非完全绞合利兹线的高频损耗特性分析与计算

Analysis and Calculation of High-frequency Loss of Incompletely-twisted Litz Wire

现有的利兹线损耗计算模型,普遍是基于每股绝缘细导线流过相同电流的假设,根据铜箔和圆形实心导体的1维和2维电流密度、涡流场函数推导而来,忽略了不完全绞合结构对股间电流分布的影响,造成计算精度偏低。为了解决利兹线高频损耗的精确数学表征问题,首先系统分析了高频条件下利兹线的磁场分布、电流密度分布以及利兹线的绞合结构特点;然后基于利兹线股线的绞合结构,通过分段等效电路法和有限元方法建立利兹线损耗的精确计算方法,即将完整绞合节距内的利兹线分段后等效为直线结构的电感元胞,通过2维有限元法计算出股线之间的阻抗矩阵,进而根据系统方程求解出股线电流向量;最后,针对3种典型的利兹线绞合结构,从计算精度和计算量的角度对新方法、传统解析法与3维有限元法进行对比分析。结果表明,新方法能快速准确计算出不同绞合结构利兹线的高频损耗电阻,其最大相对偏差≤2.34%,并且借助新方法明确了绞合结构、频率对利兹线高频损耗电阻、电流流动模式的影响规律。

The existing loss calculation model of Litz wire is generally based on the assumption that each insulated conductor flows through the same current.The model is derived from the one-dimensional and two-dimensional current density and eddy current field function of copper foil and round solid conductor,in which the influence of incompletely twisted structure on the current distribution between strands is ignored,thus it has a low calculation accuracy.In order to solve the accurate mathematical representation of the high-frequency losses of the Litz wire,we first systematically analyzed the magnetic field distribution,current density distribution,and the characteristics of the twisted structure of the Litz wire under the high-frequency condition.Then,based on the structure of the Litz wire strands,the accurate loss calculation method of Litz wire was established through the segmented equivalent circuit method and the finite element method(FEM).The Litz wire in the complete twisting pitch was segmented and equivalent to the inductance cell of the linear structure.The impedance matrix between the strands was calculated by the 2D FEM,and then the strand current vector was solved according to the system equation.Finally,the new method,the traditional analytical method,and the three-dimensional finite element method were compared and analyzed from the point of view of calculation accuracy and calculation amount for three typical Litz wire twisted structures.The results show that the new method can be adoped to quickly and accurately calculate the high-frequency loss resistance of different twisted Litz wires,and the maximum relative deviation is less than 2.34%.With the help of the new method,the influence of the twisted structure and frequency on the high frequency loss resistance and current flow mode of Litz wire is clarified.