A NEW METHODOLOGY TO ANALYZE THE DYNAMIC OF DAILY POWER DEMAND WITH ATTRACTORS INTO THE MANDELBROT SET

Abstract

The time series plot of electricity daily load demand is seasonal as shown by its regular repetitive pattern during the same period each year. Its behavior is determined by phase-space diagrams that are able to identify any of the following states of the series: fixed point, periodic, or chaotic. The first two deal with predictable systems. This paper focuses on presenting a new methodology to analyze the dynamics of the series in reference by using the curve formed by attractors that move in the complex plane over the Mandelbrot set according to the law dictated by the load curve. Because electrical power is a variable, it is also defined in the complex plane with the components of active power on the real axis and reactive power on the imaginary axis. Therefore, electrical power facilitates a new field of analysis in Mandelbrot fractal space. The obtained temporal curve confirms that the profile of the electric power demand is also mapped with the new fractal geometric space of the Mandelbrot set, thus providing a new contribution that extends knowledge about the dynamics of systems in fractal geometry.