Induction motor vector control

[Ryc92]

Hi, Maths question here:

Induction machine rotating frame voltage equations:

Vqs = RsIqs + d(flux linkage qs)/dt + (omega x flux linkage ds)
Vds = RsIds + d(flux linkage ds)/dt - (omega x flux linkage qs)

Sorry I couldn't do the symbol for flux linkage, omega or the differential operator properly.

My question is this, if the two axis (q and d) are orthogonal, then how can the last term of each equation exist? The last term is referred to as 'speed voltage due to rotation of axis' and is shown that a voltage is impressed on the d axis, for example, by flux linkage in the q axis?

The equation is obviously correct, not arguing that, I would just like to know how this can happen when the 'effective' windings are at 90 degrees, hence zero flux coupling? (that being the whole foundation of the field orientated control scheme).

Many thanks in advance!

Ryan

 

[cswilson]

I think the simplest way to understand this intuitively is to realize that the flux linkage terms are inductive terms (FluxLinkage = L * i) and the the voltage and current in an inductor are 90 degrees out of phase with each other. So the "q" current affects the "d" voltage through these terms, and vice versa.

Field oriented control attempts to decouple these two equations by trying to ensure that the stator flux linkage is purely in the "d" orientation (so the "q" component is 0). To the extent that this is successful, the (omega x flux linkage ds) term simply represents the back EMF component of the voltage.

Curt Wilson
Delta Tau Data Systems