Defining the Wake Decay Constant as a Function of Turbulence Intensity to Model Wake Losses in Onshore Wind Farms

Abstract: Modelling the wake effect generated by wind turbines is an essential part for calcu- lating a wind farm’s expected energy production. Operating wind turbines disturb the flow of the wind, which results in decreased production of downwind turbines. The N. O. Jensen model is an industry standard wake model that assumes a linear expansion of the downstream wake. The only adjustable parameter in the model is the wake decay constant (WDC), which has traditionally been derived semi em- pirically from terrain surface roughness. However, the WDC defines the expansion rate of the generated wake, and therefore can be linked to the ambient turbulence intensity (TI): high ambient turbulence leads to a faster decay of the generated wake, and therefore to lower wake losses, and vice-versa. Since the influence of the roughness on the ambient turbulence intensity is expected to be less significant at higher heights, these roughness-based WDC values are rather uncertain for the hub heights employed nowadays. The following study presents the results of a comparison between observed and mod- elled wake losses based on different WDC values. To investigate how a change in height affects the wake modelling, two wake scenarios occurring between two tur- bine sets with different hub heights are selected from an operational wind farm. By modelling the wakes using roughness as well as turbulence intensity-based WDCs, conclusions can be drawn on how the predictive capability of the N.O. Jensen model depends on the selection of a suitable WDC value. Finally it is concluded that the goodness of fit between modelled and observed wake losses shows a clear dependency on the wind speed/power production inter- val. At higher wind speeds, the TI-based WDC resulted in a better accuracy of the modelled wake losses as compared to the roughness-based WDC, while for lower wind speeds the N. O. Jensen model performed most accurately when using WDC = 0.075. However, for the investigated cases the overall accuracy of the modelled wake appears to be higher when choosing WDC = 0.075 instead of a TI-based WDC.