## 3 Results
### Sizing of OESD  
The sizing of On-Board Energy Storage Devices (OESD) depends on several factors, including the vehicle type, itinerary, degree of electrification, and the operational duties of the railway unit. Preliminary values can be inferred from past experiences, scientific literature, and manufacturer data, although specific details are often unavailable. As mentioned in Section 2, the German ETA series (EMU) required 528 kWh of energy to cover a 300 km trip using lead-acid batteries. Reference [17] suggests that for routes with 20% electrification, approximately 2100 kWh of battery storage is needed, while the minimum storage size for routes with 36% electrification is 544 kWh. The system must also handle peak currents of around 6000 A, achieved using Lithium Titanate Oxide (LTO) batteries. The DC bus operates at a rated voltage of 750 V, which is consistent with the voltage used in third-rail electrification in the UK. In [14], the authors propose limiting charge and discharge rates to 0.5 C and 1 C, respectively, to optimize battery capacity, resulting in a required storage range of 2200 to 4800 kWh for a six-car Battery Electric Multiple Unit (BEMU) intercity train. They emphasize that lower C-rates reduce battery degradation and extend their operational lifetime, as supported by the literature [52]. SoC is also limited to a range from 0.9 to 0.2. Partial storage systems were also analyzed in [19] to manage RPS peak loads caused by the synchronization of train timetables. In this context, a combination of batteries (approximately 100 kWh) and EDLCs was proposed. However, these systems primarily operate under electrified tracks, and the battery sizing aligns more with last-mile applications than  
Figure 16: Demand/braking characteristics from the simulation of a 1300-ton freight train from Cartagena to Murcia: **(a)** Load Duration Curve (LDC, for double S333.3 hauling) **(b)** Bar plot of throttle (N) and braking (DB). Notes: PnB means that pneumatic braking was applied. Idle position has been omitted because of its large difference in magnitude in actual freight duties. with the hybridization goals of this study. Table 8 summarizes the main OESD options for some representative railway systems. Based on manufacturer proposals and on the requirements of our freight route, a 550 kWh capacity for OESD is assumed. As the reader can see in Table 8, European manufacturers prefer LTO batteries due to their higher current, but [57] is confident in LiFePO\({}_{4}\) technology for its Joule BEL due to three reasons: its thermal stability, inherent safety, and energy density. Moreover, this manufacturer (a Caterpillar company expert in diesel-electric engines, formerly EMD) also rebuilds middle-aged locos. These improvements on middle-aged series have usually been used by operators, and it has also been applied in Spain for S333.3. Especially both the original AC generators and the diesel engine remain in refurbished units. For this reason, it is interesting to depict some characteristics of this generator (GT26 according to the EMD catalog; see Figure 17). The current requirements for the six traction motors are approximately 3600 A at 650 V. For the hybrid system, a DC bus operating at around 750 V is assumed, this being a typical rated voltage for trans and third-rail railway systems [17]. This voltage facilitates  
Figure 17: Main Generator GT26 voltage vs. current curve and data from a real acceleration test of the generator of the original locomotive of 333 series (an international platform by EMD).