As an important parameter in power electronic converters, the leakage inductance of high-frequency transformers is of great significance in improving the operating mode and power transmission characteristics of isolated DC-DC converters. Compared with the solid round wire, the Litz wire can reduce eddy current losses in high-frequency magnetic components. However, the complicated structure of the Litz-wire windings poses a serious challenge to predicting leakage inductance in high-frequency transformers. On the one hand, it is difficult to precisely extract the magnetic field energy in various regions of the core window. On the other hand, it is hard to accurately characterize the multi-stranded and twisting structures of the Litz wires. Therefore, this paper presents a fast calculation method of leakage inductance in the high-frequency transformer with Litz-wire winding.

Firstly, a homogenized equivalent process for Litz wire is proposed to enhance the flexibility of modeling and the efficiency of computation. The magnetic field energy variation with frequency inside the Litz-wire conductors are analyzed. Then, the 2-D magnetic field energy inside the core window is extracted based on the method of images to eliminate the impact of the edge effect. The internal and external magnetic fields at different locations in the winding are accurately characterized by introducing the meshing into the method of images, and a coordinate transformation method is proposed to consider the twisting structure of the Litz wires. Finally, two high-frequency transformer prototypes with different structures are designed and fabricated. Compared with the measurement results and two existing methods, the accuracy and efficiency of the proposed approach are verified.

The following conclusions can be drawn. (1) A homogenized equivalent model of the Litz-wire twisting structure is developed by introducing the relative complex permeability, which simplifies the model building and reduces the computational cost. The variation of the magnetic field energy in the Litz wires with frequency is analyzed, and the magnetic field energy stored in the Litz wires gradually decreases with the frequency increase. (2) The meshing process is introduced into the method of images, and the coordinate transformation method is proposed to characterize the twisting structure of the Litz wire. It can counteract a part of the external magnetic field and reduce the magnetic field energy in the conductors. (3) Considering the twisting characteristics of the Litz wire and the high-frequency effect, a leakage inductance prediction model is developed based on the magnetic field energy variation with frequency. (4) The accuracy and efficiency of the proposed method are verified compared with the measurement and the current two analytical methods. The maximum error does not exceed 4% throughout the measurement frequency range, and the calculation time is about 20 seconds. Moreover, the proposed method can be effectively applied to fast iterative calculations in the optimal design of high-frequency transformers.