26,781 research outputs found

    Reliability of Partial k-tree Networks

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    133 pagesRecent developments in graph theory have shown the importance of the class of partial k- trees. This large class of graphs admits several algorithm design methodologies that render efficient solutions for a large number of problems inherently difficult for general graphs. In this thesis we develop such algorithms to solve a variety of reliability problems on partial k-tree networks with node and edge failures. We also investigate the problem of designing uniformly optimal 2-trees with respect to the 2-terminal reliability measure. We model a. communication network as a graph in which nodes represent communication sites and edges represent bidirectional communication lines. Each component (node or edge) has an associated probability of operation. Components of the network are in either operational or failed state and their failures are statistically independent. Under this model, the reliability of a network G is defined as the probability that a given connectivity condition holds. The l-terminal reliability of G, Rel1 ( G), is the probability that any two of a given set of I nodes of G can communicate. Robustness of a network to withstand failures can be expressed through network resilience, Res( G), which is the expected number of distinct pairs of nodes that can communicate. Computing these and other similarly defined measures is #P-hard for general networks. We use a dynamic programming paradigm to design linear time algorithms that compute Rel1( G), Res( G), and some other reliability and resilience measures of a partial k-tree network given with an embedding in a k-tree (for a fixed k). Reliability problems on directed networks are also inherently difficult. We present efficient algorithms for directed versions of typical reliability and resilience problems restricted to partial k-tree networks without node failures. Then we reduce to those reliability problems allowing both node and edge failures. Finally, we study 2-terminal reliability aspects of 2-trees. We characterize uniformly optimal 2-trees, 2-paths, and 2-caterpillars with respect to Rel2 and identify local graph operations that improve the 2-terminal reliability of 2-tree networks

    Topological analysis of the power grid and mitigation strategies against cascading failures

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    This paper presents a complex systems overview of a power grid network. In recent years, concerns about the robustness of the power grid have grown because of several cascading outages in different parts of the world. In this paper, cascading effect has been simulated on three different networks, the IEEE 300 bus test system, the IEEE 118 bus test system, and the WSCC 179 bus equivalent model, using the DC Power Flow Model. Power Degradation has been discussed as a measure to estimate the damage to the network, in terms of load loss and node loss. A network generator has been developed to generate graphs with characteristics similar to the IEEE standard networks and the generated graphs are then compared with the standard networks to show the effect of topology in determining the robustness of a power grid. Three mitigation strategies, Homogeneous Load Reduction, Targeted Range-Based Load Reduction, and Use of Distributed Renewable Sources in combination with Islanding, have been suggested. The Homogeneous Load Reduction is the simplest to implement but the Targeted Range-Based Load Reduction is the most effective strategy.Comment: 5 pages, 8 figures, 1 table. This is a limited version of the work due to space limitations of the conference paper. A detailed version is submitted to the IEEE Systems Journal and is currently under revie
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