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Highlights • Proposes a second-order dynamic model to represent an actual So–Nick BESS. • An input–output identification procedure is proposed for parameters identification. • The procedure is based on the Sensitivity theory involving the Lyapunov function. • Experimental tests prove the practical applicability of the proposed methodology. Abstract The aim of this paper is to derive an accurate input/output dynamic equivalent model of a So–Nick Battery Energy Storage System (BESS). For this purpose, an on-line identification methodology has been applied. By this methodology, unknown model parameters are identified in the continuous time domain by solving an optimization problem aimed at minimizing the error between output trajectories of the physical system and its dynamic equivalent model. The methodology is based on the Sensitivity theory involving the Lyapunov function, ensuring the stability of the algorithm. Experimental results are used to validate the proposed approach by adopting the Sodium–Nickel Battery Energy Storage System (BESS) embedded into the experimental Prince Lab of the Polytechnic University of Bari, Italy. [ABSTRACT FROM AUTHOR]