The Point of Turbulence Detrending
The physical loads on a wind turbine depend strongly on the turbulence intensity, so wind energy modelers strive to determine accurately the turbulence conditions to which turbines will be exposed. But the fact that the wind industry tends to record wind resource data on 10-minute intervals makes this determination more difficult.
Of particular importance to fatigue loads in the turbines are the high-frequency (on the order of 1Hz) fluctuations in the wind. Historically the wind industry has assumed that the quantity of such high-frequency fluctuations is well approximated by the raw turbulence intensity, defined as the ratio of the standard deviation of measurements made with the 10-minute time step to the mean of those measurements. That assumption is accurate in the absence of a trend in the wind speed over that 10-minute time step. But if the wind is trending strongly up or down over that time step, then the standard deviation over the time step will result partly from that trend and partly from the high-frequency fluctuations superimposed over the trend. The point of turbulence detrending is to subtract the contribution of the longer-term trend and thereby calculate more accurately the quantity of high-frequency fluctuations within each 10-minute time step.
The use of wind speed standard deviation as the basis of turbulence intensity (TI) assumes a constant mean wind speed or at least a mean wind speed which is varying by a small amount compared to the turbulent fluctuations around that mean. However, significant ramp events, both up and down, do occur in the data collected by meteorological masts used as the basis for wind resource assessment. The standard deviation of a data time-series with zero turbulence or noise but a constant rate of change is non-zero and so it stands to reason that wind speed standard deviation divided by the mean wind speed is by no means a perfect measure of the turbulence during the same measurement period. For this reason, IEC61400-1 recommends removing the portion of the standard deviation which is due to ramps or trends in the mean wind speed from one measurement period to the next, especially when assessing fatigue loading due to turbulence. This process is commonly referred to as turbulence de-trending and is referred to only once in section 11.3.4 of IEC61400-1 edition 4.
Method Used
One of the best known publications on this topic is that by Hansen and Larson which can be found here.
The algorithm used to detrend Ti in Openwind is based on code shared by Kurt Hansen, one of the authors cited above. The code can be found here.
While every effort has been made to recreate the DTU code in every detail (ignoring obvious bugs), the algorithm is highly unstable and tends to amplify tiny rounding errors in the input data. That being said though, the differences in the Matlab DTU code and our reimplementation into C++, occur in a tiny minority of time steps and there is no discernible pattern. More importantly, the overall decrease in ambient TI over the range of wind speeds experienced at a site, agrees very well between the two implementations.
