Dqo transformation

$Shown above is the dqo transform as applied to the stator of a synchronous machine. There are three windings separated by 120 physical degrees. The three phase currents are equal in magnitude and are separated from one another by 120 electrical degrees. The three phase currents lag their corresponding phase voltages by \delta. The d-q axis is shown rotating with angular velocity equal to \omega, the same angular velocity as the phase voltages and currents. The d axis makes an angle \ heta = \omega t with the A winding which has been chosen as the reference.The currents I_d and I_q are constant DC quantities.$

In electrical engineering, direct–quadrature–zero transformation or zero–direct–quadrature transformation is a mathematical transformation used to simplify the analysis of three-phase circuits.

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Symmetrical components

\alpha\eta\gamma transform