  Robust charging schedules in a growing market of battery electric bus (BEB)
fleets are a critical component to successful adoption. In this paper, a BEB
charging scheduling framework that considers spatiotemporal schedule
constraints, route schedules, fast and slow charging, and battery dynamics is
modeled as a mixed integer linear program (MILP). The MILP is modeled after the
Berth Allocation Problem (BAP) in a modified form known as the Position
Allocation Problem (PAP). Linear battery dynamics are included to model the
charging of buses while at the station. To model the BEB discharges over their
respective routes, it is assumed each BEB has an average kWh charge loss while
on route. The optimization coordinates BEB charging to ensure that each vehicle
remains above a specified state-of-charge (SOC). The model also minimizes the
total number of chargers utilized and prioritizes slow charging for battery
health. The model validity is demonstrated with a set of routes sampled from
the Utah Transit Authority (UTA) for \A buses and \N visits to the charging
station. The model is also compared to a heuristic algorithm based on charge
thresholds referred to as the Qin-Modified method. The results presented show
that the slow chargers are more readily selected and the charging and
spatiotemporal constraints are met while considering the battery dynamics and
minimizing both the charger count and consumption cost.
