The most common cause of wind farm under-performance was solved 100 years ago.

Every year, a few owners ask us about one of their wind farms that is under-performing badly. Often in the 5% to 20% range. It can be painful: Asset value write-downs, debt restructure and PPA breaches. They often have an armful of technical reports by several providers, none of which contain a clear answer.

The questions are the same: Why is this happening, and what can we do about it?

There are usually several unrelated contributions - performance issues, curtailments, downtime and so on. One cause of under-performance is actually over-expectation though. It is also very easy to mitigate, long before the first hole is dug.

Let's do this!

It's the shear my dear

Most wind farms are financed with analysis involving a mast. Taller masts are much more expensive, so developers use ones that are less tall than hub height to save cost.

During the analysis there are two challenges. The first is to work out the wind speed at the height of the mast. Then after that, working out the wind speed up at turbine hub height. We call the change of wind speed with height 'shear'.

The planetary boundary layer

When air flows near something, aerodynamicists (yep that's me) call that air flow the 'boundary layer'. Boundary layers are found on many scales, from the wings of a butterfly, to those of an aircraft.

At even bigger scales, wind farms usually live entirely in the planetary boundary layer. i.e. the boundary layer of the atmosphere as it flows over the surface of the world, usually hundreds of metres thick.

The theory came first...

You can think of Ludwig Prandtl, and Theodore von Kármán as the fathers of boundary layer theory, published in 1930.

Prandtl and von Kármán found that changes in wind speed were proportional to changes in the logarithm of distance from the surface (height in our case). This is often called Log Law but has other names too. If we know the wind speed at two different lower heights, we can use this equation to predict wind speeds at hub height.

...then the engineers got involved

Engineers like to come up with so-called 'engineering approximations'. The log law can be unintuitive, and a simpler Power Law is a decent fit in most cases. With Power Law we can characterise shear with a single number (often termed the alpha coefficient). 0.08 is very low shear. 0.4 is very high shear. Higher values mean bigger changes of wind speed with height. Nice and easy.

Most preconstruction analysis used in wind farm financing uses power law rather than log law to predict hub height wind speed at wind farms.

As you can see from the figure at the top, log law and power law are very similar. In normal wind farm analysis applications though, using power law usually results in a slightly higher hub height wind prediction than using log law. Most of the time, this is an over-prediction.

(It is notable that the log/power decision has long been a factor, even when hub heights were half what they were now, since it is height ratios that matter not distances in metres. A mast at 2/3 or 3/4 of hub height will present a risk at any scale)

Strongly held beliefs

The truth is that it is very difficult to measure shear accurately enough to discern whether the log or power law is more accurate in any one specific case. It tends to be obscured by anemometer uncertainties and correlation scatter.

Also real world boundary layers have all manner of shapes, varying with surface roughness, terrain shape and atmospheric stability. Both log and power law are approximations.

There are also very strongly held opinions, and a great deal of inertia, caution and reluctance to change.

To avoid distraction, I'm actually going to gloss over the theoretical debate, and focus on real outcomes, at real wind farms.

Hard won experience

Looking back over 20 years of experience, including numerous performance reviews and reconciliations, things become clearer.

A large proportion of under-performing projects have something in common: They tend to be in places with relatively high shear, with a mast shorter than hub height, and the analysis has been done with power law.

Put simply, the over-prediction of wind speed at hub height is a very common contribution, even when very good quality masts are used.

Use of log law often materially closes the gap, by as much 5% of long-term energy yield, and occasionally more.

Are we learning though?

The truth is that if these analyses had been done using log law, in most cases a more realistic estimate of long-term production would have been known before construction rather than after.

So let's assume for now that Prandtl and von Karman were right in 1930 with the Log Law, and although the power law is a nice easy approximation, it is not as accurate. The technical fix then is very easy. Simply use log law in hub height wind speed prediction, at least in most situations.

The main blocker though is not technical, but commercial and reputational. Lower energy numbers are uncomfortable for everyone, so power law will continue to see widespread use, and be defended to the hilt by those that do.

Wind farm owners unite!

The solution really comes from those who end up carrying the cost of over-prediction - the long-term owners of wind farms. They are the ones that could insist on analysis using log law during the acquisition of wind farms.

It would be a pity if one of the key causes of asset under-performance, discovered nearly 100 years ago, wasn't used to inform investment.

Try Boxkite

Boxkite now accepts wind measurement datasets. It is fast and easy to use, and the next update will do shear analysis, using log law. If you'd like to try Boxkite for your next acquisition, or you're on the sell-side and want to know what impact it will have, get in touch at [email protected].