# Optimal Sizing of Battery Energy Storage System for Implicit Flexibility in Multi-Energy Microgrids
## 3 Results
### Sensitivity Analysis of DAM Price Spread to Incentivize Pure BESS Arbitrage  
In this section, we investigate how much the DAM price spread within a single day would need to widen to make it economically attractive for the MEMG, with its _optimal_ BESS configuration (2 MW/4 MWh), to engage in pure energy arbitrage. Specifically, we aim to identify the minimum DAM price spread that would incentivize the system to operate the BESS solely to buy electricity from the grid when prices are low and sell it back when prices are high, taking advantage of the benefits offered by the Italian tariff scheme for NIE. Figure 10 presents the results for 15 July, illustrating how the system's optimal scheduling evolves as the parameter \(\Delta\) increases from 2 to 10. This parameter artificially amplifies the daily price spread: First, the average DAM price for the day is calculated. Then, every hourly price above this daily average is multiplied by \(\Delta\), while every hourly price below the average is divided by \(\Delta\). In this way, higher \(\Delta\) values simulate increasingly extreme price differences within the day, highlighting when pure arbitrage becomes profitable for the system. Comparing Figure 10 with Figure 8, which shows the optimal scheduling under the actual DAM prices for 15 July, we observe that when \(\Delta\) is set to 2--increasing the DAM price spread to around EUR 250/MWh instead of the actual EUR 70/MWh--the optimizer slightly increases the BESS discharge to export additional electricity to the grid during the evening peak. However, as shown in Table 15 in the Appendix B, the total daily energy exported to the grid in this scenario is still only about 87 kWh. Moreover, the price differential is not yet large enough to make it worthwhile to draw additional power from the grid during midday low-price hours and resell it during the high-price peak since this would increase \(p^{\text{POD}_{MAX\text{min}}}\), resulting in higher _EUR/kV_ charges on the electricity bill. When \(\Delta\) is increased to 3, the impact on the MEMG's optimal scheduling remains similar, with the total electricity exported still limited to about 1 MWh. Pushing the scenario further with \(\Delta=5\), we see that in this case, the peak grid import \(p^{\text{POD}_{MAX\text{min}}}\) does increase because under these extremely variable DAM prices--which are clearly unrealistic today--it would  
Figure 9: Comparison of 15-min electric and thermal power flows in the MEMG between the reference and optimal BESS-integrated (2 MW/4 MWh) configurations on 12 December 2024.  
actually be economically rational to draw more power from the grid during low-price hours and sell it back during peak hours in the evening. This effect becomes even more pronounced when \(\Delta\) is increased to 10. Interestingly, however, even with \(\Delta=10\), the system does not make use of the incentives related to NIE. This is because, in practice, a 2 MW battery would have to charge at a rate exceeding the on-site generation for the charging energy to qualify as NIE. For this MEMG, which combines a 2 MW CHP and approximately 1 MW of PV, operating in this manner would be highly suboptimal, as it would reduce the benefit of self-generation. Figure 11 presents the results for 12 December, which is selected as the representative day with the highest DAM price during the year. In this case, even under actual market conditions shown in Figure 9, the DAM price spread reaches approximately EUR 150/MWh. This spread is already sufficient to make it economically optimal for the system to export electricity to the grid during the peak DAM price hours. As \(\Delta\) increases to 2 and 3, the amount of energy injected into the grid to capture these price peaks also rises, as detailed in Table 10. However, the DAM price spread is still not large enough to justify an increase in the system's maximum power withdrawal \(p^{POD_{MAXmin}}\), which only becomes economically viable in the more extreme scenarios of \(\Delta=5\) and \(\Delta=10\).