A comparison of efficient AEP models for Wind Farm Layout Optimization

Abstract. As wind farms scale up to benefit from cost reductions, wake effects create significant challenges, increasing the importance of the Wind Farm Layout Optimization (WFLO) problem. Current methods to maximize Annual Energy Production (AEP) by minimizing wake losses are computationally intensive, requiring hundreds of iterations and multiple optimizations per project. In this work we present the results of testing several AEP models with a variety of simplifications, assumptions and approaches as the objective function in gradient based optimizations, comparing them against a reference. These include the conventional rectangular quadrature in different forms and the novel approaches FLOWERS and Bayesian Quadrature, alongside the Stochastic Gradient Descent (SGD) optimization algorithm. Four different wind farms encompassing different boundaries, wind roses, sizes and types of constraints were used. Three different wake models are considered here, introducing the FLOWERS derivation for Nygaard TurbOPark. The results showed that FLOWERS achieved the greatest balance between efficiency (optimization time) and efficacy (quality of the layout found), with time reductions of over 95 % and layouts comparable to the reference, although it encountered difficulties with strongly unimodal wind roses. Similar layouts were found using rectangular quadrature with a coarse wind direction binning; however, this method was not as efficient as FLOWERS, and worked well only in combination with the Gaussian Bastankhah wake model, with optimization time reductions between 40 and 70 %. Nevertheless, it proved to be more versatile, even for strongly unimodal wind roses. The work also highlights the struggles for probabilistic methods to properly capture the physics and turbine interactions in the problem, not properly reflecting the positive or negative effects of modifying the layout despite their ability to estimate AEP accurately. The similarity in results between using the local wind speed or the free flow wind speed to compute the thrust coefficient in a WFLO framework is pointed out. Finally, SGD was found to obtain consistent layouts, albeit with the highest computational cost out of all methods.