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1. Quantifying the Interdependency Strength Across Critical Infrastructure Systems Using A Dynamic Network Flow Redistribution Model.

   Wang, Y.; Yu, J.; Baroud, H. (July 2020, Proceedings of the 30th European Safety and Reliability Conference and 15th Probabilistic Safety Assessment and Management Conference.)

   Baraldi, P.; null; Zio, E. (Ed.)

   Critical infrastructure networks are becoming increasingly interdependent which adversely impacts their performance through the cascading effect of initial failures. Failing to account for these complex interactions could lead to an underestimation of the vulnerability of interdependent critical infrastructure (ICI). The goal of this research is to assess how important interdependent links are by evaluating the interdependency strength using a dynamic network flow redistribution model which accounts for the dynamic and uncertain aspects of interdependencies. Specifically, a vulnerability analysis is performed considering two scenarios, one with interdependent links and the other without interdependent links. The initial failure is set to be the same under both scenarios. Cascading failure is modeled through a flow redistribution until the entire system reaches a stable state in which cascading failure no longer occurs. The unmet demand of the networks at the stable state over the initial demand is defined as the vulnerability. The difference between the vulnerability of each network under these two scenarios is used as the metric to quantify interdependency strength. A case study of a real power-water-gas system subject to earthquake risk is conducted to illustrate the proposed method. Uncertainty is incorporated by considering failure probability using Monte Carlo simulation. By varying the location and magnitude of earthquake disruptions, we show that interdependency strength is determined not only by the topology and flow of ICIs but also the characteristics of the disruptions. This compound system-disruption effect on interdependency strength can inform the design, assessment, and restoration of ICIs. 

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2. Community vulnerability perspective on robust protection planning in interdependent infrastructure networks

   https://doi.org/10.1177/1748006X21991038  

   Lobban, Hannah; Almoghathawi, Yasser; Morshedlou, Nazanin; Barker, Kash (October 2021, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability)

   Critical infrastructure networks, including water, power, communication, and transportation, among others, are necessary to society’s functionality. In recent years, the threat of different types of disruptions to such infrastructure networks has become an increasingly important problem to address. Due to existing interdependencies, damage to a small area of one of the networks could have far-reaching effects on the ability to meet demand across the entire system. Common disruption scenarios include, among others, intentional malevolent attacks, natural disasters, and random failures. Similar works have focused on only one type of scenario, but combining a variety of disruptions may lead to more realistic results. Additionally, the concept of social vulnerability, which describes an area’s ability to prepare for and respond to a disruption, must be included. This should promote not only the protection of the most at-risk components but also ensure that socially vulnerable communities are given adequate resources. This work provides a decision making framework to determine the allocation of defensive resources that accounts for all these factors. Accordingly, we propose a multi-objective mathematical model with the objectives of: (i) minimizing the vulnerability of a system of interdependent infrastructure networks, and (ii) minimizing the total cost of the resource allocation strategy. Moreover, to account for uncertainty in the proposed model, this paper incorporates a means to address robustness in finding the most adaptable network protection plan to reduce the vulnerability of the system of interdependent networks to a variety of disruption scenarios. The proposed work is illustrated with an application to social vulnerability and interdependent power, gas, and water networks in Shelby County, Tennessee. 

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3. A socio-technical approach for the assessment of critical infrastructure system vulnerability in extreme weather events

   https://doi.org/10.1038/s41560-023-01315-7  

   Montoya-Rincon, Juan P.; Mejia-Manrique, Said A.; Azad, Shams; Ghandehari, Masoud; Harmsen, Eric W.; Khanbilvardi, Reza; Gonzalez-Cruz, Jorge E. (July 2023, Nature Energy)

   The recurrence of extreme weather events has led to the development of methods for assessing the vulnerability and interdependencies of physical and human systems. A case example is Hurricane Maria (H-Maria), where Puerto Rico experienced damage to 80% of its electrical power system, leading to massive disruptions of essential services for months. Here we evaluate the effectiveness of various interventions aimed at reducing vulnerability by considering power and water infrastructure and respective water–power dependencies while also considering the social vulnerability of affected communities associated with the physical infrastructure upgrades. On the basis of the current infrastructure configuration, we found that all communities suffered enormously from power and water outages. As one upgrade option, we show that incorporating regional energy grids would reduce outages in an H-Maria scenario. However, a large portion of disadvantaged communities will face service disruption under this option. In contrast, hardening transmission lines, as the second option, would improve service delivery and, most importantly, provide uninterrupted service to the higher portion of the vulnerable population. 

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4. A Mean-risk Mixed Integer Nonlinear Program for Network Protection

   https://doi.org/liojoin  

   Burton, Amy (January 2020, Thesis for Clemson University)

   d. Many of the infrastructure sectors that are considered to be crucial by the Department of Homeland Security include networked systems (physical and temporal) that function to move some commodity like electricity, people, or even communication from one location of importance to another. The costs associated with these flows make up the price of the network’s normal functionality. These networks have limited capacities, which cause the marginal cost of a unit of flow across an edge to increase as congestion builds. In order to limit the expense of a network’s normal demand we aim to increase the resilience of the system and specifically the resilience of the arc capacities. Divisions of critical infrastructure have faced difficulties in recent years as inadequate resources have been available for needed upgrades and repairs. Without being able to determine future factors that cause damage both minor and extreme to the networks, officials must decide how to best allocate the limited funds now so that these essential systems can withstand the heavy weight of society’s reliance. We model these resource allocation decisions using a two-stage stochastic program (SP) for the purpose of network protection. Starting with a general form for a basic two-stage SP, we enforce assumptions that specify characteristics key to this type of decision model. The second stage objective—which represents the price of the network’s routine functionality—is nonlinear, as it reflects the increasing marginal cost per unit of additional flow across an arc. After the model has been designed properly to reflect the network protection problem, we are left with a nonconvex, nonlinear, nonseparable risk-neutral program. This research focuses on key reformulation techniques that transform the problematic model into one that is convex, separable, and much more solvable. Our approach focuses on using perspective functions to convexify the feasibility set of the second stage and second order conic constraints to represent nonlinear constraints in a form that better allows the use of computational solvers. Once these methods have been applied to the risk-neutral model we introduce a risk measure into the first stage that allows us to control the balance between an efficient, solvable model and the need to hedge against extreme events. Using Benders cuts that exploit linear separability, we give a decomposition and solution algorithm for the general network model. The innovations included in this formulation are then implemented on a transportation network with given flow demand 

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5. Risk Assessment and Mitigation of Cascading Failures Using Critical Line Sensitivities

   https://doi.org/10.1109/TPWRS.2023.3305093  

   Dai, Yitian; Noebels, Matthias; Preece, Robin; Panteli, Mathaios; Dobson, Ian (March 2024, IEEE Transactions on Power Systems)

   Security concerns have been raised about cascading failure risks in evolving power grids. This paper reveals, for the first time, that the risk of cascading failures can be increased at low network demand levels when considering security-constrained generation dispatch. This occurs because critical transmission cor- ridors become very highly loaded due to the presence of central- ized generation dispatch, e.g., large thermal plants far from de- mand centers. This increased cascading risk is revealed in this work by incorporating security-constrained generation dispatch into the risk assessment and mitigation of cascading failures. A se- curity-constrained AC optimal power flow, which considers eco- nomic functions and security constraints (e.g., network con- straints, 𝑵 − 𝟏 security, and generation margin), is used to pro- vide a representative day-ahead operational plan. Cascading fail- ures are simulated using two simulators, a quasi-steady state DC power flow model, and a dynamic model incorporating all fre- quency-related dynamics, to allow for result comparison and ver- ification. The risk assessment procedure is illustrated using syn- thetic networks of 200 and 2,000 buses. Further, a novel preventive mitigation measure is proposed to first identify critical lines, whose failures are likely to trigger cascading failures, and then to limit power flow through these critical lines during dispatch. Results show that shifting power equivalent to 1% of total demand from critical lines to other lines can reduce cascading risk by up to 80%. 

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