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Continuous adjoint formulation for wind farm layout optimization: A 2D implementation

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  • Antonini, Enrico G.A.
  • Romero, David A.
  • Amon, Cristina H.

Abstract

Current methodologies to optimize wind farm layouts to maximize the farm energy production rely on simple analytical models for wake loss estimations. In this paper, we present an innovative continuous adjoint formulation for gradient calculations within the framework of a gradient-based wind farm layout optimization. The developed optimization methodology integrates high-fidelity CFD models and, thanks to the adjoint method, overcomes the computationally high costs of a CFD-based optimization. The proposed continuous adjoint formulation allows for a derivation of the general adjoint equations, before any discretization is being applied, and therefore allows for a more flexible implementation in CFD software packages. Adjoint formulations for different conditions in the flow equations, namely, laminar, frozen-turbulence and turbulent flows are presented. The proposed formulation was implemented in a 2D domain and verified by comparing the calculated gradients with finite-difference approximations. Gradient calculations using the developed adjoint method were implemented in a gradient-based optimization methodology with open source software libraries, and were used to solve a 2D wind farm layout optimization problem under a wide array of wind resource scenarios. Our results showed that the annual energy production (AEP) of a given wind farm layout can be effectively improved within 30–60 iterations, depending on the initial layout and wind resource distribution. Improvements in AEP were found to be in the range of 7–37%, with an average of 15%.

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  • Antonini, Enrico G.A. & Romero, David A. & Amon, Cristina H., 2018. "Continuous adjoint formulation for wind farm layout optimization: A 2D implementation," Applied Energy, Elsevier, vol. 228(C), pages 2333-2345.
    • Handle: RePEc:eee:appene:v:228:y:2018:i:c:p:2333-2345
    DOI: 10.1016/j.apenergy.2018.07.076
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    Cited by:

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    3. Hu, Weicheng & Yang, Qingshan & Chen, Hua-Peng & Guo, Kunpeng & Zhou, Tong & Liu, Min & Zhang, Jian & Yuan, Ziting, 2022. "A novel approach for wind farm micro-siting in complex terrain based on an improved genetic algorithm," Energy, Elsevier, vol. 251(C).
    4. Antonini, Enrico G.A. & Romero, David A. & Amon, Cristina H., 2019. "Improving CFD wind farm simulations incorporating wind direction uncertainty," Renewable Energy, Elsevier, vol. 133(C), pages 1011-1023.
    5. Antonini, Enrico G.A. & Romero, David A. & Amon, Cristina H., 2020. "Optimal design of wind farms in complex terrains using computational fluid dynamics and adjoint methods," Applied Energy, Elsevier, vol. 261(C).
    6. Reddy, Sohail R., 2020. "Wind Farm Layout Optimization (WindFLO) : An advanced framework for fast wind farm analysis and optimization," Applied Energy, Elsevier, vol. 269(C).
    7. Nouri, Reza & Vasel-Be-Hagh, Ahmad & Archer, Cristina L., 2020. "The Coriolis force and the direction of rotation of the blades significantly affect the wake of wind turbines," Applied Energy, Elsevier, vol. 277(C).
    8. Nardecchia, Fabio & Groppi, Daniele & Astiaso Garcia, Davide & Bisegna, Fabio & de Santoli, Livio, 2021. "A new concept for a mini ducted wind turbine system," Renewable Energy, Elsevier, vol. 175(C), pages 610-624.
    9. Dhoot, Aditya & Antonini, Enrico G.A. & Romero, David A. & Amon, Cristina H., 2021. "Optimizing wind farms layouts for maximum energy production using probabilistic inference: Benchmarking reveals superior computational efficiency and scalability," Energy, Elsevier, vol. 223(C).
    10. Antonini, Enrico G.A. & Caldeira, Ken, 2021. "Atmospheric pressure gradients and Coriolis forces provide geophysical limits to power density of large wind farms," Applied Energy, Elsevier, vol. 281(C).
    11. Masoudi, Seiied Mohsen & Baneshi, Mehdi, 2022. "Layout optimization of a wind farm considering grids of various resolutions, wake effect, and realistic wind speed and wind direction data: A techno-economic assessment," Energy, Elsevier, vol. 244(PB).

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