Simplicial complexes using vector visibility graphs for multivariate classification of faults in electrical distribution systems

The reliability and efficiency of electrical distribution systems are required for ensuring an uninterrupted power supply and minimizing operational disruption, as failures could lead to significant power outages and safety hazards. This work proposes a novel approach for the classification of electrical faults in distribution systems, utilizing an advanced machine learning technique combined with the vector visibility graphs (VVG). Initially, electrical signal data from the distribution system are collected and transformed into a visibility network, by mapping multivariate time series data to vector space and establishing visibility criteria between vectors. Also, complex network parameters as features from obtained visibility network. Subsequently, a simplicial complex is constructed from the visibility network to explore the topology and connectivity patterns inherent in the electrical data. The Bron-Kerbosch algorithm is employed to detect maximal cliques within the network, serving as a robust method for identifying intricate relationships and anomalies indicative of faults. Characterization of the simplicial complex is performed using both vector and scalar quantities, to extract meaningful features from the electrical signals. These features are then synthesized to capture the maximum values of vectors, focusing on the most significant attributes for fault classification. Then, the feature set is fed into a support vector machine (SVM) classifier for training and validating to distinguish between fault and no fault conditions. The proposed methodology demonstrates superior performance in fault classification, significantly enhancing an accuracy of 99.51% of fault detection in electrical distribution systems.