Cascading failures in spatially-embedded random networks

Cascading failures constitute an important vulnerability of interconnected systems. Here we focus on the study of such failures on networks in which the connectivity of nodes is constrained by geographical distance. Specifically, we use random geometric graphs as representative examples of such spatial networks, and study the properties of cascading failures on them in the presence of distributed flow. The key finding of this study is that the process of cascading failures is non-self-averaging on spatial networks, and thus, aggregate inferences made from analyzing an ensemble of such networks lead to incorrect conclusions when applied to a single network, no matter how large the network is. We demonstrate that this lack of self-averaging disappears with the introduction of a small fraction of long-range links into the network. We simulate the well studied preemptive node removal strategy for cascade mitigation and show that it is largely ineffective in the case of spatial networks. We introduce an altruistic strategy designed to limit the loss of network nodes in the event of a cascade triggering failure and show that it performs better than the preemptive strategy. Finally, we consider a real-world spatial network viz. a European power transmission network and validate that our findings from the study of random geometric graphs are also borne out by simulations of cascading failures on the empirical network.Comment: 13 pages, 15 figure

Reducing Cascading Failure Risk by Increasing Infrastructure Network Interdependency

Increased coupling between critical infrastructure networks, such as power and communication systems, will have important implications for the reliability and security of these systems. To understand the effects of power-communication coupling, several have studied interdependent network models and reported that increased coupling can increase system vulnerability. However, these results come from models that have substantially different mechanisms of cascading, relative to those found in actual power and communication networks. This paper reports on two sets of experiments that compare the network vulnerability implications resulting from simple topological models and models that more accurately capture the dynamics of cascading in power systems. First, we compare a simple model of topological contagion to a model of cascading in power systems and find that the power grid shows a much higher level of vulnerability, relative to the contagion model. Second, we compare a model of topological cascades in coupled networks to three different physics-based models of power grids coupled to communication networks. Again, the more accurate models suggest very different conclusions. In all but the most extreme case, the physics-based power grid models indicate that increased power-communication coupling decreases vulnerability. This is opposite from what one would conclude from the coupled topological model, in which zero coupling is optimal. Finally, an extreme case in which communication failures immediately cause grid failures, suggests that if systems are poorly designed, increased coupling can be harmful. Together these results suggest design strategies for reducing the risk of cascades in interdependent infrastructure systems

Network resilience

Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a "tipping point," such as mass extinctions in ecological networks, cascading failures in infrastructure systems, and social convention changes in human and animal networks. Such a regime shift demonstrates a system's resilience that characterizes the ability of a system to adjust its activity to retain its basic functionality in the face of internal disturbances or external environmental changes. In the past 50 years, attention was almost exclusively given to low dimensional systems and calibration of their resilience functions and indicators of early warning signals without considerations for the interactions between the components. Only in recent years, taking advantages of the network theory and lavish real data sets, network scientists have directed their interest to the real-world complex networked multidimensional systems and their resilience function and early warning indicators. This report is devoted to a comprehensive review of resilience function and regime shift of complex systems in different domains, such as ecology, biology, social systems and infrastructure. We cover the related research about empirical observations, experimental studies, mathematical modeling, and theoretical analysis. We also discuss some ambiguous definitions, such as robustness, resilience, and stability.Comment: Review chapter

Mitigation of cascade failures in complex networks: theory and application

Complex networks such as transportation networks, the Internet, and electrical power grids are fundamental parts of modern life, and their robustness under any attack or fault has always been a concern. Failure and intentional removal of components in complex networks might affect the flow of information and change balance of flows in the network. This phenomenon may require load redistribution all over the network. Component overloaded can act as a trigger for a chain of overload failures. This overload, could, for example, increase the amount of information a router must transmit and ultimately make internet congestion. One of the major applications of complex network theory is to study power systems. Power systems are the most complex human-made infrastructures, and almost every individual's life is dependent on electrical energy and resilient functioning of power systems. Recently, there have been many reports about massive power outages leaving vast areas without power that sometimes takes a few days to have the power back. One of the most critical areas in the power system is the root cause analysis of such catastrophes and trying to resolve them. From an electrical engineering point of view, these power outages occur following an initial failure due to problems, such as generators tripping, transformers overheating, faulty power generation units, damage to the transmission system, substations or distribution systems, or overloading of the power system. A faulty protection relay or malicious attack to control centres can also trigger it. In any of these cases, the failed component will be out of service immediately and to keep the robust power delivery to all customers, their loads should be redistributed across the power system, and henceforth some of them might become overloaded as well, and accordingly get out of service. This chain of failures can be propagated all over the system and lead to a catastrophic blackout. This thesis conducts a full study on how to mitigate cascade failures in complex networks. First, cascade depth is applied to quantify nodes criticality for cascade failures. Then, a wide range of node centrality parameters is considered to find out the relationship between the node vitality and these centralities. To discover the structure of cascade propagation in complex networks, the edge geodesic distance is considered for computing the structural distance between two arbitrary edges in the network. Then, starting with the single edge removal events, the route that cascade tends to spread is studied. In the next step, the impact of two or three concurrent edge removals on the way the cascade spreads are examined. Besides, the power system vulnerability is studied using the maximum flow algorithm based on Ford-Fulkerson method and critical capacity parameters are identified. A synthetic model with the same properties as a real power system is generated and examined. For a power line, to be overloaded, a new method is developed to overpass across the network and shortlist the busbars for load reduction. Next, a novel sensitivity method is formulated based on AC load flow analysis to rank the loads according to their effect on the lines power flow