| Summary: | Many systems such as traffic or electrical flow can be described as flows following paths of least resistance in networks. The efficiency and resilience of these networks define the system’s ability to function effectively. Research into network efficiency and resilience often focuses on the role of network topology, with the aim of uncovering optimal network structures that boost system performance. However, little attention has been paid to the role of node behaviour. This thesis bridges that gap by analysing the efficiency and resilience of networks whose nodes have heterogeneous behaviour. The nodes may variably be sources or sinks of the flow. The nodes may also be equipped with the ability to adjust their behaviour in response to the state of the network. The efficiency and resilience of networks are evaluated as a function of their composition of node types and behaviours. The primary motivation for this is the proliferation of renewable sources of electrical power in energy grids. The resulting electrical networks have highly dynamic and heterogeneous nodes. This thesis provides a framework in which to analyse the behaviour of these systems.
A variety of mathematical methods are utilised throughout this thesis. The efficiency of network flows is analysed using a measurement from game theory called the Price of Anarchy, from which an equivalency between least resistance network flows and Nash equilibria is also identified. The average variation of efficiency with node composition is found to be approximately invariant across different network structures. The highest inefficiencies are found to always occur when there are an equal number of source and sink nodes.
Resilience is investigated using models of cascading network failures. Both a steady state and a dynamical model are employed. Analytical results for cascades on simple lattices are derived, while for complex networks it is shown that resilience can often be improved by increasing the numbers of source and sink nodes. This analysis is employed on a test case of electrical networks, constructed using real household power consumption and photovoltaic generation data. The impact of the dynamic variability of these data-driven networks on resilience is analysed. Lowest resiliences are found
during times when high numbers of photo-voltaic source nodes are active.
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