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

## TL;DR

This paper introduces a novel fractal graphical method using Julia sets to visualize and analyze hourly power demand patterns, revealing insights into consumption behaviors throughout the day.

## Contribution

It presents a new approach to represent power demand through Julia set fractals, linking topological properties to load consumption patterns.

## Key findings

- Identified distinct fractal patterns for different power consumption levels
- Observed similar behaviors in fractal diagrams across different hours
- Facilitated understanding of daily load demand variations

## Abstract

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.