Statistical Classification of Cascading Failures in Power Grids

We introduce a new microscopic model of the outages in transmission power grids. This model accounts for the automatic response of the grid to load fluctuations that take place on the scale of minutes, when the optimum power flow adjustments and load shedding controls are unavailable. We describe extreme events, initiated by load fluctuations, which cause cascading failures of loads, generators and lines. Our model is quasi-static in the causal, discrete time and sequential resolution of individual failures. The model, in its simplest realization based on the Directed Current description of the power flow problem, is tested on three standard IEEE systems consisting of 30, 39 and 118 buses. Our statistical analysis suggests a straightforward classification of cascading and islanding phases in terms of the ratios between average number of removed loads, generators and links. The analysis also demonstrates sensitivity to variations in line capacities. Future research challenges in modeling and control of cascading outages over real-world power networks are discussed.Comment: 8 pages, 8 figure

Hierarchical Consensus Formation Reduces the Influence of Opinion Bias

We study the role of hierarchical structures in a simple model of collective consensus formation based on the bounded confidence model with continuous individual opinions. For the particular variation of this model considered in this paper, we assume that a bias towards an extreme opinion is introduced whenever two individuals interact and form a common decision. As a simple proxy for hierarchical social structures, we introduce a two-step decision making process in which in the second step groups of like-minded individuals are replaced by representatives once they have reached local consensus, and the representatives in turn form a collective decision in a downstream process. We find that the introduction of such a hierarchical decision making structure can improve consensus formation, in the sense that the eventual collective opinion is closer to the true average of individual opinions than without it. In particular, we numerically study how the size of groups of like-minded individuals being represented by delegate individuals affects the impact of the bias on the final population-wide consensus. These results are of interest for the design of organisational policies and the optimisation of hierarchical structures in the context of group decision making.Comment: 12 pages, 5 figure

Betweenness Preference: Quantifying Correlations in the Topological Dynamics of Temporal Networks

We study correlations in temporal networks and introduce the notion of betweenness preference. It allows to quantify to what extent paths, existing in time-aggregated representations of temporal networks, are actually realizable based on the sequence of interactions. We show that betweenness preference is present in empirical temporal network data and that it influences the length of shortest time-respecting paths. Using four different data sets, we further argue that neglecting betweenness preference leads to wrong conclusions about dynamical processes on temporal networks.Comment: 10 pages, 4 figure