Electrical – How does line impedance of a BLDC motor relate to the RPM of its rotor

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I am curious about the impedance of the three phase BLDC motor when it is in operation. If the speed of the rotor of a BLDC motor is proportional to the frequency of the three phase current, and the reactance of the stator windings is also proportional frequency of the three phase current, then wouldn’t the impedance be proportional to the speed of the rotor (as inductive reactance of the stator windings can be defined as 2*pifL)? In this case, wouldn’t the motor draw less current as the RPM increases, but only due to impedance (not considering back-emf or other effects).

Or is the increase in impedance (with RPM) balanced out by some other factor in the design of a BLDC motor? If so, what exactly balances it out?

Best Answer

the speed of the rotor of a BLDC motor is proportional to the frequency of the three phase current

Beware of the above phrase: there are two frequencies involved. The most important is the synchronous one, i.e. the commutation of the phases carried by electronics in order to generate a rotating magnetic field. For example, a BLDC motor rotating at 1 turn/second could have a driving frequency of 6 Hz (six-step for one turn). For this frequency, I would not say that the speed is "proportional", I would say that it has to match exactly. Try to vary the frequency while the motor is running, and bad things will happen (big vibrations, big current consumption and spikes, heating). In reality, the frequency of the phases is dictated by the motor speed, not the contrary. To vary the speed of the motor you vary the voltage to it (using the duty cycle of the PWM).

The other frequency involved is normally around 20 kHz, it's the frequency of the PWM used by the output bridge, but it has nothing (or very little) to do with the speed of the motor. The inductance of the motor has a lot to do with this frequency.

When the speed of the motor increases, it draws less current because:

  1. The BEMF increases and contrasts the power supply.
  2. The commutation times decrease, so there is less time to pump current in the coil. As soon as the current start to rise, it's time to give up to pass to the next coil. A lower inductance lets the current rise more quickly than a higher inductance.
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