Improvement of the Finite-Element Analysis of 3-D, Nonlinear, Periodic Eddy Current Problems Involving Voltage-Driven Coils Under DC Bias

Different techniques are investigated to improve the performance of the solution process of 3-D, time-periodic, nonlinear, voltage-driven eddy current problems under the influence of dc bias by the means of the finite-element method. The underlying nonlinear iteration technique is the time-periodic fixed-point method. The benefit of a static approximation to generate an initial solution, i.e., of a static initialization is pointed out. A secant method and a Schur complement technique to carry out the static initialization are compared. The procedures developed are applied to 3-D models of one- and three-phase benchmark transformer problems with dc bias.

I. Introduction

The main goal of this investigation is to analyze different ways to solve the finite-element equation system of 3-D nonlinear, time-periodic problems when a direct current (dc) bias is present in the excitation. Direct currents in transformer windings are mostly geomagnetically induced currents [1], [2]. The resulting dc components lead to adverse effects on power distribution transformers by adding a dc bias to the magnetization current. As a consequence, the core of the transformer gets saturated within the half period in which the magnetization current and the dc bias are in the same direction resulting in increasing noise level, additional core losses as well as eddy current losses due to the higher leakage flux resulting [3], [4]. To predict these effects, numerical investigations involving such waveforms are necessary. In this paper, simplified benchmark problems of a single-phase transformer and of a three-phase transformer are investigated by the means of a 3-D finite-element analysis.