LLC平面变压器绕组损耗与漏感改进有限元计算方法

Improved Finite Element Method of Winding Loss and Leakage Inductance for Planar Transformer Used in LLC Converter

有限元法常被用于平面变压器绕组损耗、漏感等参数的精准计算。然而,受到计算与存储成本的限制,在设计周期较为紧张的条件下,可精确计算的设计方案数量有限,增加了将局部最优点选为最终设计方案的风险。为缩减有限元法的计算与存储成本,该文针对有限元法资源占用较大的线性方程组构建与求解这一过程进行改进。首先,通过分析平面变压器磁场强度分布规律,依据边缘效应影响强弱,将求解区域划分为强边缘效应区域与弱边缘效应区域;其次,引入更为契合弱边缘效应区域的一维线性单元,从而减少描述求解域场量的节点数与单元数,进而减少线性方程组系数矩阵阶数,达到节约计算与存储资源的目的;再次,通过调节相邻单元节点分布规律,解决由于引入一维线性单元而产生的单元兼容、系数矩阵构建等问题;最后,搭建平面变压器模型,通过对比绕组损耗、漏感的实验值与计算值以及对比该文方法与有限元法计算、存储成本,验证了该文方法的有效性。

The finite element method is often used to accurately calculate the performance parameters such as winding loss and leakage inductance of planar transformers.However,due to high storing and calculating costs,in the case of a tight design cycle,the number of design schemes that can be accurately calculated is limited,which increases the risk of selecting the local optimum point as the final design scheme.Therefore,the process of constructing and solving linear equations that occupy many resources is improved.Firstly,by analyzing the magnetic field intensity distribution of the planar transformer,according to the strength of the edge effect,the solution region of the planar transformer is divided into the strong edge effect region and the weak edge effect region.Secondly,a one-dimensional linear element that is more suitable for the weak edge effect region is introduced to reduce the number of nodes and elements necessary to describe the solution region’s field,saving computing and storing resources.Thirdly,by restricting the distribution of adjacent element nodes,the problems of element compatibility and coefficient matrix construction caused by the introduction of one-dimensional linear elements are solved.Finally,planar transformer models are built.The winding loss and leakage inductance of calculated and experimental values,as well as the calculating and storing costs of the proposed method and the finite element method,are compared,which verifies the proposed method.