New Mathematical Model and Vector Simulator of Permanent-Magnet Synchronous Motors with both Space-Varying Rotor Flux and Space-Varying Stator Inductance

Abstract

This paper proposes a new mathematical model and simulator for permanent-magnet synchronous motors, which generate both magnet and reluctance torque ripples changing with the rotor position. The proposed model has the following features. (a) It. introduces a concept called “space-variability” of both rotor magnet and stator inductance, and successfully reproduce the magnet and reluctance torque ripples changing with the rotor position. (b) It presents new “proportional and differential torques” caused by the space-variable rotor flux and space-variable stator inductance. (c) It consists of three self-consistent basic equations, such as circuit, torque evolution, and energy transmission equations. (d) It has the generality in the sense that it is constructed in the general reference frame. The proposed simulator yields accurate reproductions of the current, flux, torque, etc. specified by the model. Moreover, it adopts the most compact structure using the vector signals in the general reference frame. The validity of the model is verified in a rigorous analytical manner and the usefulness of the simulator is demonstrated through simulations reproducing torque ripple that changes with the rotor position.