Optimization Design of Power Supply Partitions and Stator Segments in High-Speed Maglev Traction System
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摘要:
为提升高速磁浮牵引供电系统的经济性，基于改进遗传算法提出一种供电分区与定子段长度的优化设计方法. 首先，通过分析双端供电模式下的等效电路建立牵引系统的数学模型，结合追踪间隔时间与牵引性能约束推导出供电分区的有效范围为20～40 km；然后，基于换步控制与牵引性能约束确定定子段的设计长度为600～
2000 m，在此基础上，采用动态约束自适应遗传算法，以综合经济成本最小化为目标，分别对供电分区与定子段长度进行优化设计；最后，选取沪杭磁浮规划线与上海磁浮示范线作为验证对象，通过硬件在环实验获取列车动态运行数据，对优化前后的牵引系统综合经济成本进行对比分析. 研究结果表明：沪杭线案例中，传统设计方案需设置7个27 km等长供电分区，优化方案调整为6个差异化分区，其中端部区段为20 km，中部区段集中在37 km左右，综合经济成本降幅为14.25%；对于上海磁浮示范线，既有方案采用25个长度约为1200 m的定子段，优化方案生成26个不等长定子段，形成“强流短距、弱流长距”的电流匹配布局，综合经济成本降幅为19.1%.Abstract:To enhance the economic efficiency of the traction power supply system of high-speed maglev, an optimization design method integrating power supply partitions and stator segment length was developed using the improved genetic algorithm. Firstly, a mathematical model of the traction system was established through analysis of equivalent circuits under dual-feeding mode. The effective range of power supply partitions was determined to be 20–40 km through comprehensive consideration of tracking intervals and traction performance constraints. Then, the design length of the stator segment was 600–2 000 m according to step-switching control and traction performance constraints. On this basis, the dynamically-constrained adaptive genetic algorithm was employed to optimize the design of the power supply partitions and stator segment length, so as to minimize the overall economic cost. Finally, the Shanghai–Hangzhou maglev planning line and the Shanghai maglev demonstration line were selected as validation subjects. Through hardware-in-the-loop simulations, dynamic train operation data was acquired to compare the comprehensive economic cost of the traction system before and after optimization. Results show that for the Shanghai–Hangzhou line, the traditional design scheme requires seven 27 km power supply partitions of equal length. In contrast, the optimized scheme uses six differentiated partitions, among which the partition at the ends is 20 km, and the central partition is about 37 km. This reduces the comprehensive economic cost by 14.25%. For the Shanghai maglev demonstration line, the existing scheme uses 25 stator segments with a length of about 1 200 m each. The optimized scheme produces 26 unequal-length segments, forming a current-matched layout with shorter segments for higher current and longer segments for lower current, which reduces the comprehensive economic cost by 19.1%.
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Key words:
- maglev /
- power supply partition /
- stator segment length /
- genetic algorithm /
- nonlinear programming
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图 1 高速磁浮牵引供电系统结构图
Figure 1. Structures of traction power supply system of high-speed maglev
图 2 双端供电模式下的牵引系统电路原理图
Figure 2. Circuit principle of traction system in dual-feeding power supply mode
图 4 基于DC-GA的供电分区优化设计流程图
Figure 4. Flowchart of optimization design for power supply partitions based on DC-GA
图 5 两步法换步时的电机定子电流与牵引力
Figure 5. Stator current and traction force of motor during two-step changing method
图 6 不同运行速度时的定子段最小长度
Figure 6. Minimum length of stator segments under different operating speeds
图 8 高速磁浮列车多分区运行时的速度与位置曲线
Figure 8. Speed and position curves of high-speed maglev in multi-partition operation
图 10 高速磁浮列车单分区运行时的速度与位置曲线
Figure 10. Speed and position curves of high-speed maglev train in single-partition operation
表 1 不同平均速度与追踪间隔下的供电分区最大长度
Table 1. Maximum length of power supply partitions under different average speeds and tracking intervals
追踪间隔/min 供电分区最大长度/km 200 km/h 300 km/h 400 km/h 500 km/h 5 16.7 25.0 33.3 41.6 6 20.0 30.0 40.0 50.0 7 23.3 35.0 46.6 58.3 8 26.6 40.0 53.3 66.6 9 30.0 45.0 60.0 75.0 
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表 2 高速磁浮供电分区长度与最高巡航速度的关系
Table 2. Correlation between power supply partition length and maximum cruising speed of high-speed maglev
供电分区长度/ km 最高运行速度/（ km•h−1） 3编组 5编组 8编组 10 521 508 467 20 514 500 457 30 501 484 443 40 485 468 430 50 469 455 417 60 457 441 406
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表 3 不同运行速度及剩余加速度下的定子段最大长度
Table 3. Maximum length of stator segment under different operating speeds and remaining accelerations
加速度/ （m•s−2） 定子段最大长度/m 100 km/h 200 km/h 300 km/h 430 km/h 500 km/h 0 5000 5000 5000 3550 2150 0.2 5000 5000 4450 2000 1250 0.4 5000 5000 2900 1300 800 0.6 5000 3800 - - -
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表 4 牵引供电系统参数
Table 4. Parameters of traction power supply system
系统参数 数值 单位长度定子绕组电阻/（Ω•km−1） 2.54 × 10−1 单位长度定子绕组电感/（H•km−1） 2.60 × 10−3 单位长度馈电电缆电阻/（Ω•km−1） 5.83 × 10−2 单位长度馈电电缆电感/（H•km−1） 1.42 × 10−4 牵引力系数/（kN•kA−1） 42 变流器容量/MVA 24 列车总质量/t 308 列车编组数 5
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表 5 供电分区设计传统方案与优化方案综合成本对比
Table 5. Comprehensive cost comparison between traditional and optimized schemes for power supply partition design
供电分区长度/km 综合成本/万元 传统方案 [27.00；27.00；27.00；27.00；27.00；27.00；27.00] 19937.26 优化方案 [20.00；37.54；37.09；37.11；37.24；20.00] 17095.34
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表 6 定子段设计现行方案与优化方案综合成本对比
Table 6. Comprehensive cost comparison between traditional and optimized schemes for stator segment design
定子段长度/km 综合成本/万元 传统方案 [ 1036 ；1159 ；1206 ；1223 ；1177 ；1189 ；1238 ；1189 ；1238 ；1192 ；1180 ；1189 ；1188 ；1220 ；1220 ；1161 ；1232 ；1176 ；1235 ；1272 ；1222 ；1218 ；1180 ；1116 ；1177 ]16588.78 优化方案 [900；704；800；790；793；874；884；952； 1064 ；1191 ；1320 ；1338 ；1602 ；1668 ；1792 ；1950；2000；1617 ；1475 ；1356 ；1120 ；985；800；744；681；600]13419.70
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