The direct-quadrature-zero (DQZ or DQ0[1] or DQO,[2] sometimes lowercase) transformation or zero-direct-quadrature[3] (0DQ or ODQ, sometimes lowercase) transformation 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 DQZ transform is the product of the Clarke transform and the Park transform, first proposed in 1929 by Robert H. Park.[4]
The DQZ transform is often used in the context of electrical engineering with three-phase circuits. The transform 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 transform to recover the actual three-phase AC results. As an example, the DQZ transform 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-phase stator and rotor quantities into a single rotating reference frame to eliminate the effect of time-varying inductances and transform the system into a linear time-invariant system