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Wind farm design and analysis heavily rely on computationally efficient engineering models that are evaluated many times to find an optimal solution. A recent article compared the state-of-the-art Gauss-curl hybrid (GCH) model to historical data of three offshore wind farms. Two points of model discrepancy were identified therein: poor wake predictions for turbines experiencing a lot of wakes and wake interactions between two turbines over long distances. The present article addresses those two concerns and presents the cumulative-curl (CC) model. Comparison of the CC model to high-fidelity simulation data and historical data of three offshore wind farms confirms the improved accuracy of the CC model over the GCH model in situations with large wake losses and wake recovery over large inter-turbine distances. Additionally, the CC model performs comparably to the GCH model for single- and fewer-turbine wake interactions, which were already accurately modeled. Lastly, the CC model has been implemented in a vectorized form, greatly reducing the computation time for many wind conditions. The CC model now enables reliable simulation studies for both small and large offshore wind farms at a low computational cost, thereby making it an ideal candidate for wake-steering optimization and layout optimization.

Wind turbines in wind farms often operate in waked or partially waked conditions, which can greatly increase the fatigue damage. Some fatigue considerations may be included, but currently a full fidelity analysis of the increased damage a turbine experiences in a wind farm is not considered in wind farm layout optimization because existing models are too computationally expensive. In this paper, we present a model to calculate fatigue damage caused by partial waking on a wind turbine that is computationally efficient and can be included in wind farm layout optimization. The model relies on analytic velocity, turbulence, and loads models commonly used in farm research and design, and captures some of the effects of turbulence on the fatigue loading. Compared to high-fidelity simulation data, our model accurately predicts the damage trends of various waking conditions. We also perform example wind farm layout optimizations with our presented model in which we maximize the annual energy production (AEP) of a wind farm while constraining the damage of the turbines in the farm. The results of our optimization show that the turbine damage can be significantly reduced, more than 10 %, with only a small sacrifice of around 0.07 % to the AEP, or the damage can be reduced by 20 % with an AEP sacrifice of 0.6 %.

Layout design and wake steering through wind plant control are each important and complex components in the design and operation of modern wind plants. They are currently optimized separately, but as more and more wind plants implement wake steering as their primary form of operation, there are increasing needs 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 the very large solution space. In this paper we present a revolutionary method that enables the coupled optimization of wind plant layout and wake steering with no additional computational expense than a traditional layout optimization. This is accomplished through the development of a geometric relationship between turbines to find an approximate optimal yaw angle, bypassing the need for either a nested or coupled wind plant control optimization. The method we present in this paper provides a significant and immediate improvement to wind plant design by enabling the co-design of turbine layout and yaw control for wake steering. A small co-designed plant shown in this paper produces 0.8 % more energy than its sequentially designed counterpart, and we expect larger comparative gains for larger plants with more turbines. This additional energy production comes with no additional infrastructure, turbine hardware, or control software; it is a free consequence of optimizing the turbine layout and yaw control together, resulting in millions of dollars of additional revenue for the wind plants of the future.

A Computational Fluid Dynamics (CFD) analysis of air entrapment and structural response during flat plate entry to water is presented. Slamming loads remain of concern for the design of safe and efficient ships and offshore structures to ensure structural integrity during extreme. Besides ships with large bow flare or horizontal stern planes, slamming events also occur for fast small craft with stepped hulls. Ditching of airplanes and vehicle wading represent non-marine applications. The advance of computational methods in engineering has enabled fluid-structure interaction (FSI) simulations for slamming. A crucial task of solving the coupled fluid and structural problem is the accurate resolution of free surface dynamics and phase interactions between water and air. Numerical ventilation on the bottom plating can arise due to discretization issues and curtail the resolution of physical aeration effects. The study at hand was based on a Finite-Volume (FV) method and the numerical solution of Reynolds-averaged Navier-Stokes (RANS) equations. Emphasis was laid on numerical techniques to contain numerical ventilation whilst limiting the increase in computational cost. In doing so, adaptive discretization schemes were employed. Namely, model-based adaptive mesh refinement (AMR) and time stepping for both motions of bodies (rigid and elastic) and the free surface. Additionally, the underlying Volume of Fluid (VoF) method was enhanced through consideration of slip between water and air to improve air entrapment predictions. Comparison was drawn to a novel experimental analysis for which both structural responses and high-resolution imagery of aeration were available. It was demonstrated that above enhancements not only lead to better capturing of air entrapment and reduced numerical ventilation, but also offered more flexible modeling concepts and potential performance gains.

Annual energy production (AEP) is often the objective function in wind plant layout optimization studies. The conventional method to compute AEP for a wind farm is to first evaluate power production for each discrete wind direction and speed using either computational fluid dynamics simulations or engineering wake models. The AEP is then calculated by weighted-averaging (based on the wind rose at the wind farm site) the power produced across all wind directions and speeds. We propose a novel formulation for time-averaged wake velocity that incorporates an analytical integral of a wake deficit model across every wind direction. This approach computes the average flow field more efficiently, and layout optimization is an obvious application to exploit this benefit. The clear advantage of this new approach is that the layout optimization produces solutions with comparable AEP performance yet is completed 2 orders of magnitude faster. The analytical integral and the use of a Fourier expansion to express the wind speed and wind direction frequency create a relatively smooth solution space for the gradient-based optimizer to excel in comparison to the existing weighted-averaging power calculation.

This paper presents a model to incorporate the secondary effects of wake steering in large arrays of turbines. Previous models have focused on the aerodynamic interaction of wake steering between two turbines. The model proposed in this paper builds on these models to include yaw-induced wake recovery and secondary steering seen in large arrays of turbines when wake steering is performed. Turbines operating in yaw-misaligned conditions generate counter-rotating vortices that entrain momentum and contribute to the deformation and deflection of the wake at downstream turbines. Rows of turbines can compound the effects of wake steering that benefit turbines far downstream. This model quantifies these effects and demonstrates that wake steering has greater potential to increase the performance of a wind farm due to these counter-rotating vortices especially for large rows of turbines. This is validated using numerous large-eddy simulations for three-turbine, five-turbine, and wind farm scenarios.

Wind energy is recognized worldwide as cost-effective and environmentally friendly and is among the fastest-growing sources of electrical energy. To further decrease the cost of wind energy, wind turbines are being designed at ever larger scales, which is challenging due to greater structural loads and deflections. Large-scale systems such as modern wind turbines increasingly require a control co-design approach, whereby the system design and control design are performed in a more integrated fashion. We overview a two-bladed downwind morphing rotor concept that is expected to lower the cost of energy at wind turbine sizes beyond 13 megawatts (MW) compared with continued upscaling of traditional three-bladed upwind rotor designs. We describe an aero-structural-control co-design process that we have used in designing such extreme-scale wind turbines, and we discuss how we were able to achieve a 25% reduction in levelized cost of energy for our final turbine design compared to a conventional upwind three-bladed rotor design.

The physics models commonly used during wind farm layout optimization include simplifying assumptions that can alter the design space compared to reality and higher-fidelity simulations. Some characteristics of these simple models may negatively influence the resulting layouts. In this paper, we perform wind farm layout optimization using a simple engineering wake model and then simulate the base and optimized layouts using large-eddy simulation (LES) to confirm that the layout was actually improved and not just an artifact of the simplifying assumptions in the low-fidelity wind farm simulation. We begin by describing the physics models used, including changes specific for use with gradient-based optimization. We then compare the simple model's output to previously published model and LES results. Using the simple models described, we performed gradient-based wind farm layout optimization using exact gradients. We optimized the wind farm twice, with high- and low-turbulence intensity (TI), respectively. We then recalculated annual energy production (AEP) using LES for the original and optimized layouts in each TI scenario and compared the results. For the high-TI case, the simple model predicted an AEP improvement of 7.7 %, while the LES reported 9.3 %. For the low-TI case, the simple model predicted a 10.0 % AEP improvement, while the LES reported 10.7 %. We concluded that the improvements found by optimizing with the simple model are not just an artifact of the model, but are real improvements assuming appropriate wind rose fidelity. We also found that the optimization did take advantage of the number of wind directions used, often aligning wind turbines in directions that were not included in the simulation. We found that, for the case studied, at least 50 wind directions are needed to avoid having the number of wind directions in the optimization significantly impact the optimized results. Future work should investigate further LES comparisons and wind rose fidelity in wind speed.

A new sub-scale field-prototype design solution is developed to realize the dynamics, structural response, and distributed loads (gravitational, aerodynamic, centrifugal) that are characteristic of a full-scale large, modern wind turbine rotor. Prior work in sub-scale wind turbine testing has focused on matching aerodynamic/aero-elastic characteristics of full-scale rotors at wind tunnel scale. However, large-scale rotor designs must expand beyond this limited set of scaling parameters for cost-effective prototyping and meet strict requirements for structural safety for field testing. The challenge lies in producing a structural design meeting two competing objectives: novel scaling objectives that prescribe the sub-scale blade to have low mass and stiffness; and traditional structural safety objectives that drive the design to have higher stiffness and mass. A 20% gravo-aeroelastically scaled wind turbine blade is developed successfully that satisfies these competing objectives. First, it achieved close agreement for non-dimensional tip deflection and flap-wise blade frequency (both within 2.1%) with a blade mass distribution constrained to produce target gravitational and centrifugal loads. Second, the entire blade structure was optimized to ensure a safe, manufacturable solution meeting strict strength requirements for a testing site that can experience up to 45 m / s wind gusts. The prototype-scale blade was fabricated and successfully proof-load tested.

Annual energy production (AEP) is often the objective function in wind plant layout optimization studies. The conventional method to compute AEP for a wind farm is to first evaluate power production for each wind direction and speed using either computational fluid dynamics simulations or engineering wake models. The AEP is then calculated by weighted-averaging (based on the wind rose at the wind farm site) the power produced across all wind directions. We propose a novel formulation for time-averaged wake velocity that incorporates an analytical integral of a wake deficit model across every wind direction. This approach computes the average flow field more efficiently, and layout optimization is an obvious application to exploit this benefit. The clear advantage of this new approach is that the layout optimization produces solutions with comparable AEP performance yet is completed about 700 times faster. The analytical integral and the use of a Fourier expansion to express the wind speed and wind direction frequency create a more smooth solution space for the gradient-based optimizer to excel compared with the discrete nature of the existing weighted-averaging power calculation.

We examine the effect of rotor design choices on the power capture and structural loading of each major wind turbine component. A harmonic model for structural loading is derived from simulations using the National Renewable Energy Laboratory (NREL) aeroelastic code FAST to reduce computational expense while evaluating design trade-offs for rotors with radii greater than 100 m. Design studies are performed, which focus on blade aerodynamic and structural parameters as well as different hub configurations and nacelle placements atop the tower. The effects of tower design and closed-loop control are also analyzed. Design loads are calculated according to the IEC design standards and used to create a mapping from the harmonic model of the loads and quantify the uncertainty of the transformation. Our design studies highlight both industry trends and innovative designs: we progress from a conventional, upwind, three-bladed rotor to a rotor with longer, more slender blades that is downwind and two-bladed. For a 13 MW design, we show that increasing the blade length by 25 m, while decreasing the induction factor of the rotor, increases annual energy capture by 11 % while constraining peak blade loads. A downwind, two-bladed rotor design is analyzed, with a focus on its ability to reduce peak blade loads by 10 % per 5∘ of cone angle and also reduce total blade mass. However, when compared to conventional, three-bladed, upwind designs, the peak main-bearing load of the upscaled, downwind, two-bladed rotor is increased by 280 %. Optimized teeter configurations and individual pitch control can reduce non-rotating damage equivalent loads by 45 % and 22 %, respectively, compared with fixed-hub designs.

Wind turbines in a wind farm typically operate individually to maximize their own performance and do not take into account information from nearby turbines. To enable cooperation to achieve farm-level objectives, turbines will need to use information from nearby turbines to optimize performance, ensure resiliency when other sensors fail, and adapt to changing local conditions. A key element of achieving a more efficient wind farm is to develop algorithms that ensure reliable, robust, real-time, and efficient operation of wind turbines in a wind farm using local sensor information that is already being collected, such as supervisory control and data acquisition (SCADA) data, local meteorological stations, and nearby radars/sodars/lidars. This article presents a framework for developing a cooperative wind farm that incorporates information from nearby turbines in real time to better align turbines in a wind farm. SCADA data from multiple turbines can be used to make better estimates of the local inflow conditions at each individual turbine. By incorporating measurements from multiple nearby turbines, a more reliable estimate of the wind direction can be obtained at an individual turbine. The consensus-based approach presented in this paper uses information from nearby turbines to estimate wind direction in an iterative way rather than aggregating all the data in a wind farm at once. Results indicate that this estimate of the wind direction can be used to improve the turbine's knowledge of the wind direction. This estimated wind direction signal has implications for potentially decreasing dynamic yaw misalignment, decreasing the amount of time a turbine spends yawing due to a more reliable input to the yaw controller, increasing resiliency to faulty wind-vane measurements, and increasing the potential for wind farm control strategies such as wake steering.

Methods of turbine wake modeling are being developed to more accurately account for spatially variant atmospheric conditions within wind farms. Most current wake modeling utilities are designed to apply a uniform flow field to the entire domain of a wind farm. When this method is used, the accuracy of power prediction and wind farm controls can be compromised depending on the flow-field characteristics of a particular area. In an effort to improve strategies of wind farm wake modeling and power prediction, FLOw Redirection and Induction in Steady State (FLORIS) was developed to implement sophisticated methods of atmospheric characterization and power output calculation. In this paper, we describe an adapted FLORIS model that features spatial heterogeneity in flow-field characterization. This model approximates an observed flow field by interpolating from a set of atmospheric measurements that represent local weather conditions. The objective of this method is to capture heterogeneous atmospheric effects caused by site-specific terrain features, without explicitly modeling the geometry of the wind farm terrain. The implemented adaptations were validated by comparing the simulated power predictions generated from FLORIS to the actual recorded wind farm output from the supervisory control and data acquisition (SCADA) recordings and large eddy simulations (LESs). When comparing the performance of the proposed heterogeneous model to homogeneous FLORIS simulations, the results show a 14.6 % decrease for mean absolute error (MAE) in wind farm power output predictions for cases using wind farm SCADA data and a 18.9 % decrease in LES case studies. The results of these studies also indicate that the efficacy of the proposed modeling techniques may vary with differing site-specific operational conditions. This work quantifies the accuracy of wind plant power predictions under heterogeneous flow conditions and establishes best practices for atmospheric surveying for wake modeling.

Wind turbine wake models typically require approximations, such as wake superposition and deflection models, to accurately describe wake physics. However, capturing the phenomena of interest, such as the curled wake and interaction of multiple wakes, in wind power plant flows comes with an increased computational cost. To address this, we propose a new hybrid method that uses analytical solutions with an approximate form of the Reynolds-averaged Navier–Stokes equations to solve the time-averaged flow over a wind plant. We compare results from the solver to supervisory control and data acquisition data from the Lillgrund wind plant obtaining wake model predictions which are generally within 1 standard deviation of the mean power data. We perform simulations of flow over the Columbia River Gorge to demonstrate the capabilities of the model in complex terrain. We also apply the solver to a case with wake steering, which agreed well with large-eddy simulations. This new solver reduces the time – and therefore the related cost – it takes to simulate a steady-state wind plant flow (on the order of seconds using one core). Because the model is computationally efficient, it can also be used for different applications including wake steering for wind power plants and layout optimization.

Optimizing turbine layout is a challenging problem that has been extensively researched in the literature. However, optimizing the number of turbines within a given boundary has not been studied as extensively and is a difficult problem because it introduces discrete design variables and a discontinuous design space. An essential step in performing wind power plant layout optimization is to define the objective function, or value, that is used to express what is valuable to a wind power plant developer, such as annual energy production, cost of energy, or profit. In this paper, we demonstrate the importance of selecting the appropriate objective function when optimizing a wind power plant in a land-constrained site. We optimized several different wind power plants with different wind resources and boundary sizes. Results show that the optimal number of turbines varies drastically depending on the objective function. For a simple, one-dimensional, land-based scenario, we found that a wind power plant optimized for minimal cost of energy produced just 72 % of the profit compared to the wind power plant optimized for maximum profit, which corresponded to a loss of about USD 2 million each year. This paper also compares the performance of several different optimization algorithms, including a novel repeated-sweep algorithm that we developed. We found that the performance of each algorithm depended on the number of design variables in the problem as well as the objective function.

In this paper we present the Serial-Refine method for quickly finding the optimal yaw angles in wake steering. The method optimizes turbine angles serially from upstream to downstream using a small number of candidate angles. The presented results show that Serial-Refine finds solutions that are at least as good as former conventional optimization approaches but that require much less computation time.

This work focuses on minimizing the computational cost of steady-state wind power plant flow simulations that take into account wake steering physics. We present a simple wake solver with a computational cost on the order of seconds for large wind plants. The solver uses a simplified form of the Reynolds-averaged Navier-Stokes equations to obtain a parabolic equation for the wake deficit of a wind plant. We compare results from the model to supervisory control and data acquisition (SCADA) from the Lillgrund wind plant; good agreement is obtained. Results for the solver in complex terrain are also shown. Finally, the solver is demonstrated for a case with wake steering showing good agreement with power reported by large-eddy simulations. This new solver minimizes the time – and therefore the related cost – it takes to conduct a steady-state wind plant flow simulation to about a second on a personal laptop. This solver can be used for different applications including wake steering for wind power plants and layout optimization, and it will soon be available within the FLOw Redirection and Induction in Steady State (FLORIS) framework.

In this paper, we present a reinforcement-learning-based distributed approach to wind farm energy capture maximization using yaw-based wake steering. In order to maximize the power output of a wind farm, individual turbines can use yaw misalignment to deflect their wakes away from downstream turbines. Although using model-based methods to achieve yaw misalignment is one option, a model-free method might be better suited to incorporate changing conditions and uncertainty. We propose an algorithm that adapts concepts of temporal difference reinforcement learning distributed to a multiagent environment that empowers individual turbines to optimize overall wind farm output and react to unforeseen disturbances.

This paper introduces a novel approach for estimating the wind field over an entire wind farm using a mobile sensor to collect limited amounts of data. The proposed method estimates the boundary conditions of a simplified turbine wake model by computing the model sensitivity matrix and using a recursive least-squares algorithm to recover the model parameters from the wind field measurements. To address the fact that it is not practical to take measurements across the entire wind farm, the proposed method classifies each area on the map based on its sensitivity to parameter variations. This classification is then used to generate a suitable path for a mobile sensor, which is charged with collecting data for the recursive least-squares algorithm. The proposed framework can successfully estimate the model boundary conditions using just the measurements collected along the path of the mobile sensor. This preliminary result paves the way for using real-time wind field estimates for the coordinated control of all the turbines within a wind farm.

Control of energy systems in buildings is an area of expanding interest as the importance of energy efficiency, occupant health, and comfort increases. The objective of this study was to demonstrate the effectiveness of a novel predictive steady-state optimal control method in minimizing the economic costs associated with operating a building. Specifically, the cost of utility consumption and the cost of loss productivity due to occupant discomfort were minimized. This optimization was achieved through the use of steady-state predictions and component level economic objective functions. Specific objective functions were developed and linear models were identified from data collected from a building on Texas A&M University’s campus. The building consists of multiple zones and is serviced by a variable air volume, chilled water air handling unit. The proposed control method was then co-simulated with MATLAB and EnergyPlus to capture effects across multiple time-scales. Simulation results show improved comfort performance and decreased economic cost over the currently implemented building control, minimizing productivity loss and utility consumption. The potential for more serious consideration of the economic cost of occupant discomfort in building control design is also discussed.

Methods of turbine wake modeling are being developed to more accurately account for spatially variant atmospheric conditions within wind farms. Most current wake modeling utilities are designed to apply a uniform flow field to the entire domain of a wind farm. When this method is used, the accuracy of power prediction and wind farm controls can be compromised depending on the flow-field characteristics of a particular area. In an effort to improve strategies of wind farm wake modeling and power prediction, FLOw Redirection and Induction in Steady State (FLORIS) was developed to implement sophisticated methods of atmospheric characterization and power output calculation. In this paper, we describe an adapted FLORIS model that features spatial heterogeneity in flow-field characterization. This model approximates an observed flow field by interpolating from a set of atmospheric measurements that represent local weather conditions. The adaptations were validated by comparing the simulated power predictions generated from FLORIS to the actual recorded wind farm output from the Supervisory Control And Data Acquisition (SCADA) recordings. This work quantifies the accuracy of wind plant power predictions under heterogeneous flow conditions and establishes best practices for atmospheric surveying for wake modeling.

Background and Purpose: Patients with severe, progressive multiple sclerosis (MS) have complex physical and psychosocial needs, typically over several years. Few treatment options are available to prevent or delay further clinical worsening in this population. The objective was to develop an evidence-based clinical practice guideline for the palliative care of patients with severe, progressive MS. Methods: This guideline was developed using the Grading of Recommendations Assessment, Development and Evaluation methodology. Formulation of the clinical questions was performed in the Patients–Intervention–Comparator–Outcome format, involving patients, carers and healthcare professionals (HPs). No uniform definition of severe MS exists: in this guideline, constant bilateral support required to walk 20 m without resting (Expanded Disability Status Scale score >6.0) or higher disability is referred to. When evidence was lacking for this population, recommendations were formulated using indirect evidence or good practice statements were devised. Results: Ten clinical questions were formulated. They encompassed general and specialist palliative care, advance care planning, discussing with HPs the patient's wish to hasten death, symptom management, multidisciplinary rehabilitation, interventions for caregivers and interventions for HPs. A total of 34 recommendations (33 weak, 1 strong) and seven good practice statements were devised. Conclusions: The provision of home-based palliative care (either general or specialist) is recommended with weak strength for patients with severe, progressive MS. Further research on the integration of palliative care and MS care is needed. Areas that currently lack evidence of efficacy in this population include advance care planning, the management of symptoms such as fatigue and mood problems, and interventions for caregivers and HPs.

This paper presents a model to incorporate the secondary effects of wake steering in large arrays of turbines. Previous models have focused on the aerodynamic interaction of wake steering between two turbines. The model proposed in this paper builds on these models to include yaw-induced wake recovery and secondary steering seen in large arrays of turbines when wake steering is performed. Turbines operating in yaw misaligned conditions generate counter-rotating vortices that entrain momentum and contribute to the deformation and deflection of the wake at downstream turbines. Rows of turbines can compound the effects of wake steering that benefit turbines far downstream. This model quantifies these effects and demonstrates that wake steering has greater potential to increase the performance of a wind farm due to these counter-rotating vortices especially for large rows of turbines. This is validated using numerous large eddy simulations for two-turbine, three-turbine, five-turbine, and wind farm scenarios.

In this paper, we present a proof-of-concept distributed reinforcement learning framework for wind farm energy capture maximization. The algorithm we propose uses Q-Learning in a wake-delayed wind farm environment and considers time-varying, though not yet fully turbulent, wind inflow conditions. These algorithm modifications are used to create the Gradient Approximation with Reinforcement Learning and Incremental Comparison (GARLIC) framework for optimizing wind farm energy capture in time-varying conditions, which is then compared to the FLOw Redirection and Induction in Steady State (FLORIS) static lookup table wind farm controller baseline.