计及悬浮系统影响的高速磁浮直线同步电机建模方法

康劲松; 丁浩; 倪菲; 汪凤翔

doi:10.3969/j.issn.0258-2724.20230431

计及悬浮系统影响的高速磁浮直线同步电机建模方法

doi: 10.3969/j.issn.0258-2724.20230431

康劲松^{1, 2,},
丁浩^{2, 3},
倪菲^4, ,,
汪凤翔⁵

1.
同济大学铁道与城市轨道交通研究院，上海 201804
2.
同济大学磁浮技术铁路行业重点实验室，上海 201804
3.
同济大学电子与信息工程学院，上海 201804
4.
同济大学国家磁浮交通工程技术研究中心，上海 201804
5.
中国科学院海西研究院电机驱动与功率电子国家地方联合工程研究中心，福建泉州 362200

基金项目: 国家自然科学基金（52277196）；上海市自然科学基金（21ZR1466900）

详细信息

作者简介:
康劲松（1972—），男，教授，博士，研究方向为高速磁浮直线电机系统及控制，E-mail：kjs@tongji.edu.cn

通讯作者:
倪菲（1985—），女，副研究员，博士，研究方向为磁浮列车鲁棒控制与可靠性分析，E-mail：fei.ni@tongji.edu.cn

中图分类号: TM359.4
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- 被引次数: 0
出版历程
- 收稿日期: 2023-08-26
- 修回日期: 2024-04-07
- 网络出版日期: 2024-05-11
- 刊出日期: 2024-04-19

Modeling of High-Speed Maglev Linear Synchronous Motors Considering Influence of Suspension System

KANG Jinsong^{1, 2
,},
DING Hao^{2, 3},
NI Fei^{4
, ,},
WANG Fengxiang⁵

1.
Institute of Rail Transit, Tongji University, Shanghai 201804, China
2.
Key Laboratory of Railway Industry of Maglev Technology, Tongji University, Shanghai 201804, China
3.
College of Electronic and Information Engineering, Tongji University, Shanghai 201804, China
4.
National Maglev Transportation Engineering R & D Center, Tongji University, Shanghai 201804, China
5.
Quanzhou Institute of Equipment Manufacturing, Haixi Institutes, Chinese Academy of Sciences, Quanzhou 362200, China

摘要

摘要:
为提高高速磁浮直线同步电机模型精度，基于电磁铁模块磁共能重构，提出一种计及悬浮系统影响的分布参数建模方法. 首先，建立高速磁浮列车电磁铁模块的有限元模型，利用有限元数值分析获取电磁铁模块在不同工况下的磁共能数据，通过对磁共能进行傅里叶级数展开及多项式拟合构建磁共能的解析模型；其次，根据磁共能解析模型推导电磁铁模块的磁链、电压和推力方程；然后，根据列车编组数量和电磁铁模块数量分别建立左右两侧直线同步电机的数学模型，并通过运动学方程计算高速磁浮列车位置和速度；最后，通过硬件在环仿真系统进行实验验证. 试验结果表明：本文所提建模方法与传统建模方法相比，推力波动幅值增加超过6.8%；并且所提方法可以准确表征悬浮系统对牵引控制的影响，当励磁电流谐波幅值增加0.5、1.0、2.0 A时，推力波动幅值分别最大增加54.3%、26.2%、83.7%；当励磁电流谐波频率为5、10、20 Hz时，推力的谐波频率最大达到5.14%，21.75%和14.17%.
- 磁悬浮 /
- 直线电机 /
- 牵引控制 /
- 悬浮系统 /
- 建模方法
Abstract:
To enhance the modeling accuracy of high-speed maglev linear synchronous motors, a distributed parameter modeling method considering the influence of the suspension system was proposed based on the magnetic co-energy reconstruction of the electromagnetic module. Firstly, a finite element model of the electromagnetic module of a high-speed maglev train was established. Finite element numerical analysis was conducted to obtain magnetic co-energy data of the electromagnet module under different operating conditions. The magnetic co-energy was then subjected to Fourier series expansion and polynomial fitting to construct an analytical model of the magnetic co-energy. Subsequently, based on the analytical model of the magnetic co-energy, equations for the flux linkage, voltage, and thrust force of the electromagnetic module were derived. Then, mathematical models for the left and right linear synchronous motors based on the number of train formations and the number of electromagnetic modules were established, and the position and velocity of the high-speed maglev train were calculated through kinematic equations. Finally, the proposed modeling method was validated through experiments using a hardware-in-the-loop simulation system. The experimental results indicate that compared to traditional modeling methods, the proposed modeling method increases the amplitude of thrust fluctuations by more than 6.8%. Moreover, the proposed method can accurately characterize the influence of the suspension system on traction control. When the harmonic amplitude of the excitation current increases by 0.5 A, 1.0 A, and 2.0 A, the maximum increase in the amplitude of thrust fluctuations is 54.3%, 26.2%, and 83.7%, respectively. Furthermore, when the harmonic frequency of the excitation current is at 5 Hz, 10 Hz, and 20 Hz, the harmonic frequency of the thrust reaches up to 5.14%, 21.75%, and 14.17%, respectively.
- magnetic levitation /
- linear motors /
- traction control /
- suspension system /
- modeling method

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图 1 电磁铁及长定子模型

Figure 1. Model of electromagnet and long stator

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图 2 不同工况下的磁共能示意

Figure 2. Magnetic co-energy under different operating conditions

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图 3 高速磁浮直线同步电机建模流程

Figure 3. Modeling flowchart of high-speed maglev linear synchronous motor

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图 4 不同电流工况下的磁共能误差分布

Figure 4. Distribution of magnetic co-energy error under different current conditions

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图 5 实验平台

Figure 5. Experimental platform

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图 6 加速阶段下不同编组数时的推力

Figure 6. Thrust force at different formations during acceleration

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图 7 不同建模方法下的推力对比

Figure 7. Comparison of thrust force with different modeling methods

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图 8 不同励磁电流谐波时的推力对比

Figure 8. Comparison of thrust force at different excitation current harmonics

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表 1 电磁铁模块主要参数

Table 1. Main parameters of electromagnet module

参数名称	数值	参数名称	数值
额定励磁电流/A	20	动子极距/mm	266.5
定子绕组匝数/匝	1	铁芯厚度/mm	185
励磁绕组匝数/匝	270	定子槽距/mm	86
定子极距/mm	258	额定气隙/mm	10

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表 2 不同励磁电流时的推力谐波含量和波动对比

Table 2. Comparison of thrust harmonics and fluctuations at different excitation currents

阶段	类型	推力谐波占比/%			推力波动/kN
阶段	类型	f =5 Hz	f =10 Hz	f =20 Hz	推力波动/kN
加速	谐波 1	1.43	0.21	0.10	25.60
	谐波 2	0.54	2.48	0.30	32.40
	谐波 3	0.29	0.16	5.14	39.30
匀速	谐波 1	4.48	2.04	1.27	20.69
	谐波 2	1.84	9.66	1.43	26.45
	谐波 3	2.10	0.63	21.75	31.46
减速	谐波 1	3.86	0.10	1.01	22.00
	谐波 2	0.59	7.98	0.37	33.40
	谐波 3	0.48	0.63	14.17	48.50

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