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

电网是一个关键的基础设施，社会依赖于许多其他追求的有效运作，包括商业，医疗保健，运输等。清单很长，因为电力使用几乎遍及人类活动的各个方面。因此，提高能源基础设施的弹性和安全性的方法是社会的深切兴趣，并对其在非常广泛的方面的正常运作具有重大的潜在影响。在过去的十年中，人们对复杂网络分析的跨学科领域中开发的工具的应用越来越感兴趣，以提高我们对电力系统行为的理解。事实上，电网可以很自然地描述为一个图，其中节点表示变压器、变电站或发电机，而边表示电气连接。复杂网络分析方法为电力系统脆弱性的基本和内在特征以及相关风险缓解策略的有效性提供了新的见解。然而，关于局部网络结构在电力系统功能中的作用的知识仍然有限。该项目开发了一种新的方法，以增强我们对各种局部网络特征在揭示真实电力系统脆弱性背后的隐藏机制及其对故障的动态响应方面的功能作用的理解。该项目设想了一种通过网络基序分析电网局部拓扑特性的新方法，网络基序是网络结构中出现的较小的循环模式。这种方法为理解高阶网络拓扑和电网功能之间的联系提供了基础。所提出的公式为电力系统稳定性、脆弱性和弹性特征的新分析方法以及检测电网故障、攻击和其他异常的算法的发展提供了广阔的平台。此外，该项目为加强我们对网络行为研究中更普遍的母题作用的理解提供了机会，这些研究可能更广泛地应用于各种网络物理环境。

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.