A Stabilized Circuit-Consistent Foil Conductor Model

The magnetoquasistatic simulation of large power converters, in particular transformers, requires efficient models for their foils windings by means of homogenization techniques. In this article, the classical foil conductor model is derived and an inconsistency in terms of circuit theory is observed, which may lead to time-stepping instability. This can be related to the differential-algebraic nature of the resulting system of equations. It is shown how the foil conductor model can be adapted to mitigate this problem by a modified definition of the turn-by-turn conductance matrix. Numerical results are presented to demonstrate the instability and to verify the effectiveness of the new adapted foil conductor model.