# Optimal Sizing of Battery Energy Storage System for Implicit Flexibility in Multi-Energy Microgrids
## 3 Results
### Optimal BESS Sizing
Notably, the configuration yielding the highest cost savings--EUR 140.2 k per year, corresponding to a 3.8% reduction relative to the benchmark scenario without BESS--is characterized by a power rating of 2 MW and an EPR of 2. At first glance, it may seem counterintuitive that this configuration has lower operational costs than do others with the same energy capacity but a higher power rating, such as the 4 MW/4 MWh BESS. One might expect that increasing the power capacity would add operational flexibility, allowing the system to charge and discharge more quickly, respond to demand peaks more effectively, and thus reduce operating costs further by offering a less constrained optimization. However, the results show that this is not necessarily the case for the MEMG under study. The reason lies in how well the BESS's rated power aligns with the typical load profile and the operational characteristics of the cogeneration unit. During off-peak periods, the electrical load frequently drops well below 4 MW. If the CHP unit is shut down to minimize fuel consumption and O&M costs during these times, the BESS must fully supply the remaining load. A larger BESS with a 4 MW inverter would, in these conditions, be forced to operate far below its rated output to match the low residual demand. This under-utilization reduces its average round-trip efficiency, because battery inverters and associated power electronics are generally less efficient when operated far from their nominal design point. In addition, surplus energy cannot always be sold back to the grid at attractive prices during these low-demand periods, limiting any potential advantage from excess discharge capacity. In contrast, a 2 MW BESS aligns much more closely with the typical residual demand in off-peak periods. Its inverter can operate nearer to its nominal output, resulting in higher average round-trip efficiency and better overall performance. During peak periods, the total electrical load usually rises to around 4 MW. However, the cogeneration unit is generally dispatched to cover a significant portion of this--typically around 2 MW--to exploit its high thermal and electrical efficiency when demand is high. This leaves only about 2 MW of residual load to be covered by the BESS. Again, a 2 MW BESS is well sized to meet this remaining demand without significant oversizing of its power electronics. A larger 4 MW inverter, in this situation, does not offer meaningful additional benefit. As a result, the 4 MW/4 MWh configuration not only provides no meaningful operational advantage  
but also suffers from a slightly lower average round-trip efficiency (94.37% compared to 94.81% for the 2 MW/4 MWh BESS). Moreover, the less efficient utilization means that the cogeneration unit must operate more often to compensate, leading to a slight increase in PDR costs (+0.19%) while achieving the same net POD costs as the 2 MW case. However, it should be noted that the 2 MW, 2 h BESS configuration should not be interpreted as the overall optimal solution since investment costs must also be taken into account alongside the operational cost savings. Additionally, battery degradation due to cycling should be considered, as it may require battery bank replacement before the end of the investment evaluation horizon. To account for these factors, the NPV is computed, as presented in (58). Figure 5 presents the NPV calculated for each of the BESS configurations considered. As shown, the NPV remains negative across all scenarios, indicating that--under assumed BESS investment costs, and electricity, and gas tariffs--the economic value generated by implicit flexibility services such as energy arbitrage and peak shaving is insufficient to justify the BESS capital expenditure. Therefore, the most cost-effective solution remains the baseline configuration without any BESS installation.