Analysing the electrical power systems’ behaviour is significantly based on power flow analysis. This paper uses a geometric algebra (GA) mathematical framework to solve the power flow problem. It can combine and extend algebraic and geometric concepts in a unified and powerful way. While complex numbers are an extension of the real number field, geometric algebra builds on the ideas of linear algebra and geometry to provide a more complete and versatile mathematical framework. Additionally, GA enables handling multivectors through geometric functions, including wedge and geometric products. Thus, it allows a straightforward interpretation because of its ability to abstract the formulation. Therefore, by utilising GA, power flow analysis may be performed efficiently and precisely, resulting in improved design and operation of power systems. This paper presents the GA-based formulation and shows the comparative results between the conventional and the proposed technique.

This study employs differential geometric algebra to offer a fresh perspective on voltage sag and swell analysis. By utilising differential geometry, simulated electrical signals can be visualised as curves. This is made possible by describing the instantaneous amplitude of a sinusoidal wave as a curve in Euclidean coordinates. This approach effectively represents the Frenet-Serret frame rotation at each point along the curve. In systems with derivative components, the velocity of the moving frame denotes the rate at which events change, as the Frenet structure is locally defined at every point along the curve. This mathematical representation, utilising the Frenet frame, enhances our understanding of phenomena such as sag and swell, in contrast to traditional approaches that rely on the Clark and Park transformations, which utilise two-dimensional forms to capture the details and portrayal of an occurrence. The work emphasises the depiction of voltage through curves and provides a geometric indicator of the pattern's evolution during operation.

Electric circuit analysis under non-sinusoidal, non-linear situations has been a hot topic for a long time. Many scientific communities hold opposing viewpoints on the additional analysis tool and domain, resulting in a variety of standards and definitions. With the advent of Power Electronic equipment, converters, and Renewable Energy sources, the electric power system has become increasingly sophisticated since its inception. Electronic equipment has transformed the electrical system and provided a slew of advantages to industrial applications. Unfortunately, this comes at the expense of power system distortion (voltage and current). Understanding power flow in non-sinusoidal linear and non-linear circuit circumstances is required for this. As a result, a novel mathematical framework to analyze the circuit in such an environment is always required. Finally, in non-sinusoidal conditions, a consensus can be reached on norms that comply with well-known, established standards. The work provided here compares the use of harmonic domain and geometric algebra in circuits with disturbances for sinusoidal and non-sinusoidal excitations in order to demonstrate the accuracy of geometrical algebra in power flow calculations.

Electric circuit analysis under non-sinusoidal, non-linear situations has been a hot topic for a long time. Many scientific communities hold opposing viewpoints on the additional analysis tool and domain, resulting in a variety of standards and definitions. With the advent of Power Electronic equipment, converters, and Renewable Energy sources, the electric power system has become increasingly sophisticated since its inception. Electronic equipment has transformed the electrical system and provided a slew of advantages to industrial applications. Unfortunately, this comes at the expense of power system distortion (voltage and current). Understanding power flow in non-sinusoidal linear and non-linear circuit circumstances is required for this. As a result, a novel mathematical framework to analyze the circuit in such an environment is always required. Finally, in non-sinusoidal conditions, a consensus can be reached on norms that comply with well-known, established standards. The work provided here compares the use of harmonic domain and geometric algebra in circuits with disturbances for sinusoidal and non-sinusoidal excitations in order to demonstrate the accuracy of geometrical algebra in power flow calculations.