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Climate change poses an existential threat to humanity. It is now indisputable that the primary cause of this threat is human activity resulting in high greenhouse gas (GHG) emissions, which began during the Industrial Revolution and have continued to rapidly accelerate. The first warnings of impending and irreversible climate change were sounded decades ago, when governmental and intergovernmental policy makers had sufficient time to enact the changes needed to avoid the dire situation we find ourselves in today.

This article presents a computational framework to evaluate the resilience of electricity distribution networks (DNs) to a class of cyber-physical failures. In our model, we consider an attacker who targets multiple DN components to maximize the loss of the DN operator. We consider two types of operator responses: i) coordinated emergency response and ii) uncoordinated autonomous disconnects, which may lead to cascading failures. To evaluate resilience under response i), we consider a bilevel mixed-integer second-order cone program. This problem is computationally challenging to solve due to mixed-integer variables in the inner problem and nonconvex constraints. Our solution approach exploits the properties of power flows on radial DNs operating in a postattack contingency state to refine the classical generalized Benders decomposition method. Specifically, we suggest a modification of the right-hand side of the generalized Benders cut to be a value determined by the sum of values of a subset of inner dual cost coefficients. We show how the size of this subset can be selected to achieve a reasonable tradeoff between solution accuracy and computational effort. Furthermore, we evaluate DN resilience under response ii) by sequentially computing autonomous component disconnects due to operating bound violations resulting from the initial attack and the potential cascading failures. Our approach is useful for estimating the gain in resilience under response i), relative to ii).

Infrastructure systems are increasingly facing new security threats due to the vulnerabilities of cyber-physical components that support their operation. In this article, we investigate how the infrastructure operator (defender) should prioritize the investment in securing a set of facilities in order to reduce the impact of a strategic adversary (attacker) who can target a facility to increase the overall usage cost of the system. We adopt a game-theoretic approach to model the defender-attacker interaction and study two models: normal form game—where both players move simultaneously—and sequential game—where attacker moves after observing the defender’s strategy. For each model, we provide a complete characterization of how the set of facilities that are secured by the defender in equilibrium vary with the costs of attack and defense. Importantly, our analysis provides a sharp condition relating the cost parameters for which the defender has the first-mover advantage. Specifically, we show that to fully deter the attacker from targeting any facility, the defender needs to proactively secure all “vulnerable facilities” at an appropriate level of effort. We illustrate the outcome of the attacker–defender interaction on a simple transportation network. We also suggest a dynamic learning setup to understand how this outcome can affect the ability of imperfectly informed users to make their decisions about using the system in the post-attack stage.

We study learning dynamics induced by myopic travelers who repeatedly play a routing game on a transportation network with an unknown state. The state impacts cost functions of one or more edges of the network. In each stage, travelers choose their routes according to Wardrop equilibrium based on public belief of the state. This belief is broadcasted by an information system that observes the edge loads and realized costs on the used edges, and performs a Bayesian update to the prior stage’s belief. We show that the sequence of public beliefs and edge load vectors generated by the repeated play converge almost surely. In any rest point, travelers have no incentive to deviate from the chosen routes and accurately learn the true costs on the used edges. However, the costs on edges that are not used may not be accurately learned. Thus, learning can be incompletein that the edge load vector at rest point and complete information equilibrium can be different. We present some conditions for complete learning and illustrate situations when such an outcome is not guaranteed.

This paper focuses on the security assessment of electricity distribution networks (DNs) with vulnerable distributed energy resource (DER) nodes. The adversary model is a simultaneous compromise of DER nodes by strategic manipulation of generation setpoints. The loss to the defender (DN operator) includes loss of voltage regulation and cost of induced load control under supply-demand mismatch caused by the attack. A three-stage defender-attacker-defender (DAD) game is formulated: in Stage 1, the defender chooses a security strategy to secure a subset of DER nodes; in Stage 2, the attacker compromises a set of vulnerable DERs and injects false generation setpoints; in Stage 3, the defender responds by controlling loads and non-compromised DERs. Solving this trilevel optimization problem is hard due to nonlinear power flows and mixed-integer decision variables. To address this challenge, the problem is approximated by a tractable formulation based on an $\epsilon$-linear power-flow model. The set of critical DER nodes and the setpoint manipulations characterizing the optimal attack strategy are computed. An iterative greedy approach to computing attacker-defender strategies for the original nonlinear problem is proposed. These results provide guidelines for optimal security investment and defender response in preattack and postattack conditions, respectively.

In this paper, we develop a novel mechanism for reducing volatility of residential demand for electricity. We construct a reward-based (rebate) mechanism that provides consumers with incentives to shift their demand to off-peak time. In contrast to most other mechanisms proposed in the literature, the key feature of our mechanism is its modest requirements on user preferences, i.e., it does not require exact knowledge of user responsiveness to rewards for shifting their demand from the peak to the off-peak time. Specifically, our mechanism utilizes a probabilistic reward structure for users who shift their demand to the off-peak time, and is robust to incomplete information about user demand and/or risk preferences. We approach the problem from the public good perspective, and demonstrate that the mechanism can be implemented via lottery-like schemes. Our mechanism permits to reduce the distribution losses, and thus improve efficiency of electricity distribution. Finally, the mechanism can be readily incorporated into the emerging demand response schemes (e.g., the time-of-day pricing, and critical peak pricing schemes), and has security and privacy-preserving properties.