# Optimal Sizing of Battery Energy Storage System for Implicit Flexibility in Multi-Energy Microgrids
## 3 Results
### Optimal BESS Sizing  
To assess the techno-economic annual performance of the MEMG described in Section 3.1. the following analysis is conducted. First, a baseline scenario without a BESS is defined and used as a reference. Then, different configurations of the MEMG with a BESS are considered, combining four power ratings ([1, 2, 3, 4] MW) and four energy-to-power (EPR) values ([1, 2, 3, 4] h). For each of the 16 BESS configurations and for the reference scenario, the MILP model presented in Section 2 is solved independently for each day of the year 2024, with a 15-min time resolution. The optimization follows a day-ahead scheduling approach under the assumption of perfect foresight of all uncertain inputs (i.e., PV generation and energy demands). Once the optimal scheduling for each day is obtained, the annual cost for each configuration is computed as the sum of the daily costs output from the optimization model. For every BESS configuration, the cost reduction \(\Delta\)_Costs_ compared to the reference scenario is then calculated. Assuming that this annual saving is consistently achieved over a 10-year horizon and applying an interest rate \(r\) of 5%, the NPV of the BESS investment is computed following the same approach outlined in [35]:  
\[NPV=-CAPEX^{BESS}+\ \sum_{t=1}^{10}\ \frac{\Delta Costs\ \Big{[}\frac{\xi}{year} \Big{]}}{(1+r)^{t}}-\sum_{t=1}^{10}\left(\frac{CAPEX^{BESS_{aw}}}{(1+r)^{t}} \right)+RV^{BESS}. \tag{58}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Electrical Load** & **PV Electrical** & **Net Electrical** & **Thermal Load** & **Cooling Load \({}^{*}\)** \\
**[MWh/y]** & **Generation [MWh/y]** & **Load [MWh/y]** & **[MWh/y]** & **[MWh/y]** \\ \hline
13,112 & 930 & 12,182 & 8422.9 & 1417.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Annual energy values of electrical, thermal, and cooling (* thermal-equivalent) demands, and PV generation for the reference year 2024. Figure 4: Schematic representation of the MEMG components included in the block-based modeling framework analyzed in this study. * The cooling load is represented as its thermal equivalent, i.e., the thermal input required by the absorption chiller to meet the cooling demand. The capital expenditure \(CAPEX^{BESS}\) is modeled as the sum of two components: an energy-related cost of EUR 250/kWh, representing the cost of the battery banks, and a power-related cost of EUR 80/kW, accounting for the inverter and grid connection. Additional investment costs are included whenever the BESS exceeds its threshold of 5000 cycles [39], requiring battery replacement. Furthermore, a residual economic value \(RV^{BESS}\) is included to account for the remaining economic value of the system at the end of the 10-year period. This residual value is estimated based on the remaining number of cycles and the unused lifetime of the components, assuming a 10-year useful life for the battery banks and 30 years for the power-related components. After computing the NPV according to Equation (58) for each BESS configuration, the one yielding the highest NPV can be identified. This allow us to estimate the optimal size of the BESS to be installed in the case study, when considering implicit flexibility provision through energy arbitrage and peak shaving strategies. Table 2 summarizes the annual cost outcomes for each of the BESS configurations analyzed. Specifically, it shows the annual cost reduction \(\Delta\)_Costs_ compared to the baseline scenario without a BESS, in which the optimized operation of the MEMG results in a total operating cost of EUR 3679 k/year. The results shown in Table 2 suggest that the main economic driver is the installed energy capacity: for each power rating, the optimal energy capacity appears to be around 4 MWh. Increasing the storage capacity beyond this threshold brings lower economic returns and in some cases, even leads to higher total costs due to the increased O&M expenses associated with a larger BESS.