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. Using the standard solid and stranded conductor models is not computationally feasible for a foil winding. In this article, the classical foil conductor model is derived and, for the first time, an inconsistency in terms of circuit theory is reported, which may lead to time-stepping instability. The inconsistency can be related to the differential-algebraic nature of the resulting system of equations. A new modified definition of the turn-by-turn conductance matrix of the foil conductor model is shown to mitigate this problem. The different structure of the systems using the alternative turn-by-turn conductance matrix definitions is examined in detail. Numerical results are presented to demonstrate the instability of the original foil conductor model and to verify the effectiveness of the new proposed model.