Modeling of a Multi-Phase Bearingless Surface Permanent Magnet Synchronous Machine in Stationary and Synchronous Coordinates

Multi-phase bearingless machines offer enhanced fault tolerance and flexible power distribution between force and torque generation. Recent research efforts have focused on winding design methodologies and advanced force modeling incorporating higher harmonic effects. This work presents a compact linear analytical motor model for bearingless machines with surface permanent magnets. The model covers both stationary and synchronous reference frames while incorporating higher harmonics and rotor eccentricity effects. The derived analytical expressions can be used during the design process to identify necessary fundamental design parameters as well as critical influence quantities on torque and force ripple. They also provide parameters directly implementable for control system design. Finite element method simulations validate the accuracy and applicability of the proposed analytical formulations.