*5.2. System Reliability*

From the numbers of Table 7, it is clear that the best choice from the energy saving point of view is the installation of three storage systems; in fact, further energy saving due the increment of the storage systems up the three units cannot be compensated by their extra-purchase costs. Some sensitive analysis for different scenarios, including different costs of electricity and storage technologies are detailed in [8]. However, installation up to 10 storage systems, although less cost-efficient, may be useful as well in order to improve the system reliability. In this regard, two possible failures have to be considered:

The first failure typology takes into consideration that all the ESSs are subjected to blackout, with the electrical feeding from the grid immediately stopped. In this way, each storage system installed must serve one train on average, allowing it to reach at least two nearest subsequent train stops. This means, by considering the sequence of train stops of the previous Figure 2, each train has to cover under these conditions a traveled distance not higher than 3 km.

From simulation results, the traction energy consumption at constant speed is in the range 2.6–3.2 kWh/km for the trains running at 50 or 70 km/h respectively. Therefore, the two considered configurations were checked. In this way, considering a mid SOC level and running at the highest speed (i.e., 70 km/h), each battery pack can move at the maximum constant speed (i.e., 70 km/h) the train for about 4.8 km or 15.2 km, respectively. Therefore, the requirement to let each train running to the nearest station has been fully met.

As second failure, it has been considered the situation in which one single ESS stops working. The failure can affect or not the stationary storage, installed in parallel. In this case, no change in normal operation is allowed, to guarantee the business continuity for the service. Naturally, both the two storage configurations have been simulated. The matrix shown in the next Table 8 shows all the considered case studied, which simulate a failure at the beginning, in the middle or at the

**Table 8.** Matrix of test cases, failure of one ESS including storage or not, for different storage systems

end of the pattern, in which electrical feeding substations (ESSs) are numbered from 1 (e.g., David, see Figure 2) to up 10 (e.g., Albino, see Figure 2). When the failure of the storage is included, it is indicated in the corresponding row, always in Table 8. Table 8 shows results from simulation outputs in terms of functionality, indicating when service interruption (-) or business continuity (x) occur, in correspondence with the hypothesized failures.



In this way, the following main remarks can be achieved. First of all, when the failure involves both the ESS and the corresponding storage, the business continuity cannot be guaranteed in each condition, if the reference power of 1 MW is installed for each ESS. In fact, due occasional overlap of acceleration and running phases of multiple trains in the same portion of the track, power peaks delivered from the ESS can reach a maximum value nearly about 1.6 MW. This is visible in the plot of the next Figure 6, where the maximum power from ESS1 is shown, in the case of all ESSs perfectly working, or when a failure concerns the nearest ESS0. How visible, the maximum extra-peak to be supplied is about 400 kW, and it remains sustainable when the full power of 2.2 MW is ye<sup>t</sup> available, i.e., with standard transformers, or with two AMT transformers installed in parallel (see Section 4.2).

**Figure 6.** Power delivered from ESSs, in the case of failure from ESS1 (top) or no failure (bottom).

On the other hand, when half-power transformers having 1.1 MW are used, the extra-power needed has to be provided by the storage systems, and losses decrease from 4.5 kW and 17.5 kW (see Table 2), at exactly the half value, i.e., 2.3 kW and 8.8 kW, respectively; thus, further reducing the amount of losses calculated in the Section 4.2.

In particular, stationary storage systems are mandatory, in order to guarantee the extra-power needed. The two storage systems may appear useful as well, although the LTO configuration is properly designed for delivering high current rates, while the LFP configuration is exploited at its maximum performance, having about 600 kW delivered, aligned to the maximum allowed current rate of 6 A/Ah. Finally, when no overlap happens among multiple trains running, the business continuity is guaranteed also in the presence of a failure concerning both the storage and the feeding substation; this is the case when the failure refers to ESS4 and ESS9, always in Table 8.
