Wind turbines are designed to align themselves with the incoming wind direction. However, turbines often experience unintentional yaw misalignment, which can significantly reduce the power production. The unintentional yaw misalignment increases for turbines operating in the wake of upstream turbines. Here, the combined effects of wakes and yaw misalignment are investigated, with a focus on the resulting reduction in power production. A model is developed, which considers the trajectory of each turbine blade element as it passes through the wake inflow in order to determine a power–yaw loss exponent. The simple model is verified using the HAWC2 aeroelastic code, where wake flow fields have been generated using both medium- and high-fidelity computational fluid dynamics simulations. It is demonstrated that the spatial variation in the incoming wind field, due to the presence of wakes, plays a significant role in the power loss due to yaw misalignment. Results show that disregarding these effects on the power–yaw loss exponent can yield a 3.5 % overestimation in the power production of a turbine misaligned by 30

As the global wind energy sector continues to grow, there is a strong demand for a decreased levelized cost of energy. With this demand comes an increasing need for accurate and efficient computational tools, which are able to improve the design of wind farms and optimize annual energy production. In the early phases of wind farm design, optimization tools provide estimates of energy production and the costs during construction, installation, and operation. The wind farm planning tools must account for the interactions between nearby wind turbines using wake models. Often, the wake effects and, therefore, the power production are not accurately modeled when employing engineering wake models, and they include substantial uncertainty; see e.g.,

Wind turbines which experience yaw misalignment show a reduction in power production. This power sensitivity to yaw misalignment can be quantified by the power–yaw loss exponent,

The investigation performed by

Considering the findings in

In recent years, there has been an increased focus on applying control strategies for both stand-alone wind turbines and entire wind farms to increase operational performance. The focus is generally on power optimization, for example,

By overcoming the assumption of a constant power–yaw loss exponent, uncertainty in wind farm modeling tools can be decreased. Low-fidelity wind farm optimization frameworks such as TOPFARM

When a downstream turbine in a full-wake situation is perfectly aligned with the incoming wind, each blade segment follows a circular trajectory relative to the mean incoming wind direction. For misaligned cases, where the turbine is yawed, each blade segment follows an elliptical path, where the eccentricity of the ellipse increases with yaw angle (Fig.

The trajectory of a blade segment close to the blade tip through a wake inflow at varying yaw angles, represented in Cartesian coordinates

This section introduces the concept of blade segment effective wind speed. For a blade segment located at radius,

From the formulation in Eq. (

Radial functions of wind speed deficit and its derivative for varying turbine spacing distances (generated using DWM,

Based on blade element momentum (BEM) theory,

To determine the value of

The aeroelastic simulations are used to validate the results produced by the analytical model. Additionally, the inclusion of LES-generated wakes in this investigation verifies the results of the DWM-generated wake, which is unable to capture the behavior of a wake in as much detail as LES. Each of the model–simulation combinations aims to determine the power output

Wind turbine layout used in analysis.

To ensure that the combination of wake generation and simulation tools produces comparable results, the free-stream wind speed is fixed at 8 m s

The aeroelastic simulations (1) and (2) are run using the aeroelastic code HAWC2

The dynamic wake meandering model, as described by

Visualizations of the LES and DWM wakes represented as the averaged wake downstream evolution

The turbine and its wake are simulated using the incompressible Navier–Stokes solver EllipSys3D coupled with the aeroelastic tool Flex5 through the actuator line method. EllipSys3D is based on a finite-volume approach with general curvilinear coordinates

Usually the spectral Kolmogorov constant is denoted by

Simulations (3) and (4) are performed using the wake profiles generated by a stand-alone version of the DWM model and the time-averaged LES wake deficit profiles, as well as the analytical formulation described in Sect.

The DWM model, originally coded within HAWC2, has been externalized for its use within optimization problems, which results in fast and accurate estimations of a wake profile for a given radial thrust distribution, ambient turbulence intensity, and turbine spacing

The wake wind field is preconditioned before being used in the analytical formulation by removing the shear profile. This is achieved by subtracting the mean wind field

Unlike the DWM model, which fully describes the radial wind function, the LES wake at a particular downstream distance is described as a time-varying two-dimensional wind field,

Figure

Normalized power output as a function of yaw angle for different turbine spacings. Both calculation methods and wake generation tools are presented. The markers indicate the sample points used in the cosine fitting.

The analytical model shows good overall agreement with the aeroelastic simulations. For a turbine spacing between

The maximum value of

Power–yaw loss exponent as a function of turbine spacing for the four power calculation methods presented in this investigation.

Relative power output due to yaw misalignment for a downstream turbine located

The estimation of

Although the analytical model presented does not consider some physical effects, such as tip losses or rotor induction, the method shows close agreement with aeroelastic simulations in estimating the power–yaw loss exponent. The results are further reinforced by being able to capture the behavior of

The investigation is limited to full-wake situations; however, by using the azimuthal-time averaging method described in Eq. (

This paper establishes the link between wake effects and the power sensitivity to yaw misalignment in a wind turbine, quantified by the power–yaw loss exponent,

The simplified model presented in this paper provides a quick and reliable method to calculate

Let

The LES data that support the findings of this study are openly available in “LES of wake flow behind 2.3 MW wind turbine” at

JL developed the theoretical formalism, performed the analytic calculations, and processed the aeroelastic simulation results. AMU performed the aeroelastic simulations using HAWC2. SJA generated the LES wake profiles. All authors contributed to the conceptualization, investigation, and reporting of the research presented in this paper.

The authors declare that they have no conflict of interest.

This paper was edited by Sandrine Aubrun and reviewed by Wim Munters and one anonymous referee.