In December 2013, Christopher Booker

in the Telegraph discusses a study by Gordon Hughes, published by the Renewable Energy Foundation in December 2012, which is said to show, due to wear and tear on their mechanisms and blades, the amount of electricity generated by wind turbines "very dramatically falls over the years".
Booker asserts that "Hughes showed his research to David MacKay, the chief scientific adviser to the Department of Energy and Climate Change, who could not dispute his findings."

**This is not true**.

In fact, I doubted Hughes's assertions from the moment I first read his study, since they were so grossly
at variance with the data.

**Figure 1:** Actual load factors of UK wind farms at ages 10, 11, and 15.

a) Histogram of average annual load factors of wind farms at age 10 years. For
comparison, the blue vertical line indicates the assertion from the Renewable Energy
Foundation's study that "the normalised load factor is 15% at age 10."

b) Histogram of average annual load factors of wind farms at age 11 years.

c) Histogram of average annual load factors of wind farms at age 15 years. For
comparison, the red vertical line indicates the assertion from the Renewable Energy
Foundation's study that "the normalised load factor is 11% at age 15."
At all three ages shown above, the histogram of load factors has a mean and standard
deviation of 24% ± 7%.
Moreover, by January 2013 I had figured out an explanation of the underlying reason for
Hughes's spurious results. I immediately

wrote a technical report about this flaw in Hughes's work, and sent it
to the Renewable Energy Foundation, recommending that they should retract the study.

I would like to emphasize that I believe the Renewable Energy Foundation
and Gordon Hughes have performed a valuable service by collating, visualizing, and making accessible
a large database containing the performance of wind farms.
This data,

*when properly analysed in conjunction
with detailed wind data*, will allow the decline in performance of wind turbines to
be better understood. Iain Staffell and Richard Green, of Imperial College, have carried out
such an analysis (in press), and it indicates that the performance of windfarms

*does* decline,
but at a much smaller rate than the "dramatic" rates claimed by Hughes. The evidence of decline is
strongest for the oldest windfarms, for which there is more data. For newer windfarms, the error bars on the decline rates are larger, but Staffell and Green's analysis indicates that the decline rates may be even smaller.

I will finish this post with a graphical explanation of the flaw that I identified

(as described
in detail in my technical report)
and that I believe underlies Hughes's spurious results.

The study by Hughes modelled a large number of energy-production measurements from 3000 onshore turbines, in terms of three parameterized functions: an
age-performance function "f(a)", which describes how the performance of a typical wind-farm declines with its age; a wind-farm-dependent parameter "u

_{i}" describing how each
windfarm compares to its peers; and a time-dependent parameter "v

_{t}" that captures national wind conditions as a function of time. The modelling method of Hughes is
based on an underlying statistical model that is

*non-identifiable*: the underlying model
can fit the data in an infinite number of ways, by adjusting rising or falling trends in
two of the three parametric functions to compensate for any choice of rising or falling
trend in the third. Thus the underlying model could fit the data with a steeply dropping age-performance function, a steeply rising trend in national wind conditions,
and a steep downward trend in the effectiveness of wind farms as a function of their
commissioning date (three features seen in Hughes's fits). But all these trends are
arbitrary, in the sense that the same underlying model could fit the data exactly as
well, for example, by a less steep age-performance function, a flat trend (long-term)
in national wind conditions, and a flat trend in the effectiveness of wind farms as a
function of their commissioning date.

The animation above illustrates this non-identifiability. The truth, for a cartoon world, is shown on the left. On the bottom-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 true site 'fixed effects 'variables u1, u2, u3 are all identical, for simplicity.) On the right, these 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).