INFLUENCE OF ROTOR CURRENT ON FLUX
Up to now all our discussion has been based on the assumption that the rotating magnetic Weld remains constant, regardless of what happens on the rotor. We have seen how torque is developed, and that mechanical output power is produced. We have focused attention on the rotor, but the output power must be provided from the stator winding, so we must turn attention to the behaviour of the whole motor, rather than just the rotor. Several questions spring to mind.
Firstly, what happens to the rotating magnetic Weld when the motor is working? Won’t the MMF of the rotor currents cause it to change?
Secondly, how does the stator know when to start supplying real power across the air-gap to allow the rotor to do useful mechanical work? And Wnally, how will the currents drawn by the stator vary as the slip is changed?
These are demanding questions, for which full treatment is beyond our scope. But we can deal with the essence of the matter without too much diYculty. Further illumination can be obtained from study of the equivalent circuit, and this is dealt with in Chapter 7.
Reduction of flux by rotor current
We should begin by recalling that we have already noted that when the rotor currents are negligible (s ¼ 0), the e.m.f. that the rotating Weld induces in the stator winding is very nearly equal to the applied voltage. Under these conditions a reactive current (which we termed the mag- netising current) Xows into the windings, to set up the rotating Xux. Any slight tendency for the Xux to fall is immediately detected by a corresponding slight reduction in e.m.f., which is reXected in a disproportionately large increase in magnetising current, which thus opposes the tendency for the Xux to fall.
Exactly the same feedback mechanism comes into play when the slip increases from zero, and rotor currents are induced. The rotor currents are at slip frequency, and they give rise to a rotor MMF wave, which therefore rotates at slip speed (sNs) relative to the rotor. But the rotor is rotating at a speed of (1 – s)Ns, so that when viewed from the stator, the rotor MMF wave always rotates at synchronous speed, regardless of the speed of the rotor.
The rotor MMF wave would, if unchecked, cause its own ‘rotor Xux wave’, rotating at synchronous speed in the air-gap, in much the same way that the stator magnetising current originally set up the Xux wave. The rotor Xux wave would oppose the original Xux wave, causing the resultant Xux wave to reduce.
However, as soon as the resultant Xux begins to fall, the stator e.m.f.
reduces, thereby admitting more current to the stator winding, and increasing its MMF. A very small drop in the e.m.f. induced in the stator is suYcient to cause a large increase in the current drawn from the mains because the e.m.f. E (see Figure 5.8) and the supply voltage V are both very large in comparison with the stator resistance volt drop, IR. The ‘extra’ stator MMF produced by the large increase in stator current eVectively ‘cancels’ the MMF produced by the rotor currents, leaving the resultant MMF (and hence the rotating Xux wave) virtually unchanged.
There must be a small drop in the resultant MMF (and Xux) of course, to alert the stator to the presence of rotor currents. But because of the delicate balance between the applied voltage and the induced e.m.f. in the stator the change in Xux with load is very small, at least over the normal operating speed range, where the slip is small. In large motors, the drop in Xux over the normal operating region is typically less than 1%, rising to perhaps 10% in a small motor.
The discussion above should have answered the question as to how the stator knows when to supply mechanical power across the air-gap. When a mechanical load is applied to the shaft, the rotor slows down, the slip increases, rotor currents are induced and their MMF results in a modest (but vitally important) reduction in the air-gap Xux wave. This in turn causes a reduction in the e.m.f. induced in the stator windings and therefore an increase in the stator current drawn form the supply. We can anticipate that this is a stable process (at least over the normal operating range) and that the speed will settle when the slip has increased suYciently that the motor torque equals the load torque.
As far as our conclusions regarding torque are concerned, we see that our original assumption that the Xux was constant is near enough correct when the slip is small. We will Wnd it helpful and convenient to continue to treat the Xux as constant (for given stator voltage and frequency) when we turn later to methods of controlling the normal running speed.
It has to be admitted, however, that at high values of slip (i.e. low rotor speeds), we cannot expect the main Xux to remain constant, and in fact we would Wnd in practice that when the motor was Wrst switched-on, with the rotor stationary, the main Xux might typically be only half what it was when the motor was at full speed. This is because at high slips, the leakage Xuxes assume a much greater importance than under normal low-slip conditions. The simple arguments we have advanced to predict torque would therefore need to be modiWed to take account of the reduction of main Xux if we wanted to use them quantitatively at high slips. There is no need for us to do this explicitly, but it will be reXected in any subsequent curves portraying typical torque–speed curves for real motors. Such curves are of course used when selecting a motor, since they provide the easiest means of checking whether the starting and run- up torque is adequate for the job in hand.