Research on Dynamic Modeling and Optimization Algorithm of Freight Trains Considering the Temperature Field of Traction Chains
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摘要: 货运列车在运行中表现出时变行为, 而静态机理模型难以捕捉这些变化, 导致优化结果与列车运行状态不相符. 此外, 不当的驾驶策略可能导致电力设备温度过高. 为此, 提出一种用于评估列车能耗与温度的动态建模方法, 并设计一种大规模自适应多策略多目标竞争群优化器(Large-scale adaptive multi-strategy multi-objective competitive swarm optimizer, LAMOCSO). 具体而言, 首先, 建立“列车−线路−电网”的机理模型, 用于计算多列车运行过程中的功率和网压; 并提出一种融合机理模型、数据驱动模型和补偿模型的混合建模方法, 用于捕捉列车和环境的时变特征. 其次, 建立电力设备的温升模型, 并设计基于拉普拉斯变换的快速求解方法. 然后, 构建一个优化牵引供电系统能效与电力设备温度的多目标优化模型, 并提出一种LAMOCSO 算法, 用于解决多列车长距离运行的大规模多目标优化问题. 最后, 实验验证了动态建模方法的有效性; 通过与四种经典算法的比较, 验证了所提算法的性能; 结果表明多列车综合优化方法可以降低变电所18.2%的能耗, 确保电力设备处于适宜的温度环境.
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关键词:
- 动态建模 /
- 列车节能 /
- 大规模综合优化 /
- 数据驱动 /
- 列车−线路−电网−温度场
Abstract: Freight trains exhibit time-varying behavior during operation, making it difficult for static mechanistic models to capture these variations, which results in optimization results that do not align with train operating conditions. Moreover, improper driving strategies may lead to excessive temperatures in electrical equipment. To address this issue, this paper proposes a dynamic modeling approach for evaluating train energy consumption and temperature and designs a large-scale adaptive multi-strategy multi-objective competitive swarm optimizer (LAMOCSO). Specifically, first, a “train-track-power grid” mechanistic model is established to calculate power and voltage during multi-train operations; Furthermore, a hybrid modeling approach that integrates mechanistic models, data-driven models, and compensation models is proposed to capture the time-varying characteristics of trains and their environment. Next, a thermal rise model for electrical equipment is developed, and a rapid solution method for temperature rise based on the Laplace transformation is designed. Then, a multi-objective optimization model is formulated to optimize both the energy efficiency of the traction power supply system and the temperature of electrical equipment. Furthermore, the LAMOCSO algorithm is proposed to address the large-scale multi-objective optimization problem in long-distance multi-train operations. Finally, experiments validate the effectiveness of the dynamic modeling approach; The performance of the proposed algorithm is verified through comparisons with four classical algorithms; The results demonstrate that the multi-train comprehensive optimization method can reduce substation energy consumption by 18.2%, while ensuring that electrical equipment operates within an appropriate temperature range. -
图 5 平行多导体传输线$\pi$型等效电路
Fig. 5 The $\pi$ equivalent circuit of a parallel multi-conductor transmission line
图 12 变流器各节点的三维温度图
Fig. 12 Three dimensional temperature map of each node of the converter
图 13 变压器各节点的三维温度图
Fig. 13 Three dimensional temperature map of each node of the transformer
图 14 五种算法优化DTLZ2的对比结果
Fig. 14 Comparison results of five algorithms for optimizing DTLZ2
图 23 多车综合优化的帕累托前沿
Fig. 23 Pareto front for comprehensive optimization of multiple trains
图 26 多车功率和网压升降原理分析图
Fig. 26 Diagram for analysis of multi-train power and grid voltage fluctuation principles
表 1 TSK-FNN的输入和输出
Table 1 Input and output of TSK-FNN
采样数据变量 含义 单位 输出 $ P_{\rm{net}}(fs) $ 列车变压器功率 kW $ v(fs) $ 列车速度 km/h 输入 $ R(fs) $ 线路曲线半径 m $ Tu(fs) $ 距隧道入口距离 km $ Sl(fs) $ 线路坡度 ‰ $ Le(fs) $ 距变电所的长度 km $ v(fs-1) $ 上次采样的列车速度 km/h $ F(fs) $ 列车控制力 kN $ AT(fs) $ 列车与AT站的距离 km 
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表 2 算法参数设置
Table 2 Algorithm parameter settings
算法 参数设置 LA-MOCSO N = 300; Net = 100; IT = 400 MOPSO N = 300; Net = 100; IT = 400; $ \omega = 0.4 $; c1 = c2 = 1.429 NSGA-II N = 300; Net = 100; IT = 400; pm = 1/I; d1 = 20; d2 = 20 KMMOPSO N = 300; Net = 100; IT = 400 cd-MOPSO N = 300; Net = 100; IT = 400; $\omega = 0.4$; c1 = c2 = 1.429; pm = 1/I; d1 = 20; d2 = 20
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表 3 IGD指标
Table 3 IGD indicator
测试函数 指标 LAMOCSO MOPSO NSGA-II KAMOCSO cdMOPSO DTLZ1 Mean 1.010E − 2 2.651E + 1 1.432E − 1 1.025E − 2 1.905E − 1 Std. 1.745E − 4 9.108E + 0 6.382E + 0 2.581E − 4 2.386E − 3 Best 8.022E − 3 1.281E − 1 4.153E − 2 8.093E − 3 6.211E − 2 Worst 1.751E − 2 4.581E + 1 2.751E − 1 1.116E − 2 5.214E − 1 DTLZ2 Mean 3.841E − 3 1.001E − 1 1.902E − 1 2.612E − 2 5.701E − 2 Std. 1.348E − 4 2.541E − 3 1.584E − 3 8.284E − 4 8.284E − 3 Best 1.254E − 3 3.284E − 2 5.311E − 2 1.607E − 2 2.201E − 2 Worst 4.017E − 3 2.401E − 1 2.610E − 1 5.113E − 2 8.087E − 2 DTLZ3 Mean 3.589E − 3 4.311E + 1 2.001E + 1 6.477E − 2 1.124E − 2 Std. 7.458E − 5 1.980E + 1 6.825E + 0 6.258E − 4 6.224E − 3 Best 1.285E − 3 4.918E − 1 9.446E − 1 2.517E − 2 8.009E − 3 Worst 3.854E − 3 8.475E + 1 6.481E + 1 8.170E − 2 2.648E − 2 WFG1 Mean 4.180E − 3 7.184E − 1 6.174E − 1 6.987E − 3 8.818E − 3 Std. 6.841E − 5 6.870E − 2 2.841E − 1 3.007E − 4 3.184E − 4 Best 3.481E − 3 4.116E − 1 7.184E − 1 4.318E − 3 8.127E − 3 Worst 8.874E − 3 1.077E + 0 8.367E − 1 8.284E − 3 9.981E − 3 WFG2 Mean 2.641E − 2 8.011E − 2 1.016E − 1 1.329E − 2 5.318E − 2 Std. 6.184E − 3 1.851E − 2 6.218E − 2 5.231E − 3 9.340E − 3 Best 7.954E − 3 6.381E − 2 6.318E − 2 1.084E − 2 3.314E − 2 Worst 1.689E − 2 9.405E − 2 1.841E − 1 1.931E − 2 7.031E − 2
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表 4 HV指标
Table 4 HV indicator
测试函数 指标 LAMOCSO MOPSO NSGA-II KAMOCSO cdMOPSO DTLZ1 Mean 1.184E + 0 6.758E − 1 8.873E − 1 9.241E − 1 7.534E − 1 Std. 3.368E − 3 7.334E − 2 3.227E − 2 6.917E − 3 4.523E − 2 Best 1.351E + 0 8.204E − 1 1.13 E + 0 1.127E + 0 1.011E + 0 Worst 8.014E − 1 4.003E − 1 3.401E − 1 6.740E − 1 8.503E − 2 DTLZ2 Mean 1.771E + 0 2.885E − 1 3.396E − 1 9.981E − 1 3.545E − 1 Std. 4.616E − 3 1.887E − 2 9.603E − 3 1.093E − 3 5.613E − 3 Best 1.971E + 0 6.155E − 1 8.369E − 1 1.532E + 0 9.358E − 1 Worst 1.575E + 0 6.528E − 2 6.126E − 2 3.253E − 1 1.536E − 1 DTLZ3 Mean 1.023E + 0 9.794E − 1 3.433E − 1 9.871E − 1 2.053E − 1 Std. 8.382E − 4 5.554E − 2 9.801E − 3 2.565E − 2 4.469E − 2 Best 1.115E + 0 1.029E + 0 6.472E − 1 1.228E + 0 8.641E − 1 Worst 9.337E − 1 5.704E − 2 5.285E − 2 6.847E − 2 9.356E − 2 WFG1 Mean 9.153E − 1 1.059E − 1 3.463E − 1 7.193E − 1 2.757E − 1 Std. 5.446E − 3 3.863E − 3 1.921E − 1 4.023E − 4 1.256E − 1 Best 1.148E + 0 2.907E − 1 8.036E − 1 1.091E + 0 8.125E − 1 Worst 6.348E − 1 5.284E − 2 1.365E − 1 5.284E − 1 9.553E − 2 WFG2 Mean 8.112E − 1 5.443E − 1 5.616E − 1 6.066E − 1 4.124E − 1 Std. 2.461E − 3 8.270E − 3 8.274E − 3 6.352E − 3 8.918E − 3 Best 9.612E − 1 6.226E − 1 6.759E − 1 9.358E − 1 7.172E − 1 Worst 6.62 E − 1 1.718E − 1 4.570E − 1 4.847E − 1 2.589E − 1
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表 5 牵引供电系统参数与列车参数
Table 5 TPSS parameters and train parameters
牵引网参数 列车参数 供电臂长度 20 km 质量 15988 tAT所位置 10.5/19.5 km 质量回转系数 0.06 额定电压 27.5 kV 最大加速度 0.07 m/s2 牵引变压器阻抗 J9.6 $\Omega$/31.5 MVA 最小加速度 −0.04 m/s2 电力系统阻抗 J9.6 $\Omega$/31.5 MVA 运行时间 1650 /1900 sAT漏抗 0.1+j0.45 $\Omega$ 运行距离 20/40 km 大地导电率 0.1+j0.45 $\Omega$ 发车时间间隔 600 s 钢轨泄漏电阻 10-4 1/$\Omega \cdot$ cm 最大起牵引力 760 kN 接地电阻 2-5 $\Omega$ 最大牵引功率 9600 kW
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表 6 电力设备各节点的发热量和最高温度
Table 6 The heat generation and maximum temperature of each node in power equipment
列车1 列车2 最高温度/℃ 发热量/kWh 最高温度/℃ 发热量/kWh 定子 63.971 5.140 64.006 5.752 绕组 110.446 10.255 110.410 12.523 转子 50.829 0.884 50.980 1.205 变流器结温 111.299 0.884 119.267 0.439 高压绕组 108.209 8.607 108.209 10.464 低压绕组 129.544 18.794 129.544 22.648 铁芯 111.185 6.258 111.185 7.431 绝缘油 40.434 − 40.434 −
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