Analysis of Lightning-Radiated Electromagnetic Fields in the Vicinity of Lossy Ground (original) (raw)
Related papers
Electromagnetic Field in the Vicinity of Lightning Protection Rods at a Lossy Ground
IEEE Transactions on Electromagnetic Compatibility, 2000
In this paper, the lightning discharge channel in the vicinity of vertical lightning protection rods is modeled in the frequency domain by a vertical mast antenna coupled with vertical parasitic elements. The ground is treated as linear, isotropic, and homogeneous lossy half-space. The vertical mast antenna and the rods are treated as a unique system as for boundary conditions that results in the electric field integral equation (EFIE) for the unknown current distributions along their axes. EFIE is numerically solved by using the method of moments and a polynomial approximation of the current distributions. The influence of the ground is taken into account through a Sommerfeld integral kernel modeled in a simple and very efficient way using one new approximation that can be classified as a two-image approximation. This approximation gives good results in the frequency domain for modeling in both near and far electromagnetic fields.
New Approaches to Modeling of Lightning Electromagnetic Field
This paper presents the results of the research on lightning electromagnetic field calculations in time domain in the case of perfectly conducting ground, so as calculations in frequency domain of electromagnetic field radiated by mast antenna above real ground. It should be emphasized that several novel approaches during this research were introduced, includ-ing application of one new function for representing lightning return stroke channel-base current and one new model for spec-tral reflection coefficient for solving problems of the real ground parameters influence. INTRODUCTION In the first section of this paper the structure of light-ning electromagnetic field (LEMF) is numerically deter-mined directly in time domain using antenna theory ap-proach and thin wire approximation of the lightning chan-nel. Within modified transmission line model with expo-nential decay, as an engineering return stroke current model, one new suitable function is applied for the ap-proximation of cha...
AN ANTENNA THEORY MODEL FOR THE LIGHTNING RETIJRN STROKE
A new approach, based on antenna theory, is used to evaluate the lightning return-stroke current as a fitnction of the and height. The lightning channel is modeled as a lossy, straight, attd vertical monopole antentla above a perfectly conducting ground, and is fed by a source voltage. The source voltage is a function of the assumed current at grotmd level and the input impedance of the tnonopole antenna. An electric field integral equation (EFIE) is employed to describe the electromagnetic behavior of the antetma. The mmterical solution of EFIE by the Method of Moments (MOM) in time domain provides the time-space distribution of the current along the lightning channel. This new atttennatheory model with specified current at the channel base requires only two adjustable parameters: the returttstroke propagation speed and the channel resistance per unit length. The new tnodel is compared to the tnost cotnmonly used lightning return-stroke models in terms of the temporal-spatial distribution of channel current and predicted electric fields.
IEEE Transactions on Electromagnetic Compatibility, 2021
The paper provides analytical expressions for the electromagnetic fields generated by a lightning return stroke characterized by a channel base current with arbitrary time waveform, in presence of either a perfectly conducting or a lossy ground, assuming the transmission line model for the current along the channel. In this second case, a time domain analytical expression for the Cooray-Rubinstein formula is presented. The main idea that leads to the derivation of analytical formulas consists of dividing the channel into intervals in which the distance between the field source point and the observation point can be approximated with a linear function of the time and of the spatial coordinates of both points. In the companion paper, a detailed comparison is proposed with the classical (numerical) approach highlighting excellent agreement both at close and far distances, considering all the values of practical interest for the ground conductivity. Moreover, the method guarantees a meaningful improvement in the computational performance.
IEEE Transactions on Electromagnetic Compatibility, 2021
The paper provides the implementation procedure, the validation and some considerations on the computational efforts of the developed analytical expressions for the lightning electromagnetic fields presented in the companion paper. The validation is presented with different configurations in terms of channel-base current, ground conductivity and distance to the lightning channel, comparing the obtained results with the numerical integration of the classical formulas. The comparative analysis shows a perfect agreement between the proposed analytical approach and reference numerical simulations. Moreover, the computational effort of the proposed method is discussed, focusing the attention on the choice of the points in which the channel has to be divided in order to maximize the CPU time savings without losing accuracy. Index Terms-Lightning electromagnetic fields, Channel base current, Engineering models I. INTRODUCTION ne of the most important causes of damages in distribution systems are lightning-induced voltages. As pointed out in Part I, their evaluation has been addressed by many researchers in the last years. It is important to note that all the proposed models for the computation of induced voltages rely on the knowledge of the electromagnetic fields. In the literature, their evaluation is usually achieved in two steps: 1) the electromagnetic fields in the presence of a perfectly conducting ground are computed assuming a vertical lightning channel [1-3], and 2) the effect of the ground conductivity is taken into account with the Cooray-Rubinstein formula [4, 5].
Journal of Geophysical Research: Atmospheres, 2008
1] In this paper, the developed formulation, which we shall call the ''reference'' one, is used to assess the validity of the most popular simplified approach for the calculation of the lightning electromagnetic field over a conducting earth, namely, the Cooray-Rubinstein (CR) approximation. This formula provides a simple method to evaluate the radial component of the electric field which is the component most affected by the finite ground conductivity and which plays an important role within the Agrawal et al. (1980) field-to-transmission line-coupling model. Several configurations are examined, with different values for the ground conductivity and different field observation points. A thorough analysis of all the simulated field components is carried out and comparisons are also made with the ''ideal'' field, namely, the field that would be present under the assumption of perfectly conducting ground. It is shown that for channel base current typical of subsequent strokes and for very low conductivities, the CR formula exhibits some deviations from the reference one but it still represents a conservative estimation of the radial field component, since it behaves as un upper bound for the exact curve. The developed algorithm is characterized by fast performances in terms of CPU time, lending itself to be used for several applications, including a coupling code for lightning induced overvoltages calculations.
IEEE Transactions on Electromagnetic Compatibility, 2000
The effects of finitely conducting ground on the signature of lightning generated magnetic fields at ground level were evaluated by numerical solution of Sommerfeld's integrals. Results are presented for distances between 10 m to 1 km from the lightning channel and for ground conductivities in the range of 0.01 and 0.0001 S/m. The results obtained from the exact theory are compared with the predictions of two frequently used analytical approximations to Sommerfeld's equations. Based on that comparison the limits of validity of these approximate theories are obtained.
Radio Science, 2011
1] In this paper we review simplified analytical expressions derived by Wait using the concept of attenuation function for the analysis of the propagation of lightning-radiated electromagnetic fields over a mixed propagation path (vertically stratified ground). Two different formulations proposed by Wait that depend on the relative values of ground surface impedances are discussed. It is shown that both formulations give nearly the same results for the time domain electric field. However, depending on the values of the normalized surface impedance for each ground section, the use of one of the two formulations is computationally more efficient. The accuracy of the Wait formulations was examined taking as reference full-wave simulations obtained using the finite difference time domain technique. It is shown that Wait's simplified formulas are able to reproduce the distant field peak and waveshape with a good accuracy.