Accurate and efficient computation of the inductance matrix of transformer windings for the simulation of very fast transients

When a transformer is subjected to very fast front transients, the penetration of the magnetic flux into the core becomes, in general, negligible. To represent this phenomenon, it is common practice to compute the winding inductance matrix (turn-to-turn) at very high frequencies using the expressions for air-core inductors. However, since the core becomes a magnetic insulating wall at very high frequencies (MHz), the distribution of the magnetic field is altered because the field cannot enter the region occupied by the core. Therefore, the air-core approximation formulae overestimate the inductance at high frequencies. This is especially true in the region inside the core window. Large errors are found when the inductances are computed with the air-core approximation. This paper presents a technique, based on the application of a multilayer method of images, to take the presence of the core into consideration. The final expressions are very simple, yet they give remarkably accurate results. Comparisons with finite-element analyses prove the excellent accuracy of the technique.