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Nowadays, wireless power transfer (WPT) gradually prevails and many researchers have devoted themselves to it because it is a safe, convenient and reliable way for recharging electric vehicles comparing to the conventional plug-in contact-based methods. Square coils are commonly used in WPT systems. However, there is few theoretical analysis of self- and mutual inductance of square coils between two magnetic shielding materials. In this paper, in order to study the spatial magnetic field distribution, the analytical model of n-turn square planar spiral coils between two semi-infinite multilayer media is developed based on the Maxwell equations and the Dual Fourier transformation. And then, by means of surface integrals, the self- and mutual inductance can be carried out, with respect to the main parameters of the WPT systems such as the operating frequency, the geometry feature of the coupling coils and the properties of the multilayer media.

For a practical pad design, a magnetic shielding layer is imperative which is made of ferrite, aluminum or some other metallic material. However, once the magnetic shielding layer is added, not only the mutual inductance but also the self-inductance of the coupling coils vary with the lateral misalignment which is inevitable for a human driver. The change of self-inductance will also result in the mistuning problem in the resonant circuit, which can significantly reduce the transmission efficiency of the whole wireless power transfer (WPT) system. This paper proposed a method of parameter identification of self-inductance based on the least square in order to solve the mistuning problem. In order to verify the proposed method, both the simulation model and the experiment set-up are built.