A semi-analytical formula for the evaluation of the indirect lightning performance of overhead power lines

The evaluation of the indirect lightning performance of an overhead power line is typically represented by means of curves reporting how many lightning faults per year the line may experience as a function of its insulation level, and so it expresses the probability that the line is subject to an overvoltage greater than its critical flashover voltage (CFO). Obtaining this curve is a very time-consuming task from a computational point of view, since the evaluation of the lightning overvoltage requires the solution of the field-to-line coupling problem and this has to be repeated a significant number of times, taking into account the possible values assumed by all the stochastic variables that influence the process. In this contribution, some mathematical properties of the probability density functions (PDF) are exploited in order to derive a formula in which the probability that an overvoltage caused by an indirect lightning event is greater than an assigned value can be computed simply by a numerical evaluation of an integral. The results have been compared with those obtained applying a classical Monte Carlo technique, showing an excellent agreement between the two approaches with a considerable CPU time reduction.