An extremely fast technique for nonlinear three dimensional finite element magnetic field computations

Abstract

A fast Newton-Raphson technique (FNR) for the determination of nonlinear three dimensional finite element magnetic fields in electrical devices is presented. The new technique provided substantial reduction in CPU time required for complete and converged nonlinear magnetic field solutions by more than 50% in comparison with the standard Newton-Raphson (NR) Technique. The significant reduction in CPU time was achieved without any sacrifice in the accuracy of the converged three dimensional magnetic field solutions or in the values of the device terminal parameters. To illustrate the great advantages of the new method, an example single phase transformer was implemented with widely varying degrees of magnetic saturation. Values of magnetic vector potential, as well as flux density components, obtained using the new technique, were compared with the values obtained using standard NR method. Furthermore, the saturated values of magnetizing inductances were obtained and compared using the new and standard NR methods. It was observed that no numerical errors were introduced as a result of using the new technique. The numerical values accurately matched not only in the whole part of the value, but also in the fraction part to the third and fourth digit. It was further observed that the higher the degree of magnetic saturation in the example considered, the faster the new technique in convergence to accurate values.