超导电动悬浮非对称系统多目标优化设计

王津; 葛琼璇; 赵鲁

doi:10.3969/j.issn.0258-2724.20240477

超导电动悬浮非对称系统多目标优化设计

doi: 10.3969/j.issn.0258-2724.20240477

王津^{1, 2,},
葛琼璇^{1, 2, ,},
赵鲁¹

1.
中国科学院电工研究所高密度电磁动力与系统全国重点实验室，北京 100190
2.
中国科学院大学，北京 100049

基金项目: 国家重点研发计划（2023YFB4302501-02）

详细信息

作者简介:
王津（1994—），女，博士研究生，研究方向大功率电力电子与直线驱动，E-mail：wj2021syg@mail.iee.ac.cn

通讯作者:
葛琼璇（1967—），女，研究员，博士生导师，研究方向为高压大功率变流器控制技术、高性能电机牵引控制技术，E-mail： gqx@mail.iee.ac.cn

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出版历程
- 收稿日期: 2024-09-24
- 修回日期: 2025-03-07
- 网络出版日期: 2025-05-14

Multi-objective Optimization of Asymmetric Null-Flux Coils for Superconducting Electrodynamic Suspension System

WANG Jin^{1, 2
,},
GE Qiongxuan^{1, 2
, ,},
ZHAO Lu¹

1.
State Key Laboratory of High Density Electromagnetic Power and Systems, Institute of Electrical Engineering, Chinese Academy of Sciences, Haidian District, Beijing 100190, China
2.
University of Chinese Academy of Sciences, Shijingshan District, Beijing 100049, China

摘要

摘要:
为提高超导电动悬浮系统性能，基于全局灵敏度分析和多目标优化算法，提出一种非对称悬浮线圈优化设计方法. 首先，基于空间谐波法建立超导电动悬浮系统的数学模型，计算超导磁体的磁感应强度以及悬浮线圈的电磁力；其次，对此模型进行非对称优化设计，采用Sobol’敏感性分析方法，以悬浮力和每公里悬浮线圈质量为目标，计算各设计参数的灵敏度，并基于灵敏度分析结果进行非支配排序遗传算法Ⅱ（NSGA-Ⅱ）优化设计；最后，通过有限元进行仿真分析，验证空间谐波法解析模型，并对优化前后的模型进行比较. 研究结果表明：空间谐波法建立的悬浮系统模型与有限元模型具有一致性；相比优化前，优化后的非对称悬浮系统悬浮力提高8.3%，每公里铺设线圈质量降低12.9%；垂直位移0.02～0.04 m时，悬浮力由262.2 kN增加到270.2 kN，磁阻力由4.5 kN增加到5.4 kN；水平位移0.17～0.20 m时，悬浮力由306.5 kN减小到228.8 kN，磁阻力由6.2 kN减小为4.6k N；悬浮力、磁阻力的波动分别约为6%、65%. 研究揭示了悬浮力和磁阻力随着位移方向的变化规律，验证了非对称设计在提升悬浮力和轻量化方面的优势，为超导电动悬浮系统的优化设计提供理论参考.
- 电动悬浮 /
- 灵敏度分析 /
- 非支配排序遗传算法II /
- 有限元仿真 /
- 超导磁体
Abstract:
In order to improve the performance of superconducting electrodynamic suspension system, an optimal design method of asymmetric null-flux coils was proposed based on global sensitivity analysis and multi-objective optimization algorithm. Firstly, the mathematical model of superconducting electrodynamic suspension system was established based on space harmonic method. Then the magnetic flux intensity of the superconducting magnets and electromagnetic forces of the null-flux coils were calculated. Secondly, the model was designed asymmetrically. Sobol' sensitivity analysis method was used to calculate the sensitivity of each design parameter with the levitation force and the mass of the null-flux coils per kilometer as the objectives. Based on the optimization parameters obtained from the sensitivity analysis, NSGA-II optimization design was carried out and the optimization results were obtained. Finally, finite element method was carried out to verify the analytic model of space harmonic method. The model before and after optimization was compared. The results indicated that the suspension system model established by space harmonic method was consistent with the finite element model. Compared with the initial system, the levitation force of the optimized asymmetric suspension system was increased by 8.3%, the mass of null-flux coils per kilometer was reduced by 12.9%, the levitation force increased from 262.2 kN to 270.2 kN and the drag force increased from 4.5 kN to 5.4 kN when the vertical deviation was 0.02～0.04 m. The levitation force decreased from 306.5 kN to 228.8 kN and the drag force decreased from 6.2 kN to 4.6 kN when the horizontal deviation was 0.17～0.2 m. The levitation force fluctuation was about 6% and the drag force fluctuation was about 65%. It revealed the variation patterns of levitation and drag forces with respect to offset directions, demonstrating the advantages of asymmetric design in enhancing levitation force and achieving lightweight performance. This provided a theoretical reference for the optimal design of superconducting electrodynamic suspension systems.
- electrodynamic suspension /
- sensitivity analysis /
- nondominated sorting genetic algorithm II /
- finite element method /
- superconducting magnets.

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图 1 EDS系统截面

Figure 1. Cross-section of EDS.

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图 2 EDS单侧结构

Figure 2. Single-side EDS system structure diagram.

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图 3 超导线圈与8字线圈的几何关系和对应参数

Figure 3. Structure diagram and geometry parameters of the SCMs and NFCs

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图 4 不同采样规模下质量和悬浮力的灵敏度分析

Figure 4. Sensitivity of the levitation of different sampling size

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图 5 悬浮力、线圈电感与线圈截面宽度的关系

Figure 5. Relationships between the levitation force, inductance and cross-section width

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图 6 基于Sobol’的NSGA-Ⅱ流程

Figure 6. The Sobol’-based NSGA-II algorithm flow chart

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图 7 悬浮力与质量的Pareto前沿

Figure 7. Pareto front of levitation force to mass.

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图 8 空间谐波法与有限元模型对比

Figure 8. Comparison of space harmonic technique and finite element model.

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图 9 悬浮力优化前后对比

Figure 9. Comparison of the levitation force of the initial system and the optimal system.

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图 10 磁阻力优化前后对比

Figure 10. Comparison of the drag force of the initial system and the optimal system

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表 1 EDS系统关键参数

Table 1. Main parameters of EDS

线圈	符号	描述	幅值
8字线圈	a₁	长度与极距比例	0.778
	b_1u	上线圈高度占比	0.500
	b_1b	下线圈高度占比	0.500
	b₁	上下线圈总高度/m	0.680
	z_u	上线圈中心高度/m	0.380
	z_b	下线圈中心高度/m	0.380
	c₁	线圈截面长度/m	0.060
	c₂	线圈截面宽度/m	0.040
	N_g	线圈匝数	24
	S_g	截面线圈每匝面积/mm²	100
	τ₁	极距/m	0.450
	g	上下线圈间隙/m	0.080
	r₁	线圈圆角半径/m	0.115
超导线圈	a₀	长度与极距比例	0.793
	b₀	高度/m	0.500
	d₁	线圈截面长度/m	0.040
超导线圈	d₂	线圈截面宽度/m	0.070
	N_s	线圈匝数	1400
	I_s	额定电流/A	500
	τ₀	极距/m	1.350
	y₁	8字线圈与超导线圈水平距离/m	0.185
	Δz	8字线圈与超导线圈中心垂直位移/m	0

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表 2 设计参数及其变量范围

Table 2. Value range of design parameters

参数	变量范围	参数	变量范围
a₁	[0.700,0.900]	g/m	[0.060,0.100]
b_1u	[0.200,0.300]	τ₁/m	[0.400,0.600]
b₁/m	[0.200,0.800]	a₀	[0.700,0.800]
r₁/m	[0.100,0.200]	b₀/m	[0.200,0.600]
n₁/匝数	[2,12]

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表 3 优化方案参数

Table 3. Indicator comparison of initial and optimization scheme

参数	目标值	参数	目标值
a₁	0.580	τ₁/m	0.600
b_1u	0.350	a₀	0.800
n₁/匝	12	b₀/m	0.500

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