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Tuesday, 11 March 2014
16:30 - 18:00 How does the wind blow behind wind turbines and in wind farms?
Science & Research  

Room: Llevant
Session description

Wind turbines operate under highly fluctuating wind conditions. It is thus important to achieve a profound understanding of the characteristic features of the micro scale meteorological conditions. Current research activities focus not only on the inflow conditions and their impact on wind turbines, but also on the wake structures and the wind conditions within a wind farm.

Learning objectives

  • Get a better understanding micro scale wind conditions
  • Learn about new advanced measuring techniques
  • See the possibilities of numerical methods to simulate complex wind conditions
  • Learn about the impact of wind on turbine components
Lead Session Chair:
Joachim Peinke, Uni Oldenburg, Germany

Jakob Mann, DTU Wind Energy
Jonas Schmidt Fraunhofer IWES, Germany
Jonas Schmidt (1) F P Bernhard Stoevesandt (1)
(1) Fraunhofer IWES, Oldenburg, Germany

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Presenter's biography

Biographies are supplied directly by presenters at EWEA 2014 and are published here unedited

Jonas Schmidt's professional interests are wake modelling, wind farm layout optimisation and wind resource site assessment, using computational fluid dynamics methods. After his Ph.D. in fundamental physics he worked for a wind turbine producer. Currently he holds a position as a post-doc in the aerodynamics department of an applied research institute that is specialised on wind energy, the Fraunhofer IWES in Oldenburg, Germany.


Wind farm layout optimisation using wakes from computational fluid dynamics simulations


The layout of a wind farm has direct impact on its yearly energy production and endurance. Each site has its own specific wind distribution, meteorological embedding and, in the on-shore case, orographic characteristics. Due to the wake effect the wind turbines interact, and finding the optimal configuration is a highly non-trivial task.

Here we present the development of a new software that addresses wind farm layout optimisation with new and, to our knowledge, unique methods. These advance the concept of single-wake superposition by incorporating the power of the computational fluid dynamics (CFD) toolbox OpenFOAM [1].


Wind farm layout software has been developed since more than two decades. Examples are PARK/UPMWAKE [2] (DTU, Danmark), FarmFlow [3] (ECN, Netherlands), WindFarmer [4] (GH, United Kingdom) and FLaP [5] (University of Oldenburg, Germany). A very common approach is to overlap simple analytical single-wake models, like the Jensen model [6] or the Ainslie model [7]. Since these can be calculated with little computational effort, they are suitable for the usage within iteration loops of optimisation codes. CFD simulations, on the other hand, can provide more accurate representations of the wake physics, but they are too costly for optimisation purposes.

Our method is based on a combination of both approaches. The single-wake deficit field is interpolated between stationary pre-calculated CFD results, carried out for a selected set of inflow wind speeds. The total wind field in the wind farm then follows by the local superposition of deficits, given a wake overlap model. Finally the total deficit is added to a background wind field, which can be uniform, a vertical velocity profile, or also the result of a CFD simulation. Since during optimisation the basic single-wake deficit data are not calculated, but interpolated from a database, the computational costs are low. This preserves the full single-wake CFD accuracy, up to the interpolation between inflow wind speeds, and makes it available for the wind farm layout optimisation.

Wind farm layout optimisation is bound to rely on modelling. Apart from the wake model, the local wind environment needs a representation. Furthermore the single wind turbines, converting the local wind field into electrical power, have to be modelled. Also the wake overlap model plays a crucial rule, since it forms the core of the basic simplifying assumption, the superposition of a number of single-wakes to a total wind field inside the park. Our new code is programmed in C++ and based on the OpenFOAM machinery, it therefore is fully modular. All model choices are up to the user during run-time, enabling systematic model studies for wind farm situations. Note that apart from layout optimisation, also wind farm calculations for wind inflow cases of interest are possible.

Main body of abstract

Wind farm optimisation is based on evaluation of an objective function, which can be a combination of the total power production, turbine loads and financial aspects. This function is evaluated many times during the optimisation iteration loop, therefore it cannot be too costly to calculate. In the wind farm application, the calculation of the objective function is related to the evaluation of the wind field at the location of the turbines. Two assumptions are commonly applied in order to achieve a fast calculation of the total wind speed: First, the resulting field can be approximated as a combination of single-wake deficits and a background. Second, the single-wake is approximated by a simple model.

Our proposal is to replace the second assumption by approximating the single-wake deficit field by arbitrarily complex CFD results. Simulated wake deficits for inflow wind speeds 10, 11, 12 and 15 m/s, and interpolated deficit fields for 13 and 14 m/s inflow wind speed are shown in the following figure: The simulations were obtained with OpenFOAM (version 2.1.1), solving Reynolds-Averaged-Navier-Stokes (RANS) equations with k-epsilon turbulence closure and a model turbine. For one specific probe point, continuous interpolation to fourth order of accuracy is performed, as demonstrated here: The black crosses mark deficits from the RANS simulations. During the calculation of the wind farm, such interpolations are evaluated many times, for all turbines that are affected by the wakes of upstream turbines.

The superposition of wakes requires a wake overlap model. Each wake contributes to the total wind velocity vector at a point with a deficit. The simplest approach is to add the local velocity deficit vectors to the background. More realistic results are obtained by vector-like addition of the deficits. For the turbine row marked in blue in the previous figure, the RANS wake discussed before and westerly wind of uniform 10 m/s wind speed, three wake overlap models are compared in the following figure: Clearly, there is an impact on the results and the models need validation.

A comparison of the RANS wake and the standard Jensen wake model for the same setup and the vector-like deficit overlap is shown in the following figure: The RANS wake shows a softer efficiency drop after the first turbine, and a more continuous approach of the lower turbine efficiency in the last row. Any kind of steady or time averaged CFD simulation can be used as a single wake model with our method, and it is an open issue which model performs best in the described approach.

As has been discussed recently in the literature, the wind direction uncertainty has to be included into the wind farm calculation [8]. In our software, the user selects an inflow case, which either is a single wind field, or a distribution over a specified set. The corresponding results are then added with statistical weights. Such distributions can be selected for wind speed and wind direction, or for a whole wind rose. The latter is either read from measured data, or defined sector by sector. Consequently, wind farm optimisation can be done with respect to best average performance for a given inflow case, for example a wind rose with wind speed and wind direction distributions for each of the sectors.

The choice of the optimiser is also up to the user. Currently, only constraint gradient-based solvers are available, but in the future also more advanced techniques will be included. Here we demonstrate that the underlying single-wake model has an impact on the final layout. The result for nine wind turbines with Jensen model wakes and uniform westerly inflow is as follows: Clearly, the local optimiser is unable to escape the wakes, which have no dependence on the radial coordinate within the central region. This trap is evaded when using the RANS wake model:

This example demonstrates that the choice of single-wake model is crucial for calculations and layout optimisation results of a wind farm. With our new tool we are now ready to explore how CFD wake models may improve the outcome of engineering model codes. The validation of the code and the models is in preparation.


Wind farm site assessment and layout optimisation rely on fast power calculations for a specific ensemble configuration. However, it is well known that the wake effect plays a major role for the result, and the CFD solution of the wake physics requires vast resources. Therefore, simple wake models are commonly used for optimisation and site assessment purposes, which are unable to capture a lot of details.

In the present paper we close the gap between wake modelling with CFD and wind farm layout optimisation. We demonstrate that sets of stationary pre-calculated single-wake simulations can be interpolated for continuous inflow wind speeds. This new CFD-interpolated wake model is suited to replace engineering models in optimisation loops and site assessment applications. Once the data base of CFD single-wake simulations is set up, all models with the same mesh have identical performance time, no matter how complex the CFD model is. The scaling with CFD mesh size is reduced by sub-mesh memorisation techniques. The impact of CFD wake model and parameter choices on fast wake superposition codes and layout optimisation can now be studied in detail. Here, we present the proof-of-concept, and show that the CFD RANS model has an effect on the park efficiency calculation and layout optimisation, compared to the Jensen model wake.

We developed a new software, based on OpenFOAM libraries, that is fully modular and hence naturally extendable. This opens the door for detailed wake and wind farm modelling, including single-wake models, wake overlap models, wind inflow models, wind turbine models and background wind fields. In the future, also complex terrain effects and wake meandering shall be included into the framework.

Next, a systematic iterative process of model improvement and validation will be decisive. Also more advanced optimisation strategies like genetic algorithms and combined local and global approaches will be introduced. We hope that this program may induce a significant step forward in wake and wind farm modelling. The final goal is to achieve improved layout optimisation, yielding higher farm efficiency and decreased turbine loads, for real-case applications.

Learning objectives
We demonstrate that fast non-CFD wind farm calculation and optimisation software is not bound to be based on engineering wake models or measured data. Instead, also complex CFD single-wake models can be used, by interpolating a given set of pre-calculated deficit fields for arbitrary inflow wind speeds.

[1] The OpenFOAM foundation. Retrieved October 19, 2013, from
[2] A. Crespo et al., ”Numerical analysis of wind turbine wakes”, Delphi Workshop on Wind Energy Applications, Delphi, Greece (1985)
[3] R.J. Barthelmie et al., ”Analytical Modelling of Large Wind Farm Clusters”, EAWE (2004)
[4] P.J. Eecen. ”Wind farm calculation and optimization with FarmFlow”, Dutch Wind Work- shop (2010)
[5] B. Lange et al., ”Modelling of Offshore Wind Turbine Wakes with the Wind Farm Program FLaP”, Wind Energy (2003); 6:87-104
[6] N.O. Jensen, ”A note on wind generator interaction”, Risø-M-2411, Risø National Laboratory (1983)
[7] J. F. Ainslie, ”Development of an Eddy Viscosity Model for Wind Turbine Wakes”, BWEA Wind Energy Conference, Oxford, U.K. (1983)
[8] Gaumond, M., Réthoré, P.-E., Ott, S., Peña, A., Bechmann, A. and Hansen, K. S. (2013), “Evaluation of the wind direction uncertainty and its impact on wake modeling at the Horns Rev offshore wind farm.” Wind Energ.. doi: 10.1002/we.1625