On the Use of Spectral Clustering for Coherent Areas Estimation

Due to the increasing use of renewable energy sources, it is imperative to dynamically estimate the inertia of each area of the interconnected system in order to assure the grid stability if a frequency oscillation occurs. At this aim, the frequency measures provided by Phasor Measurement Units (PMUs) are a powerful tool. The first step is the recognition of areas participating to the same oscillation, whose inertia can be estimated. Therefore, the paper focuses on clustering PMU data into coherent areas, which requires prior knowledge of the modal characteristics of the interconnected system. An algorithm based on spectral clustering theory is used to divide the set of PMU data into clusters. The Laplacian matrix of the absolute values of correlation coefficients of PMU data is analyzed to determine the spectral mapping and partition the data into suitable clusters. Numerous sensitivity analyses have made it possible to confirm the benefit of exploiting filtering in case of low Signal-to-Noise Ratio (SNR), allowing effective clustering even with a SNR of -10 dB. As regards the length of the time window, from the various analyses carried out it emerges that the time length of 120 s seems to be the most effective for the purpose of decomposition.