Singular Value Decomposition-Based Load Indexes for Load Profiles Clustering

Choosing suitable load indexes of load profiles is of vital importance for load profiles clustering, which has wide applications in load forecasting, power grid planning and electricity price designing. To obtain a set of load indexes with rigorous mathematical theory and clear physical meaning, this study proposed a singular value decomposition (SVD) based method to extract indexes. First, empirical rank-l approximation derived from SVD is proposed to extract load indexes. The relationship between singular values and relative approximation error guarantees the indexes retain major characteristics of load profiles, while the invariance of right singular vectors over seasons and sample sizes endows the indexes with good generalisation ability. Then the right singular vectors are discretised to determine definition of indexes and reveal physical meanings of the indexes. Finally, the new set of indexes extracted by the proposed method are applied in indirectly clustering in the case study, which verify the validity of the indexes, the performance of the clustering method and the advantages of the new indexes over the existing load shape indexes.