2020/02/23 by Francisco G. Montoya, Montoya, Francisco Gil, Alfredo Alcayde +7
Arts and Humanities · Mathematics · #Algebraic and Geometric Analysis #FOS: Electrical engineering #Philosophy and Historical Thought #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2002.10011
openalex publication_date 2020/02/23 · openalex created_date 2020/03/06 · openalex updated_date 2026/07/28
Traditional power theories and one of their most important concepts --apparent power-- are still a source of debate and, as shown in the literature, they present several flaws that misinterpret the power-transfer phenomena under distorted grid conditions. In recent years, advanced mathematical tools such as geometric algebra (GA) have been applied to address these issues. However, the application of GA to electrical circuits requires more consensus, improvements and refinement. In this paper, power theories based on GA are revisited. Several drawbacks and inconsistencies of previous works are identified and modifications to the so-called geometric algebra power theory (GAPoT) are presented. This theory takes into account power components generated by cross-products between current and voltage harmonics in the frequency domain. Compared to other theories based on GA, it is compatible with the traditional definition of apparent power calculated as the product of RMS voltage and current. Also, mathematical developments are done in a multi-dimensional Euclidean space where the energy conservation principle is satisfied. The paper includes a basic example and experimental results in which measurements from a utility supply are analysed. Finally, suggestions for the extension to three-phase systems are drawn.