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Second-life batteries (SLBs, automotive batteries that have lost their usefulness for vehicular applications) can provide low-cost environment-friendly solutions for grid-connected systems. The estimation of the remaining useful life (RUL) of SLBs is a fundamental step for the development of appropriate business models. This paper aims at unveiling correlations between the SLB's power profile and aging performance by defining appropriate metrics. A widely accepted empirical degradation model, that can predict calendar and cycling aging, is considered for this study. Several grid-connected power profiles are analyzed, such as peak shaving for DC-fast charge stations and frequency regulation. The results of this analysis show a correlation between the SLB's replacement rate with the minimum daily SoC.