A Phase Transition Approach for Predicting Cascading Failure in Networked Systems

随着电网、通信网络和互联网等工程系统规模的扩大，以及社会对这些网络可靠运行的依赖程度的增加，系统工程师寻求更好地理解单个元素的小规模故障如何传播到产生全球系统范围的故障是至关重要的。本文提出的工作主要受到电力系统应用的推动，以及将分析稳定性技术应用于级联线和发电机跳闸问题的挑战。目标是捕捉在指定的初始扰动之后的瞬态动态响应的作用，并检查当沿着状态轨迹超过单个元素的操作阈值时引起的后续（“级联”）元素故障。这种方法将利用出现在电力系统动力学和相关网络系统中的“类哈密顿”结构，其中控制行为的微分方程通常与易于识别的存储函数密切相关。通过将元件失效与网络元件中最大允许能量存储的阈值相关联，该工作将寻求开发一种易于处理的、平滑的元件失效模型，该模型适用于李亚普诺夫型稳定性分析。有人认为，级联元件失效可以被捕获为潜在盆地之间关于（可能）稳定平衡的一系列过渡，每个平衡由部分退化的网络配置定义。

As the scale of engineered systems such as electric power grids, communication networks, and the internet expands, and as society's dependence upon reliable operation of these networks increases, it is vital that system engineers seek a better understanding of how small scale failures of individual elements may propagate to produce global system-wide failures. The work proposed here is motivated largely by the electric power systems application, and the challenge in bringing analytic stability techniques to bear on the problem of cascading line and generator tripping. The goal is to capture the role of transient dynamic response following a specified initiating disturbance, and examine subsequent ("cascading") element failures that are induced when operating thresholds for individual elements are exceeded along the state trajectory. This approach will exploit "Hamiltonian-like" structure that appears in power system dynamics and related classes of networked systems, in which the differential equations governing behavior are often closely related to an easily identified storage function. By relating element failure to thresholds of maximally allowable energy storage in network elements the work will seek to develop a tractable, smooth model for element failure that is amenable to Lyapunov type stability analysis. It will be argued that cascading element failure can then be captured as a sequence of transitions between potential basins about (possibly) stable equilibria, with each equilibrium defined by a partially degraded network configuration.