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<strong class="journal-contentHeaderColor">Abstract.</strong> The magnitude of wake interactions between individual wind turbines depends on the atmospheric stability. We investigate strategies for wake loss mitigation through the use of closed-loop wake steering using large eddy simulations of the diurnal cycle, in which variations in the surface heat flux in time modify the atmospheric stability, wind speed and direction, shear, turbulence, and other atmospheric boundary layer (ABL) flow features. The closed-loop wake steering control methodology developed in Part 1 (<span class="cit" id="xref_altparen.1"><a href="#bib1.bibx33">Howland et al.</a>, <a href="#bib1.bibx33">2020</a><a href="#bib1.bibx33">c</a></span>, <a href="https://doi.org/10.5194/wes-5-1315-2020">https://doi.org/10.5194/wes-5-1315-2020</a>) is implemented in an example eight turbine wind farm in large eddy simulations of the diurnal cycle. The optimal yaw misalignment set points depend on the wind direction, which varies in time during the diurnal cycle. To improve the application of wake steering control in transient ABL conditions with an evolving mean flow state, we develop a regression-based wind direction forecast method. We compare the closed-loop wake steering control methodology to baseline yaw-aligned control and open-loop lookup table control for various selections of the yaw misalignment set-point update frequency, which dictates the balance between wind direction tracking and yaw activity. In our diurnal cycle simulations of a representative wind farm geometry, closed-loop wake steering with set-point optimization under uncertainty results in higher collective energy production than both baseline yaw-aligned control and open-loop lookup table control. The increase in energy production for the simulated wind farm design for closed- and open-loop wake steering control, compared to baseline yaw-aligned control, is 4.0 %–4.1 % and 3.4 %–3.8 %, respectively, with the range indicating variations in the energy increase results depending on the set-point update frequency. The primary energy increases through wake steering occur during stable ABL conditions in our present diurnal cycle simulations. Open-loop lookup table control decreases energy production in the example wind farm in the convective ABL conditions simulated, compared to baseline yaw-aligned control, while closed-loop control increases energy production in the convective conditions simulated.

Abstract. Wind farm control strategies are being developed to mitigate wake losses in wind farms, increasing energy production. Wake steering is a type of wind farm control in which a wind turbine's yaw position is misaligned from the wind direction, causing its wake to deflect away from downstream turbines. Current modeling tools used to optimize and estimate energy gains from wake steering are designed to represent wakes for fixed wind directions. However, wake steering controllers must operate in dynamic wind conditions and a turbine's yaw position cannot perfectly track changing wind directions. Research has been conducted on robust wake steering control optimized for variable wind directions. In this paper, the design and analysis of a wake steering controller with wind direction variability is presented for a two-turbine array using the FLOw Redirection and Induction in Steady State (FLORIS) control-oriented wake model. First, the authors propose a method for modeling the turbulent and low-frequency components of the wind direction, where the slowly varying wind direction serves as the relevant input to the wake model. Next, we explain a procedure for finding optimal yaw offsets for dynamic wind conditions considering both wind direction and yaw position uncertainty. We then performed simulations with the optimal yaw offsets applied using a realistic yaw offset controller in conjunction with a baseline yaw controller, showing good agreement with the predicted energy gain using the probabilistic model. Using the Gaussian wake model in FLORIS as an example, we compared the performance of yaw offset controllers optimized for static and dynamic wind conditions for different turbine spacings and turbulence intensity values, assuming uniformly distributed wind directions. For a spacing of five rotor diameters and a turbulence intensity of 10 %, robust yaw offsets optimized for variable wind directions yielded an energy gain equivalent to 3.24 % of wake losses recovered, compared to 1.42 % of wake losses recovered with yaw offsets optimized for static wind directions. In general, accounting for wind direction variability in the yaw offset optimization process was found to improve energy production more as the separation distance increased, whereas the relative improvement remained roughly the same for the range of turbulence intensity values considered.

The wake steering control in wind farms has gained significant attention in the last years. This control strategy has shown promise to reduce energy losses due to wake effects and increase the energy production in a wind farm. However, wind conditions are variable in wind farms, and the measurements are uncertain what should be considered in the design of wake steering control strategies. This paper proposes using the probabilistic learning on manifold (PLoM), which can be viewed as a supervised machine learning method, to enable the wake steering optimization under uncertainty. The expected power generation is estimated considering uncertainties in wind speed and direction with good accuracy and reduced computational cost for two wind farm layouts, which expand the application of machine learning models in wake steering. Furthermore, the analysis shows the potential gain with the application of wake steering control.

Abstract. High-fidelity flow modeling with data assimilation enables accurate representation of the wind farm operating environment under realistic, nonstationary atmospheric conditions. Capturing the temporal evolution of the turbulent atmospheric boundary layer is critical to understanding the behavior of wind turbines under operating conditions with simultaneously varying inflow and control inputs. This paper has three parts: the identification of a case study during a field evaluation of wake steering; the development of a tailored mesoscale-to-microscale coupling strategy that resolved local flow conditions within a large-eddy simulation (LES), using observations that did not completely capture the wind and temperature fields throughout the simulation domain; and the application of this coupling strategy to validate high-fidelity aeroelastic predictions of turbine performance and wake interactions with and without wake steering. The case study spans 4.5 h after midnight local time, during which wake steering was toggled on and off five times, achieving yaw offset angles ranging from 0 to 17°. To resolve nonstationary nighttime conditions that exhibited shear instabilities, the turbulence field was evolved starting from the diurnal cycle of the previous day. These background conditions were then used to drive wind farm simulations with two different models: an LES with actuator disk turbines and a steady-state engineering wake model. Subsequent analysis identified two representative periods during which the up- and downstream turbines were most nearly aligned with the mean wind direction and had observed yaw offsets of 0 and 15°. Both periods corresponded to partial waking on the downstream turbine, which had errors in the LES-predicted power of 4 % and 6 %, with and without wake steering. The LES was also able to capture conditions during which an upstream turbine wake induced a speedup at a downstream turbine and increased power production by up to 13 %.

Wake steering strategies often seek to gain power at the expense of increased fatigue loads. Here, we investigate the feasibility of applying wake steering at an above-rated condition. In such a condition, the farm is operating at rated power, and thus, increased power output is not the goal. Instead, wake steering is considered in the context of load reduction. We perform a sweep of wind directions and yaw misalignment angles, ranging from negative to positive values. This approach allows us to obtain trends and identify asymmetries in turbine response for symmetric scenarios. We use a wind farm consisting of five aligned IEA Wind 15-MW reference wind turbines, and analyze trends related to the blade-root, low-speed shaft, and tower-base moments, both in terms of standard deviation and damage equivalent loads. We show that for any given fixed wind direction, the turbines can be yawed such that the fatigue loads are reduced. Reductions of up to 5% (depending on the component) in terms of standard deviation and damage equivalent loads can be achieved by negatively yawing the turbine. A negative yaw misalignment has shown to be the direction of larger improvements. Such results contrast those found for below-rated conditions, where a positive yaw misalignment is typically preferred. However, since load reduction is not uniform across all component loads, more study and consideration is required before operational recommendations can be made.

Quantifying the impacts on turbine loads during wind farm control is an important consideration in assessing power production benefits. Wake steering controls aim to improve total wind farm performance by coordinating the control actions of individual turbines, wherein an upstream turbine is intentionally yawed at an offset angle from the measured wind direction. Consequently, this redirects its wake for improved power production and potentially reduces fatigue loads of the downstream turbines. This paper studies the lifetime fatigue loads associated with wake steering by using utility-scale wind turbine experimental data to conduct an analysis on a pair of wind turbines. This study was part of a large field experiment in which a group of five GE 1.5-MW SLE CWE turbines were selected as targets for conducting wake steering research. A standard loads instrumentation package and data acquisition system were installed on two turbines within the cluster to measure turbine fundamental loads. The time-series databases were used to calculate loads statistics as well as short-term and lifetime damage equivalent loads. Fatigue calculations followed the guidance in Annex H of the International Electrotechnical Commission standard 61400-1, Edition 4. Lifetime fatigue calculation results are presented in this analysis; three methods of assessing lifetime fatigue were used to determine percent difference for blade root moments, main shaft moments, main shaft torque, and tower top torque. For all three fatigue treatments, some components’ lifetime fatigue increases for the controlled turbine; however, the downwind turbine experienced a reduction in lifetime fatigue and combined effect for the turbine pair results in a reduction of fatigue when wake steering controls are applied.

Wind farms experience significant power losses due to wake interactions between turbines. Research shows that wake steering can alleviate these losses by redirecting the flow through the farm. However, dynamic closed‐loop implementations of wake steering are rarely presented. We present a model‐free closed‐loop control method using reinforcement learning methodology known as policy gradients in combination with recursive least squares to perform real‐time wake steering in a wind farm. We present dynamic simulations of a four‐turbine wind farm row using HAWC2Farm, implementing the reinforcement learning control method for various inflow conditions and controller configurations. By controlling the three most upstream turbines, mean power gains of and (95% confidence interval) are observed in partial wake and full wake conditions respectively at 7.5% turbulence intensity. The study helps to bridge the gap between theoretical wind farm control and real‐world wind farm systems.

Ideally, optimum power for a single turbine is obtained when the wind-turbine is aligned with the wind direction. However in multi-turbine wind-farm set-up, wake effects lead to decreased power production from downstream turbine [1, 2, 3, 4, 5]. Hence, a control strategy based on wake steering involves misalignment of upstream turbines with the wind direction causing their wakes to deflect away from downstream wind turbines needs to be investigated. A great deal of work has been put into dynamically controlling the orientation of the individual wind turbines to maximize the power output of the farm [6, 7, 8, 9]. In the wake-steering based control, the misaligned wind turbines produce less power, while the performance of downstream turbines gets enhanced which increases overall net power gain for the wind power plant. Traditionally, the benefits of wake steering have been demonstrated assuming fixed wind directions (e.g., using high-fidelity modeling). Amongst the most recent techniques, particularly promising is the use of Reinforcement learning (RL), which is a branch of machine learning where models are trained to make decisions based on observations of their environment. It is a flexible framework for devising strategies for solving optimal control problems in a broad range of applications across the sciences. Early attempts at using Reinforcement learning for wake steering have been carried out [7, 8, 9], and show promising results. In practice, however, wake-steering controllers must operate in dynamic wind environments in which the wind conditions are estimated from imperfect measurements. Hence, a reinforcement learning framework is developed in this work for dynamic wind conditions. The results show that the framework is promising, and we compare the deep reinforcement learning approach against a considerably more expensive traditional optimization approach which serves as a good baseline. Future work could include looking at more realistic wake models, steering in the presence of noisy observations, and incorporating weather predictions.

Wind fields are intermittent and nonlinear to meteorological factors and external environmental conditions. Statistical models have been proposed based on various approaches to precisely predict wind speed and energy production. However, determining the most suitable approach is challenging, regardless of the conditions. Currently, only wind speed, wind direction, temperature, atmospheric pressure, and humidity have been used as input features of models in most wind-power forecasting studies. However, few studies have described each feature's contribution to prediction performance when using meteorological factors, such as atmospheric stability and turbulence components, as input features. This study predicted the 10 min average power and daily energy production of a wind farm using four machine learning (ML) algorithms and 13 meteorological factors. The ultimate goal was to present the individual prediction contribution of meteorological factors using the Shapley additive explanations algorithm, which is an explainable artificial intelligence technique, based on the prediction results. Wind speed showed a dominant influence in the determination of energy production, followed by turbulent kinetic energy, turbulence intensity, and turbulence dissipation rate. Thus, insights into the detailed contribution of turbulence components to predict the performance facilitate the advancement of ML-based approaches, which can yield significant benefits in increasing the predictability of actual wind energy, thereby ensuring efficiency and stability in wind farm operations.

Abstract. Wind-farm control strategies aim to increase the efficiency, and therefore lower the levelized cost of energy, of wind farms. This is done by using turbine settings such as the yaw angle, blade pitch angles, or generator torque to manipulate the wake that negatively affects downstream turbines in the farm. Two inherently different wind-farm control methods have been identified in the literature: wake steering (WS) and active wake mixing (AWM). As one of two companion papers focused on understanding practical aspects of these two wind-farm control strategies using large-eddy simulation (LES), we below analyze the wake quantities of interest for a single wind turbine performing WS and AWM, while the companion article (Frederik et al., 2025) focuses on turbine quantities of interest including power and structural loads for the same computational setup and also includes two-turbine arrays with full and partial wake overlap. The simulations, which are based in the LES solver AMR-Wind, are tailored to have inflow conditions representative of measurements from a site off the East Coast of the US, including with strong veer and low turbulence. The turbine, which is modeled in OpenFAST and coupled to the LES, is the IEA 15 MW, an open-source offshore design. After presenting an overview of the wake recovery for the different wake-control cases, the analysis probes the fluid-dynamic causes for the different performance of the arrays reported in the companion article by examining control volumes around the wakes and the budget of the mean-flow kinetic energy (MKE) within these volumes. In the high veer environment considered, the MKE recovery is dominated by mean convection, and this is shown to especially benefit the WS strategy when a neighboring turbine is directly downstream: there is ≈65 % more available power for a downstream turbine than in the baseline case, and this power is gained primarily through mean convection on the left-tip and top-tip faces of the control volume. However, the case with imperfect knowledge of the exact wind direction favors the pulse-type AWM strategy, largely because of ≈9 % increased turbulent entrainment from aloft versus the baseline that could be related to an apparent resistance to skewing in the pulsed wake. The general reduced effectiveness of helix-type and other individual-pitch-based AWM strategies for inflow with high veer and low turbulence as reported in the companion paper is due, in part, to low magnitudes of phase-averaged turbulent entrainment. Two main findings of this study are thus that veer has a significant impact on the effectiveness of different wake-control strategies and that pulse-type AWM may be a useful strategy when the objective is power maximization in realistic, offshore flow environments with imperfect knowledge of the exact wake overlap position on the downstream turbine.

Wake losses from neighboring plants may become a major factor in wind plant design and control as additional plants are constructed in areas with high wind resource availability. Because plant wakes span a large range of physical scales, from turbine rotor diameter to tens of kilometers, it is unclear whether conventional wake models or turbine control strategies are effective at the plant scale. Wake steering and axial induction control are evaluated in the current work as means of reducing the impact of neighboring wind plants on power and levelized cost of electricity. FLOw Redirection and Induction in Steady State (FLORIS) simulations were performed with the Gauss–Curl Hybrid and TurbOPark wake models as well as two operation and maintenance models to investigate control setpoint sensitivity to wake representation and economic factors. Both wake models estimate losses across a range of atmospheric conditions, although the wake loss magnitude is dependent on the wake model. Annual energy production and levelized cost of electricity are driven by wind direction frequency, with frequently aligned plants experiencing the greatest losses. However, both wake steering and axial induction are unable to mitigate the impact of upstream plants. Wake steering is constrained by plant geometry, since wake displacement is much less than the plant wake width, while axial induction requires curtailing the majority of turbines in upstream plants. Individual turbine strategies are limited by their effective scale and model representation. New wake models that include plant-scale physics are needed to facilitate the design of effective plant wake control strategies.

Abstract. Wake steering strategies are employed to increase the overall power production of wind farms by deflecting wakes of upstream turbines away from downstream ones. The gain in net power comes at the expense of increased fatigue loads experienced by downstream turbines. In this work we investigate performance and fatigue loading characteristics of a small farm consisting of five aligned International Energy Agency Wind Technology Collaboration Programme 15 MW wind turbines. A parametric study is performed where, for every wind direction from −20 to 20°, the yaw misalignment angle varies from −25 to 25°. This setup allows us to investigate asymmetries and identify optimal conditions for a given wind direction. In general, we find that positive yaw configurations are preferred and that yaw configurations that result in attractive power differences when compared to a baseline no-yaw scenario (25 %) come with significant increase in fatigue loading (we use the standard deviation and damage-equivalent load (DEL) of the blade-root, low-speed shaft, and tower-base moments as proxies for fatigue load). We find that for any given positive wind inflow angle, yaw angles between −2.5 and 15° yield power differences of 10 %–20 % over a no-yaw baseline, and positive yaw is preferred because of lower fatigue loading. For any given negative wind inflow angles, positive yaw also results in lower magnitudes of standard deviation and DEL for the channels investigated. A small power loss of up to 2 % is observed for some positive yaw angles under negative wind directions (as compared to symmetric negative yaw and positive wind cases), but improvements in terms of loads exceed 25 % and may be enough to justify a positive yaw configuration under negative winds as well. We show that such behavior can be explained by partial waking and the direction of the rotation of the rotor.

This paper defines a new procedure for optimising wind farm turbine placement by means of Monte Carlo simulation method. To verify the algorithm’s accuracy, an experimental wind farm was tested in a wind tunnel. On the basis of experimental measurements, the error on wind farm power output was less than 4%. The optimization maximises the energy production criterion; wind turbines’ ground positions were used as independent variables. Moreover, the mathematical model takes into account annual wind intensities and directions and wind turbine interaction. The optimization of a wind farm on a real site was carried out using measured wind data, dominant wind direction, and intensity data as inputs to run the Monte Carlo simulations. There were 30 turbines in the wind park, each rated at 20 kW. This choice was based on wind farm economics. The site was proportionally divided into 100 square cells, taking into account a minimum windward and crosswind distance between the turbines. The results highlight that the dominant wind intensity factor tends to overestimate the annual energy production by about 8%. Thus, the proposed method leads to a more precise annual energy evaluation and to a more optimal placement of the wind turbines.

Differences in wind farm energy production based on the atmospheric stability dissipation rate: Case study of a 30 MW onshore wind farm

Abstract. Layout design and wake steering through wind plant control are important and complex components in the design and operation of modern wind power plants. They are currently optimized separately, but with more and more computational and experimental studies demonstrating the gains possible through wake steering, there is a growing need from industry and regulating bodies to combine the layout and control optimization in a co-design process. However, combining these two optimization problems is currently infeasible due to the excessive number of design variables and large solution space. In this article, we present a method that enables the coupled optimization of wind power plant layout and wake steering with no additional computational expense than a traditional layout optimization. We developed a geometric relationship between wind turbines to find an approximate optimal yaw angle, bypassing the need for either a nested or coupled wind plant control optimization. It also provides a significant and immediate improvement to wind power plant design by enabling the co-design of turbine layout and yaw control for wake steering. A small co-designed plant shown in this article produces 0.8 % more energy than its sequentially designed counterpart. This additional energy production comes with no additional infrastructure, turbine hardware, or control software; it is simply the outcome of optimizing the turbine layout and yaw control together, resulting in millions of dollars of additional revenue for the wind power plants of the future.