This dissertation deals with research on the numerical modelling of electrical discharges in laboratory long air gaps excited with positive switching impulses. It begins with the preliminary work of several scientists during the last decades, making a detailed analysis of different approaches for modelling all the stages in a full discharge. The relations between these models are identified as well as the effect on the outcome when modifying some important input parameters. The general concept describing the discharge phenomenon usually includes three main elements: the streamer inception, the streamer-to-leader transition and the stable leader propagation. These elements are present in many of the analysed models and the main differences between them are the assumptions and simplifications made by each author at a specific point in their methodologies. The models are usually simplified by assigning experimentally determined values to physical constants pertinent to different stages of the full discharge. These constants are the potential gradient in the leader-corona region to sustain the leader propagation, the charge per unit length along the leader channel which depends on the atmospheric conditions and the voltage impulse wave shape; and the leader propagation velocity, which is closely related to the discharge current. The dissertation includes the results of laboratory work related the study of leaders in long gap discharges, electrical parameters and optical records. By reconstructing the three-dimensional leader propagation for the rod-to-plane configuration, it was possible to study the random tortuous path followed by the leader as it propagates. One important element included in the discharge modelling is the representation of the leader-corona region in front of the leader tip as it propagates towards the grounded electrode. For the calculation of the net charge available in the leader-corona region, two new methodologies were pro-posed based on the electrostatic potential distribution obtained from a finite element method solver. This allowed the inclusion of more elements representing different parts of the discharge in the simulation domain. In the final part, all the analysed elements and the new proposed ones were included in a new methodology for the modelling of electrical dis-charges in long air laboratory gaps. The results obtained from this methodology were compared to experimental data. A good agreement was found between the simulation results and the experimental data.

The research work presented here is concerned with numerical simulations of two different electrical phenomena: Long gap electrical discharges under switching impulses and the lightning attachment process associated with positive upward leaders. The development of positive upward leaders and the progression of discharges in long gaps are attributable to two intertwined physical phenomena, namely, the leader channel and the streamer zone. The physical description and the proposed calculations of the above-mentioned phenomena are based on experimental tests conducted in long spark gaps. The methodology presented here proposes a new geometrical approximation for the representation of the streamer and the calculation of the accumulated electrical charge. Furthermore, two different approaches to representing the leader channel are applied and compared. 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. A reasonable agreement was found between the physical model and the experimental test results. A model is proposed to simulate the negative discharges produced by switching impulses using the methodology developed to simulate positive leader discharges and the physics underlying the negative leader phenomena. The validation of the method demonstrated that phenomena such as the pilot leader and negative leader currents are successfully represented. In addition, based on previous work conducted on the physics of lightning and the lightning attachment process, a new methodology is developed and tested. In this new approach, the background electric field and the ionized region, considered in conjunction with the advance of the leader segment, are computed using a novel method. The proposed methodology was employed to test two engineering methods that are accepted in international standards, the mesh method and the electro-geometrical method. The results demonstrated that the engineering approximations are consistent with the physical approach. In addition to the electrical phenomena mentioned above, one should remember that, to simplify the calculation, there are certain real effects arising from the lightning attachment process that have not been considered. In fact, when a structure is subjected to a strong electric field, it is possible to generate multiple upward leaders from that structure. This effect has not been taken into account in the numerical models available previously, and therefore the process of generating multiple upward leaders incepted over a structure is incorporated here. The results have shown that a slight advantage from the background electric field is enough for one upward connecting leader to take over, thereby forcing the others to abort the attachment process.