Electric Bus Scheduling Method Considering Differences in the State of Health of Batteries

doi:10.12141/j.issn.1000-565X.230279

Abstract

Abstract:

Electric buses (EBs) have the advantages of zero-emission and low energy consumption in operation. The electrification of urban buses is being vigorously promoted in many countries to reduce carbon emissions and promote the realization of the “Carbon peaking and Carbon neutrality” goals. However, due to financial constraints and the fact that fuel buses have not yet reached the end of life and bus companies usually replace fuel buses with EBs in batches, there are differences in the battery health degree and driving range of each bus on the line, which makes the optimization of the vehicle scheduling scheme more complicated. Considering the impact of battery differences in the state of health and time-of-use tariff, this paper proposed an optimized scheduling model for single-route, with the objective of minimizing average daily charging costs, EB acquisition costs, and battery loss costs. Then, the model was transformed into two sub-problems, the vehicle scheduling problem and the charging scheduling problem. In the outer layer, the vehicle scheduling problem was solved by the improved simulated annealing algorithm (ISAA), whose perturbation strategy is designed with the operating intensity differences among EBs. And Gurobi was employed to solve the charging scheduling problem in the inner layer. Finally, an actual EB route was taken as an example to verify the effectiveness of the method, and the method was compared with the simulated annealing algorithm in the perturbation strategy which does not consider differences in vehicle operating intensity. Results show that the ISAA can increase the convergence speed by 31.8% and achieve high-quality solutions in a short time. Moreover, the generated scheduling scheme can not only arrange EBs to be charged preferentially in the off-peak period of electricity prices but also reduce the EB fleet size.

Key words: public transportation, electric bus, route scheduling, battery state of health, simulated annealing algorithm

CLC Number:

U491.1⁺7

BIE Yiming, ZHU Aoze, CONG Yuan. Electric Bus Scheduling Method Considering Differences in the State of Health of Batteries[J]. Journal of South China University of Technology(Natural Science Edition), 2023, 51(10): 11-21.

Figures/Tables 12

Fig.1

Fig.2

Fig.3

Table 1

Bus scheduling parameters"

参数类别	具体参数	参数值
班次参数	行程时间/min	50~90
	行程能耗/（kW·h）	25~35
	班次总数/个	133
充电桩参数	充电功率/kW	180
最短充电时间	$t c h m i n$ /min	10
缓冲时间	$t 0 b u f f e r$ /min	2
电池SOC变化区间	$λ 2, λ 1$	［0.3， 1.0］

Table 1

Table 2

Bus battery capacity parameters"

车辆编号	$τ k$ /%	$τ k W k$ /（kW·h）		$τ k$ /%	$τ k W k$ /（kW·h）
1	86.2	250	13	93.1	270
2	86.2	250	14	93.1	270
3	86.2	250	15	93.1	270
4	86.2	250	16	93.1	270
5	86.2	250	17	100	290
6	86.2	250	18	100	290
7	86.2	250	19	100	290
8	86.2	250	20	100	290
9	93.1	270	21	100	290
10	93.1	270	22	100	290
11	93.1	270	23	100	290
12	93.1	270	24	100	290

Table 2

Table 3

Table 4

Parameters of algorithm"

参数	权值		权值
$θ 0$	5 500	t	100
$ε$	0.9	$c k$ /（元·辆^-1）	700 000
$ζ$	1/2	$c k b$ /（元·块^-1）	300 000
$N p o p$	80	$T$ /年	8
$μ$	40

Table 4

Table 5

Table 6

Table 7

Fig.4

Fig.5

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序号	时段	电价/（元·（kW·h）^-1）
1	07：00~08：30	1.2
2	08：30~11：00	1.5
3	11：00~12：00	1.2
4	12：00~13：00	1.0
5	13：00~14：30	1.2
6	14：30~21：00	1.5
7	21：00~23：00	1.2
8	23：00~07：00（次日）	1.0

车辆编号	车辆调度计划	充电时间/min
车辆编号	车辆调度计划	峰	谷	平
1	场站发车→24→38→55→75→104→返回场站	0	0	0
2	场站发车→12→30→49→69→92→111→返回场站	0	0	0
3	场站发车→2→充电→25→36→54→70→107→126→返回场站	0	10	0
4	场站发车→15→32→58→充电→80→101→132→返回场站	0	27	0
5	场站发车→16→43→62→充电→86→109→123→返回场站	0	30	0
6	场站发车→10→27→41→充电→83→97→110→131→返回场站	0	30	0
7	场站发车→6→充电→39→57→71→100→114→返回场站	0	10	0
8	场站发车→1→29→51→68→充电→88→102→124→130→返回场站	0	10	0
9	场站发车→9→35→64→90→106→120→返回场站	0	0	0
10	场站发车→8→充电→23→42→60→充电→76→89→13→119→返回场站	0；0	10；11	0；0
11	场站发车→19→48→72→113→返回场站	0	0	0
12	场站发车→7→充电→34→52→74→94→116→128→返回场站	0	10	0
13	场站发车→5→22→37→53→充电→81→98→122→返回场站	0	39	0
16	场站发车→3→21→40→61→78→91→返回场站	0	0	0
17	场站发车→11→26→66→85→112→121→129→返回场站	0	0	0
18	场站发车→13→56→73→87→125→返回场站	0	0	0
19	场站发车→14→31→50→充电→77→99→108→返回场站	0	17	0
20	场站发车→0→充电→28→45→63→79→95→105→返回场站	0	10	0
21	场站发车→20→44→59→充电→82→96→118→返回场站	0	30	0
22	场站发车→4→17→46→67→充电→93→115→127→返回场站	0	24	0
23	场站发车→18→33→47→65→84→117→返回场站	0	0	0

参数	方案A	方案B
总成本/元	11 226.5	11 353.3
日/夜间充电成本/元	804/3 066.1	1 017/2 853.1
总充电成本/元	3 870.1	3 870.1
车辆使用成本/元	5 034.2	5 273.9
电池损耗成本/元	2 322.1	2 209.2

车辆编号	车辆调度计划	充电时间/min
车辆编号	车辆调度计划	峰	谷	平
1	场站发车→10→40→60→充电→82→100→114→返回场站	0	29	0
2	场站发车→5→23→32→48→75→122→返回场站	0	0	0
4	场站发车→16→41→64→充电→88→108→127→返回场站	0	29	0
5	场站发车→14→27→46→充电→84→99→110→返回场站	0	29	0
6	场站发车→11→50→68→充电→86→101→124→返回场站	0	19	0
7	场站发车→28→44→62→充电→78→105→121→返回场站	0	18	0
8	场站发车→6→充电→49→66→充电→85→96→119→返回场站	0；0	10；20	0；0
9	场站发车→18→33→53→充电→76→90→112→126→返回场站	0	11	0
10	场站发车→12→26→37→61→充电→79→93→125→返回场站	0	29	0
11	场站发车→4→19→36→58→73→87→113→返回场站	0	0	0
12	场站发车→7→21→42→72→95→129→返回场站	0	0	0
13	场站发车→22→34→52→67→115→返回场站	0	0	0
14	场站发车→30→45→59→充电→81→98→返回场站	0	29	0
15	场站发车→0→充电→15→38→56→充电→77→返回场站	0	10	0
16	场站发车→1→17→29→54→109→118→返回场站	0	0	0
17	场站发车→13→51→69→充电→89→106→返回场站	0	12	0
18	场站发车→20→39→55→71→94→111→返回场站	0	0	0
19	场站发车→3→24→35→57→充电→80→92→103→116→132→返回场站	0	35	0
20	场站发车→8→充电→74→107→117→128→返回场站	0	10	0
21	场站发车→31→64→91→131→返回场站	0	0	0
22	场站发车→9→43→63→充电→83→102→120→130→返回场站	0	29	0
23	场站发车→2→充电→25→47→70→97→104→123→返回场站	0	10	0

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