Sensitivity of array-like and optimized wind farm output to key factors and choice of wake models

The creation of wakes, with unique turbulence characteristics, downstream of turbines significantly increases the complexity of the boundary layer flow within a wind farm. In conventional wind farm design, analytical wake models are generally used to compute the wake-induced power losses, with different wake models yielding significantly different estimates. In this context, the wake behavior, and subsequently the farm power generation, can be expressed as functions of a series of key factors. A quantitative understanding of the relative impact of each of these factors is paramount to the development of more reliable power generation models; such an understanding is however missing in the current state of the art in wind farm design. In this paper, we quantitatively explore how the farm power generation, estimated using four different analytical wake models, is influenced by the following key factors: (i) incoming wind speed, (ii) land configuration, and (iii) ambient turbulence. The sensitivity of the maximum farm output potential to the input factors, when using different wake models, is also analyzed. The extended Fourier Amplitude Sensitivity Test (eFAST) method is used to perform the sensitivity analysis. The power generation model and the optimization strategy is adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. In the case of an array-like turbine arrangement, both the first-order and the total-order sensitivity analysis indices of the power output with respect to the incoming wind speed were found to reach a value of 99%, irrespective of the choice of wake models. However, in the case of maximum power output, significant variation (around 30%) in the indices was observed across different wake models, especially when the incoming wind speed is close to the rated speed of the turbines.