Robust optimization for transmission defense against multi-period attacks with uncertainties

Abstract

The power system is under increasing threat of terrorist attacks, and it is important to develop efficient methods to improve the power system resiliency for defending against the attacks. In this paper, the defense strategy of the transmission system in case of multi-period attacks considering uncertainties is investigated. The problem formulation involves a multi-stage decision process: first, the defender chooses the critical branches to harden for the purpose of minimizing the expected damage; second, the attacker may launch multiple attacks to disrupt the branches aiming to maximize the damage; third, following each of the attacks, the operator performs the optimal power re-dispatch to minimize the load shedding. A novel robust optimization-based Defender-Sequential-Attacker-Operator (DSAO) model is developed, which considers game-theoretic interactions between different agents (the defender, attacker and operator), selection of attacking targets, as well as the probabilities of attacks and correlations between attacks. A hybrid solution approach consisting of both robust optimization and stochastic programming is developed to solve the DSAO model. Case studies based on the IEEE RTS79 and 118-bus systems validate the proposed approach. In addition, detailed comparisons are made with the explicit enumeration method and the recent trilevel defender-attacker-defender (DAD) model, which demonstrates the accuracy and computational efficiency of the proposed approach.