Magnetic Field Behavior of a Deeply Saturated Soft-Iron Core with a Concentrated Winding

In a study of the harmful effects of geomagnetically induced currents on transformers, a literature search revealed that there is not a good technical description of deep saturation effects for soft-iron cores with concentrated windings. As a first step in studying such a condition, a simple configuration was chosen: a toroidal core with a single concentrated magnetizing winding. The paper shows that nonuniform magnetization in the core can exist if the magnetizing ampere-turns are high. With a view to showing how this nonuniform magnetization condition affects the field behavior, a detailed field analysis on the two-dimensional core is performed. The analysis adopts the existing finite-element Newton-Raphson numerical techniques but takes into full account the field-dependent nonlinear characteristics of soft iron. Numerical results for the total field B¿ inside the core, in the conductor winding, and in the air-space are presented. In particular, the interplay between the iron field B¿m (i.e. magnetic flux density due to the magnetized iron core itself) and the current field B¿c (i.e. magnetic flux density due to the magnetizing current in the winding) is stressed.