## 3 Results
### Sizing of OESD
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Operator,** & **Rail System** & **Vehicle, Manufacturer** & **ESS** & **Energy (MWh)** & **Power (kW)** & **Other** & **Ref** \\ \hline DB, Germany, 1959 & BMU & \begin{tabular}{c} ETA 515, Orenstein \\ and Koppel, W \& M \\ Donauwörth, MAN \\ \end{tabular} & Lead acid & 0.528 & 200 & \begin{tabular}{c} 100 km/h \\ 300 km \\ \end{tabular} & [10] \\ \hline DB Regio, Germany, 2022 & EMU, \begin{tabular}{c} ETM \\ regional \\ \end{tabular} & Flirt Akku, Stadler & LTO & 0.18 & N/A & \begin{tabular}{c} 150 km/h \\ 224 km 1 \\ \end{tabular} & [53] \\ \hline SNCF, France, 2019–2023  & DBEMU, \begin{tabular}{c} TER Regiois, \\ regional \\ \end{tabular} & LTO & 0.14 & 600 & \begin{tabular}{c} 80 km w/o \\ catenary \\ \end{tabular} & [54] \\ \hline OBB, Austria, 2019, 2023  & EMU, \begin{tabular}{c} Cityjet Desiro, \\ Siemens \\ \end{tabular} & LTO & 0.53 & 1300 & 100 km/h 2  & [55] \\ \hline Rumo Logistics, \begin{tabular}{c} Rrazil, 2023 \\ \end{tabular} & Freight & \
\begin{tabular}{c} GT38H Joule \\ (hybrid), Progress \\ Rail \\ \end{tabular} & LiFePO\({}_{4}\) & 0.55 & 2200 & 60 km/h & [56] \\ \hline Prototype tests, USA, 2020 & Freight &
\begin{tabular}{c} SD70J EMD Joule \\ (BEL), Progress Rail \\ \end{tabular} & LiFePO\({}_{4}\) & 2.4–8 & 3200 & 120 km/h & [57] \\ \hline Zanzeff project, USA, 2021 & Freight & ET44C4, BNSF & N/A & 2.4 & 3000 & \textless{}100 km/h & [13] \\ \hline \end{tabular}
\end{table} 
Table 8: Battery and diesel options and characteristics for EMU in Europe and USA. the availability of DC-DC converters, such as 3 kV-to-750 V converters [58], which can be used for supply and braking energy transfer to and from the OLE and locomotives. It also enables the potential recharging of batteries from the diesel-electric unit without requiring dedicated charging infrastructure at wayside locations or train stops. Using LiFePO\({}_{4}\) batteries (commonly applied in prosumer energy management) and considering a maximum current of approximately 3600 A (for a diesel unit alone), the OESD would require between 36 and 72 rows of batteries. For instance, each row would consist of 62 Victron 100 A batteries to reach 750 V. However, this configuration presents significant challenges for a fully battery-electric locomotive (BEL). Achieving adequate storage capacity would require 2200-4000 batteries (e.g., 62 \(\times\) 36 elements, each providing 1.28 kWh) and a total storage capacity of approximately 2700 MWh. Although this sizing aligns with data from BEL manufacturers, such as the SD70J by Progress Rail (see Table 8), it exceeds the storage constraints for a hybrid unit. Consequently, European reports like [12] conclude that batteries alone are not a feasible solution for stand-alone locomotives in heavy freight services. Given the need for fast response from the OESD, a hybrid approach combining batteries with Electric Double-Layer Capacitors (EDLCs) is proposed. The primary hypotheses used for sizing this hybrid solution are as follows:  
* Track Characteristics and Urban Mobility Trends: In the scenario analyzed, the Murcia (MC) station will integrate a new transportation hub, including a bus station, parking facilities, and a tramway line. This infrastructure development suggests the need for fast charging points for electric buses. Additionally, passenger train traffic (especially high-speed trains) requires rapid adjustments in demand and generation, which EDLCs are well-suited to handle. The hybrid locomotive could serve as a mobile generation resource for both Railway Power Systems (RPS) and Public Power Systems (PPS). According to the authors' previous work [17], passenger trains generate 20-45 kWh during braking, while acceleration demands 40-50 kWh--levels difficult to achieve and store using only batteries. * Demand and braking profiles: The track's demand profiles, as shown in Figure 15, exhibit both base and fluctuating demand patterns.