A Comparison of Standard Coherence Models for Inflow Turbulence With Estimates from Field Measurements

Abstract

The Long-term Inflow and Structural Test (LIST) program, managed by Sandia National Laboratories, Albuquerque, NM, is gathering inflow and structural response data on a modified version of the Micon 65/13 wind turbine at a site near Bushland, Texas. With the objective of establishing correlations between structural response and inflow, previous studies have employed regression and other dependency analyses to attempt to relate loads to various inflow parameters. With these inflow parameters that may be thought of as single-point-in-space statistics that ignore the spatial nature of the inflow, no significant correlation was identified between load levels and any single inflow parameter or even any set of such parameters, beyond the mean and standard deviation of the hub-height horizontal wind speed. Accordingly, here, we examine spatial statistics in the measured inflow of the LIST turbine by estimating the coherence for the three turbulence components (along-wind, across-wind, and vertical). We examine coherence spectra for both lateral and vertical separations and use the available ten-minute time series of the three components at several locations. The data obtained from spatial arrays on three main towers located upwind from the test turbine as well as on two additional towers on either side of the main towers consist of 291 ten-minute records. Details regarding estimation of the coherence functions from limited data are discussed. Comparisons with standard coherence models available in the literature and provided in the International Electrotechnical Commission (IEC) guidelines are also discussed. It is found that the Davenport exponential coherence model may not be appropriate especially for modeling the coherence of the vertical turbulence component since it fails to account for reductions in coherence at low frequencies and over large separations. Results also show that the Mann uniform shear turbulence model predicts coherence spectra for all turbulence components and for different lateral separations better than the isotropic von Ka´rma´n model. Finally, on studying the cross-coherence among pairs of turbulence components based on field data, it is found that the coherence observed between along-wind and vertical turbulence components is not predicted by the isotropic von Ka´rma´n model while the Mann model appears to overestimate this cross-coherence.

Using Large-Eddy Simulations to Define Spectral and Coherence Characteristics of the Hurricane Boundary Layer for Wind-Energy Applications

“…3) is a function of frequency with a value between zero and one, indicating how well two spatially-separated time series are correlated. The square of the cross-power spectral density (CPSD) function between two time series, separated by some distance, is normalized by the product of the auto-power spectral densities (PSD) of each of the two time series x 1 and x 2 (Larsen and Hansen 2004;Saranyasoontorn et al 2004),…”

“…In addition, coherence is an essential component in three-dimensional wind-field simulators, because it describes how turbulence is correlated as a function of spatial separation. Although established models for coherence are codified in design standards (IEC 61400-1, IEC 2007), limited observational studies suggest that coherence is more widely variable than assumed in these standards (Saranyasoontorn et al 2004). To assess the spatial coherence in the HBL, we calculate coherence across the 21 × 21 (200 m × 200 m) subdomain of the S10 simulation.…”

“…Saranyasoontorn et al (2004) analyzed the spatial coherence (i.e., the magnitude squared of the cross spectrum normalized by the auto power spectrum of two different signals) of inflow into an onshore turbine using data collected from a turbine and an array of five upwind towers during the Long-term Inflow and Structural Test (LIST) program. Specifically, they found that the IEC exponential coherence model (described in Sect.…”

Investigations of a practical wind-induced fatigue calculation based on nonlinear time domain dynamic analysis and a full wind-directional scatter diagram

“…However, it is observed that this coherence model was originally developed only for along-wind components. Measurements on land have shown that coherence in the across-wind direction is higher than in the along-wind direction (Saranyasoontorn et al 2004). Therefore, a more appropriate coherence model may be needed for any future study.…”

Measurements of Surface-Layer Turbulence in a Wide Norwegian Fjord Using Synchronized Long-Range Doppler Wind Lidars

“…The number of overlapping segments is chosen to reduce the bias of the coherence estimate and the measurement noise [51,52] while keeping the frequency resolution as high as possible. Wind data with a mean wind velocity between 6 m·s −1 and 14 m·s −1 are considered (189 samples) and the coherence is expressed as a function of the wavenumber k to reduce the scatter of the coherence estimates due to the dependence of the lateral coherence on wind velocity.…”