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Reliability of Partial k-tree Networks
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
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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