# Optimal Sizing of Battery Energy Storage System for Implicit Flexibility in Multi-Energy Microgrids
## 1 Introduction
### Literature Review  
Several studies in the literature investigate the optimal planning of MES deployment. For instance, [PERSON] et al. [8] propose a bi-level optimization framework for the joint siting, sizing, and operation of multiple interconnected MES within a large-scale integrated energy system (IES) comprising coupled electricity, gas, and heat networks. Their work addresses the theme of co-optimizing the deployment of multiple MES units across hybrid energy infrastructures while explicitly considering peer-to-peer (P2P) energy trading and demand response (DR) programs. The proposed model aims to minimize both investment and operational costs while enhancing the overall IES performance. To validate their approach, the authors apply it to a case study involving a 16-bus, 33 kV electricity distribution network, a 30-node district heating network, and a 20-node gas network. The results highlight the model's ability to identify optimal locations, component sizes, and configurations for energy hubs, achieving substantial cost savings and improved network performance. Similarly, [PERSON] et al. [9] develop a resilience-oriented multi-agent planning framework for interconnected microgrid clusters, incorporating P2P energy trading and the impact of extreme events. Their model minimizes planning costs while ensuring resilience against both internal uncertainties (e.g., renewable variability, load fluctuations) and external transaction disruptions. Key contributions include a linearized formulation, an incentive compatible P2P pricing strategy derived from the dual problem, and a privacy-preserving distributed solution method. Case studies on islanded microgrids show that the proposed framework achieves economic efficiency, enhanced resilience, and stakeholder privacy. Several studies specifically address the optimal sizing of MES components. [PERSON] et al. [10] develop a multi-objective planning framework for sizing components (PV, wind, electric and thermal storage, CHP, and heat pumps) in a standalone MEMG. The model aims to balance system costs, renewable energy integration, and curtailment shares while considering the interaction between electric and thermal networks. The optimization problem is solved using NSGA-II to generate Pareto-optimal solutions, with TOPSIS helping to select the best configuration based on weighted criteria. A novel indicator, the relative grid size (RGS), is introduced to quantify the balance between electric and thermal infrastructure. The model is applied to a Norwegian case study with 30 households, and the results reveal that high renewable shares (>70%) significantly increase curtailment and costs, while a balanced RGS (~1.11) improves system resilience. The optimal renewable share is found to lie between 50% and 70%, achieving a balanced trade-off among cost, sustainability, and efficiency. [PERSON] et al. [11] investigate the impact of explicitly modeling the thermal vector on the optimal sizing of battery energy storage systems (BESSs) in a local MES. Using a non-convex, mixed-integer, quadratically constrained programming formulation and the COMANDO framework, they compare two system architectures: one that includes explicit thermal modeling (covering heat pump behavior, building thermal inertia, and the heating network) and one that assumes an all-electric demand. Based on two case studies in Germany (a single building and a local energy community), under varying electricity tariffs and solar irradiation levels, the results show that neglecting the thermal vector leads to BESS oversizing, higher annual costs (up to 8%), and a greater environmental impact. The oversizing effect is particularly pronounced under time-varying tariffs and high solar scenarios. Similarly, [PERSON] et al. [12] address the challenge of optimal sizing and operation of electric and thermal storage within a net-zero multi energy system (NZMES), investigating how different storage technologies and renewable energy mixes influence overall system costs and self-sufficiency.