Resilience-oriented battery sizing for renewable microgrids: A cumulative energy approach with joint severity index

The increasing penetration of renewable energy sources in microgrids has made battery energy storage system sizing a critical challenge, especially when high energy autonomy is required under prolonged deficit conditions. Existing approaches often determine storage capacity through economic or multi-objective optimisation, whereas the minimum capacity needed to achieve a prescribed autonomy target remains less explicitly defined. Moreover, pre-critical state-of-charge depletion and the combined effect of deficit duration and intensity are rarely addressed within a transparent analytical framework. This work proposes a cumulative-energy-based methodology for determining the minimum storage capacity required to achieve a specified level of energy autonomy in renewable-based microgrids. Three contributions are introduced: a critical energy requirement Ecrit evaluated over the full deficit-recovery cycle; a joint severity index Sj combining deficit duration and intensity in a normalised plane, whose coverage threshold is governed by a single design parameter pS; and a pre-critical residual term R accounting for variability in the storage state of charge at the onset of the design period. The methodology is applied to three case studies and verified through microgrid operation simulations also under realistic battery parameters. The results confirm that the self-sufficiency rate increases monotonically with pS and that intermediate coverage levels (pS = 0.50–0.75) provide a favourable compromise between energy autonomy and storage oversizing. The framework simultaneously identifies the minimum capacity for full energy autonomy (pS = 1) and quantifies deviations from full self-sufficiency when complete autonomy is not feasible, providing a transparent sizing baseline for microgrids and energy communities.