The numerical modeling of electrical discharges occurring in atmospheric air has been in continuous development during the past decades in different fields, such as high-voltage techniques and lightning protection. Different methodologies have been proposed to represent the physical phenomena taking place at a single full discharge event, departing both from experimental and theoretical approaches. The implementation of these methodologies in numerical routines combined with the use of numerical methods to determine the electric potential distribution permits the creation of models whose predictions closely agree with the real case situations, where electrode arrangements might have nonsymmetric geometries. In this paper, we present an improved version of a simulation methodology for representing electrical discharges in long air gaps. This simulation methodology includes new elements like: 1) the 3-D leader channel tortuosity based on laboratory experimental measurements and 2) two new methods for the estimation of the electric charge contained in the so-called leader-corona region based on the electrostatic potential of fictitious potential rings representing the active region in front of the leader tip. Results from the simulation were compared with experimental records and a reasonably good agreement is found between them.

The main propose of this paper is to present a physical model of long air gap electrical discharges under positive switching impulses. The development and progression of discharges in long air gaps are attributable to two intertwined physical phenomena, namely, the leader channel and the streamer zone. Experimental studies have been used to develop empirical and physical models capable to represent the streamer zone and the leader channel. The empirical ones have led to improvements in the electrical design of high voltage apparatus and insulation distances, but they cannot take into account factors associated with fundamental physics and/or the behavior of materials. The physical models have been used to describe and understand the discharge phenomena of laboratory and lightning discharges. However, because of the complex simulations necessary to reproduce real cases, they are not in widespread use in the engineering of practical applications. Hence, the aim of the work presented here is to develop a model based on physics of the discharge capable to validate and complement the existing engineering models. The model presented here proposes a new geometrical approximation for the representation of the streamer and the calculation of the accumulated electrical charge. The model considers a variable streamer region that changes with the temporal and spatial variations of the electric field. The leader channel is modeled using the non local thermo-equilibrium equations. Furthermore, statistical delays before the inception of the first corona, and random distributions to represent the tortuous nature of the path taken by the leader channel were included based on the behavior observed in experimental tests, with the intention of ensuring the discharge behaved in a realistic manner. For comparison purposes, two different gap configurations were simulated. A reasonable agreement was found between the physical model and the experimental test results.

A physical model based on the mechanism observed in experimental investigations is introduced to describe the formation of negative leader steps. Starting with a small length of a space leader located at the periphery of the negative streamer system of the stepped leader, the model simulates the growth and the subsequent formation of the leader step. Based on the model, the step length, the step forming time, and the propagation speed of stepped leaders as a function of the prospective return stroke peak current are estimated. The results show that the step length and the leader speed increase with increasing prospective return stroke current. The results also show that the speed of the stepped leader increases as it approaches the ground. For prospective return stroke currents in the range of 15 kA–60 kA, the step lengths lie within the range 5 m–100 m, the step forming times lie within the range 10 μs–250 μs, and the leader speed lies within the range 10⁵ m/s −1.5 × 10⁶ m/s. The results obtained are in reasonable agreement with the experimental observations.