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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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Turbulence and Control of Wind Farms
The dynamics of the turbulent atmospheric boundary layer play a fundamental role in wind farm energy production, governing the velocity field that enters the farm as well as the turbulent mixing that regenerates energy for extraction at downstream rows. Understanding the dynamic interactions among turbines, wind farms, and the atmospheric boundary layer can therefore be beneficial in improving the efficiency of wind farm control approaches. Anticipated increases in the sizes of new wind farms to meet renewable energy targets will increase the importance of exploiting this understanding to advance wind farm control capabilities. This review discusses approaches for modeling and estimation of the wind farm flow field that have exploited such knowledge in closed-loop control, to varying degrees. We focus on power tracking as an example application that will be of critical importance as wind farms transition into their anticipated role as major suppliers of electricity. The discussion highlights the benefits of including the dynamics of the flow field in control and points to critical shortcomings of the current approaches. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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- PAR ID:
- 10313304
- Date Published:
- Journal Name:
- Annual Review of Control, Robotics, and Autonomous Systems
- Volume:
- 5
- Issue:
- 1
- ISSN:
- 2573-5144
- 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/10.1146/annurev-control-070221-114032
