Abstract
We extend the infinite wind-farm boundary-layer (IWFBL) model of Frandsen to take into account atmospheric static stability effects. This extended model is compared with the IWFBL model of Emeis and to the Park wake model used in Wind Atlas Analysis and Application Program (WAsP), which is computed for an infinite wind farm. The models show similar behavior for the wind-speed reduction when accounting for a number of surface roughness lengths, turbine to turbine separations and wind speeds under neutral conditions. For a wide range of atmospheric stability and surface roughness length values, the extended IWFBL model of Frandsen shows a much higher wind-speed reduction dependency on atmospheric stability than on roughness length (roughness has been generally thought to have a major effect on the wind-speed reduction). We further adjust the wake-decay coefficient of the Park wake model for an infinite wind farm to match the wind-speed reduction estimated by the extended IWFBL model of Frandsen for different roughness lengths, turbine to turbine separations and atmospheric stability conditions. It is found that the WAsP-recommended values for the wake-decay coefficient of the Park wake model are (i) larger than the adjusted values for a wide range of neutral to stable atmospheric stability conditions, a number of roughness lengths and turbine separations lower than ∼ 10 rotor diameters and (ii) too large compared with those obtained by a semiempirical formulation (relating the ratio of the friction to the hub-height free velocity) for all types of roughness and atmospheric stability conditions. © 2013 The Authors. Wind Energy published by John Wiley & Sons, Ltd.
Highlights
Most wind Park wake (WPW) models are able to estimate wind-speed reductions within the wind farm for a wide range of wind speeds, assuming neutral atmospheric conditions in most cases
Since Frandsen developed his model for neutral conditions only, we extend it for diabatic atmospheric conditions by using local atmospheric stability corrections to the logarithmic wind profile and the resistance law constants of the geostrophic drag law
Computational fluid dynamics (CFD) methods have been extensively applied for multiple wind turbines and in the last couple of years, large eddy simulation (LES) methods have gained popularity compared with the Reynolds averaged Navier–Stokes (RANS) turbulence models
Summary
Most wind Park wake (WPW) models are able to estimate wind-speed reductions within the wind farm for a wide range of wind speeds, assuming neutral atmospheric conditions in most cases. There are other techniques to study the wind-speed reductions due to wind turbine wakes.[11] Computational fluid dynamics (CFD) methods have been extensively applied for multiple wind turbines and in the last couple of years, large eddy simulation (LES) methods have gained popularity compared with the Reynolds averaged Navier–Stokes (RANS) turbulence models This is partly due to the extension of LESs to account for atmospheric stability conditions other than neutral, which allows LES results to be compared with benchmark cases.[12] The LES technique has been used to study large arrays of wind farms,[12,13,14] which can provide the information needed to adjust the wake-decay coefficient of the Park wake model. Analysis of such data is as challenging as the modeling itself,[16] for different atmospheric stability conditions because since most wind farms have no means to estimate stability, it is difficult to separate the effect on wind-farm power production of stability, wind speed and turbulence from real data[6] and because in large wind farms, turbines do not operate concurrently and optimally all the time
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