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

## TL;DR

This paper introduces a novel fractal-based method using Mandelbrot set orbit diagrams to visually analyze and identify patterns in real and reactive power load demand over a day, aiding operational and planning decisions.

## Contribution

It presents a new geometrical approach employing Mandelbrot orbit diagrams to represent and analyze load demand behaviors in power systems.

## Key findings

- Repetitive fractal patterns observed during daily power consumption.
- Orbit diagrams effectively capture load behavior and changes.
- Method offers a visual tool for operational decision-making.

## Abstract

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.