Multifractal analysis and modelling of lightning stroke maps for power systems

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Faghfouri, Aram
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Since electric power is one the most important necessities for today’s life and industry, its service reliability must be maintained in an extremely high level. Thunderstorms often reduce this quality of service. Since cloud-to-ground lightning strokes are among the most frequent yet least understood causes of service interruption, predicting the geographical and temporal distribution of the lightning strokes can help power system planners and designers improve the protection of new and existing transmission lines. Such a prediction needs a model that is based on physical properties of the phenomenon and acquired data. This approach requires several stages including modelling, simulation, and characterization. Characterization provides metrics for comparison between the physical and simulated data. The distributions of the lightning stroke densities (aka lightning stroke maps (LSMs)) have patterns that are highly nonlinear, nonstationary, and stochastic. Ordinary analyzes and metrics are insufficient to characterize such patterns. Multiscale analysis of these patterns indicates their self-affinity over multiple scales, which is an indication of their multifractality. Consequently, multifractal analysis methods such as the Rényi fractal dimension spectrum are appropriate candidates for characterization of these density maps. This work uses the lightning stroke data collected by Canadian lightning detection network for Manitoba from 1998 to 2006, employs a multifractal analysis of the lightning stroke maps, and investigates the consistency of such a characterization over time. The results indicate that the LSMs of Manitoba have multifractal distributions, both locally and globally. The results also indicate a convergence in statistical distribution for the LSMs and strong sensitivity of the Rényi spectra to the data variations. For modelling such data, multifractal approaches such as diffusion limited aggregation, percolation, or cellular automata are appropriate candidates. This work provides diffusion limited aggregate modelling and simulation for the maps and compares the physical and simulated lightning stroke maps through Rényi spectra, where the results indicate a high similarity, both visually and analytically. Since lightning strokes are global phenomena, the same methods and techniques can be used for LSMs anywhere in the world. In addition, the utilized methods and approaches for analysis and modelling can be used for similarly complicated phenomena.
Lightning stroke map, multifractal