Completely Analytical Model of Inductance for Circular Coils With Bilateral Finite Magnetic Cores and Al Plates in WPT Systems
Tianyi Zhang, Guo Wei, Ruolan Li, Jing Feng, Chunbo Zhu
Abstract
Circular coils are essential components in wireless power transfer systems. While some research has focused on analytical inductance calculations, a completely analytical model for circular coils with finite magnetic cores and aluminum (Al) plates is lacking. This article addresses this gap by introducing a completely analytical model (CAM) using the Truncated Region Eigenfunction Expansion (TREE) method. The model comprises two variants: the coaxial complete analytical model (CCAM) and the non-coaxial complete analytical model (NCCAM). In the CCAM, the width of cores (wcore) is considered by using a Truncation Region (TR). Additionally, an effective technique is proposed to separate expansion coefficients related to Al plate width (wAl) and eigenvalues by assuming wAl equals TR, which is valid when wAl≥1.2wcore in practical applications. The CCAM encompasses all design parameters. Meanwhile, the NCCAM is applied to evaluate the fluctuation of mutual inductance when horizontal misalignment occurs. By assuming an extension of core width to TR, the NCCAM incorporates an equivalent relative permeability (ERP). Real-time ERP is extracted from the CCAM model when the self-inductance changes. Experiment shows that the analytical results of inductance have an error of 5.12% or less, regardless of alignment between the transfer and pickup sides.