A dynamic nonlinear model for permanent magnet synchronous machines

Advanced mathematical models are essential for the simulation of the dynamic nonlinear operating behavior of a permanent magnet synchronous machine (PMSM). Usually rotor or stator oriented systems featuring constant parameters are used. Concerning sophisticated control strategies, especially for sensorless control, the dependence of the inductance on angle and load condition can no longer be neglected. Especially for machines with a low rotor angle dependency of the inductance the influence of saturation is crucial in sensorless control. This paper presents an approach to obtain an easy model for a complex nonlinear situation including the effects of saturation based on finite element (FE) analyses. The procedure necessary to obtain the model parameters can easily be automated, which is one major advantage. This goes hand in hand with the fact that several symmetry considerations allow a dramatic reduction in simulation time while still keeping the general case in mind. The derived method is based on an energy approach and hence independent of the actual motor cross section.