The paper provides a comprehensive battery storage modelling approach, which accounts for operation- and degradation-aware characteristics, i.e., variable efficiency, internal resistance growth, and capacity fade. Based on the available experimental data from the literature, we build mixed-integer linear programming compatible lithium iron phosphate (LiFePO$_4$) battery model that can be used in problems related to various applications, i.e., power system, smart grid, and vehicular applications. Such formulation allows finding the globally optimal solution using off-the-shelf academic and commercial solvers. In the numerical study, the proposed modelling approach has been applied to realistic scenarios of peak-shaving, where the importance of considering the developed models is explicitly demonstrated. For instance, a time-varying operation strategy is required to obtain the optimal utilization of the LiFePO$_4$ battery storage. Particularly, during the battery operational lifetime its optimal average SoC may change by up to $20%$, while the duration of charging process may increase by $75%$. Finally, using the same LiFePO$_4$ benchmark model from the literature, we compare the results of using the proposed approach to the state-of-the-art in the optimal sizing and scheduling problems. The proposed approach led to a $12.1%$ reduction of battery investment and operating costs compared to the state-of-the-art method.
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