*3.1. Energetic Assessments*

The simulation results are presented in Figures 6 and 7. Knowing that our dataset consists of 40 users, it would be ine ffective to illustrate 40 individual plots into the same figure. Instead, we selected five quantile elements at which the cumulative probability becomes 5%, 25%, 50%, 75% and 95%. This gives us a better view of the statistical distribution of each performance metric.

**Figure 6.** Simulation results: (**a**) Peak reduction-to-capacity (left), (**b**) peak reduction (right).

**Figure 7.** Simulation results: (**a**) SoC active time (left), (**b**) Battery utilization (middle), (**c**) Consumption increase (right).

From both Figure 6a,b, it can be concluded that the peak reduction increase decreases with the battery capacity (second derivative of the function in Figure 6b is negative) or in other words: as the battery capacity increases, peak shaving becomes more difficult. For a battery capacity 2 times the mean power (e.g., a user with 30 kW mean power installs a 60 kWh battery) seventy percent of the users between Q5 and Q75 achieve peak reduction in the range 0.26–1.5 times their mean power (Figure 6a). The same group of users achieves peak reduction up to 6–27% of their peak power (Figure 6b). For a battery capacity of 10 times the mean power (e.g., a user with 30 kW mean power installs a 300 kWh battery) the peak reduction for that group (Q5–Q75) varies within 0.4–2.8 times their mean power (Figure 6a) and 20–44% of their peak power (Figure 6b).

Regarding the SoC active time (Figure 7a), it increases with the battery capacity. The reason is that as the battery capacity increases, the peak threshold is reduced and consequently, the battery is used more frequently. An important conclusion to note is that, for most users, the SoC active time remains very low, even for large battery capacities. Seventy percent of the users between Q5 and Q75 with a battery capacity 10 times the mean power deploy their battery in the range of 0–20%, or in other words the battery stays idle for at least 80% of the time during the year. This fact in itself opens up new research opportunities.

If peak shaving does occur rarely, then we could possibly hybridize our energy managemen<sup>t</sup> system including other services as well (e.g., ancillary services, increasing the self-sufficiency of renewable energy installations). Figure 7b provide another indication that the battery is underutilized, here, however in terms of lifetime expectancy. Over the entire battery capacity dimension, for ninety-five percent of the users (Q0–Q95), the battery does not deliver more than 80 cycles per year. This number is considerably lower compared to the cycle lifetime of nowadays' state-of-the-art Lithium-ion technologies (above 5000 cycles) [28]. At such low utilization rates, the battery can endure several years of use (more than a decade). Finally, it will be due to another reason why the battery was decommissioned such as a maintenance issue or simply because the battery has reached the end of its calendar lifetime. (The capacity fade effect of Lithium-ion batteries is both time-dependent (calendar lifetime) and cycle-number dependent (cycle lifetime). Regardless of its utilization, after a certain time period the battery loses a part of its initial capacity. Usually, the End of Life (EoL) of a battery is defined when its initial capacity is reduced by 20%, in many critical applications (e.g., EVs) this is the time when the battery needs to be either decommissioned or repurposed for another application.)

The consumption increase is shown in Figure 7c. It is worth noting once more that the battery technology in the present study exhibits a very high energy efficiency. Undoubtedly, if other technologies

were used (e.g., lead acid, flow batteries), the consumption increase would be higher. As can be seen from the figure, obviously, the higher the battery capacity, the higher the absolute energy losses. One reason why this happens is due to the increase of the battery utilization (see Figure 7b) and another reason is because both the battery and the dc/ac converter become bigger in size. Consider, for instance, a user with 30 kW mean power and a battery capacity of 300 kWh (capacity-to-mean power is 10). Only the converter losses to (dis)charge the battery at 1 C are approximately 15 kW (at 95% dc/ac efficiency). If the battery capacity was 30 kWh (capacity-to-mean power is 1), those losses would be significantly lower (1.5 kW).
