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This paper presents an advanced experimental model of storage efficiency that accurately captures the efficiency dynamics of the battery and power converter, distinguishing between charging and discharging operational regimes. The model introduces a state-dependent representation of storage efficiencies as functions of key operating parameters, namely power rate and state of charge, which makes it particularly suitable for direct integration into optimization frameworks for Battery Energy Storage System (BESS) operation. The proposed model is derived through ad hoc fitting methods applied to data from an extensive testing campaign on the Li-Ion BESS installed at the SGILab in JRC Ispra. The applicability of the proposed approach is demonstrated through its implementation in a Dynamic Programming (DP) framework for combined optimization of the short-term operational scheduling of the BESS and its long-term capacity revamping strategy due to cyclic degradation. A case study examining a BESS participating in the Italian Wholesale Energy Market, while maintaining sufficient energy capacity to meet the contractual obligations of the Capacity Market, demonstrates that the proposed methodology enhances the overall system performance compared with previous approaches. Specifically, the improved efficiency formulation developed in this work allows for a +22.0% increment in the net economic profits throughout the entire asset lifetime with respect to standard approaches relying on constant BESS efficiency. Technical results allow for a better characterization of the BESS operational regime, which foster mild power rates, striking a balance between capacity degradation - triggered by large power rates - and inefficient energy conversions - typical of small power rates. • Considering battery efficiency beyond that of the power electronics is crucial. • The efficiency-degradation interplay noticeably affects the battery's operation. • Dynamic programming can handle non-linearities of efficiencies and degradation. • Optimal operation combines short-term scheduling and long-term capacity revamping. • The optimal management of the efficiencies' dynamics boosts the battery's revenues.