Characterization of Statistically Forced Oscillations : A Spectral Proper Orthogonal Decomposition Approach

In this paper, a method for statistical analysis is developed to estimate patterns of behavior and their amplification from the observed system response to random variations. Spectral proper orthogonal decomposition (SPOD) is utilized to examine gains and phase relationships between signals from simulated data. Based on frequency domain and Fourier analysis, SPOD is employed to decompose forced oscillations into a set of space-time orthogonal modes. By such an approach, the ability of Fourier analysis to study stochastically forced oscillations in complex power system models is improved. Analytical criteria for describing the energy relationships in the observed oscillations are derived, and a physical interpretation of the stochastic modes is suggested. The methodology is demonstrated using simulated random oscillations of a realistic test power system.