an investigation of dual stator winding induction machines

dependent frequency voltage components are generated having frequencies which are
ω1 − 2Pω
1 r , ω2 ( − 1 − P2
) r
+ P ω and + ( P − P ) ωr
. The additional frequency voltage
ω2 1 2
components induced in the XYZ winding set are 2P
ωr
( − P ) r
ω1 2 1
222
ω2 2
ω1 2 1
+ − P − P ω and
− , ( ) r
+ P ω . All the voltages with harmonic frequencies (such as − 2Pω
r ,
+ ( − P − P ) ωr
and ( − P ) r
ω2 1 2
ω2 1 2
ω1 1
+ P ω ) induce harmonic currents. These harmonic
currents subsequently induce other higher-level harmonic voltages, and so on and so
forth. However, since the magnitudes of the harmonic currents and voltages are much
less than the fundamental components, they are insignificant and can be ignored.
From the torque equations, an average torque generated individually by the ABC and
XYZ winding sets is given by the last terms of the equations (5.109-5.110). In addition,
by constraining the supply voltage frequencies of the windings, a potential average torque
can be obtained as discussed below.
(A) The first term in (5.109-5.110) potentially contributes to the average torque when
the following frequency equation is met.
ω 1 ω2
+ ( − P1 − P2
) ω = 0 or ω1 = ( 1 + P2
) ωr
−ω
2
+ r
P (5.111)
The frequency constraint in (5.111) is such that if the rotor speed and the input
frequency of the ABC winding set are fixed, the frequency of the voltage in the
XYZ winding set can be controlled according to (5.111) to create an additional
torque component. If the slip frequencies of the stator windings are defined as
ωs1 = ω1
− Pω 1 r , ωs 2 ω2
− P2ω r
= , then ω ω = 0 . It follows that an additional
s1
+ s2
torque may be available when the slip frequencies of two stator windings have the
same magnitude but of opposite signs. Under this constraint, one three-phase