# Optimal Sizing of Battery Energy Storage System for Implicit Flexibility in Multi-Energy Microgrids
## 3 Results
### Techno-Economic Impact of BESS Deployment  
Figure 6 shows the variation in the system's operational cost components between the benchmark case without BESS (_reference_) and the configuration with the BESS that achieves the lowest annual costs (_optimal_). The cost items can be grouped into three categories: interactions with the electricity grid, natural gas purchases, and O&M costs for production units and the BESS. As shown in Figure 6, the most significant absolute cost reduction is observed in the PDR-related charges, followed by a decrease in POD-related costs. Additionally, a reduction in O&M costs is observed. Despite the additional expenses associated with BESS operation, the storage system allows the CHP to remain \begin{table}
\begin{tabular}{c|c|c|c|c|c} \hline  & **EPR = 0.5 h** & **EPR = 1 h** & **EPR = 2 h** & **EPR = 3 h** & **EPR = 4 h** \\ \hline \multirow{4}{*}{P = 1 MW} & EUR 3638 k/y & EUR 3590 k/y & EUR 3571 k/y & EUR 3564 k/y & **EUR 3562 k/y** \\  & \(\Delta\) = EUR 41.6 k/y & \(\Delta\) = EUR 88.8 k/y & \(\Delta\) = EUR 108.2 k/y & \(\Delta\) = EUR 114.9 k/y & \(\Delta\) = EUR 117.6 k/y \\  & \(BESS\_cycles\) = 791 & \(BESS\_cycles\) = 880 & \(BESS\_cycles\) = 593 & \(BESS\_cycles\) = 424 & \(BESS\_cycles\) = 339 \\ \hline \multirow{4}{*}{P = 2 MW} & EUR 3581 k/y & EUR 3553 k/y & **EUR 3539 k/y** & EUR 3539 k/y & EUR 3545 k/y \\  & \(\Delta\) = EUR 97.7 k/y & \(\Delta\) = EUR 125.7 k/y & \(\Delta\) = EUR 140.2 k/y & \(\Delta\) = EUR 139.7 k/y & \(\Delta\) = EUR 133.2 k/y \\  & \(BESS\_cycles\) = 1076 & \(BESS\_cycles\) = 798 & \(BESS\_cycles\) = 452 & \(BESS\_cycles\) = 313 & \(BESS\_cycles\) = 239 \\ \hline \multirow{4}{*}{P = 3 MW} & EUR 3566 k/y & EUR 3544 k/y & **EUR 3541 k/y** & EUR 3551 k/y & EUR 3565 k/y \\  & \(\Delta\) = EUR 113.5 k/y & \(\Delta\) = EUR 134.8 k/y & \(\Delta\) = EUR 138.2 k/y & \(\Delta\) = EUR 127.9 k/y & \(\Delta\) = EUR 114.3 k/y \\  & \(BESS\_cycles\) = 956 & \(BESS\_cycles\) = 591 & \(BESS\_cycles\) = 324 & \(BESS\_cycles\) = 220 & \(BESS\_cycles\) = 166 \\ \hline \multirow{4}{*}{P = 4 MW} & EUR 3559 k/y & **EUR 3545 k/y** & EUR 3558 k/y & EUR 3576 k/y & EUR 3596 k/y \\  & \(\Delta\) = EUR 120.0 k/y & \(\Delta\) = EUR 134.2 k/y & \(\Delta\) = EUR 120.7 k/y & \(\Delta\) = EUR 103.0 k/y & \(\Delta\) = EUR 83.1 k/y \\  & \(BESS\_cycles\) = 801 & \(BESS\_cycles\) = 468 & \(BESS\_cycles\) = 246 & \(BESS\_cycles\) = 167 & \(BESS\_cycles\) = 124 \\ \hline \end{tabular}
\end{table} 
Table 2: Annual costs for each BESS configuration, including the cost difference compared to the reference case without BESS (EUR 3679 k) and the corresponding number of battery cycles per year. off when not needed, supplying the load directly with stored electricity. This operational shift eliminates the CHP's variable O&M costs in certain time steps. However, it is worth noting that the greatest relative cost reduction occurs in the POD-related charges, with a 19.9% decrease--compared to a 2.47% reduction for PDR costs and 2.51% for O&M costs. Understanding the mechanisms behind this significant relative decrease in POD costs is essential for interpreting the impact of BESS integration. Figure 7 provides a detailed breakdown of the POD-related cost components for both the _reference_ and the _optimal_ configuration. This analysis not only identifies the most significant cost items affecting the analyzed MEMG but also demonstrates how the implicit flexibility offered by the BESS can be strategically leveraged to reduce both variable energy charges and monthly peak-related costs. The first key insight is the BESS's capability to perform effective energy arbitrage. Specifically, it takes advantage of the time-of-use structure of retail electricity prices--leading to a reduction in _supply costs_--and of the varying capacity market-related charges between peak and off-peak hours, resulting in lower _capacity costs_. These reductions are driven not only by the arbitrage activity itself but also by the decreased volume of electricity withdrawn from the grid.