On the Performance of Wind Farms in the United Kingdom

David MacKay

pdf. (version 6.0 uploaded Tue 28/5/13)

This paper identifies a significant flaw in a recent study `The Performance of Wind Farms in the United Kingdom and Denmark,' published by the Renewable Energy Foundation, which claimed that wind farms in the UK wear out sooner than expected, and that recently-commissioned farms are substantially less efficient than older farms. The statistical model that underlies the method used in the study to infer the age-performance function of windfarms is non-identifiable, which means that no matter how much data is available, the age-performance function cannot be deduced by that model; the underlying model can fit the data in an infinite number of ways, with age-performance functions that fall or rise arbitrarily steeply. The method used in the study is believed to have resolved this non-identifiability in arbitrary ways; as a consequence, most of the conclusions of the Renewable Energy Foundation study are believed to be spurious. There is nothing wrong with the valuable data that was presented in the Renewable Energy Foundation's study, however, and it will be possible to use that data — either with different models, or alongside additional data (for example, weather data) that resolve the non-identifiability. Simple graphing of the data from the older farms suggests that their load factor has declined by roughly 2% per year, rather than the 5%, 6.5% or 12.8% per year asserted by the Renewable Energy Foundation. (All these percentages are fractional reductions per year.) How much of this downward trend should be attributed to intrinsic deterioration of the wind farm, and how much to a down-turn in the wind conditions over the period 2002-2011 is not resolved by my paper, but could readily be resolved by an approach that includes wind data. The REF study claims that `normalized load factors' of wind farms decline to 15%, 8%, 13%, or 7% in the 10th year of operation (with the number depending on the details of the fitting method). All these numbers appear inconsistent with the raw data which show that the actual load factors of 10-year-old farms are about 24% +/- 7%. The raw data show that even 15-year old farms have actual load factors of about 24% +/- 7%.

The animation below summarises the message of this technical report. On the left, the data from three farms (born in 87, 91, and 93) are shown in yellow, magenta, and grey; they are the sum of a age-dependent performance function f(a) [top left] and a wind variable v_t [middle left]. (The site 'fixed effects 'variables u1, u2, u3 are all actually identical in this cartoon example.) On the right, the identical data can be produced by adding the orange curve f(a) to the site-dependent 'fixed effects' variables u1, u2, u3 (shown in green), thus obtaining the orange curves shown bottom right, then adding the wind variable [middle right] shown in blue (v_t). This model (which I call "the underlying model" in the paper) has an unconstrained degree of freedom. The underlying model can, for example, fit the data with a steeply dropping age-performance function (f), a steeply rising trend in national wind conditions (v), and a steep downward trend in the effectiveness of wind farms as a function of their commissioning date (u1, u2, u3); this parameter-fit fits the data exactly as well as the true parameter setting.

The model actually used by Hughes differs in a a few detailed ways from the "underlying model"; in particular, some time-dependent variables are represented with month resolution, and some with year resolution. The statements that I have made apply to the underlying model, and only approximately to the actual Hughes model. Nevertheless, I am confident that the flaw I have identified in the underlying model is the essential explanation of the spurious results from Hughes's analysis.

related publications.
David MacKay's: home page, publications. bibtex file.
Canadian mirrors: home page, publications. bibtex file.