Extension of a d-q model of a permanent magnet excited synchronous machine by including saturation, cross-coupling and slotting effects

For the description of a permanent magnet excited synchronous machine the idealized equations of common synchronous machines can be used omitting the damping windings and replacing the current excitation by a permanent flux. For a more accurate modeling, nonideal behavior like saturation, cross-coupling magnetization and slotting effects can be included. This is done by extending the common d-q equations by additional elements. This also includes the time dependent variations of the parameters causing additional induced voltages especially at high currents and speed. The elements of the extended equations are extracted from a finite element analysis of the device under test. The derivation of the equations and a simulation of a permanent magnet excited synchronous machine with the applied theory are presented.