Model refinements of transformers via a subproblem finite element method

This paper aims to develop a methodology for progressive finite element (FE) modeling of transformers, from simple to complex models of both magnetic cores and windings.

The progressive modeling of transformers is performed via a subproblem (SP) FE method. A complete problem is split into SPs with different adapted overlapping meshes. Model refinements are performed from ideal to real flux tubes, one-dimensional to two-dimensional to three-dimensional models, linear to nonlinear materials, perfect to real materials, single wire to volume conductor windings and homogenized to fine models of cores and coils, with any coupling of these changes.

The proposed unified procedure efficiently feeds each SP via interface conditions (ICs), which lightens mesh-to-mesh sources transfers and quantifies the gain given by each refinement on both local fields and global quantities, with a clear view on its significance to justify its usefulness, if any. It can also help in education with a progressive understanding of the various aspects of transformer designs.

Models of different accuracy levels are sequenced with successive additive corrections supported by different adapted meshes. The way the sources act at each correction step, up to the full models with their actual geometries, is given a particular care and generalized, allowing the proposed unified procedure. For all the considered corrections, the sources are always of IC type, thus only needed in layers of FE along boundaries, which lightens the required mesh-to-mesh projections between subproblems.