The most probable optimum solution in the controlled islanding of power systems is when it is torn into two pieces since such an approach would lead to larger islands when compared with multisection tearing of the power system. Moreover, the restoration of such a bisectioned power system would be easier than the restoration of a power system torn into many pieces. Spectral and Multilevel Kernel k-means approaches to the islanding of power systems have previously been reported by the authors. In this paper, a review of the potential applications of graph partitioning is presented and the classical and the newer spectral and multilevel k-means approaches to solving these problems for power system islanding are described. The computational burden of each approach is presented for a large power system abstracted as a graph G(N,B),with an example of the IEEE 9 bus bisectioned and the computational time requirements of actual bisectioning of the power system on the IEEE 118 bus, the IEEE 300 bus and the 2746 bus Polish power system are compared with previously reported computational requirements. The results presented may also be used in many other fields such as VLSI design, parallel processing, circuit and layout design, transient stability studies, optimal load flow, fault estimation, and dynamic security assessment.

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