Robotics

Park transform

ActivePublished: 21 October 2026Updated: 21 October 2026Published

Key innovation

Introduced a rotor-synchronized rotating reference frame (d,q,0) that turns sinusoidally varying three-phase quantities into steady-state constants and linearizes the synchronous-machine model whose inductances depend on rotor position.

How it works

The transform is a composition of the Clarke transform and a rotation. Step 1: the three-phase abc quantities are projected onto the stationary αβ frame (Clarke transform), isolating the common-mode (homopolar) part as the zero-sequence component. Step 2: the αβ frame is rotated by the instantaneous electrical angle θ (rotor position) so that the d and q axes spin synchronously with the rotor flux vector. As a result, balanced sinusoidal waveforms at the rotor-speed frequency become constant in the new frame. The inverse Park transform maps the dq quantities back to actual three-phase quantities, e.g. before inverter modulation.

Problem solved

Analyzing and controlling three-phase AC machines is hard because phase quantities vary sinusoidally in time and a synchronous machine's inductances depend on the instantaneous rotor position (a time-varying model). This complicates controller design and torque computation. The Park transform removes that dependence by moving the description into a rotating frame where the quantities become constant and the model becomes linear with constant coefficients.