# Synchronous Homopolar Generator without Permanent Magnets for Railway Passenger Cars
## 6 Conclusions  
This article discusses the methodology and results of optimizing a synchronous homopolar generator (SHG) with an output power of approximately 35 kW without permanent magnets for railway passenger cars. Because the rotational speed of the generator changes as the velocity of the train changes, the performance of the generator is optimized for the required speed range. To reduce the saturation and the currents at low speeds, a constant mechanical power speed range (CPSR) strategy widely used for traction motors is proposed for the undercar generator. The CPSR of the SHG is from 750 rpm to 3450 rpm. The SHG starts to produce electric energy at the speeds much lower than the low boundary of the CPSR, which is a significant advantage when the passenger car starts with the discharged batteries. Thus, it produces 8.03 kW at 300 rpm. An optimization procedure was adapted to use the single-criteria, unconstrained Nelder-Mead method. The optimization minimizes the SHG average power loss over the CPSR, the current capacity of the semiconductor rectifier, and the torque ripple. The optimization results show a significant improvement of the target performances of the SHG with ferrite magnets. Compared to the nonoptimized design, the following were reduced: average generator losses by 14.6%, required current capacity of the semiconductor rectifier by 24.8%, and torque ripple by 18.2%. The calculated characteristics of the SHG were compared with the catalogue characteristics of a commercial undercar generator. The comparison shows that the volume of the SHG electromagnetic core is 2.1 times smaller than that of the commercial generator. At the same time, the calculated efficiency of the SHG is much higher than that of the commercial generator in the entire operating speed range. In addition, the reduced input (mechanical) power due to the reduction of power loss of the SHG results in reducing the load on the transmission elements and wheels of the car, which will increase their lifetime. Conceptual approach, V.D. and V.P. ; data duration, 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. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **EGV.08.1 (PEMZ) [31]** & **Optimized Design of the SHG** \\ \hline \multirow{2}{*}{Output electric power, kW} & \multirow{2}{*}{35} & \(\approx\)35 \\  & & (36.2 kW at 3500 rpm; \\  & & 32.0 kW at 800 rpm) \\ \hline Average output power, kW & 35 & 34.1 \\ \hline Number of poles & 24 & 12 \\ \hline Electric frequency at maximum speed, Hz & 690 & 350 \\ \hline Stator outer diameter (excluding cooling fins) \(D\), mm & 380 & 370 \\ \hline Machine length without end winding parts \(L\), mm & 357 * & 180 \\ \hline Active parts volume \(\pi\)-\(L\)-\(D^{2}\)/4, m\({}^{3}\) & 0.04 & 0.019 \\ \hline Efficiency @ 750 rpm \% & 72 & 79.8 \\  & & (without taking into account mechanical losses) \\ \hline Efficiency @ 3450 rpm, \% & 85 & 90.4 \\  & & (without taking into account mechanical losses) \\ \hline Number of phases & 3 & 3 \\ \hline Cooling type & Air cooling without fan & Air cooling without fan \\ \hline \hline \end{tabular}  
* Note: The length of the stator stack of a mass-produced generator was calculated taking into account its outline drawing from the manufacturer’s website [31] and a sketch from the book [36], which shows that the length of the stator package is approximately 70% of the distance between the bearing shields.  
\end{table} 
Table 4: Performance comparison of the optimized SHG design with a commercially available undercar generator. **Funding:** 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. **Institutional Review Board Statement:** Not applicable.