Statistical Characterization of Power System Nonlinear Behavior Using Higher-Order Spectra

A general, statistically-based framework based on higher-order cumulant spectra is developed for nonlinear characterization of system dynamic behavior. The method permits the extraction, from a set of data obtained from the system response to random excitation, of modal information and provides a rigorous mathematical framework for the description of nonlinear random processes. A system dynamic model is first proposed that enables characterization of random input signals. Using this model, an ensemble of data representing the system response to random excitation is then derived that captures dominant modal interactions. Cross-cumulant spectrums from input and output signals are utilized to identify first-and high-order frequency response functions. On the basis of this model, nonlinearities are detected and quantified and an optimal linear model that retains nonlinear statistically significant effects is suggested. This method has statistical validity since it considers multiple realizations of random processes. The proposed technique is applied to a single-machine infinite bus. Results of the identification study are presented and discussed, and comparisons between the identified model and conventional analyses are made.