Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 2, No. 1,
April 201
6, pp. 79 ~ 87
DOI: 10.115
9
1
/ijeecs.v2.i1.pp79
-87
79
Re
cei
v
ed
Jan
uary 12, 201
6
;
Revi
sed Ma
rch 1
0
, 2016;
Acce
pted Ma
rch 2
4
, 2016
Transient Analysis of a Multi-phase Induction Machine
Operating as Generator
Alok Kum
a
r Mohan
t
y
*
1
, K B Yadav
2
1
Researc
h
sch
olar, De
partme
n
t of Electrical
and El
ectron
ics Engg, NIT
Ja
mshed
pur, Indi
a
2
Departme
n
t of Electrical a
nd
Elec
tron
ics En
gg, NIT
Jamshedp
ur, India
*Co
rre
sp
ondi
ng autho
r, email: alokm
o
h@g
m
ail.com
A
b
st
r
a
ct
Multi-ph
ase
machi
nes are
c
onsi
dere
d
s
e
ri
ous
c
onte
nder
s as c
o
mp
are
d
to t
he t
h
re
e p
has
e
mac
h
i
nes
for varia
b
le ap
plic
ations in ge
ne
rating mod
e
.
T
h
is
pa
per pr
esents
th
e
tra
n
sie
n
t
perfor
m
an
c
e
ana
lysis of
a mu
lti-ph
ase
in
ductio
n
mac
h
i
ne oper
atin
g
i
n
six-p
has
e
mode
for p
o
w
e
r ge
nerati
on. In
th
i
s
pap
er the si
mulati
on a
nd ex
peri
m
e
n
tal a
n
a
l
ysis of
a six-p
hase
mac
h
in
e
in ge
nerati
ng
mo
de h
a
ve b
e
e
n
ma
de. T
he s
i
mulati
ons ar
e
made
an
d the
machi
ne fu
ncti
on
ality w
a
s inv
e
stigate
d
d
u
rin
g
n
o
-lo
ad a
nd w
h
e
n
subj
ected to
d
i
fferent types
of lo
ads. Exp
e
r
imental
re
s
u
lt
s are
provi
d
e
d
to confir
m th
e a
b
il
ity of the
s
e
mo
de
ls to
rep
r
esent
duri
n
g
no
loa
d
as w
e
ll
as
dur
ing
l
oad
p
e
rio
d
an
d the
res
u
lt w
e
re fo
un
d to
be
satisfactory for pow
er gen
erati
o
n
.
Ke
y
w
ords
: Mu
lti-ph
ase, self-e
xcited,
Inducti
o
n
gen
erator, transi
ent
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
The incre
a
si
ng co
ncern
of the enviro
n
men
t, esp
e
c
ially the gre
enho
use effects, ha
s
motivated th
e wo
rld to
ward
s expl
orin
g the u
s
e
of ren
e
wable
energy sources a
nd
red
u
c
e
s
depe
nden
cy
on fossil fuel
s. Most of th
e ren
e
wabl
e energy
so
urces,
such as wind,
mini
-hy
d
ro,
etc. are u
s
ual
ly available in
remote
area
s. A
self
-excit
ed ind
u
ctio
n
gene
rato
r is f
ound to
be v
e
ry
suitabl
e to ge
nerate
ele
c
tri
c
al po
we
r in
remote a
r
e
a
s from ren
e
wa
ble ene
rgy source
s, su
ch
as
wind an
d min
i
-hydro turbin
es [1]. A SEIG has
ma
ny advantag
eou
s feature
s
ov
er its co
unterpart
synchro
nou
s gene
rator.
These features a
r
e
lo
w cost, hig
h
reliability, maintena
nce
and
operational
simplicity, rug
ged
con
s
truction, bru
s
hl
e
s
s op
eratio
n, prote
c
tion
a
gain
s
t overl
o
ads
and sh
ort ci
rcuits, etc. Even though a
SEIG is very
suitable for
wind an
d min
i
-hydro plants,
it
can
also efficiently be u
s
e
d
with
prim
e
movers d
r
ive
n
by othe
r en
ergy
sou
r
ces,
su
ch
as
die
s
el,
bioga
s, natu
r
al ga
s, gasoline, etc.In
compa
r
i
s
on
with three
pha
se ma
chi
nes, multiph
a
se
machi
n
e
s
are con
s
ide
r
e
d
as an alternative fo
r variable
spee
d
applicatio
ns.
As there is
a
increa
se in
d
e
mand
of en
ergy de
man
d
durin
g
the l
a
st few
de
ca
des, the
use
of rene
wa
ble
energy so
urces h
a
s
be
co
me e
s
sentia
l
and a
s
a
re
su
lt of this, the i
n
vestigatio
n
of the self
-ex
c
ited
indu
ction ge
n
e
rato
r ha
s ga
ined impo
rta
n
ce a
s
it
is p
a
rticul
arly for rene
wabl
e p
o
we
r gen
eration
appli
c
ation
s
[2, 3, 4]. The
applicatio
n of self-exc
ite
d
indu
ction g
enerator du
e
to its decre
a
s
ed
unit cost,
si
mple to
ope
rate an
d e
a
se in
maintai
n
ing i
s
m
o
st
suite
d
in
re
newable
ene
rgy
system
s. Th
e advantage
s of self
excited ind
u
cti
on gen
erato
r
are no sep
a
rate sou
r
ce
for
excitation is
required, protection
from o
v
erload, g
ood
transi
ent pe
rforman
c
e,
simple an
d ro
b
u
st
con
s
tru
c
tion
and ea
se in
maintena
nce. As the ra
tin
g
of power i
s
increa
sed a
nd high
relia
bility
requi
rem
ents,
rese
arch in t
he are
a
of multi-pha
se m
a
chin
es [2, 3, 4, 5] have been increa
sin
g
.
In this pape
r the analytical an
d exp
e
rime
ntal
an
alysis of a
self excited
indu
ction
gene
rato
r op
erating i
n
six phase mo
de ha
s b
een
ca
rrie
d
out.
The math
e
m
atical m
o
d
e
l is
impleme
n
ted in simulatio
n
platform for conne
ction
of pure
resi
stive
load, re
si
stive-ind
u
ctive lo
ad
and resi
stive-indu
ctive-cap
a
citive load
with cert
ain v
a
lue of
capa
citor that i
s
conne
cted
across
self excite
d i
ndu
ction g
e
n
e
rato
r op
erati
ng in
six ph
ase
mode. E
x
perime
n
tatio
n
is d
one
on
a
prototype of
six-pha
se in
du
ction ge
ne
rat
o
r mad
e
for t
he analy
s
is t
o
validate the
results obtai
ned
in the simulati
on.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 1, April 2016 : 79 – 87
80
2. Modeling of a Multi-Ph
ase Self Exci
ted Induc
tio
n
Gener
a
tor
The sche
ma
tic diagram of the basic two-
pol
e si
x-pha
se ind
u
ction g
ene
rator is
discu
s
sed i
n
[
5
].
A Six pha
se i
ndu
ction
gene
rato
r
co
nsi
s
ts
of two
stator wi
ndin
g
sets nam
el
y abc
and 123, wh
ose ma
gneti
c
axes are di
splaced by an
arbitra
r
y an
gle
α
. The winding
s of ea
ch
three
-
ph
ase set are unifo
rmly distrib
u
t
ed and h
a
ve
axes that are displa
ced
120
0
ap
art. The
three
-
ph
ase rotor wi
ndin
g
s ar, br, cr a
s
sho
w
n in
Fig
u
re 1
are
also sin
u
soi
dally
distrib
u
ted a
nd
has
axes tha
t
are di
spla
ced by 120
0
.
The eq
uation
s
for the
self
excited ind
u
c
tion g
ene
rat
o
r
operating in
six pha
se
mo
de, de
scrib
e
s the be
havio
r of a multi-ph
ase
ma
chine,
it is a
s
sume
d
that the
neutral of
both th
e
stator
wi
ndin
g
sets are
se
parate
so th
a
t
if a fault
occurs in
on
e
set
of
the stator win
d
ing
s
it does not propag
ate to
the other set. The followin
g
voltage equation
s
are
written fo
r a
multi-ph
ase indu
ction ma
chine a
s
sho
w
n in e
quival
ent circuit of
the machine
in
Figure 2.
Figure 1. Phasor di
ag
ram repre
s
e
n
tation
of st
ator and
rotor
windi
ng
s of six-p
hase indu
ction
gene
rato
r
Figure 2. Circuit representa
t
ion self e
x
ci
ted induction generator in six phase operation
For
th
e
d
e
vel
opment
of
m
odel of
the si
x-pha
se ma
chine ope
ratin
g
in gen
erati
ng
m
ode
the differe
ntia
l equ
ation
s
a
r
e de
rived f
r
o
m
the
equi
val
ent ci
rcuit of t
he ma
chi
ne.
From
the
abo
ve
equivalent
ci
rcuit we get
the equatio
ns [5] and the model
was bei
ng sim
u
lated in Ma
tlab/
Simulink pl
atform.
3. Simulation Resul
t
s an
d Discus
s
io
ns
The sim
u
lati
on mod
e
l a six-ph
ase self excited ind
u
ction g
ene
rator is
sho
w
n in the
Figure 3. Th
e blo
c
ks ma
de for the
machi
ne
in
cl
ude six-ph
ase
machine block,
mag
n
etic
indu
ction bl
o
ck, to
rqu
e
bl
ock an
d the l
oad bl
ock
[6,
7]. The dyna
mic respon
se
of the sy
ste
m
is
analyzed in
MATLAB plat
form
whe
n
th
e ma
chin
e i
s
at no lo
ad
co
ndition a
nd
when
su
bjecte
d to
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Tran
sie
n
t Analysis of a Mu
lti-pha
se I
ndu
ction Ma
chin
e Operating a
s
Gen
e
rato
r
(
A
lok Kum
a
r M.)
81
different type
s of lo
ad
s. Th
e data
of the
machi
ne
use
d
for the
sim
u
lation m
odel
are
given in
the
Appendix.
Figure 3. Simulation mod
e
l
of six-pha
se
indu
ction ge
n
e
rato
r
3.1. Voltage
and Cur
r
en
t Ch
arac
teri
stics
w
h
en
Excited by
Capa
citan
c
e
under No L
o
ad
Conditio
n
Figure 4.sh
o
w
s the voltag
e build up of
the inductio
n
machine u
nder n
o
load
conditio
n
whe
n
the m
a
chi
ne is ex
cited by exci
tation cap
a
cit
ances valu
es. The machi
ne is excite
d
by
41µF. It is observe
d that the magnitud
e
voltage and
cu
rrent rise fro
m
their initial small value
s
of
voltage a
nd
currents to th
e
stea
dy
state
voltage
and
curre
n
t.
The
excitation cu
rrent
i
s
depi
ct
e
d
in the fig
u
re
and it i
s
observed th
at th
e mag
n
it
ude
of cu
rrent in
crea
se
s
with t
he in
crea
se i
n
cap
a
cit
a
nc
e v
a
lue
s
.
3.2. Voltage
and Curren
t
Ch
arac
teri
stics
w
h
en
the Six-Pha
s
e
Machine i
s
subjec
ted
to
Resis
t
iv
e Lo
ad
In this mo
de
of ope
ration,
at time
t
= 0.
3s the
ma
chi
ne is l
oad
ed
by a load
of
R
= 200
ohm with a
c-b
ank
co
n
necte
d acro
ss both the
three
-
ph
ase windi
ng sets
abc an
d 1
2
3
respe
c
tively. The re
sult
s a
r
e shown in
Figure
5. The
terminal voltage ha
s de
creased from 2
4
0
volts to 20
0
whe
n
the m
a
chin
e is subje
c
ted to l
oad
a
t
0.3 se
co
nd
s. The effe
ct o
f
the de
cre
a
se in
terminal voltage will cause a decrease i
n
the capac
it
or current; this furt
her affects the voltage
regul
ation of the gen
erato
r
.
Figure 4. Phase voltage a
n
d
curre
n
t at both the se
ts o
f
the machine
during n
o
loa
d
con
d
ition
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 1, April 2016 : 79 – 87
82
Figure 5. Phase voltage a
n
d
curre
n
t at both t
he sets o
f
the machine
during
re
sisti
v
e load
condition
Figure 6. Phase voltage a
n
d
curre
n
t at both the se
ts o
f
the machine
during
re
sisti
v
e inductive
load conditio
n
Figure 7. Phase voltage a
n
d
curre
n
t at both the se
ts o
f
the machine
during
re
sisti
v
e inductive
load conditio
n
3.3. Voltage
and Curre
n
t
Char
ac
teri
stics
w
h
e
n
the Six-Phas
e Machine i
s
Subjecte
d
t
o
Resis
t
iv
e-In
ductiv
e
Load
At
t
= 0 s,
a shunt cap
a
citor
with capa
citan
c
e 4
1
μ
F is co
nn
ected a
c
ross both the
windi
ng te
rmi
nals of th
e in
ductio
n
g
ene
rator with
out
any loa
d
, a
n
d
voltage
i
s
gene
rated.
T
he
load is
switch
ed on at
t
=
0.22 s. It is o
b
se
rved that
the term
inal
voltage is red
u
ce
d by bigg
er
value. RL loading
operation caus
es
a poor voltage charac
teris
t
ic
of the SPSEIG. This
is
due to
the main disa
dvantage of this ge
nerator
and can
be e
x
plained a
s
resultin
g from
unde
r excitati
on
of the machin
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Tran
sie
n
t Analysis of a Mu
lti-pha
se I
ndu
ction Ma
chin
e Operating a
s
Gen
e
rato
r
(
A
lok Kum
a
r M.)
83
3.4. Voltage
and Curre
n
t
Char
ac
teri
stics
w
h
e
n
the Six-Phas
e Machine i
s
Subjecte
d
t
o
Resis
t
iv
e-In
ductiv
e
-Cap
acitiv
e
Load
The transient
response of
the SPSEIG i
s
feeding an RLC load (200 ohm. 08H, 12
μ
F) a
s
sho
w
n. The l
oad is switch
ed on at
t
= 1s. It is observ
ed from the result
s sho
w
n
that the termina
l
voltage an
d current attain t
heir
new ste
a
d
y-state
ope
ration, but wit
h
a
slight red
u
ction
of outp
u
t
voltage. The effect of the RLC load on
the SPSEI
G
output voltage can be com
pensated usi
ng a
seri
es
(and/o
r
parallel
)
ca
p
a
citor. However, it
can be seen that for the RL
C load
use
d
in the test,
the SPSEIG
output voltage is still
consi
derably affected by t
he connection of the load.
4. Experimental Set Up of Six-Phas
e Induc
tion M
a
chine Oper
ating in Gener
a
ting Mode
In orde
r to validate the re
sults o
b
taine
d
fr
om the si
mulated sy
stem
a prototype of six-
pha
se ma
chi
ne set up wa
s made. A three ph
ase induc
tio
n
mach
ine whi
c
h co
nsi
s
ts of thirty six
slots, 2.9A, 4
15volts, 1 Kw squi
rrel
cag
e
machi
ne
was used. Th
e se
venty two terminals
of stator
were taken o
u
t of the ma
chine in
ord
e
r
to test the m
a
chi
ne for
six
-
pha
se
ope
ra
tion and l
oadi
ng
test to b
e
p
e
r
forme
d
in
th
e ma
chin
e. T
he multi
-
ph
ase ma
chin
e
was
co
nne
cted
to a
DC m
o
tor
whi
c
h act
s
as a prime
mover whi
c
h
is
rotatin
g
at
100
0 rpm
.
At
first
the
self
excitati
on
phen
omen
on
of multi-pha
se i
ndu
ction
gene
rato
r
wa
s a
nalyzed b
y
plotting the
magn
etizati
o
n
cha
r
a
c
teri
stics. The ma
gn
etizat
ion
cu
rve sho
w
s the i
n
tersectio
n
of
the no load t
e
rmin
al voltage
with the
cap
a
citor load
line. At no-lo
a
d
, the ca
pa
ci
tor current Ic = V/Xc mu
st
be eq
ual to
the
magneti
z
ing
curre
n
t Im=V/Xm. The voltage is a fun
c
t
i
on of Im, linearly risi
ng unt
il the saturati
on
point of the
magneti
c
core is rea
c
hed.
The outp
u
t frequ
en
cy of the self
-excite
d
gene
rato
r i
s
,
f=
1/(2
π
CXm) and
ω
=2
π
f where
C is self-exciting
cap
a
citan
c
e.
Figure 8. Multi-pha
se in
du
ction gene
rato
r co
n
n
e
c
ted to the excitation ca
pa
citors and
trans
former
Figure 9. Win
d
ing pattern o
f
a six-pha
se
indu
ction ge
n
e
rato
r
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 1, April 2016 : 79 – 87
84
Figure 10. Magneti
z
ation
curve of
a
six-pha
se in
du
ction gen
erato
r
4.1 Self Excitation Tr
ansi
ents o
f
Six-P
h
ase Induc
ti
on Gener
a
to
r
To dem
on
strate the volta
ge an
d cu
rre
n
t transi
ent d
u
ring th
e an
alysis
duri
n
g
no load
con
d
ition
at first
excitation
is
bein
g
p
r
o
v
ided to th
e
set a
b
c by
conne
cting
a
delta
con
n
e
c
ted
cap
a
cito
r ban
k of 38 microf
arad to one o
f
the two
stator set
s
and the machine i
s
driven at 10
00
rpm by a pri
m
e mover an
d the voltage and cu
rre
nt
transi
ents a
r
e observed a
nd in the se
cond
ca
se the ex
citation cap
a
ci
tor ban
k is
conne
cted to
the 123
set and the volta
ge and
cu
rre
n
t
transi
ent a
r
e
ob
serve
d
[8
, 9]. The
st
eady
st
ate v
o
ltage
and
current
wavef
o
rm
s of
du
ring
excitation at either of the two sets have
been a
nalyze
d whi
c
h is a
s
sho
w
n in Fig
u
re 11
-1
3.
A
B
Figure 11. (A) Excitation at set ab
c, V/I tr
ansi
ent at set
123 (B)
stea
dy
state voltage & current
waveform at set 123
whe
n
excitation at set ab
c
A
B
Figure 12. (A) Excitation at set ab
c, V/I tr
ansi
ent
at set
abc (B
) stea
dy state voltage & current
waveform at set ab
c wh
en
excitation at set ab
c
0
100
200
300
400
0
5
10
15
20
Vg (v
o
l
t)
Im (amp)
Self-
excitation
of
IM
w
i
th
shunt capacitors at
nominal frequenc
y
Magnetization curve
Csh= 90
mF
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Tran
sie
n
t Analysis of a Mu
lti-pha
se I
ndu
ction Ma
chin
e Operating a
s
Gen
e
rato
r
(
A
lok Kum
a
r M.)
85
A
B
C
D
Figure 13. (A) Excitation at set 123, V/I transi
ent
at set
abc (B
) Excitation at set 1
23, V/I
transi
ent at set 123 (C) ste
ady state voltage &
cu
rre
nt waveform at
set 123
whe
n
excitation at
set 123
(D) st
eady state vo
ltage & curre
n
t wavefo
rm
at set abc
wh
en excitation
at set 123
4.2 Loading
Transien
ts o
f
the Six-Ph
a
se Inductio
n
Genera
tor
Duri
ng thi
s
a
nalysi
s
the
si
x-pha
se
indu
ction
ma
chin
e is loa
ded
a
nd the
tra
n
si
ents
are
observed at t
he two
stator
sets.
To find
possibilit
y of
supplying two different l
oads from one
si
x-
pha
se ma
chi
ne, static three-p
h
a
s
e
sta
r
co
nne
cted
resi
stan
ce l
o
ad we
re
con
necte
d to ea
ch
three
-
ph
ase
windi
ng
set. The voltage
a
nd current
wa
veforms
of th
e set
s
ab
c
an
d 123 fo
r lo
ad
ing
at one
set an
d the tra
n
si
en
ts at the othe
r set
have
b
e
en
an
alyze
d
as sho
w
n
i
n
Figures 14-1
7
.
It
is fou
nd that
loadin
g
at a
n
y
of the two
three
-
p
h
a
s
e
sets affe
cts th
e voltage
an
d current of
b
o
th
windi
ng sets.
A
B
C
Figure 14. (A) Excitation at set ab
c, V/I tr
ansi
ent
at set
abc when re
sistively load
ed with lo
ss o
f
transfo
rme
r
i
nput 123 (B
) Excitation at set ab
c, V
/I tr
ansi
ent at set
abc wi
th lo
ss of transform
er
input ab
c (C)
Excitation at set ab
c, V/I tr
ansi
ent
at set
abc for
step
unloa
ding fro
m
transfo
rme
r
output
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 1, April 2016 : 79 – 87
86
Figure 15. Steady state vo
ltage & curre
n
t waveform
at set abc
wh
en excitation
at set abc fo
r a
resi
stive load
A
B
Figure 16. (A) Excitation at set ab
c, V
/I tr
ansi
ent at set
123 for ste
p
loadin
g
(B) Excitation
at set abc, V/I transient at
set 123 d
u
rin
g
unloa
ding
Figure 17. Steady state vo
ltage & curre
n
t waveform
at set 123 wh
en excitation
at set abc fo
r a
resi
stive load
5. Conclusio
n
s
In
this pap
er an
a
nalytical
model of
a
si
x-pha
se
indu
ction gen
erat
or have been
mod
e
led
in whi
c
h
tra
n
s
ient
behavio
r of the
ma
chi
ne
when
subj
ected
to different types
of l
oad
s have
be
en
analyzed. To
demon
strate
the ability of the si
x-ph
a
s
e ma
chi
ne
to feed two
different loa
d
s
con
n
e
c
ted a
c
ro
ss its
sta
t
or termin
als experim
ent
al re
sults
h
a
ve bee
n prese
n
ted. In
the
experim
ental
analysi
s
the
voltage an
d
cu
rre
nt tran
sient a
nd
ste
ady stat
e be
havior of
cu
rrent
have bee
n a
nalyze
d
du
rin
g
no loa
d
an
d loade
d co
n
d
itions
whe
n
excitation is
being p
r
ovide
d
to
either of the
two stato
r
windi
ng sets.
It is f
ound that the six-p
hase gen
erator is
ca
pabl
e
of
sup
p
lying
to
different
lo
ad
s con
n
e
c
ted across
it
s
stat
or
te
rminal
s a
nd can
be
ex
cited witho
u
t an
y
probl
em
s u
s
i
ng a
3-pha
se
ca
pa
citor. It
implies that
l
o
ss of
excitat
i
on at
one
of
the thre
e-pha
se
sets can
be
su
stain
ed
a
nd o
peration
undi
srupted.
The
r
efo
r
e
a
six-pha
se
machi
ne ca
n
be
con
s
id
ere
d
re
liable a
s
com
pare
d
to thre
e pha
se ma
chine
s
.
Appe
ndix
The
par
am
et
ers
of
the
s
i
x
p
h
a
s
e
s
e
l
f
-
e
x
c
i
t
e
d
ind
u
ct
io
n
gen
erat
or
u
s
ed
in
simu
la
tio
n
are
a
s
foll
ows: Resi
stan
ce
s in the stator
windi
ng:
r
1
= r
2
= 1.
8
ohm
,
Lea
ka
ge
i
n
d
u
c
t
a
n
c
e
s
in th
e stator
windi
ng:
L
l1
= L
l2
= 0.01
33
H,
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Tran
sie
n
t Analysis of a Mu
lti-pha
se I
ndu
ction Ma
chin
e Operating a
s
Gen
e
rato
r
(
A
lok Kum
a
r M.)
87
Re
sista
n
ce in
the rotor wi
n
d
ing:
r
r
= 2.2
ohm
,
L
eak
ag
e
in
duc
tan
c
e in the ro
to
r
w
i
n
d
i
n
g
:
L
lr
= 0.01
33
H,
L
lm
’
= 0.011
1
H,J = 0.03
K
g
/m
2
a
= 0.
1
4
1
,
b
= 0.
001
,
c
= -0.
0
0
1
,
a
nd
d
= 0.0
0
0
0
5
0
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Evaluation Warning : The document was created with Spire.PDF for Python.