Optimal Charging Schedule Planning for Electric Buses Using Aggregated Day-Ahead Auction Bids

Abstract

This study aims to plan a cost-minimizing charging schedule for electric buses with fast charging stations. The paper conceptualizes the problem as a three-stage procedure, which is oriented around the participation of an electric bus aggregator in a day-ahead energy auction. First, the aggregation stage determines the bid parameters of buses. With bid parameters, aggregated cost-minimizing charging plans are obtained in the second stage conceived as the hourly day-ahead auction. The disaggregation of hourly plans into feasible minutely charging schedules is the third stage. The main contribution is the formulation of mixed-integer linear programming aggregation models to determine charging availability expressed as minimum and maximum hourly energy requirements taking into account detailed, minutely characteristics and constraints of the charging equipment and the buses. No price forecasts are required, and the plans adjust to the wholesale prices of energy. Defining only a few aggregated bids parameters used in linear programming constraints and incorporating them into the auction model is another contributing factor of this paper, allowing the scheduling of storage-based participants economically. The proposed methodology has been verified on a recently published case study of a real-world bus service operated on the Ohio State University campus. We show that the auction-based charging of all 22 buses outperforms as-soon-as-possible schedules by 7% to even 28% of daily cost savings. Thanks to the aggregated bids, buses can flexibly shift charges between high- and low-price periods while preserving constraints of the charging equipment and timetables.