Mode Shape Estimation using Complex Principal Component Analysis and k-Means Clustering

We propose an empirical method for identifying low damped modes and corresponding mode shapes using frequency measurements from a Wide Area Monitoring System. The method consists of two main steps: Firstly, Complex Principal Component Analysis is used in combination with the Hilbert Transform and Empirical Mode Decomposition to provide estimates of modes and mode shapes. The estimates are stored as multidimensional points. Secondly, the points are grouped using a clustering algorithm, and new averaged estimates of modes and mode shapes are computed as the centroids of the clusters. Applying the method on data resulting from a non-linear power system simulator yields estimates of dominant modes and corresponding mode shapes that are similar to those resulting from modal analysis of the linearized system model. Encouraged by the results, the method is further tested with real PMU data at transmission grid level. Initial results indicate that the performance of the proposed method is promising.