# Optimal Sizing of Battery Energy Storage System for Implicit Flexibility in Multi-Energy Microgrids
## 1 Introduction
### Literature Review
[17] propose a techno-economic and environmental framework for distributed multi-generation systems, demonstrating how the integration of technologies such as CHP, electric heat pumps, and TES allows systems to respond to electricity price signals while reducing emissions and improving energy savings. [PERSON] et al. [18] focus on thermal networks, identifying the flexibility potential embedded in the thermal inertia of buildings and highlighting the role of hybrid control strategies--combining centralized optimization and decentralized decision-making--as an effective means to managing complex heating and cooling systems. [PERSON] et al. [19] advance the discussion on dynamic flexibility by proposing a two-timescale MPC strategy to operate CHP units within IES, enabling the system to quickly respond to electrical fluctuations while maintaining indoor thermal comfort. Finally, [PERSON] et al. [20] introduce a conceptual and mathematical modeling approach based on multi-energy nodes and flexibility maps to quantify and visualize the flexibility potential of distributed MESs, highlighting how different forms of arbitrage and operational constraint relaxation can be exploited to support low-carbon energy systems. Building on the flexibility potential highlighted in previous studies, several works have explored the economic benefits and technical challenges of providing ancillary services with MES. [PERSON] and [PERSON] [21] develop a techno-economic framework to evaluate the participation of MESs in the provision of ancillary services, focusing on how these systems can explicitly offer flexibility to the electrical grid. Through numerical applications involving trigeneration systems in tertiary buildings and aggregated district heating loads, the authors illustrate how profitability maps can effectively visualize the conditions under which ancillary services provision becomes economically attractive. This approach shows that internal energy source switching within MESs can be leveraged to unlock new value streams in energy markets. [PERSON] et al. [22] develop a techno-economic framework to assess the business case for an MEMG that simultaneously provides energy, frequency reserve, and reliability services. Their methodology combines a MILP model with sequential Monte Carlo simulations to account for dynamic, non-linear pricing signals, particularly for reliability services. Through application to two representative configurations--one with CHP and TES, the other with PV and BESS--connected to a real 11 kV distribution network, the study evaluates performances across various pricing scenarios. The results show that MEMGs can co-optimize service provision effectively, as synergies between energy arbitrage, reserve provision, and reliability support often emerge. [PERSON] et al. [23] propose a techno-economic framework to assess the arbitrage potential of distributed MESs in providing explicit flexibility to the power grid via ancillary services, without compromising end-user comfort. The approach leverages energy shifting across electricity, heating, and cooling vectors. A novel indicator, the maximum profit electricity reduction (MPER), is introduced to quantify the optimal reduction in grid electricity input that maximizes profit under given availability and utilization fee structures. The framework relies on efficiency matrices and black-box modeling to simulate MES behavior and applies profit functions based on ancillary services remuneration. Through two case studies--one during winter and one during summer--the work demonstrates that significant economic gains can be achieved even with moderate electricity reductions, particularly in summer conditions with flexible cooling options. Overall, the results highlight the value of multi-vector flexibility for grid services, with MPER serving as a key metric for decision-making.