同轴多层筒式空心线圈自感和互感解析计算方法  

Analytical Calculation for Self and Mutual Inductance of Coaxial Multi Layer Cylindrical Hollow Coils

作　　者：陈彬[1,2] 姜鹏飞[1] 万妮娜 冯昱璋 黄力 Chen Bin;Jiang Pengfei;Wan Nina;Feng Yuzhang;Huang Li(College of Electrical Engineering and New Energy,China Three Gorges University,Yichang 443002,China;Hubei Provincial Engineering Technology Research Center for Power Transmission Line,China Three Gorges University,Yichang 443002,China;Yichang Electric Company,State Grid Hubei Electric Power Company,Yichang 443000,China;Wuhan Electric Company,State Grid Hubei Electric Power Company,Wuhan 430000,China)

机构地区：[1]三峡大学电气与新能源学院,宜昌443002 [2]三峡大学湖北省输电线路工程技术研究中心,宜昌443002 [3]国网湖北省电力有限公司宜昌供电公司,宜昌443000 [4]国网湖北省电力有限公司武汉供电公司,武汉430000

出　　处：《电工技术学报》2024年第20期6270-6281,共12页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金青年科学基金项目(52107006);湖北省自然科学基金面上项目(2021CFB149)资助。

摘　　要：在电磁耦合的无线电能传输系统中,准确获取线圈电感参数是设计和优化无线电能传输系统的重要理论依据。现有的无线电能传输系统研究大多针对平面板结构线圈,同轴多层筒式空心线圈相比于平面板线圈具有更高的传输功率和传输效率。因此,该文针对同轴多层筒式空心线圈,提出了一种考虑高频涡流效应的自感和互感解析计算方法。首先,将单匝线圈截面离散等效为数量众多、形状相同的网格带电圆环单元,采用离散等效求和法推导出单匝线圈的自感和线圈间互感的解析式;然后,基于筒式空心线圈的整体结构以及考虑高频涡流效应,推导出基于第一类、第二类完全椭圆积分和开尔文函数的一、二次线圈自感和总互感计算的理论解析式;最后,以两种不同排布方式的筒式空心线圈为例,对比解析计算、有限元计算和实验测量结果,验证了所提解析法的可行性,同时也为筒式空心线圈的设计提供参考依据。In the electromagnetic coupling of wireless power transmission systems,accurate calculation of the coil inductance parameters is an important theoretical basis.The existing analytical calculations for coil inductance mostly focus on planar plate coils to study the relationship between coil inductance and coil structure,ignoring the influence of frequency.However,the coaxial multilayer cylindrical structure of the air-core transformer(ACT)has a higher coupling coefficient and transmission efficiency than the planar plate coil under the same quality conditions.However,since the ACT has no magnetic conductive material,it has no specific magnetic flux path,and the magnetic field cannot be bound to a certain part.Usually,it is calculated using the three-dimensional finite element method,which requires a high computer configuration,a large amount of storage space,and sufficiently fast computing speed,resulting in high computational costs.Therefore,this paper proposes an analytical calculation method for the self and mutual inductance of coaxial multilayer cylindrical hollow coils considering high-frequency eddy current effects.Firstly,the magnetic chain method derives the analytical equations for the self and mutual inductance of a single-turn coaxial parallel charged circular ring.Secondly,the cross-section of the single-turn coil is discretized into grid-charged circular ring elements with the same shape.The analytical equations for the single-turn coil’s self-inductance and the coils'mutual inductance are derived using the discrete equivalent summation method.Based on the first and second types of complete elliptic integrals and Kelvin functions,analytical formulas are derived to calculate the self-inductance of the primary and secondary coils and the total mutual inductance.Finally,taking two different arrangements of cylindrical hollow coils as examples,the proposed analytical method is verified by comparing analytical calculations,finite element calculations,and experimental measurements.This method considers t

关 键 词：无线电能传输 电感参数 筒式空心线圈 离散等效 涡流效应 解析计算 

分 类 号：TM724[电气工程—电力系统及自动化]