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Risk? What risk? Photocredit.

Our abilities in predicting the future are very limited, but that does not stop people from trying. As a rule of thumb I would recommend not trusting those who seem most certain since they are most likely to hide risks and use their divinations for personal goals. In energy discussions one commonly occurring tool of divination is the “learning curve”. It tells that for each doubling of the capacity of some technology you get certain fractional change in unit costs (a bit more than 20% reduction in the photovoltaics module cost, for example). The message that is usually delivered is that even though something is costly now, it soon will not be… if we stay the course and double the capacity sufficiently many times. Very few acknowledge that the learning curve is not a law of nature, but rather a rule of thumb that might work…until it doesn’t.  Discussion about implicit risks is almost always non-existent. In this post, I will dig into this issue a bit deeper highlighting some of the hidden risks involved.

To do this I will choose one specific future scenario and one specific technology. I choose to focus on the PV module costs, assume that we will increase the capacity by a factor of 100 to around 50TW by 2045. This implies (unrealistic in my opinion) exponential growth of the installed capacity with around 17% yearly growth (see figure below). This is somewhat artificial in a sense that for photovoltaics most of the costs are not from the module anymore, but I do this in any case to illustrate the math of the learning curve. I take the historical module costs and assume that technology has now matured and the module cost will remain the same from now on until 2045. What happens to our learning curves?


Capacity of photovoltaics in this thought experiment

As we proceed to the future, I recompute the learning curve every year by fitting the data to the new, stagnant, cost. We start with the learning rate somewhat above 20% today and then…almost nothing happens! How very exciting.


Learning rate from least square fit as capacity raised to around 50TW without any cost reductions.

To illustrate this I show below the learning curve at 2045 after almost 30 years
without cost reductions while capacity increased by a factor of 100. Learning curve fit is almost insensitive to the future costs since data points decades ago dominate the fit. It can enable the narrative of rapid cost reductions even after a generation of exponential growth without any cost reductions. It seems to be a tool perfectly designed to hide risks. It cannot identity when technology has matured (which might even be useful for marketers or thought leaders looking for lucrative career around single grand narrative).

There are ways to fix this though and the other fit demonstrates this. In this fit I choose to weight the points with the yearly installed capacity with the thought that data from building 100GW of panels is more informative than data from building 1MW. Now the fit does care about recently realized cost and the learning rate collapses. Fit is no longer good for points decades ago, but from the 2045 perspective it reflects what happened recently better.


Designed to enable hype ad infinitum. (Black line aims to get a more useful indicator. In the fit data points are weighted with installed capacity that year. Typo on y-axis label…should be $/kW.)

What would this imply for the costs of building all those panels? The last figure shows the required capital as a function of learning rate. There is an uncertainty of around 15000 billion $. If one only uses the highest learning rate, there is a possibility of understating the capital required for modules by a factor of around 4.


Panel investments as a function of learning rate. Factor of 4 underestimate possible. Who carries this risk? (Maybe another 30-40 trillion or so from balance of system costs?)

Things to ask/look for in cost studies:

  1. What was assumed about the learning effects? Constant learning ad infinitum for some techs and no learning for others? Is there a floor cost or not? There should be.
  2. Was the sensitivity for the learning rate analyzed? If not, then there is an attempt to burden someone (public) with risks (which is a cost) they were not informed about. As I wrote this I found this very recent presentation by Carrara et al., but it is worrying that this is not standard. Presentation tells us (see figure for example) that in our old friend REMIND-model PV share collapses from dominant to 10% range if learning stalls. Sensitivity is also asymmetric so that the sensitivity is larger for decreasing learning rates.  Because of this one would imagine a need to be extra careful in identifying technology maturation.

    Screenshot 2019-01-24 at 16.23.35.png

    PV share in the IAM models is very sensitive to assumed learning.

  3. Was the same learning rate used even after cost structure changed? For example, learning rates for PV are computed for modules, but costs are nowadays dominated by balance of system costs which have different (lower) “learning rate”.  I have read countless of articles and publications where this change of the cost structure is casually ignored. Since the risk seems to be towards lower learning rates than assumed, there seems to be substantial risk of too rosy IAM scenarios in the literature.
  4. Are the costs prior to the imagined future costs discussed? It is bizarre, but some actually imagine costs for 2050 which they then use to make claims about economical options today. Cost comparisons become disconnected from the real world with this one handy trick.

In case you were wondering if obstinately sticking to a narrative well past its best before date could actually happen, see how the wind turbine costs have developed. Costs today are about the same as 15 years ago.


Cost of US wind turbines according to “Wind technologies market report 2017”. Costs today are about the same as 15 years ago.

Meanwhile for example IRENA (and many others) still use the learning curve as if nothing has happened. How come?

screenshot 2019-01-24 at 16.05.40

There is something funny going on on the right hand side don’t you think? Shouldn’t you be a bit more careful with those fits? “No there isn’t. No I shouldn’t.”: IRENA 2017


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