VP11-03 The Analytical Calculation Model for Litz Wire Winding Loss in High-Power High-Frequency Transformers
Creators: Xiang Li
Shuaichao Yue
Yongjian Li
and Zhenyu Wan
Publisher: name: IEEE
Year: 2025

High-power HFT, as key electromagnetic energy conversion components in high-power power electronic converters, account for approximately 30% of the total equipment loss. The calculation of winding loss is one of the primary focuses in the loss calculation of high-power HFT. Currently, Litz wire, composed of multiple smaller diameter strands intertwined, is selected as the winding material for high-power HFT due to its reduced high-frequency skin effect[1-2]. For the calculation of Litz wire winding loss, a theoretical analytical calculation model was proposed by Tourkhani in 2001[3], which has been widely applied in the efficient calculation of high-frequency transformer winding losses. However, as HFTs are increasingly applied in high-power scenarios, Litz wire windings are required to carry larger currents. Larger currents necessitate an increase in the cross-sectional area and the number of strands of each Litz wire, thereby imposing stricter requirements on the calculation of Litz wire winding loss. Through experimental measurements, it has been observed that the calculation error of the Tourkhani model increases as the number of Litz wire strands increases[4]. To address this drawback, an analytical calculation model suitable for high-current conditions is proposed in this paper. The analytical calculation model presented in this paper incorporates Ferreira's two-dimensional loss calculation model for round conductors. The fine strands within the Litz wire are thoroughly decomposed into magnetic field influences, specifically the internal magnetic field influence of other strands within the Litz wire (Hint) and the external magnetic field influence of other turns of Litz wire in the winding (Hext). In the traditional Tourkhani model, due to excessive simplifications during the magnetic field decomposition and derivation process, accurate winding loss calculations are achieved for Litz wire windings with fewer strands. However, as the number of strands increases to hundreds or thousands, the calculation accuracy significantly decreases. The significance of the proposed analytical model lies in the accurate calculation of the AC resistance coefficient for Litz wire windings with a larger number of strands.References: [1] Wojda R P, Kazimierczuk M K. Winding resistance and power loss of inductors with Litz and solid-round wires[J]. IEEE Transactions on Industry Applications, 2018, 54(4): 3548-3557. [2] Niyomsatian K, Gyselinck J J C, Sabariego R V. Experimental extraction of winding resistance in Litz-wire transformers—influence of winding mutual resistance[J]. IEEE Transactions on Power Electronics, 2019, 34(7): 6736-6746. [3] F. Tourkhani and P. Viarouge, “Accurate analytical model of winding losses in round Litz wire windings,” IEEE Trans. Magn., vol. 37, no. 1, pp. 538–543, Jan. 2001. [4] C. Peng, G. Chen, B. Wang, and J. Song, “Semi-Analytical AC Resistance Prediction Model for Litz Wire Winding in High-Frequency Transformer,” IEEE Trans. Power Electron., vol. 38, no. 10, pp. 12730–12742, Oct. 2023.
High-power HFT, as key electromagnetic energy conversion components in high-power power electronic converters, account for approximately 30% of the total equipment loss. The calculation of winding loss is one of the primary focuses in the loss calculation of high-power HFT. Currently, Litz wire, composed of multiple smaller diameter strands intertwined, is selected as the winding material for high-power HFT due to its reduced high-frequency skin effect[1-2]. For the calculation of Litz wire winding loss, a theoretical analytical calculation model was proposed by Tourkhani in 2001[3], which has been widely applied in the efficient calculation of high-frequency transformer winding losses. However, as HFTs are increasingly applied in high-power scenarios, Litz wire windings are required to carry larger currents. Larger currents necessitate an increase in the cross-sectional area and the number of strands of each Litz wire, thereby imposing stricter requirements on the calculation of Litz wire winding loss. Through experimental measurements, it has been observed that the calculation error of the Tourkhani model increases as the number of Litz wire strands increases[4]. To address this drawback, an analytical calculation model suitable for high-current conditions is proposed in this paper. The analytical calculation model presented in this paper incorporates Ferreira's two-dimensional loss calculation model for round conductors. The fine strands within the Litz wire are thoroughly decomposed into magnetic field influences, specifically the internal magnetic field influence of other strands within the Litz wire (Hint) and the external magnetic field influence of other turns of Litz wire in the winding (Hext). In the traditional Tourkhani model, due to excessive simplifications during the magnetic field decomposition and derivation process, accurate winding loss calculations are achieved for Litz wire windings with fewer strands. However, as the number of strands increases to hundreds or thousands, the calculation accuracy significantly decreases. The significance of the proposed analytical model lies in the accurate calculation of the AC resistance coefficient for Litz wire windings with a larger number of strands.References: [1] Wojda R P, Kazimierczuk M K. Winding resistance and power loss of inductors with Litz and solid-round wires[J]. IEEE Transactions on Industry Applications, 2018, 54(4): 3548-3557. [2] Niyomsatian K, Gyselinck J J C, Sabariego R V. Experimental extraction of winding resistance in Litz-wire transformers—influence of winding mutual resistance[J]. IEEE Transactions on Power Electronics, 2019, 34(7): 6736-6746. [3] F. Tourkhani and P. Viarouge, “Accurate analytical model of winding losses in round Litz wire windings,” IEEE Trans. Magn., vol. 37, no. 1, pp. 538–543, Jan. 2001. [4] C. Peng, G. Chen, B. Wang, and J. Song, “Semi-Analytical AC Resistance Prediction Model for Litz Wire Winding in High-Frequency Transformer,” IEEE Trans. Power Electron., vol. 38, no. 10, pp. 12730–12742, Oct. 2023.