The analytical wind farm efficiency and wake model EFFWAKE

About 10 years ago the analytical wind farm efficiency and wake model EFFWAKE was developed which is based on a simple budget consideration between extracted momentum from the wind by a wind farm and re-supplied momentum from higher atmospheric levels (Emeis 2010). The spread-sheet-based model is able to calculate the efficiency and the length of the trailing wake of infinitely large wind farms as a function of farm power density, roughness of the surface on which the farm is built, and atmospheric thermal stability. Driving force is the undisturbed wind speed at hub height. In its latest version (Emeis 2018) EFFWAKE also considers the turbulence generated by the operating wind turbines.

When EFFWAKE was developed it could only be checked against existing other numerical wind farm models, because large wind farms which came close to the assumptions on which EFFWAKE is based were not yet existing. Main assumption is that replenishment of extracted momentum only happens by turbulent fluxes from above but not from the sides of the farm. The impact of this assumption will be demonstrated by a comparison with an industry model in which the farm size is varied while keeping the spatial power density of the farm constant.
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Meanwhile, large offshore wind farms have been erected which come closer to EFFWAKE’s assumptions. The research project WIPAFF conducted in 2015 to 2019 was the first project within which in situ aircraft measurements of wakes of large offshore wind farms in the North Sea were made (a summary of the results is given in Platis et al. 2020a). This offered the unique chance to check EFFWAKE with real measured data. Given the simplicity of EFFWAKE the checks were satisfying but also pointed to weaknesses of the simple analytical approach (Platis et al. 2020b). Some highlights from this comparison will be shown.

Finally, a recent application of EFFWAKE is shown. Based on the confidence deduced from the above mentioned checks, EFFWAKE can be used for first a priory estimations of wind farm efficiency and lengths of farm wakes for future even larger wind farms without using any noteworthy computational resources. An example for such estimations is the efficiency of planned large offshore wind farms. EFFWAKE can be used to estimate the efficiency of such farms as function of the installed power density, i.e., the number of wind turbines per unit area. One feature of EFFWAKE’s simplicity is that only the power density of a farm can be specified irrespective of the actual spatial arrangement of the turbines within a wind farm. This also means that wind direction is no relevant input parameter of EFFWAKE. By series of runs of EFFWAKE the relation between the wind speed distribution (either measured or taken from a climatology) and the rated wind speed of the designated wind turbines can be included into the estimations as well. This will support the efforts to effectively use the available offshore areas for a reliable electrical power supply.

Emeis, S., 2010: A simple analytical wind park model considering atmospheric stability. Wind Energy, 13, 459-469. DOI: 10.1002/we.367
Emeis, S., 2018: Wind Energy Meteorology - Atmospheric Physics for Wind Power Generation. 2nd Edition. Springer, Heidelberg etc., XXVI+255 pp. DOI: 10.1007/978-3-319-72859-9.
Platis, A., J. Bange, K. Bärfuss, B. Cañadillas, M. Hundhausen, B. Djath, A. Lampert, J. Schulz-Stellenfleth, S. Siedersleben, T. Neumann, S. Emeis, 2020a: Long-range modifications of the wind field by offshore wind parks – results of the project WIPAFF. Meteorol. Z. (Contr. Atm. Sci.), 29, 355-376. DOI: 10.1127/metz/2020/1023
Platis, A., M. Hundhausen, M. Mauz, S. Siedersleben, A. Lampert, K. Bärfuss, B. Djath, J. Schulz‐Stellenfleth, B. Canadillas, T. Neumann, S. Emeis, J. Bange, 2020b: Evaluation of a simple analytical model for offshore wind farm wake recovery by in situ data and Weather Research and Forecasting simulations. Wind Energy, online first. DOI: 10.1002/we.2568