Numerical analysis of electromagnetic fields by Proper Generalized Decomposition in electrical machines

为了发展和改进电磁电路，目前普遍采用数值方法。在电机问题的分析中，由于复杂的几何形状，通常采用有限元方法。在后处理过程中对模拟的场解进行评估和显式分析。数值方法的最新应用是二维和数值扩展的三维模型。每个模拟代表一个特定的已定义领域问题，每个问题都有其特定的已定义边界条件。因此，无论是几何参数、材料参数还是激励参数的变化都是按照严格和确定的数值分析链的顺序进行的，在设计工程师自发地希望改变一个或多个参数的情况下，由于目前使用的数值分析链的计算时间很长，因此不可能看到这些变化对现场解的直接影响。所提出的方案将是迈向电磁场数值实时仿真的重要一步。对定义的电磁场问题进行模型降阶是显着减少计算时间的重要关键。因此，本课题研究了模型降阶方法对电机分析领域中常见的磁场问题的可行性，旨在实现电机分析中常见的非线性、时间和激励相关的电磁场问题的模型降阶方法。模型降阶在此类领域中的应用尚不存在，因此是新的。实际运行项目的头两年的结果清楚地表明，适当的广义分解在电磁学领域的应用是可行的。将适当的广义分解方法应用到有限元方法中，并与运行项目的第一部分中新发展的误差准则相结合，给出了不同问题类的一般用途。用这种方法解决了静力问题和暂态问题，并显著降低了自由度。结合该项目的连续研究，将有可能以确定的精度隔离解域中的局部影响，以减少在参数变化的情况下模拟整个问题域的数值工作量。这种方法将改进和简化对磁场局部集中效应的分析。这种分析的一个例子是电机铁心的局部损耗分布。

For the development and improvement of electromagnetic circuits, numerical methods are generally used nowadays. For the analysis of problems concerning electrical machines the Finite Element Method is commonly applied due to the complicated geometries. The evaluation and explicit analysis of the simulated field solution is performed in a post-process. State of the art applications for the numerical methods are two- and numerically extensive three-dimensional models. Each simulation represents one specific defined field problem, each with its specific defined boundary conditions. Therefore, variations, whether of geometry-, material- or excitation-parameters, are performed a-priori in a strict and determined sequences of the numerical analysis chain.In the case a design engineer spontaneously wishes to vary one or more parameter, it is not possible to see the direct impact of the changes on the field solution due to the long computation time in todays used numerical analysis chain. The proposed project will be a significant step towards a numerical real-time simulation in electromagnetics.The model order reduction of the defined electromagnetic field problem is an important key to reduce the computation time significantly. Therefore, in this project model order reduction methods are studied for their feasibility to magnetic field problems which can be found e.g. in the field of electric machine analysis.The project aims on the realization of model order reduction methods for non-linear, time- and excitation-dependent electromagnetic field problems which are common tasks in the analysis of electrical machines. The applications of model order reduction on such field problems is not existent and therefore new.The results of the first two years of the accepted actually running project indicate clearly, that the Proper Generalized Decomposition is feasible for application in the field of electromagnetics. The approach of the Proper Generalized Decomposition can be employed into the Finite Element Method and by the combination with the in the first part of the running project newly developed error criteria a general use for different problem classes is given. Static as well as transient problems have been solved with this approach and the degrees of freedom were significantly reduced. In combination with the consecutive studies of the project it will be possible to isolate local effects in the solution domain with a defined accuracy to reduce the numerical effort for the simulation of the overall problem domain in case of a variation of parameter. This methodology will improve and simplify the analysis of locally concentrated effects of the magnetic field. An example for such an analysis is the local loss distribution in the iron core of electrical machines.