Comparison of alternative formulations of 3-dimensional magnetic-field and eddy-current problems at power frequencies

The numerical calculation of 3-dimensional eddy currents is complicated by the need to use vector functions to describe the interlinked flux and current distributions. The three vector components are coupled, particularly by the conditions imposed by the copper and iron surfaces, and by other changes in material properties. The range of choice of magnetic and electric vector potentials is examined, including the ¿ and H vectors as particular examples, and it is shown that the problem formulation is greatly affected by the choice of gauge, or vector-potential divergence. This introduces scalar potentials which can be used in various ways. They control the coupling conditions between the vector components. One advantage of an electric vector potential, or generalised H, formulation is that the gauge can be chosen so that the vector is zero outside the conductors, and is replaced by a scalar. Magnetic vector-potential formulations are generally less attractive, both because the vector has to be computed throughout the region of interest and because of the greater complexity of the magnetic-and electric-interface conditions.