## 1 Introduction  
Recently, due to the increasing consumption of rare earth resources, the prices of various raw materials such as rare earths have been increasing [1, 2]. Since rare earth is a non-renewable resource, in order to reduce the dependence on rare earth resources, permanent-magnet-assisted synchronous reluctance motors (PMA-SynRMs) are gradually entering into the public's view [3]. The PMA-SynRM combines the advantages of permanent magnet synchronous motors (PMSMs) and synchronous reluctance motors, characterized by high output torque, high power density, high efficiency, and good speed regulation performance [4, 5]. A multilayer flux barrier structure is generally applied in the PMA-SynRMs to maximize the utilization of their reluctance torque [6, 7]. Only a small amount of permanent magnets remains in the flux barrier structure of the PMA-SynRM to assist the excitation [8, 9], which provides permanent magnet torque for the PMA-SynRM. The PMA-SynRM typically utilizes fewer permanent magnet compared to PMSM for the same volume of PMA-SynRM [10, 11]. Therefore, the cheaper price and better performance give the PMA-SynRM a wide range of applications in the field of variable speed drives for electric vehicles, water pump compressors, household appliances, medical devices, etc. [12, 13, 14, 15, 16, 17]. Currently, the research for PMA-SynRM topology is centered on the design of the flux barrier structure, permanent magnet, and magnetic circuit [18; 19]. In the design of the flux barrier structure, a variety of flux barrier structures such as U-shaped flux barrier, V-shaped flux barrier, and arc-shaped flux barrier have been proposed [20; 21]. [PERSON]'s team [22] at the University of Padua effectively reduced the torque ripple of the PMA-SynRM by axially combining two rotors with different flux barrier angles. In terms of permanent magnet design, different numbers, volumes, shapes, arrangements, and magnetization directions of permanent magnets have been proven to have an impact on the torque performance of the PMA-SynRM [23; 24]. [PERSON] et al. [25] in Korea investigated the effect of different arrangements of permanent magnets within the flux barrier and found that the PMA-SynRM had the smallest torque ripple when the permanent magnets were all located in the middle of the flux barrier. [PERSON] et al. [26], from Shandong University, China, designed a pole-biased PMA-SynRM to enhance the torque of the PMA-SynRM by varying the angle between the permanent magnet flux linkage and the _d-axis_, so that both the permanent magnet torque and the reluctance torque are maximized at the same current phase angle. [PERSON] et al. [27], from Harbin University of Science and Technology, China, similarly improved the utilization of the reluctance torque and the permanent magnet torque by mixing NdFeB and Ferrite permanent magnets of different sizes, which resulted in an offset of the permanent magnet chain. The conventional PMA-SynRM permanent magnet arrangement is less efficient in utilizing the magnetic force of the permanent magnets. Without modifying the amount of permanent magnet, an asymmetric-rotor PMA-SynRM model with magnetic-axis-shift (MAS) effect is proposed in this paper in combination with a Halbach array. This permanent magnet arrangement not only enhances the permanent magnet auxiliary excitation effect of the PMA-SynRM but also offsets the permanent magnet chain. The permanent magnet torque and reluctance torque of the proposed model can reach their maximum value with a similar current phase angle, and the total torque is significantly improved. Firstly, the stator-rotor topology of the conventional and proposed models is presented in this paper. The torque characteristics of the two models are theoretically analyzed by building a simplified analytical model of the two models, with core saturation and cross-coupling neglected. The two models are also simulated and analyzed under no-load conditions as well as under load conditions based on the finite element method.