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
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.
Zhao Zhigang,Wang Limei,Chen Tianyuan等. Calculation Model of Winding Loss of Litz-Wire Based on Equivalent Complex Permeability[J]. Transactions of China Electrotechnical Society, 2024, 39(4): 947-955.
[1] Mogorovic M, Dujic D.100 kW, 10 kHz medium- frequency transformer design optimization and experimental verification[J]. IEEE Transactions on Power Electronics, 2019, 34(2): 1696-1708. [2] She Xu, Huang A Q, Burgos R.Review of solid-state transformer technologies and their application in power distribution systems[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2013, 1(3): 186-198. [3] 赵义焜, 张国强, 韩冬, 等. 基于材料绝缘寿命的高频变压器绕组绝缘试验电压确定方法[J]. 电工技术学报, 2020, 35(13): 2932-2939. Zhao Yikun, Zhang Guoqiang, Han Dong, et al.An insulation test method based on the dielectric insulation life for windings in high-frequency trans- former[J]. Transactions of China Electrotechnical Society, 2020, 35(13): 2932-2939. [4] 孙凯, 卢世蕾, 易哲嫄, 等. 面向电力电子变压器应用的大容量高频变压器技术综述[J]. 中国电机工程学报, 2021, 41(24): 8531-8545. Sun Kai, Lu Shilei, Yi Zheyuan, et al.A review of high-power high-frequency transformer technology for power electronic transformer applications[J]. Proceedings of the CSEE, 2021, 41(24): 8531-8545. [5] 张珂, 曹小鹏, 乔光尧, 等. 高频变压器绕组损耗解析计算分析[J]. 中国电机工程学报, 2019, 39(18): 5536-5546. Zhang Ke, Cao Xiaopeng, Qiao Guangyao, et al.Analysis of winding loss calculation methods for high frequency transformers[J]. Proceedings of the CSEE, 2019, 39(18): 5536-5546. [6] 王迎迎, 程红. 应用于功率变换器的多绕组高频变压器模型[J]. 电工技术学报, 2021, 36(19): 4140-4147. Wang Yingying, Cheng Hong.Dual multi-winding high-frequency transformer equivalent circuit for power converter applications[J]. Transactions of China Electrotechnical Society, 2021, 36(19): 4140-4147. [7] 胡义, 周晓晟. 利兹绕组线研制及应用探索研究[J]. 上海大中型电机, 2021(3): 27-31. Hu Yi, Zhou Xiaosheng.Research on the application development of Litz winding wire[J]. Shanghai Dazhongxing Dianji, 2021(3): 27-31. [8] Zhang R Y, White J K, Kassakian J G.Fast simulation of complicated 3-D structures above lossy magnetic media[J]. IEEE Transactions on Magnetics, 2014, 50(10): 1-16. [9] Dowell P L.Effects of eddy currents in transformer windings[J]. Proceedings of the Institution of Electrical Engineers, 1966, 113(8): 1387. [10] Tourkhani F, Viarouge P.Accurate analytical model of winding losses in round Litz wire windings[J]. IEEE Transactions on Magnetics, 2001, 37(1): 538-543. [11] Stoll R L.The analysis of eddy current[M]. Oxford: Clarendon Press, 1974. [12] Moreau O, Popiel L, Pages J L.Proximity losses computation with a 2D complex permeability model- ling[J]. IEEE Transactions on Magnetics, 1998, 34(5): 3616-3619. [13] Podoltsev A D, Kucheryavaya I N, Lebedev B B.Analysis of effective resistance and eddy-current losses in multiturn winding of high-frequency mag- netic components[J]. IEEE Transactions on Magnetics, 2003, 39(1): 539-548. [14] Gyselinck J, Dular P.Frequency-domain homo- genization of bundles of wires in 2-D magneto- dynamic FE calculations[J]. IEEE Transactions on Magnetics, 2005, 41(5): 1416-1419. [15] Kharezy M, Eslamian M, Thiringer T.Estimation of the winding losses of medium frequency trans- formers with Litz wire using an equivalent per- meability and conductivity method[C]//2020 22nd European Conference on Power Electronics and Applications (EPE'20 ECCE Europe), Lyon, France, 2020: 1-7. [16] Nan Xi, Sullivan C R.An equivalent complex permeability model for Litz-wire windings[J]. IEEE Transactions on Industry Applications, 2009, 45(2): 854-860. [17] Zhang Ke, Chen Wu, Cao Xiaopeng, et al.Accurate calculation and sensitivity analysis of leakage inductance of high-frequency transformer with Litz wire winding[J]. IEEE Transactions on Power Electronics, 2020, 35(4): 3951-3962. [18] 陈彬, 李琳, 赵志斌, 等. 电感集成式大容量高频变压器精细化设计方法[J]. 中国电机工程学报, 2018, 38(5): 1356-1368. Chen Bin, Li Lin, Zhao Zhibin, et al.Design method of inductor-integrated high-power high-frequency transformers[J]. Proceedings of the CSEE, 2018, 38(5): 1356-1368. [19] Sullivan C R, Zhang R Y.Analytical model for effects of twisting on Litz-wire losses[C]//2014 IEEE 15th Workshop on Control and Modeling for Power Electronics (COMPEL), Santander, Spain, 2014: 1-10. [20] Igarashi H.Semi-analytical approach for finite- element analysis of multi-turn coil considering skin and proximity effects[J]. IEEE Transactions on Magnetics, 2017, 53(1): 1-7. [21] Ollendorff F.Magnetostatik der massekerne[J]. Archiv Für Elektrotechnik, 1931, 25(6): 436-447. [22] Ferreira J A.Improved analytical modeling of conductive losses in magnetic components[J]. IEEE Transactions on Power Electronics, 1994, 9(1): 127-131. [23] 叶建盈, 黄文彬, 李睿, 等. 基于低测试阻抗角的高频电感绕组损耗测试与分析[J]. 磁性材料及器件, 2022, 53(2): 57-61. Ye Jianying, Huang Wenbin, Li Rui, et al.The test and analysis of winding losses of high-frequency inductor based on low test impedance angle[J]. Journal of Magnetic Materials and Devices, 2022, 53(2): 57-61. [24] 汪涛, 骆仁松, 文继峰, 等. 基于辅助绕组的高频变压器绕组损耗测量方法[J]. 电工技术学报, 2022, 37(10): 2622-2630, 2655. Wang Tao, Luo Rensong, Wen Jifeng, et al.A measurement method of winding loss for high- frequency transformer based on auxiliary winding[J]. Transactions of China Electrotechnical Society, 2022, 37(10): 2622-2630, 2655.
2024, Vol. 39 
