Why do we measure wind at hub height?

In this age of Doppler wind lidar, we can measure at all heights up to the top of the atmospheric boundary layer if we want, of course. In wind resource and site suitability assessment the parameters used to characterise wind power sites typically include hub height (HH) wind speed. It may seem like a silly question, but silly questions are how we scrutinise received wisdom: why is HH picked out for special attention?

The established procedures in the wind industry were originally developed on the basis of the capabilities of instruments mounted on temporary meteorological masts (met masts). The HH of wind turbines proposed for a particular site seemed a reasonable choice for the height of masts deployed pre-construction to acquire data necessary to assess the site, evaluate the incident wind resource, and predict the wind conditions that would prevail over the lifetime of the project. 

Now that we deploy lidars, we often require them to emulate the capabilities of met masts in order to allow continuity with established procedures based on these met mast capabilities. But should we? We restrict our use of lidars unnecessarily and fail to exploit their full capabilities and unlock the value they make available if we only use them to do what met masts can do. And if we have to choose a single height, why should it be HH? Indeed, even when we were restricted to using met masts at a small number of heights, it may have seemed the obvious choice, but was HH actually the sensible choice?  

We don't measure at HH because we rely on instruments mounted on the wind turbine nacelle post-construction, after the turbines are built, for monitoring absolute performance with any significant degree of precision. They may be useful for relative assessments, such as compring different periods of production from the same turbine. However, they are not suitable for assessments that require the wind to be evaluated in a manner that is consistent with the way it was evaluated during pre-construction resource and site assessment, and with equivalent precision and accuracy. 

For example, you wouldn't (or shouldn't) use a power curve obtained using nacelle mounted cup anemometry to calculate a reliable energy yield from the HH wind speed distribution obtained during pre-construction resource assessment. We have more sophisticated power performance testing procedures, described by IEC 61400-12-1:2017, for doing that. These measurements may be close to HH, but we do not use them to compare the incident wind resource with production and develop power curves compatible with pre-construction resource assessments, in anything other than the most approximate way. These measurements are typically not accurate enough, with significant uncertainties arising due to the the influence of the rotor (nacelle transfer function), substandard calibration, poor mounting, and so on, and so we make alternative arrangements. 

We establish a relationship between the wind conditions at the turbine location and another reference location during pre-construction site calibration, in accordance with IEC 61400-12-1:2017, and use that relationship (in all but the most simple terrain) and the reference measurements post-construction if we want to acquire accurate wind measurements suitable for evaluating the efficiency of the turbine. Nacelle mounted instruments are not involved in this process, so there is no need for the procedure to relate to wind speeds at that specific height. The availability of instruments on the nacelle is not a reason to situate instruments at the same height pre-construction. 

What about turbine control? This is not conducted in relation to HH wind speed measured by nacelle mounted anemometry. It is done in relation to rotor effective wind speeds, which are rarely equal to HH wind speed in the turbine location due to various terrain, induction zone and drive train influences. 

Maybe wind speeds at HH are intrinsically the best indication of the incident wind resource? But we know they aren't. One of the motivations for revising the power performance testing standard IEC 61400-12-1 and published the second edition in 2017 was the need to accommodate the variation in resource across the full rotor disk. Guidance is now provided for the calculation of the rotor equivalent wind speed (REWS) when relating the power output of the turbine to the knetic energy flux across the entire rotor. 

And, crucially, the average wind speed over the height interval between lower and upper rotor tip height does not occur in the middle of that interval, at HH, anyway. In fact, if we assume neutral atmospheric stability and a logarithmic wind shear profile (a reasonable assumption, and certainly no more unreasonable than the assumptions involved in measuring at HH), it can be demonstrated that the average wind speed does indeed always occurs at the same height, irrespective of roughness length, but this height is not HH, due to the non-linearity of the shear profile. 

This "rotor equivalent" height (REH) (as one might term it, by analogy with REWS) at which the average wind speed always occurs is below HH and is entirely a function of the rotor geometry (the HH h and radius r in the expressions below) and nothing else, as shown below. That is, it can be predicted in advance, and so instruments can be configured to measure there in advance, during pre-construction resource and site assessment, and during site calibration for power performance tests. This independence of REH from roughness length is an example of a rather nice property of logarithms which is seen in other fields. 

You can see in the diagram that normalising three different logarithmic wind shear profiles, characterised by three different roughness lengths, by the average value they have across the interval of heights between lower and upper rotor tip gives a value of unity at the same height (REH) which lies below HH. That is, the average value occurs at the same REH, irrespective of roughness length.

You can see why this should be from the following considerations. Take a simple logarithmic wind shear profile describing how wind speed u varies with height z.

Average this by integrating between lower and upper tip height and dividing by two times the radius.

When you rearrange this you see it is still a logarithmic expression, entirely analogous with the wind shear profile given above.

However, in this instance, the average wind speed is seen to occur at a REH which is given by the following expression.

As mentioned, REH is seen to be a function only of the rotor geometry in terms of HH h and radius r, that is, it is independent of the terrain and wind conditions, assuming neutral stability and therefore logarithmic shear. Therefore we can define REH in a manner that is useful pre-construction.

In practice, REWS does not occur at REH because wind shear is typically more complex than the models we conventionally use to represent it, such as simple logarithmic or power law relationships, and REWS is weighted by rotor area. But if we were to base our procedures on an assumption of neutral stability and logarithmic wind shear, and we were to limit ourselves to characterising the site wind speed with measurements at a single height, it could be argued we should measure, not at HH, but REH. 

So is HH wind speed, in the final analysis, just as much an arbitrary convention and a matter of convenience as the unrealistic models we use to represent wind shear, with no basis in genuinely apposite technical considerations? Do we now appreciate these considerations enough to move on to more sophisticated approaches to quantifying the incident wind resource that can accommodate, for example, complex wind shear scenarios? 

My intention with this article is not to undermine established procedures, but just to remind people to scrutinise received wisdom, rather than just calmly accept it, and remember that the limitations on which our established procedures are based may themselves have been overcome, and that our procedures in general should always be amenable to review and revision to take full advantage of the technical capabilities of the tools available to us. The wind industry is a young industry which still offers exciting technical and scientific challenges.