Charging Schedule Optimization of Battery Electric Bus Considering Nonlinear Charging Profile

doi:10.12141/j.issn.1000-565X.230524

Abstract

Abstract:

Battery electric buses are increasingly applied and promoted in public transportation systems due to their advantages, such as low emissions and low noise levels. However, their limited driving range and long charging time necessitate frequent charging during daily operations, thus leading to a new charging scheduling problem. A reasonable charging schedule is of great significance in reducing the construction cost of charging facilities and charging costs. However, current research on optimizing electric bus charging schedules typically assumes a linear relationship between charging time and state of charge (SOC), and often neglects the comprehensive optimization of charging schedules and charging station operations, resulting in poor scenario reproduction and resource inefficiencies. Therefore, this paper further studied the optimization of charging schedules based on a predefined set of bus trip schedules. A mixed-integer programming model was developed to minimize the total system cost by optimizing the occurrence periods, the start and end times of charging, and the schedules of the charging piles synchronously. The model also fully considers time-of-use electricity pricing policy, partial charging strategies, and the nonlinear characteristics of battery charging. To solve the problem, this paper first linearized the nonlinear charging function of the battery into a piecewise linear one and then used the commercial solver Gurobi to obtain the optimal solution. Additionally, a tailored algorithm was designed based on the minimum-cost-maximum-flow theory and the deficit function. Multiple sets of experiments were conducted to validate the effectiveness of the proposed algorithm based on five bus routes in Beijing. The results, obtained through both Gurobi and the proposed optimized algorithm, demonstrate that the proposed algorithm can achieve a significant reduction in total system costs, ranging from 28.34% to 56.1% across various scenarios. These findings confirm the efficiency of the algorithm and its potential to optimize charging schedules effectively.

Key words: battery electric bus, charging schedule, nonlinear charging characteristics, optimized algorithm

CLC Number:

U491.1

XIONG Jie, LAI Kefan, LI Tongfei, et al. Charging Schedule Optimization of Battery Electric Bus Considering Nonlinear Charging Profile[J]. Journal of South China University of Technology(Natural Science Edition), 2024, 52(9): 115-130.

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路线	发车时间	车辆数	车次数	车次里程/km	车次耗电量变化范围/（kW·h）	空驶里程/km	空驶耗电量变化范围/（kW·h）
1	08：00—22：30	25	100	19.6	73~98	3.7	12~16
2	06：00—22：00	13	65	12.4	55~76	3.2	11~16
3	08：00—22：00	5	55	8.0	25~40	2.7	6~10
4	06：00—21：30	15	107	10.0	31~59	3.5	8~15
5	06：00—22：00	7	56	5.7	20~35	0.5	2~3

时间	电价/（元·（kW·h）^-1）
00：00—07：30	1.41
07：30—22：30	3.29
22：30—24：00	1.97

路线	车辆数	车次数	总成本/ （元·d^-1）	模型M2的变量数/个	总成本/ （元·d^-1）	用时/s	总成本/ （元·d^-1）	用时/s	误差率/%
路线	车辆数	车次数	初始充电计划		Gurobi		两阶段充电优化算法		误差率/%
1	25	100	43 956.25	12 786	31 113.95	1 485.27	31 500.14	1.29	1.24
2	13	65	41 906.77	5 091	18 393.53	57.71	18 393.53	0.59	0.00
3	5	55	10 946.16	3 890	5 264.63	1 267.58	5 474.27	6.06	3.98
4	15	107	40 013.56	11 780	—	超时	18 623.82	10.67	—
5	7	56	8 065.26	3 954	4 234.79	157.49	4 234.79	2.53	0.00
总网络	65	383	142 158.00	118 099	—	超时	76 042.54	55.12	—

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