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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Wind plant wake losses: Disconnect between turbine actuation and control of plant wakes with engineering wake models

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.

Scott, Ryan (ORCID:0000000328107574)↗
DOE OSTI2020

Modelling and assessing the near-wake representation and turbulence behaviour of control-oriented wake models

Due to the interaction between the wake of an upstream turbine on a downstream turbine, power losses and increased fatigue loads occur. By yawing the upstream turbine with regard to the wind direction, one can potentially reduce the power losses of the downstream turbine and reduce the fatigue loads. The evolution of the wake depends on the pressure gradient within the near-wake region and the turbulent kinetic energy and must be incorporated in existing wake steering algorithms to provide an accurate estimation of the wake flow. This paper will show a first approach to implement a near-wake model and a turbulence model in the curled wake model within the controls-oriented framework FLORIS. The near-wake model is based on an analytical expression of the velocity profile to model the pressure gradient. Furthermore, two turbulence models are incorporated within the curled wake model based on a Gaussian-distribution and a mixing length formulation. The adapted curled wake model is then assessed with the measurement data acquired in the wind tunnel at ForWind – University of Oldenburg. The evaluation of the models show good agreement for the velocity deficit and representation of the near-wake region. Furthermore, the turbulent kinetic energy behaved as expected in comparison to other work, showing a ring of high turbulent kinetic energy at non-yawed condition which is deflected to a curled shape at large yaw angles with the turbulence model based on a mixing length formulation.

FLORIS↗
DOE OSTI2022

Data-driven wind turbine wake modeling via probabilistic machine learning

Wind farm design primarily depends on the variability of the wind turbine wake flows to the atmospheric wind conditions and the interaction between wakes. Physics-based models that capture the wake flow field with high-fidelity are computationally very expensive to perform layout optimization of wind farms, and, thus, data-driven reduced-order models can represent an efficient alternative for simulating wind farms. In this work, we use real-world light detection and ranging (LiDAR) measurements of wind-turbine wakes to construct predictive surrogate models using machine learning. Specifically, we first demonstrate the use of deep autoencoders to find a low-dimensional latent space that gives a computationally tractable approximation of the wake LiDAR measurements. Then, we learn the mapping between the parameter space and the (latent space) wake flow fields using a deep neural network. Additionally, we also demonstrate the use of a probabilistic machine learning technique, namely, Gaussian process modeling, to learn the parameter-space-latent-space mapping in addition to the epistemic and aleatoric uncertainty in the data. Finally, to cope with training large datasets, we demonstrate the use of variational Gaussian process models that provide a tractable alternative to the conventional Gaussian process models for large datasets. Furthermore, we introduce the use of active learning to adaptively build and improve a conventional Gaussian process model predictive capability. Overall, we find that our approach provides accurate approximations of the wind-turbine wake flow field that can be queried at an orders-of-magnitude cheaper cost than those generated with high-fidelity physics-based simulations.

Deep neural networks↗
DOE OSTI2021

The curled wake model: a three-dimensional and extremely fast steady-state wake solver for wind plant flows

Abstract. 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.

17 WIND ENERGY↗
DOE OSTI2021

Design and analysis of a wake model for spatially heterogeneous flow

Abstract. 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.

17 WIND ENERGY↗
DOE OSTI2020

Comparison of modular analytical wake models to the Lillgrund wind plant

Efficient and accurate wake models are required for wind plant performance modeling and the suite of engineering processes that support wind plant layout, control, and monitoring. Although many analytical and engineering wake models with low computational costs have been proposed, their ability to represent the power production of large wind plants in a wide range of atmospheric conditions is not completely understood. The following validation study reviews the underlying theory for analytical wake models, outlines quality control procedures for observational data, and compares model results with observational data from the Lillgrund Wind Plant. Lillgrund makes a valuable case study for wake modeling because of its regular arrangement and the relatively close spacing of constituent wind turbines, which lead to regular and significant wake interactions within the wind plant and the development of deep array flow conditions. Formulations for the velocity deficit, wake-added turbulence, and wake superposition methods are considered in a modular sense, yielding many possible configurations to represent wind turbine wakes, of which seven are examined in detail. Velocity deficit models that account for flow conditions in the near wake are better able to reproduce power production for wind turbines in the transitional region of the wind plant, where wind turbines experience as many as five wakes from upstream turbines. Finally, in the deep array, where power production reaches asymptotic values and wake statistics become quasi-periodic, wake superposition schemes become the largest driver in error reduction; using the linear or maximum wake superposition methods can reduce the relative root mean square error by as much as 40% in the deep array.

17 WIND ENERGY↗
DOE OSTI2024

Comparison of steady-state analytical wake models implemented in wind farm analysis software

A common set of mathematical wind turbine wake models are implemented in a few, well-adopted computational tools for wind farm wake modelling. Although the referenced mathematical formulations are common, implementation details may lead to differences in results. This study presents a systematic comparison of the implementation of mathematical wake models in open source, Python-based wind turbine wake modelling software, and a set of the models are directly compared. Despite aligning only the mathematical model parameters and retaining the default computational model parameters, good agreement is found across most of the model implementations, and additional agreement is expected upon further parameters alignment.

17 WIND ENERGY↗
DOE OSTI2022

A time‐varying formulation of the curled wake model within the FAST.Farm framework

Abstract In this article, we present a time‐varying formulation of the curled wake model that we implemented in FAST.Farm. The curled wake model, originally developed for steady‐state conditions, is used to produce realistic wake profiles behind a wind turbine in yawed (or skewed) conditions. We begin by introducing the key elements of the FAST.Farm framework. Then, after briefly summarizing the original wake dynamics formulation of FAST.Farm based on a polar wake profile, we present the new time‐varying formulation of the curled wake model, compare the two, and highlight the differences with the original curled wake model. After discussing some implementation details, we present different applications with increasing levels of complexity: single turbine with uniform and turbulent inflow, fixed and transient yaw, and multiple turbines. We verify our results using the original FAST.Farm implementation and large‐eddy simulations. The results with the new curled wake model are improved compared to the original implementation, as they include cross‐flow velocities and wake asymmetry. Yet, large‐eddy simulation results show a more pronounced lateral convection of the wake and a stronger concentration of vorticity at the top vortex. The new curled wake implementation in FAST.Farm should enable the calculation of not only generator power but also wind turbine structural loads for applications involving intentional or unintentional skewed flow and wind‐farm control involving wake steering.

17 WIND ENERGY↗
DOE OSTI2020

Toward flow control: An assessment of the curled wake model in the FLORIS framework

In this work, a new controls-oriented wake model is modified and compared to an analytical Gaussian wake model, high-fidelity simulation data, and experimental wind tunnel campaign. This model, called the curled wake model, captures a wake phenomenon that occurs behind yawed turbines, modeled as a collection of vortices shed from the rotor plane. Through turbine simulations, these vortices are shown to have a significant impact on the prediction of the wake steering's performance. Overall, the results support the concept of secondary steering, or a yawed turbine's ability to deflect the wake of a downstream turbine, and suggest that future turbine wake studies and yaw optimizations should include the curled wake phenomenon.

17 WIND ENERGY↗
DOE OSTI2026

Benchmarking of three DWM-based wake models at below-rated wind speeds

Wind turbine wake models are essential tools for predicting power losses and structural loads in wind farms. Among these, the dynamic wake meandering (DWM) model, included as a recommended approach in the International Electrotechnical Commission design standard, is a widely used engineering-fidelity method that balances accuracy and computational cost. This study compares the performance of three DWM-based wake model implementations (from the Technical University of Denmark, the National Renewable Energy Laboratory, and the Institute for Energy Technology) under below-rated wind speed conditions. Model predictions of wake flow, power output, and structural loads for a four-turbine row are evaluated across different ambient turbulence levels and wind-direction misalignments and compared against high-fidelity large-eddy simulation results. All three models captured the overall wake evolution and mean turbine performance with reasonable accuracy; their predicted time-averaged thrust and power were typically within 5 %–10 % of the large-eddy simulation benchmark. However, notable differences emerged in wake structure and unsteady load predictions, with discrepancies increasing for turbines further downstream. These differences highlight the importance of modelling choices such as wake summation and turbulence treatment, which strongly influence power-deficit and fatigue-load predictions. Comparison with large-eddy simulations reveals each approach's strengths and weaknesses, indicating where improvements are needed. Overall, the findings point to specific refinements for DWM models to improve their fidelity, ultimately enabling more robust wake predictions for wind farm design and operation.

17 WIND ENERGY↗
DOE OSTI2020

The curled wake model: equivalence of shed vorticity models

In this work, we explore the spanwise velocities in the wake of a yawed wind turbine. In the curled wake model, these motions are induced by a collection of vortices shed from the rotor plane. The direction of the vorticity generated by yaw is aligned with the main flow (streamwise) direction. The streamwise vorticity induces velocities in the spanwise directions. These are the motions responsible for creating the curled wake mechanism. In this work, we explore a more accurate formulation for this mechanism, using a vortex cylinder. Under certain assumptions, the new and original curled wake models yield the same mathematical formulation. Also, both models predict an elliptic distribution of vortex strength, where the main difference is the location of the vortices.

17 WIND ENERGY↗
DOE OSTI2023

A Three-Dimensional, Analytical Wind Turbine Wake Model: Flow Acceleration, Empirical Correlations, and Continuity

A new, three-dimensional, analytical, steady-state wake model is presented that includes local flow acceleration near the rotor, improving the wake description compared to existing models. Wake structures such as the momentum deficit and regions of accelerated flow are concisely described with compound and normal Gaussian functions. Large-eddy simulations (LES) are used as training data to develop the model using two in-line turbines under various inflow conditions parameterized by hub-height wind speed and turbulence intensity. Mass conservation is considered by fixing two components of the wake velocity model and optimizing the third to best satisfy continuity; after which, the model performs comparably if not better than existing work with regards to both relative error and mass consistency. The final model demonstrates a high degree of flexibility, making use of empirical correlations to scale across different inflow conditions. The inclusion of these effects is capable of revealing unused opportunities for enhanced power generation by aligning wake trajectories with these regions of accelerated flow.

modeling↗
DOE OSTI2026

Introduction to and comparison of deep learning and optimization approaches to analytical wake modeling of a tilted wind turbine

This paper introduces innovative optimization and deep learning techniques to enhance the prediction of complex wake dynamics in the downstream wind velocity of tilted wind turbines. Traditional methods for calibrating the Bastankhah wake model often lead to increased errors in wind velocity distribution due to overfitting of the local wake characteristics. To address this issue, we propose an additional global optimization step to reduce errors in wind velocity predictions with respect to various wake parameters. Despite this improvement, the Bastankhah model's axisymmetric Gaussian wake shape limits its accuracy for complex wake structures. Therefore, we also propose a deep learning approach, which demonstrates promising results by accurately modeling complex wake shapes across a broader range of tilt angles with minimal computational cost. The deep learning approach achieves near-identical predictions to high-fidelity large-eddy simulations, representing a promising advancement in wake modeling.

17 WIND ENERGY↗
DOE OSTI2023

Comparison of three DWM-based wake models at above-rated wind speeds

In this study we investigate three mid-fidelity wind turbine wake models based on the dynamic wake meandering (DWM) model principle, and compare their performance with a reference dataset, produced with large-eddy simulations using the actuator line model. The models are compared with respect to flow field, power, and loads on a row of four 5MW reference turbines experiencing above-rated wind conditions. In general, the DWM models show fairly good agreement with large-eddy simulation for the time-averaged flow fields, blade forces and power, with increasing differences along the turbine row. Also when comparing fatigue loads of blade root moments, the differences between the models increase further into the row, with deviations up to 25 % of the reference case. However, while the development in blade root moment fatigue along the turbine row is predominantly driven by the energy content at the frequency corresponding to the turbine's rotational period (1 P ) for the DWM models, the large-eddy simulation results suggest that the key drivers for the blade root and tower loads are the increase in meandering and energy at higher frequencies (> 1 P ) deeper into the turbine row. For the tower loads, the DWM models highly underestimate the fatigue for the waked turbines. From these results, we suggest priorities for future model developments so that robust model implementations can be used in wind farm design and operation.

17 WIND ENERGY↗
DOE OSTI2023

FLORIS v3.5 Wake Modeling and Wind Farm Controls Software [SWR-17-43 and SWR-14-20]

FLORIS is a controls-focused wind farm simulation software incorporating steady-state engineering wake models into a performance-focused Python framework. It has been in active development at NREL since 2013 and the latest release is FLORIS v3.5.Online documentation is available at https://nrel.github.io/floris. The software is in active development and engagement with the development team is highly encouraged. If you are interested in using FLORIS to conduct studies of a wind farm or extending FLORIS to include your own wake model, please join the conversation in GitHub Discussions! https://www.nrel.gov/wind/floris.html

Fleming, Paul↗
DOE OSTI2025

Gaussian FLOWERS: Wind-rose-based analytical integration of Gaussian wake model for extremely fast AEP estimation

A major cost in the study of wind farm layout optimization is the repeated evaluation of the annual energy production (AEP). The current approach to estimating AEP requires a large set of flow simulations to be performed that cover each discrete wind speed and direction combination contained within the wind rose, followed by a probability-weighted sum of the power production resulting from each simulation. Even with inexpensive engineering wake models, this numerical integration scheme can lead to high computational costs. In this paper, we derive an analytical formulation for estimating farm AEP across every wind direction, based on a Gaussian wake velocity model, which reduces the number of wind farm simulations to a single function evaluation. As a result, we find that the Gaussian-FLOWERS approach reduces the time for AEP calculations by more than two orders of magnitude with a small trade-off in accuracy when compared to a conventional approach. This massive reduction in computation cost is useful to reduce overall costs in wind farm layout optimization studies.

17 WIND ENERGY↗
DOE OSTI2022

FLOW Estimation and Rose Superposition (FLOWERS): an integral approach to engineering wake models

Abstract. 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.

17 WIND ENERGY↗
DOE OSTI2023

Addressing deep array effects and impacts to wake steering with the cumulative-curl wake model

Abstract. 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.

17 WIND ENERGY↗