Hierarchical Clustering in Power System Based on Fuzzy Transitive Closure

This paper presents the applications of hierarchical clustering to the generators in a power system. A useful application of fuzzy mathematics is that the correction of clustering results and determination of whether it can obtain correct transitive closure. Thus, the fuzzy transitive closure plays an important role in hierarchical clustering. Based on the fuzzy relation matrix, the hierarchical cluster analysis can be achieved by using firstly computing a transitive closure matrix on which serial α-cut operations are to be performed. A specific feature of the proposed method is that the hierarchical clustering work can be performed in parallel with the algorithm. The proposed method retains the correctness of transitive closure by reducing the computation complexity. Results from applying the method to a power system are demonstrated to show the validity and effectiveness of the proposed method. Key-Words: Hierarchical Clustering, Power System, Fuzzy Transitive Closure, Fuzzy Similarity Relation, α-cut Operation, Complexity.