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This paper discusses the application of nonstationary time-frequency analysis techniques to identify nonlinear trends and filtering frequency components of the dynamics of large, interconnected power systems. Two different analytical approaches to examine nonstationary features are investigated. The first method is based on selective empirical mode decomposition (EMD) of the measured data. The second is based on wavelet shrinkage analysis. Experience with the application of these techniques to quantify and extract nonlinear trends and time-varying behavior is discussed and a physical interpretation of the proposed algorithms is provided. The practical application of these techniques is tested on time-synchronized phasor measurements collected by phasor measurement units (PMUs). Numerical simulations computed using time-energy nonstationary methods are critically compared with conventional approaches.