Substations contain many components such as switches, transformers, and reactor coils that generate electromagnetic fields. The strong fields emanating from the transformers must frequently be shielded so as to protect other equipment and systems in and around the substation. In this process, however, the enclosure or shield walls are subject to eddy currents, which can heat the wall material enough to lead to melting.

The multiphysics coupling between heat and electromagnetics was modeled with COMSOL, but in this model, a different problem arose. An important parameter in electromagnetic shielding is the ratio of the layer thickness, d, to the penetration (skin) depth, δ. In many situations, d ≥ δ, particularly at higher frequencies or for very thick layers.

Figure 3. Model of Three Current-Carrying Coils of different phase (left) and the inductive heating in the electromagnetic shield (right).
The finite element method (FEM) is well suited for modeling arbitrary shapes and coupled phenomena, but it often requires a very fine mesh if it is to resolve the interior of very thin structures such as a metal wall, as in the case of these shields. With standard grid shapes, modeling such walls and other thin conducting layers in three dimensions often leads to an excessive number of mesh elements.

One approach to reduce the number of elements is to work with scaled or elongated objects, but in many cases this still leads to a number of elements that is difficult or slow to handle. The software enables implementation of an expression for the conducting layer, and while it treats the 3D structure as a 2D surface, it simulates the layer's 3D behavior. To include the influence of the layer on the electromagnetic fields in the surrounding 3D domain, appropriate boundary conditions were applied across the surface (Figure 2). Thus, while significantly reducing the amount of memory needed and the solution time by treating the wall layer as a 2D boundary, engineers could still simulate the substation enclosure's inductive wall heating and the shielding efficiency.

These methods have been applied to simulate such cases within microwave phenomena and electromagnetic compatibility, where an equation at the boundary replaces the need to model the thin domain. An added advantage is that this system of equations can also simulate internal borders such as shielding layers modifying the nearfield in a cellular phone such as between the antenna and other components (Figure 2).

In this specific application, a model was developed of an enclosed substation with three current-carrying coils designed to reduce reactive power; that is, to minimize the phase shift between current and voltage. In this situation, the currents induced in the wall are very strong, leading to high temperatures. In particular, current density in the regions near openings and slits can become so high that the temperature reaches the metal's melting point.

The model results show that the heating is greatest around the porthole at the front of the electromagnetic shield. Figure 3 (left) shows simulation results for three current-carrying coils of different phases and reveals the size and direction of the magnetic flux. The figure on the right illustrates inductive heating in the electromagnetic shield.

The model uses aluminum as the shielding material, and the results confirm that heating is greatest around the porthole at the front of the electromagnetic shield. Adjustments in the design are likely necessary in order to reduce the maximum temperature.

This work was done by Dr. Göran Eriksson of the Saab Group, using software from COMSOL. For more information, Click Here .