On the use of proper orthogonal decomposition to describe inflow turbulence and wind turbine loads

ABSTRACT: We discuss an application of Proper Orthogonal Decomposition (POD) to characterize the in-flow turbulence random field experienced by a wind turbine. A methodology is proposed that employs low-dimensional POD models of the turbulence field to predict the wind turbine load statistics for the design pur-poses. The efficiency of the proposed strategy is assessed by evaluating rates of convergence of load statistics derived based on different numbers of inflow POD modes. Influence on convergence due to different spatial and temporal sampling resolutions of the inflow data is also investigated. Results suggest that the appropriate number of POD modes needed to accurately describe wind turbine blade and tower loads depends primarily on the dynamic characteristics of the turbine loads under consideration as well as on the rotational sampling of the inflow turbulence. In general, a small number of inflow POD modes can faithfully account for the low-frequency energy in the turbine load measures studied. At higher frequencies, where the inflow turbulence field exhibits weak coherence at spatial separations on the order of rotor dimensions, a larger number of modes may be required. Based on this study limited to a single two-bladed 600 kW wind turbine, results from several spatial and temporal samplings of the inflow turbulence show that data from spatial grids with dimensions on the order of one-third the rotor diameter and sampling frequencies of 2.5-5 Hz or higher can yield adequate representations of important POD modes useful for establishing accurate turbine loads. This was verified by comparing loads resulting from such efficient POD representations of inflow fields with those from sampled data on very fine grids and at high sampling rates.