Geometric Algebra Applied to Power Systems: the swiss army knife for the power engineer

In this lecture, we'll delve into a mathematical framework that has been gaining significant traction in the scientific community - Geometric Algebra, or GA. This mathematical language transcends the capabilities of traditional tools such as complex numbers, quaternions, matrices, or tensors, offering a unified approach for solving complex problems in various disciplines of engineering and physics. GA has found applications in advanced areas such as quantum theory and relativity, as well as in applied disciplines like computer vision and robotics. In electrical engineering, GA provides a comprehensive framework for analyzing complex electrical systems. We will explore the theoretical underpinnings of Geometric Algebra, its application to circuit theory, and its role in the analysis of power flow in single-phase and multi-phase power systems, both in the time and frequency domain. We will also discuss the concept of power-free current compensation, the process of parameter identification in electrical circuits, and the implementation of various electrical transformations, among other interesting applications. This exploration of Geometric Algebra aims to provide a fresh perspective and inspire the integration of this mathematical language into your research and work. Let's embark on this journey of discovery and learning together.