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• A semi-analytical approach is developed to obtain the BESS power reserve for FFR. • The local minimum power reserve is derived to avoid UFLS under a large contingency. • The proposed method bridges the gap of the trial-and-error approaches. • The effectiveness of the proposed method is validated with an actual network model. • The methodology will advance grid services estimation and battery management. The large-scale renewable energy integration faces a challenge of frequency stability due to low inertia in weak power grids. One solution to mitigate this issue is via the fast frequency response service provided by battery storage systems so that the overall grid response during a large power outage can be improved. The battery power reserve is crucial to ensure the frequency ancillary services provision. However, grid operators currently investigate the contingency reserve of batteries through inefficient processes, such as extensive simulations or trial-and-error methods. Therefore, this paper proposes a semi-analytical methodology to quantitively determine the minimum required battery power reserve for preventing under-frequency load shedding when a severe generation trip occurs. This minimum reserve is derived from the time-variant kinetic energy of a given dispatch case. Case study results of the Mexican network demonstrate that the calculated battery power reserve can provide a cost-effective fast frequency response for a real islanded network. The research outcomes offer valuable insights for battery management and grid ancillary services requirement estimation in the transition to power networks dominated by converter-interfaced renewable energy resources. [ABSTRACT FROM AUTHOR]