Speed control of a PSC induction motor, how does it actually work?

I'm trying to understand the physics and engineering behind speed control on PSC induction motors, usually seen in fans/HVACs.

I have come across this link, but I don't quite understand everything that is presented. Controlling speed of PSC induction motor (Questions about operating at high slip)

My main question is regarding the claim that an induction motor is similar to an auto transformer. If I was to apply 120 V AC to the low tap, what is the voltage difference between the high and neutral? Is this an AC voltage divider or is it an autotransformer where voltage is dependent on the windings?

In an autotransformer you usually also have an attached load, what is the load in this case, is it the capacitor on the auxiliary winding, or is it an inductive load (the spinning rotor)? I'm assuming the main winding is the common winding of the autotransformer (correct me if I am wrong, though).

Finally, is the speed being varied due to the resistances introduced by the additional windings (lower current draw, therefore weaker B field), or is it being varied due to the stepping down of the voltage, e.g. if we used additional windings without any resistance would the speed reduction still be present thereby indicating the autotransformer phenomena?

• I'm a bit confused about your diagram. What are the extra windings?I get the main winding and the auxilary. Most of the models I see online don't have the extra windings. Commented Aug 23, 2022 at 6:34

Some assumptions:

1. If this is the type of motor like many ceiling and box fans use (PSC or shaded pole),
2. And they aren't switching pole arrangements around,
3. And the windings are literally just that, extra turns on the same poles, then:

The torque curve is the same for all three settings, just scaled vertically. This is reflected in the diagram:

The blue curve's height is scaled proportional to applied voltage. Running at a greater step-down ratio, reduces the voltage on the stator, reducing the torque curve.

The load curve is the same in any case (red), defined by the propeller, and the medium it's pushing (air).

The curves intersect at different points, thus different steady-state speeds will be seen.

The autotransformer question is covered by assumption #3. In that case, the "high" tap will be at some lower voltage, when "low" is powered; conversely, when "high" is powered, the "low" tap will be at quite a bit higher voltage! What ratios exactly, I have no idea; that's determined by the manufacturer's desired speed settings.

This assumption also covers the question about coupling: the "extras" are extensions of the "main" winding, on the same poles. The "aux" winding is made on opposite poles.

The load is the rotor; the capacitor only provides phase shift, and isn't a (real) load by itself. (Whether a capacitor counts as a load, is more contextual: it certainly draws current, so is a load in that sense. But that current is out of phase: it doesn't dissipate power, loading down the power company's generators in the process. AC is weird and wonderful like that.) The load is only mildly inductive by itself (a "squirrel cage" rotor having very low resistance, acting as a shorted turn), and the balance of the inductivity is due to winding leakage and self-inductance.

Due to the high-slip condition, the efficiency, and especially power factor, will be especially poor at the low settings; but that's somewhat beside the point. More to the point, it need not be due to winding resistance. (That would be an adequate method, and I think has been used in the past. Obviously, it's very poor efficiency.) The power factor could be corrected by wiring a capacitor in parallel (though you'd need a different value for each tap, wired with a separate switch pole), but isn't worthwhile in practice.

A clarification on magnetism: flux density is proportional to applied voltage, and inversely proportional to frequency. (And we can ignore the latter since this is all at mains frequency.) We are completely uninterested in magnetizing current, or other current flows: importantly, as this is a transformer (of sorts), the primary current is the sum of magnetizing plus load current, and we can twist ourselves into knots trying to figure out which one is which. Far better to stick with flux here.