Derivation of the Clarke Park transformations and SVM in the STSpin library

[TypeKazt]

Hello,

Looking over the STSpin implementation of the Clarke Park transforms and SVM has raised some questions about the derivation of the transform.

Typically the the Clarke Transform takes the form of:

𝐼𝛼=𝐼𝑎

𝐼𝛽=1√3(𝐼𝑎+2𝐼𝑏

STSpin's implementation effectively rotates the Beta component by 180 degrees with a sign flip:

𝐼𝛼=𝐼𝑎

𝐼𝛽= -1√3(𝐼𝑎+2𝐼𝑏)

Next, the Park transform usually takes the form of:

𝐼𝑑=𝐼𝛼∗cos(𝜃)+ 𝐼𝛽∗sin(𝜃)

𝐼𝑞=𝐼𝛽∗cos(𝜃)−𝐼𝛼∗sin(𝜃)

Where as STSpin seems to rotate each dq component by 90 degrees by using the opposite trigonometric functions on the alpha/beta vectors

𝐼𝑑=𝐼𝛼∗sin(𝜃) + 𝐼𝛽∗cos(𝜃)

𝐼𝑞=𝐼𝛼∗cos(𝜃)−𝐼𝛽∗sin(𝜃)

Considering Beta is negative in the STSpin Clarke, it seems that Iq is actually equal to Id in the "correct" Park transform. Does anyone have an explanation for this?

Separately, the SVM seems to be empirically 120 degrees out of phase with an SVM implementation from this paper. Is this to compensate for the different reference frame in the STM transformations?

[Laurent Ca...]

Dear TypeKazt

Do you have still this problem to solve?

Best regards

Laurent Ca...

[TypeKazt · Accepted solution]

Hello Laurent,

We're not having issues with the implementation per se, more so just trying to understand it so we can spot any issues. I found this PDF over the weekend which seems to deeply describe the derivation of both the SVM and FOC in the STSpin library, could you verify that it is correct?

[Laurent Ca...]

Dear @TypeKazt​ 

Your question is very specific.

I you use SDK V4.3 indeed it is the reference document.

Best regards

Laurent Ca...

[mckmk]

Vector signs may vary to the direction of the vector that the designer refers to.

[GenuineDeveloper]

Dear @TypeKazt​ ,

Were you able to arrive at a logical conclusion as to why the ST developer might have changed the sign (direction) of the vector? Does it ease calculations? Any input would be of great help!

Best Regards

Tinkerer.

[federico.rodighiero87]

Same problem here, sign conventions are important, I don't understand why they change beta sign.