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Abstract Modifying turbine blade pitch, generator torque, and nacelle direction (yaw) are conventional approaches for enhancing energy output and alleviating structural loads. However, the efficacy of such methods is challenged by the lag in adjusting such settings after atmospheric variations are detected. Without reliable short-term wind forecasting tools, current practice, which mostly relies on data collected at or just behind turbines, can result in sub-optimal performance. Data-assimilation strategies can achieve real-time wind forecasting capabilities by correcting model-based predictions of the incoming wind using various field measurements. In this paper, we revisit the development of a class of prior models for real-time estimation via Kalman filtering algorithms that track atmospheric variations using ground-level pressure sensors. This class of models is given by the stochastically forced linearized Navier-Stokes equations around the three-dimensional waked velocity profile defined by a curled wake model. The stochastic input to these models is devised using convex optimization to achieve statistical consistency with high-fidelity large-eddy simulations. We demonstrate the ability of such models in reproducing the second-order statistical signatures of the turbulent velocity field. In support of assimilating ground-level pressure measurements with the predictions of said models, we also highlight the significance of the wall-normal dimension in enhancing two-point correlations of the pressure field between the ground and the computational domain.
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Stochastic Dynamical Modeling of Wind Farm Turbulence
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.
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- Award ID(s):
- 1916776
- PAR ID:
- 10490010
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Energies
- Volume:
- 16
- Issue:
- 19
- ISSN:
- 1996-1073
- Page Range / eLocation ID:
- 6908
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/en16196908
