Graphic of the Week: What’s the required build rate for a sustainable energy system?

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One aspect of energy system that’s largely ignored is the ultimate sustainable capacity that can be achieved with a given rate of installation. Accustomed as we are to news about renewables breaking new installation records, we may overlook the fact that these installations will eventually reach the end of their lives and need to be replaced. And that, at some point, the entire production capacity will be devoted to nothing else but simply maintaining the current production level.

Calculating this equilibrium level can be a bit tricky, so I did the maths for you. Or, more to the point, I ordered my NetLogo to do so; you may download this wonderful (and free!) simulation environment here, and the .nlogo file I used here. Feel free to use and extend to your purposes.

The results are shown in the graph above. It shows the ultimate equilibrium production level reached for 1 GW of annually installed capacity, as a function of capacity factor and plant lifetime in years. In other words, it tells you what kind of an energy system you can have if you are able to install a gigawatt of generating capacity every year from here to eternity.

What you may instantaneously note about the graph is the importance of plant lifetime. The longer the lifetime, the less often you need to build new plants simply to replace old ones. Therein may lie a problem: the lifetime of the most popular and anticipated renewable generators (solar PV and wind) is likely to be around 25 years. What this means that the acclaimed record-high installation rates that have been achieved lately – for example, Germany’s 2012 record of about 7.6 GW solar per year – are simply not enough. If this rate could have been sustained indefinitely, the equilibrium production in Germany (where the capacity factor of solar PV hovers around 0.1) is about 173 terawatt hours, or TWh.

Last year, German wind power installations amounted to about 2.3 GW, yielding an equilibrium level of about 160 TWh (assuming average capacity factor of 0.3, which may be tad high). Solar slumped to 3.6 GW, which yields an equilibrium at about 82 TWh. As the primary energy consumption in Germany is annually about 3800 TWh (which is used, among other things, to produce ca. 590 TWh of electricity), one may be excused for exhibiting symptoms of panic.

Furthermore, given that the current German government is bent on reducing and eliminating renewable subsidies, it seems rather unlikely that even this poster boy of renewable revolution will see even similar installation rates again any time soon – if ever. Even farther seems to be the day when the installation rates soar to heights required for decarbonization: even to produce just electricity sustainably from renewable sources would require an annual installation rate of (say) 10 GW/a for solar and 5 GW/a for wind. Can even these rates be achieved – and sustained? Perhaps. Perhaps not.

And if one would want to replace fossil fuels in other uses of energy, such as transport fuels and sources of process heat, one would need to generate anything between – say – 1000 to 3800 TWh per year. One thousand terawatt hours could be sustained by installing (for example) 20 GW of solar and 8 GW of wind. Per year, every year. For 3800 TWh, the required installation rates jump to 76 GW of solar and 30.4 GW of wind.

Finally, it should be noted that the above computations give the physical maximum that can be produced. It completely ignores important difficulties, such as whether the power is produced at the time when it’s demanded. If this is not the case (and it will not be the case when the production is dependent on the weather), options such as energy storage are required – causing energy losses and necessitating further increases in build rates. As an example, well-informed renewable boosters have proposed to alleviate problems inherent in the variable renewable sources by simply building so many generators that enough of them operate at any given moment of time. Commonly seen estimates for this “overbuild” range from 2 to more than 10; that is, we may need 2 to 10 times as many renewable generators than the best case above would suggest.

Anyone willing to bet whether we’re ever going to see build rates that can sustain even a 2x overbuild in an industrialized economy?

POSTSCRIPT: What about nuclear?

In this calculation, nuclear power has two great virtues. First, nuclear plants last at least two times as long as renewable generators – new plants are designed for 60 years, and it seems possible to extend that to 80 years. Second, overbuild is much less an issue when you have a generator that typically produces power 80-90% of the time.

If the Germans were to utterly reverse their nuclear exit (fat chance, I know) and instead build approximately one new gigawatt class reactor per year, nuclear power would eventually stabilize to about 426.3 TWh. Combined with current renewable build rates, this would result to an equilibrium level of some 666 (\,,/) TWh of carbon-free electricity per year. Not enough to decarbonize fully, but significantly better than the current trajectory.

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About J. M. Korhonen

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6 Responses to Graphic of the Week: What’s the required build rate for a sustainable energy system?

  1. Nice, thank you! This is so obvious that I am constantly amazed how so few who talk about decarbonization understand this. Btw. I would guess that you could get pretty much the same result from equating the final capacity to yearly addition*life time. This should be about right as t–>> infinity. No? It is just that my instincts tell me to write a differential equation and then look for the steady state solution. Spherical cows type of preference…

  2. Oh yes, that’s the embarrassingly simple derivation I completely ignored :- chalk it up on being an engineer, if something can be done numerically then it’s done numerically, by Jove! :D

    Also, I have Plans ™ to extend this towards a more complete simulation model, whereby I might be able to study things such as variability. Maybe within ten years :D.

    • Well, naturally if the idea is to extend the computations later then it makes a lot of sense to spend some time in programming early on. Simple thing is also missing any transient effects that might be non-trivial. Let us say: What if funding for energy source X is pro-cyclical so that construction rate has booms and busts? (Could perhaps happen…who knows.) What happens to the capacity mix then? If, for example, lots of boom induced capacity drops out later in the time-evolution, they will presumably require corresponding capacity boom in the future. Some sources might require decade or so planning so choises for filling the hole caused by boom-bust cycle are more limited. How much variation will this cause in the resources required? Will it lock out some pathways without additional political decisions?

  3. kap55 says:

    Rather than simulation, direct calculation works too. For example, if plant lifetime is L and capacity factor is C, a 1 GW plant will have to be replaced in L years, which means a 1 GW plant needs 1/L GWs replaced per year. So if we’re building out 1 GW/year of any generator, the number of nameplate GW in the system at equilibrium is simply L.gigawatts. And the number of TWh that L gigawatts produce is simply L*C*8.766, which closely matches all the simulation results given above.

    • Indeed. If I had spent more than five minutes thinking before coding, I might have realized this, too. However. I’m planning to integrate this with couple other models anyway, in which this numerical approach has certain advantages.

  4. Pingback: 4. Vi behöver alla verktyg | Vänsterteknik

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