## 8 Conclusions  
This article evaluates the improvement in performance of a synchronous homopolar machine by adding ferrite magnets to the rotor in the case of a 35 kW passenger car generator considering its operating speed range. For a fair comparison, the characteristics of the generator configurations with ferrite magnets and without magnets are optimized using the same method. The single-criterion unconstrained Nelder-Mead algorithm and the two-dimensional finite element method are used.  
The following optimization objectives were selected: decreasing the average losses over the entire range of operating speeds, decreasing the installed power capacity of the solid-state rectifier, and the reduction of the torque ripple. As a result of optimization, the characteristics of the generator have been significantly improved. Compared to the non-optimized design, the following were reduced: average generator loss by 16.9%, upper limit of the solid-state rectifier current by 26.9%, symmetrized (output) torque ripple by 12.2%.  
The non-symmetrized torque ripple, which has the lowest power in the objective function defined by Equation (6), became higher after optimization. Despite this, the output (symmetrized) torque ripple even decreased after optimization, indicating that the torque waveforms of the individual stator-rotor stack combinations (SRSCs) are in opposite phases and cancel each other out.  
When comparing the SHG characteristics with and without ferrite magnets, we can conclude that the addition of ferrite magnets significantly improves the target characteristics: average generator losses are reduced by 23.4%; torque ripple is reduced by 23.9%; the total weight of active materials, stator housing, and rotor sleeve is reduced by 19.3%; and the length of the electromagnetic core is reduced by 16.7%. The current rating requirement for a semiconductor rectifier for the SHG with ferrite magnets is slightly higher than that for an SHG without magnets by 3.5%. At the same time, the cost of materials for the generator without magnets is 1.4 times less, since ferrite magnets are not used in it.  
In general, as a result of comparing the characteristics of the SHGs with ferrite magnets and without magnets, it can be concluded that the use of the SHG with ferrite magnets in this application is promising, since the efficiency of the generator has been improved significantly, and the dimensions and weight have also been significantly reduced, with a relatively small increase in cost.  
The limitation of the proposed approach is that the optimization of electromagnetic characteristics of the SHG is carried out without taking into account thermal and hydrodynamic (ventilation) processes. In future work, the comparison between the SHM with ferrite magnets and other types of electrical machines for passenger car generators and other applications will be carried out. Also, the presented SHM model with ferrite magnets will be supplemented by considering thermal and hydrodynamic processes.  
Conceptual approach, V.D. and V.P.; data curation, V.D. and V.K.; software, V.D. and V.P.; calculations and modeling, V.D., V.K. and V.P.; writing--original draft, V.D., V.K. and V.P.; visualization, V.D. and V.K.; review and editing, V.D., V.K. and V.P. All authors have read and agreed to the published version of the manuscript.  
The research funding from the Ministry of Science and Higher Education of the Russian Federation (Ural Federal University Program of Development within the Priority-2030 Program) is gratefully acknowledged.  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors thank the editors and reviewers for careful reading and constructive comments.  
The authors declare no conflict of interest.