Cyber-physical attacks and defences in the smart grid: a survey <s> Mitigation <s> We present a trilevel optimization model of resource allocation in electric power network defense. This model identifies the most critical network components to defend against possible terrorist attacks. The goal of defense is to minimize the economic cost that the attacks may cause, subject to resource constraints. We describe a decomposition approach for finding an optimal solution to the trilevel model, which is based on iteratively solving smaller nested bilevel problems. Our testing results demonstrate the advantages of trilevel optimization over bilevel optimization in network defense. <s> BIB001 </s> Cyber-physical attacks and defences in the smart grid: a survey <s> Mitigation <s> This paper addresses the vulnerability analysis of the electric grid under terrorist threat. This problem is formulated as a mixed-integer nonlinear bilevel program. In the upper-level optimization, the terrorist agent maximizes the damage caused in the power system, which is measured in terms of the level of system load shed. On the other hand, in the lower- level optimization, the system operator minimizes the damage by means of an optimal operation of the power system. The distinctive modeling feature introduced in this paper is that, among the different corrective actions available, the system operator has the capability to modify the network topology. Due to its nonconvexity and nonlinearity, exact solution techniques are not currently available. This paper proposes a novel genetic algorithm approach to achieve near optimal solutions in moderate computing times. Some numerical results obtained by the proposed algorithm are provided and compared with those published, based on the IEEE Reliability Test System. <s> BIB002 </s> Cyber-physical attacks and defences in the smart grid: a survey <s> Mitigation <s> This paper addresses the vulnerability analysis of the electric grid under terrorist threat. This problem is formulated as a mixed-integer non-linear bilevel program. In the upper-level optimization, the terrorist agent maximizes the damage caused in the power system, which is measured in terms of the level of system load shed. On the other hand, in the lower-level optimization, the system operator minimizes the damage by means of an optimal operation of the power system. The distinctive modeling feature introduced in this paper is that, among the different corrective actions available, the system operator has the capability to modify the network topology. <s> BIB003 </s> Cyber-physical attacks and defences in the smart grid: a survey <s> Mitigation <s> Recently, game theory has been used to design optimized strategies for defending an electric power system against deliberate attacks. In this paper, we extend the current static model to a more generalized framework which includes several interaction models between defenders and attackers. A new criterion of reliable strategies for defending power systems has been derived. In addition, two allocation algorithms have been developed to seek reliable strategies for two types of defense tasks. The new criterion and algorithms are complementary to current security criteria and can provide useful information for decision-makers to protect their power systems against possible targeted attacks. Numerical simulation examples using the proposed methods are given as well. <s> BIB004 </s> Cyber-physical attacks and defences in the smart grid: a survey <s> Mitigation <s> Critical power system applications like contingency analysis and optimal power flow calculation rely on the power system state estimator. Hence the security of the state estimator is essential for the proper operation of the power system. In the future more applications are expected to rely on it, so that its importance will increase. Based on realistic models of the communication infrastructure used to deliver measurement data from the substations to the state estimator, in this paper we investigate the vulnerability of the power system state estimator to attacks performed against the communication infrastructure. We define security metrics that quantify the importance of individual substations and the cost of attacking individual measurements. We propose approximations of these metrics, that are based on the communication network topology only, and we compare them to the exact metrics. We provide efficient algorithms to calculate the security metrics. We use the metrics to show how various network layer and application layer mitigation strategies, like single and multi-path routing and data authentication, can be used to decrease the vulnerability of the state estimator. We illustrate the efficiency of the algorithms on the IEEE 118 and 300 bus benchmark power systems. <s> BIB005 </s> Cyber-physical attacks and defences in the smart grid: a survey <s> Mitigation <s> Applications of cyber technologies improve the quality of monitoring and decision making in smart grid. These cyber technologies are vulnerable to malicious attacks, and compromising them can have serious technical and economical problems. This paper specifies the effect of compromising each measurement on the price of electricity, so that the attacker is able to change the prices in the desired direction (increasing or decreasing). Attacking and defending all measurements are impossible for the attacker and defender, respectively. This situation is modeled as a zero sum game between the attacker and defender. The game defines the proportion of times that the attacker and defender like to attack and defend different measurements, respectively. From the simulation results based on the PJM 5 Bus test system, we can show the effectiveness and properties of the studied game. <s> BIB006 </s> Cyber-physical attacks and defences in the smart grid: a survey <s> Mitigation <s> Electricity grids are critical infrastructures. They are credible targets of active (e.g., terrorist) attacks since their disruption may lead to sizable losses economically and in human lives. It is thus crucial to develop decision support that can guide administrators in deploying defense resources for system security and reliability. Prior work on the defense of critical infrastructures has typically used static or Stackelberg games. These approaches view network interdictions as one-time events. However, infrastructure protection is also a continual process in which the defender and attacker interact to produce dynamic states affecting their best actions, as witnessed in the continual attack and defense of transmission networks in Colombia and Yemen. In this paper, we use zero-sum Markov games to model these interactions subject to underlying uncertainties of real-world events and actions. We solve equilibrium mixed strategies of the players that maximize their respective minimum payoffs with a time-decayed metric. We also show how the defender can use deception as a defense mechanism. Using results for a 5-bus system, a WECC 9-bus system, and an IEEE standard 14-bus system, we illustrate that our game model can provide useful insights. We also contrast our results with those of static games, and quantify the gain in defender payoff due to misinformation of the attacker. <s> BIB007 </s> Cyber-physical attacks and defences in the smart grid: a survey <s> Mitigation <s> The anticipated proliferation of cyber components for collecting information and controlling operations of smart grids increases their vulnerability to a variety of cyber attacks. For instance, a large-scale simultaneous attack on smart meters to destabilize the grid could be feasible via cyber means, which is not viable via physical attacks alone. The interactions between the providers and attackers of the smart grid and their optimal strategies can be modeled as a Markov game. However, the computational complexity of such a game grows exponentially with the size of the infrastructure, making it impractical for smart grids of reasonable sizes. In this paper, we show that when the players' current interest is a subset of the states only and they are willing to accept small inaccuracies in the game solutions, many Markov game states can be pruned. We present a pruning algorithm in which a threshold parameter is used to control qualitatively the tradeoff between computation time and solution accuracy. The algorithm is iterative with decoupled state values in each iteration, and we parallelize the state estimations to reduce the overall computation time. We illustrate with examples that the pruning algorithm reduces the computation time greatly without losing much precision in the game solutions, and that parallelization further reduces the computation time. <s> BIB008 </s> Cyber-physical attacks and defences in the smart grid: a survey <s> Mitigation <s> Vulnerability analysis of a power grid, especially in its static status, is often performed through solving a bi-level optimization problem, which, if solved to optimality, yields the most destructive interdiction plan with the worst loss. As one of the most effective operations to mitigate deliberate outages or attacks, transmission line switching recently has been included and modeled by a binary variable in the lower level decision model. Because this bi-level (or an equivalent min-max) problem is a challenging nonconvex discrete optimization problem, no exact algorithm has been developed, and only a few recent heuristic procedures are available. In this paper, we present an equivalent single-level reformulation of this problem, and describe a column-and-constraint generation algorithm to derive the global optimal solution. Numerical study confirms the quality of solutions and the computational efficiency of the proposed algorithm. Discussion and analysis of the mitigation effect of line switching are presented. <s> BIB009 </s> Cyber-physical attacks and defences in the smart grid: a survey <s> Mitigation <s> Data injection attacks have recently emerged as a significant threat on the smart power grid. By launching data injection attacks, an adversary can manipulate the real-time locational marginal prices to obtain economic benefits. Despite the surge of existing literature on data injection, most such works assume the presence of a single attacker and assume no cost for attack or defense. In contrast, in this paper, a model for data injection attacks with multiple adversaries and a single smart grid defender is introduced. To study the defender-attackers interaction, two game models are considered. In the first, a Stackelberg game model is used in which the defender acts as a leader that can anticipate the actions of the adversaries, that act as followers, before deciding on which measurements to protect. The existence and properties of the Stackelberg equilibrium of this game are studied. To find the equilibrium, a distributed learning algorithm that operates under limited system information is proposed and shown to converge to the game solution. In the second proposed game model, it is considered that the defender cannot anticipate the actions of the adversaries. To this end, we proposed a hybrid satisfaction equilibrium - Nash equilibrium game and defined its equilibrium concept. A search algorithm is also provided to find the equilibrium of the hybrid game. Numerical results using the IEEE 30-bus system are used to illustrate and analyze the strategic interactions between the attackers and defender. Our results show that by defending a very small set of measurements, the grid operator can achieve an equilibrium through which the optimal attacks have no effect on the system. Moreover, our results show how, at equilibrium, multiple attackers can play a destructive role towards each other, by choosing to carry out attacks that cancel each other out, leaving the system unaffected. <s> BIB010 </s> Cyber-physical attacks and defences in the smart grid: a survey <s> Mitigation <s> Cyber intrusions to substations are critical issues to a power grid, which must be defended and mitigated. Essentially, to better understand a cyber intrusion, reconnaissance activities should be modeled. Then, strategies of cyber attacker and defender can be studied, which help to identify substations vulnerable to cyber-attacks. In this paper, a successful intrusion is regarded as a probabilistic event related to reconnaissance activities. Its probability can be approximated by the Poisson distribution of the number of vulnerabilities discovered by the attacker. Furthermore, models of intrusion and defense in competition for control of the substations are proposed using Markov decision process (MDP). Key characteristics of target substation, attacker and defender are considered for determining probabilistic state transitions related to intrusion and defense actions. Thus, by solving the MDP models, the optimal strategies (action policies) of both the attacker and defender can be obtained. With these optimal strategies, the cyber security status of a substation can be evaluated within varied time frames. The case study validates the proposed models and method, including time-based strategies of the attacker and defender. <s> BIB011
When signs of an attack have been confirmed, mitigation efforts are made by the system operator to minimise the potential disruptions and damages. If the attack has been cleared from the system, existing mitigation and restoration mechanisms can effectively resume the secure and reliable power system operations. However, if the attack threat has not been resolved, the operator needs to consider persisting malicious attempts in the system. In such interactive scenarios, mitigation strategies are commonly modelled and solved by bi-level optimisation or game-theoretic approaches. An attacker-defender game has been developed against generic attacks on power system components BIB004 , and a zero-sum game between an informed cyber-attacker and a system operator has been proposed under different network configurations  . To deceive an attacker with misinformation so the attack damage can be reduced, a zero-sum Markov game has been proposed in BIB007 , based on which a scalable solution has been further developed BIB008 . For mitigation against interdiction, a tri-level optimisation has been developed, which introduces countermeasures of the defender in a third-level minimisation into the problem BIB001 . Alternatively, line switching has been proposed as an effective strategy to mitigate the interdiction, which is introduced directly in the lower/ inner-level of the bi-level optimisation. The solutions with the minimal cost of the operator can be obtained by genetic algorithm BIB002 , Benders decomposition BIB003 , and single-level reformulation BIB009 . In addition, MDP has also been integrated to model the attack-defence interaction in a substation intrusion BIB011 . By modelling a successful intrusion as a probabilistic event, the investigation has formulated a competition to gain access of multiple substations between the attacker and the operator. The optimal solution is obtained with consideration of system parameters, the attacker's resources, and the operator's budgets. A coordinated mitigation framework for the mitigation against FDIA has been developed in BIB005 . Security metrics have been proposed within the framework to evaluate the importance of substations and measurements. Strategies in both the network layer and the application layer have been developed to mitigate the threat of attacks. Game-theoretic approach has also been applied to achieve an optimal equilibrium given the resources and costs of attackers and defenders BIB010 , where a notable strategy has been identified for the multi-attacker scenario: the defender can use the game-theoretic approach to achieve a critical equilibrium, at which the impacts from multiple attackers can be cancelled even when the operator has no knowledge of the attacker's intentions. The zero-sum game approach has also been applied for the mitigation of attacks on electricity market where the attacker is given limited resources BIB006 .