Monday, January 30, 2012

Interminable innumeracy: "renewables" versus nuclear

Back to the Future Delorean
Interestingly, Doc Brown's modified Delorean was also the
equivalent output of a modern nuclear plant. Heavy.
A confession - I listen to and read a fair amount of science stories. (Yes, self-outing as a nerd right out the gate). And whenever the topic of renewable energy sources comes up, invariably a spurious comparison to the generating capacity to nuclear plants will come up. For example, identified resources for say, offshore wind will be identified somewhere in the realm of tens of gigawatts, to which the guest will inevitably state, "That's the equivalent of dozens of nuclear plants!" (i.e., about 1 GW each). Naturally, no clarification is given to the important factors here - as in, just how many wind turbines / solar cells / magical crystal arrays (okay, so maybe I'm exagerating with the last one) are required to accomplish this task, much less the inherent capacity factor in such a generating system. (In other words, the sun doesn't shine and the wind doesn't blow all the time, meaning these generators sit idle for more time than they actually generate power).

A basic unfamiliarity with these concepts (i.e., the scale of individual energy generators and their respective availability factors) tends to produce a pervasive level of innumeracy, which in turn leads to genuinely terrible energy policy positions, such attempting to displace some or all of baseload capacity (including nuclear) with intermittent sources. In an effort to combat this epidemic (and inspired by the old Total cereal commercials which used to air back when I was growing up) I've put together an infographic to demonstrate just how many of these types of generators one needs to replace just one baseload unit.

Comparison of generating requirements of nuclear, solar PV, and wind

I've made high-resolution versions available for download and reuse as well (svg and pdf).

The next time someone claims that renewable energy sources can somehow "displace" nuclear sources for baseload (such as say, Germany is attempting to do), I invite you to ask just how many units (and at what assumed capacity) will be required to accomplish the task. Chances are very good the advocate either doesn't know or simply isn't being honest with the numbers.

An aside: Does this mean I don't think we should use renewable sources at at all? Not really - if sources which coincide with peak demand (such as solar) can shave off demand for "peak unit" power (typically provided by fast-response units like natural gas turbines) and do so at an economically competitive price, more power to them. But don't count on inherently diffuse sources of energy providing baseload power needs anytime soon.


  1. Great graphic, Steve! A similar one comparing land area would be useful, though one would need to make average assumptions about turbine and panel spacing. I hope the viewers of the graphic notice that each turbine or panel icon corresponds to *five* actual turbines or panels. - Mark N.

  2. I think it is a bad idea to represent 5 turbines or 5 "installations" of solar PV with one icon. Otherwise the graphic would illustrate the point even more dramatically.

  3. Hey Steve, saw your post through Mike. In general,I agree with you, but some of your numbers seem off. An 11,000 MW nuclear facility would require at least 7 reactors. It seems like it would be more accurate to put your numbers in terms of a single reactor. Also, you did not include any discussion of energy cost. Wind power is cheap. It is almost one third the cost of nuclear per kilowatt hour. Alternatives have their place offsetting some baseload. True, it's not dispatchable, but a large interconnected network would come pretty close.

    1. A large interconnected network is such a good idea that it's worth more to the consumers than to the producers. But it doesn't come anywhere near eliminating the random walk of wind power. The trouble is, that if you take 100 arrays each of N random numbers, and add the I-th elements together to obtain an array of N numbers, the array that you get is still an array of random numbers.

  4. @Shyam - Thanks for reading, but I think you're misreading the graph itself. The indication is for one 1,000 MW reactor - not 11,000 of nuclear capacity - i.e., one reactor is roughly 1,000 MW (a little more for the newer designs).

    I'm skeptical of any claim that wind power is 1/3 the cost of nuclear - I am left to question under what conditions this bears out (i.e., post feed-in tariffs?) No study I've seen so far puts wind energy at this price point - this is far cheaper than natural gas, which utilities have been rushing to build.

    EIA's estimates for levelized cost of electricity don't bear out this extreme prediction of cost at all - they put wind around $96.1/MWh for onshore and $244 for offshore, with advanced nuclear around $114; and combined cycle natural gas even cheaper. So there's just no way the claim that wind is 1/3 the cost of nuclear is true.

    Further, amortized nuclear - in other words, existing plants whose capital costs have been paid off - are insanely cheap, given the extremely low fuel cost for nuclear.

    Finally, one issue with baseload is predictability - wind power is notoriously unpredictable, unlike even solar (which is relatively stable by comparison). This isn't even a matter of dispatchability - it's fundamentally a matter of being able to enter into long-term electricity contracts, something which fundamentally cannot be done (at least at an individual producer level) given the inherent intermittency of wind.

    1. My number for wind was coming from memory of a presentation (at a design firm that designed both nuclear and fossil plants) I saw 4 years ago. The numbers must have been after subsidies. It seems inaccurate not to include a spent fuel storage costs in nuclear energy.

      This is the article I read on making wind dispatchable:

    2. Shyam: Many (if not most) nuclear cost studies I have seem account for disposal costs; further, disposal costs are paid by ratepayers, at the rate of $0.001/kWh, per the 1982 Nuclear Waste Policy Act. Regardless, it seems useful to identify electricity on a total cost to total cost basis - i.e., total cost per unit energy, neglecting feed-in tariffs and other end-buyer subsidies. (Disentangling the more embedded subsidies may be a more difficult and contentious task.)

      Interesting article about dispatching - although it seems like in this case, it's less about dispatching wind power itself as it is taking "credit" for energy produced and then using those production credits later - at least the "banking" part of it.

      The P-curves (i.e., production guarantees) at least seems like an interesting way of dealing with the problem of planning out time-dependent wind energy capacities.

    3. I believe that the costs per kWh of energy from wind turbines and nuclear are incommensurable. The capital costs in both cases are dominant, wind seems to be free, and the fuel cost of uranium is negligible compared with the capital cost. But in both cases, the capital cost is huge and dependent upon public perception and its manipulation. The longer the lawyers spend quarrelling about nuclear plant construction, the more expensive it gets. If we had a Coal Regulatory Council process as expensive as the Nuclear Regulatory Commission's licensing process, and one for Gas Fracking as well, nuclear would come out way ahead.
      But there is, and has been since about 1986 to 1994, a nuclear option in which the fuel for the next 200 years, for all our present energy demand, would be stuff now embarrassing us as "waste" and "depleted uranium". It was called the Integral Fast Reactor, and a descendant of it is designed to give 100 MW for 20 years on a 20 .3 ton fuel core that only needs about 2.5 tons of actual waste removed at the end of that period, then can be refurbished with natural, or depleted, or "spent" uranium.

      Even that may not be the best option, since the LFTR has the advantage of slightly more plentiful fuel (thorium) and a liquid fuel medium that easily sequesters the most inconvenient of the fission products, the neutron-absorbing xenon-133.

      Note also that because these breeder reactors do not treat spent fuel and trans-uranides as waste, the nuclear waste is both small in quantity and short-lived.

  5. Steve, it is a good graphic, but I agree with Krzysztof. If you are trying to show how many wind turbines or solar panels are needed to generate the same amount of electricity as one nuclear reactor it doesn't make sense to have one turbine icon equalling five actual turbines.

    Also, the relative sizes of the icons might be misleading. Cooling towers and wind turbines of the capacity you are considering are quite similar heights. By having the size of the wind turbine icon much smaller it gives the impression the 'amount' of wind turbines needed is less in comparison with NPPs than might be the case (putting aside the issue of representing nuclear with cooling towers, which many NPPs don't have and other thermal power stations do.)

    Finally, it might give the wrong impression to just add greyed-out additional icons to represent the difference in capacity factor. The point is you can't just add more wind turbines or solar panels to deal with the intermittency. You could have a million solar panels and they won't match any nuclear power plant once the sun goes down. As you say, solar's daytime generation can be very useful for addressing peak loads and displacing peaking gas or coal. But 755 solar panels do not equal one nuclear power plant.

  6. @Jonathan: All valid points. To be honest, I'd considered some of the issues you'd brought up (i.e., capacity is not simply an arithmetic substitution, given the inherent intermittency of certain sources), however my first-order goal here was to just convey the idea of the radical difference in actual capacity from nameplate capacity to begin with - this is where I think the problems begin.

    To that end of course, some choices were inherently artistic - for example, even though plenty of NPPs lack cooling towers (and some fossil plants actually have the hyperbolic towers), to the public they are an iconic representation of nuclear units. With respect to the 5:1 ratio - this was originally the design concept I had originally attempted, although it became quickly unwieldy - difficult to work with and the actual message drowned out in a sea of wind turbines. (Again, perhaps that the point, but I think even at a 5:1 ratio the point is relatively obvious).

    Finally, you are absolutely correct that it is simply not a matter of "add more units." Again, this is getting to a higher level of analysis - fundamentally, I think one of the problems the public does not comprehend is how many units are required just to reach the capacity of a nuclear unit alone, much less how inherently limited they are by capacity. Perhaps this is something I can attempt in a second version.

    Thanks for reading!

  7. Your capacity factors for wind and solar are quite generous. I think you can safely cut them both in half and still be fair. This would make your point all the more obvious, not that you need it.

    1. @Anonymous @ 6:10 AM - absolutely so. However, to avoid objection by wind/solar proponents, I used numbers published by the EIA (referenced in the URLs on the chart) - numbers which I agree seem rather generous compared to other estimates I have seen. Then again, as you say - even with the most generous assumptions of capacity, the point stands.