基于参数优先级划分的飞轮电机多目标优化

张维煜; 李凯; 杨鑫

doi:10.3969/j.issn.0258-2724.20220845

基于参数优先级划分的飞轮电机多目标优化

doi: 10.3969/j.issn.0258-2724.20220845

江苏大学电气信息工程学院，江苏镇江 212013

基金项目: 国家自然科学基金（52077099）

详细信息

作者简介:
张维煜（1986—），女，教授，博导，研究方向为磁悬浮飞轮电池系统，E-mail：zwy@ujs.edu.cn

中图分类号: TM30；TP18
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- 被引次数: 0
出版历程
- 收稿日期: 2022-12-05
- 修回日期: 2023-03-24
- 网络出版日期: 2023-06-21
- 刊出日期: 2023-03-30

Multi-Objective Optimization for Flywheel Motors Based on Parameter Priority Division

School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China

摘要

摘要:
为改善电机转矩性能，同时降低永磁材料成本，首先，根据飞轮电池的运行模式，提出飞轮电机的设计要求，并选取输出转矩、转矩脉动和永磁体用量为设计目标；在此基础上，采用等效磁路法和有限元法计算电机的主要尺寸和性能，同时确定合适的槽极配合以及初始结构参数；其次，使用相关系数法分析该电机各结构参数与优化目标之间的相关性，并合理划分转子尺寸和定子尺寸的优先级；最后，采用有限元代理模型和多目标优化算法（非支配排序遗传算法Ⅱ，NSGA-Ⅱ）相结合的方法对设计参数进行逐级寻优，并通过场路联合仿真和样机实验进行验证. 研究结果表明：采用参数优先级划分的方式可以减少优化过程中数据点的采样，缩短了整个过程中有限元分析的时间；优化后，电机反电势梯形化程度更高，转矩脉动减小了40%，永磁体用量降低了8%.
- 飞轮电池 /
- 永磁同步电机 /
- 参数优先级划分 /
- 多目标优化
Abstract:
This paper aims to improve the torque performance of a flywheel motor and reduce its permanent magnet cost. Firstly, according to the operating mode of the flywheel battery, the design requirements of the flywheel motor were proposed, and the output torque, torque ripple, and consumption of permanent magnets were selected as the design objectives. On this basis, the equivalent magnetic circuit method and finite element method were used to calculate the main size and performance of the motor, and the appropriate number of slots and poles and initial structural parameters were determined. Secondly, the correlation coefficient method was utilized to analyze the correlation between the structural parameters of the motor and the optimization objectives, and the priority of rotor sizes and stator sizes was divided reasonably. Finally, the finite element surrogate model and the multi-objective optimization algorithm, namely the non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) were used to optimize the design parameters step by step, and the correctness of optimization results was verified by the field-circuit co-simulation method and prototype experiment. The results show that the proposed method of parameter priority division can reduce the sampling of data points in the optimization process and shorten the time of finite element analysis in the whole process. After optimization, the back electromotive force of the motor is more trapezoidal. The torque ripple is reduced by 40%, and the consumption of permanent magnets is reduced by 8%.
- flywheel battery /
- permanent magnet synchronous motor /
- parameter priority division /
- multi-objective optimization

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图 1 飞轮电池结构示意

Figure 1. Structure of flywheel battery

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图 2 飞轮电池运行模式、电机设计要求和运行状态三者间的关系

Figure 2. Relationship among operating modes of flywheel battery, design requirements, and operating states of motor

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图 3 电机有限元模型和空载磁密云图

Figure 3. Finite element model of motor and magnetic field distribution of motor under no load

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图 4 表贴式永磁同步电机参数化模型

Figure 4. Parameterized model of SPMSM

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图 5 设计变量对目标的灵敏度

Figure 5. Sensitivity of design variables to objectives

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图 6 DOE采样点的分布

Figure 6. Distribution of sampling points by DOE

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图 7 NSGA-Ⅱ的流程

Figure 7. Flowchart of NSGA-Ⅱ

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图 8 优先级1有限元代理模型

Figure 8. Finite element surrogate model in priority 1

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图 9 优先级1帕累托前沿

Figure 9. Pareto front in priority 1

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图 10 优先级2有限元代理模型

Figure 10. Finite element surrogate model in priority 2

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图 11 优先级2帕累托前沿

Figure 11. Pareto front in priority 2

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图 12 优化前后反电势波形和谐波分析

Figure 12. Back electromotive force waveforms and harmonics analysis before and after optimization

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图 13 优化前后转矩波形和谐波分析

Figure 13. Torque waveforms and harmonics analysis before and after optimization

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图 14 飞轮电池样机和电机样机

Figure 14. Prototypes of flywheel battery and motor

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图 15 联合仿真驱动控制框图

Figure 15. Co-simulation drive and control

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图 16 实测和仿真波形

Figure 16. Measured and simulated waveforms

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图 17 不同电流时电机转矩仿真值和实测计算值对比

Figure 17. Comparison of simulated and measured torque values of motor with different currents

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表 1 SPMSM主要尺寸参数

Table 1. Main size parameters of SPMSM

参数	电机
参数	12 极 14 槽	24 极 28 槽
转速/（r·min⁻¹）	4000
驱动方式	无刷直流
有效轴长/mm	8
转子外径/mm	100
定子外径/mm	73
定子内径/mm	40
气隙长度/mm	0.5
永磁体用量/kg	0.02
导体线径/mm	0.6 （8 股并绕）
电流密度/（A·mm⁻²）	8
槽满率/%	75
槽总面积/mm²	912	1248
每相串联匝数/匝	36	48
反电势平均值/V	6.52	8.70
输出转矩/（N·m）	0.78	1.03

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表 2 电机设计变量初始值和优化范围

Table 2. Initial value and optimal ranges of motor design variables mm

设计变量	初值	范围
H_s0	1.0	[0.8,1.2]
H_s1	0.5	[0.4,0.6]
H_s2	10	[8,12]
B_s0	2.0	[1.6,2.4]
B_s1	6.0	[4.8,7.2]
a_PM	0.90	[0.64,0.96]
h_PM	1.6	[1.2,1.8]
h_g	0.5	[0.2,0.8]

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表 3 参数优先级

Table 3. Priority of parameters

优先级	目标	参数变量
优先级 1	T_avg， T_r	H_s0，H_s1，H_s2，B_s1
优先级 2	T_avg，T_r，V_PM	a_PM，h_PM，h_g

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表 4 NSGA-Ⅱ算法的参数设定值

Table 4. Parameter setting values of NSGA-II algorithm

参数	设定值
初始种群/个	100
迭代数目/个	80
交叉概率/%	90
变异概率/%	5
最大迭代次数/次	20
最大允许帕累托百分比/%	70

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表 5 优先级1优化结果

Table 5. Optimization results in in priority 1

设计变量	初始点	优化结果
H_s0/mm	1.0	0.8
H_s1/mm	0.5	0.4
H_s2/mm	10.0	11.9
B_s1/mm	6.00	5.58
T_avg /（N·m）	1.04	1.08
T_r/%	20.9	16.1
K_f/%	76	75

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表 6 优先级2优化结果

Table 6. Optimization results in priority 2

设计变量	优先级 1 结果	优先级 2 优化结果
a_PM /mm	0.9	0.8
h_PM/mm	1.60	1.25
h_g/mm	0.5	0.6
T_avg/（N·m）	1.08	1.02
T_r/%	16.1	14.7
V_PM /mm³	2430	2234

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参考文献(29)

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基于参数优先级划分的飞轮电机多目标优化

doi: 10.3969/j.issn.0258-2724.20220845

作者简介: 张维煜（1986—），女，教授，博导，研究方向为磁悬浮飞轮电池系统，E-mail：zwy@ujs.edu.cn

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出版历程

Multi-Objective Optimization for Flywheel Motors Based on Parameter Priority Division

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出版历程

目录

作者简介:
张维煜（1986—），女，教授，博导，研究方向为磁悬浮飞轮电池系统，E-mail：zwy@ujs.edu.cn