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Theoretical analysis of the processes involved in lightning attachment to earthed structures

A theoretical analysis is presented for the processes involved in natural lightning attachment to earthed structures. This analysis is based on physical criteria for upward leader inception and propagation during the approach of the downward lightning leader. Analytical expressions for the equivalent voltages and their time variation are obtained for earthed structures before and after upward leader inception. Equivalent voltages in lightning rods of varying height are calculated for different values of the peak stroke current of lightning, taking into account the process of upward leader development. Significant values of equivalent voltages and their derivatives at the final jump phase of a downward leader are predicted. It is shown that there is a time interval between the moment of upward leader inception and the time when the upward leader propagation condition is fulfilled. The implications of these results for testing in a high voltage laboratory are also discussed.