Frandsen Wake Model Stability Fix

The Problem

It has been noted in the literature that the Frandsen class of wake models (i.e. models which simulate wakes as differential shear profiles due to turbines being represented as areas of increased roughness) fail to respond appropriately to changes in atmospheric stability. The DAWM used by UL is one such model and this is one reason that UL always uses this model with Neutral Monin-Obukhov Length (represented by the special value zero in Openwind). Pena and Rathman (2014) discussed and illustrated this failure and the figure below is taken from their paper.

In the figure below, IWFBL (infinite wind farm boundary layer) is a Frandsen-style boundary layer wake model like DAWM. The WAsP wake model does not respond to changes in stability (although of course it can be configured to respond to changes in turbulence intensity). Only the IPW (infinite park wake) model responds sensibly to changes in stability in that: wakes decrease with increasing instability due to increased atmospheric mixing; and increase with increasing stability due to low turbulence and decreased atmospheric mixing as well as potentially capping inversions and stratification. The IWFBL model shows a weakening of wake effects with increasing instability but responds far too strongly to increases in stable values of the Monin-Obukhov Length before reaching an inflection point after which increases in atmospheric stability result in decreased wake losses which continues past the point at which wakes losses are less than those estimated for a neutral atmosphere. Neither Pena and Rathmann nor Stefan Emeis, who worked closely with Sten Frandsen and collaborated on many papers, consider this behaviour to be reflective of the real world. We can recreate the IWFBL results using Openwind and the DAWM EV wake model. The figures below show variation in overall average array efficiency with changes in Monin-Obukhov length for four windfarms: two onshore and two offshore.

Windfarm 1: DAWM EV simulating 80 2MW turbines in the midwestern US with 80 hub height.

Windfarm 2: DAWM EV simulating 165 1.5MW turbines in a valley gap with 80m hub height.

Windfarm 3: DAWM EV simulating 260 offshore turbines with an average hub height around 100m

Windfarm 4: DAWM EV simulating around 200 offshore 3.6-6MW turbines at 90-95m hub height.

As can be seen from the charts above, the behaviour is similar to or even worse than the behaviour outlined by Pena and Rathmann. In the case of the onshore turbines, there is also an inflection in the array efficiency in increasingly unstable conditions which again seems implausible. The Solution There are alternative infinite wind-farm boundary layer models such as the one described by Stefan Emeis in chapter 6 of his 2013 book Wind Energy Meteorology. Openwind contains a finite wind-farm version of that model in the form of the Area Slow-down Model (ASM). The ASM also attempts to simulate variable blockage losses with stability and thrust coefficient. However, it has so far proved challenging to validate the ASM, largely due to the lack of publicly available datasets showing blockage effects in front of a windfarm although efforts to validate the ASM are still ongoing. There are also models such as the WRF-WFP model as well as approaches such as LES which may be capable of behaving in a more realistic fashion with changes in stability, although these more sophisticated models come at a cost in terms of processing time. For the purposes of wind-farm layout optimisation it is important that we have access to fast engineering approximations of the complex behaviour found in these more sophisticated models. For those wanting immediate access to a fast wind-farm wake model which can react sensibly to changes in stability, we are proposing, for now, that the MOL in Openwind be scaled by a factor of 20 times. This takes the portion of the charts above that lies between the two inflection points and stretches out to approximate the shape of the IPW model in the Pena and Rathman model. For the four wind farms simulated above in Openwind, this results in the behaviour shown in the charts below.

Windfarm 1: Using a MOL scale factor of 20

Windfarm 2: Using a MOL scale factor of 20

Windfarm 3: Using a MOL scale factor of 20

Windfarm 4: Using a MOL scale factor of 20

This admittedly somewhat arbitrary scaling may require further tuning but should prove adequate for the purposes of investigating whether or not the addition of MOL can increase the overall accuracy of the DAWM EV.