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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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A Wake Modeling Paradigm for Wind Farm Design and Control
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.
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- Award ID(s):
- 1635430
- PAR ID:
- 10204203
- Date Published:
- Journal Name:
- Energies
- Volume:
- 12
- Issue:
- 15
- ISSN:
- 1996-1073
- Page Range / eLocation ID:
- 2956
- 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/en12152956
