Electric Bus Scheduling Optimization in Cold-Region Cities Based on Battery-Vehicle Matching

doi:10.12141/j.issn.1000-565X.250244

Abstract

Abstract:

To address the challenges such as accelerated battery lifespan degradation and significant fluctuations in driving range caused by extreme temperature variations in cold-region electric buses, this study proposes an integrated scheduling strategy based on “battery-vehicle matching”. This strategy involves equipping buses with batteries of different capacities according to seasonal temperatures and route load demands, enabling public transport operators to formulate more efficient operational plans. In terms of modeling, a mixed-integer programming model is established with the objective of minimizing operator cost. The model comprehensively calculates vehicle battery procurement expenses, daily maintenance costs, and charging expenses that consider time-of-use electricity pricing and demand charges. It quantifies both cyclic and calendar degradation of batteries and integrates them into a comprehensive battery lifespan degradation function incorporated into the overall cost calculation. For algorithm design, a hybrid genetic algorithm ( HGA ) incorporating a post-processing refinement strategy is developed to efficiently solve this NP-hard model. A case study based on actual bus routes in Harbin demonstrates that the optimized strategy reduces the annualized total cost by 17.8%, decreases the required fleet size by 16.4%, and lowers maintenance costs by 16.8%. It is obvious that the dual battery configuration reduces the annualized degradation cost of battery ownership cost by 39.7 %, effectively extending the actual service life of battery assets. Sensitivity analysis shows that appropriately relaxing the state-of-charge (SOC) upper limit during moderate-temperature seasons (e.g., spring and autumn) can reduce cycling frequency, thereby better mitigating battery aging. Finally, the applicability of the model to larger-scale scenarios is discussed. This study provides a theoretical model and optimization tool for the sustainable operation of electric buses in cold regions, and plays an important role in formulating seasonal operation strategies for operators.

Key words: electric bus, vehicle scheduling, genetic algorithm, battery degradation, hybrid battery configuration

CLC Number:

U491.1⁺7

HU Baoyu, ZHANG Yuheng. Electric Bus Scheduling Optimization in Cold-Region Cities Based on Battery-Vehicle Matching[J]. Journal of South China University of Technology(Natural Science Edition), 2026, 54(3): 91-103.

Figures/Tables 16

Fig. 1

Fig. 2

Table 1

Table 2

Time-of-use electricity rates"

$t$	$Ψ / (元 · k W - 1 · h - 1)$
06：00 — 07：00，09：00 — 11：30，15：30 — 20：00	1.137
07：00 — 09：00，11：30 — 15：30，20：00 — 22：30	0.766
22：30 — 06：00	0.395

Table 2

Table 3

Demand charge"

参数	取值		取值
$μ b a s e / (元 · k W - 1 · 月 - 1)$	33	$μ p e a k / (元 · k W - 1 · 月 - 1)$	1.3 $μ b a s e$
$P m a x / k W$	60	$μ v a l l e y / (元 · k W - 1 · 月 - 1)$	0.75 $μ b a s e$
$P c o n / k W$	1 000	$μ o v e r / (元 · k W - 1 · 月 - 1)$	45

Table 3

Table 4

Seasonal temperature distribution"

$s$	温度范围/℃	平均温度 $/ ℃$
春季	8~23	16
夏季	22~36	30
秋季	-1~16	5
冬季	-36~-6	-25

Table 4

Table 5

Model parameters"

参数	取值		取值
$γ 1$	-4.09e-4	$α 1$	37.73
$γ 2$	-2.167	$β 1$	3 332.31
$γ 3$	1.408e-5	$α 2$	41.56
$γ 4$	6.13	$β 2$	-2.73

Table 5

Fig. 3

Table 6

Comparison of optimization results"

解	总车队规模/辆	电池数量/块	电池拥有成本退化值/（元· $年 - 1$ ）	车辆维护费/（元· $年 - 1$ ）	充电费用/（元· $年 - 1$ ）	需求费用/（元· $年 - 1$ ）
$A 0$	134	134（小）	2.82×10⁶	7.37×10⁶	6.89×10⁶	3.95×10⁵
$A 0 (大)$	111	111（大）	1.84×10⁶	6.10×10⁶	5.62×10⁶	2.98×10⁵
$A 0 (小)$	129	129（小）	2.37×10⁶	7.10×10⁶	6.37×10⁶	6.54×10⁵
$A 1$	112	91（大） 26（小）	1.70×10⁶	6.13×10⁶	5.74×10⁶	5.73×10⁵
解	$F 春 / (元 · 日 - 1)$	$F 夏 / (元 · 日 - 1)$	$F 秋 / (元 · 日 - 1)$	$F 冬 / (元 · 日 - 1)$	$F 总 / (元 · 年 - 1)$	初始总购置费用/元
$A 0$	94 202	109 461	95 824	113 699	3.76×10⁷	1.82×10⁸
$A 0 (大)$	92 017	101 147	91 122	106 851	3.56×10⁷	1.61×10⁸
$A 0 (小)$	93 842	104 146	92 255	109 789	3.64×10⁷	1.74×10⁸
$A 1$	81 798	86 128	81 694	87 470	3.09×10⁷	1.61×10⁸

Table 6

Fig. 4

Fig. 5

Fig. 6

Table 7

Comparison of results for temperature ranges"

季节

S 1 (± 0 ℃)

S 2

（-10

℃

）

S 3

（-5

℃

）

S 4

（+5

℃

）

S 5

（+10

℃

）

春季

91大

19小

89大

21小

90大

20小

92大

18小

91大

19小

夏季

88大

24小

91大

21小

89大

23小

85大

27小

82大

30小

秋季

87大

23小

84大

26小

83大

27小

89大

21小

91大

19小

冬季

86大

26小

79大

33小

82大

30小

87大

25小

88大

24小

Table 7

Fig. 7

Table 8

Fig. 8

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线路	51路	379路	364路	120路
单程长度/km	25.5	23	28	24.6
单程行程时间/h	1.5	1.27	1.3	1.5
平均行程速度/（km·h^-1）	17	18.4	21.5	16.4
发车频率/（车次·h^-1）	9	11~13	6	6~7

场站	所在区域	主要线路
通江湿地	道里区	23路、42路、47路、126路、旅游观光2线
博物馆环岛	南岗区	6路、7路、8路、10路、14路、104路
哈西公路客运站	南岗区	11路、31路、120路、336路、51路、379路、364路
平房新疆大街	平房区	210路、220路、343路、370路、399路
松北科技创新城	松北区	35路、146路、环线1/2路、商务班车S5