Lightning return stroke current radiation in presence of a conducting ground: 2. Validity assessment of simplified approaches

Abstract

[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.Citation: Delfino, F., R. Procopio, M. Rossi, F. Rachidi, and C. A. Nucci (2008), Lightning return stroke current radiation in presence of a conducting ground: 2. Validity assessment of simplified approaches,

Lightning return stroke current radiation in presence of a conducting ground: 1. Theory and numerical evaluation of the electromagnetic fields

“…[76] In the second part of this work [Delfino et al, 2008], the results obtained by the developed theory are used to assess the validity of the most used approximate approach, namely, the Cooray-Rubinstein formula [Rubinstein, 1996].…”

Horizontal Electric Field in the Vicinity of Structures Hit by Lightning

“…Figure 3 shows the structure and its main parameters, where the point of interest for the horizontal electric field calculation is at the ground surface and at a distance x from the axis of the structure. Combining Equation (8) and Equation (13) leads to:…”

Overview of Recent Progress in Lightning Research and Lightning Protection

“…Several studies have shown that the Cooray-Rubinstein formula yields a satisfactory approximation of the above-ground horizontal electric field at close (100 m), intermediate (some kilometers), and far (tens of kilometers) distances [109], [111]. Delfino et al [96] showed that only for very low conductivities, does the CoorayRubinstein formula exhibit some deviations from the reference one, but it still gives a conservative estimate of the radial field component, since it behaves as an upper bound for the exact curve. General limits of validity of the Cooray-Rubinstein approximation were theoretically examined by Wait [113].…”

“…The resulting equations involve the so-called Sommerfeld integral, which is highly oscillatory and difficult to evaluate numerically. Recently, Delfino and coworkers developed an efficient algorithm for the evaluation of the exact expression for both the above-ground and underground fields generated by a lightning discharge [94]- [96]. The algorithm was used, in particular, to test the validity of simplified approaches.…”