Change the speed of an induction motor with an additional capacitor

Question

I have a three phase induction motor (a fan motor) that get power from a two phase power line. To start the motor I have a start capacitor.

I need to change the speed of the motor to reach the 70% of the nominal one, a colleague of mine said that I can use the scheme of CASE 2, so I have to add an additional capacitor. I was not aware of this configuration, so I seached on the internet. I find some example: Speed control on a ceiling fan induction motor

I understand that the additional capacitor produce a phase shift to reach the desired speed.

My question is related to the sizing of the two capacitors to reach the target speed. If I know the motor data how can I size the additional capacitor C2 to reach the desired speed value? Do I need to use some equivalent motor circuit?

^{simulate this circuit – Schematic created using CircuitLab}

Answer 1

I had the same task and just connected capacitor in series with fan. It works. Case shifting capacitor was not changed. Speed of asynchronous induction motors depend of voltage frequency, but rotor turns slower than magnetic field. That turns difference create torgue. Connecting capacitor in series reducing actual voltage on motor. So for the same load turns difference should increase and motor turns slower. To achieve desired speed you need to try different capacitor values.

Answer 2

Adding a capacitor to a SINGLE phase motor can change the torque and thus the speed, that's how multi-speed ceiling fans work. But that would not change the speed of a 3 phase motor that is trying to be started with a capacitor. When you do this, you are ALREADY losing about 1/2 of the motor torque by running it from single phase, so assuming that was accounted for in the design, if you increase the slip even more (assuming that's what would happen), you will probably just stall the motor.