Why Im_ref = 2⋅T ref /3⋅p⋅λ pm for Interior PMSM? in MTPA Control Reference

according to equation: Te= 3/2*p*(λpm*iq+(Ld− Lq)*id*iq)

Im_ref should not equal to 2⋅T ref /3⋅p⋅λ pm for interior PMSM, right? Thanks!

[Rik]

Can you give a bit more detail? Without the context it isn't clear to me how this even relates to Matlab.

[aSpinningCoin]

Hi Rik,

I found those equations at below page and feel confused about it.

https://ww2.mathworks.cn/help/mcb/ref/mtpacontrolreference.html

[Rik]

This is too deep for me. If it is incorrect, you should contact support to have that verified and corrected.

If it is correct but you simply do not understand, I suspect your question is better suited elsewhere.

[aSpinningCoin]

Fine, thanks for your reply.

Answer 1

[Joel Van Sickel]

The first equation your have underlined is the maximum current reference limit used for a specific type of control ( MTPA) while the other equation is the mathematical model of of a motor (albeit a simplified equation as this is for a lumped parameter motor model). These equations are not the same nor should they be, although the controller algorithm is derived from the mathematical model equation (elimnate the (Ld-Lq)*id*iq by setting id to zero and they are identical. Further work is required in the controller after calculating maximum current to calculate reference id and iq current values.

[aSpinningCoin]

Hi Joel Van Sickel,

Thanks for your reply.

So, if Id is Not 0 (say, in MTPA control), then Te doesn't equal 3/2*p*λpm*iq, right?

if above is right, then Im would not equal 2⋅Te /(3⋅p⋅λ pm), right?

Thanks again.

[Joel Van Sickel]

you are correct, it would be slightly different, which is why the equation for the model is more specific to account for this case.