*5.1. Storage System Sizing*

The architecture of each ESS, when equipped with some storage capability, in the next Figure 4, while the final sizing of the considered stationary storage system is instead shown in Table 6. The first rows show the two different lithium-based technologies which have been considered. The first one is based on LFP cells [17], while the second one is based on LTO cells [18].



**Table 6.** Storage system sizing.

According to manufacturer indications [18], the maximum allowed charging cell current is extremely higher for LTO, which value has been calculated from the declared input power, fixed at 1500 W. It must also be said that the LFP manufacturer [17] does not give precise indications regarding performance in the case of charging pulses, which have been prudently fixed to 6 A/Ah, with respect to

10 A/Ah declared for discharging pulses. Finally, cell costs have been estimated from experience by the authors [8].

The sizing of the battery pack was made having as reference the peak of charging current, which the battery is subjected during the train braking phases, i.e., about 1000 A with 10 trains on the line corresponding to a rush hour. How visible from the last rows of Table 6, the 160 Ah-capacity selected for the LFP cell perfectly matches this performance requirement. However, the capacity has to be selected also to guarantee a corresponding SOC variation compatible with the expected life of that battery. In this way, the number of charging-discharging cycles, having every day up to 10 trains on the line, which are continuously engaged in acceleration and braking phases, can reach hundreds of thousands in a few years. This solicitation can be sustained from the battery only when the corresponding SOC variation during cycling is within the range 5–10% [20–22]. In the case of the LFP solution, because of their worst performance, SOC variation under this condition must not overcome 5%. Regarding the LTO solution, although a smaller capacity would be acceptable as well regarding the maximum stress required, a capacity of at least 50 Ah is needed to stay within the indicated SOC variation, to preserve the battery life. Moreover, di fferent lithium cell technologies (e.g., NMC, NCA, etc.) could at least be used in theory; however, as first approximation their general characteristics can be aligned to the typologies here described, and their performance within the considered range, mainly LTO oriented when able to sustain high charging/discharging current rates. An additional example describing the utilization of high-power batteries is detailed in [23].

The quantity of the braking energy to be recovered in the di fferent scenarios was analyzed by means of a simulation tool developed in Modelica language [24] in order to evaluate the power and energy flows on the overall system. In this way, the supply network, the catenary, and the trains running have been simulated, following the same approach as in [6,25].

The tool was then validated by the utilization of the daily and annual energy flows, respectively shown in Tables 3 and 4. Obviously, daily energy flows have made it possible to correctly calibrate the ESS model parameters, the braking energy control strategy and the trains energy consumptions, by setting the maximum allowed speed along the di fferent sections of the route, and the di fferent mix of auxiliary loads. In this way, the tool was able to be aligned with the indicated energy required for traction in the last row of Table 4, with a gap of about 1%.

Once validated, the tool was to evaluate the energy saving gained from the installation of storage systems, from one up to ten, e.g., one for each ESS. Energy saving was evaluated as di fference between the total energy delivered by the ESSs in the configuration without storage, and the total energy delivered by the ESSs in the configuration with the number of the storage systems examined. Results, taken from [9] for clarity, are in the next Table 7.


**Table 7.** ESSs energy demand for traction and related energy saving, for different storage systems option.

It is apparently questionable if the storage sizing needs to be updated when the number of storages rises up from one up to ten units. In fact, at equal number of trains, power, and energy flows to be managed would be shared in a larger number of storages; thus, allowing a downsizing in terms of nominal capacity. However, it is also possible to observe how the need to preserve the SOC fluctuation within a narrow band, makes the choice of maintaining the original storage sizing. This is visible also in the next Figure 5, where battery current and SOC are shown in the case of ten storage systems, for which LTO technology has been chosen. As said before, current peaks do not overcome 1000 A, and SOC variation is about 10%. Figure 5 refers to the case of a rush hour, with 10 trains running.

**Figure 5.** Battery current and SOC when having 10 storage systems installed, rush hour (ten trains running).
