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.
For calculating the fractal dimension, the standard method uses a compass that with a specific radius, an arc is drawn to find the points that intercept the curve. An important consideration when making a measurement using the compass or ruler method is to consider the impact of the observer. Most of the rules are read by the user and are therefore very susceptible to misreading or visual errors. The main contribution of this work lies in the development of an algorithm for calculating the fractal dimension of fluctuating continuous functions, over a fractally divided space, from which it is possible to obtain also the integral of the function with an acceptable precision using the trapezoid rule compound.
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