Abstract
Power flow study is critical to electrical power system analysis. This study solves the power flow problem using a mathematical framework based on geometric algebra (GA). Geometric algebra expands on the concepts of linear algebra and geometry to offer a comprehensive and more flexible mathematical framework. In contrast, complex numbers are a continuation of the real number field. Furthermore, GA allows the handling of multivectors using geometric functions like wedges and geometric products. Because it can abstract the formulation, it thus permits a simple interpretation. Consequently, power flow analysis may be carried out accurately and effectively using GA. This paper presents the GA-based formulation and shows the comparative results between the conventional and the proposed technique. The study compares geometric algebra with complex numbers, concentrating on two case studies: a nimble 9-bus system and a comprehensive 68-bus network. The results demonstrate geometric algebra's scalability, stability, and computing benefits, as faster processing times indicate. This study validates the benefits of geometric algebra and encourages more investigation and practical applications to fully assess its potential in revolutionising power system analysis.