TY - JOUR
T1 - An optimal charging scheduling model and algorithm for electric buses
AU - Bao, Zhaoyao
AU - Li, Jiapei
AU - Bai, Xuehan
AU - Xie, Chi
AU - Chen, Zhibin
AU - Xu, Min
AU - Shang, Wen Long
AU - Li, Hailong
N1 - Funding Information:
The authors highly appreciate two anonymous reviewers who provided many constructive comments for improving the quality of the paper. The authors are also grateful to many colleagues from the Transport and Energy Systems Laboratory at Tongji University , especially Xinyan Li, Hanjun Fu, and Jiaxuan Ding for their technical and spiritual help at the initial stage of this study. The core method presented in this paper was initially developed for a research project for the 2020 New Energy Vehicle Big Data Application Innovation Competition for National Colleges and Universities and our research team won the grand prize of the competition. This research is sponsored by the National Natural Science Foundation of China (Grant No. 72171175 , 72111540273 , 72021102 , 71890970 , 72101153 , 72061127003 ) and the Fundamental Research Funds of Central Universities. Dr. Min Xu’s research work is support by the Research Committee of the Hong Kong Polytechnic University under project code UAKQ.
Funding Information:
The authors highly appreciate two anonymous reviewers who provided many constructive comments for improving the quality of the paper. The authors are also grateful to many colleagues from the Transport and Energy Systems Laboratory at Tongji University, especially Xinyan Li, Hanjun Fu, and Jiaxuan Ding for their technical and spiritual help at the initial stage of this study. The core method presented in this paper was initially developed for a research project for the 2020 New Energy Vehicle Big Data Application Innovation Competition for National Colleges and Universities and our research team won the grand prize of the competition. This research is sponsored by the National Natural Science Foundation of China (Grant No. 72171175, 72111540273, 72021102, 71890970, 72101153, 72061127003) and the Fundamental Research Funds of Central Universities. Dr. Min Xu's research work is support by the Research Committee of the Hong Kong Polytechnic University under project code UAKQ.
Publisher Copyright:
© 2022 Elsevier Ltd
PY - 2023/2/15
Y1 - 2023/2/15
N2 - Electrification poses a promising low-carbon or even zero-carbon transportation solution, serving as a strategic approach to reducing carbon emissions and promoting carbon neutrality in the transportation sector. Along the transportation electrification pathway, the goal of carbon neutrality can be further accelerated with an increasing amount of electricity being generated from renewable energies. The past decade observed the rapid development of battery technologies and deployment of electricity infrastructure worldwide, fostering transportation electrification to expand from railways to light and then heavy vehicles on roadways. In China, a massive number of electric buses have been employed and operated in dozens of metropolises. An important daily operations issue with these urban electric buses is how to coordinate their charging activities in a cost-effective manner, considering various physical, financial, institutional, and managerial constraints. This paper addresses a general charging scheduling problem for an electric bus fleet operated across multiple bus lines and charging depots and terminals, aiming at finding an optimal set of charging location and time decisions given the available charging windows. The charging windows for each bus are predetermined in terms of its layovers at depots and terminals and each of them is discretized into a number of charging slots with the same time duration. A mixed linear integer programming model with binary charging slot choice and continuous state-of-charge (SOC) variables is constructed for minimizing the total charging cost of the bus fleet subject to individual electricity consumption rates, electricity charging rates, time-based charging windows, battery SOC bounds, time-of-use (TOU) charging tariffs, and station-specific electricity load capacities. A Lagrangian relaxation framework is employed to decouple the joint charging schedule of a bus fleet into a number of independent single-bus charging schedules, which can be efficiently addressed by a bi-criterion dynamic programming algorithm. A real-world regional electric bus fleet of 122 buses in Shanghai, China is selected for validating the effectiveness and practicability of the proposed charging scheduling model and algorithm. The optimization results numerically reveal the impacts of TOU tariffs, station load capacities, charging infrastructure configurations, and battery capacities on the bus system performance as well as individual recharging behaviors, and justify the superior solution efficiency of our algorithm against a state-of-the-art commercial solver.
AB - Electrification poses a promising low-carbon or even zero-carbon transportation solution, serving as a strategic approach to reducing carbon emissions and promoting carbon neutrality in the transportation sector. Along the transportation electrification pathway, the goal of carbon neutrality can be further accelerated with an increasing amount of electricity being generated from renewable energies. The past decade observed the rapid development of battery technologies and deployment of electricity infrastructure worldwide, fostering transportation electrification to expand from railways to light and then heavy vehicles on roadways. In China, a massive number of electric buses have been employed and operated in dozens of metropolises. An important daily operations issue with these urban electric buses is how to coordinate their charging activities in a cost-effective manner, considering various physical, financial, institutional, and managerial constraints. This paper addresses a general charging scheduling problem for an electric bus fleet operated across multiple bus lines and charging depots and terminals, aiming at finding an optimal set of charging location and time decisions given the available charging windows. The charging windows for each bus are predetermined in terms of its layovers at depots and terminals and each of them is discretized into a number of charging slots with the same time duration. A mixed linear integer programming model with binary charging slot choice and continuous state-of-charge (SOC) variables is constructed for minimizing the total charging cost of the bus fleet subject to individual electricity consumption rates, electricity charging rates, time-based charging windows, battery SOC bounds, time-of-use (TOU) charging tariffs, and station-specific electricity load capacities. A Lagrangian relaxation framework is employed to decouple the joint charging schedule of a bus fleet into a number of independent single-bus charging schedules, which can be efficiently addressed by a bi-criterion dynamic programming algorithm. A real-world regional electric bus fleet of 122 buses in Shanghai, China is selected for validating the effectiveness and practicability of the proposed charging scheduling model and algorithm. The optimization results numerically reveal the impacts of TOU tariffs, station load capacities, charging infrastructure configurations, and battery capacities on the bus system performance as well as individual recharging behaviors, and justify the superior solution efficiency of our algorithm against a state-of-the-art commercial solver.
KW - Bi-criterion dynamic programming
KW - Charging scheduling
KW - Charging windows
KW - Electric buses
KW - Electricity load capacity
KW - Time-of-use tariffs
UR - https://www.scopus.com/pages/publications/85144328290
U2 - 10.1016/j.apenergy.2022.120512
DO - 10.1016/j.apenergy.2022.120512
M3 - Journal article
AN - SCOPUS:85144328290
SN - 0306-2619
VL - 332
JO - Applied Energy
JF - Applied Energy
M1 - 120512
ER -
SDG 7 Affordable and Clean Energy
SDG 11 Sustainable Cities and Communities