Park transform, why is it not the mechanical angle?

[fabiodl]

In the control of a motor with a multi pole-pair permanent magnet rotor the park transform is done (if I am correct) using the electrical angle, and not the mechanical angle.
If we use the motor as a generator, the generated wave will be at the frequency of the electric angle, so it makes sense that the opposite (i.e. using the machine as a motor) should use the electric angle as well
BUT
If I imagine the field created by the stator as a magnet that pulls the stator it would make much more sense to imagine it to rotate at the same speed of the rotor, i.e. to use the mechanical angle. What is the fallacy in the argument in support of the mechanical angle? Do you know any books explaining WHY we should use the electric angle and not the mechanical angle from a physical standpoint?

[Someone]

Motors come with different numbers of poles, electrical drive remains the same and doesn't care (you can unwrap a motor into a linear drive).

[Phoenix]

A 2 pole motor will have 1 electrical revolution for 1 mechanical revolution
A 4 pole motor will have 2 electrical revolutions for 1 mechanical revolution
so on...

The electrical angle is used because the current/torque/commutation controller cares about the position of the magnetic fields - which rotates at the electrical rate.

[fabiodl]

A 2 pole motor will have 1 electrical revolution for 1 mechanical revolution
A 4 pole motor will have 2 electrical revolutions for 1 mechanical revolution
so on...

The electrical angle is used because the current/torque/commutation controller cares about the position of the magnetic fields - which rotates at the electrical rate.

Yes this is my understanding. But now imagine the field induced by the stator is a physical magnet. Why shouldn’t it turn at a certain speed and the rotor rotate at the same speed, keeping the relative position between this virtual magnet and one of the poles of the stator constant?

[Phoenix]

Sure, you can measure the mechanical angle, but then you will need to convert it to the appropriate electrical angle for the transform given the number of poles.

Another way to look at it is that the transform converts (frequency shifts) the AC measurement into DC signals. But this only works if you use the correct/electrical angle.

[Doctorandus_P]

... the generated wave will be at the frequency of the electric angle,

It seems like you are mixing up some terms, which makes it hard to give a good answer.
Motors with permanent magnets are synchronous devices, so the electrical and mechanical frequencies are always the same (for a normally operating motor).

I also am not good with names.
Clarke & Park transform is, if I remember well, a part of the FOC algorithm.
The goal with FOC is to generate and maintain a 90 degree phase shift between the magnetic fields generated by the coils and the rotor to optimize efficiency.

[eugene]

As has been implied by other responses, there is a relationship between the mechanical angle of the rotor and the electrical angle. If you happen to have a high-resolution encoder on the stator of a sensorless BLDC motor, then you could characterize your motor and come up with a function that converts stator absolute mechanical angle to electrical angle. You would then use that calculated electrical angle to perform commutation, including park transformation or not.

Is that where your thinking is headed?

[Martinn]

The goal with FOC is to generate and maintain a 90 degree phase shift between the magnetic fields generated by the coils and the rotor to optimize efficiency.

Not sure about this. You could based on the rotor angle calculate the three phase currents and use these as setpoints for three PI current controllers (two actually, as the sum of the currents is zero). This would be called sinusoidal commutation and would be from motor side be indistinguishable from FOC. The point of FOC as I understand it is that the D and Q current controllers have constant setpoints over one rotation (assuming set torque is constant), while with sinusoidal commutation setpoints would follow phase currents.
On top FOC is as I understand it usually used together with SVM midpoint shift (although it is actually unrelated), increasing available bus voltage.

[jkostb]

Hi,

You asked for books where the Park/Clarke transformations are explained. An excellent introductionary reference is:
Electromechanical Motion Devices from Krause. This book explains and derives the mathematical transformations used for field oriented control. 

Other reference: Analysis of electric machinery and drive systems Krause (This is more advanced and considered as the bible for  many).

Permanent magnet syncrhonous and brushless DC motors from Krishnan (This is also more advanced)

[fabiodl]

It seems like you are mixing up some terms, which makes it hard to give a good answer.
Motors with permanent magnets are synchronous devices, so the electrical and mechanical frequencies are always the same (for a normally operating motor).

No. If the motor has more than two poles, the mechanical angle is 2/N (N number of poles) of the electric angle.

[fabiodl]

Hi,

You asked for books where the Park/Clarke transformations are explained. An excellent introductionary reference is:
Electromechanical Motion Devices from Krause. This book explains and derives the mathematical transformations used for field oriented control. 

Other reference: Analysis of electric machinery and drive systems Krause (This is more advanced and considered as the bible for  many).

Permanent magnet syncrhonous and brushless DC motors from Krishnan (This is also more advanced)

Thank you, I'll take a look.

[fabiodl]

As has been implied by other responses, there is a relationship between the mechanical angle of the rotor and the electrical angle. If you happen to have a high-resolution encoder on the stator of a sensorless BLDC motor, then you could characterize your motor and come up with a function that converts stator absolute mechanical angle to electrical angle. You would then use that calculated electrical angle to perform commutation, including park transformation or not.

Is that where your thinking is headed?

The conversion between the two is completely clear. The question is why does the Park conversion use the electric angle and not the mechanical angle, as would be suggested by the intuition of a virtual magnet, generated by the stator coils, pulling the actual magnets of the rotor?

[uer166]

As has been implied by other responses, there is a relationship between the mechanical angle of the rotor and the electrical angle. If you happen to have a high-resolution encoder on the stator of a sensorless BLDC motor, then you could characterize your motor and come up with a function that converts stator absolute mechanical angle to electrical angle. You would then use that calculated electrical angle to perform commutation, including park transformation or not.

Is that where your thinking is headed?

The conversion between the two is completely clear. The question is why does the Park conversion use the electric angle and not the mechanical angle, as would be suggested by the intuition of a virtual magnet, generated by the stator coils, pulling the actual magnets of the rotor?

You're overthinking it. Here's a thought: more poles means higher electrical frequency for a given mechanical RPM at the motors' phase terminals. E.g. a motor with 4 poles will create 2 times higher frequency at its' phase outputs vs one with with 2 poles. The motor controller (the thing that uses Park transform), now needs to handle 2x frequency. Ergo, mechanical angle is irrelevant (in fact is is invisible to the controller), only electrical angle is visible and acted upon.

[fabiodl]

You're overthinking it. Here's a thought: more poles means higher electrical frequency for a given mechanical RPM at the motors' phase terminals. E.g. a motor with 4 poles will create 2 times higher frequency at its' phase outputs vs one with with 2 poles. The motor controller (the thing that uses Park transform), now needs to handle 2x frequency. Ergo, mechanical angle is irrelevant (in fact is is invisible to the controller), only electrical angle is visible and acted upon.

Thank you. Programming the control loop is indeed no problems at all. I would just like to grasp what actually happens at the physical level for a personal curiosity. 

[Phoenix]

the intuition of a virtual magnet, generated by the stator coils, pulling the actual magnets of the rotor?

A 2 pole motor is a single pair of poles (one N, one S pole) spinning around.

A 4 pole motor has 2 pole pairs (alternating N, S, N, S) spinning around. Using your analogy, if you pull on only a single N/S pole pair with a magnet you're only going to have half the torque - it will still spin. You really want to pull on both N/S pole pairs simultaneously for maximum torque (like having 2 virtual stator magnets) - the windings are already wound to achieve this outcome. Given the symmetry of the 4P motor it only takes half a mechanical rotation before electrically everything is back to 0º starting point.

[fabiodl]

Thank you Phoenix, this is the reasoning I was looking for. I just found a similar reasoning at page 55 of the ANALYSIS OF ELECTRIC MACHINERY AND DRIVE SYSTEMS, Krause, third edition, suggested by  jkostb.
Thank you guys!