an investigation of dual stator winding induction machines

for the steady state condition, the additional average torque from the interaction of
the two stator winding sets may be obtained during the transient condition.
(B) The second term in (5.109-5.110) contributes to the average torque only when the
following conditions are meet :
ω 1 − ω2
+ ( P2 − P1
) ωr
= 0 or ω 1 = ( 1 − P2
) ωr
+ ω2
P , ω ω = 0 (5.116)
224
s1
− s2
If the rotor speed and the input frequency of the ABC winding set are fixed, the
frequency of the supply voltage to the XYZ winding set can be controlled
according to (5.116) to create a possible additional torque component. This
additional torque component will be available when the slip frequencies of the
two stator winding sets have the same value implying that both winding sets are
either working as motors or generators. Following the same derivation process for
case (A), the possible additional torque from the second term of T eABC is
expressed as:
T
*
N
2
r
⎧ µ 0r
[ ( )( 1)
]
Re 2
⎛
P1
2 1
3
⎞
j P + P ⋅ i−
⋅α
⎫ r + ε
π rl ⎨ j ⎜ Cs1
⋅ I s1
⋅C
R ⎟⋅
I R2
⋅e
⎬ = 0 (5.117)
⎩ gP1
⎝
⎠ i 1
⎭
eABC2
= ∑
=
It is obvious that this possible additional torque term will also be zero under
steady state condition although it may not be zero during the transient condition.
The same result can be obtained for the second term of T eXYZ .
(C) The third term in (5.109-5.110) may contribute to the average torque when any
the rotor angular speed is the same as the angular speed of the supply voltage
corresponding to synchronous operating conditions. That is, ω r p1
= ω1,
ω p = ω . Unfortunately at synchronous rotor speeds, the rotor currents are
r
2
2
zero, hence no electromagnetic torque results. Synchronous operation, which is