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| Calculation Model of Winding Loss of Litz-Wire Based on Equivalent Complex Permeability |
| Zhao Zhigang1,2, Wang Limei1,2, Chen Tianyuan1,2, Zhao Anqi1,2, Lu Ziqi1,2 |
1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment Hebei University of Technology Tianjin 300401 China;
2. Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province Hebei University of Technology Tianjin 300401 China |
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Abstract Asan important component of the overall loss of high-frequency transformers, winding loss is a key parameter affecting the volume, efficiency, and temperature rise of magnetic components. Litz-wire is widely used in high-frequency transformer winding because of its ability to achieve conductor in-turn transposition and reduce losses due to the skin effect and proximity effect. The homogenization technique, using a region with the equivalent complex material properties instead of the winding region, can realize the characterization of the eddy current effect by the two-dimensional magnetic field and reduce the computational cost of refinement modeling. However, the material properties of the equivalent region are obtained using numerical methods, making the calculation complex. Therefore, this paper establishes a loss calculation model of Leeds wire winding based on equivalent complex permeability to calculate winding losses accurately and efficiently.
Firstly, the winding loss calculation model is established based on the orthogonality of the skin and proximity effects. The equivalent complex permeability of the winding is calculated using the factory data of the Litz-wire. Then, the overall modeling of Litz-wire winding is carried out in the simulation software, and the external magnetic field value of the winding is extracted for the proximity effect loss calculation. Finally, the skin effect loss is calculated using the analytical formula. The actual winding model of AC resistance in the wide frequency (20 Hz~1 MHz) range shows that AC resistance in the low-frequency band (20 Hz~100 kHz)is approximately equal to DC resistance. At this time, the calculation error can be almost neglected, and the calculation accuracy mainly depends on the calculated value of the DC resistance. The skin effect in the medium-frequency band (100 kHz~500 kHz) becomes gradually obvious, and AC resistance rises rapidly. The highest error is around 300 kHz, and the maximum is 10.07%. In the high-frequency band (500 kHz~1 MHz), the proximity effect between the winding makes the AC resistance rise rapidly. The maximum error in the high-frequency band is 15.22%, and the error in the rest of the frequency is about 10%.
The following conclusions can be obtained: (1) By describing the equivalent complex permeability of the circular Litz-wire winding analytically, the preprocessing of the basic unit is avoided, and the calculation process is simplified. (2) The homogenized finite element method is used for overall modeling. The eddy current is analyzed in the three-dimensional structure of the Litz-wire winding based on the two-dimensional static magnetic field distribution and combined with the complex permeability model. The calculation accuracy and speed are improved. (3) Considering the influence of the winding section shape on the loss, the skin effect and proximity effect are characterized, increasing the applicability of the model at high frequency and realizing the accurate loss prediction at wide frequency.
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Received: 17 November 2022
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2024, Vol. 39 
