AMPS: Collaborative Research: Analysis of Local Power Grid Properties: From Network Motifs to Tensors

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Power grids are a critical infrastructure upon which society relies for effective operation of many other pursuits, including commerce, healthcare, transportation, etc. The list is quite long, as electricity use pervades almost every aspect of human activity. Thus, methods for improving the resilience and security of the energy infrastructure are of deep interest to society and have substantial potential impact on its proper functioning across a very broad front. The past decade has seen an increasing interest in the application of tools developed in the interdisciplinary field of complex network analysis to improve our understanding of power system behavior. Indeed, a power grid can be naturally described as a graph where nodes represent, e.g., transformers, substations or generators, and edges represent electrical connections. Methods of complex network analysis have provided new insights into the fundamental and intrinsic characteristics of power system vulnerability and the effectiveness of associated risk mitigation strategies. However, knowledge on the role of local network structures in functionality of power systems yet remains limited. The project develops a new methodology to enhance our understanding on a functional role of various local network features in unveiling hidden mechanisms behind vulnerability of real power systems and their dynamic response to malfunctions. This project contemplates a new approach to analysis of the local topological properties of power grids via network motifs, which are smaller recurrent patterns occurring in network structure. This methodology provides a basis for understanding linkages between higher-order network topologies and functionality of power grids. The proposed formulation presents a broad platform for the development both of new analytical methods for characterizing power system stability, vulnerability and resilience, and of algorithms for detecting faults, attacks and other anomalies in power grids. Furthermore, the project provides opportunities for strengthening our understanding of the role of motifs more generally in the study of network behavior that may be applied more broadly in a variety of cyber-physical settings.