From Watts Up With That?

FOREWORD: There has been a lot of back-and-forth over this topic, perhaps so much that it has become tiresome. A lot of the back and forth could have been avoided if the so-called “Pollack limit” was simply refererred to as a curve. Therefore this will absolutely be the last essay published at WUWT on this. No rebuttals, no, “yes buts”, no exceptions; my “limit” has been exceeded. Take it to direct email or peer review. – Anthony Watts

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By Chistopher Monckton of Brenchley

The Pollock limits on the amount of wind or solar power that may be installed in a given grid without disproportionate increases in cost and waste have aroused much interest in many quarters, particularly among grid operators.

Willis Eschenbach, has contributed an interesting post in which he shows that the Falkland Islands, Denmark, Lithuania, Ireland and Uruguay are generating wind power in excess of what appears to be a global mean capacity factor of 26%.

However, electricity grids are local, and the capacity factors for the weather-dependent renewable generation sources likewise vary from place to place, depending upon regional weather. Seeking to apply a global average wind capacity factor is, therefore, inapposite.

The Falkland Islands (I was there) have ideal conditions for generation by windmills. I do not know what the grid capacity factor for the Islands is, but it will considerably exceed 26%.

Willis also proposes Ireland as a counter-example to the Pollock limits. He cites BP’s estimate that the Irish wind capacity factor (also its Pollock limit) is 27% on average, and shows that, following recent increases in installed wind capacity, wind power is contributing to grid output about 5% more electricity than the corresponding Pollock limit.

The grid operator, however, puts the multi-year mean capacity factor at 28.5%, suggesting that the overage in the past year or two is only 3.5%. One reason why it is physically possible (though wildly uneconomic) to generate above the Pollock limits is that in some years – 2022 was a striking example – the weather was atypically favourable to wind and solar generation.

Another influence on the Irish grid in recent years is frequent thermal-generation outages, caused by the dash for wind and the consequent failure to maintain adequate thermal supply. In 2021-2 thermal availability was 12% below the usual 77%.

Furthermore, as I have already pointed out, even if wind or solar power on a grid approaches but does not exceed the Pollock limit, costly and wasteful over-generation will occur at times when wind and sun are strong and demand is low. A fortiori, wasteful excess generation will occur where the Pollock limit is breached, and the cost, waste and grid destabilization will rapidly increase the greater the excess of installed capacity over the Pollock limit.

Sure enough, EIRgrid has been making wasteful do-not-generate orders on a large scale in recent years. Willis’ initial reaction was that no cost to consumers would result. However, the subsidy-farmers will either pass on the cost of the downtime to their customers or have priced in such stop orders in their existing price structure. It is ultimately the consumer who pays.

Likewise, EIRgrid is interconnected to the far larger UK grid and can dump excess power to it, though usually at heavily loss-making prices. In this respect, the UK grid is acting as though it were battery backup for the Irish grid.

However, Willis also fair-mindedly concludes that there does appear to be evidence of an asymptote above which adding wind or solar power does not commensurately increase renewables penetration. To that question I now turn.

Let me simplify the derivation of the Pollock limit, beginning with some definitions.

The mean grid capacity factor Z of wind or solar power is the ratio of generation achieved by that source in multi-year-averaged annual mean weather to its nameplate capacity in a grid.

The grid penetration factor f is the fraction of total multi-year-averaged annual generation actually contributed by wind or solar generation to a grid.

The grid penetration coefficient q of wind or solar is the multiple of Z required to achieve the grid penetration factor fof that source. These definitions lead to the equation

A grid penetration factor freaches its economic maximum f_max, the maximum value of fattainable without wasteful surplus generation, where there is enough wind or solar capacity to meet the entire grid output: i.e., where q= 1.

Where q = 1, as the equation shows, f_max = Z. Therefore, the economic maximum grid penetration factor f_max for wind or solar generation is equal to that source’s capacity factor Z on that grid (for example, 25-30% for wind generation in a typical western European grid).

Penetration factors qfor illustrative Z= 0.25 and f= 0.15, 0.25, 0.35

Above the Pollock limit Z, any wind or solar capacity added to the grid causes excess generation (see the diagram above), which must either be exported to neighboring grids (usually at a loss) or prevented by capacity-constraint payments (expensive and market-distorting) or desist orders (a waste of capital invested in Pollock-breaching capacity) unless used for backup by static batteries (expensive and, at global scale, impossible) or by “green”-hydrogen generation (again prohibitively expensive, not least thanks to the large second-law-of-thermodynamics loss in conversion of electricity to hydrogen and then back to electricity, and in the use of rare and costly iridium and platinum in the oxygen-hydrogen barrier).

In Ireland’s grid, then, with a multi-year mean wind capacity factor Z = 28.5% (the Irish grid’s wind-power Pollock limit), the economic maximum grid penetration factor f_max for wind power is also 28.5%. Generation in excess of that limit is already causing heavy expense.

Most grid authorities know by hard experience what the long-run average grid capacity factors for wind and solar power are on their grids, given the average weather patterns in their regions. Therefore, no complex calculations on their part are needed. In Ireland, penetration appreciably above the Pollock limits would be disproportionately wasteful and expensive.

Wind and solar power are already disproportionately wasteful and expensive. Given that thermal backup for all unreliables must be kept turning at wasteful and inefficient spinning reserve at all times, it follows that if the windmills and solar panels were altogether discarded the existing thermal capacity would be capable of generating the entire grid output. Accordingly, the entire cost of wind and solar power is an undesirable and unnecessary net addition to the grid, and a gross imposition on the grid’s hapless customers.

For this reason, it is doubly important that the Pollock limits be widely understood and respected by grid authorities, so that the already grossly wasteful wind and solar boondoggle does not fling those nations whose governments have been foolishly captured by net-zero mania into outright bankruptcy.

Take Britain. Thanks to the Thatcher effect, by the end of her term of office foreign direct inward investment used to exceed the entire FDI of the rest of the European tyranny-by-Kommissar. However, the price of electricity (higher in the UK than just about anywhere else on Earth) is no small part of the reason why foreign firms no longer see us as a good place to invest. Manufacturing, as a fraction of GDP, has rapidly collapsed to just 8%, and the last few heavy industries still standing are already begging for subsidies to keep them here or simply upping sticks and going to China, which has announced that it is about to double its capacity to generate coal-fired power.

Now, the generating companies, which usually hold a mix of thermal and unreliable power sources, would be delighted to conceal the existence of the Pollock limits, because they benefit hugely from the savage increases in the cost of electricity that, through the idiocy of net-zero-obsessed governments, they get away with inflicting on the mere proles.

However, grid authorities, though in the new climate of intolerance and censorship they do not dare to say so publicly, are privately concerned at the implications of nut zero not only for electricity prices to end-users but also for the increasingly difficult task of trying to stabilize the grid as Pollock-breaching weather-dependent unreliables capacity is added.

To grid authorities everywhere, the Pollock limits will come as a revelation and a lifeline. Now, the operators will be able to say to their governments, “Enough is enough!”