PEEC method for evaluating magnetic shielding by metal structures at low frequency

Abstract

With the proliferation of electrical and electronic systems, the electromagnetic environment in modern buildings has been increasingly concerned as the EM fields can cause interference to sensitive equipment and potential adverse health effects. The EM field is mainly contributed by power equipment including cables running at power frequency. The large-size metal plates are frequently employed as barriers to isolate the power equipment from the public area. For the power lines passed through the office space, enclosures, such as metallic trunking is applied to isolate the wires from the outside world. The amount of reduction depends very much upon shield material and, its thickness, the size of the shielded volume and the frequency of the fields of interest. It is not unusual for the performance of a shield to be found unsatisfactory after the shield has been completely installed in a building. It is then necessary to have an efficient numerical tool for evaluation of shielding performance prior to shield construction and erection. Low-frequency magnetic field issues in the presence of metal parts have been addressed extensively, but the calculation methods developed are valid only for small-scale metallic elements or those metallic parts with simple geometry. In addition, the evaluation of magnetic environments in buildings with large metal plates, where the skin effect is significant, has received only limited attention. In this thesis, the partial element equivalent circuit (PEEC) method is developed for modeling of large and complex metal shields used in buildings. This method has been widely employed to study EM behavior on a wire structure. It provides a full wave solution to EM problems while transforming the problem into the circuit domain where circuit analysis techniques can be used. The focus of this thesis is to provide efficient solution procedures for the evaluation of low-frequency magnetic fields in the buildings. The characteristics of distribution of induced current and magnetization excited by a source current, and the resultant magnetic fields will be investigated by using the following proposed numerical methods. First of all, the classic PEEC method (named "M0") based on the uniform distribution of EM components on the plates is provided. Both non-magnetic and magnetic materials have been considered for investigation. In non-magnetic plates, the solutions of both induced current and the resultant magnetic field around the plate can be obtained easily. In magnetic plates, the magnetizing current needs to be taken into account, and the skin effect becomes an important factor. Due to the significant variation of EM components inside the metal plate, the dense grid is required and the method is hard to model large structures. However, the high accurate results can be obtained when there is a high density of grid. Secondly, the analytical expression of double exponential function arising from the skin effects is applied to describe the variation of both induced current and magnetization. With this approximation the discretization over the cross section of the plate is avoided and a new method (named "M1") is proposed, where the number of unknowns is reduced greatly and the accuracy is retained. Due to the irregular distribution of EM components is existed when magnetic material is involved, the non-uniform meshing is assigned for the plate corresponding to the location of external current sources. The refinement is particularly done in the edge area to improve the accuracy of solutions. Especially, an improved method (named "IM1") is also presented for the non-magnetic thin plate. In this method, the electric field integral equation is established on the middle plane of the plate. There is only one unknown for each cell. The total number of unknowns is then reduced. It is efficient to solve the eddy-current or shielding problems containing non-magnetic plates. Thirdly, after investigation of the irregular distribution of EM components on the edge region of the plate, a hybrid method (named "M3") using both M0 and M1 is proposed. This method is particularly for magnetic material. The distribution of EM components on the majority area is determined by an analytical expression. On the edge region, the mesh refinement is assigned where the EM components are assumed to be constant in each cell. This method reduces the number of unknowns in the central area and improves the accuracy in the edge region. Fourthly, a new method (named "M2") based on volume and surface cell is proposed. The contribution to the vector potential from the magnetization can be divided into two parts, one is associated with the volume current and the other is with the surface current. The former one has an algebraic relation with the induced current. Therefore, this item can be merged with the item contribution to the induced current. The EM components now become the induced current distributed in volume cell and the magnetization current on the surface cell. This method provides a new way to process the magnetization current just on the surface of the object. M0 and M1 can be used to model both non-magnetic and magnetic structures, M2 and M3 are particular for magnetic material. M0 is available to simulate small shielding structures and validate the other numerical models. M1 is convenient for modeling and easy to understand. This procedure is simple and suitable for practical engineering problems. M2 processes the magnetization on the outer surface and is meaningful when the thickness is comparable to the other characteristic dimensions of the plate. M3 is a hybrid method and has more accuracy compared to other methods although there is a considerable amount of unknowns. It is suitable for investigation the characteristics of distribution of induced current and magnetization. To solve the shield problem efficiently use the proposed methods, the techniques for reduction the number of unknowns, such as loop method and the symmetrical modeling technique have also been proposed. All the above methods and techniques have been validated by numerical approaches and experiments. Finally, the proposed PEEC modeling methods and techniques have been applied to establish complex computation models for actual shielding structures, such as large shielding plates and "U-shape" shields. The main contributions of this thesis are listed as follows: 1. Different numerical methods (M0, M1, M2 and M3) have been proposed and discussed. The corresponding solution packages have been developed. 2. Every solver based on the method (M0, M1, M2 and M3) contains 2D and 3D modules, which can be used to deal with different cases. 3. The non-uniform meshing techniques for PEEC models have been proposed. 4. The techniques, such as loop method and the symmetrical modeling technique have been proposed for reduction of the number of unknowns. 5. Application of the proposed PEEC numerical methods for evaluating the shielding characteristics and performance in the presence of metal shields, including different structures, materials, frequencies, etc.