Abstract：When the permanent magnet assisted synchronous reluctance motor（PMaSynRM）runs at highspeed with flux-weakening control，the DC bus voltage utilization is not high，and the efficiency and torque output capacity of the motor are low. Therefore，a flux-weakening control strategy of permanent magnet assisted

synchronous reluctance motor based on hexagonal trajectory was proposed. Firstly，based on the d-q axis equivalent circuit of the permanent magnet assisted synchronous reluctance motor，the voltage and current constraints of the flux-weakening process were derived，and the root cause of the flux-weakening control to improve the speed regulation ability of the motor was proved. Secondly，in order to give full play to the advantages of high-power density under high-speed operation of permanent magnet assisted synchronous reluctance motor，the overmodulation algorithm was derived. It was applied to the flux-weakening operation of permanent magnet assisted synchronous reluctance motor to achieve higher DC bus voltage utilization. Finally，the effectiveness of the

proposed method was verified by simulation.

      Key word：flux-weakening control；permanent magnet assisted synchronous reluctance motor（PMaSynRM）；voltage utilization；over-modulation