an investigation of dual stator winding induction machines

The expressed for the self-inductance of phase A can be simplified as:
2π
[ ]
µ 0rl AA = ∫ nA
( θ ) ⋅ nA
( θ ) − n ( θ ) ⋅ dθ
(3.38)
g
L A
where, ( θ )
A
0
0
n is the averages of the phase A winding functions.
Similar expressions can be found for phases B and C.
2π
[ ]
µ 0rl BB = ∫ nB
( θ ) ⋅ nB
( θ ) − n ( θ ) ⋅ dθ
(3.39)
g
L B
0
0
2π
[ ]
µ 0rl CC = ∫ nC
( θ ) ⋅ nC
( θ ) − n ( θ ) ⋅ dθ
(3.40)
g
L C
0
where, n ( θ ) and ( θ )
B
respectively.
0
n are the averages of the phases B and C winding functions
C
The self-inductances of three phases have the same value and the value of the self-
inductances is:
L
AA
= L
BB
= L
0
CC
µ 0rl
=
g
0
2π
5⋅π
2µ
0rl
⎡
218
2
=
⋅
⎢ 3 Cs1d
g ∫ ⋅π
θ +
0 ⎣ 2⋅18
127πµ
0rl
2
= Cs1
9g
∫
0
N
A
7⋅π
2⋅18
5⋅π
2⋅18
∫
( θ ) ⋅ N ( θ )
33⋅π
2 ( ) 218
2
2C
dθ
+ ⋅ ( 3C
) dθ
+ 2⋅18(
2C
)
s1
A
⋅ dθ
∫
7⋅π
2⋅18
100
s1
∫
35⋅π
33⋅π
2⋅18
s1
2
dθ
+
37⋅π
2⋅18
35⋅π
2⋅18
∫
C
2
s1
(3.41)
where, C s1
is the number of turns per slot for the ABC winding set; P 1 is the number of
pole for ABC stator winding set and S is the number of stator slots. This expression of
self-inductance calculation is only good for this particular machine design.
⎤
dθ
⎥
⎦