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Due to the increasing reliance on networks, defending a cyber system is of vital importance. In this paper, we consider an important mechanism of early warning for defending a cyber system that has become a key component of constructing network defense in practice. We study the reliability of a system under attack from single or multiple sources. In particular, we discuss the effect of an early warning mechanism on the system reliability. We then propose the optimal strategy for defending a cyber system with early warning components in the worst attack scenario. The theoretical results are further validated by simulation evidence.

Phasor measurement units (PMUs) have been integrated into the smart grid for monitoring the operational state of system and improving the reliability. Due to the high cost of PMU installment, the optimal placement strategies have attracted considerable attention in the literature. However, the impacts of cyber threats on the placement have been largely ignored owing to the cyber complexities. This paper initializes the study on the optimal PMU placement in a smart grid under the cyber threats. A probabilistic model is developed for assessing the unobservable risk of the power grid. We characterize the impacts of several cyber factors on the PMU placements including the number of directly attacked PMUs, the dependence among attack outcomes, and risk propagation. We further study the impacts of cyber attacks on the allocation strategies under a bi-level placement model. In particular, a novel ‘greedy’ algorithm for PMU placement is introduced with the presence of cyber risks. Our studies show that the cyber risk can significantly increase the unobservability risk of a power system which in turn requires additional PMU allocations, and the dependence among cyber attacks can lead to more unobservable risk.