Characterisation of Electrical Power Systems Based on Electrical Curves and their properties

Due to the proliferation of renewable energy systems, the study of voltage and frequency stability is a crucial aspect. Recently, this problem has been approached from a purely geometrical point of view with interesting results. The present work investigates the properties of the so-called electrical curves described by arbitrary voltage or current vectors in Euclidean spaces. Through the invariants of these curves, certain indices can be constructed to detect abnormal operation or irregular characteristics in electrical power systems. Different scenarios and examples have been solved in this work to support the proposed theory.