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浙江大学学报(工学版)
浙江大学学报(工学版)  2025, Vol. 59 Issue (1): 141-151    DOI: 10.3785/j.issn.1008-973X.2025.01.014
机械工程、能源工程     
分数阶磁耦合谐振双向无线电能传输系统参数优化
李若琼1(),翁源1,李欣2,*()
1. 兰州交通大学 自动化与电气工程学院，甘肃 兰州 730070
2. 兰州交通大学 新能源与动力工程学院，甘肃 兰州 730070
Parameter optimization of fractional-order magnetically-coupled resonant bidirectional wireless power transfer system
Ruoqiong LI1(),Yuan WENG1,Xin LI2,*()
1. School of Automation and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
2. School of New Energy and Power Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
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摘要：

磁耦合谐振双向无线电能传输（BD-WPT）系统的参数多，导致系统影响程度不一致和参数配置困难，为此结合灰色关联度分析（GRA）和多目标粒子群优化（MOPSO）算法提出分数阶磁耦合谐振BD-WPT系统多目标参数优化方法. 在分析系统传输特性和线圈参数解析式的基础上，采用GRA进行系统各个参数的影响评估，确定了5个核心参数. 为了提高系统传输效率和线圈功率密度，采用MOPSO算法优化系统参数，结果表明通过GRA有选择性地优化核心参数，可使算法输出的解集优于未采用GRA的解集. 结合电动汽车实际需求，选取最优解用于BD-WPT系统的设计参考. 仿真结果显示，相校于国标参数对称系统，BD-WPT系数的传输效率提高了4.5个百分点，线圈功率密度提高了0.42 kW/m2.
关键词： 双向无线电能传输（BD-WPT）;  磁耦合谐振;  灰色关联度分析（GRA）;  多目标优化;  多目标粒子群优化（MOPSO）算法    
Abstract:

The magnetically-coupled resonant bidirectional wireless power transfer (BD-WPT) system has many parameters, and the problems of inconsistent influence on the system and difficult parameter configuration were caused by the parameters. Combining the grey relation analysis (GRA) with the multi-objective particle swarm optimization (MOPSO) algorithm, a multi-objective parameter optimization method for fractional-order magnetically-coupled resonant BD-WPT system was proposed. Based on the analysis of the system’s transmission characteristics and coil parameter analytical expressions, the GRA was employed to assess the influence of each system parameter and identify five core parameters. With the aim of enhancing the system’s transmission efficiency and coil power density, the MOPSO algorithm was utilized to optimize the system parameters. Results showed that the GRA allowed for the selective optimization of the core parameters so that the solution set output by the algorithm is better than the solution set without GRA. In light of the actual requirements of electric vehicles, the optimal solution was chosen as a reference for the design of the BD-WPT system. The simulation results indicated that compared with the national standard parameter symmetric system, the transmission efficiency of the BD-WPT system had increased by 4.5 percentage points, and the coil power density had risen by 0.42 kW/m2.
Key words: bidirectional wireless power transfer (BD-WPT)    magnetically-coupled resonant    grey relation analysis (GRA)    multi-objective optimization    multi-objective particle swarm optimization (MOPSO) algorithm
收稿日期: 2023-11-29 出版日期: 2025-01-18
CLC:  TP 724  
基金资助: 国家自然科学基金资助项目（51767015）；甘肃省科技计划甘肃省自然科学基金重点项目（22JR5RA317）；甘肃省高等学校产业支撑计划项目（2023CYZC-39）.
通讯作者: 李欣     E-mail: liruoqiong26@163.com;lxfp167@163.com
作者简介: 李若琼（1979—），女，教授，从事新型电能变换技术和电工理论与新技术研究. orcid.org/0000-0003-4452-8256. E-mail：liruoqiong26@163.com
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引用本文:

李若琼,翁源,李欣. 分数阶磁耦合谐振双向无线电能传输系统参数优化[J]. 浙江大学学报(工学版), 2025, 59(1): 141-151.

Ruoqiong LI,Yuan WENG,Xin LI. Parameter optimization of fractional-order magnetically-coupled resonant bidirectional wireless power transfer system. Journal of ZheJiang University (Engineering Science), 2025, 59(1): 141-151.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2025.01.014    或    https://www.zjujournals.com/eng/CN/Y2025/V59/I1/141

图 1  分数阶磁耦合谐振双向无线电能传输系统结构图
图 2  分数阶磁耦合谐振双向无线电能传输系统等效电路
图 3  非紧密缠绕平面圆形螺线圈等效模型
图 4  平面同心圆环载流线圈间互感模型
图 5  线圈互感计算模型
系统η/%f/kHzLf/μHCf/nFLt/μHR/ΩM/μHr1/mh/mN
189.8685.52017443.80.3411.300.280.1511
287.3880.01526415.00.154.080.200.107
389.0483.51820429.00.247.610.250.139
492.1587.02513471.00.4720.000.350.1712
592.9090.030104106.00.6329.300.400.2014
表 1  分数阶磁耦合谐振双向无线电传输系统的参数
系统ηfLfCfLtRMr1hN
11.001.001.001.001.001.001.001.001.001.00
20.970.940.751.520.340.430.360.710.670.64
30.990.970.901.180.660.710.670.890.870.82
41.031.021.250.771.621.351.761.251.131.09
51.031.051.500.602.431.842.591.431.331.27
表 2  分数阶磁耦合谐振双向无线电传输系统的参数归一化处理结果
系统$\xi $
fLfCfLtRMr1hN
11.001.001.001.001.001.001.001.001.00
20.950.780.590.550.590.560.750.720.70
30.970.900.810.700.730.710.890.860.82
40.990.780.750.570.700.510.780.880.92
50.980.620.640.360.490.330.660.720.76
关联度0.980.810.760.640.700.620.820.840.84
表 3  分数阶磁耦合谐振双向无线电传输系统传输效率影响因素的灰色关联度及灰色关联度系数
图 6  系统参数多目标粒子群优化算法流程图
图 7  多目标粒子群优化算法的Pareto前沿解
图 8  采用灰色关联度分析前后的算法优化结果对比
f/HzLf/Hr1/mh/mNη/%ρ/(kW·m?2)
90 0002.98×10?50.450.101596.354.91
89 9832.02×10?50.440.101195.846.68
88 1183.28×10?50.430.10794.7110.47
90 0003.32×10?50.380.10592.9817.78
表 4  多目标粒子群优化算法结果中的部分前沿解
参数数值参数数值
f/kHz90N6
Lf/μH24.03Cα/(F·sα?1)1.798×10?7
r1/m0.44α1.008
h/m0.10Cf/nF130.4
R/Ω0.276η/%94.32
Lt/μH39.71ρ/(kW·m?2)12.35
表 5  多目标粒子群优化算法优化后的参数
图 9  双向无线电能传输系统开关信号波形
图 10  多目标粒子群优化算法优化的双向无线电能传输系统二次侧输出功率
图 11  多目标粒子群优化算法优化的双向无线电能传输系统线圈损耗功率
图 12  国标中参数对称的双向无线电能传输系统二次侧输出功率
图 13  国标中参数对称的双向无线电能传输系统线圈损耗功率
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