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Topological bounds and hierarchical clustering for network reliability assessment

Funding: National Science Foundation
Collaborators: Mauricio Sánchez-Silva, Universidad de Los Andes, Bogotá Colombia.
Students: Keivan Rokneddin

Infrastructure systems such as power transmission grids constitute the backbone of modern societies. Large infrastructure systems are complex networks, and therefore their response to component failure cannot be studied by only focusing on individual components, but on their interconnection patters as well. Any disruptions to the functionality of components in infrastructure systems may result in widespread performance loss, such as blackouts in the power transmission grid. Systematic investigation of component failures and their impact on the reliability of the networks provides unique insights by exploring all possible perturbation scenarios.  However, such approach is known to pose computational demands that grow exponentially with the size of the systems. Providing bounds on the performance of the systems may yield a rapid estimate to their response under either natural hazards or deliberate attacks without the need for computationally-exhaustive simulations.  This research introduces a topology-based reliability approach to measure reliability bounds and reliability metrics of large power transmission networks in the form of network operational indices.

 Topological bounds for the connectivity reliability assessment of power transmission systems

 minimum greedy
Two extreme topological formations, the Minimum Spanning Tree and the Greedy Triangulation show that bounds on the topology of the network also provide bounds on the response of the system to component failures.

Response of connectivity loss to the ratio of removed nodes in a network reliability assessment.