Direct-quadrature-zero transformation

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The direct-quadrature-zero (DQZ, DQ0 or DQO, sometimes lowercase) or Park transformation (named after Robert H. Park) is a tensor that rotates the reference frame of a three-element vector or a three-by-three element matrix in an effort to simplify analysis. The transformation combines a Clarke transformation with a new rotating reference frame. The Park transformation is often used in the context of electrical engineering with three-phase circuits. The transformation can be used to rotate the reference frames of AC waveforms such that they become DC signals. Simplified calculations can then be carried out on these DC quantities before performing the inverse transformation to recover the actual three-phase AC results. As an example, the Park transformation is often used in order to simplify the analysis of three-phase synchronous machines or to simplify calculations for the control of three-phase inverters. In analysis of three-phase synchronous machines, the transformation transfers three...

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