Magnetic devices analysis by Face FEM coupled with standard reluctance network

A Finite Element Method (FEM) mesh is converted to a reluctance network through an original magnetostatic formulation based on face shape functions. This meshed reluctance network is coupled with an standard one, characterizing a 0D system. Both approaches are fully-compatible and the hybridized problem can be solve with a single circuit solver. The approach is tested in 2D on a magnetic circuit with an air gap and compared to classical FEM nodal formulation. Index Terms-Reluctance network, Finite Element Method (FEM), face shape functions, Face FEM I. INTRODUCTION Optimizing electromagnetic devices can require a large amount of data that might be provided by numerical simulations. Many numerical methods are used to model electromagnetic devices, but the RNM (Reluctance Network Method) and FEM (Finite Element Method) are the most widely used for magnetostatic modeling. The FEM is well known by its flexibility and generality, once the mathematical formulations are based on a mesh. Furthermore, it is noticeable the knowledge base available for this method, for instance [1]. However, it leads to an high number of degrees of freedom and so quite long computation times. On the other hand, the RNM is one of the most primitive methods for magnetic modeling and its application is based on a reluctance network. This method has remained useful due to its coherent results obtained with low computational effort and low computational simulation time [2] and has been largely applied to model power transformers [3] [4]. This method is also largely applied to model rotating electrical machines [5][6][7] and transmission lines [8]. Nevertheless, it is important to notice that these applications are based on a reluctance network defined manually, that might imply an hard, long and non-general task. In [9] is presented a methodology that couples nodal/edge FEM with external reluctances network. In this paper, we go a step forward by proposing a formulation fully-compatible with both numerical approaches and solved with a single 0D circuit solver. Finally, the results of modeling a actuator with the classical nodal FEM and with the proposed methodology are compared.