Clarke Transformation

[450x]

Hi
I am reading into the Clarke transformation that is used to convert the 3 phase stator currents into a two dimensional orthogonal system for field oriented control of ac motors. The equations are shown below.
isα = ia
isβ = (1/√3)*ia + (2/√3)*ib
I cannot find any literature that shows how this transformation was derived.
Where
isβ isβ, = New transformed current vectors
ia = Stator current phase a
ib = Stator current phase b
Can anyone point me in the right direction (no pun intended)?


Thanks

 

[xnuke]

Try the original paper "Determination of Instantaneous Currents and Voltages by Means of Alpha, Beta, and Zero Components." It's available from IEEE Xplore Digital Library.

xnuke
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[xnuke]

Just realized the answer: it's a change of basis problem in linear algebra, with the original basis given by {(1,0), (-1/2, -[√]3/2)} as defined by the original A and B phasors, and the new basis given by {(1,0), (0,-1)} as given by the [α] and [β] phasors. The transformation matrix is [1, 0; 1/[√]3, 2/[√]3].

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[electricpete]

That sounds like the right idea to me, although I haven't checked it.

Krause's textbook has a good writeup on transformations in general - presenting a general transformation where Park, Clark and the rest are just special cases.

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(2B)+(2B)' ?

 

[450x]

Thanks gentlemen