Complex Empirical Orthogonal Function Analysis of Wide-Area System Dynamics

A statistical approach to the dynamic characterization of system temporal behavior based on complex Empirical Orthogonal Function (EOF) analysis is developed. This technique allows identification of the dominant spatial and temporal patterns in complex space-time data sets and is thus ideally suited for the study of propagating and standing features that can be associated with wide-area dynamics. A general technique for the computation of empirical orthogonal basis functions is suggested. In this procedure, measured data from multiple Phasor Measurement Units (PMUs) are used to build an optimal set of orthonormal basis functions that best approximate the original data set. Complex EOF analysis is then used to extract information on dominant non-stationary spatial, temporal and frequency patterns of the observed oscillations. Algorithm are presented which provide accurate extraction and characterization of propagating features in the data using complex singular value analysis. Data obtained from GPS-based phasor measurement units from a real event in northern Mexico are used to study the practical applicability of the method. The results indicate that PMU data from geographically remote stations can be efficiently compressed and that the dominant modes of behavior can be identified and isolated. Comparison of extracted modal information to conventional spectral analysis indicates that the proposed algorithm produces near optimal approximations coupled with accurate modal properties.