Gradient-based wind farm layout optimization with inclusion and exclusion zones

Gradient-based wind farm layout optimization with inclusion and exclusion zones

14 March 2024 | Javier Criado Risco, Rafael Valotta Rodrigues, Mikkel Friis-Møller, Julian Quick, Mads Mølgaard Pedersen, and Pierre-Elouan Réthoré
This paper presents a novel methodology for integrating multiple disconnected and irregular domain boundaries in wind farm layout optimization problems. The method relies on the analytical gradients of the distances between wind turbine locations and boundaries, represented by polygons. This approach allows for a continuous optimization formulation. However, when combined with gradient-based solvers, the initial placement of wind turbines within the nearest polygons can significantly affect the solution quality. To address this, two independent strategies are proposed: (1) boundary relaxation, which expands the inclusion zones to allow for better design space exploration, and (2) a heuristic algorithm called "smart-start," which improves the allocation of wind turbines within the inclusion polygons based on potential wind resources and available area. A case study is presented to demonstrate the applicability of the method and the proposed strategies. The study aims to maximize the annual energy production (AEP) of a wind farm in complex terrain with several irregularly shaped and disconnected inclusion zones. The problem is constrained by the minimum distance between wind turbines and five irregular polygon boundaries. The optimization is performed using three approaches: (1) a baseline approach with a gradient-based solver, (2) the baseline approach combined with boundary relaxation, and (3) the application of the smart-start algorithm prior to gradient-based optimization. The results show that the boundary relaxation combined with a gradient-based solver achieves an average AEP increase of +10.2% over the baseline, while the smart-start algorithm, combined with a gradient-based solver, finds an average AEP increase of +20.5% compared to the baseline and +9.4% compared to the relaxation strategy.This paper presents a novel methodology for integrating multiple disconnected and irregular domain boundaries in wind farm layout optimization problems. The method relies on the analytical gradients of the distances between wind turbine locations and boundaries, represented by polygons. This approach allows for a continuous optimization formulation. However, when combined with gradient-based solvers, the initial placement of wind turbines within the nearest polygons can significantly affect the solution quality. To address this, two independent strategies are proposed: (1) boundary relaxation, which expands the inclusion zones to allow for better design space exploration, and (2) a heuristic algorithm called "smart-start," which improves the allocation of wind turbines within the inclusion polygons based on potential wind resources and available area. A case study is presented to demonstrate the applicability of the method and the proposed strategies. The study aims to maximize the annual energy production (AEP) of a wind farm in complex terrain with several irregularly shaped and disconnected inclusion zones. The problem is constrained by the minimum distance between wind turbines and five irregular polygon boundaries. The optimization is performed using three approaches: (1) a baseline approach with a gradient-based solver, (2) the baseline approach combined with boundary relaxation, and (3) the application of the smart-start algorithm prior to gradient-based optimization. The results show that the boundary relaxation combined with a gradient-based solver achieves an average AEP increase of +10.2% over the baseline, while the smart-start algorithm, combined with a gradient-based solver, finds an average AEP increase of +20.5% compared to the baseline and +9.4% compared to the relaxation strategy.
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[slides and audio] Gradient-based wind farm layout optimization with inclusion and exclusion zones