Transform Back-EMFs to stationary reference frame

[powersys]

transform from stationary reference frame

I'm referring to 3-ph permanent magnet brushless motor with internal rotor.

Say the open-circuit phase back-emfs are EA, EB, and EC, which are contributed by the permanent magnet on the rotor.

Say the rotating reference frame is called d-q reference frame. d-axis is aligned with the north pole of the permanent magnet on the rotor.

Say the stationary reference frame is called α-β reference frame. α-axis is aligned with the phase-A winding axis.

Say the angle between the d-q and α-β reference frames is Qr.

I wish to transform the EA, EB and EC to Eα and Eβ quantities in α-β reference frame. How could I do it?

Thanks

 

[hakeen]

stationary dq reference frame

How many poles you have?

 

[powersys]

If, let's say, it has one pole-pair. Thanks.

 

[hakeen]

I see. If I dont misremember, I had got known with Clarke Transform for this purpose. Unfortunately I dont have any details, but after some search in internet I found some algortihms below:

General info:
http://www.embedded-control-europe.com/c_ece_knowhow/229/ecejun08p26.pdf

Some codes (at the bottom of the page):
http://decibel.ni.com/content/docs/DOC-2386

Hope it helps, at least for your further source searching.