Line Failure Localization of Power Networks Part I: Non-cut Outages

TL;DR

This paper develops a mathematical framework to understand how power line failures propagate non-locally in transmission networks, focusing on connected post-contingency states and their topological influences.

Contribution

It introduces a novel graph-theoretic approach to characterize failure propagation and localization in power networks, emphasizing the role of network subtrees and block decomposition.

Findings

Distribution of subtrees influences power redistribution patterns

Block decomposition aids in understanding long-distance failure propagation

Mathematical theory captures Kirchhoff's Law in network topology

Abstract

Transmission line failures in power systems propagate non-locally, making the control of the resulting outages extremely difficult. In this work, we establish a mathematical theory that characterizes the patterns of line failure propagation and localization in terms of network graph structure. It provides a novel perspective on distribution factors that precisely captures Kirchhoff's Law in terms of topological structures. Our results show that the distribution of specific collections of subtrees of the transmission network plays a critical role on the patterns of power redistribution, and motivates the block decomposition of the transmission network as a structure to understand long-distance propagation of disturbances. In Part I of this paper, we present the case when the post-contingency network remains connected after an initial set of lines are disconnected simultaneously. In Part II, we present the case when an outage separates the network into multiple islands.