Evaluation of the Lightning Performance of an Overhead Multiconductor Transmission Line System

The lightning performance of an overhead Multiconductor Transmission Line (MTL) system is typically represented by means of curves reporting how many lightning faults per year the system may experience as a function of its insulation level [1]. In other words, it expresses the probability that the lines are subject to an overvoltage greater than their critical flashover voltage (CFO). Such curves can be obtained by means of a statistical approach (typically a Monte Carlo method is applied): first of all, a large number of lightning events is randomly generated, each one characterized by a specified point of impact and a channel-base current peak following a specified distribution (log-normal for the current and uniform for the point of impact). Then, the adoption of the electro-geometrical (or similar) model allows to determine whether each event originates a direct or an indirect strike [2]. The power system simulation provides the corresponding maximum overvoltage on the overall system. This latter step, especially in the case of indirect strikes, is a delicate task from a computational point of view, since the lightning overvoltage calculation requires the evaluation of the electromagnetic fields and the solution of the field-to-line coupling equations. Therefore, it is necessary to have at disposal an efficient algorithm that can evaluate the lightning-induced overvoltages in an accurate manner, with a reasonable computational effort. Moreover, a smart application of the Monte Carlo method is required in order to limit the number of calls to the coupling simulator [3]. In the paper, the attention will be focused on this latter aspect: defining a methodology that allows to determine the optimal sample size (number of runs) as the best trade-off between the experimental cost/time and the accuracy of the expected results. The methodology proposed allows to control the experimental error (Mean Square Pure Error − MSPE for short)) which affects the Monte Carlo model output, i.e. the uncertainty in the final result due to the chosen number of runs. This is addressed by examining the curves which describe the evolution of the MSPE of the mean and of the MSPE of the standard deviation varying the replicated number of runs. These curves, with their typical “knee shape”, after a first phase of fluctuation, become stationary with the increasing of the replicated number of runs, approaching zero for a number of runs tending to infinity. When the two curves are in the stationary phase, the number of runs is sufficient to obtain a stable (and known) experimental error. So the number of runs can be chosen as the first value of the stationary phase or the following ones depending on the desired experimental error. 21, rue d’Artois, F-75008 PARIS International Colloquium on