Modelling cascading failures in lifelines using temporal networks

Lifelines are critical infrastructure systems with high interdependency. During a disaster, the interdependency between the lifelines can lead to cascading failures. In the literature, the approaches used to analyze infrastructure interdependencies within the social, political, and economic domains do not properly describe the infrastructures’ emergency management. During an emergency, the response phase is very condensed in time, and the failures that occur are usually amplified through cascading effects in the long-term period. Because of these peculiarities, interdependencies need to be modeled considering the time dimension. The methodology proposed in this paper is based on a modified version of the Input-output Inoperability Model. The lifelines are modeled using graph theory, and perturbations are applied to the elements of the graph, simulating natural or man-made disasters. The cascading effect among the interdependent networks has been simulated using a spatial multilayer approach. The adjancency tensor has been used to for the temporal dimension and its effects. Finally, the numerical results of the simulations with the proposed model are represented by probabilities of failure for each node of the system. As a case study, the methodology has been applied to a nuclear power plant. The model can be adopted to run analysis at different scales, from the regional to the local scales

Distributed and Optimal Resilient Planning of Large-Scale Interdependent Critical Infrastructures

The complex interconnections between heterogeneous critical infrastructure sectors make the system of systems (SoS) vulnerable to natural or human-made disasters and lead to cascading failures both within and across sectors. Hence, the robustness and resilience of the interdependent critical infrastructures (ICIs) against extreme events are essential for delivering reliable and efficient services to our society. To this end, we first establish a holistic probabilistic network model to model the interdependencies between infrastructure components. To capture the underlying failure and recovery dynamics of ICIs, we further propose a Markov decision processes (MDP) model in which the repair policy determines a long-term performance of the ICIs. To address the challenges that arise from the curse of dimensionality of the MDP, we reformulate the problem as an approximate linear program and then simplify it using factored graphs. We further obtain the distributed optimal control for ICIs under mild assumptions. Finally, we use a case study of the interdependent power and subway systems to corroborate the results and show that the optimal resilience resource planning and allocation can reduce the failure probability and mitigate the impact of failures caused by natural or artificial disasters

Dynamic Modeling of Cascading Failure in Power Systems

The modeling of cascading failure in power systems is difficult because of the many different mechanisms involved; no single model captures all of these mechanisms. Understanding the relative importance of these different mechanisms is an important step in choosing which mechanisms need to be modeled for particular types of cascading failure analysis. This work presents a dynamic simulation model of both power networks and protection systems, which can simulate a wider variety of cascading outage mechanisms, relative to existing quasi-steady state (QSS) models. The model allows one to test the impact of different load models and protections on cascading outage sizes. This paper describes each module of the developed dynamic model and demonstrates how different mechanisms interact. In order to test the model we simulated a batch of randomly selected $N-2$ contingencies for several different static load configurations, and found that the distribution of blackout sizes and event lengths from the proposed dynamic simulator correlates well with historical trends. The results also show that load models have significant impacts on the cascading risks. This dynamic model was also compared against a QSS model based on the dc power flow approximations; we find that the two models largely agree, but produce substantially different results for later stages of cascading.Comment: 8 pages, 9 figures, 5 tables, submitted to IEEE transaction

Finding KK Contingency List in Power Networks using a New Model of Dependency

Smart grid systems are composed of power and communication network components. The components in either network exhibit complex dependencies on components in its own as well as the other network to drive their functionality. Existing, models fail to capture these complex dependencies. In this paper, we restrict to the dependencies in the power network and propose the Multi-scale Implicative Interdependency Relation (MIIR) model that address the existing limitations. A formal description of the model along with its working dynamics and a brief validation with respect to the 2011 Southwest blackout are provided. Utilizing the MIIR model, the $K$ Contingency List problem is proposed. For a given time instant, the problem solves for a set of $K$ entities in a power network which when failed at that time instant would cause the maximum number of entities to fail eventually. Owing to the problem being NP-complete we devised a Mixed Integer Program (MIP) to obtain the optimal solution and a polynomial time sub-optimal heuristic. The efficacy of the heuristic with respect to the MIP is compared by using different bus system data. In general, the heuristic is shown to provide near optimal solution at a much faster time than the MIP

Critical Utility Infrastructural Resilience

The paper refers to CRUTIAL, CRitical UTility InfrastructurAL Resilience, a European project within the research area of Critical Information Infrastructure Protection, with a specific focus on the infrastructures operated by power utilities, widely recognized as fundamental to national and international economy, security and quality of life. Such infrastructures faced with the recent market deregulations and the multiple interdependencies with other infrastructures are becoming more and more vulnerable to various threats, including accidental failures and deliberate sabotage and malicious attacks. The subject of CRUTIAL research are small scale networked ICT systems used to control and manage the electric power grid, in which artifacts controlling the physical process of electricity transportation need to be connected with corporate and societal applications performing management and maintenance functionality. The peculiarity of such ICT-supported systems is that they are related to the power system dynamics and its emergency conditions. Specific effort need to be devoted by the Electric Power community and by the Information Technology community to influence the technological progress in order to allow commercial intelligent electronic devices to be effectively deployed for the protection of citizens against cyber threats to electric power management and control systems. A well-founded know-how needs to be built inside the industrial power sector to allow all the involved stakeholders to achieve their service objectives without compromising the resilience properties of the logical and physical assets that support the electric power provision

Topological Performance Measures as Surrogates for Physical Flow Models for Risk and Vulnerability Analysis for Electric Power Systems

Critical infrastructure systems must be both robust and resilient in order to ensure the functioning of society. To improve the performance of such systems, we often use risk and vulnerability analysis to find and address system weaknesses. A critical component of such analyses is the ability to accurately determine the negative consequences of various types of failures in the system. Numerous mathematical and simulation models exist which can be used to this end. However, there are relatively few studies comparing the implications of using different modeling approaches in the context of comprehensive risk analysis of critical infrastructures. Thus in this paper, we suggest a classification of these models, which span from simple topologically-oriented models to advanced physical flow-based models. Here, we focus on electric power systems and present a study aimed at understanding the tradeoffs between simplicity and fidelity in models used in the context of risk analysis. Specifically, the purpose of this paper is to compare performances measures achieved with a spectrum of approaches typically used for risk and vulnerability analysis of electric power systems and evaluate if more simplified topological measures can be combined using statistical methods to be used as a surrogate for physical flow models. The results of our work provide guidance as to appropriate models or combination of models to use when analyzing large-scale critical infrastructure systems, where simulation times quickly become insurmountable when using more advanced models, severely limiting the extent of analyses that can be performed

Distributed Monitoring for Prevention of Cascading Failures in Operational Power Grids

Electrical power grids are vulnerable to cascading failures that can lead to large blackouts. Detection and prevention of cascading failures in power grids is impor- tant. Currently, grid operators mainly monitor the state (loading level) of individual components in power grids. The complex architecture of power grids, with many interdependencies, makes it difficult to aggregate data provided by local compo- nents in a timely manner and meaningful way: monitoring the resilience with re- spect to cascading failures of an operational power grid is a challenge. This paper addresses this challenge. The main ideas behind the paper are that (i) a robustness metric based on both the topology and the operative state of the power grid can be used to quantify power grid robustness and (ii) a new proposed a distributed computation method with self-stabilizing properties can be used to achieving near real-time monitoring of the robustness of the power grid. Our con- tributions thus provide insight into the resilience with respect to cascading failures of a dynamic operational power grid at runtime, in a scalable and robust way. Com- putations are pushed into the network, making the results available at each node, allowing automated distributed control mechanisms to be implemented on top

Evaluating Cascading Impact of Attacks on Resilience of Industrial Control Systems: A Design-Centric Modeling Approach

A design-centric modeling approach was proposed to model the behaviour of the physical processes controlled by Industrial Control Systems (ICS) and study the cascading impact of data-oriented attacks. A threat model was used as input to guide the construction of the CPS model where control components which are within the adversary's intent and capabilities are extracted. The relevant control components are subsequently modeled together with their control dependencies and operational design specifications. The approach was demonstrated and validated on a water treatment testbed. Attacks were simulated on the testbed model where its resilience to attacks was evaluated using proposed metrics such as Impact Ratio and Time-to-Critical-State. From the analysis of the attacks, design strengths and weaknesses were identified and design improvements were recommended to increase the testbed's resilience to attacks

An Interaction Model for Simulation and Mitigation of Cascading Failures

In this paper the interactions between component failures are quantified and the interaction matrix and interaction network are obtained. The quantified interactions can capture the general propagation patterns of the cascades from utilities or simulation, thus helping to better understand how cascading failures propagate and to identify key links and key components that are crucial for cascading failure propagation. By utilizing these interactions a high-level probabilistic model called interaction model is proposed to study the influence of interactions on cascading failure risk and to support online decision-making. It is much more time efficient to first quantify the interactions between component failures with fewer original cascades from a more detailed cascading failure model and then perform the interaction model simulation than it is to directly simulate a large number of cascades with a more detailed model. Interaction-based mitigation measures are suggested to mitigate cascading failure risk by weakening key links, which can be achieved in real systems by wide area protection such as blocking of some specific protective relays. The proposed interaction quantifying method and interaction model are validated with line outage data generated by the AC OPA cascading simulations on the IEEE 118-bus system.Comment: Accepted by IEEE Transactions on Power System

A Simplified Self-Consistent Probabilities Framework to Characterize Percolation Phenomena on Interdependent Networks : An Overview

Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the percolation phenomena of these systems, different mathematical frameworks have been proposed including generating functions, eigenvalues among some others. These different frameworks approach the phase transition behaviors from different angles, and have been very successful in shaping the different quantities of interest including critical threshold, size of the giant component, order of phase transition and the dynamics of cascading. These methods also vary in their mathematical complexity in dealing with interdependent networks that have additional complexity in terms of the correlation among different layers of networks or links. In this work, we review a particular approach of simple self-consistent probability equations, and illustrate that it can greatly simplify the mathematical analysis for systems ranging from single layer network to various different interdependent networks. We give an overview on the detailed framework to study the nature of the critical phase transition, value of the critical threshold and size of the giant component for these different systems