  This paper presents mixed integer linear programming (MILP) formulations to
obtain optimal sizing for a battery energy storage system (BESS) and solar
generation system in an extreme fast charging station (XFCS) to reduce the
annualized total cost. The proposed model characterizes a typical year with
eight representative scenarios and obtains the optimal energy management for
the station and BESS operation to exploit the energy arbitrage for each
scenario. Contrasting extant literature, this paper proposes a constant power
constant voltage (CPCV) based improved probabilistic approach to model the XFCS
charging demand for weekdays and weekends. This paper also accounts for the
monthly and annual demand charges based on realistic utility tariffs.
Furthermore, BESS life degradation is considered in the model to ensure no
replacement is needed during the considered planning horizon. Different from
the literature, this paper offers pragmatic MILP formulations to tally BESS
charge/discharge cycles using the cumulative charge/discharge energy concept.
McCormick relaxations and the Big-M method are utilized to relax the bi-linear
terms in the BESS operational constraints. Finally, a robust optimization-based
MILP model is proposed and leveraged to account for uncertainties in
electricity price, solar generation, and XFCS demand. Case studies were
performed to signify the efficacy of the proposed formulations.
