考虑驾驶策略的高速列车运行图节能优化方法

革新; 张玉召

doi:10.3963/j.jssn.1674-4861.2022.06.012

考虑驾驶策略的高速列车运行图节能优化方法

doi: 10.3963/j.jssn.1674-4861.2022.06.012

革新,
张玉召^,

兰州交通大学交通运输学院兰州 730070

基金项目:

国家自然科学基金项目 71761025

中央引导地方科技发展资金项目 22ZY1QA005

甘肃省教育厅双一流重大科研项目 GSSYLXM-04

详细信息

作者简介:
革新(1995—), 硕士研究生.研究方向: 高速列车时刻表优化.E-mail: gexindmu@163.com

通讯作者:
张玉召(1981—), 博士, 教授.研究方向: 从事轨道交通运输组织与优化研究.E-mail: yuzhaozhang@126.com

中图分类号: U292.4+1
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出版历程
- 收稿日期: 2022-04-22
- 网络出版日期: 2023-03-27

An Energy-saving Method Based on Optimized Timetable for High-speed Trains Considering Driving Strategy

GE Xin,
ZHANG Yuzhao^,

School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China

摘要

摘要: 为了降低高速列车从始发站至终到站运行的牵引能耗, 研究了针对多列车区间运行时分同步分配的列车运行图节能优化方法。基于高速列车在站间采用的“四阶段”操纵策略构建最优驾驶策略集, 以牵引距离和巡航距离为变化因子, 以牵引能耗和区间运行时分为计算目标, 求解出最优驾驶策略集里牵引能耗与区间运行时分的线性关系。在此基础上构建多列车区间运行时分最优分配的节能运行图模型。模型以牵引能耗最低为目标, 考虑了列车总运行时间约束、变量取值范围约束以及安全间隔时分约束。在模型求解方面, 选取拉格朗日松弛算法, 将复杂约束松弛至目标函数当中, 从而把原问题分解为各区间可独立求解的子问题, 利用次梯度优化的方法得出精确解, 实现了多列车区间运行时分同步分配的目标。以宝兰高速铁路为背景进行算例验证, 结果表明: 通过重新分配区间运行时分, 10列车总共节约了595.958 kW·h牵引能耗, 平均节能率达到了1.2%;从运行图的层面分析, 该算例下通过调整区间运行时分的节能方法对其影响幅度较小, 具有较强的现实意义; 所提出的模型及算法的计算时间为10 s, 针对列车开行对数较多的高速铁路, 可有效提高求解效率。
- 高速铁路 /
- 列车运行图 /
- 节能优化 /
- 拉格朗日松弛算法 /
- 牵引能耗
Abstract: In order to reduce the traction-energy consumption for high-speed trains running from the origin station to the destination station, an energy-saving optimization method for train timetable was proposed considering synchronous allocation of the travel time between stations for multiple trains. Firstly, a set of driving strategies are developed based on the "four-stage" maneuvering strategy adopted by high-speed trains. In addition, taking traction distance and cruising distance as change factors, traction energy consumption and travel time between stations are divided into calculation objectives, and the linear relationship between traction energy consumption and travel time between stations in the optimal driving strategy set was solved. Finally, with the goal of minimizing the traction-energy consumption, an energy-saving timetable model for high-speed trains is developed based on the optimal allocation of travel time between stations. The model considers the constraints of the multiple trains' total travel time, variable value range constraints and safety interval time constraints of the train timetable. In terms of model estimation, Lagrange relaxation algorithm is used. The original problem is decomposed into several sub-problems that could be solved independently in each section by relaxing complex constraints into the objective function. Therefore, the exact solution is obtained by subgradient optimization, and the model achieve the goal of synchronous allocation of travel time between stations for multiple trains. In the end, the validity of the proposed model is further examined by a case study of Baoji-Lanzhou high-speed railway corridor. The results show that the 10 trains totally saved 595.958 traction-energy and the average energy-saving rate reached 1.2% by re-allocating the travel time between stations. From the perspective of timetable, the energy saving method by adjusting the travel time between stations is of great practical significance with the reason that it has a small impact on the magnitude of the adjustment of train timetable. In addition, the calculation time of the proposed model and algorithm is 10 s, which can effectively improve the solving efficiency for the high-speed railway with a large number of trains
- high-speed railway /
- train timetable /
- energy saving optimization /
- Lagrangian Relaxation Algorithm /
- traction energy consumption

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图 1 速度-距离曲线

Figure 1. Speed-distance curve

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图 2 牵引能耗-区间运行时分曲线拟合

Figure 2. Curve fitting of traction energy-interval running time

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图 3 不同区间E-T曲线

Figure 3. E-T curves of different interval

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图 4 榆中-通渭的E-T拟合曲线

Figure 4. Fitting curve renderings

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图 5 拉格朗日松弛算法计算过程

Figure 5. The calculation process of the Lagrangian relaxation algorithm

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图 6 优化前后运行区间能耗比较

Figure 6. Comparison of energy consumption between operating stations before and after optimization

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图 7 优化前后运行图

Figure 7. Timetables before and after optimization

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表 1 CRH3动车组参数

Table 1. Parameters of CRH3 EMU

参数名称	参数特性
总重/t	380
长度/m	200
运营速度（/km/h）	350
单位基本阻力/（N/kN）	w₀ = 0.79 + 0.006 40v + 0.000 115v²
牵引制动特性/kN	$\begin{gathered} F_{\text {牵 }}=\left\{\begin{array}{l} -0.285 v+300, 0 \leqslant v \leqslant 119 \\ 31500 / v, 119<v \leqslant 350 \end{array}\right. \\ F_{\text {制 }}=\left\{\begin{array}{l} 59.8 v, 0 \leqslant v \leqslant 5 \\ -0.285 v+300, 5<v \leqslant 106.7 \\ 28800 / v, 106.7<v \leqslant 350 \end{array}\right. \end{gathered} $

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表 2 节能效果

Table 2. Energy saving effect

车次	T (k)/s	优化前		优化后		节能率/%
车次	T (k)/s	运行时分/s	牵引能耗/（kW·h）	运行时分/s	牵引能耗/（kW·h）	节能率/%
1	5 530	（1 480，1 830，740，1 480）	4 867.417	（1 441，1 891，757，1 441）	4 806.669	1.24
2	5 650	（1 480，1 830，740，740，860）	4 791.159	（1 417，1 862，748，749，874）	4 732.758	1.21
3	5 580	（1 480，1 300，880，740，1 480）	4 194.015	（1 466，1 288，893，767，1 466）	4 143.441	1.2
4	5 530	（1 480，1 830，740，1 480）	4 867.417	（1 441，1 891，757，1 441）	4 806.669	1.25
5	5 340	（740，1 800，1 320，1 480）	5 180.776	（747，1 783，1 399，1 411）	5 101.792	1.52
6	5 580	（1 480，1 300，1 320，1 480）	4 597.467	（1 442，1 270，1 427，1 441）	4 507.816	1.84
7	5 530	（1 480，1 830，740，1 480）	4 867.417	（1 441，1 891，757，1 441）	4 806.669	1.25
8	5 230	（1 480，2 270，1 480）	5 432.488	（1 470，2 290，1 470）	5 387.120	0.83
9	5 230	（1 480，2 270，1 480）	5 432.488	（1 470，2 290，1 470）	5 387.120	0.83
10	5 230	（1 480，2 270，1 480）	5 432.488	（1 470，2 290，1 470）	5 387.120	0.83
总计			49 663.132		49067.174	1.2

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表 3 优化前后发到时刻比较

Table 3. Comparison of depart and arrive time before and after optimization

车次	优化前发到时刻	优化后发到时刻	偏离量/s
1	(06:00:00, 06:24:40, 06:26:40, 06:57:10, 06:59:00, 07:11:30, 07:13:30, 07:38:10)	(06:00:00, 06:24:01, 06:26:01, 06:57:32, 06:59:32, 07:12:09, 07:14:09, 07:38:10)	26.25
2	(06:05:00, 06:29:40, 06:31:40, 07:02:10, 07:04:10, 07:16:30, 07:18:30, 07:30:50 07:32:00, 07:47:10)	(06:05:24, 06:29:01, 06:31:30, 07:02:32 07:04:32, 07:19:25, 07:21:25, 07:33:54 07:35:54, 07:50:28)	108.3
3	(06:10:00, 06:34:40, 06:36:40, 06:58:20, 07:08:32, 07:23:12, 07:30:27, 07:42:47 07:44:47, 08:09:27)	(06:10:24, 06:34:50, 06:36:50, 06:58:18, 07:09:30, 07:24:23, 07:32:26, 07:45:13 07:47:13, 08:11:39)	71.9
4	(06:17:00, 06:41:40, 06:45:42, 07:16:12, 07:18:12, 07:30:32, 07:32:32, 07:57:12)	(06:17:49, 06:41:50, 06:45:52, 07:17:23, 07:19:23, 07:32:00, 07:34:00, 07:58:01)	55
5	(06:22:00, 06:34:20, 06:41:32, 07:11:32, 07:15:47, 07:37:47, 07:39:47, 08:04:27)	(06:22:49, 06:35:16, 06:42:47, 07:12:30, 07:16:54, 07:40:13, 07:42:13, 08:05:44)	84.25
6	(06:37:48, 07:02:28, 07:04:28, 07:26:08, 07:28:08, 07:50:08, 07:52:08, 08:16:48)	(06:39:03, 07:03:05, 07:05:05, 07:26:15, 07:28:15, 07:52:02, 07:54:02, 08:18:03)	58.25
7	(06:42:48, 07:07:28, 07:17:30, 07:48:00, 07:57:09, 08:09:29, 08:11:29, 08:36:09)	(06:44:04, 07:08:05, 07:18:08, 07:49:38, 07:58:48, 08:11:25, 08:13:54, 08:37:55)	83.63
8	(06:55:50, 07:20:30, 07:26:39, 08:04:29, 08:06:29, 08:31:09)	(06:56:37, 07:21:07, 07:28:15, 08:06:25, 08:08:25, 08:32:55)	86.33
9	(07:04:59, 07:29:39, 07:36:39, 08:14:29, 08:16:29, 08:41:09)	(07:06:45, 07:31:15, 07:38:44, 08:16:54, 08:18:54, 08:43:24)	85.21
10	(07:14:50, 07:39:39, 07:41:39, 08:19:29, 08:21:29, 08:46:09)	(07:17:14, 07:41:44, 07:43:44, 08:21:54, 08:23:54, 08:48:24)	87.42

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