Cascading Failures in Power Grids - Analysis and Algorithms

Abstract

This paper focuses on cascading line failures in the transmission system of the power grid. Recent large-scale power outages demonstrated the limitations of percolation- and epid- emic-based tools in modeling cascades. Hence, we study cascades by using computational tools and a linearized power flow model. We first obtain results regarding the Moore-Penrose pseudo-inverse of the power grid admittance matrix. Based on these results, we study the impact of a single line failure on the flows on other lines. We also illustrate via simulation the impact of the distance and resistance distance on the flow increase following a failure, and discuss the difference from the epidemic models. We then study the cascade properties, considering metrics such as the distance between failures and the fraction of demand (load) satisfied after the cascade (yield). We use the pseudo-inverse of admittance matrix to develop an efficient algorithm to identify the cascading failure evolution, which can be a building block for cascade mitigation. Finally, we show that finding the set of lines whose removal has the most significant impact (under various metrics) is NP-Hard and introduce a simple heuristic for the minimum yield problem. Overall, the results demonstrate that using the resistance distance and the pseudo-inverse of admittance matrix provides important insights and can support the development of efficient algorithms.

References in corpus (8)

• Emergence of scaling in random networks
• Finding and evaluating community structure in networks
• Catastrophic cascade of failures in interdependent networks
• Classes of behavior of small-world networks
• Structural Vulnerability of the North American Power Grid
• Evaluating North American Electric Grid Reliability Using the Barabasi-Albert Network Model
• Comparing the Topological and Electrical Structure of the North American Electric Power Infrastructure
• Incremental Computation of Pseudo-Inverse of Laplacian: Theory and Applications

Cited by in corpus (2)

• Limits of Predictability of Cascading Overload Failures in Spatially-Embedded Networks with Distributed Flows
• Distribution of blackouts in the power grid and the Motter and Lai model