Curvature-based shape recognition: characterising and analysing voltaje dips

Abstract

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.