Modelling the wake effect generated by wind turbines is an essential part for calcu- lating a wind farm’s expected energy production. Operating wind turbines disturb the flow of the wind, which results in decreased production of downwind turbines. The N. O. Jensen model is an industry standard wake model that assumes a linear expansion of the downstream wake. The only adjustable parameter in the model is the wake decay constant (WDC), which has traditionally been derived semi em- pirically from terrain surface roughness. However, the WDC defines the expansion rate of the generated wake, and therefore can be linked to the ambient turbulence intensity (TI): high ambient turbulence leads to a faster decay of the generated wake, and therefore to lower wake losses, and vice-versa. Since the influence of the roughness on the ambient turbulence intensity is expected to be less significant at higher heights, these roughness-based WDC values are rather uncertain for the hub heights employed nowadays. The following study presents the results of a comparison between observed and mod- elled wake losses based on different WDC values. To investigate how a change in height affects the wake modelling, two wake scenarios occurring between two tur- bine sets with different hub heights are selected from an operational wind farm. By modelling the wakes using roughness as well as turbulence intensity-based WDCs, conclusions can be drawn on how the predictive capability of the N.O. Jensen model depends on the selection of a suitable WDC value. Finally it is concluded that the goodness of fit between modelled and observed wake losses shows a clear dependency on the wind speed/power production inter- val. At higher wind speeds, the TI-based WDC resulted in a better accuracy of the modelled wake losses as compared to the roughness-based WDC, while for lower wind speeds the N. O. Jensen model performed most accurately when using WDC = 0.075. However, for the investigated cases the overall accuracy of the modelled wake appears to be higher when choosing WDC = 0.075 instead of a TI-based WDC.

As wind energy technology continues to mature, farm sizes grow and wind farm layout design becomes more difficult, in part due to the number of design variables and constraints. Wind farm layout optimization is typically approached using gradient-free methods because of the highly multi-modal shape of the wind farm layout design space. Gradient-free method performance generally degrades with increasing problem size, making it difficult to find optimal layouts for larger wind farms. However, gradient-based optimization methods can effectively and efficiently solve large-scale problems with many variables and constraints. To pave the way for effective and efficient wind farm layout optimization for large-scale wind farms, we have worked to overcome the primary barriers to applying gradient-based optimization to wind farm layout optimization. To improve model/algorithm compatibility, we adjusted wake and wind farm models, adding more realistic curvature and smoothness to enable optimization algorithms to travel through areas in the design space where they had previously gotten stuck. We reduced the number of function calls required for gradient-based wind farm layout optimization by over three orders of magnitude for large farms by using algorithmic differentiation to compute derivatives. We reduced the multi-modality of the wind farm layout design space using wake expansion continuation (WEC). We developed WEC to work with existing optimization algorithms, enabling them to get out of local optima while remaining fully gradient-based. Across four case studies, WEC found results with lower wake loss, on average, than the other methods we tested. To resolve concerns about optimization algorithms exploiting model inaccuracies, we compared the initial and optimized layouts to large-eddy simulation (LES) results. The simple models predicted an AEP improvement of 7.7% for a low-TI case, and LES predicted 9.3%. For a high-TI case, the simple models predicted a 10.0% improvement in AEP and LES predicted 10.7%. To resolve uncertainty regarding relative solution quality for gradient-based and gradient-free methods, we collaborated with seven organizations to compare eight optimization methods. Each method was managed by researchers experienced with them. All methods found solutions of similar quality, with optimized wake loss between 15.48 % and 15.70 %. WEC with SNOPT was the only purely gradient-based method included and found the third-to-best solution.