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

电力系统基础设施的故障可能导致意外的负载中断，并对我们社会的几乎每个方面的正常运作产生严重影响，从水、食品和燃料供应到交通控制到执法到医疗、金融和电信系统。因此，开发新的方法以改进我们对电力系统脆弱性背后隐藏机制的了解，是保护经济稳定和人类生命并促进社会广泛复原力的关键一步。复杂网络提供了电力系统的自然表示，其中发电机和变电站被指定为顶点，电力线被绘制为边。利用复杂网络分析电力系统一般有两种主要方法。第一种方法基于电网的纯拓扑属性，第二种混合方法旨在将阻抗、最大功率等电气工程概念合并到复杂网络分析中，这通常导致将电网表示为加权有向图。这两种方法都对电力系统功能背后的隐藏机制提供了重要的补充见解，而且这两种方法都不能被视为普遍首选的方法。该项目旨在将拓扑数据分析的新概念引入电力系统研究，利用复杂网络工具和电气工程概念的优势。该项目将促进我们对潮流网格的理解，以及更广泛地理解地方一级的关键基础设施的功能性、可靠性和健壮性。该项目旨在开发新的方法来更系统地、数据驱动地和几何增强地对潮流网格进行推理，同时考虑电网的动态高阶拓扑结构和电网的电气工程特征，并研究持久同调在扩大我们对电网在广泛的现实世界场景中隐藏的弹性背后的机制的理解的作用。此外，该项目将研究拓扑数据分析的视野和局限性，以模拟潮流电网的可靠性，并更广泛地描述和监控关键能源基础设施对包括网络攻击、自然灾害和随机故障在内的广泛风险的恢复能力。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.