Model Order Reduction Techniques for Electro-Quasistatic Simulation Methods in Electrical Power Transmission Technology

该研究项目的目标（后续申请人在DFG资助下成功开展的同名研究项目）是开发高效的模拟方法，用于确定高压系统组件的尺寸，并特别考虑电场分级材料。这些包括金属氧化物压敏电阻材料或混合聚合物材料，其具有基于碳化硅和氧化锌的粒状微压敏电阻作为用于非线性电阻电场分级的填充材料。目前，这些材料正在被深入研究，以验证其在电力工程设备中的运行能力，如高压能源电缆、电缆附件、绝缘子涂层、终端电晕保护或紧凑型高压套管。由于这些场分级材料的特殊非线性特性，在这类系统的部件设计中，时域计算机仿真是必要的。这导致时间密集的电准静态场分布的数值计算，需要考虑到这些材料的非线性特性。申请人在DFG资助下开发的数学模型降阶技术（莫尔技术）的研究结果已经允许成功地减少这些电准静态时域方法的计算时间要求，并且甚至首次实现了具有非线性场分级的高压设备的2D FEM模型的不确定性量化分析模拟。在这个后续的研究项目中，这些数学技术将被改进和扩展新的方法和替代问题的配方。这些新的技术将在数值效率和精度方面进行研究。其目的是提高非线性电-准静态时域模拟方法的效率，使得参数优化和不确定性量化分析方法甚至可以在合理的计算时间内用于高分辨率的3D FEM模型。

The goal of this research project (following up a successful research project of the applicant with the same title supported under DFG-grant is the development of efficient simulation methods for dimensioning high voltage system components with special consideration of electric field grading materials. These include metal oxide varistor materials or hybrid polymeric materials with granular microvaristors based on silicon carbide and zinc-oxide as filler materials used for non-linear resistive electric field grading. Currently, these materials are studied intensively in order to verify their operational capability in power engineering devices such as high-voltage energy cables, cable accessories, insulator coatings, terminal corona protections or compact high-voltage bushings. Due to the special non-linear characteristics of these field grading materials computer simulations in time-domain are necessary in the component design of such systems. This leads to time intensive numerical calculations of electro-quasistatic field distributions which need to take into account the non-linear characteristics of these materials. The research results of the applicant on mathematical model-order-reduction techniques (MOR techniques) developed under DFG grant already allow to successfully reduce the computational time requirements of these electro-quasistatic time-domain methods and for first time even enabled uncertainty quantification analysis simulations for 2D FEM models of high-voltage devices with nonlinear field grading. In this follow up research project these mathematical techniques are to be refined and extended with novel approaches and alternative problem formulations. These novel techniques will be studied with respect to numerical efficiency and accuracy. The aim is to improve the efficiency of the nonlinear electro-quasistatic time-domain simulation methods such that parameter optimization and uncertainty quantification analysis methods can be used even for high resolution 3D FEM models within reasonable computational times.