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会导致不可预测的负载中断，并严重影响我们社会几乎每个方面的正常运作，从水，食品和燃料供应到运输控制，执法到医疗保健，金融和电信系统。因此，开发新的方法来提高我们对电力系统脆弱性背后隐藏机制的理解，是保护经济稳定和人类生命以及促进广泛的社会复原力的关键一步。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，电线被绘制为边。 一般有两种主要的方法来分析电力系统使用复杂网络。第一种方法基于电网网络的纯拓扑性质，第二种混合方法旨在结合电气工程概念，例如阻抗、最大功率等，复杂网络分析通常会将网格表示为加权有向图。这两种方法提供了重要的互补的洞察隐藏的机制背后的电力系统的功能，没有一种方法可以被视为一个普遍的首选方法。 本项目旨在将拓扑数据分析的新概念引入电力系统的研究中，以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，更普遍地说，在地方层面上，关键基础设施的功能性，可靠性和鲁棒性。该项目旨在开发新的程序，用于更系统的，数据驱动的和几何增强的潮流网格推理，同时考虑动态高阶拓扑结构和电网网络的电气工程特性，并研究持续同源性在扩大我们对电网弹性背后隐藏机制的理解方面的效用，在广泛的现实世界场景中。此外，该项目还将研究拓扑数据分析的范围和局限性，以建模电力流电网的可靠性，更普遍地用于表征和监测关键能源基础设施对各种风险的弹性，包括网络攻击，该奖项反映了NSF的法定使命，并通过使用基金会的智力价值进行评估，更广泛的影响审查标准。

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.