an investigation of dual stator winding induction machines

otor speed ω m ( ωr1 = 0.
5Pω
1 m for the ABC winding set, ωr 2 = 0.
5P2ω
m for the XYZ
winding set) Then, the slip frequencies are ωs1 ω1
−ω
r1
182
= and ωs 2 ω2
−ω
r 2
= , where the
angular rotor speeds corresponding to the windings with P 1 and P 2 poles are ω r1
and
ω r 2 respectively. Since the interactions between ω 1 and ω s2
, ω 1 and ω 2 , ω s2
and 1
ω s1
and s2
ω are nonexistent, the corresponding terms such as P( ω )
eliminated and the final equations (4.14) are:
( ω ) P(
ω − ω )
P
ω
1
1
= −
1
1
ω − ω
s1
s1
( ω ) P(
ω −ω
)
P
ω
s1
s1
Hence,
= −
s1
ω −ω
s1
( ω ) P(
ω ) P(
ω )
P
ω
1
1
=
ω
s1
s1
= −
1
1
ω
r1
r1
( ω ) P(
ω −ω
)
P
ω
2
2
2
s2
1 s2
ω ,
ω − should be
2 s2
= −
(4.14)
ω −ω
( ω ) P(
ω − ω )
P
ω
s2
s2
= −
s2
ω − ω
s2
( ω ) P(
ω ) P(
ω )
P
ω
2
2
=
The electromagnetic torques from two stator windings and the total electromagnetic
torques can be written as:
( ω )
P
Te 1 =
ω
1
1
P
( ω )
where, ω 1 = 2π f1
and 2 2π f 2
ω
s2
s2
= −
2 Te 2 = T e Te1
+ Te2
ω2
ω = .
2
2
ω
r 2
r 2
= (4.15)
The average active powers going into the ABC and XYZ winding sets, which are
P ( ω ) and ( ω )
1
P
P
P , are given as :
2
( ω1
) = vaia
2 2 2
+ vbib
+ vcic
− rs1(
ia
+ ib
+ ic
)
( ω ) = v i + v i + v i − r
2 2 2 ( i + i + i )
2
x x
y
y
z z
s2
x
y
z
(4.16)