Influence of Rotor Current on Flux
Up to now, all our discussion in previous articles has been based on the assumption that the rotating magnetic field 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 field 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 finally, 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 difficulty.
Reduction of Flux by Rotor Current
We should begin by recalling that we have already noted that when the rotor currents are negligible (s = 0), the e.m.f. that the rotating field induces in the stator winding is very nearly equal to the applied voltage.
Under these conditions a reactive current (which we termed the magnetising current) flows into the windings, to set up the rotating flux. Any slight tendency for the flux to fall is immediately detected by a corresponding slight reduction in e.m.f., which is reflected in a disproportionately large increase in magnetising current, which thus opposes the tendency for the flux 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 flux wave’, rotating at synchronous speed in the air-gap, in much the same way that the stator magnetising current originally set up the flux wave. The rotor flux wave would oppose the original flux wave, causing the resultant flux wave to reduce.
However, as soon as the resultant flux 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 sufficient to cause a large increase in the current drawn from the mains because the e.m.f. E 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 effectively ‘cancels’ the MMF produced by the rotor currents, leaving the resultant MMF (and hence the rotating flux wave) virtually unchanged.
There must be a small drop in the resultant MMF (and flux) 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 flux with load is very small, at least over the normal operating speed range, where the slip is small.
In large motors, the drop in flux 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 flux 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 sufficiently 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 flux was constant is near enough correct when the slip is small.
We will find it helpful and convenient to continue to treat the flux 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 flux to remain constant, and in fact we would find in practice that when the motor was first switched-on, with the rotor stationary, the main flux might typically be only half what it was when the motor was at full speed.
This is because at high slips, the leakage fluxes 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 modified to take account of the reduction of main flux if we wanted to use them quantitatively at high slips.
There is no need for us to do this explicitly, but it will be reflected 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 runup torque is adequate for the job in hand.
Stator Current Speed Characteristics
In the previous section, we argued that as the slip increased, and the rotor did more mechanical work, the stator current increased. Since the extra current is associated with the supply of real (i.e. mechanical output) power (as distinct from the original magnetising current which was seen to be reactive), this additional ‘work’ component of current is more or less in phase with the supply voltage, as shown in the phasor diagrams (Figure 1).
The resultant stator current is the sum of the magnetising current, which is present all the time, and the load component, which increases with the slip. We can see that as the load increases, the resultant stator current also increases, and moves more nearly into phase with the voltage. But because the magnetising current is appreciable, the difference in magnitude between no-load and full-load currents may not be all that great.
The simple ideas behind Figure 1 are based on an approximation, so we cannot push them too far: they are fairly close to the truth for the normal operating region, but breakdown at higher slips, where the rotor and stator leakage reactances become significant. A typical current locus over the whole range of slips for a cage motor is shown in Figure 2.
We note that the power factor becomes worse again at high slips, and also that the current at standstill (i.e. the ‘starting’ current) is perhaps five times the full-load value.
Very high starting currents are one of the worst features of the cage induction motor. They not only cause unwelcome volt drops in the supply system, but also call for heavier switchgear than would be needed to cope with full-load conditions.
Unfortunately, for reasons discussed earlier, the high starting currents are not accompanied by high starting torques, as we can see from Figure 3, which shows current and torque as functions of slip for a general-purpose cage motor.
We note that the torque per ampere of current drawn from the mains is typically very low at start up, and only reaches a respectable value in the normal operating region, i.e. when the slip is small.