The “Pollock Limit”

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From Watts Up With That?

Guest Post by Willis Eschenbach

Christopher Monckton recently put up a fascinating post entitled “The Final Nail in The Coffin Of “Renewable” Energy”. In it, he references the work of a man named Douglas Pollock who has proposed that there is a limit to the share of energy that a given renewable source can supply to the grid without battery backup. Further, Pollock says that the limit is the “capacity factor”, the fraction of the nameplate capacity that a renewable source can actually supply.

A rebuttal of this was put up as a post entitled “Sealing The Coffin Of “Renewable” Energy May Take A Few More Nails“, and Lord Monckton posted up a re-rebuttal entitled “Why Climate Skepticism Has Not Yet Succeeded“.

(Unfortunately, in the comments of the latter post I fear I waxed wroth when Christopher falsely accused me of being “openly and deliberately dishonest” … ah, well, I know that science is a blood sport, but I won’t take that from any man. However, I digress …)

While interesting, Lord Monckton’s posts are theoretical exercises. He has not provided any actual data to back them up. And when I looked at the data, I found a problem—most countries are well below the “Pollock limit”, and thus they can’t say anything at all about what happens when the windpower share of total electrical generation nears the Pollock limit.

Figure 1. Percentage of electricity from wind by country. Dotted line shows the global average wind capacity factor, which is the average fraction of the nameplate capacity that a wind turbine can actually supply in the real world.

However, a couple of countries have renewables shares that are above the Pollock limit. I picked Ireland as a test case. I got the annual information on the Irish electrical supply from the BP Statistical Review of World Energy. Here, on a year-by-year basis, is the annual windpower share of total Irish electricity versus the annual installed capacity (red/black line), as well as the annual capacity factor (yellow/black line).

Figure 2. Annual Irish wind share versus installed wind capacity, and wind capacity factor. 2022 values are from here and are preliminary.

There are several interesting insights from Figure 2. First, in contradiction to the proposed numerical value of the Pollock limit as being equal to the capacity factor, the wind power share of total Irish electricity is well above the wind capacity factor.

Next, it’s interesting how much the wind capacity factor varies year to year, swinging about ± 5% above and below the average value,

Next, in agreement with the concept of the Pollock limit, as the installed capacity has increased, the windpower share has moved more and more in parallel with the wind capacity factor.

Finally, the last four years are particularly interesting. From 2019 to 2022 Ireland added about 4 TWh of wind nameplate capacity … but the share of the total generated by wind only increased slightly. So it certainly appears as though it’s approaching some kind of limit.

These facts taken together suggest that there is a limit, as the Pollock limit states, but that in the Irish case, it’s higher than the capacity factor.

To visualize this in a different way, I looked at the annual windpower share as a percent of the annual capacity factor. Here’s that result (yellow line), along with theoretical calculations of what it should look like if the Pollock limit were 100% of the capacity factor (blue/black dashed line), and also what the real limit curve might be (red/black line).

Figure 3. Irish annual windpower share of total generation as a percentage of annual wind capacity factor (“Pollock limit”)(yellow), along with theoretical Pollock (blue-dashed) and possible real-world (red) limits.

In Figure 3, the curves show the situation when as the share of total generation approaches some physical li limit, each addition of wind capacity will make less and less difference as it slowly approaches the limit.

So … is there a limit?

The Irish data strongly implies that such a limit exists. And at least in the case of Ireland, it’s likely higher than the current value of 22.5% above the Pollock limit. Is it on the order of 40% above the Pollock limit as the speculative red curve illustrates? Perhaps. Perhaps not.

The problem is that we don’t really have enough data to say definitely what the limit is for Ireland, or even if such a limit exists. What’s shown in Figure 3 could just be a temporary slowdown … or not. A few more years should make things much clearer.

And that’s what I have found out about the Pollock limit. I have exactly zero idea why Ireland is able to exceed the Pollock limit. The claim is that, absent grid-scale batteries, the Pollock limit is a real physical limit equal to the capacity factor. But that is certainly not the case for Ireland. It’s already 22% above the capacity factor. Why? How?

The reason cannot be economics, because Christopher’s mathematical derivation in his original post doesn’t contain any economics-related terms. (Or alternatively, if economics is the reason, then Christopher’s math must be incomplete.)

All thoughts on that question considered, although perhaps not replied to. So many drummers, so little time …

My best to all, and thanks to Christopher, Lord Monckton for highlighting Pollock’s most interesting theory.

w.

As Always: When you comment please quote the exact words you are referring to. I can defend my own words. I cannot defend your (mis)interpretation of my words. Thanks.

A Footnote Worth Noting: I am an honest man. I do my very best to tell the truth as I know and see it. Yes, I have been wrong, and more than once. And when I’m wrong, I admit it. Heck, I even have a whole post called “Wrong Again“, and to cap that off, another post called “Wrong Again, Again — who does that but a scrupulously honest man?

But despite being wrong at times in matters big and small, wrong far more times in my life than I’d prefer, I do my honest best to not ever lie, shade the truth, misstate facts, or deceive people.

So I’ll thank everyone to avoid accusing me of any of those misdeeds, as it angrifies my blood. And if that happens, it may well result in me conjecturing about the probable species and personal hygiene of some of your recent progenitors … and it also would involve a significant chance of me politely inviting you to engage in anatomically improbable acts of sexual auto-gratification and self-congress …