# Optimal Sizing of Battery Energy Storage System for Implicit Flexibility in Multi-Energy Microgrids
## 3 Results
### Impact of Power-Based Tariff Design on Peak Power Withdrawal Reduction  
In this section, we investigate to what extent the power-based tariff in the electricity bill should be differentiated between peak and off-peak hours to effectively incentivize the analyzed MEMG to reduce its grid power withdrawal during system-wide peak periods. Specifically, since the MEMG is located in the city of Milan, we identify system peak hours  
Figure 11: Impact of increasing the DAM price differential on the optimal electrical scheduling of the MEMG with the _optimal_ BESS configuration (2 MW/4 MWh) on 12 December 2024.  
based on the time intervals during which the local distribution system operator, Unareti, has launched auctions for upward active power reserves under the MiNDFlex pilot project [40]. MiNDFlex aims to test a local flexibility market in Milan and, to date, has been activated in the summer months of June and July (2024 and 2025), defining flexibility products for the 10:00-23:00 time window. Using the same representative day (15 July) previously analyzed under the current electricity bill structure, we assessed how the optimal scheduling of the MEMG with its optimal BESS configuration changes when different ToU power-based tariffs are applied. Figure 12 shows the results of this sensitivity analysis. It is important to highlight that under the current electricity bill scheme with a flat power-based tariff, the optimal scheduling for the day considered (as illustrated in Figure 8) requires increasing the maximum power withdrawn from the grid in July from the previous value of 367 kW to 499 kW, resulting in an associated cost of EUR 566. For simplicity, in all ToU capacity tariff scenarios analyzed, the maximum monthly peak demand established by the preceding July days is kept constant at 367 kW for both peak and off-peak periods. The analysis then focuses on how different ToU capacity tariff schemes affect the maximum power withdrawn from the grid relative to the 499 kW reference value. As a first step, we applied a ToU power-based tariff which allocates the current charge of EUR 4.29/kW by applying three-quarters of it to the peak demand during system peak hours (10:00-23:00) and one-quarter to the peak recorded during the remaining off-peak hours. This tariff structure will hereafter be referred to as _ToU level 0_. Under this tariff structure, a user with constant demand who is unable to shift consumption away from system peak hours would pay the same as under the current flat tariff, while a user who can shift demand would benefit from minimizing its peak during system peak hours. Interestingly, Figure 12 shows that for the analyzed MEMG with a 2 MW/4 MWh BSS, the resulting optimal scheduling behaves in the opposite way to what the ToU tariff aims  
Figure 12: Impact of time-of-use power-based charges on the optimal electrical scheduling of the MEMG with the _optimal_ BESS configuration (2 MW/4 MWh) on 15 July 2024.  
to encourage. Specifically, rather than maintaining a peak of 499 kW for both peak and off-peak periods, the analyzed MEMG is incentivized to increase the peak demand during system peak hours to 534 kW and reduce the off-peak peak to 389 kW, thus slightly lowering the total power-based cost to EUR 560. This counterintuitive outcome is mainly due to the fact that the BESS is already operating close to its technical SOC limits to minimize peak grid withdrawals. As a result, it cannot further reduce demand during peak hours without significantly increasing the peak during off-peak hours, which still incurs a charge of EUR 1.07/kW. To address this, we hypothesized an alternative tariff structure (_ToU level 1_), in which the charge applied to peak demand during system peak hours is doubled compared to the current value (EUR 8.58/kW), while the off-peak charge is halved (EUR 2.15/kW). In this scenario, any user unable to shift their demand away from peak hours would be penalized compared to the current flat tariff.