an investigation of dual stator winding induction machines

that L AB = L BA , L BC = L CB and L CA = L AC . These equations confirm expectations from
the linear magnetic circuit theory.
4.2.3 Self Inductances of the XYZ Winding Set
Similar expression of the self-inductance calculation can be found for the XYZ
winding set,
2π
'
'
[ A + A ( θ −θ
) ] ⋅ n ( θ ) ⋅[
n ( θ ) − n ( θ ) − K ( θ ) ] ⋅ dθ
Lii = µ rl ∫ 0 1
rm i i
i
i rm
0 cos (4.8)
0
2π
' A1
'
where, K ( θ rm ) = ∫ ni
( θ ) cos(
θ −θ
rm )
i dθ
and i = X , Y,
Z .
2π
A
0
0
Since the XYZ winding set is a 6 pole winding set, the Fourier series of the XYZ
winding function is composed of 3 θ component, 6 θ component, …, 3 kθ
component,
etc, where k = 1, 2,
L,
∞ . The integration of the multiplication of two cosine functions
will be zero except both have the same frequency. Therefore it is obvious that in the XYZ
'
winding set, ( )
K θ will always be zero, which is not the case with the 2-pole ABC
i
rm
winding set. This explains why the stator self-inductances of the XYZ winding set are not
simple three times repetition of the stator self-inductance waveform of the ABC winding
set; they are quite different from each other. The same reason explains the difference
between the mutual inductances of the ABC winding and XYZ winding sets. If a precise
model of the inverse of the air gap function including more high order components is
used in the analysis, the characteristics found in the mutual inductances of the ABC
winding set may be observed in the mutual inductances of the XYZ winding set also.
161