Correlation between Rotating LIDAR Measurements and Blade Effective Wind Speed

Abstract

Preview wind speed measurements from a forward looking Light Detection and Ranging (LIDAR) system located in the hub of a wind turbine can be used by a feedforward blade pitch control system to mitigate structural loads. For individual blade pitch control, a separate preview estimate of the effective wind speed encountered by each blade must be available. One way of providing an estimate of the blade effective wind speed is to implement a hub mounted spinning lidar that scans the wind field at the rotational rate of the rotor such that the measured wind will reach the blade after some delay. In this way, both the lidar measurement and the wind turbine blade rotationally sample the wind field. The benefit gained by using preview wind speed measurements strongly depends on the correlation between the measured wind and the wind that interacts with the blades. In this research, the coherence between rotating lidar measurements and blade effective wind speed is calculated and analyzed using a spectral model of the wind field. The simulated wind field uses an isotropic von Karman spectrum and contains a model of wind evolution described by a longitudinal spatial coherence function. The coherence between stationary measurements and stationary blade effective wind speeds decreases to zero near the 1P rotational frequency of the turbine. However, measurement coherence between rotating lidar measurements and blade effective wind speed remains much higher and does not decay until higher frequencies. Nomenclature CPSD

Reducing LIDAR wind speed measurement error with optimal filtering

“…7. Rotational sampling causes a redistribution of power from low frequencies to harmonics of the rotational rate, and hence the high correlation at low frequencies is also present at the harmonics [19]. Since the bandwidth of coherent measurements is much higher than it is for the rotor effective case, we thus analyze a larger band of frequencies.…”

“…Both the blade and the LIDAR rotationally sample the wind field, producing spectra with most of the power concentrated around harmonics of the rotational speed of 12.1 RPM (0.202 Hz). More details about the spectra of rotationally sampled wind are given in [19]. Fig.…”

“…A preview distance of d = 90 m and a scan radius of r = 44.1 m are used (resulting in a LIDAR focus distance of 100.2 m). A scan radius of r = 44.1 m (70% rotor radius) is used because wind speeds near the outboard part of the blades affect power capture the most, as discussed in [19].…”

“…However, since the deviation from the mean wind speed of 11.4 m/s is of interest, a linearized form of (28) that acts on zero-mean wind disturbances u is used to estimate the linearized rotor effective wind speed u rotor . Additional details on the variation of C P (r) r as a function of r are provided in [19]. Rotor effective wind speed is estimated by taking the average of the LIDAR measurements over one rotation.…”

“…For both scenarios, the PSDs of the effective wind speeds at the turbine and the LIDAR measurements, as well as the CPSD between the two signals are calculated based on the spectral model of the wind field and the LIDAR and rotor properties using techniques outlined in [8] and [19]. The chosen preview distance of d = 90 m is near optimal for estimation of rotor effective wind speed, but is far from the optimal preview distance of d = 170 m found for estimating blade effective wind speed in [19]. Therefore, the impact of prefiltering is examined for measurement scenarios with both high and low degrees of measurement quality.…”