Orthogonal horizontal wind vectors were retrieved from the radial velocity using a sector Velocity Azimuth Display method. Streamlines were plotted to determine the potential sites for a correlation of upstream wind speed with wind speed at downstream locations near the wind farm. A "virtual wind turbine" was "placed" in locations along the streamline by using the time-series velocity data at the location as the input to a modeled wind turbine, to determine the extractable energy content at that location. The relationship between this time-dependent energy content upstream and near the wind farm was studied. By correlating the energy content with each upstream location based on a time shift estimated according to advection at the mean wind speed, several fits were evaluated. A prediction of the downstream energy content was produced by shifting the power output in time and applying the best-fit function. This method made predictions of the power near the wind farm several minutes in advance. Predictions were also made up to an hour in advance for a large ramp event. The Magnitude Absolute Error and Standard Deviation are presented for the predictions based on each selected upstream location.
The first part of the dissertation begins with an application of a coherent Doppler lidar to wind gust characterization for wind farm control. This application focuses on wind gusts on a scale from 100 m to 1000 m. A detecting and tracking algorithm is proposed to extract gusts from a wind field and track their movement. The algorithm was implemented for a three-hour, two-dimensional wind field retrieved from the measurements of a coherent Doppler lidar. The Gaussian distribution of the gust spanwise deviation from the streamline was demonstrated. Size dependency of gust deviations is discussed. A prediction model estimating the impact of gusts with respect to arrival time and the probability of arrival locations is introduced. The prediction model was applied to a virtual wind turbine array, and estimates are given for which wind turbines would be impacted.
The second part of this dissertation describes a Time-of-Flight lidar simulation. The lidar simulation includes a laser source module, a propagation module, a receiver module, and a timing module. A two-dimensional pulse model is introduced in the laser source module. The sampling rate for the pulse model is explored. The propagation module takes accounts of beam divergence, target characteristics, atmosphere, and optics. The receiver module contains models of noise and analog filters in a lidar receiver. The effect of analog filters on the signal behavior was investigated. The timing module includes a Time-to-Digital Converter (TDC) module and an Analog-to-Digital converter (ADC) module. In the TDC module, several walk-error compensation methods for leading-edge detection and multiple timing algorithms were modeled and tested on simulated signals. In the ADC module, a benchmark (BM) timing algorithm is proposed. A Neyman-Pearson (NP) detector was implemented in the time domain and frequency domain (fast Fourier transform (FFT) approach). The FFT approach with frequency-domain zero-paddings improves the timing resolution. The BM algorithm was tested on simulated signals, and the NP detector was evaluated on both simulated signals and measurements from a prototype lidar (Bhaskaran, 2018).
Remote sensors like Doppler lidars can map the winds with high accuracy and spatial resolution. One shortcoming of lidars is that the radial velocity measured by the lidar does not give a complete picture of the windfield necessitating additional data processing to reconstruct the windfield. Most of the popular vector retrieval algorithms rely on the homogenous wind field assumption which plays a vital role in reducing the indeterminacy of the inverse problem of obtaining Cartesian velocity from radial velocity measurements. Consequently, these methods fail in situations where the flow is heterogeneous e.g., Turbine wakes. Alternate methods are based either on statistical models (e.g., optimal interpolation [1]) or computationally intensive four dimensional variational methods [2]. This study deals with a 2D variational vector retrieval for Doppler lidar that uses the radial velocity advection equation as an additional constraint along with a tangential velocity constraint derived from a new formulation with gradients of radial velocity. The retrieval was applied on lidar data from a wind farm and preliminary analysis revealed that the algorithm was able to retrieve the mean wind field while preserving the small scale flow structure.