Multifractal description of wind power fluctuations using arbitrary order Hilbert spectral analysis

Abstract

The objectives are to study and model the aggregate wind power fluctuations dynamics in the multifractal framework. We present here the analysis of aggregate power output sampled at 1 Hz during three years. We decompose the data into several Intrinsic Mode Functions (IMFs) using Empirical Mode Decomposition (EMD). We use a new approach, arbitrary order Hilbert spectral analysis, a combination of the EMD approach with Hilbert spectral analysis (or Hilbert–Huang Transform) and the classical structure-function analysis to extract the scaling exponents or multifractal spectrum ζ(q): this function provides a full characterization of a process at all intensities and all scales. The application of both methods, i.e. structure-function and arbitrary-order Hilbert spectral analyses, gives similar results indicating that the aggregate power output from a wind farm, possesses intermittent and multifractal properties. In order to check this result, we generate stochastic simulations of a Multifractal Random Walk (MRW) using a log-normal stochastic equation. We show that the simulation results are fully compatible with the experimental results.