Scheduling Battery-Electric Bus Charging under Stochasticity using a Receding-Horizon Approach

TL;DR

This paper presents a receding-horizon charging scheduling approach for battery electric buses that accounts for stochastic factors, improving cost efficiency and robustness over traditional methods.

Contribution

It introduces a hierarchical receding horizon planner with a novel non-linear partial charging model, enhancing scheduling fidelity under uncertainty.

Findings

Up to 52% cost savings over non-time-of-use methods

Significant robustness improvements compared to open-loop planning

Effective handling of stochasticity in charging schedules

Abstract

A significant challenge of adopting battery electric buses into fleets lies in scheduling the charging, which in turn is complicated by considerations such as timing constraints imposed by routes, long charging times, limited numbers of chargers, and utility cost structures. This work builds on previous network-flow-based charge scheduling approaches and includes both consumption and demand time-of-use costs while accounting for uncontrolled loads on the same meter. Additionally, a variable-rate, non-linear partial charging model compatible with the mixed-integer linear program (MILP) is developed for increased charging fidelity. To respond to feedback in an uncertain environment, the resulting MILP is adapted to a hierarchical receding horizon planner that utilizes a static plan for the day as a reference to follow while reacting to stochasticity on a regular basis. This receding horizon planner is analyzed with Monte-Carlo techniques alongside two other possible planning methods. It is found to provide up to 52\% cost savings compared to a non-time-of-use aware method and significant robustness benefits compared to an optimal open-loop method.