Cascades in interdependent flow networks

In this manuscript, we investigate the abrupt breakdown behavior of coupled distribution grids under load growth. This scenario mimics the ever-increasing customer demand and the foreseen introduction of energy hubs interconnecting the different energy vectors. We extend an analytical model of cascading behavior due to line overloads to the case of interdependent networks and find evidence of first order transitions due to the long-range nature of the flows. Our results indicate that the foreseen increase in the couplings between the grids has two competing effects: on the one hand, it increases the safety region where grids can operate without withstanding systemic failures; on the other hand, it increases the possibility of a joint systems’ failure

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

Mitigating Cascading Failures in Interdependent Power Grids and Communication Networks

In this paper, we study the interdependency between the power grid and the communication network used to control the grid. A communication node depends on the power grid in order to receive power for operation, and a power node depends on the communication network in order to receive control signals for safe operation. We demonstrate that these dependencies can lead to cascading failures, and it is essential to consider the power flow equations for studying the behavior of such interdependent networks. We propose a two-phase control policy to mitigate the cascade of failures. In the first phase, our control policy finds the non-avoidable failures that occur due to physical disconnection. In the second phase, our algorithm redistributes the power so that all the connected communication nodes have enough power for operation and no power lines overload. We perform a sensitivity analysis to evaluate the performance of our control policy, and show that our control policy achieves close to optimal yield for many scenarios. This analysis can help design robust interdependent grids and associated control policies.Comment: 6 pages, 9 figures, submitte

Enhancing Infrastructure Resilience Under Conditions of Incomplete Knowledge of Interdependencies

Today’s infrastructures — such as road, rail, gas, electricity and ICT — are highly interdependent, and may best be viewed as multi-infrastructure systems. A key challenge in seeking to enhance the resilience of multi-infrastructure systems in practice relates to the fact that many interdependencies may be unknown to the operators of these infrastructures. How can we foster infrastructure resilience lacking complete knowledge of interdependencies? In addressing this question, we conceptualize the situation of a hypothetical infrastructure operator faced with incomplete knowledge of the interdependencies to which his infrastructure is exposed. Using a computer model which explicitly represents failure propagations and cascades within a multi-infrastructure system, we seek to identify robust investment strategies on the part of the operator to enhance infrastructure resilience. Our results show that a strategy of constructing redundant interdependencies may be the most robust option for a financially constrained infrastructure operator. These results are specific to the infrastructure configuration tested. However, the developed model may be tailored to the conditions of real-world infrastructure operators faced with a similar dilemma, ultimately helping to foster resilient infrastructures in an uncertain world

How motifs condition critical thresholds for tipping cascades in complex networks: Linking Micro- to Macro-scales

In this study, we investigate how specific micro interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erd\"os-R\'enyi networks and an exemplary moisture recycling network of the Amazon rainforest. Within these networks, decisive small-scale motifs are the feed forward loop, the secondary feed forward loop, the zero loop and the neighboring loop. Of all motifs, the feed forward loop motif stands out in tipping cascades since it decreases the critical coupling strength necessary to initiate a cascade more than the other motifs. We find that for this motif, the reduction of critical coupling strength is 11% less than the critical coupling of a pair of tipping elements. For highly connected networks, our analysis reveals that coupled feed forward loops coincide with a strong 90% decrease of the critical coupling strength. For the highly clustered moisture recycling network in the Amazon, we observe regions of very high motif occurrence for each of the four investigated motifs suggesting that these regions are more vulnerable. The occurrence of motifs is found to be one order of magnitude higher than in a random Erd\"os-R\'enyi network. This emphasizes the importance of local interaction structures for the emergence of global cascades and the stability of the network as a whole

Estimating the Propagation of Interdependent Cascading Outages with Multi-Type Branching Processes

In this paper, the multi-type branching process is applied to describe the statistics and interdependencies of line outages, the load shed, and isolated buses. The offspring mean matrix of the multi-type branching process is estimated by the Expectation Maximization (EM) algorithm and can quantify the extent of outage propagation. The joint distribution of two types of outages is estimated by the multi-type branching process via the Lagrange-Good inversion. The proposed model is tested with data generated by the AC OPA cascading simulations on the IEEE 118-bus system. The largest eigenvalues of the offspring mean matrix indicate that the system is closer to criticality when considering the interdependence of different types of outages. Compared with empirically estimating the joint distribution of the total outages, good estimate is obtained by using the multitype branching process with a much smaller number of cascades, thus greatly improving the efficiency. It is shown that the multitype branching process can effectively predict the distribution of the load shed and isolated buses and their conditional largest possible total outages even when there are no data of them.Comment: Accepted by IEEE Transactions on Power System