Analysis and Mitigation of Cascading Failures Using a Stochastic Interaction Graph with Eigen-analysis

Abstract

In studies on complex network systems using graph theory, eigen-analysis is typically performed on an undirected graph model of the network. However, when analyzing cascading failures in a power system, the interactions among failures suggest the need for a directed graph beyond the topology of the power system to model directions of failure propagation. To accurately quantify failure interactions for effective mitigation strategies, this paper proposes a stochastic interaction graph model and associated eigen-analysis. Different types of modes on failure propagations are defined and characterized by the eigenvalues of a stochastic interaction matrix, whose absolute values are unity, zero, or in between. Finding and interpreting these modes helps identify the probable patterns of failure propagation, either local or widespread, and the participating components based on eigenvectors. Then, by lowering the failure probabilities of critical components highly participating in a mode of widespread failures, cascading can be mitigated. The validity of the proposed stochastic interaction graph model, eigen-analysis and the resulting mitigation strategies is demonstrated using simulated cascading failure data on an NPCC 140-bus system.

References in corpus (8)

• Do topological models provide good information about vulnerability in electric power networks?
• Dynamic Modeling of Cascading Failure in Power Systems
• Cascading Power Outages Propagate Locally in an Influence Graph that is not the Actual Grid Topology
• An Interaction Model for Simulation and Mitigation of Cascading Failures
• A Markovian influence graph formed from utility line outage data to mitigate large cascades
• Interaction Graphs for Cascading Failure Analysis in Power Grids: A Survey
• A Tutorial on the Spectral Theory of Markov Chains
• Mitigation of Cascading Outages Using a Dynamic Interaction Graph-Based Optimal Power Flow Model