摘要 CLLLC变换器因其宽电压范围、高功率密度、高效率和低电磁干扰而备受关注。现有CLLLC变换器的变压器损耗计算方法准确性不足,其解析设计方法未考虑交流电阻系数和填充系数等变量对效率优化的限制,并且未虑及励磁频率对优化设计通用性的限制。因此,该文提出一种提升CLLLC变换器效率的变压器解析设计方法,并构建变压器本质设计变量的闭合优化方程。首先,基于面积积法和绕组匝数推导了独立磁通密度的磁心损耗通用性模型;其次,通过等效面积模型、涡流效应正交性和开尔文函数线性等效推导了近似修正Ferreira模型,提高了绕组损耗预测精度。该方法考虑了交流电阻系数和填充系数的优化过程,保证了设计方法的优化性;然后,研究了励磁频率对变压器优化设计的约束条件,拓展了近似修正Ferreira模型适用条件,并且保证了设计方法的通用性;最后,利用变压器解析设计方法构建了CLLLC变换器的变压器优化设计流程,并基于最佳方案制作了一台120 W/48 V CLLLC实验样机,通过实验验证了所提高频变压器优化解设计方法的有效性。
Abstract：Under high-frequency conditions, the transformer winding losses of the CLLLC converter are influenced by eddy current effects and complex structures. The trade-offs between total transformer losses, size, and temperature rise pose significant challenges for the design of electromagnetic structures that require high power density and efficiency. Traditional transformer design methods often overlook the constraints of temperature rise and the impact of complex structures on winding losses, relying solely on the area-product approach to derive performance-compliant parameter values. It is difficult to achieve optimal transformer design. Existing transformer optimization analytical design methods consider temperature rise constraints and analyze winding losses under high-frequency conditions. However, most methods lack sufficient accuracy in predicting transformer losses, neglect the impact of variable AC resistance and fill factors on efficiency optimization, and fail to address the limitations of excitation frequency on the generality of the optimization design. Furthermore, these methods often involve high computational costs. Therefore, this paper proposes an analytical design method to improve the efficiency of CLLLC converters and formulates a closed-form optimization equation for the essential design variables of the transformer. First, based on the MSE and IGSE methods under non-sinusoidal excitation, an independent flux density core loss model is derived. The response patterns of area-product and winding turns to core losses are analyzed, revealing the intrinsic relationship between the loss model and transformer structural parameters. Second, an approximate correction of the Ferreira model is proposed to improve the accuracy of winding loss predictions by the derivation of the equivalent area model, the orthogonality of eddy current effects, and the linear equivalence of the Kelvin function. Third, an analytical function is established for the error threshold and the approximation conditions of the winding loss model, which mitigates the influence of winding structural parameters on the analytical function. A constraint condition model for the error threshold and excitation frequency is constructed. Finally, combined with the independent flux-density core loss model and the approximately corrected Ferreira winding loss model, a transformer optimization closed-form equation for temperature rise constraints is derived using the Lagrange function. The response patterns of transformer efficiency to the area-product and winding turns are analyzed. The discrete structural parameters of the transformer are further optimized, and a transformer optimization design process is established. The finite element simulation of the transformer indicates that the simulated winding losses within the frequency range of 1 kHz to 1 MHz closely match the predictions of the approximately corrected Ferreira model. The simulated total transformer loss, optimal winding, and optimal strand number align well with the values predicted by the analytical method. A 120 W/48 V CLLLC experimental prototype is built based on the optimal transformer design. The soft-switching characteristics of the CLLLC resonant tank are tested under under-resonant, quasi-resonant, and over-resonant conditions across a 20% to 100% load range. The results demonstrate that soft switching can be achieved under all three operating conditions. The output power and efficiency of the three CLLLC designs are measured under fixed frequency (200 kHz) with varying loads and fixed load (full load) with varying frequencies. The experimental results show that the highest optimized transformer loss is 56.72%, and the maximum efficiency improvement of the CLLLC resonant converter is 0.529%. The optimized loss difference agrees with the simulation data and the predictions from the analytical method. The proposed approximately corrected Ferreira model and the independent flux-density core loss model are verified. A comprehensive evaluation of existing analytical design methods shows that this approach balances transformer optimization design methodologies’ accuracy, optimization, simplicity, and generality.
[1] 蔡瑞佳, 马运东, 王鹏飞, 等. 基于双向半桥CLLLC谐振变换器的锂电池均衡电路[J]. 电工技术学报, 2024, 39(15): 4868-4882. Cai Ruijia, Ma Yundong, Wang Pengfei, et al.Lithium-ion battery equalization circuit based on bidirectional half-bridge CLLLC resonant converter[J]. Transactions of China Electrotechnical Society, 2024, 39(15): 4868-4882. [2] 陶霞, 方东平, 汪莹洁, 等. 基于最大功率点跟踪下垂控制的光储一体化系统研究[J]. 电气技术, 2024, 25(4): 38-46. Tao Xia, Fang Dongping, Wang Yingjie, et al.Research on integrated photovoltaic and energy storage system with maximum power point tracking based droop control[J]. Electrical Engineering, 2024, 25(4): 38-46. [3] 唐西胜, 李伟, 沈晓东. 面向新型电力系统的储能规划方法研究进展及展望[J]. 电力系统自动化, 2024, 48(9): 178-191. Tang Xisheng, Li Wei, Shen Xiaodong.Research progress and prospect of energy storage planning method for new power system[J]. Automation of Electric Power Systems, 2024, 48(9): 178-191. [4] 张新闻, 刘文泽, 杨树德, 等. MOSFET输出电容对CLLLC谐振变换器模型的优化[J]. 电工技术学报, 2024, 39(22): 7228-7238. Zhang Xinwen, Liu Wenze, Yang Shude, et al.Optimization of CLLLC resonant converter modeling by MOSFET output capacitance[J]. Transactions of China Electrotechnical Society, 2024, 39(22): 7228-7238. [5] 周国华, 王淇, 邓伦博. 宽增益高效率CLLLC变换器的变频双移相调制策略[J]. 电工技术学报, 2024, 39(8): 2511-2522. Zhou Guohua, Wang Qi, Deng Lunbo.Variable-frequency dual-phase-shift modulation strategy for CLLLC converter with wide voltage gain and high efficiency[J]. Transactions of China Electrotechnical Society, 2024, 39(8): 2511-2522. [6] Jiang Peng, Feng Hao, Ran Li.ZVS analysis and a design method for unidirectional medium-voltage LLC-DCX with high step-up ratio[J]. IEEE Transa-ctions on Power Electronics, 2024, 39(3): 2948-2953. [7] Esteve V, Jordán J, Dede E J, et al.Comparative analysis and improved design of LLC inverters for induction heating[J]. IET Power Electronics, 2023, 16(10): 1754-1764. [8] 李小强, 马永超, 黄金伟, 等. 基于双脉宽调制的交错Boost集成型CLLLC谐振变换器宽增益控制策略[J]. 电工技术学报, 2022, 37(20): 5313-5323. Li Xiaoqiang, Ma Yongchao, Huang Jinwei, et al.Wide-gain-range control scheme for interleaved boost integrated CLLLC resonant converter based on dual pulse width modulation[J]. Transactions of China Electrotechnical Society, 2022, 37(20): 5313-5323. [9] 廖嘉睿, 杭丽君, 但志敏, 等. 宽范围CLLLC双向同步整流数字控制方法[J]. 电工技术学报, 2022, 37(14): 3632-3642. Liao Jiarui, Hang Lijun, Dan Zhimin, et al.Digital control method of wide-range CLLLC bidirectional synchronous rectification[J]. Transactions of China Electrotechnical Society, 2022, 37(14): 3632-3642. [10] Ma Wenjie, Li Hui, Yin Shan, et al.Design of hybrid SiC/Si based T-type three-level LLC resonant converter with wide-input range and low conduction loss for automotive auxiliary power module[J]. IET Power Electronics, 2023, 16(2): 209-226. [11] 程鹤, 徐恺, 李朋圣, 等. 三相CLLC谐振变换器磁集成平面变压器设计与优化[J]. 电工技术学报, 2024, 39(12): 3774-3786. Cheng He, Xu Kai, Li Pengsheng, et al.Design and optimization of three-phase CLLC resonant converter with magnetic integrated planar transformer[J]. Transactions of China Electrotechnical Society, 2024, 39(12): 3774-3786. [12] 姜盟瀚, 伍群芳, 王勤, 等. 一种考虑损耗与寄生参数的LLC四元平面矩阵变压器集成优化设计[J]. 电工技术学报, 2025, 40(10): 3195-3208. Jiang Menghan, Wu Qunfang, Wang Qin, et al.Integrated optimization design of LLC four-element-matrix planar transformer considering loss and parasitic parameters[J]. Transactions of China Elec-trotechnical Society, 2025, 40(10): 3195-3208. [13] 周子航, 高祎韩, 刘懿静, 等. 基于平面磁元件的LLC变换器相关参数的整体优化设计方法[J]. 电工技术学报, 2024, 39(15): 4820-4829, 4895. Zhou Zihang, Gao Yihan, Liu Yijing, et al.Parameters global optimization design method for LLC converter with planar magnetic[J]. Transactions of China Electrotechnical Society, 2024, 39(15): 4820-4829, 4895. [14] Esfahani A G, Adib E.Very high step-down coupled inductor two-phase Buck converter with single mag-netic element and inherent clamp voltage capability[J]. IET Power Electronics, 2024, 17(5): 640-648. [15] Ansari S A, Davidson J N, Foster M P.Fully-integrated transformer with asymmetric primary and secondary leakage inductances for a bidirectional resonant converter[J]. IEEE Transactions on Industry Applications, 2023, 59(3): 3674-3685. [16] 王弘珺, 郁专, 谢少军. 双向CLLC谐振变换器的参数设计方法研究[J]. 电源学报, 2025, 23(1): 11-20. Wang Hongjun, Yu Zhuan, Xie Shaojun.Study on parameter design method for bi-directional CLLC resonant converters[J]. Journal of Power Supply, 2025, 23(1): 11-20. [17] 王佳宁, 邹强, 胡嘉汶, 等. 一种中压绝缘大功率中频变压器的优化设计方法[J]. 电工技术学报, 2022, 37(12): 3048-3060. Wang Jianing, Zou Qiang, Hu Jiawen, et al.An optimal design method for medium-voltage insulated high-power medium-frequency transformer[J]. Transa-ctions of China Electrotechnical Society, 2022, 37(12): 3048-3060. [18] 王议锋, 陈晨, 陈博, 等. LLC谐振变换器的变压器绕组优化设计[J]. 电工技术学报, 2022, 37(5): 1252-1261. Wang Yifeng, Chen Chen, Chen Bo, et al.Optimal design of transformer winding of LLC converter[J]. Transactions of China Electrotechnical Society, 2022, 37(5): 1252-1261. [19] 骆仁松, 汪涛, 文继峰, 等. 大功率高频变压器三维温升计算及优化设计方法[J]. 电工技术学报, 2023, 38(18): 4994-5005, 5016. Luo Rensong, Wang Tao, Wen Jifeng, et al.Three-dimensional temperature calculation and optimization design method for high power high-frequency trans-former[J]. Transactions of China Electrotechnical Society, 2023, 38(18): 4994-5005, 5016. [20] 曹小鹏, 陈武, 宁光富, 等. 基于多目标遗传算法的大功率高频变压器优化设计[J]. 中国电机工程学报, 2018, 38(5): 1348-1355. Cao Xiaopeng, Chen Wu, Ning Guangfu, et al.Optimization design of high-power high-frequency transformer based on multi-objective genetic algo-rithm[J]. Proceedings of the CSEE, 2018, 38(5): 1348-1355. [21] Ahmed D, Wang Li.Optimal peak flux density model (OPFDM) for non-iterative design of high-frequency gapped transformer (HFGT) in LLC resonant con-verters[J]. IET Power Electronics, 2020, 13(5): 942-952. [22] Park H C, Yang J U, Jang J S, et al.Transformer design technique based on the magnetic equivalent model of high-frequency isolated LLC converter with high accuracy and reduced design time[J]. IEEE Access, 2024, 12: 3948-3959. [23] 赵志刚, 白若南, 陈天缘, 等. 基于智能优化算法的高频变压器电磁结构优化设计[J]. 电工技术学报, 2024, 39(18): 5610-5625. Zhao Zhigang, Bai Ruonan, Chen Tianyuan, et al.Optimization design of electromagnetic structure of high frequency transformer based on intelligent optimization algorithm[J]. Transactions of China Electrotechnical Society, 2024, 39(18): 5610-5625. [24] Barrios E L, Ursúa A, Marroyo L, et al.Analytical design methodology for Litz-wired high-frequency power transformers[J]. IEEE Transactions on Indu-strial Electronics, 2015, 62(4): 2103-2113. [25] Barrios E L, Urtasun A, Ursúa A, et al.High-frequency power transformers with foil windings: maximum interleaving and optimal design[J]. IEEE Transactions on Power Electronics, 2015, 30(10): 5712-5723. [26] Wojda R P, Kazimierczuk M K.Analytical optimi-zation of solid-round-wire windings[J]. IEEE Transactions on Industrial Electronics, 2013, 60(3): 1033-1041. [27] 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. [28] Kazimierczuk M K, Wojda R P.Maximum drain efficiency class F3 RF power amplifier[C]//2011 IEEE International Symposium of Circuits and Systems (ISCAS), Rio de Janeiro, Brazil, 2011: 2785-2788. [29] Wojda R P.Thermal analytical winding size opti-mization for different conductor shapes[J]. Archives of Electrical Engineering, 2015, 64(2): 197-214. [30] Hurley W G, Wolfle W H, Breslin J G.Optimized transformer design: inclusive of high-frequency effects[J]. IEEE Transactions on Power Electronics, 1998, 13(4): 651-659. [31] Forest F, Laboure E, Meynard T, et al.Analytic design method based on homothetic shape of magnetic cores for high-frequency transformers[J]. IEEE Transactions on Power Electronics, 2007, 22(5): 2070-2080. [32] Hurley W G, Wölfle W H.Transformers and Inductors for Power Electronics, Theony, Design and Applications[M]. Chichester: John Wiley & Sons Ltd., 2013. [33] Yu Xiang, Su Jianhui, Lai Jidong, et al.Analytical optimization of nonsaturated thermally limited high-frequency transformer/inductor design considering discreteness of design variables[J]. IEEE Transactions on Power Electronics, 2020, 35(6): 6231-6250. [34] (美) 卡罗尼尔. 麦克莱曼. 变压器与电感器设计手册, 第四版. 周京华译[M]. 北京: 中国电力出版社, 2014. [35] Elizondo D, Barrios E L, Ursúa A, et al.Analytical modeling of high-frequency winding loss in round-wire toroidal inductors[J]. IEEE Transactions on Industrial Electronics, 2023, 70(6): 5581-5591. [36] Yu Xiang, Su Jianhui, Lai Jidong.Winding loss calculation revisited for medium-frequency trans-former in applications of DC generation of new energy[C]//8th Renewable Power Generation Con-ference (RPG 2019), Shanghai, China, 2019: 1-8. [37] Zhao Yuhu, Ming Zhengfeng, Han Binbin.Analytical modelling of high-frequency losses in toroidal inductors[J]. IET Power Electronics, 2023, 16(9): 1538-1547. [38] 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. [39] 史方圆, 李睿, 蔡旭. 35kV全SiC光伏发电单元中高频隔离变换器的寄生参数影响及抑制方法[J]. 中国电机工程学报, 2020, 40(6): 1787-1801. Shi Fangyuan, Li Rui, Cai Xu.Influence of parasitic parameters and its suppression methods of high frequency isolated converter in 35kV all-SiC photo-voltaic generation unit[J]. Proceedings of the CSEE, 2020, 40(6): 1787-1801. [40] 许赟, 陈丽霞, 陈翼龙, 等. 基于拉格朗日数乘法的高频高压变压器分布电容优化设计[J]. 中国电机工程学报, 2017, 37(3): 939-946. Xu Yun, Chen Lixia, Chen Yilong, et al.Optimal design based on Lagrange multiplier approach for parasitic capacitance of high frequency high voltage transformers[J]. Proceedings of the CSEE, 2017, 37(3): 939-946. [41] 惠琦, 任小永, 陈乾宏. 采用环形变压器的小功率隔离型DC-DC变换器共模电磁干扰噪声建模与抑制[J]. 电工技术学报, 2024, 39(22): 7126-7138. Hui Qi, Ren Xiaoyong, Chen Qianhong.Common-mode electromagnetic interference noise modeling and suppression for low-power isolated power converter using toroidal transformer[J]. Transactions of China Electrotechnical Society, 2024, 39(22): 7126-7138. [42] 王建渊, 郭俊玲, 闫瑾, 等. 基于CLLLC变频扩展移相分段调制的宽增益车载充电机研究[J/OL]. 电工技术学报, 2025: 1-14. https://doi.org/10.19595/j.cnki.1000-6753.tces.241310. Wang Jianyuan, Guo Junling, Yan Jin, et al. Research on wide gain vehicle charger based on CLLLC frequency conversion extended phase shift segment modulation[J/OL]. Transactions of China Electrotech-nical Society, 2025: 1-14. https://doi.org/10.19595/j.cnki.1000-6753.tces.241310. [43] 张新闻, 刘百林, 杨树德. CLLLC谐振变换器电流应力抑制策略[J/OL]. 电源学报, 2025: 1-14. http://kns.cnki.net/kcms/detail/12.1420.TM.20231130.1749.007.html. Zhang Xinwen, Liu Bailin, Yang Shude. Current stress suppression strategy for CLLLC resonant converter[J/OL]. Journal of Power Supply, 2025: 1-14. http://kns.cnki.net/kcms/detail/12.1420.TM.20231130.1749.007.html.
2025, Vol. 40 
