
Retur
n
Conductor
Phase A
W
1
4,
5,
6,
7,
8
79,
80,
81,
82,
83
W
2
34,
34,
36,
37,
38
109,
110,
11
1,
112
,
113
W
3
39,
40,
41,
42,
43
114,
115,
11
6,
117
,
118
W
4
9,
10,
11,
12,
13
84,
85,
86,
87,
88
Phase B
W
5
54,
55,
56,
57,
58
69,
70,
71,
72,
73
W
6
24,
25,
26,
27,
28
99,
100,
101,
10
2,
103
W
7
29,
30,
31,
32,
33
104,
105,
10
6,
107
,
108
W
8
59,
60,
1,
2,
3
74,
75,
76,
77,
78
Phase C
W
9
44,
45,
46,
47,
48
119,
120,
61,
62,
6
3
W
10
14,
15,
16,
17,
18
89,
90,
91,
92,
93
W
11
19,
20,
21,
22,
23
94,
95,
96,
97,
98
W
12
49,
50,
51,
52,
53
64,
65,
66,
67,
68
4. E
X
PE
RIM
E
NTAL SET
U
P
A com
m
on 37
k
W
In
d
u
ct
i
on
m
achi
n
e i
s
used fo
r t
h
e ex
pe
ri
m
e
nt
al set
u
p
sho
w
n i
n
Fi
g
u
re
12
. The
exi
s
t
i
ng st
at
o
r
wi
n
d
i
n
g has
b
een rem
ove
d a
nd
repl
ace
d
by
a do
u
b
l
e
l
a
y
e
red
,
di
st
ri
but
e
d
, t
h
ree
pha
se a
nd
4-
pol
e
wi
n
d
i
n
g.
The exi
s
t
i
n
g c
o
i
l
wi
re di
am
et
er i
s
”1.
22m
m
”
(18
gau
g
e
num
ber)
. T
h
e exi
s
t
i
ng
wi
n
d
i
ng i
s
a
conce
n
t
r
at
e
d
wi
n
d
i
n
g wi
t
h
4 st
ra
nds a
n
d
11 t
u
r
n
s.
It
i
s
m
odi
fi
ed t
o
3
st
ran
d
s a
nd
11
t
u
r
n
s o
f
sam
e
wi
r
e
diam
e
t
er in order t
o
accommodate the
s
earc
h
coil in the m
a
in stator sl
ots.
Searc
h
coils has bee
n
use
d
t
o
find
the 2-pole
.
4-pole and
6-pol
e
field positions
. The existing rot
o
r ha
d ”0.8
m
m
”
longe
r shaft. It is
m
odified to
”1.8m
”
long s
h
aft t
o
m
a
ke
the sy
stem
f
l
ex
ib
le. 330
0 XL Prox
im
i
t
y t
r
an
sdu
cer h
a
s b
e
en
u
s
ed
f
o
r
th
e
m
easurem
ent
of
rot
o
r
di
spl
a
cem
e
nt
s i
n
t
h
r
ee l
o
cat
i
ons s
h
ow
n i
n
Fi
g
u
re
12
. I
n
eac
h l
o
c
a
t
i
on, t
w
o
pr
o
x
i
m
i
t
y
sens
ors
hav
e
b
een use
d
t
o
m
easure t
h
e r
o
t
o
r res
p
o
n
ses i
n
X an
d Y
di
rec
t
i
on. Si
x v
o
l
t
a
ge t
r
an
sd
ucer
s
hav
e
been
used to
measure t
h
e three m
a
in
ph
ase supp
ly vo
ltages as
w
e
ll as t
h
ree
p
h
ase
b
r
i
dge
vol
t
a
ges
s
h
o
w
n i
n
Figure
13. LT
S 15- NP (Hal
l Effect tra
n
s
d
ucer) c
u
rren
t t
r
ans
d
ucers
we
re used to m
easure
the t
h
ree
phase
bri
dge
cu
rre
nt
s
.
T
h
e
out
put
l
e
ads
of
t
h
e
p
r
o
x
i
m
i
t
y
sensors
,
v
o
l
t
a
ge t
r
a
n
s
d
ucer
, a
n
d
cu
rre
nt
t
r
a
n
sd
uce
r
s
were
connected t
o
the Data Ac
quisition System
NI P
X
I-6
221 m
odule through SCB-68 c
o
nnector box s
hown
i
n
Fig
u
re 14
.
A perfo
r
ated
d
i
sc
h
a
s b
e
en
in
sert
ed
in
th
e sh
aft
in
o
r
d
e
r to
create th
e u
n
b
a
lance to
th
e system with
t
h
e k
n
o
w
n m
a
ss u
nbal
a
nce s
h
o
w
n i
n
Fi
gu
r
e
15
. I
n
t
h
e
pr
esent
anal
y
s
i
s
,
onl
y
t
h
e m
easure
d
b
r
i
d
ge c
u
rre
nt
s
have
been
di
sc
usse
d i
n
or
de
r t
o
i
d
ent
i
f
y
t
h
e un
bal
a
nce
pres
ent
i
n
t
h
e sy
st
em
. The out
put
of cu
rr
ent
t
r
an
s
duce
r
is a vo
ltag
e
si
gn
al wh
ich h
a
s
a lin
ear correlatio
n
with
the cu
rren
t.
Fig
u
r
e
12
. A
m
o
d
i
f
i
ed
37
kW
In
du
ction
m
ach
in
e
Fig
u
r
e
13
. A
pan
e
l
bo
ar
d
I
n
Figu
r
e
12
, 1
-
Bear
i
n
g
Housin
g
at ND
end
,
2
-
Beari
n
g Housing
at D end, 3
-
Test Machine, 4 –
Per
f
or
ated
D
i
sc,
5, 6
an
d
7
- Lo
cation
s
f
o
r
t
h
e r
o
t
o
r
r
e
sp
onses, 8
-
Panel
bo
ard
.
In Fi
gure 13,
1 - Switches for
bri
dges
,
2
- Curre
nt trans
duce
r
s,
3 -
Am
plifiers for displacem
ent
sens
ors
,
4 -
V
o
l
t
a
ge t
r
ans
d
uce
r
s.
5. RES
U
LTS AN
D DIS
C
US
SION
The i
m
port
a
nt
pa
ram
e
t
e
rs such
as m
a
i
n
s
u
p
p
l
y
cu
rre
nt
and
b
r
i
d
ge c
u
rre
nt
ha
ve
bee
n
pl
ot
t
e
d
i
n
MATLAB
TM
with
th
e u
s
e of Op
era 2D/RM lo
g
file. The co
m
p
ariso
n
o
f
bridg
e
curren
ts and
m
a
in
su
pp
ly
currents of zero
eccent
r
icity
induction m
a
c
h
ine m
odel wi
th the
10%
static
eccentricity
induction m
a
chine
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Nu
m
e
rica
l and Exp
e
ri
m
e
n
t
a
l
I
n
vestiga
tion
of Brid
g
e
Cu
rren
ts
o
f
an
I
ndu
ctio
n
…
(S
ivaram
a
k
rishn
a
n
N
a
tesa
n
)
1
269
m
odel
has bee
n
p
r
ese
n
t
e
d i
n
t
i
m
e
do
m
a
i
n
as wel
l
as fre
q
u
e
ncy
d
o
m
a
i
n
has sh
ow
n i
n
Fi
gu
re 1
6
t
o
Fi
g
u
re
25
.
Com
p
arison
of
FFT plots of bridge
c
u
rrents
of ze
ro ecce
ntricity
m
odel
with
10%
static eccentricity
m
o
del has
been
pre
s
ent
e
d
i
n
Fi
gu
re 2
6
t
o
Fi
g
u
re
28
. E
xpe
ri
m
e
nt
s are con
d
u
c
t
e
d at
20
Hz an
d
30
H
z
sup
p
l
y
fre
qu
ency
.
An
am
ount
of
3
5
0
g
m
kn
ow
n m
a
ss un
bal
a
nce i
s
i
n
t
r
od
u
ced i
n
t
h
e
pe
r
f
o
r
at
ed
di
sc.
B
r
i
dge
cu
rr
ent
s
we
re
m
easured i
n
t
w
o cases i
e
.,
w
h
en t
h
e
r
e i
s
no
un
bal
a
nce i
n
t
h
e di
sc an
d w
h
en 3
5
0
g
m
kno
wn m
a
ss unbal
a
nce i
s
adde
d t
o
t
h
e
di
sc. E
xpe
ri
m
e
ntal
resul
t
s
ha
ve
been
p
r
ese
n
t
e
d
fr
om
Fi
gu
re
2
9
t
o
Fi
g
u
r
e
40
.
Fig
u
r
e
14
. A
NI
DAQ
system
Fig
u
r
e
15
. A
per
f
o
r
ated
d
i
sc w
ith
k
now
n
mass
un
bal
a
nce
5.1. Oper
a 2D/RM Resul
t
s for
Z
ero
Eccentricity Model
Fi
gu
re
16
an
d
Fi
gu
re
17
s
h
o
w
s t
h
e
t
h
ree
ph
ase m
a
i
n
supply currents a
n
d
three
phase
bri
dge
curre
nt
s
in tim
e
dom
a
i
n for zero eccentricity in the
model. T
h
e FF
T
of m
a
in supply currents a
nd
bridge curre
nts
have
been
pl
ot
t
e
d t
o
get
h
e
r
i
n
Fi
g
u
r
e
1
8
t
o
Fi
g
u
r
e
20
.
Fi
gu
re
1
6
.
A t
h
ree
phase
m
a
i
n
su
ppl
y
c
u
r
r
e
n
t
s
f
o
r
zero eccent
r
icity
m
odel
Figu
re
1
7
.
A t
h
ree
phase
b
r
id
g
e
cu
rre
nts f
o
r z
e
ro
eccentricity model
Fi
gu
re 1
8
. A F
F
T pl
ot
of Pha
s
e
A b
r
i
d
ge
c
u
r
r
ent
wi
t
h
main supply c
u
rre
nt at 50Hz
for zero ecce
ntricity
m
odel
Fi
gu
re 1
9
. A F
F
T pl
ot
of Pha
s
e
B
b
r
i
d
ge
c
u
r
r
ent
wi
t
h
main supply c
u
rre
nt at 50Hz
for zero ecce
ntricity
m
odel
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1262 –
1274
1
270
Figure 20. A FFT plot of Pha
s
e
C
br
idge c
u
rrent
with m
a
in
supply c
u
rrent
at 50Hz
for ze
ro ecce
ntricity
m
odel
5.2. Oper
a 2D/RM Resul
t
s for 10%
Static Eccentricity Model
Fi
gu
re
2
1
.
A t
h
ree
phase
m
a
i
n
su
ppl
y
c
u
r
r
e
n
t
f
o
r
10% ecce
ntricity
m
odel
Fig
u
r
e
22
.
A
t
h
r
ee
p
h
a
se br
idge cur
r
e
n
t
fo
r 10
%
eccentricity model
Fi
gu
re 2
3
. A F
F
T pl
ot
of Pha
s
e
A b
r
i
d
ge
c
u
r
r
ent
wi
t
h
main supply c
u
rre
nt at 50Hz
for 10% ecce
ntricity
m
odel
Fi
gu
re 2
4
. A F
F
T pl
ot
of Pha
s
e
B
b
r
i
d
ge
c
u
r
r
ent
wi
t
h
main supply c
u
rre
nt at 50Hz
for 10% ecce
ntricity
m
odel
Fi
gu
re 2
5
. A F
F
T pl
ot
of Pha
s
e
C
b
r
i
d
ge
c
u
r
r
en
t
with
m
a
in
su
pp
ly cu
rren
t
at 5
0
Hz
fo
r
10%
eccentricity mode
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Nu
m
e
rica
l and Exp
e
ri
m
e
n
t
a
l
I
n
vestiga
tion
of Brid
g
e
Cu
rren
ts
o
f
an
I
ndu
ctio
n
…
(S
ivaram
a
k
rishn
a
n
N
a
tesa
n
)
1
271
Fi
gu
re
21
an
d
Fi
gu
re
22
s
h
o
w
s t
h
e
t
h
ree
ph
ase m
a
i
n
supply currents a
n
d
three
phase
bri
dge
curre
nt
s
in tim
e
dom
ain for
10% static eccentric
ity of t
h
e airgap l
e
ngt
h gi
ven in
th
e m
odel. The
FFT
of m
a
in supply
cur
r
ent
s
an
d
br
i
dge c
u
rre
nt
s
h
a
ve
been
pl
ot
t
e
d t
o
get
h
e
r
i
n
Fi
gu
re
2
3
t
o
Fi
g
u
r
e
25
.
5.3. Comparis
on of
Three P
h
ase
Bridge Curren
ts
for wi
th
and without Eccentricity
Model
The
bri
dge c
u
rrents
of z
e
ro e
ccentricity
m
odel ha
s bee
n
c
o
m
p
ared with the
induce
d
bri
dge curre
nts
of 10%
static eccentricity model. Figur
e
26 to Fi
gure
28 shows the
FFT
com
p
arison of
three
phase
bridge
currents
of ze
ro ecce
ntricity m
ode
l and
10% static eccent
r
icity
m
odel.
Fi
gu
re 2
6
.
C
o
m
p
ari
s
on of
F
F
T pl
ot
s of
P
h
ase
A
bri
dge
curre
nt
at zero eccent
r
icity
m
odel with
10%
eccentricity model
Fi
gu
re 2
7
.
C
o
m
p
ari
s
on of
F
F
T pl
ot
s of
P
h
ase
B
bri
dge
curre
nt
at zero eccent
r
icity
m
odel with
10%
eccentricity model
Figure
28. C
o
m
p
arison
of FFT
plots
of Phase C brid
ge c
u
rrent at z
e
ro e
ccen
tricity
m
odel with 10%
eccentricity model
5.
4. E
x
peri
me
ntal
Res
u
l
t
s
Ex
peri
m
e
nt
s have bee
n
car
ri
ed o
u
t
at
20
Hz
and
30
Hz. T
h
e bri
d
ge c
u
r
r
e
n
t
s
ha
ve bee
n
m
easured
fo
r
t
w
o cases i
e
., (
i
) W
i
t
h
o
u
t
un
b
a
l
a
nce i
n
t
h
e perf
orat
e
d
di
sc,
(i
i
)
W
i
t
h
3
5
0
g
m
unbal
a
nce i
n
t
h
e per
f
o
r
at
e
d
di
sc.
Fi
gu
re 2
9
t
o
F
i
gu
re 3
4
s
h
o
w
s t
h
e FFT
pl
ot
s of m
easure
d
t
h
ree
phase
bri
dge c
u
r
r
e
n
t
s
w
h
en t
h
e B
r
i
d
ge
i
s
i
n
OFF an
d
ON p
o
s
ition
.
Th
e co
m
p
ariso
n
o
f
FFT p
l
o
t
s of
measu
r
ed
b
r
i
d
g
e
curren
t
s of
with
ou
t unb
alan
ce and
w
ith
th
e unb
al
an
ce
o
f
350
g
m
is pr
esen
ted
i
n
Figu
r
e
35
t
o
Fig
u
r
e
4
0
.
Fi
gu
re
2
9
. C
o
m
p
ari
s
on
of
P
h
ase A
B
r
i
d
ge c
u
r
r
ent
s
wh
en
bridg
e
is in
OFF
and
ON p
o
s
ition
at 20
Hz
Fi
gu
re
3
0
. C
o
m
p
ari
s
on
of
P
h
ase B
B
r
i
d
ge c
u
r
r
ent
s
wh
en
bridg
e
is in
OFF
and
ON p
o
s
ition
at 20
Hz
Evaluation Warning : The document was created with Spire.PDF for Python.