In the wireless power transfer (WPT) system, the magnetic shielding of finite permeability and finite dimensions is practically used with the primary and secondary coils. Generally, the analytical model is used to design such coils having magnetic shields. However, the reported analytical models in the literature include the magnetic shield with different assumptions, which introduces errors in the calculated results. In this context, this article presents a 3-D analytical model that does not consider such assumptions. This 3-D model is developed by the superposition of two 2-D analytical models. These 2-D models are developed based on the subdomain technique. Since 2-D models are invariant in their third direction (i.e., in the $y$ -direction for the $xz$ -plane and the $x$ -direction for the $yz$ -plane), a correction factor is introduced for 2-D subdomain models to make it variant in their third directions. The results obtained from the subdomain model are compared with finite element analysis (FEA) and experimental results, which are found in good agreement. The proposed subdomain model can be used in the initial design and optimization of the coils used in the WPT system.

中文翻译：

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用于无线电力传输系统的具有有限尺寸和有限磁导率的磁屏蔽线圈系统的子域分析模型

在无线电力传输 (WPT) 系统中，有限磁导率和有限尺寸的磁屏蔽实际上与初级和次级线圈一起使用。通常，分析模型用于设计具有磁屏蔽的此类线圈。然而，文献中报道的分析模型包括具有不同假设的磁屏蔽，这会在计算结果中引入误差。在这种情况下，本文提出了一个不考虑此类假设的 3-D 分析模型。该 3-D 模型是通过叠加两个 2-D 分析模型而开发的。这些二维模型是基于子域技术开发的。由于二维模型在其第三方向（即在 $y$ - 方向 $xz$ -平面和 $x$ - 方向 $yz$ -plane)，为二维子域模型引入了一个校正因子，使其在第三方向变化。将从子域模型获得的结果与有限元分析 (FEA) 和实验结果进行比较，发现它们具有良好的一致性。所提出的子域模型可用于 WPT 系统中使用的线圈的初始设计和优化。