Juan Ramón Hermoso Costa
In lightning protection techniques a basic aspect is the identification of the impact point possible, which is determined by the evolution of the initial phase of the lightning, known as the stepped leader, the ground geometry and structures on it. In general, the available theoretical models are consistent with ideal situations and do not include situations such as non-vertical trajectories, non-flat terrain or complex structures. This work reviews and compares the most outstanding models in the literature on this subject and proposes a model for the study of the stepped leader based on the Finite Element Method (FEM). With the intention of bringing the process to the real situation of progress of a downward negative leader, who can follow a trajectory 3D, several modeling aspects are contemplated, as: adjusting the charge density in the channel, the length and direction of jump, which can be modified depending on the height that is the leader, and the propagation delays caused by the distance from the observation point. On the other hand, the model allows the implementation of 3D geometries and the incorporation of complex structures and non-flat terrain, providing results in situations when it is not possible to have theoretical approaches. Simulations have been performed with different proposals for charge distribution in the channel, in situations of leader vertical, inclined and 3D trajectory. The model has been evaluated, comparing their results with theoretical ideal cases and reproducing some real situations from field measurements. The application of the model in simulating real cases for downward negative leader provides parameter values that are not available through the recorded measurements and are useful for studying this type of discharge. In this work we have focused on some of them, and we have obtained interesting results as: estimating the speed of the leader according of height (from the measures of ¿E (t)), the definition of new relationships between charge density in the channel, ¿Emax (leader close to ground), the return peak current and the observation point distance, as well as we can verify the conditions of inception for a discharge into a storm cloud. Finally, we use the model to evaluate the striking distance, a basic concept on protection techniques. It is inferred a new equation for its calculus and the results are compared with proposals available in the literature, showing good agreement with the recommendation of IEC 62305-1. The results encourage to continue the study and they open the possibility to extend the method to other stages, not only on the downward leader, but also on other phenomena related to the formation and evolution of storm situations.
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