Integral equations method for the analysis and design of ELF conductive and magnetic shields

Abstract

SUMMARYThe need to shield ELF (extremely low frequency) magnetic fields generated by power and industrial installations arises for two main reasons: the first one is a typical EMC (electromagnetic compatibility) problem related to possible interference among electric and electronic devices while the second one is related to potential health effects due to magnetic field exposure. Different techniques exist to reduce the magnetic field mainly depending on the kind of source considered; here we treat only the shielding action offered by long and metallic structures like slabs, sheets, and foils with respect to the field produced by long sources like power cables, bus-bars, and wires. In particular, we focus our attention on magnetic metallic shields where the shielding action is due to both 'magnetic flux shunting' and 'eddy current cancellation' mechanisms. From the design point of view, it is useful to have at disposal a calculation tool able to predict the magnetic field reduction, in a given region of space, as a function of the shield characteristics (geometry, material) and source characteristics (conductors disposition, distance from the shield). The typical calculation technique used in this kind of problem is based on the finite elements method (FEM) that is broadly described in the technical literature. Here, we want to propose a different approach that is based on integral equations (IE) and is able to model shields made by materials like iron, steel, and mumetal having both conductive and magnetic properties; nevertheless, as special cases, the algorithm is also able to deal with purely conductive shields like copper and aluminium, (frequently used in applications) where only the eddy current shielding action exists, and with purely magnetic shields, under the action of a d.c. source, where only the magnetic flux shunting effect is present. The main hypothesis that is necessary to adopt in the model is the linear behaviour of the magnetic material; such hypothesis is certainly reasonable in many real situations where the material is far from saturation.

Principles of power-frequency magnetic shielding with finite-width plates

“…Numerical methods have been applied for metal parts processing a complex geometry, e.g. the finite‐element method and the integral equation methods . These methods themselves cannot lead to insight into the shielding mechanism and give physical interpretation of shielding phenomena.…”