  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.
