## 1 Introduction  
Due to the advantages of its robust rotor structure, high torque density and wide speed range, the synchronous reluctance motor (SynRM) has become a research hotspot. But the SynRM has a high torque ripple and low power factor, which limits its development [1; 2; 3]. Therefore, permanent magnets can be added to the rotor magnetic barrier, which forms a permanent-magnet-assisted synchronous reluctance motor (PMA-SynRM). The permanent magnets can improve its electromagnetic performance, such as its power factor and output torque [4; 5; 6]. Induction machines (IM) are widely used in industrial and residential applications because of their high reliability, simplicity of implementation and ability to be powered directly by a sinusoidal power source [7]. The interior permanent-magnet machine (IPM) has a high efficiency and power factor. However, its production cost is high [8]. At the same time, the different losses generated during operation lead to different motor temperatures, and temperature is also an important factor affecting the electromagnetic performance of the motor. Therefore, a comprehensive comparison of the electromagnetic performance, material cost and temperature distribution of the four motors is very necessary. This will provide a reference for designers when selecting motor types for different applications. Most of the available literature on these four kinds of motor compares the electromagnetic properties and the design optimization of the motor structure. In recent years, the SynRM and the PMA-SynRM have become the focus of research [9; 10; 11]. In order to validate that these two types of motor can be used as alternatives to the IM and the IPM, the performance improvement of the two kinds of motor has been studied by many researchers. The SynRM and the PMA-SynRM have a large torque ripple, but asymmetric stator and rotor structures can be used to decrease the torque pulsation [12; 13]. The power factor, efficiency, output torque and torque density of the motor are improved by optimizing the rotor magnetic barrier structure [14; 15]. As for the IM, optimizing the rotor structure and using special materials can improve its efficiency and torque density [16; 17], while for the IPM, the appropriate internal magnetic barrier structure should mainly be explored. Through the optimization of the structure, the motor can obtain a high power factor, high efficiency, high torque density and a wider speed range [18; 19; 20]. In addition, there are some studies in the literature on the comparison of the four motors. For the output torque, the IM is greater than that of the SynRM at the same current density [21]. At the same loss, the output torque and efficiency of the SynRM are higher, but the power factor is lower than that of the IM [22]. In [23], it is easy to learn that the electromagnetic properties of the SynRM are much lower than those of the IPM. The ferrite-assisted SynRM is more competitive in terms of its torque, efficiency and power factor. The NdFeB-assisted SynRM has performance close to that of the IPM but with a higher torque ripple. The cost of these three motors is much lower than the cost of the Prius 2010 IPM. In [24], the electromagnetic performance, mechanical strength and electromagnetic cost are compared. It can be seen that the PMA-SynRM has the maximum output torque during the rated operation. The power factor of the PMA-SynRM is higher than that of the SynRM but lower than that of the IPM. The SynRM has the lowest efficiency, and the IPM has the highest efficiency. When all three motors achieve the same output capability, the SynRM has the lowest weight and lowest cost, but the PMA-SynRM has the best overall performance. As can be seen from the above description, with the increasing price of rare-earth permanent magnets, SynRMs and PMA-SynRMs have attracted more and more attention. Most of the existing literature only focuses on the comparison of the electromagnetic performance of the three motors (the SynRM, PMA-SynRM and IPM).