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\begin{document}

\title{Curvature-based shape recognition: characterising and analysing voltaje
dips}



\author[1]{Nitin Sundriyal}%
\author[2]{Juan Ramirez}%
\author[1]{Eduardo Bayro-Corrochano}%
\affil[1]{Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional}%
\affil[2]{Centre for Research and Advanced Studies Unit Monterrey}%


\vspace{-1em}



  
  \date{May 20, 2024}


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\begin{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.%
\end{abstract}%



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