Joint Optimization of Electric Bus Charging Station Siting and Vehicle Scheduling

doi:10.12141/j.issn.1000-565X.250098

Abstract

Abstract:

Pure electric buses have become an important component of urban public transportation due to their environmental benefits. However, their widespread adoption is constrained by limited driving range, placing high demands on the planning of charging infrastructure and the formulation of vehicle schedules. Existing research often treats charging station siting and vehicle scheduling as independent problems, overlooking their interdependence. Moreover, most studies focus on single-depot or small-scale scenarios, which cannot adequately address the requirements for coordinated, cross-regional dispatching in large-scale and complex networks. To address these issues, this study constructs an integrated optimization model for electric bus charging station siting and vehicle scheduling. The model is built upon a spatio-temporal network framework designed for a multi-depot electric bus system. The objective is to minimize the total system cost, subject to various constraints including charging station construction, trip connection, state-of-charge(SOC) maintenance, vehicle scheduling, and charger matching.In order to accurately describe the operating cost, the model introduces the time-of-use electricity pricing and accounts for the parallel charging capacity of stations. To effectively solve this high-dimensional, discrete combinatorial optimization problem, an enhanced cultural memetic algorithm is designed. The algorithm incorporates improved genetic operators, introduces local search strategies such as trip-chain relocation and merging, and integrates a hierarchical constraint repair mechanism to ensure solution feasibility. The model and algorithm are validated using a case study based on a partial bus network in Chancheng District, Foshan City. The results demonstrate their effectiveness in handling problems of varying scales. Compared to traditional genetic algorithm and simulated annealing algorithm, the proposed algorithm can achieve better cost reduction in both small and large-scale instances. Sensitivity analysis further reveals that increasing battery capacity and reducing unit energy consumption can significantly reduce the total cost of the system, while the electricity pricing policy, especially off-peak rates, has a decisive influence on the operating cost. The study also confirms that charging station siting indirectly affects total cost by influencing scheduling efficiency, highlighting the necessity of joint optimization. This research enriches the theoretical framework for electric bus charging station siting and vehicle scheduling. The findings provide valuable, simultaneous insights for both the strategic planning and day-to-day operational decision-making of electric bus systems.

Key words: electric bus, charging station siting, vehicle scheduling, joint optimization

CLC Number:

U491.2

HU Yucong, HUANG Weibin, CHEN Junhua, WU Weitiao. Joint Optimization of Electric Bus Charging Station Siting and Vehicle Scheduling[J]. Journal of South China University of Technology(Natural Science Edition), 2026, 54(3): 79-90.

Figures/Tables 20

Table 1

Main symbols of the model"

集合	含义
$T$	车次集合， $t ∈ T = 1,2, . . ., T$
$K$	车场集合， $k ∈ K = 1,2, . . ., K$
$S$	充电活动集合， $s ∈ S = 1,2, . . ., S$
$L$	充电站选址集合， $l ∈ L = 1,2, . . ., L$
$A k$	车场 $k$ $(k ∈ K)$ 的可行连接集合
$A$	所有的可行连接集合
$Π$	起点车场集合， $π ∈ Π = 1,2, . . ., Π$ ，车场 $k$ 的起始节点表示为 $θ k$
$Π'$	终点车场集合， $π' ∈ Π = 1,2, . . ., Π'$ ，车场 $k$ 的结束节点表示为 $θ k'$
参数	含义
$r 0$	贴现率
$D$	一年的运营天数
$γ$	规划年限
$f 11 l$	充电站 $l$ $(l ∈ L)$ 固定建设费用中一次性需要支出的基本建设费用
$f 11 l'$	充电站 $l$ $(l ∈ L)$ 每天的维护费用
$f 12 l$	充电站 $l$ $(l ∈ L)$ 建设一个充电桩需要支出的基本建设费用
$f 12 l'$	充电站 $l$ $(l ∈ L)$ 中每个充电桩每天的维护费用
$f 2$	单辆电动公交购置的一次性费用
$f 2'$	单辆电动公交每天的维护费用
$c i$	节点 $i$ $(i ∈ S)$ 对应时段的单位电价
$e i j$	车辆从节点 $i$ 的终点站点前往节点 $j$ 的起点站点需要消耗的电量
$e i$	执行节点 $i$ 的耗电量
$e 0$	平均每辆车在夜间车场和充电站之间来回的空驶耗电量
$V l m a x$	候选站点 $l$ 充电桩的建设数量上限
$E b$	标定的电池容量
$Q m a x$	最高荷电状态
$Q m i n$	最低荷电状态
$B k m a x$	车场 $k$ 能够容纳的车辆数量上限

Table 1

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Table 2

Parameter values"

参数	取值		取值
$r 0$	0.08^［31］	$c i$	分时电价
$D$	365天	$e i j$	模拟生成
$γ$	5年	$e i$	模拟生成
$f 11 l$	与充电站关联	$e 0$	模拟生成
$f 11 l'$	与充电站关联	$V l m a x$	与充电站关联
$f 12 l$	15万元^［32］	$E b$	220 kW·h
$f 12 l'$	5元^［33］	$Q m a x$	90%
$f 2$	75万元^［34］	$Q m i n$	15%
$f 2'$	5元^［33］	$B k m a x$	50

Table 2

Table 3

Table 4

Table 5

Fig.10

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Table 6

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算例	算法	总成本/ 万元	电动公交购置费用/ 万元	充电费用/ 万元	充电站建设费用/ 万元	总成本的标准差/ 万元	总成本的变异系数/%	求解时间/s
小规模算例	SA	1 664.91	1 385.35	231.88	47.69	173.26	10.41	2.79
	GA	1 591.49	1 365.56	187.11	38.82	147.69	9.28	49.75
	EB-MA	1 438.20	1 217.13	195.89	25.18	72.00	5.01	77.15
大规模算例	SA	6 487.36	5 462.23	858.02	167.11	1214.06	18.71	33.56
	GA	5 605.22	4 878.40	604.27	122.55	823.92	14.70	296.47
	EB-MA	5 022.40	3 176.40	1 645.50	200.50	423.53	8.43	925.35

成本项	费用/ 万元	成本项细分	费用/ 万元	占比/%
充电站建设费用	200.5	充电站固定建设费用	126.1	2.51
充电站建设费用	200.5	充电桩建设费用	74.4	1.48
电动公交购置费用	3 176.4	电动公交购置费用	3 176.4	63.24
充电费用	1 645.5	运营期间充电费用	1 235.1	24.59
充电费用	1 645.5	夜间充电费用	410.4	8.17
总成本	5 022.4

城市	高峰电价	平峰电价	低谷电价
北京	0.892	0.654	0.412
上海	1.076	0.701	0.388
佛山	1.092	0.675	0.352
深圳	1.181	0.784	0.285
杭州	1.111	0.673	0.256