an investigation of dual stator winding induction machines

constant. The offset angle λ in (3.16) is zero for all the above calculations. Changing the
value of angle λ will only create a common phase shift in all the waveforms. All the
figures have the same limit in the y-axis for better comparison.
4.2.2 Mutual Inductances of the ABC Winding Set
The general expression for the mutual inductance calculation is:
2π
1
Lij = µ 0rl
∫ ⋅ ni
j
g
where, ( θ )
i
0
( θ,
θ )
rm
( θ ) ⋅ N ( θ ) ⋅ dθ
n is the turn function of th
winding; g( θ )
θ, is the air gap function.
rm
i winding; ( θ )
158
j
(4.6)
N is the winding function of
Substituting the inverse of the air gap equation and general winding function into
(4.6) and simplifying,
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 (4.7)
0
2π
' A1
'
where, K ( θ rm ) = ∫ n j ( θ ) cos(
θ −θ
rm )
j dθ
, n j ( θ ) is the turn function of j winding.
2π
A
0
0
The calculation method and process for mutual inductance calculation are similar to
the one for self-inductance, except the number of linear regions needed for the calculation
is more. The simulation results of the stator winding mutual inductances can be found in
Figures 4.4, 4.5 and 4.6.
th
j