## 1 Introduction  
### Disadvantages of Induction Motors and Motors with Rare Earth Magnets  
At present, most traction drives, including those of trains, trains, submways, and mining dump trucks, use induction motors (IM). However, traction drives with IMs have the following disadvantages:  
1. Large loss and heating in the rotor [1, 2], which can lead to unacceptably high temperatures of the rotor, shaft, and bearings, even despite the liquid cooling of the rotor [3];
2. Continuous torque capability is significantly worse than permanent magnet synchronous motors (PMSM) [4];
3. Higher inverter power rating with a required constant power speed range (CPSR) over 3:1 [5, 6]. For example, a study [5] presents a traction drive based on an IM with a mechanical power of 50 kW and a CPSR of 3.5:1, and the power rating of the traction inverter is 125 kVA. Study [6] presents a traction drive based on an IM with a mechanical power of 50 kW and a CPSR of 4:1, and the power rating of the traction inverter is 125 kVA.  
To overcome these disadvantages, rare earth permanent magnet synchronous motors (PMSM) are used, which have a larger specific torque, lower loss, and a higher power factor [7]. However, PMSMs have the following disadvantages:  
1. The production of PMSMs necessitates costly rare-earth magnets, which experience significant price fluctuations within a short span of a year or two. This variability arises due to a limited pool of magnet suppliers in the global market [8; 9; 10];
2. In the near future, a shortage of materials for the production of rare earth magnets is predicted due to the rapid growth in the production of electric vehicles and wind turbines, which very often use rare earth permanent magnets [11];
3. Rare-earth element extraction has an adverse environmental impact [12];
4. The demagnetization of rare-earth magnets can occur in high-power density PMSMs due to the presence of strong magnetic fields and high temperatures;
5. The task of maintaining high efficiency at speeds near the maximum becomes challenging when aiming for a wide constant power speed range, primarily due to increased copper loss that occurs in the field weakening mode [13];
6. Furthermore, in electrical power applications such as subway and railway trains, the rotational motion of PMSM induces a significant uncontrolled electromotive force (EMF) in the winding. This situation presents a significant risk of fire in the event of an emergency short circuit. Given the high inertia of the trains, which makes them unable to stop in time in such critical situations, it is recommended to refrain from using the PMSM in this application.  
Due to the disadvantages of IM and PMSM, the development of synchronous motors for the subway without rare earth magnets becomes relevant.  
The utilization of ferrite magnets proves advantageous due to their significantly lower cost compared to rare-earth magnets and their widespread production across numerous countries worldwide [14; 15].  
In addition, ferrite magnets have no losses due to eddy currents and high-temperature strength [14; 16]. A challenge of using ferrites in motor design is their low coercive force [14; 17]. For this reason, when optimizing motors with ferrite magnets, special attention must be paid to limiting irreversible demagnetization.