This article presents a method for performing noise-constrained optimization of wind farms by changing the operational modes of the individual wind turbines. The optimization is performed by use of the TopFarm optimization framework and wind farm flow modelling in PyWake as well as two sound propagation models: the ISO 9613-2 model and the parabolic equation model, WindSTAR. The two sound propagation models introduce different levels of complexity to the optimization problem, with the WindSTAR model taking a broader range of parameters, like the acoustic ground impedance, the complex terrain elevation and the flow field from the noise source to the receptor, into account. Wind farm optimization using each of the two sound propagation models is therefore performed in different atmospheric conditions and for different source/receptor setups, and compared through this study in order to evaluate the advantage of using a more complex sound propagation model. The article focuses on wind farms in flat terrain including dwellings at which the noise constraints are applied. By this, the study presents the significant gain in using a higher fidelity sound propagation model like WindSTAR over the simple ISO 9613-2 model in noise-constrained optimization of wind farms. Thus, in certain presented flow cases a power gain of up to

As the demand for onshore wind farms increases, the social acceptance of wind turbines becomes a larger challenge. One of the main factors contributing to neighbour annoyance is the aerodynamic noise from the wind turbine blades. Previous social studies have shown how neighbours to wind farms experience annoyance and sleep disturbances caused by the noise emitted from wind farms

Previous studies have shown how the wind direction or the upward/downward refraction of the atmosphere can have an effect on the propagation of sound

The paper is organized as follows. Section

The modelling in the presented framework is divided into two parts: the wind farm wake modelling and the sound propagation modelling. By flow modelling and wind farm performance results obtained in PyWake, the operational modes are altered to maximize the power output by the optimizer in Topfarm. Thus, PyWake and Topfarm work in conjunction to achieve the optimal operational mode configuration of the considered wind farm. By setting a noise constraint at each receptor close to the wind farm in Topfarm, the noise level estimation is given by the considered sound propagation model and the operational modes of the wind turbine type. The following gives a brief overview of the three modelling parts, namely the PyWake flow modelling, the Topfarm optimizer and the WindSTAR and ISO 9613-2 sound propagation modelling.

The sound pressure level,

Generally, the frequency,

The bottom boundary condition of the GTPE is defined by the acoustic impedance at the ground surface computed by the model of

Due to the different complexities of the two sound propagation models, the computational time varies significantly as well. While the ISO 9613-2 model can be evaluated on a laptop, the amount of physics included in the WindSTAR model require a cluster for the computations. As an example, the sound propagation from a wind turbine to a receptor 1000 m away for all octave band frequencies requires a computational time of 0.005 s with the ISO 9613-2 model and

The optimization framework used is the Topfarm framework developed at the Technical University of Denmark (DTU)

The wind farm modelling is performed in the PyWake framework

In short, the optimization problem when using either of the two sound propagation models can be mathematically described as

Figure

Flow chart of the optimization framework structure. The flow chart can both be used for the ISO 9613-2 model and the WindSTAR model.

It is noted that for some wind speeds or wind directions it may be necessary to shut down a wind turbine completely if the operational modes do not provide the needed reduction in noise emission. Such a mode is, however, not included in the presented work. The updated operational mode,

The flow chart can similarly be used to describe the optimization when the ISO 9613-2 model is applied to the sound propagation modelling. In this case only the effective wind speed at each wind turbine in the wind farm is needed from the (

For the optimizations done in this article, a wind farm in flat terrain is considered. For the layout of the wind turbines, the Lillgrund wind farm is used as a reference site. Although being an offshore wind farm, Lillgrund provides a flat terrain case consisting of a wind turbine type with various noise reducing operational modes. The Lillgrund wind farm has a size of 48 wind turbines, but only parts of the wind farm have been used for the tests performed in this work. Thus, the tests consider one row of the wind farm consisting of seven wind turbines and the north-east corner of the wind farm consisting of a layout of 4x5 wind turbines. Furthermore, artificial receptors, at which the noise constraints must be satisfied, are arbitrarily placed around the wind farm with a distance to the nearest wind turbine no closer than 4 times the total height of the wind turbine type.

The specifications of the wind turbine types used in this study are listed in Table

Specifications of the two wind turbine types.

SWT-2.3-93: the power,

SWT-DD-142: the power,

The wind turbines in the Lillgrund wind farm are of the type Siemens SWT-2.3-93. A number of defined operational modes are provided for this wind turbine type with information about the

For the initial tests of the optimization, the row of seven wind turbines either of the type SWT-2.3-93 or SWT-DD-142 is used. As mentioned, the distances between the turbines are scaled to fit the rotor diameter of the turbine type. As mentioned, four receptors are positioned in arbitrarily chosen locations but in such a way that some of the receptors will either be in the upwind or downwind positions of wind turbines in the farm. By choosing these positions, some of the distinct differences between the computed noise by WindSTAR and by ISO 9613-2 caused by refraction in the atmosphere are expected to be captured

In the final optimization of the presented work, the described layout of 4x5 wind turbines is considered. In this layout the larger SWT-DD-142 turbine is used. In a similar way as for the row of seven wind turbines, four receptors at different arbitrarily chosen positions near the wind farm are considered. The chosen layout results in

A large downside of the current optimization framework is the computational time. Thus, since the main contributor to the long computational time of the optimization framework is the computations of the sound propagation in WindSTAR, it is tested whether the sensitivity of WindSTAR results to the updated operational mode,

The first setup considers one wind turbine with a receptor line positioned in the wake and reaching 3 km from the wind turbine. The operational mode of the wind turbine is thus switched between mode 0, 3 and 6 for different hub height wind speeds: 6, 10 and 14 m s

Setup 1: the transmission loss, TL, obtained from WindSTAR computations from a single SWT-DD-142 wind turbine subject to changing operational modes at each octave band frequency at a free field wind speed of

Setup 2: the transmission loss, TL, obtained from WindSTAR computations from a single SWT-DD-142 wind turbine positioned in the wake of a wind turbine subject to changing operational modes at each octave band frequency at a free field wind speed of

In the results presented in Fig.

As mentioned, the optimization of the wind farm operation is done for both a row of seven SWT-2.3-93 turbines and a row of seven SWT-DD-142 turbines. The flow fields through the row of wind turbines for the chosen flow cases with the two different wind directions

The flow field at hub height through the row of seven SWT-DD-142 wind turbines at the wind direction

The operational mode,

The convergence of the total power output; the operational modes of each wind turbine,

Scatter plots of the operational modes of each wind turbine along with the corresponding

Scatter plots of the operational modes of the seven SWT-2.3-93 wind turbines before

Overall

During the optimization it is observed that the noise reducing modes are distributed to all wind turbines when using the ISO 9613-2 model, while the WindSTAR optimization only modifies two–three turbines. For the optimum, all wind turbines are switched to a noise reducing mode in the ISO 9613-2 optimization while the operation of only two turbines, close to the receptors initially being subject to constraint violations, is modified in the WindSTAR optimization. For the ISO 9613-2 optimal mode it is observed that the turbines in the outer positions of the row have the highest curtailment while the turbines in the centre are less noise curtailed. This occurs even though the receptors closest to the centre of the row initially are exposed to the highest

Convergence plots are similarly presented for the optimization of the row of seven SWT-DD-142 turbines in Fig.

The operational mode,

The scatter plot in Fig.

Scatter plots of the operational modes of the seven SWT-DD-142 wind turbines before

The optimization of the row of seven turbines is further performed for a flow case with a wind direction of

The flow field at hub height through the row of seven SWT-DD-142 wind turbines at the wind direction

When comparing the convergence for the SWT-2.3-93 turbine in Fig.

A different behaviour of the optimizer is noticed when considering the row of SWT-DD-142 turbines in Fig.

The operational mode,

The operational mode,

Lastly, the larger wind farm layout of

Example of flow at hub height through the

The convergence of the ISO 9613-2 and WindSTAR optimization, respectively, of the 4x5 wind farm is presented in Fig.

The operational mode,

Scatter plots of the operational modes of the

In the optimizations performed in the presented work, the optimization method using a random search algorithm has been applied

The use of any of the two sound propagation models introduces an uncertainty to the predicted sound pressure level at each receptor. First of all, both the WindSTAR model and the ISO 9613-2 model compute the sound propagation based on simplified flow fields using a logarithmic inflow profile and an engineering wake model. Thus, these simplifications introduce uncertainties already in the flow field modelling, which is expected to propagate as uncertainties in the sound propagation modelling. It should however be noted that the use of the logarithmic inflow profile is deemed acceptable for the flat terrain in the studied wind farm cases. For a complex terrain wind farm, higher fidelity flow modelling like RANS should be considered in order to obtain the speed-ups in the flow field. In addition, the turbulence effects in the atmosphere are neglected due to the high computational costs. This will in some scenarios, i.e. when considering receptors in the upwind position of a wind turbine, lead to higher uncertainties due to the omitted scattering of sound. Turbulence can further have a significant impact on the noise generation at the wind turbine rotor, which is not accounted for by the noise reducing operational modes of the turbine. The turbulence effects in the sound propagation modelling of WindSTAR could be included by, i.e. developing a surrogate model based on a limited amount of model evaluations

In general the ISO 9613-2 model is observed to estimate higher sound pressure levels at the different receptors compared to the WindSTAR model. Although this suggests that the ISO 9613-2 model is more conservative, it on the other hand gives a higher insurance that the noise constraints are not violated. Thus, the lower estimated sound pressure level of WindSTAR may lead to that the noise constraints in reality are not satisfied at the obtained optimal mode. This could, i.e. be accounted for by adding the uncertainty of the WindSTAR model to the integrated sound pressure levels prior to the optimization. However, in general the higher fidelity model gives a better prediction of the noise at each receptor and allows for a broader exploration of the flow parameters and their influence on the

Through the work of this article a new approach for performing optimization of wind farm operation was presented. The optimization considers noise constraints at nearby receptors of an onshore wind farm. By the use of the ISO 9613-2 and WindSTAR sound propagation models as well as the Topfarm optimization framework and PyWake flow model the overall power output is optimized in a specific flow case while assuring that the sound pressure level satisfies the given noise constraints. This is done by individually changing the defined operational modes of each wind turbine in the wind farm. The approach was tested on a smaller wind farm of seven wind turbines and four receptors, which showed a fast convergence for both sound propagation models and a significant gain in power output when using the WindSTAR model over the ISO 9613-2 model. Especially for cases in which one or more receptors are in the upwind positions of the wind farm, the use of the WindSTAR model in the optimization results in lower estimated sound pressure levels at the receptors and a higher overall power output of the wind farm. While being a more advanced sound propagation model, it is also evident that the use of the WindSTAR model requires longer computational times. It was therefore tested whether the sensitivity of the WindSTAR model to the operational modes is negligible, such that the WindSTAR computations can be performed once prior to the optimization and later used as a transfer function during the iterations in the optimization. It was shown that variations in the sound attenuation are most apparent for far distances where the sound pressure levels are already low. These variations were therefore omitted and WindSTAR was used as a transfer function. As an analysis for future work with the presented framework, the potential and uncertainty in replacing WindSTAR computations at the cases of high frequencies and long distances with ISO 9613-2 computations will be investigated. This is already done for frequencies and distances where the memory of the computations becomes too excessive. However, there is a potential value in implementing this replacement at shorter distances for

As the optimization is performed for a single flow case with constant wind speed profile, wind direction, temperature profile and ground conditions, this can lead to uncertainties when applied to the operation of the wind turbines during, e.g. a day. Thus, the sound propagation achieved especially from WindSTAR is sensitive to the flow and temperature in the wind farm which experience frequent changes and the ground acoustic impedance which can experience seasonal changes (for example going from snow covered terrain in the winter to grass covered in the summer). Thus, to obtain the full operational strategy of a wind farm, a structured sensitivity study of WindSTAR with respect to these parameters is needed.

Finally, the optimization framework has been tested on an artificial onshore wind farm of the size of 4x5 SWT-DD-142 4.1 MW wind turbines and four nearby receptors. Although being a larger wind farm, both sound propagation models show that the sound pressure levels at each receptor do not necessarily increase, implying that the noise characteristics of the nearest wind turbines are of higher importance than the number of turbines in the considered wind farm.

As it has been discussed, the use of a random search algorithm for the optimization does not guarantee a global optimum. In order to fully exploit the capabilities of the framework and to further approach a globally optimal solution, a gradient-based approach should be implemented. This requires that the gradient of the sound pressure level at each receptor with respect to the operational modes of each wind turbine is derived. Thus, this is considered the next step in the development of the framework.

In extension to the study done in Sect.

Setup 1:

Setup 1:

Setup 2:

Setup 2:

Topfarm is an open source optimization framework developed at the Technical University of Denmark. The implemented ISO 9613-2 standard model is open source, while the WindSTAR is proprietary software of the Technical University of Denmark.

Data will be made available upon request.

CMN: conceptualization, coupling of the ISO 9613-2 and WindSTAR sound propagation models to Topfarm, analysis of the sound propagation and optimization results, visualization, writing of the draft article. AF: conceptualization, analysis of the sound propagation results, supervision. PER: analysis of the optimization results, supervision. JF: conceptualization, supervision. All authors contributed to editing and finishing the article.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors would like to thank Wen Zhong Shen at Yangzhou University for the valuable discussions regarding the optimization framework and the WindSTAR model. The authors would further like to acknowledge Jaime Liew from the Technical University of Denmark for his great help with the visualizations.

This paper was edited by Alessandro Bianchini and reviewed by Alessandro Fontanella and one anonymous referee.