Lubos Buzna

Transient dynamics increasing network vulnerability to cascading failures.

We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws. It is found that considering the flow dynamics may imply reduced network robustness compared to previous static overload failure models. This is due to the transient oscillations or overshooting in the loads, when the flow dynamics adjusts to the new (remaining) network structure. The robustness of networks showing cascading failures is generally given by a complex interplay between the network topology and flow dynamics.

Robustness of trans-European gas networks

Here, we uncover the load and fault-tolerant backbones of the trans-European gas pipeline network. Combining topological data with information on intercountry flows, we estimate the global load of the network and its tolerance to failures. To do this, we apply two complementary methods generalized from the betweenness centrality and the maximum flow. We find that the gas pipeline network has grown to satisfy a dual purpose. On one hand, the major pipelines are crossed by a large number of shortest paths thereby increasing the efficiency of the network; on the other hand, a nonoperational pipeline causes only a minimal impact on network capacity, implying that the network is error tolerant. These findings suggest that the trans-European gas pipeline network is robust, i.e., error tolerant to failures of high load links.

Efficient response to cascading disaster spreading.

We study the effectiveness of recovery strategies for a dynamic model of failure spreading in networks. These strategies control the distribution of resources based on information about the current network state and network topology. In order to assess their success, we have performed a series of simulation experiments. The considered parameters of these experiments are the network topology, the response time delay, and the overall disposition of resources. Our investigations are focused on the comparison of strategies for different scenarios and the determination of the most appropriate strategy. The importance of prompt response and the minimum sufficient quantity of resources are discussed as well.

Modelling of cascading effects and efficient response to disaster spreading in complex networks

In order to assess cascading effects in directed networks, we present a model for the dynamics of failure spreading. The model combines network nodes as active, bistable elements and delayed interactions along directed links. Through simulations, we study the dynamics behaviour of generic sample networks. Besides evaluating the failure cascades, for which we observe a critical threshold for the undamped spreading of failures in a network, we simulated the effect of different strategies for the management of spreading disasters. Our recovery strategies are based on the assumption that the interaction structure of the challenged network remains unchanged, while additional resources for mitigation actions, improving the recovery capacities of system components, can be distributed over the network. The simulations clearly demonstrate that the topology of a network is a crucial factor both for the behaviour under external disturbances and for the optimality of different strategies to cope with an evolving disaster. Our model may be used to improve disaster preparedness and anticipative disaster response management.

Role of network topology in the synchronization of power systems

AbstractWe study synchronization dynamics in networks of coupled oscillators with bimodal distribution of natural frequencies. This setup can be interpreted as a simple model of frequency synchronization dynamics among generators and loads working in a power network. We derive the minimum coupling strength required to ensure global frequency synchronization. This threshold value can be efficiently found by solving a binary optimization problem, even for large networks. In order to validate our procedure, we compare its results with numerical simulations on a realistic network describing the European interconnected high-voltage electricity system, finding a very good agreement. Our synchronization threshold can be used to test the stability of frequency synchronization to link removals. As the threshold value changes only in very few cases when applied to the approximate model of European network, we conclude that network is resilient in this regard. Since the threshold calculation depends on the local connectivity, it can also be used to identify critical network partitions acting as synchronization bottlenecks. In our stability experiments we observe that when a link removal triggers a change in the critical partition, its limits tend to converge to national borders. This phenomenon, which can have important consequences to synchronization dynamics in case of cascading failure, signals the influence of the uncomplete topological integration of national power grids at the European scale.

Synchronization in symmetric bipolar population networks

We analyze populations of Kuramoto oscillators with a particular distribution of natural frequencies. Inspired by networks where there are two groups of nodes with opposite behaviors, as for instance, in power-grids where energy is either generated or consumed at different locations, we assume that the frequencies can take only two different values. Correlations between the value of the frequency of a given node and its topological localization are considered in both regular and random topologies. Synchronization is enhanced when nodes are surrounded by nodes of the opposite frequency. The theoretical result presented in this paper is an analytical estimation for the minimum value of the coupling strength between oscillators that guarantees the achievement of a globally synchronized state. This analytical estimation, which is in a very good agreement with numerical simulations, provides a better understanding of the effect of topological localization of natural frequencies on synchronization dynamics.

Resilience of Natural Gas Networks during Conflicts, Crises and Disruptions

Human conflict, geopolitical crises, terrorist attacks, and natural disasters can turn large parts of energy distribution networks offline. Europes current gas supply network is largely dependent on deliveries from Russia and North Africa, creating vulnerabilities to social and political instabilities. During crises, less delivery may mean greater congestion, as the pipeline network is used in ways it has not been designed for. Given the importance of the security of natural gas supply, we develop a model to handle network congestion on various geographical scales. We offer a resilient response strategy to energy shortages and quantify its effectiveness for a variety of relevant scenarios. In essence, Europes gas supply can be made robust even to major supply disruptions, if a fair distribution strategy is applied.

The evolution of the topology of high-voltage electricity networks

The electricity network represents an example of an evolving complex system. The first local networks contained only a few nodes, but within several decades, they have evolved into a highly connected continental system. The growth of these networks was influenced by various factors such as economic, demographic, political and technological developments. In this paper, we analyse the growth of the French 400 kV electricity transmission network from its establishment in 1960 until the year 2000. We study the different topological characteristics that describe the intensity of the growth process, such as the number of nodes, the number of lines, the average node connectivity and the overall length of wires. We compare these results with several economic and demographic indicators in order to identify the factors which correlate with the growth rate of the electricity network. Apart from this, we evaluate how the topological efficiency and vulnerability measures (clustering coefficient, information centrality, betweenness centrality) evolve in the course of time. The decisions regarding the power grid topology are influenced by many, very often contradictory factors, such as costs, the size of the covered area, demand, fault tolerance, reliability and quality of service. Our results yield a deeper insight into the process of Critical Infrastructure (CI) construction.

Fair sharing of resources in a supply network with constraints

This paper investigates the effect of network topology on the fair allocation of network resources among a set of agents, an all-important issue for the efficiency of transportation networks all around us. We analyze a generic mechanism that distributes network capacity fairly among existing flow demands. The problem can be solved by semianalytical methods on a nearest-neighbor graph with one source and sink pair, when transport occurs over shortest paths. For this setup, we uncover a broad range of patterns of intersecting shortest paths as a function of the distance between the source and the sink. When the number of intersections is the maximum and the distance between the source and the sink is large, we find that a fair allocation implies a decrease of at least 50% from the maximum throughput. We also find that the histogram of the flow allocations assigned to the agents decays as a power law with exponent -1. Our semianalytical framework suggests possible explanations for the well-known reduction of the throughput in fair allocations. It also suggests that the combination of network topology and routing rules can lead to highly uneven (but fair) distributions of resources, a remark of caution to network designers.

Critical behaviour in charging of electric vehicles

The increasing penetration of electric vehicles over the coming decades, taken together with the high cost to upgrade local distribution networks, and consumer demand for home charging, suggest that managing congestion on low voltage networks will be a crucial component of the electric vehicle revolution and the move away from fossil fuels in transportation. Here, we model the max-flow and proportional fairness protocols for the control of congestion caused by a fleet of vehicles charging on distribution networks. We analyse the inequality in the charging times as the vehicle arrival rate increases, and show that charging times are considerably more uneven in max-flow than in proportional fairness. We also analyse the onset of instability, and find that the critical arrival rate is indistinguishable between the two protocols.The increasing penetration of electric vehicles over the coming decades, taken together with the high cost to upgrade local distribution networks and consumer demand for home charging, suggest that managing congestion on low voltage networks will be a crucial component of the electric vehicle revolution and the move away from fossil fuels in transportation. Here, we model the max-flow and proportional fairness protocols for the control of congestion caused by a fleet of vehicles charging on two real-world distribution networks. We show that the system undergoes a continuous phase transition to a congested state as a function of the rate of vehicles plugging to the network to charge. We focus on the order parameter and its fluctuations close to the phase transition, and show that the critical point depends on the choice of congestion protocol. Finally, we analyse the inequality in the charging times as the vehicle arrival rate increases, and show that charging times are considerably more equitable in proportional fairness than in max-flow.