The domino effect in power failure Sometimes a power failure can be fairly local, but other times, a seemingly identical initial failure can cascade to cause a massive and costly breakdown in the system. Yang et al. built a model for the North American power grid network based on samples of data covering the years 2008 to 2013 (see the Perspective by D'Souza). Although the observed cascades were widespread, a small fraction of all network components, particularly the ones that were most cohesive within the network, were vulnerable to cascading failures. Larger cascades were associated with concurrent triggering events that were geographically closer to each other and closer to the set of vulnerable components. Science, this issue p. eaan3184; see also p. 860 Cascading failures in the U.S. power grid are most likely to occur within cohesive parts of the grid. INTRODUCTION Cascading failures in power grids are inherently network processes, in which an initially small perturbation leads to a sequence of failures that spread through the connections between system components. An unresolved problem in preventing major blackouts has been to distinguish disturbances that cause large cascades from seemingly identical ones that have only mild effects. Modeling and analyzing such processes are challenging when the system is large and its operating condition varies widely across different years, seasons, and power demand levels. RATIONALE Multicondition analysis of cascade vulnerability is needed to answer several key questions: Under what conditions would an initial disturbance remain localized rather than cascade through the network? Which network components are most vulnerable to failures across various conditions? What is the role of the network structure in determining component vulnerability and cascade sizes? To address these questions and differentiate cascading-causing disturbances, we formulated an electrical-circuit network representation of the U.S.–South Canada power grid—a large-scale network with more than 100,000 transmission lines—for a wide range of operating conditions. We simulated cascades in this system by means of a dynamical model that accounts for transmission line failures due to overloads and the resulting power flow reconfigurations. RESULTS To quantify cascade vulnerability, we estimated the probability that each transmission line fails in a cascade. Aggregating the results from multiple conditions into a single network representation, we created a systemwide vulnerability map, which exhibits relatively homogeneous geographical distribution of power outages but highly heterogeneous distribution of the underlying overload failures. Topological analysis of the network representation revealed that the transmission lines vulnerable to overload failures tend to occupy the network’s core, characterized by links between highly connected nodes. We found that only a small fraction of the transmission lines in the network (well below 1% on average) are vulnerable under a given condition. When measured in terms of node-to-node distance and geographical distance, individual cascades often propagate far from the triggering failures, but the set of lines vulnerable to these cascades tend to be limited to the region in which the cascades are triggered. Moreover, large cascades are disproportionately more likely to be triggered by initial failures close to the vulnerable set. CONCLUSION Our results imply that the same disturbance in a given power grid can lead to disparate outcomes under different conditions—ranging from no damage to a large-scale cascade. The association between large cascades and the triggering failures’ proximity to the vulnerable set indicates that the topological and geographical properties of the vulnerable set is a major factor determining whether the failures spread widely. Because the vulnerable set is small, failures would often repeat on the same lines in the absence of interventions. Although the power grid represents a complex system in which changes can have unanticipated effects, our analysis suggests failure-based allocation of resources as a strategy in upgrading the system for improved resilience against large cascades. Cascade-resistant portion of the U.S.–South Canada power grid. The network is visualized on a cartogram that equalizes the density of nodes. (Top) Power lines that never underwent outage in our simulations under any grid condition are shown in green, whereas all the other lines—whose vulnerability varies widely—are in gray. (Bottom) Spreading of a cascade triggered by three failures at time t = 0 (arrows), which resulted in 254 failures at t = 100 (the end of the cascade in linearly rescaled time). The understanding of cascading failures in complex systems has been hindered by the lack of realistic large-scale modeling and analysis that can account for variable system conditions. Using the North American power grid, we identified, quantified, and analyzed the set of network components that are vulnerable to cascading failures under any out of multiple conditions. We show that the vulnerable set consists of a small but topologically central portion of the network and that large cascades are disproportionately more likely to be triggered by initial failures close to this set. These results elucidate aspects of the origins and causes of cascading failures relevant for grid design and operation and demonstrate vulnerability analysis methods that are applicable to a wider class of cascade-prone networks.

中文翻译：

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小型易受攻击集决定了电网中的大型网络级联

停电中的多米诺骨牌效应 有时，停电可能是相当局部的，但有时，看似相同的初始故障可能会级联，导致系统发生大规模且代价高昂的故障。杨等人。基于 2008 年至 2013 年的数据样本，为北美电网建立了模型（参见 D'Souza 的观点）。尽管观察到的级联很普遍，但所有网络组件中的一小部分，尤其是网络中最具凝聚力的组件，容易受到级联故障的影响。更大的级联与并发触发事件相关联，这些事件在地理上彼此更接近，更靠近易受攻击的组件集。科学，这个问题 p。eaan3184; 另见第。美国860级联故障 电网最有可能发生在电网的有凝聚力的部分。引言 电网中的级联故障本质上是网络过程，其中最初的小扰动会导致一系列故障，并通过系统组件之间的连接传播。防止大停电的一个悬而未决的问题是将引起大级联的干扰与看似相同但仅产生轻微影响的干扰区分开来。当系统很大并且其运行条件在不同年份、季节和电力需求水平之间变化很大时，对此类过程进行建模和分析具有挑战性。基本原理需要对级联漏洞进行多条件分析来回答几个关键问题：在什么条件下，初始扰动会保持局部状态而不是通过网络级联？哪些网络组件最容易在各种条件下发生故障？网络结构在确定组件脆弱性和级联大小方面的作用是什么？为了解决这些问题并区分引起级联的干扰，我们制定了美国-加拿大南部电网的电路网络表示，这是一个具有 100,000 多条传输线的大型网络，适用于各种运行条件。我们通过动态模型模拟了该系统中的级联，该模型考虑了由于过载和由此产生的功率流重新配置引起的输电线路故障。结果 为了量化级联脆弱性，我们估计了每条传输线在级联中出现故障的概率。将来自多个条件的结果聚合到单个网络表示中，我们创建了一个系统范围的漏洞图，该图展示了断电的相对同质的地理分布，但基础过载故障的高度异质分布。网络表示的拓扑分析表明，易受过载故障影响的传输线往往占据网络的核心，其特征是高度连接的节点之间的链接。我们发现，在给定条件下，网络中只有一小部分传输线（平均远低于 1%）容易受到攻击。当以节点到节点的距离和地理距离衡量时，单个级联通常远离触发故障传播，但易受这些级联影响的线路集往往仅限于触发级联的区域。此外，靠近易受攻击集的初始故障更有可能不成比例地触发大型级联。结论 我们的结果表明，给定电网中的相同扰动会在不同条件下导致不同的结果——从无损害到大规模级联。大型级联与触发故障与易受攻击集的接近程度之间的关联表明，易受攻击集的拓扑和地理属性是决定故障是否广泛传播的主要因素。因为脆弱集小，在没有干预的情况下，失败往往会在同一条线上重演。虽然电网是一个复杂的系统，其中的变化可能会产生意想不到的影响，但我们的分析表明，基于故障的资源分配是升级系统以提高对大型级联的弹性的一种策略。美国-南加拿大电网的抗级联部分。网络在均衡节点密度的图表上可视化。（顶部）在我们的模拟中在任何电网条件下从未中断过的电力线以绿色显示，而所有其他线路（其脆弱性差异很大）以灰色显示。（底部）由时间 t = 0 时的三个故障触发的级联传播（箭头），导致在 t = 100（线性重新调整时间级联的结束）时发生 254 次故障。由于缺乏可解释可变系统条件的现实大规模建模和分析，对复杂系统中级联故障的理解受到阻碍。使用北美电网，我们识别、量化和分析了在多种条件下容易发生级联故障的网络组件集。我们表明，易受攻击的集合由网络的一个小但拓扑中心的部分组成，并且大的级联更有可能被接近该集合的初始故障触发。这些结果阐明了与电网设计和运行相关的级联故障的起源和原因的各个方面，并展示了适用于更广泛的级联倾向网络的脆弱性分析方法。