Page 404 - Power Electronics Handbook

Electrical machine control 393
Instead of segmenting the rotor it is possible to attenuate the quadrature
axis flux by using flux guides or barriers, as in Figure 14.44. Two forms are
illustrated here, in both cases it being seen that the quadrature axis flux is
decreased to a greater extent than the direct axis flux, due to the position
of the guides.
It has been seen by the above discussion that a reluctance motor is in
effect a synchronous machine with unexcited rotor poles. Both machines,
on the other hand, behave like an induction motor during run-up periods,
and can be considered as special cases of the induction machine. The
torque on the rotor of an induction motor is caused by induced currents
produced by a rotating stator field. If Nl and N2 are the speeds of this field
and of the rotor respectively, then the slip S is defined by equation (14.5).
Nl - N2
S= (14.5)
Nl
The magnitude of the rotor torque is proportional to stator flux,
rotor-induced current and the cosine of the angle between these two
phases, being given by equation (14.6) where T is the torque on the rotor, S
is the slip, El is the stator applied voltage,f, is the stator frequency, R2 is the
rotor resistance and X, is the rotor reactance.

(14.6)

Tar (zy (14.7)
Equation (14.6) gives the maximum torque T,,, which occurs at a slip S,,
derived from equations (14.7) to (14.9).

R2
s, a - (14.8)
fl

x2 arfl (14.9)
Substituting these values in equation (14.6) gives the result as in equation
(14.10).
q-r.
T= ' (14.10)
1,
SmlS + SIS,
The input power, which crosses the air gap between stator and rotor, is
primarily used in producing copper losses and torque output. These two
are divided in the ratio of S/( 1 - S) so that motor efficiency is equal to that in
equation (14.11).
qm=l-S (14.11)
In a commutator motor, as with some types of induction motors when
the motor winding is brought out to slip rings and brushes, a resistor
connected in series with the rotor would result in power loss. This would
mean that the output power of the machine is reduced and it must slow
down to supply the same torque. A further advantane of mmmlltrrtnr