arXiv subjects

John E. Candelo-Becerra

Publications and source records attributed to John E. Candelo-Becerra.

3 recordsLinked to original sources

arXiv2018

Geometrical representation of real and reactive powers of load demand by orbit diagrams in the Mandelbrot set

This paper presents the geometrical representation of the load demand by using orbits diagrams in the Mandelbrot set, to identify changing behaviors during a day period of the real and reactive powers. To perform this, different power combinations were used to represent the fractal diagrams with an algorithm that considers the mathematical model of Mandelbrot set and orbits diagrams. A qualitative analysis of the orbits is performed to identify the fractal graphic patterns with respect to the real and reactive power consumptions. The results show repetitive graphic patterns in the fractal space of the power consumption during the day, which help represent the consumption behavior on a daily load demand curve. The orbit diagrams save form and structure relations during the daily behavior of the power consumption. This work shows a different method of evaluating load demand behavior by using orbit diagrams as a potential tool that will lead to identify load behavior, useful in operational decisions and power system planning.

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arXiv2018

Fractal representation of the power daily demand based on topological properties of Julia sets

In a power system, the load demand considers two components such as the real power (P) because of resistive elements, and the reactive power (Q) because inductive or capacitive elements. This paper presents a graphical representation of the electric power demand based on the topological properties of the Julia Sets, with the purpose of observing the different graphic patterns and relationship with the hourly load consumptions. An algorithm that iterates complex numbers related to power is used to represent each fractal diagram of the load demand. The results show some representative patterns related to each value of the power consumption and similar behaviour in the fractal diagrams, which allows to understand consumption behaviours from the different hours of the day. This study allows to make a relation among the different consumptions of the day to create relationships that lead to the prediction of different behaviour patterns of the curves.

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arXiv2018

Topological properties of fractal Julia sets related to the signs and magnitudes of the real and reactive powers

In AC electrical systems, the power depends on the real power (P) due to resistive elements and the reactive power (Q) due to the inductive and capacitive elements, which are commonly studied by using phasor and scalar methods. Thus, this paper focuses on applying the fractal Julia sets to observe the topological properties related to the signs and magnitudes of the real and reactive powers consumed or supplied by an electrical circuit. To perform this, different power combinations were used to represent the fractal diagrams with an algorithm that considers the mathematical model of Julia sets. The study considers three type of loads: the first study considers the change of real power when the reactive power is fixed; the second study deals with the change of the reactive power when the real power is fixed; and finally, the third study contemplates that both real and reactive powers change. Furthermore, the fractal diagrams of the power in the four quadrants of the complex plane are studied to identify the topological properties that each sign and magnitude represent. A qualitative analysis of the diagrams helps to identify that the complex power loads present some fractal graphic patterns, with respect to the signs and magnitudes considered in the different quadrants of the complex planes. The diagrams represented in the complex planes save a relation in the forms and structure with other points studied, concluding that the power is related to other figures in other quadrants. Thus, this result allows a new study of the behavior of the power in an electrical circuit, showing a clear relation of the different fractal diagrams that the Julia sets obtained.

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