Residential battery energy storage systems (BESS) are increasingly deployed alongside photovoltaic (PV) generation to reduce household energy costs under volatile time-of-use (TOU) tariffs. Model predictive control (MPC) is a widely adopted optimisation strategy for home energy management systems (HEMS), typically formulated to minimise net energy cost, subject to physical and operational constraints. However, battery degradation is rarely embedded in the optimisation objective, meaning its cost is unquantified and aggressive; high-cycle-count strategies could incur significant losses once deployed to physical systems. This paper presents a receding-horizon mixed-integer linear programming (MILP) baseline for a UK residential HEMS, using demand data from the REFIT dataset. A 3 by 3 sensitivity study is conducted across three battery sizes and three PV array sizes, with post-hoc degradation cost estimated using the Naumann stress model and rainflow cycle counting. Results show that degradation remains constant for each battery size and can exceed energy cost savings by up to 1,060 %. These results demonstrate that energy-cost-only optimisation systematically underestimates the true system cost, motivating a degradation-aware control formulation.

翻译：住宅电池储能系统与光伏发电相结合的应用日益增多，旨在分时电价波动背景下降低家庭能源成本。模型预测控制是家庭能源管理系统中广泛采用的优化策略，通常以最小化净能源成本为目标，并受物理和运行约束。然而，电池退化很少被纳入优化目标函数，这意味着其成本未被量化且具有激进行为：高循环次数的策略一旦部署到物理系统中，可能产生显著损失。本文基于英国住宅家庭能源管理系统，采用REFIT数据集中的需求数据，构建了一个滚动时域混合整数线性规划基准模型。通过设置三种电池容量和三种光伏阵列规模，进行了3×3敏感性研究，并采用Naumann应力模型和雨流循环计数法估算事后退化成本。结果表明，退化成本对于每种电池容量保持恒定，且可能超过能源成本节约高达1060%。这些结果证明，仅优化能源成本会系统性低估系统真实总成本，从而激发对退化感知控制方案的探索。