# Optimal Sizing of Battery Energy Storage System for Implicit Flexibility in Multi-Energy Microgrids
## 1 Introduction
### Literature Review
Their study couple long-term planning with short-term operational optimization through a predictive control strategy, formulating daily dispatch problems as MILP models. A case study of a Polish rural village demonstrates that combining diverse RES sources (PV and wind) generally yields lower levelized costs of energy and higher self-sufficiency compared to PV-only scenarios due to more stable generation profiles. The results highlight that thermal energy storage (TES) often proves more cost-effective than BESS when excess electricity can be sold, while BESS becomes complementary in PV-dominant or zero-export price contexts in managing higher intermittency and enhance self-consumption. The study underlines the trade-off between pursuing high self-sufficiency and managing energy costs, emphasizing that energy policy frameworks and export incentives significantly affect the optimal sizing of storage technologies in an NZMES. Many studies in the literature focus on optimizing the operation of already-designed MESs from both economic and environmental perspectives. [PERSON] et al. [13] propose a multi-objective optimization approach for IES, incorporating exergy analysis to account for both the quantity and quality of energy. The approach aims to optimize economics, environmental impact, and energy efficiency while addressing the challenge of long solution times in multi-objective optimization. To overcome this, they introduce a variable step-size approximation method, reducing solution time by up to 97.84% compared to the traditional methods. The TOPSIS method is used for decision-making to select the optimal solution. A case study demonstrates that including exergy efficiency in the optimization process provides a more comprehensive solution, balancing energy efficiency, operational costs,and GHG emissions. [PERSON] et al. [14] focus on optimizing the coordinated energy dispatch of a MEMG, highlighting the lack of studies on multi-energy scheduling in islanded mode. They propose an optimal scheduling method using MILP models to minimize net operational costs in the grid-connected mode and consider objectives such as minimizing fuel costs and emissions in islanded mode. A case study of the Semakau Island microgrid in Singapore demonstrates that the proposed method is effective in both modes, with distinct objectives for each. [PERSON] et al. [15] develop a min-max optimization strategy to improve the operation of renewable energy-based combined cooling, heating, and power (CCHP) systems by addressing forecast errors in renewable energy sources and load. The goal is to minimize operational costs while enhancing system robustness under prediction errors. They introduce a model predictive control (MPC) approach, incorporating prediction errors into the optimization model. This strategy accounts for the dynamic behavior of storage units (batteries and thermal storage) and uses statistical and gray models for error forecasting. A case study of a hypothetical CCHP building in China show that the strategy effectively reduces the impact of forecasting uncertainties and minimizes operational costs. In a related context, [PERSON] et al. [16] propose an online energy management strategy for grid-connected residential microgrids based on a prioritized sum-tree experience replay strategy with a double-delayed deep deterministic policy gradient (PSTER-TD3). By formulating the problem as a Markov decision process, they enhance convergence speed and achieve reliable optimization of electricity cost, thermal comfort, and electric vehicle charging, demonstrating the potential of advanced deep reinforcement learning for real-time multi-energy system control. The concept of flexibility in MES is addressed from various perspectives in recent literature. [PERSON] et al.