EAGER: Collaborative Research: Local Topological Properties of Power Flow Networks, and Their Role in Power System Functionality

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Failures of power system infrastructure can result in unpredicted load interruptions and severe implications for proper functioning of virtually every aspect of our society, from water, food and fuel supply to transportation control to law enforcement to healthcare, finance, and telecommunication systems. Developing new methods for improving our understanding of hidden mechanisms behind power system vulnerability is, hence, a critical step towards protecting economic stability and human life and facilitating societal resilience on a broad front. Complex networks offer a natural representation of power systems, where generators and substations are specified as vertices and electric lines are sketched as edges. There are generally two main approaches to the analysis of power systems using complex networks. The first approach is based on purely topological properties of a grid network, and the second hybrid approach aims to incorporate electrical engineering concepts, e.g. impedance, maximum power, etc., into the complex network analysis, which typically results in a representation of a grid as a weighted directed graph. Both approaches provide important complementary insights into hidden mechanisms behind functionality of power systems, and neither approach can be viewed as a universally preferred method. This project aims to introduce novel concepts of topological data analysis into studies of power systems that will capitalize on strengths of both complex network tools and electrical engineering concepts. The project will facilitate our understanding of power-flow grids and, more generally, of critical infrastructure functionality, reliability, and robustness, at a local level.This project aims to develop novel procedures for more systematic, data-drivenand geometrically enhanced inference for power flow grids, while accounting both for dynamic higher order topological structure and for electrical engineering characteristics of a grid network, and to study the utility of persistent homologies in amplifying our understanding of hidden mechanisms behind power grid resilience in a broad range of real-world scenarios. Furthermore, the project will examine horizons and limitations of topological data analysis for modeling reliability of power-flow grids and more generally for characterizing and monitoring resilience of critical energy infrastructures to a wide range of risks, including cyber-attacks, natural hazards and random failures.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.