## 2 Representation of the Train Flow Pattern in the Motor Optimization Routine  
The movement of the subway train, as depicted in Figure 1, encompasses several stages: acceleration with a constant torque, acceleration with a constant power, coasting at a steady speed (with any minimal deceleration disregarded), deceleration with a constant power, and deceleration with a constant torque. The maximum torque remains constant at \(T_{0}=1240\) N-m for both motor and generator modes. The speed of transitioning between constant power and constant speed modes is \(n_{m}=1427\) rpm during acceleration and \(n_{g}=2854\) rpm during braking. The maximum attainable speed is \(n_{max}=4280\) rpm.  
Figure 2 illustrates the torque dependency on rotational speed, with two separate abscissa axes representing the motor and generator modes. The optimization routine of the FaSHM for specific operating points 1, 2, 3, 4, and 5 depicted in Figure 2 is detailed in [14]. This optimization process encompasses all stages of the operating cycle, excluding coasting. The optimization function incorporates objectives such as weighted average electric losses evaluated over the cycle, with the weight coefficients \(w_{i}\) determined using the trapezoid quadrature formula. Building upon this research, the present study further refines the optimization procedure for traction motors with magnets in subway trains, considering the core losses during coasting mode. Despite the motor being switched off, magnetic fluxes induced by the magnets still result in coasting-related losses. Therefore, this study  
Figure 1: Dynamic speed (green line) and torque (blue line) profiles of the subway train’s traction motor.  
is necessary both to consider the two-dimensional geometry of a pair of stator and rotor packages (Figure 3b) and to consider the design of the axial elements: the stator housing and the rotor sleeve (Figure 3c).  
Table 2 shows the main design parameters of the motors. Figure 3 illustrates the motor phases using capital letters A to C to indicate their order. The presence of a minus sign in Figure 3 signifies the reverse direction of the current within a winding layer. Both considered motors have a 3-phase 8-pole winding. The FaSHM stator has 60 slots, and the number of slots per pole and per phase \(q=60/(8\cdot 3)=2.5\). The FaSynRM stator has 48 slots, and the number of slots per pole and per phase \(q=48/(8\cdot 3)=2\). Unlike the FaSHM, the FaSynRM has only one set of stator and rotor stacks and does not have an excitation winding and its fastening elements, which makes it easier to assemble.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **FaSHM** & **FaSynRM** \\ \hline Phase number & & 3 \\ Pole number & & 8 \\ Ferrite magnet grade & & Y30H-2 \\ Excitation winding & Yes & No \\ Number of sets of stator and rotor stacks & 2 & 1 \\ Stator slot number & 60 & 48 \\ Number of the armature winding layers & 2 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Design features of the FaSHM and the FaSynRM.  
Figure 3: Motor design representation. Red arrows mark the directions of magnetization of the permanent magnets. (**a**) Ferrite-assisted synchronous reluctance motor (FaSynRM), 2-Pole area, red, blue and green colors indicate the different phases of the armature winding; (**b**) Ferrite-assisted synchronous homopolar motor (FaSHM), 1/4 cross-section and stator armature winding layout; (**c**) 3D cutout view of FaSHM with 1/2 stator cutout and unobstructed rotor.  
Figure 4 illustrates the power supply circuit for the FaSHM, comprising a standard three-phase inverter for the multiphase armature winding and a chopper for the excitation winding. On the other hand, the FaSynRM solely necessitates a three-phase inverter without the need for a chopper.