• Energy Research

Abstract. As many coastal regions experience a rapid increase in offshore wind farm installations, inter-farm distances become smaller with a tendency to install larger turbines at high capacity densities. It is however not clear how the wake losses in wind farm clusters depend on the characteristics and spacing of the individual wind farms. Here, we quantify this based on multiple COSMO-CLM simulations, each of which assumes a different, spatially invariant combination of the turbine type and capacity density in a projected, future wind farm layout in the North Sea. An evaluation of the modelled wind climate with mast and lidar data for the period 2008–2020 indicates that the frequency distributions of wind speed and wind direction at turbine hub height are skillfully modelled and the seasonal and inter-annual variations in wind speed are represented well. The wind farm simulations indicate that at a capacity density of 8.1 MW km-2 and for SW-winds, inter-farm wakes can reduce the capacity factor at the inflow edge of wind farms from 59 % to between 55 % and 40 % depending on the proximity, size and number of the upwind farms. However, the long-term impact of wake losses in and between wind farms is mitigated by adopting next-generation, 15 MW wind turbines instead of 5 MW turbines, as the annual energy generation over all wind farms in the simulation is increased by 24 % at the same capacity density. In contrast, the impact of wake losses is exacerbated with increasing capacity density, as the layout-integrated, annual capacity factor varies between 54.4 % and 44.3 % over the considered range of 3.5 to 10 MW km-2. Overall, wind farm characteristics and inter-farm distances play an essential role in cluster-scale wake losses, which should be taken into account in future wind farm planning.

Abstract. Wind farm flow control (WFFC) is a topic of interest at several research institutes, industry and certification agencies world-wide. For reliable performance assessment of the technology, the efficiency and the capability of the models applied to WFFC should be carefully evaluated. To address that, FarmConners consortium has launched a common benchmark for code comparison under controlled operation to demonstrate its potential benefits such as increased power production. The benchmark builds on available data sets from previous field campaigns, wind tunnel experiments and high-fidelity simulations. Within that database, 4 blind tests are defined and 13 participants in total have submitted results for the analysis of single and multiple wake under WFFC. Some participants took part in several blind tests and some participants have implemented several models. The observations and/or the model outcomes are evaluated via direct power comparisons at the upstream and downstream turbine(s), as well as the power gain at the wind farm level under wake steering control strategy. Additionally, wake loss reduction is also analysed to support the power performance comparison, where relevant. Majority of the participating models show good agreement with the observations or the reference high-fidelity simulations, especially for lower degrees of upstream misalignment and narrow wake sector. However, the benchmark clearly highlights the importance of the calibration procedure for control-oriented models. The potential effects of limited controlled operation data in calibration is particularly visible via frequent model mismatch for highly deflected wakes, as well as the power loss at the controlled turbine(s). In addition to the flow modelling, sensitivity of the predicted WFFC benefits to the turbine representation and the implementation of the controller is also underlined. FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings and model complexities for the (initial) assessment of farm flow control benefits. It forms an important basis for more detailed benchmarks in the future with extended control objectives to assess the true value of WFFC.

We investigate the use of optimal coordinated control techniques in large eddy simulations of wind farm boundary layer interaction with the aim of increasing the total energy extraction in wind farms. The individual wind turbines are considered as flow actuators, and their energy extraction is dynamically regulated in time, so as to optimally influence the flow field. We extend earlier work on wind farm optimal control in the fully-developed regime (Goit and Meyers 2015, J. Fluid Mech. 768, 5–50) to a ‘finite’ wind farm case, in which entrance effects play an important role. For the optimal control, a receding horizon framework is employed in which turbine thrust coefficients are optimized in time and per turbine. Optimization is performed with a conjugate gradient method, where gradients of the cost functional are obtained using adjoint large eddy simulations. Overall, the energy extraction is increased 7% by the optimal control. This increase in energy extraction is related to faster wake recovery throughout the farm. For the first row of turbines, the optimal control increases turbulence levels and Reynolds stresses in the wake, leading to better wake mixing and an inflow velocity for the second row that is significantly higher than in the uncontrolled case. For downstream rows, the optimal control mainly enhances the sideways mean transport of momentum. This is different from earlier observations by Goit and Meyers (2015) in the fully-developed regime, where mainly vertical transport was enhanced.

AbstractIn large wind farms, self‐induced turbulence levels significantly increase the variability of generated power in a range of time scales from a few seconds to several minutes. In the current study, we investigate the potential for reducing this type of variability by dynamically controlling the rotating kinetic energy reserves that are present in the farm's wind turbines. To this end, we reduce the burden of frequency regulation on remaining conventional units when they are displaced in favor of wind turbines. We focus on the development of a theoretical benchmark framework in which we explore the trade‐off between high energy extraction and low variability using optimal coordinated control of multiple turbines subject to a turbulent wind field. This wind field is obtained from a large‐eddy simulation of a fully developed wind farm boundary layer. The controls that are optimized are the electric torque and the pitch angles of the individual turbines as function of time so that turbines are accelerated or decelerated to optimally extract or store energy in the turbines' rotating inertia. Results are presented in terms of Pareto fronts (i.e., curves with optimal trade‐offs), and we find that power variations can be significantly reduced with limited loss of extracted energy. For a one‐turbine case, such an optimal control leads to large potential reductions of variability but mainly for time scales below 10 s if we limit power losses to a few percent. Variability over longer time scales (10–100 s) is reduced considerably more for coordinated control. For instance, restricting the energy‐loss incurred with smoothing to 1%, and looking at time scales of 50 s, we manage to reduce variability with a factor of 6 for a coordinated case with 24 turbines, compared with a factor of 1.4 for an uncoordinated case. Copyright © 2014 John Wiley & Sons, Ltd.

Abstract. Recently, it has been shown that flow blockage in large wind farms may lift up the top of the boundary layer, thereby triggering atmospheric gravity waves in the inversion layer and in the free atmosphere. These waves impose significant pressure gradients in the boundary layer, causing detrimental consequences in terms of a farm's efficiency. In the current study, we investigate the idea of controlling the wind farm in order to mitigate the efficiency drop due to wind-farm-induced gravity waves and blockage. The analysis is performed using a fast boundary layer model which divides the vertical structure of the atmosphere into three layers. The wind-farm drag force is applied over the whole wind-farm area in the lowest layer and is directly proportional to the wind-farm thrust set-point distribution. We implement an optimization model in order to derive the thrust-coefficient distribution, which maximizes the wind-farm energy extraction. We use a continuous adjoint method to efficiently compute gradients for the optimization algorithm, which is based on a quasi-Newton method. Power gains are evaluated with respect to a reference thrust-coefficient distribution based on the Betz–Joukowsky set point. We consider thrust coefficients that can change in space, as well as in time, i.e. considering time-periodic signals. However, in all our optimization results, we find that optimal thrust-coefficient distributions are steady; any time-periodic distribution is less optimal. The (steady) optimal thrust-coefficient distribution is inversely related to the vertical displacement of the boundary layer. Hence, it assumes a sinusoidal behaviour in the streamwise direction in subcritical flow conditions, whereas it becomes a U-shaped curve when the flow is supercritical. The sensitivity of the power gain to the atmospheric state is studied using the developed optimization tool for almost 2000 different atmospheric states. Overall, power gains above 4 % were observed for 77 % of the cases with peaks up to 14 % for weakly stratified atmospheres in critical flow regimes.

We use large-eddy simulations (LES) to investigate the impact of stable stratification on gravity-wave excitation and energy extraction in a large wind farm. To this end, the development of an equilibrium conventionally neutral boundary layer into a stable boundary layer over a period of 8 h is considered, using two different cooling rates. We find that turbulence decay has considerable influence on the energy extraction at the beginning of the boundary-layer transition, but afterwards, energy extraction is dominated by geometrical and jet effects induced by an inertial oscillation. It is further shown that the inertial oscillation enhances gravity-wave excitation. By comparing LES results with a simple one-dimensional model, we show that this is related to an interplay between wind-farm drag, variations in the Froude number and the dispersive effects of vertically-propagating gravity waves. We further find that the pressure gradients induced by gravity waves lead to significant upstream flow deceleration, reducing the average turbine output compared to a turbine in isolated operation. This leads us to the definition of a non-local wind-farm efficiency, next to a more standard wind-farm wake efficiency, and we show that both can be of the same order of magnitude. Finally, an energy flux analysis is performed to further elucidate the effect of gravity waves on the flow in the wind farm.

Abstract. Turbine-wake and farm-atmosphere interactions can reduce wind farm power production. To model farm performance, it is important to understand the impact of different flow effects on the farm efficiency (i.e., farm power normalised by the power of the same number of isolated turbines). In this study we analyse the results of 43 large-eddy simulations (LES) of wind farms in a range of conventionally neutral boundary layers (CNBLs). First, we show that the farm efficiency ηf is not well correlated with the wake efficiency ηw (i.e., farm power normalised by the power of front row turbines). This suggests that existing metrics, classifying the loss of farm power into wake loss and farm blockage loss, are not best suited for understanding large wind farm performance. We then validate the assumption of scale separation in the two-scale momentum theory (Nishino & Dunstan, J. Fluid Mech., vol. 894, 2020, p. A2) using the LES results. Building upon this theory, we propose two new metrics for wind farm performance, a turbine-scale efficiency ηTS, reflecting the losses due to turbine-wake interactions, and a farm-scale efficiency ηFS, indicating the losses due to farm-atmosphere interactions. The LES results show that ηTS is insensitive to the atmospheric condition, whereas ηFS is insensitive to the turbine layout. Finally, we show that a recently developed analytical wind farm model predicts ηFS with an average error of 5.7 % from the LES results.