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。由于电机的几何形状复杂，通常采用有限元法分析电机问题。在后处理中执行模拟场解的评估和显式分析。数值方法的最新应用是二维和数值上广泛的三维模型。每个模拟都代表一个特定的定义域问题，每个问题都有其特定的定义边界条件。因此，无论是几何参数、材料参数还是激励参数的变化，都是在数值分析链的严格和确定的顺序中先验地进行的。在设计工程师自发地希望改变一个或多个参数的情况下，由于当今使用的数值分析链的计算时间很长，因此不可能看到变化对场解的直接影响。该项目将是电磁学数值实时仿真的重要一步。定义的电磁场问题的模型降阶是显着减少计算时间的重要关键。因此，本课题研究模型降阶方法在电机分析等领域的磁场问题中的可行性。本课题旨在实现电机分析中常见的非线性、时间和励磁相关的电磁场问题的模型降阶方法。模型降阶在这类场问题上的应用是不存在的，因此是新的，已接受的实际运行项目的前两年的结果清楚地表明，本征广义分解在电磁学领域的应用是可行的。本征广义分解的方法可以应用到有限元方法中，并通过与运行项目第一部分中新开发的误差准则相结合，给出了不同问题类的一般用途。静态以及瞬态问题已经解决了这种方法和自由度显着减少。 结合该项目的连续研究，将有可能以定义的精度隔离解决方案域中的局部影响，以减少参数变化情况下整个问题域模拟的数值工作。这种方法将改进和简化磁场局部集中效应的分析。这种分析的一个例子是电机铁芯中的局部损耗分布。

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.