Modelling the impact of the stator currents on inductance-based sensorless control of brushless DC-machines

Inductance-based sensorless control methods allow to estimate the rotor position by tracking the magnetic anisotropy linked to the rotor, partly caused by the magnetic saturation of the iron. In most salient-pole machines, the magnetic field in the air-gap may be approached by a sinusoidal function along the air-gap. Furthermore, the stator self-inductance mainly varies with two times the electrical rotor angle. In brushless DC-machines however, inductance-based estimations are affected by an important harmonic content in the magnetic field. Besides, it is well-known that large stator currents cause position estimation errors due to a variable magnetic state. This paper proposes a simple analytical model to take into account the combined effects of the stator currents and the harmonics. The goal is to understand these effects on the position estimation through simulations. The model is specifically developed for surface-mounted permanent-magnet brushless DC-machines with diametric single-slot-pair windings. The results suggest that the combined effects could be used to compensate for the position estimation error.