an investigation of dual stator winding induction machines

C
C
= k
π ⋅ d
s2
s2
s2
199
(5.19)
where, C s2
is the number of series connected turns per phase; d is the mean air gap
diameter; k s2
is the fundamental winding factor for the XYZ winding set.
The three-phase balance currents flowing through the phases can be expressed as:
⎧
⎪i
⎪
⎪
⎪
⎨i
⎪
⎪
⎪i
⎪
⎩
X
Y
Z
jω2t
() t = Re(
2 I e )
() t
() t
⎛
= Re⎜
⎜
⎝
⎛
= Re⎜
⎜
⎝
2 I
2 I
s2
s2
s2
e
e
⎞
⎟
⎟
⎠
⎞
⎟
⎟
⎠
⎛ 2π
⎞
j⎜
ω2t−
⎟
⎝ 3 ⎠
⎛ 2π
⎞
j⎜
ω2t+
⎟
⎝ 3 ⎠
(5.20)
where, I s2
is the current magnitude in complex form and the electric speed of the current
is ω 2 .
By using the same idea and process as the ABC winding set, the field equations for
the XYZ winding set are given as:
J
B
2
2
j(
ω2t−
P2θ
)
( θ,
t)
Re{
2(
3C
⋅ I ) e }
= (5.21)
s2
s2
( )
( ) [ ( ) ] ⎬
⎭ ⎫
⎧ µ 0r
j ω2t−
P2θ
θ,
t = Re j 2 3C
⋅ I e
⎨
⎩
gP
2
s2
( )
( ) [ ( ) ] ⎬
⎭ ⎫
2 ⎧ µ 0ω2r
j ω2t
−P2θ θ,
t = Re − j 2 3C
⋅ I e
s2
(5.22)
E 2 ⎨
2
s2
s2
(5.23)
⎩ gP2
u
s2
() [ ( ) ] ⎬
⎭ ⎫
2 ⎧ µ r *
0ω2
jω2t
t = 2 rl Re − j C 2 3C
⋅ I e
π ⎨
s2
s2
s2
(5.24)
2
⎩ gP2