The improved PEEC method for grounded structures above lossy ground for lightning analysis

Abstract

Lightning is a kind of electromagnetic phenomena that occurs frequently in nature. It poses a greater threat to the safety of human beings, facilities and structures on the ground. In severe cases, it can cause power supply interruption, equipment damages and injuries to living beings. In 2018, signaling systems in electrified railway systems were damaged by lightning during a severe thunderstorm in London. Railway services in several major city lines were interrupted for more than 6 hours, which caused traffic chaos in the entire city. Nowadays, lightning protection and disaster prevention have been long-standing issues of concern in the community. In order to provide effective protection against lightning, research on lightning protection for the structures on the ground has been conducted extensively. Computer simulation of lightning transients in the grounded structures is one of effective approaches for designing systems for minimizing the damages caused by lightning. In the past decades, many simulation approaches have been developed and applied for lightning analysis in the grounded structures, particularly in wire structures. These approaches include the Finite-Difference and Finite-Time Method (FDTD), the Finite Element Method (FEM), the Moment Method (MoM) and the Partial Element Equivalent Circuit Method (PEEC). The domain methods (FDTD and FEM) have great advantages in dealing with complex geometries and material properties. However, in the analyzing lightning transients research in a complicated structure with many large plates and short wires in open boundary problem, they have not been any successful application by use those methods. The PEEC method is the effective one for modeling 3D interconnected thin-wire structures. It is inferred starting with mixed potential integral equations, and transforms an electromagnetic problem into the circuit domain. The PEEC method has been successfully applied for lighting analysis in wire structures because of its high computational efficiency and excellent compatibility with nonlinear devices. However, there are a couple of issues unresolved, which may become a hurdle in the PEEC application for lightning analysis, such as modelling of conductors with a large cross section area, modelling of lossy ground and modelling of an incident field, etc. This thesis aims at addressing lightning analysis in a grounded structure, such as a building during either a direct lightning strike or an indirect strike using an improved PEEC method. The ground structure may consist of a set of wires and plates situated above the ground. The wires may have an arbitrary cross section. The PEEC model for the conductors with arbitrary cross section is derived in this thesis. The concept of internal impedance and external inductance is adopted, and explicit formulas are derived to compute circuit parameters. A special technique with the analytical function of current density is applied for modeling large thin plates so that the number of unknowns for the plates' parameters is significantly reduced and the computation efficiency remains. A time-domain solution procedure is developed to analyze lightning transients in a building structure with frequency-dependent circuit parameters. The PEEC modelling and simulation methods are tested both experimentally and numerically. Good agreements are observed. In the thesis the effect of a lossy ground is modeled using dyadic Green's functions. An equivalent circuit is derived for the first time by taking into account correction terms arising from the presence of the lossy ground. Circuit parameters are expressed using Sommerfeld integrals, which can be evaluated numerically and be presented with lookup tables. The low-frequency model of the lossy ground is derived, and the comparison of circuit parameters calculated with this model and the Sommerfeld integrals is made. The proposed method is validated numerically with the numerical computation code (NEC2) in the frequency domain, and the FDTD method in the time domain. Good agreements are observed. The proposed method is then applied to analyze lightning transients in a building structure over the lossy ground. It is concluded that the lossy ground can be replace with the low-frequency model for electromagnetic transient analysis. The computational burden in the time-domain simulation can be significantly relieved. This thesis also presents the time-domain PEEC analysis of induced transients in a wire structure during an indirect lightning strike. The full-wave PEEC formulation with an external incident field is employed. The incident field is calculated with either the Uman's or the Jefimenko's formula by using the engineering model of a lightning channel. An instability problem is, however, observed. It becomes a hurdle in the application of PEEC for evaluating induced transient currents in closed wire loops. The problem is investigated, and is primarily caused by discretization of electric field in numerical evaluation of external voltage source. An improved algorithm is provided to solve this instability problem, and is tested in both near and far field zones. It is validated by the FDTD method. The issue of time step and segment length is addressed. It is also found that the Uman's formula is generally incapable of producing stable induced currents in a wire-loop structure. Finally the proposed PEEC procedure is applied to evaluate induced lightning transients in a PV panel during an indirect lightning strike.