Network partitioning techniques based on network natural properties for power system application
In this thesis, the problem of partitioning a network into interconnected sub-networks is addressed. The goal is to achieve a partitioning which satisfies a set of specific engineering constraints, imposed in this case, by the requirements of the decomposed state-estimation (DSE) in electrical power systems. The network-partitioning problem is classified as NP-hard problem. Although many heuristic algorithms have been proposed for its solution, these often lack directness and computational simplicity. In this thesis, three new partitioning techniques are described which (i) satisfy the DSE constraints, and (ii) simplify the NP-hard problem by using the natural graph properties of a network. The first technique is based on partitioning a spanning tree optimally using the natural property of the spanning tree branches. As with existing heuristic techniques, information on the partitioning is obtained only at the end of the partitioning process. The study of the DSE constraints leads to define conditions of an ideal balanced partitioning. This enables data on the balanced partitioning to be obtained, including the numbers of boundary nodes and cut-edges. The second partitioning technique is designed to obtain these data for a given network, by finding the minimum covering set of nodes with maximum nodal degree. Further simplification is then possible if additional graph-theoretical properties are used. A new natural property entitled the 'edge state phenomenon' is defined. The edge state phenomenon may be exploited to generate new network properties. In the third partitioning technique, two of these, the 'network external closed path' and the 'open internal paths', are used to identify the balanced partitioning, and hence to partition the network. Examples of the application of all three methods to network partitioning are provided.