A network approach to the numerical solution of Eddy-current problems

Numerical methods are generally applied to induction devices by assuming 2-dimensional geometry, and are difficult to extend to 3 dimensional eddy currents because the field relationships require vector functions, each with 3 interdependent components. A simpler description is sought by replacing the field quantities by two coupled networks, one electric and one magnetic. These provide an insight into the behaviour of the device, since they combine a terminal equivalent circuit with a topological description, and they are suitable for numerical solution. Their key property is their interlinkage. It is shown that this can be manipulated to provide a scalar-potential description of the 3-dimensional eddy-current problem, corresponding to the dynamic equivalent of a magnetic shell. The same approach can be used to derive a variety of equivalent circuits for induction devices and, when applied to a transformer, shows that the magnetising, and not the leakage reactance, should be split into two components. The scalar-potential formulation is particularly simple when applied to thin plates, backed by unsaturated iron, and its validity has been demonstrated by comparing calculated and measured flux distributions around a square copper plate. It is here applied to conductors of large cross-section, and the results compared with the customary vector-potential formulation in 2 dimensions.