Proper battery modelling to schedule an isolated microgrid with a chance constrained spinning reserve

Accurate modelling of battery energy storage systems (BESS) plays a crucial role in the optimal scheduling and planning of isolated microgrids with high penetration of renewable energy sources (RES). However, most mixed-integer linear programming (MILP) based scheduling models neglect the simultaneous representation of efficiency and degradation effects, which leads to inaccurate cost estimation and suboptimal operational decisions. This paper proposes an advanced MILP formulation for isolated microgrid scheduling that integrates a linearised BESS model capturing variable efficiency and combined cycle and calendar ageing to represent the capacity fade of the asset. The two ageing models integrated into the MILP formulation are data-driven, built upon publicly available open-access datasets. The formulation linearises efficiency and calendar ageing characteristics through a piecewise affine interpolation approach, which achieves high modelling accuracy while maintaining computational tractability. The study validates the BESS model through two distinct formulations applied to a real-world isolated microgrid case study supplying Lipari Island in Italy. A deterministic planning simulation demonstrates the model's low computational effort. The proposed BESS formulation uses only two binary variables per time step and optimises a full-year horizon (8760 time steps) in less than 20 s. The results show that explicitly modelling efficiency variations and battery degradation strongly affects scheduling decisions and operating costs. In addition, the paper evaluates the performance of the BESS model proposed in a 24-hour chance-constrained spinning reserve formulation that ensures reliable microgrid operation under uncertainty. The BESS model integrates seamlessly with this complex formulation and confirms that the storage deployment improves microgrid reliability without increasing operating costs.