Why the equations of BLDC motor model in Matlab (AC7 drive) are for the sinusiodal back EMF voltage expressed in rotor reference frame (dq) but for trapezoidal back EMF voltage in stator reference frame (a,b,c). Is there any particular reason for this?
I believe that is just a matter of convenience. With sinusoidal back-EMF, in the rotor-linked dq referential, the flux is a constant and the DQ equations are simpler in this case. And it's a classic case in many textbooks. With the trapezoidal flux case, it's easier to compute the model directly in the phase domain (what is done actually in SPS, they actually integrate the voltage difference between terminal and back-EMF voltage). I think it's equivalent to a stator-reference dq model. Then, why not use phase domain for the sinusoidal back-EMF case? I would answer that torque calculation in the phase domain is more tricky than in the dq model with non-constant inductance matrice (i.e. Ld not equal to Lq) . In this condition, very common in PMSM, the torque has a reluctance component, a term with (Ld-Lq) in the dq model, easy to compute. In the phase domain, it could be more difficult, one may need the derivative of L. In some papers, they compute it based on power input (Te=V*I/w, neglecting losses here, w is the speed), but don't say what they do at null speed! Hope it helps!
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