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The first contribution of this dissertation is the use of complex network theory for the vulnerability analysis of power systems, taking into considerations various electrical parameters of the power grid into forming a graph corresponding to the power grid. An algorithm is presented to find critical elements from any power grid once the load flow analysis data is available on the system. A relation between the vulnerability and stability is found to exist, i.e., removal of important components found from proposed methodology shows transient behavior in the power angle oscillations. Various standard IEEE test systems have been used to demonstrate the utility of the proposed method. The proposed betweenness centrality based method is novel than previously existing ones employing complex network framework in better capturing several electrical characteristics of the electricity grid as well in finding stable and unstable regions within the grid. Secondly, this thesis develops a modified flow based betweenness centrality measure to identify critical elements of a power system. The proposed method overcomes the limitation of concentrating on shortest paths in calculating centrality indices; instead the method considers all possible paths through which the power can flow from source nodes to load nodes, giving a more realistic modeling choice of the power grid. Standard IEEE test systems have been used to exhibit the utilization of the method in finding critical components of the grid. Finally, various centrality measures like degree centrality, closeness centrality, and betweenness centrality used in complex network framework based analysis are applied for the power grid application. New definitions of these measures are proposed to capture the realistic power flow scenario of the grid. A new matrix, which contains the information of dependency of bus pairs in a power system, is also presented. An algorithm of finding the bus dependency matrix from the system is demonstrated with real power grid examples. Several characteristics, e.g., the correlation between bus dependency matrix with the electrical closeness centrality and the electrical betweenness centrality; non-symmetric property, are analyzed in detail. |
