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Thread: Clarke transform - from 3-phase to 2-phase transformation

  1. #1
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    Clarke transform - from 3-phase to 2-phase transformation

    I was reading about: https://www.switchcraft.org/learning...ol-for-dummies

    I don't understand why do we write at Clarke transform to convert from 3-phase system to 2-phase orthogonal:

    $\displaystyle I_{\beta} =\frac{\sqrt{3}}{2}I_b - \frac{\sqrt{3}}{2}I_c $



    If you see the picture between $a$ and $b$ is an angle of 120. Between $\alpha$ and $\beta$ is 90. So between $\beta$ and $b$ is 30. If we use SOH-CAH-TOA, and get that the $I_{\beta}$ is:
    $\displaystyle I_{\beta} = cos(30)b$

    Why do we need then $c$? Maybe because the net vector is rotating? Can someone derive or explain?

    Thanks.
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  2. #2
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    Re: Clarke transform - from 3-phase to 2-phase transformation

    It looks like what is happening is conversion of currents that are present for both vectors I_b and I_c into the equivalent operating on vector I_beta (and also I_alpha, though you don't mention that). The cosine of the angle between vectors beta and c is -sqrt(3)/2, hence the contribution of current I_c to I_beta is -sqrt(3)/2 I_c.
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