Does FOC for PMSM change with the number of rotor poles?

Hi,

I'm having some issues regarding FOC applied to PMSM, in particular when the rotor has more than 1 pole pair. I don't fully understand how is it possible that the FOC principle that is widely explaind for a motor of 1 pole pair, i.e stator magnetic flux orientatio being perpendicular to the rotor direct component, can be aplied in the same way to a rotor with higher number of poles. In the figure I represented PMSM with a 4 pole pair rotor. In Figure "a)" the stator flux is oriented such that there is a maximum torque and in Figure "b)" the direct and quadtrature axis of the rotor.

Based on this I deduce that if I want to apply FOC to this motor the park transformation should be modified sin the rotatory axis has a 25 º shear in it so that we can adjust the currents of the stator.

That means that the transformation should be (φ is the angle between the d and q axis):

Is this correct?

The reason for why I'm asking this is because I havent manage to find any literature that talks about this and I don't know why, I feel that I'm missing something...

Answer 1

[Sabin]

In Field Oriented Control we need to apply Park transform to the stator quantities (currents, voltages, fluxes) so we obtain a model in d-q reference frame where we can use the q-axis to control the torque and d-axis to control the flux. Now in the mathematical transform we need the rotor electrical angle and electrical angle is dependent of the number of polepairs. The d and q components are 90 degrees apart. I hope this answers your question.

[Santiago Alfonso Ospina Botero]

So if I understand correctly, it's true that in the rotor reference frame the the q axis is phi=360°/#poles apart from the d axis (in this case phi=22.5°) but if we now switch to the stator ref frame the q axis is 90° apart from the d axis and thanks to the electrical and mechanical angle conversion the abc to dq converted stator quantities during one electrical rotation will happen every 1/(#poles/2) electrical degrees in the rotor ref frame. Basically we don't need to project the stator quantities to the dq axis of the rotor because the mechanical degrees are different from the electrical degrees and this is taken into account in the electromechanical angle conversion that depends on the #poles