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In this contribution, a systematic approach to analyze and characterize the temporal evolution of nonlinear, time-varying processes in power systems is developed. The method combines the Hilbert-Huang transform and concepts from vibrating systems theory and can be used to approximate the dynamic behavior of quasi-stationary oscillations. Us- ing the notion of empirical mode decomposition, data from transient stability simulations is transformed into a series of mono-component signals. A new analytical framework for characterizing and modeling the nonlinear temporal evolution of the oscillations is presented and techniques for identifying the modal content of the most dominant motion components are developed. Analytical expressions are then obtained that provide approximate solutions to the instantaneous frequency and amplitude of the oscillation, and a physical interpretation of the model is provided. The efficiency of this technique for capturing the temporal evolution of the modal content of data from transient stability simulations is assessed. Results determined from the low-order models are found to be in qualitative agreement with detailed system simulations.

Analysis and Characterization of Power System Nonlinear Oscillations Using Hilbert Spectral Analysis