## 4 Objectives and Parameters of the Optimization  
Since the external dimensions of the motor are essentially determined by the corresponding dimensions of the car bogie and correspond to the commercial induction motors already used in the drive under consideration, the main emphasis in optimizing the performance is on reducing losses in the duty cycle (see Figure 1) and on reducing the current rating power modules of the traction inverter. When optimizing, it is also necessary to limit torque ripple and prevent irreversible demagnetization of weakly coercive ferrite magnets. Since the applied Nelder-Mead method is an unrestricted method, the constraints are also set by additional terms of the optimization function. Therefore, the objective function is formulated based on four objectives:  
1. Minimizing the average electrical losses, denoted as \(<\)_Ploss d\(>\)_, which is calculated as a weighted average of losses at different operating points;
2. Minimizing the maximum armature winding current, indicated by max(\(I_{arm\,i}\)), across operating points 1-5;
3. Minimizing the maximum torque ripple, indicated by max (\(TR_{i}\)), across operating points 1-5;
4. Reducing to zero \(\delta\)demag, which represents the cross-section area of magnets exposed to a demagnetization magnetic field stronger than the marginal demagnetization field \(H_{0}\), relative to the overall cross-section area of the magnets. When developing an electric motor, it is important to consider the discrete nature of certain parameters, such as the number of turns (\(N_{sec}\)) in the armature winding section and the standardized values of rectangular wire width and height outlined in [32]. However, this study disregards the discreteness of these values and allows them to have any positive real value, aiming to provide a more objective assessment. Random factors arising from different technical specifications in motor development can lead to optimal values of these parameters varying between designs. Specifically, the number of turns in the armature winding (\(N_{sec}\)) is chosen so that \(V_{DC\,\,ntnd}=\max(V_{i}/k_{i})\)[23]. Figure 4: Layout of the three-phase inverter with a DC breaker designed to supply the excitation winding; letters A, B, and C represent the armature winding phases. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **FaSHM** & **FaSynRM** \\ \hline Number of the stator slots per pole and phase \(q\) & 2.5 & 2 \\ Rotor slot number & 4 & - \\ Rotor flux barrier number per pole & - & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._An additional target for FaSHM is the maximum nonsymmetrized torque ripple \(\max(TRnonsym_{i})\). This type of torque ripple is generated by a single pair of stator and rotor stacks, whereas a symmetrized torque ripple is produced by the entire FaSHM, involving all pairs of stator and rotor stacks. The details of the terms \(TR\) and \(TRsym\) are elaborated in [27]. In the FaSynRM, a significant contribution to the torque is generated by the reluctance torque, and the ferrite magnets play an assisting role. Therefore, when properly designed, the FaSynRM is comparatively strong to irreversible demagnetization. To ensure the strength of FaSynRM to such factors as temperature decrease, transients, or failures of the control system with an overcurrent, the maximum value of the demagnetizing field is constrained to \(H_{0}\) = 2 kOe. In [14], for the FaSHM, the demagnetizing field was not constrained in the objective function, but it was shown that the demagnetizing field does not exceed 3.2 kOe, while the coercive force of ferrite magnets can be 4 kOe. In contrast to [14], in this paper, \(H_{0}\) is constrained for the FaSHM as well since it is under comparison with the FaSynRM, in which irreversible demagnetization is also possible. Moreover, in the FaSHM, the magnets make up for the disadvantage of a magnet-free SHM using only half the poles for torque production [14].