基于磁耦合度的多导体系统互连参数提取及稀疏化研究

The key constraints of the application of partial element equivalent circuit method (PEEC) for conductor system are the high order and density of the parameter matrix from extraction. The reduction and sparse are the effective approaches for realizing compression of the PEEC model, and which are concerned in this project. Firstly, a screening algorithm based on the magnetic coupling strength is proposed for the interconnect parameters. The strength of magnetic coupling is defined according to the effective coupling distance, the shielding effect by other conductors, as well as the difference between active and passive conductors. The coupling parameters which are less than the strength will be neglected. Secondly, a hybrid mesh method is proposed, which is based on the double exponential function and bilinear basis function. The distribution of electromagnetic parameters on the conductor can be described by the functions. As a result, the traditional grid based on the volume element is replaced by the three dimensions distribution functions with nonuniformity. This technique improves the matching accuracy of geometric discretization for the actual distribution of the electromagnetic field, and greatly reduces the number of unknowns. Thirdly, some modeling techniques, such as: symmetrical way, hierarchical modeling way, and a calculation multiplexing technique, will be developed for the special structures. Finally, an iterative method based on the Krylov subspace is given. These techniques could help lay a foundation for applying the PEEC method to the larger and more complex object, and obtaining more information on the simulation.

部分元等效电路法（PEEC）在多导体系统数值模拟中的主要制约因素为提取的参数矩阵的高阶性与稠密性，降阶和稀疏化是实现模型缩减的有效手段。本项目提出一种基于磁耦合度的互连参数筛选算法。通过合理定义有效耦合距离，考虑多导体的屏蔽作用，以及有源与无源导体磁耦合的差别，构建科学的磁耦合度判据，筛除显著小项，实现互连参数矩阵的稀疏化。提出一种基于双指数函数和双线性基函数的混合型分布式网格剖分方法，用三个维度且兼具非均匀性的分布函数替代传统的体积元网格，在实现降阶的同时，提高了网格与实际电磁场分布的匹配精度。对特定导体结构分别提出分级建模法、对称建模法、中间复用法等模型缩减方法，可有效降低模型阶数、提高参数提取效率、压缩参数矩阵规模。最后，提出一种基于预条件处理和Krylov子空间的迭代求解法。该项工作为PEEC在大尺寸复杂多导体系统上的应用奠定了基础。

本项目成功将PEEC法应用到大型导体结构的电磁建模和求解计算中，以超大尺寸海上风力发电机为研究载体，对风机塔筒进行网格剖分，提取其等效电阻、自感、互感，将导体塔筒转化为由众多支路互连构成的电路网络。重点解决了圆筒形结构剖分后，曲面导体片的自感以及片与片之间互感的量化问题。针对提取参数矩阵高阶的问题，提出了一种参数筛选方法——球壳半径加速法，通过选取合理的截取半径，筛除矩阵中的显著小项参数，实现参数矩阵的降阶和稀疏化，大大加快了模型的求解速度和计算容量。数值验证表明截取半径为塔筒几何尺寸70%左右时，可实现计算精度与计算速度的较好平衡。针对薄板状导体，提出了一种基于趋肤效应的双指数函数，用来描述导体中电磁参量的分布，通过导体表面电磁参数和分布函数即可表达导体内任意位置电磁分布值，避免了传统的体积元网格剖分，大大减少了网格数，同时保证了网格精度。针对规则导体结构，通过分析其内部电磁分布规律，提出了对称建模技术，可将建模对象压缩到原始模型的四分之一，大幅减少了未知数提高了计算速度。计算结果表明该建模技术有效。通过构建风机完整雷电通道的电磁暂态模型，计算并观察塔筒上等效支路的电流和节点电位，可了解雷击过程中塔筒上的电气响应特性，为开展风机防雷工作提供了技术支撑。本项目通过场路耦合的思路，将开放场空间的电磁耦合问题转换为电路互感问题，将电磁场问题与电路问题统一到电路求解中来，为剖析导体内部电磁现象的本质提供了有力工具。