an investigation of dual stator winding induction machines

4.4 Mutual Inductances Calculation
The mutual inductances are the inductances between stator windings and rotor loops,
which is a very important and interesting part of the inductance calculation. Mutual
inductances changing by the rotor angle under the constant air gap condition are shown in
the previous chapter. The mutual inductances shown here are under different rotor
eccentricity conditions. These mutual inductances are quite different from those when the
machine is under the constant air gap condition as shown in the upcoming figures.
4.4.1 Stator Rotor Mutual Inductances of the ABC Winding Set
From the general winding function definition, the equation of stator rotor mutual
inductance can be expressed as:
2π
[ ] ⋅ dθ
'
'
[ A + A ( θ −θ
) ] ⋅ n ( θ ) ⋅ n ( θ ) − n ( θ ) − K ( θ )
Lij = µ rl ∫ 0 1
rm i j
j
j rm
0 cos (4.12)
0
2π
' A1
'
where, K ( θ rm ) = ∫ n j ( θ ) cos(
θ −θ
rm )
loop, ( θ )
j
j dθ
, n i ( θ ) is the turn function of
2π
A
th
i rotor
0
0
n is the turn function of stator th
inverse of the air gap function.
'
j winding and A A ( θ −θ
)
175
+ is the
0 1 cos rm
The stator rotor mutual inductance under the static rotor eccentricity, dynamic rotor
eccentricity and mixed rotor eccentricity conditions are shown in Figure 4.22, Figure 4.23
and Figure 4.24 respectively.