基于镜像法的高频圆导线变压器漏感计算模型  

Leakage Inductance Calculation Model of High-frequency Round Conductor Transformer Based on Image Method

作　　者：赵志刚[1] 郑宇萱 陈天缘 刘朝阳 葛雅婕 ZHAO Zhigang;ZHENG Yuxuan;CHEN Tianyuan;LIU Zhaoyang;GE Yajie(State Key Lab of Reliability and Intelligence of Electrical Equipment(Hebei University of Technology),Beichen District,Tianjin 300401,China;Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province(Hebei University of Technology),Beichen District,Tianjin 300401,China)

机构地区：[1]省部共建电工装备可靠性与智能化国家重点实验室(河北工业大学),天津市北辰区300401 [2]河北省电磁场与电器可靠性重点实验室(河北工业大学),天津市北辰区300401

出　　处：《中国电机工程学报》2024年第16期6697-6706,I0034,共11页PROCEEDINGS OF THE CHINESE SOCIETY FOR ELECTRICAL ENGINEERING

基　　金：国家自然科学基金项目(52077053);河北省人才工程培养资助项目(A201902009)。

摘　　要：高频变压器漏感是影响固态变压器功率传输特性及运行可靠性的一个重要参数,在设计阶段需要对其进行快速、精确的预测。由于数值法计算成本高昂,难以满足变压器设计阶段快速预测漏感的要求,目前常采用解析法计算漏感参数。基于一维磁场假设的计算模型忽略了绕组端部效应的影响,无法准确估计漏感。多数二维计算模型虽然考虑了横向漏磁通的影响,但泊松方程的求解及电流密度的级数表征导致其计算过程过于繁琐。因此,该文基于镜像原理准确提取磁芯窗口区域的漏磁场,推导该区域直流漏磁能量的解析表达式,并引入计及绕组集肤效应和邻近效应的频率相关因子,揭示宽频区间内漏感的衰减规律,建立能够同时考虑频变特性和绕组端部效应的漏感解析计算模型。最后,搭建漏感测量平台,针对具有不同孔隙率的变压器样机开展详细的实验研究。结果表明:所建模型的最大相对误差不超过5%,验证了该模型的准确性和有效性。The leakage inductance of high-frequency transformers is an important parameter affecting the power transmission characteristics and operational reliability of solid-state transformers,so it needs to be predicted quickly and accurately during the design stage.Due to the high computational cost of the numerical method,it is difficult to meet the requirements of quickly predicting leakage inductance during the transformer design stage.Currently,the analytical method is often used to calculate leakage inductance parameters.The calculation models based on one-dimensional magnetic field assumption ignore the influence of the winding edge effect and cannot accurately estimate leakage inductance.Although most two-dimensional calculation models consider the influence of transverse leakage flux,the solution of Poisson equation and the representation of current density in terms of series lead to an overly cumbersome calculation process.Therefore,this paper accurately extracts the leakage magnetic field in the core window based on the image principle,derives an analytical expression for the DC leakage magnetic energy in this area,and introduces frequency-dependent factors that take into account the skin effect and proximity effect of the winding to reveal the attenuation law of leakage inductance in a wide frequency range,and establishes an analytical calculation model for leakage inductance that can simultaneously consider the frequency-dependent characteristic and winding edge effect.Finally,a leakage inductance measurement platform is built and a detailed experimental study is carried out on transformer prototypes with different porosities to verify the accuracy and validity of the proposed model.

关 键 词：圆导线变压器 漏感 镜像原理 端部效应 频变特性 

分 类 号：TM433[电气工程—电器]