skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Data-driven Parameter Calibration in Wake Models
Physical interactions among wind turbines, called wake effects, are known to be one of the significant factors that affect power generation performance in wind power systems. Among several wake modeling approaches, physics-based engineering models, such as Jensen's model, have been widely used due to their computational tractability. Although substantial efforts have been made to improve the accuracy of engineering wake models, few studies suggest calibrating the model parameters in the literature. We propose a new data-driven calibration approach for adjusting the model parameters using real operational data.  more » « less
Award ID(s):
1741166
PAR ID:
10384641
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proceeding of the 36th Wind Energy Symposium, the 2018 American Institute of Aeronautics and Astronautics Science and Technology (AIAA SciTech) Forum and Exposition
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Abstract. Engineering wake models provide the invaluable advantage to predict wind turbine wakes, power capture, and, in turn, annual energy production for an entire wind farm with very low computational costs compared to higher-fidelity numerical tools. However, wake and power predictions obtained with engineering wake models can be insufficiently accurate for wind farm optimization problems due to the ad hoc tuning of the model parameters, which are typically strongly dependent on the characteristics of the site and power plant under investigation. In this paper, lidar measurements collected for individual turbine wakes evolving over a flat terrain are leveraged to perform optimal tuning of the parameters of four widely used engineering wake models. The average wake velocity fields, used as a reference for the optimization problem, are obtained through a cluster analysis of lidar measurements performed under a broad range of turbine operative conditions, namely rotor thrust coefficients, and incoming wind characteristics, namely turbulence intensity at hub height. The sensitivity analysis of the optimally tuned model parameters and the respective physical interpretation are presented. The performance of the optimally tuned engineering wake models is discussed, while the results suggest that the optimally tuned Bastankhah and Ainslie wake models provide very good predictions of wind turbine wakes. Specifically, the Bastankhah wake model should be tuned only for the far-wake region, namely where the wake velocity field can be well approximated with a Gaussian profile in the radial direction. In contrast, the Ainslie model provides the advantage of using as input an arbitrary near-wake velocity profile, which can be obtained through other wake models, higher-fidelity tools, or experimental data. The good prediction capabilities of the Ainslie model indicate that the mixing-length model is a simple yet efficient turbulence closure to capture effects of incoming wind and wake-generated turbulence on the wake downstream evolution and predictions of turbine power yield. 
    more » « less
  2. As turbines continue to grow in hub height and rotor diameter and wind farms grow larger, consideration of stratified atmospheric boundary layer (ABL) processes in wind power models becomes increasingly important. Atmospheric stratification can considerably alter the boundary layer structure and flow characteristics through buoyant forcing. Variations in buoyancy, and corresponding ABL stability, in both space and time impact ABL wind speed shear, wind direction shear, boundary layer height, turbulence kinetic energy, and turbulence intensity. In addition, the presence of stratification will result in a direct buoyant forcing within the wake region. These ABL mechanisms affect turbine power production, the momentum and kinetic energy deficit wakes generated by turbines, and the turbulent mixing and kinetic energy entrainment in wind farms. Presently, state-of-practice engineering models of mean wake momentum utilize highly empirical turbulence models that do not explicitly account for ABL stability. Models also often neglect the interaction between the wake momentum deficit and the turbulence kinetic energy added by the wake, which depends on stratification. In this work, we develop a turbulence model that models the wake-added turbulence kinetic energy, and we couple it with a wake model based on the parabolized Reynolds-averaged Navier–Stokes equations. Comparing the model predictions to large eddy simulations across stabilities (Obukhov lengths) and surface roughness lengths, we find lower prediction error in both power production and the wake velocity field across the ABL conditions and error metrics investigated. 
    more » « less
  3. Low-fidelity engineering wake models are often combined with linear superposition laws to predict wake velocities across wind farms under steady atmospheric conditions. While convenient for wind farm planning and long-term performance evaluation, such models are unable to capture the time-varying nature of the waked velocity field, as they are agnostic to the complex aerodynamic interactions among wind turbines and the effects of atmospheric boundary layer turbulence. To account for such effects while remaining amenable to conventional system-theoretic tools for flow estimation and control, we propose a new class of data-enhanced physics-based models for the dynamics of wind farm flow fluctuations. Our approach relies on the predictive capability of the stochastically forced linearized Navier–Stokes equations around static base flow profiles provided by conventional engineering wake models. We identify the stochastic forcing into the linearized dynamics via convex optimization to ensure statistical consistency with higher-fidelity models or experimental measurements while preserving model parsimony. We demonstrate the utility of our approach in completing the statistical signature of wake turbulence in accordance with large-eddy simulations of turbulent flow over a cascade of yawed wind turbines. Our numerical experiments provide insight into the significance of spatially distributed field measurements in recovering the statistical signature of wind farm turbulence and training stochastic linear models for short-term wind forecasting. 
    more » « less
  4. Analytical wake models provide a computationally efficient means to predict velocity distributions in wind turbine wakes in the atmospheric boundary layer (ABL). Most existing models are developed for neutral atmospheric conditions and correspondingly neglect the effects of buoyancy and Coriolis forces that lead to veer, i.e., changes in the wind direction with height. Both veer and changes in thermal stratification lead to lateral shearing of the wake behind a wind turbine, which affects the power output of downstream turbines. Here we develop an analytical engineering wake model for a wind turbine in yaw in ABL flows including Coriolis and thermal stratification effects. The model combines the new analytical representation of ABL vertical structure based on coupling Ekman and surface layer descriptions developed in Narasimhan et al. [Boundary Layer Meteorol. 190, 16 (2024)] with the vortex sheet-based wake model for yawed turbines proposed in Bastankhah et al. [J. Fluid Mech. 933, A2 (2022)], as well as a new method to predict the wake expansion rate based on the Townsend-Perry logarithmic scaling of streamwise velocity variance. The proposed wake model's predictions show good agreement with large-eddy simulation results, capturing the effects of wind veer and yawing, including the curled and sheared wake structures across various states of the ABL, ranging from neutrally to strongly stably stratified atmospheric conditions. The model significantly improves power loss predictions from wake interactions, especially in strongly stably stratified conditions where wind veer effects dominate. 
    more » « less
  5. null (Ed.)
    Wake models play an integral role in wind farm layout optimization and operations where associated design and control decisions are only as good as the underlying wake model upon which they are based. However, the desired model fidelity must be counterbalanced by the need for simplicity and computational efficiency. As a result, efficient engineering models that accurately capture the relevant physics—such as wake expansion and wake interactions for design problems and wake advection and turbulent fluctuations for control problems—are needed to advance the field of wind farm optimization. In this paper, we discuss a computationally-efficient continuous-time one-dimensional dynamic wake model that includes several features derived from fundamental physics, making it less ad-hoc than prevailing approaches. We first apply the steady-state solution of the model to predict the wake expansion coefficients commonly used in design problems. We demonstrate that more realistic results can be attained by linking the wake expansion rate to a top-down model of the atmospheric boundary layer, using a super-Gaussian wake profile that smoothly transitions between a top-hat and Gaussian distribution as well as linearly-superposing wake interactions. We then apply the dynamic model to predict trajectories of wind farm power output during start-up and highlight the improved accuracy of non-linear advection over linear advection. Finally, we apply the dynamic model to the control-oriented application of predicting power output of an irregularly-arranged farm during continuous operation. In this application, model fidelity is improved through state and parameter estimation accounting for spanwise inflow inhomogeneities and turbulent fluctuations. The proposed approach thus provides a modeling paradigm with the flexibility to enable designers to trade-off between accuracy and computational speed for a wide range of wind farm design and control applications. 
    more » « less