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| Three-dimensional temperature calculation and optimization design method for high power high-frequency transformer |
| Luo Rensong, Wang Tao, Wen Jifeng, Wang Zilong, Zhang Maoqiang |
| NR Electric Co. Ltd. Nanjing 211102 China |
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Abstract Temperature rise calculation is a difficult problem in modeling high-power high-frequency transformers (HFT) and accurate and fast thermal model is of great significance for optimal design and stable operation of HFT. At present, lumped parameter thermal network model is usually built by the way of dimensionality reduction, whose precision of calculation is easily affected by structural parameters, and it is difficult to achieve accurate hot spot prediction in the optimization of wide parameter range.
A three-dimensional thermal model of HFT considering anisotropic thermal conductivity is constructed based on the finite difference method (FDM). The discretization error of the three-dimensional thermal model is quantitatively analyzed, which is mainly affected by the loss density, thermal conductivity and size of the finite difference element. In order to minimize the number of finite differential elements while ensuring the calculation accuracy of the thermal model, three-dimensional sizes of the differential element are adjusted actively according to the discretization error expression. For HTF with nanocrystalline core and litz wire winding, the element sizes in the direction along the width, height of winding and the thickness of core are the key parameters affecting the accuracy of temperature rise calculation.
The parameter adaptability of the proposed thermal model is verified in detail with finite element simulation, including structural parameters, loss density and heat dissipation conditions, and the verification results show that the maximum error of the model is less than 10% in a wide range of parameters. However, the error of the traditional lumped parameter thermal network model is significantly affected by the structural parameters, and the error varies in the range of 10%~80% within the same parameter variation range.
Based on the proposed thermal model, the efficiency-power density optimal design of a 10kHz 150kW transformer was carried out with parameters scanning method, in which the upper limit of temperature rise was set to 100K, and the differential element sizes were adjusted according to the error less than 5K. The optimization design program completed the calculation of 500,000 design points within 371s with parallel computing, in which the average time of three-dimensional thermal model calculation for a single design point was 2.8ms. The temperature rise calculation results of the design points on the optimal design boundary were verified, and the error was less than 5.5%. Compared with finite element simulation and the lumped parameter thermal network model, the proposed three-dimensional thermal model based on FDM achieves a balance between calculation accuracy and calculation speed.
On the optimal design boundary, with the increase of power density, the transformer efficiency gradually decreases, and the temperature rise gradually increases. The maximum power density to meet the requirement of 100K temperature rise was about 9kW/L, and the transformer efficiency was about 99.82%. A150kW transformer prototype was processed according to the optimized design point with maximum power density, and the maximum temperature rise of the transformer prototype was 103K under rated working conditions.
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