# Optimal Sizing of Battery Energy Storage System for Implicit Flexibility in Multi-Energy Microgrids
## 4 Discussion  
In this study, a block-based MILP framework to optimize the operations of a MEMG is developed, with a specific focus on modeling electricity and natural gas billing structures in Italy. The proposed framework, named HOMES, is applied to a real-world case study to evaluate the added economic value of installing a BESS, under the assumption that the storage system is used exclusively to minimize bill costs, without considering active participation in electricity markets. The primary finding is that under current tariff schemes, market prices, and BESS costs in Italy, investing in a BESS solely for implicit flexibility provision is not economically viable. For all 16 combinations of power ratings and EPR values considered, the NPV of BESS investment remains negative, indicating that the optimal solution under current conditions is not to install the BESS. However, the economic attractiveness of BESS deployment could be significantly improved by adopting more advanced operational strategies, such as participating in electricity markets through optimized bidding strategies [41] or by enabling service stacking to combine multiple revenue streams [42]. Additionally, a detailed analysis of the operational cost savings associated with each BESS-integrated configuration reveals that the main cost-reduction driver is the energy capacity of the battery, with an optimal value around 4 MWh. Particularly, the configuration achieving the greatest reduction in annual operational costs corresponds to P = 2 MW and EPR = 2 h, yielding a 3.8% cost reduction with respect to the benchmark configuration without BESS. Further investigation into the cost components most affected by the BESS integration show a significant decrease in PDR (natural gas) costs, primarily due to improved self-consumption efficiency and reduced operation of the CHP unit, whose capacity factor dropped by about 2%. Additionally, a substantial reduction in POD (electricity) costs is observed, driven by the significant decrease in grid interactions. In fact, the BESS maximizes self-consumption, lowering the annual energy exchanged with the grid from 1312 MWh to 243 MWh (an 82% reduction). This reduces the revenue from grid injections but, more importantly, minimizes electricity purchase costs, which are subject to heavy tariffs related to system charges. The BESS is also used for energy arbitrage, taking advantage of the time-of-use electricity tariffs and the capacity market charges that vary between peak and off-peak hours. Moreover, peak shaving plays a crucial role, accounting for nearly 40% of the total POD cost reduction. Finally, BESS operation enables O&M cost savings by covering the electrical load during certain periods and allowing the CHP unit to be turned off. Overall, it is observed that the BESS enhances the exploitation of electric-thermal synergies. During thermal load peaks, instead of being exported as excess electricity from the CHP to the grid, energy is stored in the BESS, where it gains more value through its potential for arbitrage, peak shaving, and CHP shutdowns aimed at minimizing O&M costs. One of the main focuses of this work is to properly model the _negative injected energy (NIE)_ of the BESS--that is, energy withdrawn from the grid for the purpose of later reinjection. The results show that, under the proposed modeling assumptions, pure price arbitrage against the day-ahead market is not economically favorable. Finally, the sensitivity analyses reveal important insights into the effectiveness of market signals and tariff structures. First, only under very high and unrealistic DAM price spreads (greater than EUR 1000/MWh) does the MEMG shift from maximizing self-consumption to increasing grid withdrawals for energy arbitrage. Second, the proposed time-of-use power-based tariff could unintentionally encourage the opposite behavior of its intended purpose, potentially shifting peak withdrawals into system peak hours if not properly designed.