不确定载重下面向峰值功率抑制的列车节能优化方法

doi:10.16097/j.cnki.1009-6744.2026.03.005

交通运输系统工程与信息 ›› 2026, Vol. 26 ›› Issue (3): 47-59.DOI: 10.16097/j.cnki.1009-6744.2026.03.005

不确定载重下面向峰值功率抑制的列车节能优化方法

莫鹏里^*1,2，连得亨²，王维巧³，杨立兴² ，高自友²

1. 南京航空航天大学，经济与管理学院，南京210016；2.北京交通大学，系统科学学院，北京100044； 3. 北京工业大学，城市交通学院，北京100124

收稿日期:2026-01-11 修回日期:2026-02-14 接受日期:2026-04-16 出版日期:2026-06-25 发布日期:2026-06-22
作者简介:莫鹏里（1994—），男，山东泰安人，副研究员，博士。
基金资助:
国家自然科学基金青年科学基金(72301065)；江苏省基础研究计划（自然科学基金） (BK20230852)。

Energy-Efficient Train Operation Method for Peak Power Shaving Under Uncertain Passenger Demand

MO Pengli^*1,2, LIAN Deheng², WANG Weiqiao³, YANG Lixing², GAO Ziyou²

1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; 2. School of Systems Science, Beijing Jiaotong University, Beijing 100044, China; 3. College of Metropolitan Transportation, Beijing University of Technology, Beijing 100124, China

Received:2026-01-11 Revised:2026-02-14 Accepted:2026-04-16 Online:2026-06-25 Published:2026-06-22
Supported by:
Young Scientists Fund of the National Natural Science Foundation of China (72301065)；Jiangsu Provincial Basic Research Program (Natural Science Foundation) (BK20230852)。

摘要/Abstract

摘要： 载重不确定性常导致列车瞬时功率持续波动，且多列车牵引过程在同一供电区段的时间重叠会放大功率波动幅度，更易引发瞬时功率超限。为兼顾能耗最小化与峰值功率削减，本文在速度曲线选择框架下构建含峰值功率约束的节能优化模型，并采用基于Wasserstein模糊集的分布鲁棒优化方法刻画列车载重概率分布的不确定性。针对峰值功率约束需在细粒度时间尺度上评估而导致的模型规模膨胀问题，本文进一步提出结合时域缩减策略的动态规划算法。该方法利用牵引功率在供电区间内的结构与周期性特性，识别并保留影响峰值判定的关键时间节点，并严格证明缩减后时域在峰值功率约束下与原始时域具有一致的可行域，在保持模型准确性的前提下有效降低检验规模。基于北京地铁亦庄线的仿真结果表明：相较于基础动态规划方法，所提算法在处理大规模实例时，效率提升约47.4%；相较于随机优化与鲁棒优化模型，分布鲁棒优化模型在维持低能耗的同时，可将最小瞬时功率稳定性比例提高至98.99%，在节能与峰值功率削减之间实现更均衡的优化表现。灵敏度分析表明，通过合理配置峰值功率上限与置信水平等削峰参数，可在能耗控制与供电安全之间获得稳定且可行的运行方案。

关键词: 铁路运输, 列车节能运行, 速度曲线优化, 峰值功率削减, 分布鲁棒优化, 动态规划

Abstract: Uncertainty in passenger load often leads to continuous fluctuations in instantaneous train power, which are further amplified when multiple trains operate simultaneously within the same power-supply section, increasing the likelihood of instantaneous power violations. To jointly address energy consumption minimization and peak power shaving, this study develops an energy-efficient optimization model with peak-power constraints within a speed profile selection framework. A distributionally robust optimization method based on the Wasserstein ambiguity set is used to characterize the uncertainty of train passenger-load probability distributions. To mitigate this challenge where evaluating peak-power constraints requires fine-grained temporal resolution and causes the model size explosion, this study proposes an exact dynamic programming algorithm enhanced with a time-domain reduction strategy. By exploiting the structural and periodic characteristics of traction power within each power supply section, the method identifies and retains only the time instants that are critical for peak-power evaluation. It further establishes that the reduced time set yields the same feasible solution space as the full temporal domain with respect to peak-power constraints, thereby reducing computational burden while preserving model fidelity. Numerical experiments based on the Beijing Subway Yizhuang Line demonstrate the effectiveness of the proposed approach. Relative to a baseline dynamic programming method, the proposed algorithm improves computational efficiency by approximately 47.4% in large-scale instances. Compared with stochastic and robust optimization models, the distributionally robust optimization model consistently achieves lower energy consumption while raising the minimum instantaneous power stability ratio to 98.99%, delivering a more balanced performance between energy saving and peak-power regulation. Sensitivity analyses further indicate that appropriate tuning of peak-power limits and confidence levels enables reliable trade-offs between energy efficiency and power-supply stability, confirming the practical applicability of the proposed framework for energy-efficient train operation.

Key words: railway transportation, energy-efficient train operation, speed curve optimization, peak power shaving, distributionally robust optimization, dynamic programming

中图分类号:

U268.6

莫鹏里, 连得亨, 王维巧, 杨立兴, 高自友. 不确定载重下面向峰值功率抑制的列车节能优化方法[J]. 交通运输系统工程与信息, 2026, 26(3): 47-59.

MO Pengli, LIAN Deheng, WANG Weiqiao, YANG Lixing, GAO Ziyou. Energy-Efficient Train Operation Method for Peak Power Shaving Under Uncertain Passenger Demand[J]. Journal of Transportation Systems Engineering and Information Technology, 2026, 26(3): 47-59.

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http://www.tseit.org.cn/CN/Y2026/V26/I3/47

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不确定载重下面向峰值功率抑制的列车节能优化方法

Energy-Efficient Train Operation Method for Peak Power Shaving Under Uncertain Passenger Demand

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