an investigation of dual stator winding induction machines

u
rpi
2π
'
k − jk θ −(
i−1)
α r
() t = rl C ⋅e
∫∑
Unless 1 P k −
−P1
C =
R
C
0
k
R
'
[ ] 1 1 0
j ( ) ( s ω t−
Pθ
)
203
1 1 1
[ 2 3C
s1
⋅ I s1
e ]
⎧ rs ω ⎛ µ r ⎞
⎫ '
⋅ Re⎨− ⎜ j ⎟
⎬ dθ
⎩ P1
⎝ gP1
⎠
⎭
= , the induced EMF in the rotor loops (5.37) is zero. If
*
P1
R
Then the induced EMF in the th
i rotor loops is given as:
u
rpi
[ ( ) ]
() [ ( ) ] ⎬
⎭ ⎫
2
⎧ µ sω
r *
0 1 P1
j s1ω1t
−P1 i−1
αr
t = π rl Re − j C 2 3C
⋅ I e
(5.37)
(5.38)
2 ⎨
R
s1
s1
(5.39)
2
⎩ gP1
The above equation shows that the field driving the ABC winding set only induces an
EMF that has P 1 pole pair distribution in the th
i rotor loop. If it is assumed that the
currents flowing in the th
i rotor loop has the same time relationship as the EMF, the th
i
rotor loop current equation becomes:
i
rpi
() { } t js1ω1
t Re 2 ⋅ I ⋅ e
= (5.40)
iR1
5.2.1.6 Voltages in Rotor Loops due to the Stator Currents Flowing in the XYZ
Winding Set. The induced voltage in the th
i rotor loop by the XYZ winding set stator
currents can be expressed as:
u
rqi
[ ( ) ]
() [ ( ) ] ⎬
⎭ ⎫
2
⎧ µ sω
r *
0 2 P2
j s2ω
2t
− P2
i−1
α r
t = π rl Re − j C 2 3C
⋅ I e
2 ⎨
R
s2
s2
(5.41)
2
⎩ gP2
The slip frequency s 2 is defined as:
ω2 − P2ω
r
s2
= (5.42)
ω
2