Analytical Model of Permanent Magnet Synchronous Machine in/around Resonance

In this paper an analytical model of a permanent magnet synchronous motor (PMSM) drive in/around torsional resonance is developed in the dq frame. The model accounts for electrical and mechanical aspects of the system, emphasizing their coupling and effects regarding voltage, torque and speed harmonics. Its aim is to obtain simple formulae which can predict electromagnetic and shaft torque response to a harmonic voltage supply, often present in variable speed drives. The model is solved by applying the small variations method and transfer functions formalism. The solution allows for predicting system behaviour in different operating conditions, especially important in/around resonance. The results are verified by extensive simulations in Matlab/Simulink environment.