MATCASC: A tool to analyse cascading line outages in power grids

Blackouts in power grids typically result from cascading failures. The key importance of the electric power grid to society encourages further research into sustaining power system reliability and developing new methods to manage the risks of cascading blackouts. Adequate software tools are required to better analyze, understand, and assess the consequences of the cascading failures. This paper presents MATCASC, an open source MATLAB based tool to analyse cascading failures in power grids. Cascading effects due to line overload outages are considered. The applicability of the MATCASC tool is demonstrated by assessing the robustness of IEEE test systems and real-world power grids with respect to cascading failures

Worst-Case Scenarios for Greedy, Centrality-Based Network Protection Strategies

The task of allocating preventative resources to a computer network in order to protect against the spread of viruses is addressed. Virus spreading dynamics are described by a linearized SIS model and protection is framed by an optimization problem which maximizes the rate at which a virus in the network is contained given finite resources. One approach to problems of this type involve greedy heuristics which allocate all resources to the nodes with large centrality measures. We address the worst case performance of such greedy algorithms be constructing networks for which these greedy allocations are arbitrarily inefficient. An example application is presented in which such a worst case network might arise naturally and our results are verified numerically by leveraging recent results which allow the exact optimal solution to be computed via geometric programming

Spectral Perturbation and Reconstructability of Complex Networks

In recent years, many network perturbation techniques, such as topological perturbations and service perturbations, were employed to study and improve the robustness of complex networks. However, there is no general way to evaluate the network robustness. In this paper, we propose a new global measure for a network, the reconstructability coefficient {\theta}, defined as the maximum number of eigenvalues that can be removed, subject to the condition that the adjacency matrix can be reconstructed exactly. Our main finding is that a linear scaling law, E[{\theta}]=aN, seems universal, in that it holds for all networks that we have studied.Comment: 9 pages, 10 figure

A general class of spreading processes with non-Markovian dynamics

In this paper we propose a general class of models for spreading processes we call the $SI^*V^*$ model. Unlike many works that consider a fixed number of compartmental states, we allow an arbitrary number of states on arbitrary graphs with heterogeneous parameters for all nodes and edges. As a result, this generalizes an extremely large number of models studied in the literature including the MSEIV, MSEIR, MSEIS, SEIV, SEIR, SEIS, SIV, SIRS, SIR, and SIS models. Furthermore, we show how the $SI^*V^*$ model allows us to model non-Poisson spreading processes letting us capture much more complicated dynamics than existing works such as information spreading through social networks or the delayed incubation period of a disease like Ebola. This is in contrast to the overwhelming majority of works in the literature that only consider spreading processes that can be captured by a Markov process. After developing the stochastic model, we analyze its deterministic mean-field approximation and provide conditions for when the disease-free equilibrium is stable. Simulations illustrate our results

An efficient hybrid model and dynamic performance analysis for multihop wireless networks

Multihop wireless networks can be subjected to nonstationary phenomena due to a dynamic network topology and time varying traffic. However, the simulation techniques used to study multihop wireless networks focus on the steady-state performance even though transient or nonstationary periods will often occur. Moreover, the majority of the simulators suffer from poor scalability. In this paper, we develop an efficient performance modeling technique for analyzing the time varying queueing behavior of multihop wireless networks. The one-hop packet transmission (service) time is assumed to be deterministic, which could be achieved by contention-free transmission, or approximated in sparse or lightly loaded multihop wireless networks. Our model is a hybrid of time varying adjacency matrix and fluid flow based differential equations, which represent dynamic topology changes and nonstationary network queues, respectively. Numerical experiments show that the hybrid fluid based model can provide reasonably accurate results much more efficiently than standard simulators. Also an example application of the modeling technique is given showing the nonstationary network performance as a function of node mobility, traffic load and wireless link quality. © 2013 IEEE

A Topological Investigation of Phase Transitions of Cascading Failures in Power Grids

Cascading failures are one of the main reasons for blackouts in electric power transmission grids. The economic cost of such failures is in the order of tens of billion dollars annually. The loading level of power system is a key aspect to determine the amount of the damage caused by cascading failures. Existing studies show that the blackout size exhibits phase transitions as the loading level increases. This paper investigates the impact of the topology of a power grid on phase transitions in its robustness. Three spectral graph metrics are considered: spectral radius, effective graph resistance and algebraic connectivity. Experimental results from a model of cascading failures in power grids on the IEEE power systems demonstrate the applicability of these metrics to design/optimize a power grid topology for an enhanced phase transition behavior of the system