New Method to Calculate the Energy and Fractal Dimension of the Daily Electrical Load

Abstract

This paper proposes a method to calculate the degree of fluctuation of the daily electrical load-curve using fractal dimension, which is a quantitative estimator of spatial complexity. The conventional methods for forecasting have not studied such a variable, being a new parameter that can be included to characterize the electrical load. The method of fractal dimension also allows us to propose a new numerical method to calculate the integral of a function, using the trapezoid rule, but splitting the curve with fractal segments, to discover other observations, which allows the elevation of new theoretical approaches. The results are compared with the other methods such as the conventional trapezoid rule and the box-counting. It is then a new contribution that expands the universal knowledge on the subject. The case study is the daily electrical load-curve, where the energy demanded corresponds to the area of the [Formula: see text] region bounded by the curve.

Numerical integration of bivariate fractal interpolation functions on rectangular domains

“…However, it is appropriate to use the fractal numerical integration method to evaluate such parameters. In [ 27 ], authors propose a new method of numerical integration using the trapezoidal rule wherein the signal has been split into fractal fragments. The observed integral value corresponds to the energy needed on the electrical load curve.…”