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Clarke Transformation

Clarke Transformation

Clarke Transformation

(OP)
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

RE: Clarke Transformation

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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RE: Clarke Transformation

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: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Clarke Transformation

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.

=====================================
(2B)+(2B)' ?

RE: Clarke Transformation

(OP)
Thanks gentlemen

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