Influence of Soil's Electrical Parameters on Lightning Stroke-current Evolution and Fields in the Close Range

Abstract

The lightning return stroke forms one of the severest natural sources of electromagnetic interference for ground-based and airborne systems. Many physical fields are involved in this complex physical phenomenon. Several pertinent aspects are somewhat unclear, and it is not practical to conduct the field measurements to resolve them. One such important aspect, which is of practical relevance, is the influence of soil's electrical properties on the stroke current evolution and the fields in the soil. It formed the genesis of the present work. The collection of the required data from on-field measurements would be nearly impossible, and hence suitable theoretical approach was considered. For that, an appropriate model for the return stroke is necessary. Among different models for the lightning return stroke, only the 'Self-consistent return stroke' model is found to be suitable. This model employs a macroscopic electrical representation of the underlying physical phenomenon and accounts for the associated dynamic electric field to emulate the stroke current evolution. However, in the past works, only perfectly conducting earth was considered, and it relied on the time-domain thin-wire formulation to evaluate the associated dynamic electromagnetic fields. On the other hand, a more realistic representation of the soil, with its frequency-dependent and non-linear parameters, is required for the present work. This necessitated a suitable adoption of the domain-based 'Finite difference time domain' (FDTD) method for field computation. It turned out that, in an FDTD framework, the modeling of the channel and its corona sheath, soil-ionization, and soil-dispersion is a challenging exercise. For the simulation, a straight vertical channel of 5 km is considered. A complex-frequency-based PML (perfectly matched layer) is employed to truncate the problem domain. The high aspect ratio of the channel does not permit the application of standard FDTD update equations with a realistic spatial discretization. The conventional subcell approach, generally used to model thin-wire structure in an FDTD framework, was also not usable for two reasons. Firstly, the channel has a dynamic conductivity, and secondly, the presence of corona-sheath surrounding the channel produces a typical field profile in the region. The channel in the soil and the non-linear ionization around it also posed a similar problem. A ‘Modified subcell approach’ was developed to handle the lightning channel, which is one of the essential contributions of the present work. In the ‘Modified subcell approach’, the spatial field variation is computed at each time step, taking into account all the relevant field contributions in the respective region. The radial current produced by the charge deposited in the corona sheath is also be taken into account separately. The frequency-dependent conductivity and permittivity of the soil require a convolution in time domain formulation. This would require a repeated calculation of the integral over each cell, a forbidden task. Based on one of the recent literature, a suitable simplification is adopted, thereby drastically minimizing the computational requirement. The soil ionization, a strongly field-dependent phenomenon, required a different set of developments. Each cell is divided into subgrids to account for the local field variation and the dynamic conductivity profile. The developed FDTD formulation is deployed to investigate the role of soil's electrical properties on the stroke current evolution and the field in the soil using the self-consistent return stroke model. For the first time, it is shown that the soil's electrical conductivity has some noticeable influence on the stroke current magnitude (up to about 45 %), and the ionization phenomenon in soil tends to reduce this influence . It is shown that the current magnitude varies most for a low magnitude fast-rising current as the soil ionization is minimal for these cases. On the other hand, for high-level slow-rising currents, the ionization process significantly matures, and as a result, the dependence of current magnitude on soil resistivity is reduced substantially. It is noted that the effect of soil permittivity and the frequency-dependent soil parameters on the return-stroke current is minimal. From the results of the detailed simulation, it is found that soil resistivity also affects the field in the soil significantly. The field in the air is increased with decreasing soil resistivity, and the increase is primarily due to the increase in channel current magnitude. For the field in the soil, in addition to modulating the field magnitude, soil resistivity also affects the temporal nature, with the field becoming peakier for lower resistivity. A comparison of the computed field demonstrates that the field is underestimated significantly by the prevalent quasi-static approach, and the difference increases with the radial distance from the channel. The frequency-dependency of the soil's conductivity, and permittivity to a lesser extent, significantly reduces the field in the soil. It is also seen that the current concentration near the surface due to skin-effect is altered at later periods by the field produced by the channel current. The presence of a second layer of lower resistivity at a shallow depth, on the other hand, effectively controls the current and field in the top layer. It is also shown that the field for a strike to a mountain can depend significantly on the mountain height. In summary, significant contributions have been made in the present work towards the FDTD formulations for modeling lightning phenomena and assessing the soil’s electrical parameters on lightning stroke current evolution and the resulting field .