Fast Identification of Vulnerable Set for Cascading Failure Analysis in Power Grid

Abstract

Past 20 years has witnessed some exorbitant fallout and large-scale blackouts in power system, particularly due to cascading failures and their propagation in the crucial yet complex and networked infrastructure. A pivotal prevention measure to steer clear from cascading events is the identification of vulnerable set, defined as the composition of specific line combinations that can trigger sequence of errors. By nature, the identification problem is NP-hard and a resort to approximation algorithms is necessary. In this article, we first construct a general yet rigorous formalism for the mathematical analysis of cascading failure in networked systems. With a tailored treatment of the propagation mechanism, a fast identification algorithm (FIA) for vulnerable set is then designed based on a key observation revealing the correlation structure among different N- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> contingencies. By analyzing the monotonic nondecreasing, quasi-submodular property of the propagation process, a theoretical lower bound of our algorithm is given in specific order. Besides, we show that the optimization framework of our algorithm can be readily extended to incorporate prior information. Numerical experiments on IEEE 30-, 118-, and 200-bus systems are performed to verify the effectiveness and efficiency of both FIA and its optimization framework.