Cyber-Physical Distributed Systems. Min Xie

data by injecting false data into measurement devices, eavesdropping estimation of system states, and deploying denial of service (DoS) attacks on communication networks [216,217,220,245]. More sophisticated attack models specifically target weaknesses to cause maximal damage [191]. In this respect, it is key to capture the uncertainties intrinsic to the behavior of the attacker and the defender.

      With respect to applications in smart grids, upgrading traditional grids to smart grids has brought many benefits to the overall management of power and energy systems, including higher reliability, better efficiency, improved integration of RERs, more flexible choice for stakeholders, and lower operation costs [246–248]. However, the core technologies, for example, communication techniques and SCADA systems [249–252], which deliver the advantages of smart grids, also open the grids to vulnerabilities that already exist in the information and communications technology (ICT) world. These vulnerabilities pose threats to smart grids, such as DoS attacks, false data injection, replay attacks, privacy data theft, and sabotage of critical infrastructure [253–255]. In addition, the failures in a smart grid caused by cyberattacks can easily cascade to other highly dependent critical infrastructure sectors, such as transportation systems, wastewater systems, health care systems, and banking systems, resulting in extensive physical damage and social and economic disruption [249,256].

      While government, the private sector, and academia are recognizing the cyber vulnerability of smart grids, the likelihood and impact of a cyberattack are difficult to quantify. Furthermore, for a smart grid, there may be mandatory standards and operational requirements from grid stakeholders. Current risk management strategies are generally qualitative or heuristic [257]. In these strategies, some assumptions, for example, constant reward with respect to successful anti‐cyberattack [258,259], may be unrealistic for most smart grids.

Chapter 7 presents a probabilistic risk analysis framework to enhance smart grid cyber security. In particular, the dynamic and stochastic characteristics of smart grids, such as uncertain demands, are taken into account to investigate the effect of defending strategies on the real operation cost. The optimal power flow (OPF) model [260] is applied to an 11‐node radial smart grid originating from the Elia grid in Belgium. Compared with the existing studies that focus on the inherent risk [254,260], such as the natural degradation and uncertain RERs for better maintenance actions and power dispatch, Chapter 7 addresses the impact of the external threat (cyberattacks) on the operation cost for effective deployment of cyber defense teams. In previous works, the cost of each attack on a node was assumed to be a constant [259]. Nevertheless, by investigating some practical scenarios, it has been found that the costs are more likely to be determined by some adversarial factors. Therefore, an adversarial cost sequence associated with each node is assumed, and a widely used variation constraint is introduced for each cost sequence. To cope with the objective of sequential decision strategies, the problem is formulated using the reinforcement learning framework [261–263]. In particular, the Bayesian prior method [259] is employed for the model parameters, and the problem is formulated as a Bayesian adversarial multi‐node bandit model. In addition, a Bayesian minimax type regret function is constructed, which is subject to the learning context.