A few days in the past (January 11, apparently shortly after midnight) on Watts Up With That, Christopher Monckton revealed a chunk that ran underneath the headline “The Ultimate Nail within the Coffin Of ‘Renewable’ Vitality.” The piece contained a brief and apparently elegant mathematical proof — which Monckton attributes to a man named Douglas Pollock — of a proposition that Monckton said as follows:
In plain English, the utmost potential fraction of whole grid technology contributable by unreliables seems to be equal to the common fraction of the nameplate capability of these reliables [sic — should be “unreliables”?] that’s realistically achievable underneath real-world situations.
Monckton (and Pollock) thus appear to be saying that if (for instance) a wind turbine system can solely generate about 35% of nameplate capability “realistically achievable underneath real-world situations,” then it’s futile to construct any extra wind generators when you get to 35% wind penetration into output, as a result of the 35% penetration is a mathematical restrict that can’t be exceeded.
My instant response was that that couldn’t probably be proper. I used to be planning to put in writing a remark over there declaring what I assumed was the flaw. However earlier than I obtained round to it there have been 300 or so feedback on the submit, which needed to a tragic diploma degenerated right into a name-calling match between Monckton and a few adversaries. So quite than writing a protracted remark there that will then be buried on the backside of all of that, I made a decision to put in writing a submit right here, which can or might not then get cross-posted at WUWT (it’s as much as them).
This matter illustrates why, once I dabble in math in my posts, I attempt to keep on with easy arithmetic. Not that mathematical proofs aren’t enjoyable — I’ve executed quite a lot of in my day — however it’s very simple to make an implicit assumption that you just don’t acknowledge and find yourself with a end result that doesn’t actually assist the conclusion you suppose it does.
First, right here’s what I feel is the flaw: Monckton/Pollock, maybe with out realizing it (or possibly, as a result of they suppose it’s too ridiculous to even think about), have assumed that there can be no “overbuilding” of intermittent technology capability. By overbuilding, I imply constructing so many mills that when the wind and solar are at full energy the system produces extra electrical energy than the demand, which electrical energy then needs to be discarded or wasted. (You usually see the time period “curtailed.”)
However sadly, overbuilding may be very a lot on the desk as a solution to get extra wind and photo voltaic enter into the system and, supposedly, scale back using fossil fuels. For example, in a submit on July 30, 2022 I compiled some statistics for the nation of Germany that had been put out by the U.S. Vitality Data Company for the yr 2020. Based on that knowledge, in 2020 Germany had common electrical energy utilization of about 57 GW, and peak utilization of about 100 GW. Nevertheless it had wind generators with “nameplate capability” of 62 GW and photo voltaic panels with nameplate capability of about 54 GW, for a complete between the 2 of 116 GW. So when the wind and solar are each producing at full energy and utilization is common, Germany has greater than twice the electrical energy it wants simply from the wind and solar even when all the pieces else is turned off. They should “curtail,” or alternatively, as I perceive it, wholesale energy costs go damaging and so they should pay Poland to take the surplus energy off their arms. And but, within the effort to get to the imaginary “all renewable” future, Germany continues to construct extra wind generators and photo voltaic panels. So, as ridiculous as it could appear, overbuilding is definitely occurring in the actual world, and extra of it’s coming.
Based on the German Umwelt Bundesamt (Federal Environmental Company), Germany obtained 41% of its electrical energy from renewables in 2021. That properly exceeds the “common fraction of nameplate capability” of the wind and photo voltaic mills that’s “realistically achievable” (nevertheless that could be outlined), which is round 30% averaged between the 2 of them. The distinction, I consider, is a results of the overbuilding. Thus the case of Germany demonstrates that overbuilding can, and in the actual world does, result in exceeding what Monckton calls the “Pollock restrict.”
As an example how this works, let me introduce some math. Nonetheless, in accordance with my observe, I’ll keep away from fancy proofs and keep on with easy arithmetic.
Think about an electrical energy system with a relentless 1 GW demand, to be provided to the extent potential with wind generators. Assume that the wind generators function at 50% of nameplate capability averaged over the course of the yr. On this location, it seems that the climate is such that the wind blows at full energy 25% of the time, half energy 50% of the time, and in no way the remaining 25% of the time. You construct 1 GW of nameplate capability of wind generators to precisely match demand when the wind is at full energy. Over the course of the yr, you get from the wind generators all your demanded electrical energy 25% of the time, half of it 50% of the time, and none the remaining 25% of the time, which as said involves a mean of fifty% over the course of the yr. The penetration of wind energy on the grid at 50% is the same as the capability issue of the wind generators at 50%, and thus is strictly on the “Pollock restrict.”
Are you able to get greater than the 50% grid penetration from wind manufacturing, although the generators solely produce at 50% of nameplate capability? Sure — by overbuilding. You may double the quantity of wind generators. Then, within the 25% of the yr when the wind blows at full energy, you’ll get double the electrical energy you want, and must discard or “curtail” half of the manufacturing. Within the 50% of the time when the wind blows at half energy, you’ll get precisely the quantity of electrical energy you want. And within the remaining 25% of the time when the wind doesn’t blow in any respect, you get nothing. Averaged over the course of the yr, although the wind generators solely function at a mean of fifty% of capability, you’ve gotten 75% of your electrical energy from the wind system, at the price of doubling the scale of the system and throwing away 25% of the electrical energy produced. And you continue to don’t have any electrical energy 25% of the time.
However suppose you wish to get nearer to all your electrical energy from the wind. Too unhealthy — you’ve maxed out. If you happen to once more double the quantity of wind generators, you should have 4x the quantity of electrical energy you want throughout the 25% of the time when the wind is at full energy, 2x the quantity you want when it’s at half energy, and nonetheless nothing when the wind is calm. In different phrases, underneath these assumptions, with a 2x overbuild, you’ve maxed out your % of electrical energy from wind at 75%. The 75% is properly greater than the 50% “Pollock restrict” of those assumptions, and occurs to correspond precisely to the period of time when there may be any usable wind in any respect. In easy phrases, overbuilding can get you above the “Pollock restrict,” however no quantity of overbuilding can clear up the issue of full calms. For photo voltaic, the identical precept applies to nights.
So how do you identify what’s the most share restrict of wind technology on a grid when overbuilding is allowed? Take into consideration this somewhat, and possibly do a few extra easy examples in your head, and you’ll notice that the next is true: with overbuilding and curtailment allowed with out restrict, the utmost penetration of renewables on a grid is 1 minus the % of time when the wind doesn’t blow and/or solar doesn’t shine sufficiently to generate any electrical energy in any respect. The place all of the renewables are wind, if the wind is totally calm (or at the least so gentle that the wind generators don’t flip) 10% of the time, then the utmost penetration of wind onto the grid is 90% (i.e., 1 minus 10%). So long as there may be even slight technology from the wind, a theoretical large overbuild might flip that into sufficient provide to satisfy demand. Suppose that one other 10% of the time the wind solely blows sufficiently to generate 1% of nameplate capability (with all different instances producing increased percentages). Then you may get nonetheless to the 90% theoretical restrict with a 100x overbuild. Even when the wind generates solely 0.1% of nameplate capability for a considerable period of time, you possibly can nonetheless hit the 90% theoretical most with a 1000x overbuild. However you possibly can by no means cowl that final 10% when the wind is totally calm, as a result of any quantity, regardless of how giant, instances zero, equals zero.
In order that’s my contribution to the mathematics of this matter. Now a number of ideas on what has occurred over at WUWT. I’m going to cite in full the phrases through which Monckton states the Pollock proof, highlighting the place I feel the flaw lies:
Let H be the imply hourly demand met by a given electrical energy grid, in MWh/h. Let R be the common fraction of nameplate capability really generated by renewables – their imply capability issue. Then the minimal put in nameplate capability C of renewables that will be required to satisfy the hourly demand H is the same as H/ R.
It follows that the minimal put in nameplate capability N < C of renewables required to generate the fraction f of whole grid technology really contributed by renewables – the renewables fraction – is the same as f C, which can be f H / R ex-ante.
Now right here comes the magic. The renewables fraction f, after all, reaches its most fmax the place hourly demand H is the same as N. In that occasion, N is the same as H ex hypothesi and in addition to fmax H/ R ex-ante, whereupon H is the same as fmax H/ R.
Since dividing either side by H reveals fmax / R is the same as 1, fmax is essentially equal to R.
I feel that within the bolded phrase “the minimal put in nameplate capability N < C of renewables” Monckton has assumed that no overbuilding is allowed. It’s removed from 100% clear, and I’ve issue parsing the sentence. I might agree that if no overbuilding is allowed then the conclusion follows that the utmost potential fraction of grid penetration by the renewables would equal the common fraction of nameplate capability at which the renewables produce averaged over the yr. The utmost would happen, at the least as one instance, when common electrical energy demand is fixed over the yr and the nameplate capability of the renewables was equal to that fixed degree of demand. If, however, demand fluctuated over the yr, then there can be instances of peak demand when even full nameplate capability of manufacturing couldn’t fulfill demand, and due to this fact the extent of grid penetration by the renewables would fall beneath their common capability issue.
Sadly, Monckton didn’t state in his conclusion (quoted in italics approach again in the beginning of this submit) that the conclusion solely utilized in a case the place there was an assumption of no overbuilding. A number of commenters at WUWT (e.g., chadb, Joe Born, “it doesn’t add up”) weighed in to offer examples from locations like Texas and the UK the place grid penetration might go above Monckton’s “Pollock restrict” with overbuilding. As a substitute of merely recognizing {that a} small modification to his conclusion was so as, Monckton then launched into a tragic spherical of name-calling. For instance, from a remark time-stamped January 11 at 2:40 PM, replying to Joe Born, Monckton calls Born “incompetent,” “idiotic,” “silly,” a “nitwit,” says he used a “half-witted phrase salad,” and may “get his kindergarten mistress to learn to him.”
Over the course of many, many feedback replying to others, I feel that Monckton finally concedes that his end result solely applies to a state of affairs the place overbuilding shouldn’t be allowed. He calls such overbuilding “wasteful” and “silly,” with which I will surely agree. Nonetheless, many governments are at the moment heading down that path. Germany is already there, and continuing farther and farther by the day. The UK is already there as properly, or at the least very shut. California and New York usually are not far behind. So I don’t suppose that we are able to simply dismiss overbuilding circumstances as so silly that nobody would ever do it.
For any readers who’re excited by a deep dive on this topic, I extremely suggest Ken Gregory’s definitive August 2022 examine titled “The Price of Internet Zero Electrification of the united statesA.” Gregory explicitly considers paths to “internet zero” within the face of the random intermittency of the renewables. Choices thought-about by Gregory embrace batteries, overbuilding, and carbon seize and storage. For what it’s price, Gregory finds that inside sure ranges and at sure assumed costs, overbuilding is a superior various to batteries for growing grid penetration of renewables — which isn’t saying rather a lot, however is saying that overbuilding, whereas it could be insane, is much less insane than different choices that seemingly everyone seems to be speaking about as in the event that they make sense.
I ought to say that I’ve reviewed Mr. Gregory’s examine extensively, and I’ve not discovered a flaw. That doesn’t imply that there aren’t any. The identical goes for my very own easy arithmetic above on this submit, which might comprise flaws as properly. If any reader discovers any such, I encourage you to level them out, and I hope that I’ll settle for the criticism with a very good spirit, and make any corrections which might be acceptable.
In the meantime, I’ve lengthy adopted Lord Monckton’s work, and revered a lot of it, and I’m saddened to see him go considerably over the sting on this one. To the extent that my feedback right here might seem crucial, they’re provided within the spirit of attempting to get the suitable reply, and hopefully of friendship and cooperation.
For the total submit click on right here.
