Analysis of multi-scale chaotic characteristics of wind power based on Hilbert–Huang transform and Hurst analysis

Abstract

The causes of uncertainty in wind farm power generation are not yet fully understood. A method for the scale division of wind power based on the Hilbert–Huang transform (HHT) and Hurst analysis is proposed in this paper, which allows the various multi-scale chaotic characteristics of wind power to be investigated to reveal further information about the dynamic behavior of wind power. First, the time–frequency characteristics of wind power are analyzed using the HHT, and then Hurst analysis is applied to analyze the stochastic/persistent characteristics of the different time–frequency components. Second, based on their fractal structures, the components are superposed and reconstructed into three series, which are defined as the Micro-, Meso- and Macro-scale subsequences. Finally, indices related to the statistical and behavioral characteristics of the subsequences are calculated and used to analyze their nonlinear dynamic behavior. The data collected from a wind farm of Hebei Province, China, are selected for case studies. The simulation results reveal that (1) although the time–frequency components can be decomposed, the different fractal structures of the signal are also derived from the original series; (2) the three scale subsequences all present chaotic characteristics and each of them exhibits its own unique properties. The Micro-scale subsequence shows strong randomness and contributes the least to the overall fluctuations; the Macro-scale subsequence is the steadiest and exhibits the most significant tendency; the Meso-scale subsequence which possesses the greatest variance contribution rate and the maximum largest Lyapunov exponent, is the dominant factor driving the fluctuation and dynamic behavior of wind power; (3) the short-term predictions of these three subsequences based on extreme learning machine (ELM) and least-squares support vector machine (LSSVM) models have validated the above analysis results, which show that the number of steps of look-ahead predictability have pursued an ordinal trend in term of the Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) and the prediction error contribution rate of the Meso-scale subsequence is the maximum. Furthermore, the short-term wind power forecasting of 6-step-ahead based on the multi-scale analysis is performed by EMD-LSSVM+ELM and the normalized Mean Absolute Error (nMAE) and normalized Root Mean Square Error (nRMSE) have been decreased by 49.45% and 44.30% compared with those of LSSVM, and 37.96% and 27.12% compared with those of EMD-LSSVM, respectively.