Machine Question No.23 - Park's equations
What are Park's equations and its benefits?

#1
Wed, September 9th, 2009 - 20:03
The dq0 transformation was introduced as a means of facilitating analysis of salient-pole machines. This means developed by R.E.Doherty,C.A.Nickle,R.H.Park, and their associates in the US. The transformation itself, known as the dq0 transformation, can be represented in a straightforward fashion in terms of the electrical angle Θme (equal to poles/2 times the spatial angle Θm) between the rotor direct axis and the stator phase axis.
The main aim of the d–q model is to eliminate the dependence of inductances on rotor position. To do so, the system of coordinates should be attached to the machine part that has magnetic saliency the rotor for SGs.
The d–q model should express both stator and rotor equations in rotor coordinates, aligned to rotor d and q axes because, at least in the absence of magnetic saturation, there is no coupling between the two axes. The rotor windings are already aligned along d and q axes.
It is only the stator voltages, VA, VB, VC, currents IA, IB, IC, and flux linkages ΨA, ΨB, ΨC that have to be transformed to rotor orthogonal coordinates. The transformation of coordinates ABC to d–q0, known also as the Park transform, valid for voltages, currents, and flux linkages as well, is as follows:

During steady state, the stator voltages and currents are sinusoidal, and the stator frequency ω1 is equal to rotor electrical speed ωr = ω1 = constant: