Mutual Inductance Calculation of Circular Coils for an Arbitrary Position With a Finite Magnetic Core in Wireless Power Transfer Systems

Mutual inductance can be increased, and magnetic leakage can be reduced by adding finite magnetic core materials to the coil structure. However, the problem of the calculation of the mutual inductance between two arbitrarily positioned circular coils with a finite magnetic core has not been resolved. In this article, an analytical formula for calculating the mutual inductance between two circular coaxial coils on a finite magnetic core is obtained based on regional hierarchical expansion analysis (RHEA), the Maxwell equation, the Bessel function, and the boundary conditions for electromagnetic fields. The mutual inductance between two arbitrarily positioned coils is obtained by using the analytical geometry method. A series of experiments are carried out to verify the analytic calculations. The experimental results for each misalignment case are compared with the calculated results and simulated results. The theoretical results and simulated results are in good agreement with the experimental data, which verifies the validity of the proposed method.

I. Introduction

Wireless power transfer (WPT) refers to an advanced technology that can supply power to the load without cables or conductors. It is widely used in transportation, medical electronics, consumer electronics, space solar energy, and many other fields due to its advantages of high convenience, safety, and high reliability [1]–[6]. For example, in the field of transportation, WPT technology is becoming increasingly important for electric vehicles. The magnetic core and magnetic coupling coils are the key components of the WPT system. In practical applications, magnetic cores are often introduced to enhance the mutual inductance of the coils and reduce magnetic leakage in the WPT system. However, the calculation of the mutual inductance between two circular coils with a finite magnetic core has always been a difficult issue. Furthermore, inevitable misalignments (horizontal or angular misalignments) between the primary coil and the secondary coil lead to a decrease in transfer efficiency and a fluctuation in transfer power. Therefore, studying the variations in mutual inductance with a finite magnetic core is of great significance [7]–[10].