Solution Of Eddy Current Problems Research Articles

Computational methods for solving static field and eddy current problems via Fredholm integral equations

Two-dimensional static field problems can be solved by a method based on Fredholm integral equations (equations of the second kind). This has numerical advantages over the mote commonly used integral equation of the first kind. The method is applicable to both magnetostatic and electrostatic problems formulated in terms of either vector or scalar potentials. It has been extended to the solution of eddy current problems with sinusoidal driving functions. The application of the classical Fredholm equation has been extended to problems containing boundary conditions: 1) potential value, 2) normal derivative value, and 3) an interface condition, all in the same problem. The solutions to the Fredholm equations are single or double (dipole) layers of sources on the problem boundaries and interfaces. This method has been developed into computer codes which use piecewise quadratic approximations to the solutions to the integral equations. Exact integrations are used to replace the integral equations by a matrix equation. The solution to this matrix equation can then be used to directly calculate the field anywhere.

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.