On the Fitting of Three-Phase Voltage Curves with Ellipses Using Geometric Algebra for Conics

Jorge Ventura(1), Jaroslav Hrdina(2), Ahmad Eid(3), Marek Stodola(2), Francisco M. Arrabal-Campos(1), Alfredo Alcayde(1) and Francisco G. Montoya(1) 1. Department of Engineering - Universidad de Almeria (Spain) 2. Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic 3. Department of Electrical Engineering, Faculty of Engineering Port-Said University, Port Fouad, Egypt 2026-01-20

Abstract

This work introduces a novel approach in power quality analysis by fitting three-phase voltage curves with ellipses using Geometric Algebra for Conics (GAC). Recognizing the limitations of current linear algebra-based methods, this paper
highlights the need for further exploration into more effective techniques. Geometric Algebra offers a potent, efficient, and
intuitive alternative for addressing power quality phenomena, such as sags, swells, and interruptions. By establishing a robust mathematical foundation with GAC and analysing the characteristics of the resulting ellipse, we propose new metrics for understanding power quality issues. This foundational paper lays the groundwork for future, more realistic studies, inviting the engineering community to explore the benefits of GA in advancing power quality analysis. Through this initial exploration, we aim to spark further research and development in this promising field.

Key words: Geometric algebra for conics, power quality, ellipse fitting, geometric electricity.

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