an investigation of dual stator winding induction machines

Substituting (3.28) and (3.29) into the above equation and simplifying,
2π
'
'
[ A + A ( θ −θ
) ] ⋅ n ( θ ) ⋅ [ n ( θ ) − n ( θ ) − K ( θ ) ] ⋅ dθ
LAA = µ rl ∫ 0 1
rm A A
A
A rm
0 cos (4.3)
0
2π
' A1
'
where, K A ( θrm
) = ∫ nA
( θ ) cos(
θ −θ
rm )
2π
A
0
0
dθ
.
Since the turn function of phase A is a piecewise linear equation, the integration can
only be done in each linear region. The final result is obtained by adding the result of
each linear region together.
Under rotor eccentricity conditions, similar equations can be found for phase B and
phase C.
2π
'
'
[ A + A ( θ −θ
) ] ⋅ n ( θ ) ⋅[
n ( θ ) − n ( θ ) − K ( θ ) ] ⋅ dθ
LBB = µ rl ∫ 0 1
rm B B
B
B rm
0 cos (4.4)
0
2π
'
'
[ A + A ( θ −θ
) ] ⋅ n ( θ ) ⋅[
n ( θ ) − n ( θ ) − K ( θ ) ] ⋅ dθ
LCC = µ rl ∫ 0 1
rm C C
C
C rm
0 cos (4.5)
0
2π
2π
' A1
'
' A1
'
where, K B ( θrm
) = ∫ nB
( θ ) cos(
θ −θ
rm ) dθ
, KC ( θrm
) = ∫ nC
( θ ) cos(
θ −θ
rm )
2π
A
0
0
155
2π
A
0
0
dθ
.
Unlike the case where the self-inductances of the three phases have the same values
when the air-gap length is constant, they are quite different under rotor eccentricity
conditions. The simulation results of the self-inductances under different eccentricity
conditions are shown in Figures 4.1, 4.2 and 4.3.