Multifractal analysis of electricity demand as a tool for spatial forecasting

Abstract

Electrical utilities need to plan their investments in substations and networks to meet future customer demand, by predicting the spatial load growth and its time trend. Several techniques are currently in use to do that, such as trending analysis or simulation methods. To study the electricity demand we used multifractal analysis. A fractal is an object whose irregularities are not smooth and have some self-similarity at different scales. If the fractal does not have strict self-similarity, we could break such fractality, if it really exists in the system, in a spectrum of sub fractals which have a self-similar structure, performing the so-called multifractal spectral analysis. Multifractal spectral analysis has been already applied to study the morphology and population growth of cities. Because electricity demand can be related to demographics of cities, it is possible to consider the hypothesis that multifractal spectral decomposition can be applied to analyze electricity demand. A variety of multifractal analyses were performed on real data from the customer demand of an electrical utility. The results show that the analyzed electricity demand is split into clear and interesting two-multifractal distribution with properties not found yet in the literature on the subject. This type of multifractal analysis could lead the way to improved spatial demand forecasting methods.