## 4 Selection of the Objective Function and Optimization Parameters
in [37].The optimization procedure fminsearch(\(F\), \(x0\)) is launched to find the vector \(x\) of optimized values of the generator parameters, where \(x0\) is a vector with initial values of the generator parameters (see Table 2). Optimization Progress and Comparative Analysis of the Generator Performances before and after Optimization  
As a result of optimization, the value of the objective function (6) converges to a minimum (Figure 8). The volume of the simplex can quickly decrease during optimization, and further optimization slows down. Therefore, after the 180 th function call, the Nelder-Mead method was restarted. The optimal solution found was used as the initial approximation. The linear dimensions of the simplex at the restart were reduced by four times compared to the initial simplex. One function call takes approximately 20 min using a laptop with two cores, 2.70 GHz processor and 16 GB of RAM. The average generator loss (Figure 9a) and the upper limit of the output current (Figure 9b) were significantly reduced through optimization. The non-symmetrized torque ripple, which is the lowest priority optimization target, according to the objective function (6), increased its value (Figure 10a). However, the noise and vibrations caused by the generator in the mechanism joining it with the wheels are deter  
Figure 8: Progress of the objective function (6) during optimization. Figure 7: Order of the SHM performance calculation during one step of the optimization. The objective function is defined by Equation (6). The input parameters are shown in Table 2.  
torque ripple, which was reduced (Figure 10b). A decrease in the symmetrized ripple with an increase in the non-symmetrized one indicates that the torque waveforms of individual pairs of rotor and stator stacks are in antiphase. In this way, the torque ripples of the individual SRSCs cancel each other out, as seen from Figure 11.  
Figure 11: The torque ripple of the individual SRSC and the symmetrized (output) torque ripple after optimization: (**a**) at 3450 rpm; (**b**) at 750 rpm. Figure 9: Change of the generator parameters during optimization: (**a**) Average losses; (**b**) Maximum magnitude of the armature winding current. Figure 10: Change of the generator parameters during optimization: (**a**) Nonsymmetrized torque ripple; (**b**) Symmetrized (output) torque ripple. Figures 12 and 13 show the geometry and 2D flux density plot of an SRSC before the first start of the optimization procedure and after optimization, correspondingly. Table 3 compares the performances of the SHG with ferrite magnets before and after optimization. Comparison of Figures 12 and 13 shows that as a result of optimization, the height and area of the stator slots has increased significantly. The air gap has become much smaller. The thickness of the rotor teeth and the thickness of the magnets in the rotor slots have been significantly reduced. Comparison of Figure 14a,b demonstrates that after optimization, the maximum demagnetization force has been slightly reduced from 3 kOe to about 2.9 kOe, while the coercive force of the magnets is greater than 3.9 kOe. It can be concluded that the proposed design does not create a risk of demagnetization of the permanent magnets. Comparison of the SHG characteristics before and after optimization presented in Table 3 allows us to draw the following conclusions:  
1. Average losses were reduced by 100% (\(5.51-4.58\))/\(5.51=16.9\%\);
2. The armature current at the maximum torque was reduced by 100% (\(957.7-700\))/957.7 = 26.9%;
3. Output (symmetrized) torque ripple at maximum torque at 750 rpm was reduced by 100% (\(9.8-8.6\))/\(9.8=12.2\%\);
4. The coercive force of the applied grade of ferrite magnet (Y30H-2) is 3.9 kOe [38], which is much greater than the demagnetizing magnetic field in the optimized design;
5. The optimized SHG with ferrite magnets is more saturated than the initial one.