Three-dimensional numerical solution of eddy currents in thin plates

Numerical methods of solving eddy-current problems are difficult to apply to 3-dimensional fields, because all the field quantities are vectors, with three components, and the electrostatic field generated by the conductor surfaces has to be taken into account in magnetic-vector-otential formulations. By treating the linked current and flux paths in network terms, it is shown that all linear and nonlinear 3-dimensional problems can be expressed in terms of two scalar functions, and that, when the currents are confined to thin conducting layers, this reduces to a magnetic-scalar-potential formulation. The network approach expresses this, simply and directly, in numerical terms. It can be readily extended to include eddy currents in iron surfaces, and to thicker conductors in which the magnitude and phase of the induced currents varies with depth. Circuits consisting of small-diameter wires can be treated in terms of an equivalent plate with a discontinuous conductivity. The calculated field distribution round a square copper plate, solved iteratively, has been found to converge rapidly and to give results in close agreement with values obtained experimentally. The method has been applied to transformer-legplate and core losses