Methodology for the characterization of the electrical power demand curve, by means of fractal orbit diagrams on the complex plane of Mandelbrot set

Abstract

The present article proposes a new geometric space in the complex plane of the Mandelbrot set, framed in the diagram of orbits and attractors, to characterize the dynamics of the curves of the demand of daily electrical power, with the purpose of discovering other observations enabling the elevation of new theoretical approaches. The result shows a different method to evaluate the dynamics of the electric power demand curve, using fractal orbital diagrams. This method is a new contribution that extends universal knowledge about the dynamics of complex systems and fractal geometry. Finally, the reader is informed that the data series used in this article was used in a previous publication, but using a different fractal technique to describe its dynamics.1. Introduction. The purpose of this article is to present a methodology for characterizing the dynamics of electric power demand curves using fractal orbit diagrams defined in the complex plane of the Mandelbrot set. On this subject, the present authors have published two (2) articles. The fractal geometrical pattern of the Julia set [16] was determined with respect to the signs in the complex plane of the active and reactive electrical power; with new data based on [17] the conclusions were extended with respect to the fractal geometric pattern that produces the daily hourly demand of electric power. The main contribution to the theory of fractal geometry consisted in the identification and qualitative interpretation of the rules of formation of the topologies of Julia sets that produce the demand of hourly daily electrical power. The article [21] focuses on presenting a new methodology to analyze the dynamics of the series in reference, using the curve formed by attractors that move