The average of a decreasing trend extrapolated as an exponential growth in the future

While writing previous post, I got intrigued by the graph representing the electricity generation forecast until 2032, especially that yellow line representing the exponential growth of solar PV and wind. To recapitulate, this is the graph I am talking about:

The authors claim that this graph represents:

Current world electricity generation trends, extrapolated to 2032

They also state that the growth rate of solar PV was 28% and that of wind was 13% between 2012 and 2016. The yellow line, being a combination of solar PV and wind, will be somewhere between those two values.

The suggestion is that this growth of solar PV and wind is somehow established between 2012 and 2016, therefor could be used to extrapolate future values that give rise to that exponentially increasing yellow graph line. I wondered whether such trend really could been found between 2012 and 2016, so I looked at the values of electricity generation that I used for previous post:

Year	Solar + wind (TWh)	Difference (%)
2012	626.92	–
2013	781.97	24.73
2014	905.63	15.81
2015	1084.23	19.72
2016	1292.58	19.22

That is interesting. The first value of 2013 (difference between 2012 – 2013) is rather high and the years that follow all have lower values. Okay, that is for only four years, what about the value of 2012 (difference between 2011 and 2012)?. In last post, I assembled the data from different BP reports, but looking closer, I made it myself rather difficult. I could as well have used the underpinning data. When I look up the difference from 2012 compared to 2011, the value is 25.07%. Which is only a tad higher than the 2013 value. If I now put that in a graph then I get this:

The average trend of those five years is 20.91% (thin green line). The authors may even used a slightly bigger trend: starting with a value of 630 TWh in 2012, it requires a 21.5% increase to get a value of a tad above 30,000 TWh in 2032 as seen in their graph (but this could be due to the inaccurate way that the graph is drawn). Whatever the case, the growth rate for that yellow line seems to be around 21%. I will use the 20.91% from the BP data in what follows.

So, they seem to have used the mean of the trend between 2012 and 2016. This is rather misleading, since the trend in their reference period is actually going down.

Okay, maybe this is just a recent trend? Let’s just double the period and look at the last ten years:

Year	Solar + wind (TWh)	Difference (%)
2006	138.82	–
2007	178.54	28.62
2008	231.65	29.74
2009	298.82	28.99
2010	375.23	25.57
2011	501.24	33.58
2012	626.92	25.07
2013	781.97	24.73
2014	905.63	15.81
2015	1084.23	19.72
2016	1292.58	19.22

This is how it looks like as a graph (the thin green line is the base trend 2012-2016 and used by the authors for projection into 2032):

It is obviously not a recent trend, it is part of a longer downward trend. If it were fluctuating around this 21% line, then I would not even been bothered by such claim, but now there is a clear trend and it is decreasing.

When I think about it, it should not be surprising that the trend is decreasing over time. Expecting an exponential growth is wonderful in theory, but can be challenging in practice. In the beginning, it is rather easy to add 21% each year, but it will get ever steeper when time goes by and then it will get tougher to meet that 21% requirement each year. As also seen in their graph.

When it now suffices to add only hundred or a couple hundreds TWh per year, from 2024 it reaches one thousand TWh and at the end it is required to add almost 6,000 TWh a year. If electricity generation from solar and wind aren’t even able to cope with a 21% growth in the reference period when production is only in the hundreds TWh, then how plausible is it to assume that it will catch up when production needs to be in the thousands TWh? Especially knowing that the capacity factor of solar PV and wind (13% for solar PV and 23% for wind in 2016).

In the period 2012 → 2016, the values drop from almost 25% to somewhat above 19%. In the period 2007 – 2016, the values drop from almost 30% to somewhat above 19%. That is roughly 1 percentage point per year in both cases. If such a 1 percentage point trend continues, then production will slam into the x-axis within two decades. Meaning that growth of solar and wind will stagnates and will flatline.

When I incorporate the decreasing growth trend (decreasing 1 percentage point per year) and compare it with the idealized growth figures (increasing 20.91% per year), then I get this:

That is quite a difference. The yellow line is the 20.91% growth scenario, similar to the yellow line of the authors. The orange line represents the decreasing growth scenario that we see between 2012 – 2016. It is not the idealized unicorn-sprinkled-with-pixies-dust extrapolation that the authors started from, it is the extrapolation of the actual trend as there was in their reference period.

Okay, but could it not be that the authors start from the assumption that production of solar PV and wind will start ramping up from 2017 on? I don’t think that is the case. Their claim was that their graph respresents “Current world electricity generation trends, extrapolated to 2032”, so they assume that the exponential increasing yellow line is a continuation of the 2012 – 2016 trend. Which is not true according to the BP figures.

Some questions to conclude.

Did solar PV and wind grew in the period 2012 – 2016? Sure, production increased from 630 TWh in 2012 to 1293 TWh in 2016.

Was the average growth of solar PV and wind production about 21% in the reference period? Sure, it was.

Does this 21% increase results in an exponential growing curve similar to the yellow line in the author’s graph? It surely does.

Is it okay then for the authors to use that number as the trend into the future? Absolutely not! There is a clear trend DOWNWARDS in their reference period (and even before that) which is not taken into account when making the extrapolation. It is misleading to use the average of a downwards trending growth and assume that this will be the future trend from then on.

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