A double-Gaussian wake model considering yaw misalignment effects on wind turbine loads

A double-Gaussian wake model considering yaw misalignment effects on wind turbine loads

A Double-Gaussian Wake Model Considering Yaw Misalignment Effects on Wind Turbine Loads

As the world accelerates its transition to renewable energy, accurately modeling the complex aerodynamics of wind turbines becomes increasingly crucial. One critical aspect is understanding the wake effects generated by individual turbines within a wind farm, which can significantly impact the performance and structural loads of downstream turbines.

Gaussian wake models have emerged as a popular analytical approach to predict the velocity deficit and wake characteristics behind wind turbines. These models rely on a Gaussian distribution to describe the wake’s velocity profile, offering a computationally efficient alternative to resource-intensive computational fluid dynamics (CFD) simulations. However, traditional Gaussian models often fall short in capturing the effects of yaw misalignment, where the turbine rotor is intentionally angled relative to the prevailing wind direction.

Yaw misalignment has gained attention as an effective wake steering technique, allowing upstream turbines to deliberately deflect their wakes away from downstream units. This approach can enhance the overall energy production of a wind farm by minimizing the negative impacts of wake interactions. Accurately modeling these yaw-induced wake effects is essential for optimizing wind turbine and wind farm design, as well as for developing advanced control strategies.

In this article, we explore the development and validation of a double-Gaussian (DG) wake model that accounts for the effects of yaw misalignment on wind turbine loads. By building upon the foundational Gaussian wake theory and incorporating the impact of rotor yaw, this model aims to provide a more comprehensive and accurate representation of the complex wake dynamics within wind farms.

Wind Turbine Wake Modeling

The wake generated by a wind turbine is a critical factor in determining the energy production and structural loads experienced by downstream turbines within a wind farm. As the wind flows through the turbine rotor, it undergoes a complex set of aerodynamic interactions that result in a region of reduced wind speed and increased turbulence intensity downstream of the turbine.

Gaussian Wake Models

Analytical Gaussian wake models have become a popular approach for predicting the velocity deficit and characteristics of wind turbine wakes. These models assume that the wake’s velocity profile can be approximated by a Gaussian distribution, which simplifies the mathematical formulation and reduces computational complexity compared to more detailed CFD simulations.

The basic Gaussian wake model calculates the velocity deficit along the centerline of the wake, as well as the lateral and vertical spread of the wake, using a set of empirical parameters. While these models provide a reasonable approximation of the wake behavior, they often fail to capture the effects of yaw misalignment, where the turbine rotor is intentionally angled relative to the prevailing wind direction.

Yaw Misalignment Effects

Yaw misalignment has emerged as a promising wake steering strategy, where upstream turbines purposefully operate with a non-zero yaw angle to divert their wakes away from downstream turbines. This technique can effectively reduce the wake-induced velocity deficits and turbulence experienced by downstream units, thereby improving the overall energy production of a wind farm.

Accurately modeling the impact of yaw misalignment on wind turbine wakes is crucial for optimizing the design and operation of wind farms. The altered wake trajectory and altered wake recovery dynamics due to yaw can have significant implications on the structural loads and fatigue experienced by the downstream turbines.

Wind Turbine Loads

The loads experienced by wind turbines are a critical design consideration, as they directly influence the structural integrity, maintenance requirements, and ultimately, the lifetime of the turbine. Wake effects, including the velocity deficit and increased turbulence, can contribute to higher blade loads, tower loads, and drivetrain loads on downstream turbines.

Incorporating the effects of yaw misalignment on wind turbine loads is essential for developing robust and reliable wind farm designs. By accurately predicting the wake-induced loads, turbine manufacturers and wind farm operators can optimize the turbine design, layout, and control strategies to mitigate the negative impacts of wake interactions.

Double-Gaussian Wake Modeling

To address the limitations of traditional Gaussian wake models in capturing yaw misalignment effects, researchers have developed more sophisticated analytical models, such as the double-Gaussian (DG) wake model.

Model Formulation

The DG wake model builds upon the foundation of Gaussian wake theory by using a superposition of two Gaussian distributions to represent the wake velocity profile. This approach allows the model to capture the asymmetric nature of the wake, which is particularly important when considering the influence of yaw misalignment.

The DG model incorporates parameters that describe the wake center position, wake width, and velocity deficit, all of which can be modified to account for the effects of yaw angle. By adjusting these parameters, the model can accurately predict the altered wake trajectory and velocity recovery patterns observed in wind turbines operating with non-zero yaw angles.

Model Parameters

The key parameters in the DG wake model include:

  • Wake center position: The lateral and vertical displacement of the wake centerline, influenced by the turbine’s yaw angle.
  • Wake width: The lateral and vertical spread of the wake, affected by the yaw angle and turbulence intensity.
  • Velocity deficit: The reduction in wind speed within the wake region, dependent on the turbine’s thrust coefficient and yaw angle.

These parameters are derived from empirical correlations and validated against high-fidelity computational fluid dynamics (CFD) simulations or experimental data.

Model Validation

To ensure the reliability and accuracy of the DG wake model, it is essential to validate the model’s predictions against benchmark datasets. Researchers have leveraged comprehensive large eddy simulation (LES) results, which provide high-fidelity numerical simulations of the wake flow fields behind wind turbines operating at various yaw angles.

By comparing the DG model’s predictions to the LES benchmark data, researchers have been able to quantify the model’s performance in capturing the complex wake dynamics under yaw misalignment conditions. Statistical metrics, such as root mean square error (RMSE) and Pearson correlation coefficient (R), have been employed to assess the model’s accuracy in predicting the wake velocity profiles and trajectories.

Yaw Misalignment Considerations

The incorporation of yaw misalignment effects into the DG wake model has significant implications for the design, operation, and control of wind turbines and wind farms.

Aerodynamic Impacts

Yaw misalignment alters the aerodynamic interactions between the wind turbine rotor and the incoming flow, leading to changes in the wake characteristics. The wake’s lateral and vertical displacement, as well as its velocity recovery rate, are directly influenced by the turbine’s yaw angle.

By accurately modeling these yaw-induced wake effects, wind farm developers can optimize the turbine layout and control strategies to minimize the negative impacts of wake interactions on downstream turbines. This can lead to increased energy production and reduced structural loads, ultimately improving the overall performance and reliability of the wind farm.

Structural Impacts

The changes in wake dynamics due to yaw misalignment can also have significant implications for the structural loads experienced by wind turbines. The altered wake velocity profiles and increased turbulence intensity can result in higher blade, tower, and drivetrain loads on downstream turbines.

Incorporating the DG wake model’s yaw misalignment predictions into the turbine design process can help engineers develop more robust and reliable wind turbine structures. This, in turn, can lead to longer turbine lifetimes, reduced maintenance requirements, and lower overall costs for wind farm operators.

Optimization Strategies

The ability to accurately model the effects of yaw misalignment on wind turbine wakes opens up new opportunities for optimization strategies in wind farm design and operation. Wind farm controllers can leverage the DG wake model to dynamically adjust the yaw angles of individual turbines, effectively steering the wakes to maximize the energy production and minimize the structural loads across the entire wind farm.

Additionally, the DG wake model can be integrated into wind farm layout optimization algorithms, allowing developers to determine the optimal turbine positions and yaw angles to capture the maximum wind energy potential while mitigating the impacts of wake interactions.

Applications and Implications

The development and validation of the DG wake model with yaw misalignment considerations have significant implications for the advancement of wind energy technology and the ongoing transition towards a sustainable, low-carbon future.

Wind Farm Performance

By accurately predicting the wake effects and associated structural loads under various yaw conditions, the DG wake model can contribute to the design and optimization of wind farms, leading to improved energy production, reduced maintenance costs, and enhanced overall performance.

Wind farm operators can leverage the DG model to implement advanced control strategies, dynamically adjusting the yaw angles of individual turbines to steer wakes and maximize the energy capture across the entire wind farm. This can result in substantial improvements in the overall energy yield and profitability of wind energy projects.

Turbine Design Considerations

The insights gained from the DG wake model’s yaw misalignment analysis can inform the design process for wind turbines, particularly in terms of structural integrity and reliability. Wind turbine manufacturers can use the model to assess the impact of wake-induced loads on critical components, such as blades, towers, and drivetrains, and optimize the turbine design accordingly.

By incorporating the DG wake model’s predictions into their design workflows, turbine manufacturers can develop more resilient and cost-effective wind energy solutions, contributing to the overall competitiveness and widespread adoption of wind power in the global energy landscape.

Operations and Control

The ability to accurately model the effects of yaw misalignment on wind turbine wakes and loads opens up new opportunities for advanced wind farm control and optimization strategies. Wind farm operators can utilize the DG wake model to develop sophisticated control algorithms that dynamically adjust the yaw angles of individual turbines, effectively steering the wakes to minimize the negative impacts on downstream units.

Moreover, the DG wake model can be integrated into wind farm layout optimization tools, enabling developers to determine the optimal turbine positions and yaw angles to capture the maximum wind energy potential while mitigating the structural loads and maintenance requirements across the entire wind farm.

As the global renewable energy landscape continues to evolve, the advancements in wind turbine wake modeling, such as the DG wake model with yaw misalignment considerations, will play a crucial role in unlocking the full potential of wind energy and supporting Europe’s transition towards a sustainable, low-carbon future.

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