By Christopher Monckton of Brenchley
Douglas Pollock will be known to many readers here as a regular and popular speaker at Heartland conferences. After several years researching the effect of unreliables on electricity grids the world over, Douglas has discovered a truly fascinating scientific result.
He had been looking at nations such as Britain, whose government has gone further towards reducing the economy to third-world status by its unhinged nut-zero policies than any other. As a direct result of this fatuity, Britain now suffers the costliest electricity prices in the world.
The manufacturing industries in which we once led the world have died or gone overseas to Communist-led China, India and Russia. Manufacturing now accounts for just 8% of Britain’s already-imploding GDP. The workshop of the world has become its workhouse.
Industries large and small are going to the wall at a record rate, wrecked by the endless hikes in electricity prices whose root cause is the enforced and pointless shuttering of long-amortized and perfectly viable coal-fired power stations that used to produce electricity at only $30 per MWh, and their replacement with wind and solar subsidy farms producing intermittent and unreliable electrical power at anything up to $11,500 per MWh.
What is more, this disastrous industrial and economic collapse has been deliberately precipitated by a once-Conservative “government” that has long abandoned the no-nonsense economic realism and free-market ideals of Margaret Thatcher and Ronald Reagan.
Curiously, though, the crazed infliction of pig-ugly, wildlife-wrecking, landscape-lacerating windmills on the British people is not reducing our electricity-driven CO2 emissions.
More and more windmills and solar panels are industrializing and destroying our formerly green and pleasant land. Yet the fraction of the nation’s electrical power contributed by unreliables stubbornly remains at just below 25%. Douglas Pollock wondered why.
He consulted widely among the ranking experts on grid management, but no one had any idea why grids such as Germany and the UK, whose installed unreliables capacity is so much greater than 25% of total generation, are incapable of getting their mean annual contribution from wind power, in particular, above 25%. True, on some days wind can generate about two-thirds of Britain’s electricity. But on average – a la larga, as they say in the casinos of Puerto Rico – the contribution of wind and solar is stuck at 25% of total grid generation.
So Douglas scratched his head and thought about it. After a good deal of research and a lot more thinking, he discovered what was wrong. It was a subtle but devastating error that none of the whinnying enviro-zomb advocates of unreliables had noticed.
Douglas’ argument is a beautifully simple and simply beautiful instance of the logical application of mathematical principles to derive a crucially-important but unexpected and hitherto wholly overlooked result. Read it slowly and carefully. Admire its elegant and irrefutable simplicity.
Let H be the mean hourly demand met by a given electricity grid, in MWh/h. Let R be the average fraction of nameplate capacity actually generated by renewables – their mean capacity factor. Then the minimum installed nameplate capacity C of renewables that would be required to meet the hourly demand H is equal to H/ R.
It follows that the minimum installed nameplate capacity N < C of renewables required to generate the fraction f of total grid generation actually contributed by renewables – the renewables fraction – is equal to f C, which is also f H / R ex-ante.
Now here comes the magic. The renewables fraction f, of course, reaches its maximum fmax where hourly demand H is equal to N. In that event, N is equal to H ex hypothesi and also to fmax H/ R ex-ante, whereupon H is equal to fmax H/ R.
Since dividing both sides by H shows fmax / R is equal to 1, fmax is necessarily equal to R.
And that’s it. In plain English, the maximum possible fraction of total grid generation contributable by unreliables turns out to be equal to the average fraction of the nameplate capacity of those reliables that is realistically achievable under real-world conditions.
For onshore wind, that capacity factor R is a depressingly low 25%. For offshore wind, one might get 30%. The reason is that a lot of the time the wind is not blowing at all, and some of the time the wind is blowing too much to allow safe rotation of the turbines.
What Douglas Pollock’s brilliant and, at first blush, unexpected result means is that the miserably low capacity factor R is in fact also the fundamental limit fmax on the contribution that unreliable can make to the grid without prohibitively expensive and logistically unachievable large-scale static-battery backup.
That means that wind and solar power cannot contribute more than about a quarter of total electricity demand on the grid, unless there is battery backup. However, as Professor Michaux’ 1000-page paper of 2021 for the Finnish geological survey has established, there are nothing like enough techno-metals to provide battery backup of the entire grid worldwide.
Just for the first 15-year generation of static-battery backup for the global grid, the Professor calculates that one would need the equivalent of 67,000 years total current annual production of vanadium, to name but one of the scarce techno-metals that would be required in prodigious quantities. In another 15 years, another 67,000 years production will be needed, for batteries are short-lived, as anyone with a cell-phone knows to his cost. So battery backup is simply not an option on a global scale, even if it were affordable.
Now consider just how devastating is Douglas Pollock’s brilliant result for the climate-Communist narrative. First, it is simple. Even a zitty teenager in high school can understand it. Secondly, it shows that even if global warming were a problem rather than a net benefit there is absolutely nothing we can realistically do about it, except sit back and enjoy the sunshine. Thirdly, it shows that the climate Communists, in placing all their eggs in the electricity basket, have a basket-case on their hands.
For the imminent, enforced replacement of gasoline-powered autos by electric buggies will not only impose an enormous extra loading on the grid – for which most grids are wholly unprepared – but, since the batteries add 30% to the weight of the typical buggy compared with a real auto, the entire transport sector will be squandering 30% more energy than it does now. And that energy is supposed to come from the already overloaded grid, powered by unreliables that can only deliver a quarter of total grid capacity in any event.
It gets worse. In the UK, the “government”, in its final thrust to destroy the British economy, is ordering every household with a perfectly good oil-fired boiler to tear it out in two years’ time and replace it with a ground-source or air-source heat pump, which will deliver far less heat at far greater cost. And where is the electricity for the heat pumps going to come from? From the grid, that’s where.
The bottom line is that, because vastly more electricity than now would be needed to achieve nut zero, and because the Pollock limit means only about a quarter of grid electricity can be delivered by unreliables, the net effect of attempts at nut zero will be to increase global emissions significantly, because, as Douglas has decisively proven, nut zero – even if it were at all desirable, which it is not – is impossible.
Nut zero, then, is a striking instance of Monckton’s Law, which states that any attempt by governments to interfere in the free market in pursuit of some political objective or another will tend to bring about a result that is precisely the opposite of that which was – however piously – intended.
York council has been accused of hiding a fleet of 25 new multi-million-pound electric-powered bin wagons because it failed to build facilities to charge them.
York Council has invested around £8m into a procurement project to replace its diesel trucks, used for general litter collection, with more eco-friendly vehicles.
There are non polluting diesel engines on the market at lower cost than EV.
no the government paid to destroy them all. its a plot
Was that an attempt at humor? If so, keep your day job.
His day job is making totally meaningless irrelevant statements. !
C’mon Mosh, you must have some pragmatism left in you.
Surely you can’t see any practicality in turning to battery powered vehicles when nobody has yet come up with an economical and practical way to generate power for the grid? Or to rebuild said grid to make it useable for the purpose?
If you are worried about CO2 levels, you’d know that more efficient engines (and more efficient power generators for that matter!) will do more to decrease emissions than this idealisitic knee-jerk nonsense.
And the excuse?
The procurement officer told the reporter that they invested this money in those vehicles before any charging infrastructure was installed because prices are anticipated to increase, in his/her opinion.
Vehicles of any sort are a depreciating item and a degrading technology from the moment they are purchased. Ideally, they should be used 24/7 to maximise the return on investment over a shorter period and replaced when worn out with newer technology.
Governments justify their existence by how much taxpayers money is spent, not by justifying how little of taxpayers money is spent.
Just like the fiscal duties investment companies have to maximise returns to their customers in the most efficient way possible, governments and local authorities are under the same obligation and should not be concerning themselves with climate issues until the financial imperative is there to do so.
Someone needs to sue York Council, and someone on York Council needs to be sacked, for their irresponsible waste of taxpayers money.
By the time they get around to building the chargers for the garbage trucks, the batteries will be junk from not being charged.
Then they’ll need to… buy more batteries! One signed paper, 4 deals with separate kickbacks. Is that not “the most efficient way possible”?
yes firing someone will always bring the cash back
Come on Steve, NOT firing someone will guarantee that that someone is still around to do more damage in the future.
AND that morons will feel free to do stupid stuff without thinking things through (cost/benefit analysis) because there will be no consequences for their incompetence.
You know, like politicians, lawyers and climate “scientists”.
Clown. It is meant to keep the next feckless bureaucrat from doing the same thing. It is also meant to let the people who pay the bills know that the entity cares more about peoples’ wellbeing than on perpetuating Leftist ideologues’ theft.
Trying to be cute is not an admirable trait in an adult trying to participate in an adult conversation. Your ability to participate has obviously deteriorated over time, Mr. Mosher.
The problem is that there will always be more feckless bureaucrats. And Steve will continue to support them.
Did anyone say that firing those repsonsible for this boondoggle would recover the money?
Or are you just desperately trying to change the subject again?
So, no embezzler should ever be prosecuted unless prosecuting him/her will repay the funds embezzled?
Continuing to pay people for doing absolutely nothing worthwhile, continues their unnecessary funding.
One wonders how you are still employed. !
His continued employment explains why he is so against accountability.
firing someone is no more about “bringing the cash back” than jailing a murderer is about “bringing back the dead”. In both cases it’s about holding people accountable for their actions.
Over a lifetime of not paying the moron, his/her salary may represent at least some of the money blown.
Didn’t hide them well enough, did they, nice aerial shot of them on the net.
Speaking of ‘laws’ I’ve always liked Aussie journalist Tim Blair’s law –
“Nothing ‘green’ ever works properly”.
Covers all applications of the lunacy really.
And Thomas Powell said
Much of the social history of the Western world over the past three decades has involved replacing what worked with what sounded good. In area after area – crime, education, housing, race relations – the situation has gotten worse after the bright new theories were put into operation. The amazing thing is that this history of failure and disaster has neither discouraged the social engineers nor discredited them.
applies in spades to green tech…..
I believe that was Thomas Sowell. If he was required reading in high school and college, we would not now be in this fix! Brilliant thinker and economist!
I don’t know. Profiteers and deviants seem to be doing rather well in this brave new world.
Kind of a corollary:
“Nothing green is ever intended to work”
As an example, plastic bag bans. Not intended to work, simply to show that the greens have the power to inflict it on the peons.
The attitude of the Parliamentary dictatorship – They Couldn’t Care Less.
Paying 4,900% over the odds to keep the lights on is judged a superior strategy to developing our own gas reserves on land and under the sea making energy at least affordable as well as reliable.
They have some very strange ideas about the working class. The Guardian’s favourite, Jack Monroe, has this advice for the cost of living crisis….
“issuing top tips such as: if you don’t own a tin-opener, how about using a sharp knife and a mallet to open your tinned grub? And: collect the fluff from your tumble dryer and turn it into an ‘extremely efficient firelighter’ for your fireplace. “
Now who has a mallet and not a tin opener? Show me the council houses and flats with open fireplaces….
The disconnect is ever-widening and we are utter scum who must be herded and told how to live as far as the elites are concerned. Net Zero is their new religion and no elections will change that. Unless you know better?
Surely she should have said collect the fluff from your tumble dryer and turn it into firelighter then rip out your tumble dryer and dry your clothes on a line outside in future.
My decision to move back to a warm part of Australia was because it is possible to survive here without home heating. I didn’t want to freeze to death waiting for the sanity to return.
No, this is wrong. They are not ordering any replacements of perfectly good oil fired boilers. They are ordering that you may not replace an oil fired boiler with same again. This means if you are off the gas grid, as almost all oil fired heating homes will be, replacing with a heat pump.
Which is bad enough. In fact for those subject to this it will be a financial bath for inadequate heating. You have to replace the rads and the pipework, and then you find yourself paying for resistive electric water heating, and for supplementing the heat pump with direct resistive electric heat when its not working well, which is when it gets really cold…!
But its not as bad as Christopher’s account. Or its differently bad.
It will lead to very long life for installed oil boilers, and to a lot of early replacements in 2024. The advice would be, if you have a non-condensing oil boiler made in the last 15 or 20 years, with an efficiency rating in the high eighties, buy another heat exchanger now. This is the part that will run out soonest. With a new heat exchanger on hand there is no reason why you should not be able to get another 20 years out of a decent boiler.
Non condensing, however. Condensing is just another complexity which shortens the life of the boiler in order to get a small increase in efficiency. And under the present regime, long life is the key. So if you have a good quality non-condensing one, its a jewel, and worth going to some trouble to preserve it.
I see on re-reading that this is not completely clear. They are not ordering anyone to take out and replace their functioning oil fired boiler. Its about replacement The regulation is that if your boiler needs replacement, eg its come to the end of life, there are no longer any spare parts, you may not replace it with another oil fired one.
So you can keep one you have installed for its entire useful life, as long as it will last. Which is why my advice above to buy in a replacement heat exchanger.
Its bad enough. But the head post is mistaken about what the regulation is.
I recommend that we all use the same reasoning for retaining our ICE cars by maintaining them properly to maximise their future life. That’s what I intend to do, and my current 14-year old car will see me out!
Perhaps some of the Cuban mechanics that have been maintaining all the 1950’s era autos on that unfortunate island will be willing to relocate and get into the boiler repair trade.
Heat pumps do not bolt into place to simply replace an oil fired boiler.
Oil fired boilers heat water for distribution throughout the house, whether to cast iron radiators, finned hot water pipes running along the bottom of walls, or tubing installed in the floor.
Heat pumps heat/cool air that is then pumped through houses via large air ducts.
Replacing an oil fired boiler with a heat pump means retrofitting the house with air duct venting systems. A not inexpensive task, especially if some of the ductwork is to be hidden in walls, ceilings or floors.
We just had two heat pumps fail at the same time, upstairs and downstairs, in a 2,000 square foot house.
Cost to replace each was $15,000, roughly double the cost to install their predecessors 15 and 20 years ago.
That cost is based on air ducts already installed when this house was built circa 1988.
Good luck retrofitting houses for heat pumps if they are much older than mine.
British heat pumps are even worse than that because the output is expected to be hot water not warm air, immediately reducing the COP. British properties rarely have room for air ducts, and the weather is cold in winter. Are heat pumps used for heating in Canada or Alaska? I rather doubt it, because the COP will be too low. The other point is that oil is used in rural locations, which often have relatively small electricity supplies (and single phase only) available. A few heat pumps will take all the capacity, and the whole lot will have to be replaced at great cost. Who will pay for that?
Are you aware that some insurance companies – like Aviva – are refusing to reinsure properties with oil fired central heating?
How did you miss that?
No, I had not heard of that. I know lots of people with oil fired heating, and it has never come up. I’ll check into it.
My point about the nature of the Government regulations stands. The regulations do not require you to replace an oil fired boiler. They just say what you may replace it with, if you decide or need to do that.
Regulations are in constant flux now. They have to be.
That’s the trouble with socialism: One can’t plan for anything because your masters are constantly dreaming up new regulations to control you. This is the economy you get without the rule of property law.
I have looked and called a couple of friends and found no evidence that insurance companies, including Aviva, are refusing home insurance to oil heated homes. There are commonly exclusions or limits related to tanks and boilers, have been for years as oil tanks in particular have very specific risks, but I have seen no evidence these have changed recently. There are specialist insurance providers that specifically cover risks associated with tanks and oil boilers at moderate expense.
But I have seen no evidence that there are refusals of home insurance because the home in question is oil heated.
I have found one report on Twitter of someone being refused, allegedly because of oil fired heating, but the context and reason was not clear, nor when the policy, if it is one, was started. It wasn’t a well known home insurance company.
If you can provide a source and a link to refusals it would be helpful. I don’t think its happening, on the evidence I have seen.
They don’t publicise it. It occurs at renewal time.
My sister and others in Dorset have had this problem. I doubt they know you.
This from LV insurance
Yes, I think you are right about Liverpool Victoria, at least on new business – down at the bottom they ask whether you have oil fired, and say that if you already have home or car insurance with them, they will accept oil fired.
So what you say about renewal is different from this, which implies that renewal should be unproblematic, but if your relatives have been refused a renewal on these grounds they must be also refusing renewals.
I wonder how long they have had this policy in effect. It certainly rules them out as a home insurer for anyone living off the gas grid, which I guess is around 2 million homes in the UK. Surprising. I don’t think oil is any more risk than anything else, except for the tank. There are still a lot of single wall tanks out there, which are very expensive if they leak, and the old plastic single skinned ones are splitting now. Sun damage, low grade plastic. So I think an exclusion or addendum about the state of the tank for coverage is quite reasonable.
A blanket refusal not so.
Generally I don’t understand the government position on oil. They are happy to have gas continue heating existing homes for another 12 years, and get replaced with gas when replacement is needed. And this is 85% of homes in the UK.
So why are they so concerned with an accelerated phasing out of oil boilers in a (relatively) small number of homes who have no real, fit for use, alternative?
That’s just a screenshot, but you get the idea.
Insurance is another lever to be used.
“Why are they so concerned…” – you could wonder similarly about the whole green agenda and how they are going about forcing it – especially the current push for electrification and resistance (even bans) on gas installations when they are just shooting themselves and their agenda in the foot, as it were. The eco grid is just not there yet, and forcing will just drive up prices, especially on the renewable technologies themselves, and make them more likely to fail, sometimes embarrassingly so, like in the big Texas freeze up, and the big European Calm.
And there in a nut shell is the root cause of the problem.
Permission is required.
Remove the diktat and the problem is solved.
The policy at the moment seems to be:
— no new installs of oil boilers from 2025
— no new build installations of gas boilers from 2030
— no new installs in existing properties of gas boilers from 2035 (heavily qualified with caveats about comparable pricing and running costs for heat pumps, so may not happen).
— no purchases of pure ICE cars after 2030, but hybrid EVs allowed.
— no purchases of hybrids after 2035. It will be all EV after that.
Its sort of obvious that trying to do this at the same time as moving the grid to wind and solar is not going to work…
Does “no purchases” apply to the used auto market, or only new cars? Who would buy a new ICE in 2029 if its trade-in value drops to zero the next year?
As far as I know the used auto market continues as now, and any ICE car registered before the cutoff can continue to be licensed and driven. I’m not an insider, but have not so far heard anything suggesting different.
That said, one can imagine that the tax regime could be shifted to move people to electric. You can also imagine restrictions being imposed on where ICE cars may be driven, or what they will be charged for (eg) entering cities. The London Ultra Low Emission Zone changes are an indicator. Being able to raise money with a tax which can be defended as saving the planet will be an irresistible temptation to councils.
I suspect this kind of thing will anyway be necessary to prevent the probable consequence of the ban on sales. That is, the niche market for EVs will be filled, and everyone else will just remain driving ICE until their cars can no longer be patched together to pass the state annual Ministry of Transport examination. Cars how have a very long life if well maintained, so replacing the installed base with EVs could take a very long time, several decades.
Britain will be like Cuba. A museum of classic cars still on the road.
Most grateful to Michel for his clarification.
Expat Cuban mechanical life-extension experts will be in high demand in the Western world. 1952 Chevy, anyone? You will own nothing and kiss your masters’ asses.
Perhaps relevant here is that they will be banning the renting of homes with oil fired heating. First to new tenants, but in due course even to sitting tenants.
Even that is an incorrect interpretation of the law. I can’t believe how wrong Monkton’s article was. The current plan is that gas or oil boilers won’t be allowed in any new build homes from 2025. These homes can be built to sufficient insulation standards to make heat pumps efficient enough to operate effectively. There is no requirement for existing homes to replace their existing boilers and even if there existing boiler fails they can replace it with another gas or oil boiler.
Perhaps greendragon should read the latest nut zero publication from the UK Government.
Speaking of coffin nails, have you heard about the reputed “biggest solar project in the world” in northern Australia? That was yesterday. Today its been put into receivership because its two ego tripping green head fat cat meal tickets can’t see eye to eye.
Their target market of Singapore runs their grid 95% on gas with a dash of waste burners and solar so they were never going to put their grid at risk with that much fickle solar and a vulnerable undersea cable.
What could possibly go wrong with a 2700 mile undersea cable ?
At Tony – solar project a no go. Go to Jo Nova to read about this.
Links please, share the theatre.
PC, I think you’ll find it will win a post of its own.
It is even being reported in the MSM here too.
I think it was more that they couldn’t scam enough government subsidies.
Here are some points for simpler people like myself that tie in with the article:
• If the number of windmills is increased five fold or even ten fold, they will be no help when the wind is not blowing or is blowing too hard.
• If the windmills are producing their maximum at a time energy use is at its lowest, I doubt we will all wake up and start using this all up or have the batteries to store this.
Not that it’s practical, but the response to that by the warmmongers like griffy is always “well, batteries”. They figure that since their cellphones can work on batteries, so can the grid.
Politics is the art of looking for trouble,
whether it exists or not,
diagnosing it incorrectly,
and then applying the wrong remedy.
Source: Sir Ernest John Pickstone Benn
Pretty much true, though it’s evolved also into making trouble in addition to looking for it.
I use the slightly different Groucho Marx version of that quote on the home page of my Election Circus blog:
“Politics is the art of looking for trouble, finding it everywhere, diagnosing it incorrectly, and applying the wrong remedies.” … Groucho Marx
There’s a certain irony(?) that he was the uncle of Antony Wedgwood Benn, one of the more bonkers UK labour MPs, and promulgator of much wrongness
You can slam those nails in all you like, brothers and sisters, it ain’t gonna help. This Green monster was a zombie, an undead demon, from the start.
Metaphorically, we need to jam a silver cross into its heart.
They would say.. “thanks for the donation”
The politicians need to explain why the UK is allowing hordes of people into their country despite the dismal and declining economy. Perhaps they need to put these economic migrants to work in their new coal mines and see how quickly they disappear without the freebies. 😉
and what are they doing, where are they going.
I ask because barely 2 miles from my front door is a 200 acre apple-tree orchard. I pass and see it from the main road as I come and go.
It appears that, this year, no-one has harvested the fruit.
Depending on variety I suppose but about half the trees are fully laden with fruit and the other half are sitting in carpets of fallen fruit.
There are red ones, yellow ones, green ones, the whole variety of cookers and eaters
How may tonnes of stuff will be there? Thousands and thousands.
Because it is The Migrants who would have done that job, picking fruit and vegetables is a job that’s a million miles a below the likes & aspirations of a country full of graduates from the school of Meedja Studdies ##
While if you visit The Nearest Tesco Supermarket, most of the apples in there came from France. I did, I made a special trip to see.
## Yet The Meedja is chock full of stories telling folks to ‘eat fruit and veg-ables‘
They are patently not, either or the advice is crap.
While we’re here on the subject of coffins –
BBC Headline:”Excess deaths in 2022 among worst in 50 years”
There I would assert:” Is where ‘climate change’ is actually killing people. Folks are now so stressed, worried and anxious they are using so much Comfort Food and other ‘comforts’ that the are eating/drinking/gambling/poisoning themselves into early graves.
The Climate ain’t killing people, the fear of it actually is – the folks promoting that really do have, increasing amounts of, blood on their hands.
Not least as the UK health service is effectively now in total meltdown
Not just the UK either:
More BBC:“France’s health system under pressure of increasing demands
No, things are not = never better.
They are now = ‘bad’ and getting exponentially worse day-by-day, as reported here at wuwt
Give all able bodied unemployed hard manual labour to support themselves – they can do evening studies for jobs they prefer – and these will no longer be crying for the nanny state to feed them and change their nappies (diapers). The lazy illegals will then look for an easier country and genuine refugees appreciate a first step up the ladder.
I guess you think the huge medical/ gene therapy experiment of the last couple of years had nothing to do with that?
Ask who owns the property, then ask if you can pick some of the fruit before it goes to waste.
Fallen apples here in the states are frequently used for making apple cider.
A small factory near where I grew up bought an apple orchard for their facility. They left most of the apple trees in place which continued to flower and fruit for many years.
My father got permission and every autumn, we’d visit the orchard, thank the manager and head home with burlap bags of tree ripened apples for the winter.
Tree ripened fruit beats ethylene ripened fruit each and every day!
US too, across the Mexico border.
Democrats see them as recipients of government aid (dependents) and eventually sure votes for Democrats. If the interlopers were believed to vote for Republicans someday, the border would be protected by a 25 foot tall wall and machine guns.
Nut-Zero ——– It – Will – Never – Happen.
Nut Zero is happening, unfortunately. But it will never succeed. Because 7 billion of 8 billion people live in nations that could not care less about Nut Zero.
Richard please have a word with Nigel Topping, UKs ‘high level champion’ (no less) for COP 26 in Glasgow.
He has recently said that “you can argue quite strongly that the whole world could get to net zero in the early 2040s and in many sectors in the late 2030s”
Either he’s delusional or living on a different planet to us.
You may be right, but how much damage will be inflicted, and at what cost, before the whackadoodles in government realise it won’t work.
That’s the question.
OK. That doesn’t need defining 10 variables and naming them with a letter. Real-world conditions change from one place to another. The UK is particularly badly suited for solar. Not many good places for hydro too. Very good for tides, but we don’t know how to extract energy from tides that makes economic sense.
The electric grids used to work properly
They were not broken. So, they did not need to be “fixed”, especially in a way that makes them less reliable, with the project led by politicians and bureaucrats who are not engineers. Only fools do that.
Thank you. I don’t consider myself to be stupid, but I find his nomenclature and this derivation confusing. Not saying he’s wrong, but it’s like watching a Three-card Monte operator at work.
Try getting a high-school student to explain the equations to you. They are really not that difficult to understand.
‘So Douglas scratched his head and thought about it. After a good deal of research and a lot more thinking, he discovered what was wrong.’
Sir, with all due respect, it clearly didn’t occur to Douglas that quickly, either. So, in the interest of harmony, since we’re both skeptical of ‘net-zero’, how about a numerical example for a typical grid, say,
24 GW peak load,
16 GW average load, and
25% average renewable utilization
Is it 6 GW or 4 GW?
And are the answers different for wind and solar, since the latter doesn’t work at night?
Frank from NoVA is perhaps unfamiliar with the process of scientific research. It may take a researcher some time to develop a new result, but he then expresses that result in the form of equations so that other mathematicians can instantly understand the argument and test it for rigor. The hard part is thinking up the concept. The easy part, for those who did not think up the concept but wish to understand it, is to work slowly through the equations (which, in the present instance, are simple) and then think about them.
As to the question about a particular sample grid, it is the right question in the wrong place. Douglas Pollock has established that there is a fundamental limit on the fraction of total grid output that is represented by non-dispatchable generating species, such as wind and solar. That limit is equal their capacity factor (also sometimes known as the load factor). If one were to add more unreliables to the grid, one would be wasting surplus electricity.
Calculation of the capacity factor must be performed with some care for a particular grid. In the UK, Professor Gordon Hughes of Edinburgh University is the ranking expert. He reckons it is about 24% of nameplate capacity for onshore wind in the UK, and perhaps 30-35% for offshore wind.
In practice, then, installing significantly more unreliables capacity than the Pollock limit will be wasteful, and the more that limit is exceeded the more wasteful the outcome.
I’ll ignore the ad-hom and go right to your erroneous conclusion that Douglas Pollock’s ‘fundamental limit’ and his / your ‘mathematical proof’ tells us anything we didn’t already know about renewable energy production or the production of any other economic good.
Let’s start with the premise that energy produced from intermittent sources (renewable e.g., wind and solar) is an inferior good compared to energy that can be produced on demand (most conventional sources). This means we might both agree that whatever prevailing utilization factor exists for these intermittent sources has to be a ‘maximum’ given any particular set of market conditions.
Now we can look at two cases (A and B), representing the unhampered (free) market and the hampered (government constrained) market, respectively:
Case A: Unhampered Market
We assume that end users are free to purchase and consume as much energy as they desire based on the availability and price of energy offered by all potential suppliers, whose prices presumably reflect all costs (capital and variable) faced by the suppliers.
In this case, every source of energy will clear the market, except those not accepted by end-users, and their respective utilization factors. f_i, will simply reflect the amount of energy dispatched by unit i, E_i, divided by its nameplate capacity, N_i. Note, there is no mathematical ‘magic’ here, as f_i is strictly a reflection of market preferences.
Within this case we can look at sensitivities. If fuel prices increase or decrease, the utilization factors of conventional and renewable units will probably change, along with the total amount of energy consumed. Again, there is no fundamental limit here, just a working market.
Similarly, since it’s a working market, additions or subtractions of nameplate capacity by suppliers will be made in accordance with unit economics, hence respective utilization factors are always subject to change.
Case B: Hampered Market
We have the same assumptions as in Case A, except the government has put its foot of the scale in order to promote the use of renewables, whether by subsidy, must take provisions, favorable dispatch rules, etc. A priori, we may agree that this is an economically sub-optimal case that subverts the desires of end-users in favor of the desires of political operatives and renewable suppliers.
In this case, since we are clearing supply and demand in a hampered market, we can expect that the utilization factors for renewable energy will be higher than previously, not only because of the government’s actions, but also because less energy will be demanded by end-users.
Again, there’s no new mathematically provable / derivable ‘fundamental limit’ at work here, just basic economics, which you’ve already alluded to in your acknowledgement that variable conditions among different countries (e.g., sun light and wind speed) will favor different renewable utilization factors.
There was no ad-hom. And the Pollock limit is proven. Just work through the equations.
‘Try getting a high-school student to explain the equations to you. They are really not that difficult to understand.’ is an ad-hom attack.
‘Just work through the equations.’
I have. Here’s my work, using the nomenclature and definitions from the article:
H [=] mean system generation,
R [=] average renewable capacity factor,
f [=] renewable generation / total generation,
N [=] min renewable nameplate capacity to meet renewable generation, and finally,
f_max [=] f given H=N, which must equal (renewable generation / total generation) given H=N, or substituting from above,
f_max = (N*R) / (N) = R
My arithmetic is much more parsimonious that Pollock’s ‘linear algebra’, since it doesn’t bother with the handwaving steps of first grossing up H to get C and then scaling it back down to get N.
So is f+max really equal to R? No, for (at least) two reasons:
First, R is an average capacity tor renewable generation (wind and solar), so it is calculated over a wide range of conditions – day / night / windy / calm / clear sky / cloudy sky / high load / low load, etc. But Pollock applies it to a very specific situation, i.e., when H = N, where obviously he has no idea what the actual output of the renewable units will be.
Second, as f can range anywhere between 0 an 1, and probably does so frequently under varying conditions, it is specious for Pollock to assume that f_max occurs precisely when N = H.
In short, Pollock’s ‘limit’ is a misleading use of arithmetic, based on sloppy definitions that apply averages to specific situations. In short, it is a futile attempt to determine an optimal generation mix that in reality can only be solved by letting energy markets work in a free manner.
I’m sure you’ll let us know if / when Pollock’s paper passes ‘peer review’. However, even if it does, I would advise caution to anyone trying to argue his result in front of any competent utility commission – the intervenors representing the wind and solar interests will blow it out of the water.
Mr Vinos is perhaps unfamiliar with the scientific method. It is necessary to prove a counter-intuitive result, and the usual way to do that – like it or not – is with equations. That is what Douglas Pollock has done. If Mr Vinos disagrees with the equations, perhaps he would be kind enough to state in what respect they are in error.
Dr. Vinós is quite familiar with the scientific method being a scientist for several decades with well-cited publications, thank you.
I just don’t think Mr. Pollock has discovered something so novel. Obscuring what he says through elemental mathematics with lots of variables does not change that. It has been known for decades that the more renewable energy is added to the grid the less it gets to be used and the more unstable the grid becomes. It is known as the penetration problem, the higher the penetration the lower the value of renewable energy to the system.
But in Spain, the share of electricity from renewable sources is 40%.
So if the UK only gets 25 % that is a specific UK problem, as no amount of mathematics says that renewable sources can only provide 25 %.
Since Dr Vinos is familiar with the scientific method, he will understand that naming variables and arranging them in equations is the vocabulary and syntax of science, and he should complain that a scientific result that he did not himself attain ought not to have been reached by the scientific method. Like it or not, the scientific method is well established and has merit.
What Mr Pollock has done is provide a simple and elegant benchmark that instantly identifies the point at which the installation of additional renewables adds to the cost of electricity without appreciably reducing grid emissions. There is no need to be jealous about it.
And if Dr Vinos will get someone to read the head posting to him, he will see that the capacity factors for wind power in the UK were stated to be exactly that – the capacity factors for the UK. The head posting neither stated nor implied that those capacity factors would apply in countries with more or steadier wind than the UK.
People like to make their own definitions to suit their needs, and it seems Lord Monckton is making his own definition. Because it looks to me that any definition of the scientific method should include the work of Charles Darwin, who forever changed our view of the place that humanity occupies in the natural order. Yet from my reading of “On the origin of species by means of natural selection” I don’t remember any variable definition and mathematical formulation.
Lord Monckton would be foolish in declaring Darwin’s work as not following the scientific method for not using mathematics, as mathematics is just a language and tool that can be used by the scientific method or not. The scientific method is based on observation followed by the elaboration of conclusions or principia, on hypothesis, that must hold true over data not available for their elaboration.
Just adding variables and mathematics to something doesn’t make it more “scientific.”
Here’s why one needs to use mathematics whee mathematics is appropriate, as of course it is here. Dr Vinos says the renewables capacity factor in Spain is 40%. However, Douglas Pollock looked up the data and found that that includes hydro-power. Deduct the hydro-power and you get a rather lower capacity factor.
In any event, capacity factors vary not only by renewable species but also by nation. for obvious reasons.
But Douglas’ result shows why it is that above a certain point – the Pollock limit – adding renewables to the grid is pointless, wasteful, expensive and destabilizing.
Douglas has consulted very widely in the industry, and, until he came upon his result, one of the commonest questions people were asking was why adding more wind and solar was somehow not increasing the fraction of total grid output that they contributed. Well, now we know why, and it would have been very difficult to come to that result without using mathematics.
Yes, Lord Monckton-san, so sad, but true about the Immutable Law of Leftist Irony…
I did a bar napkin calculation on how much JUST THE HARDWARE would cost to have a 100% solar grid with just a one-week battery backup and came up the following:
Cost of installed home solar system/average home: $30,000/home
Cost of installed 1-week Tesla PowerWall battery backup:$40,000/home
Lifespan of hardware: 15 years
Number of US households: 131.2 million
Residential percentage of total US power consumption: 16%
($70,000*131.2 million)/.16= $57 trillion every 15 years=** $382.3 trillion/century…
**Doesn’t include labor costs to run and maintain a solar grid, or the land it would occupy, or all the other electrical grid infrastructure costs…it is just the cost of solar panels and batteries.
If one assumes EVs will eventually replace all ICE modes of transportation, add around 30% to the above.
This is obviously economically impossible, moreover, there aren’t enough techno-metals to manufacture the required batterie to backup the solar grid.
Leftists are insane.
What governments should be doing is developing Thorium MSRs, which are capable of producing power 24/7/365 at an estimated energy cost of $0.03/kWh.
The Chinese are currently running tests on a prototype Thorium MSR, and expect to have a working commercial design by 2030.
Since there are no cooling towers (no water required), and no containment dome required (runs at 1 atmosphere of pressure), they’re very small and relatively cheap to build.
Thorium is also very abundant all around the world and cheap ($100/kg) and just 200 grams of the stuff is enough to provide a lifetime of energy per person.
As yet their are no deployable designs for thorium based reactors, and there are a number of technical problems that remain unresolved.
Actually, thorium fuel was demonstrated to breed in the Shipping port plant, back in the 1970s.
Yes a proof of concept MSR was built and tested at Oak Ridge Labs In the 70’s, but Nixon killed the Thorium MSR development because we were at the height of the Cold War, and LWRs were much better at producing plutonium for nuclear bombs,
I realize there are currently no commercial LFTRs, and in the US, there never will be until politicians and bureaucrats pass laws and regulations for test parameters and approval procedures to allow the private sector to invest in their development..
I’ve been in contact with Senator Rand Paul’s officd, and he and his staff are working on getting this done, but no real progress has been made so far..
A lot of lobbyists, Leftists and large companies never want LFTRs developed…
You know, after they build out the infrastructure for the off shore wind, in places like Virginia, a businessman could build barge mounted LFTR’s in some country that will allow it, for example Cuba, awaiting the day that the offshore wind is due for replacement. Then drag the reactor to an area near the cables running to shore and plug it in to the grid.
The free market at work, without the meddling of large government interference.
BUT we all know that anyone wanting to build these reactors want to be subsidized by big governments.
Look at Musk, almost every penny of his net worth can be traced directly to the tax subsidies and cash for CAFE standards paid to Tesla from ICE manufacturers to reduce their overall MGP.
Which will need replacing first, off shore wind turbines or the high power cables connecting them across significantly long undersea distances?
Thorium is like fusion – lots of research, lots of promises, but a commercial, working, reliable, affordable thorium reactor, like a commercial, working, reliable, affordable fusion reactor, was 30 years away when I was 30 and is 70 years away now that I am 29.
MSR technology via Bill Gates’ first commercial operation is supposedly to debut prior to 2030. I hope so.
Accelerated testing methods of the corrosion resistant materials required will have to satisfy regulators and investors. Such testing over a 5 or more likely 10-year period seems necessary to find the “best” materials but the “best” materials need to last 40+ years to be commercial. I see comments about “cladding” for MSR corrosion resistance, but I suspect there’s patent protection issues that will discourage cooperation and extend timeframes.
The best hope (only hope?) we have for phasing in nuclear technology from 2030-2040 is NuScale’s small scale modular reactors, while molten salt fast neutron reactors are being perfected IMHO. I’m not by any stretch an expert, just a seriously interested old man who wants to see the beginning of the new generation nuclear renaissance before I kick off!
TerraPower will run tests with depleted uranium, which is not used in fission, to determine which materials can hold molten salt without being damaged by corrosion
Hastelloy N has not been qualified for use in nuclear construction, and significant additional characterization would be required for Code qualification. …
… It is recommended that a systematic development program be initiated to develop new nickel alloys that contain a fine, stable dispersion of intermetallic particles to trap helium at the interface between the matrix and particle, and with increased solid-solution strengthening from addition of refractory elements.
With support from computational materials science tools, a speculative time frame for a down-selection program, using 20-30 kg heats, is about four to five years….
I recently listened to a podcast of Steven Levitt’s interview of Nathan Myhrvoid in which TerraPower came up. Sounded very intriguing.
Myhrvold, not Myhrvoid
The ecoloons, would even object to a Thorium reactor.
Yes, Thorium MSRs are hated by the eco-wackos and would drive them utterly insane if the US ever started building them, which is just a bonus aspect for LFTRs.
Add office buildings retail stores, mines, factories etc.
Just $382 trillion?
That’s mo big deal !
I’ll contribute $1
If everyone contributes $1, that will help
The rich folks should contribute at least $2 each
Aiko Toyoda head of Toyota has said in the past that
“Japan (for one) would run out of electricity in the summer if all cars were running on electric power”
And piles of Thorium are already building up as waste from rare earth mining – there’s literally decades of reserves built up and accelerating.
Canada’s Chalk River, Ontario operated such a research reactor from 1947 to ~1990. It could even gobble up standard uranium fission waste. Chalk River collaborated with Oak Ridge US in their thorium reactor built in the early 1950s which was ordered shut down 10yrs later because it didnt make radionuclides suitable for weaponry!
Canada has just had its first small modular reactor (SMR) licenced for use.
Did you know Canada’s heavy water Candu Reactor uses unenriched U238? It synergistically captures stray neutrons causing partial fission of the U238. It is modular (doesn’t need the environmental proctology of new plants), it is installed in 3 years with no cost overruns. The world’s largest nuclear plant at Bruce Point, Ontario is made up of 7 modules.
The plants operates flawlessly for 27 years, followed by a planned upgrade for an extension to 40yrs full life. There’s more! The latest upgrades produce power for 2½ cents US a kWh and it is the only reactor that does not have to be shut down to refuel!!
Gary Pearse is right about the Candu reactor. When I was writing my thesis for my postgraduate course in journalism, I took the question of what nuclear reactors would be best, reviewed all the then options and concluded that Candu was the best by a country mile.
That sounds very much like the concept discussed by Nathan Myhrvold when he was interviewed by Steven Levitt.
Leftist’s truly are insane, “willfully uninformed”, or corrupt. The cause of their behavior doesn’t matter, the effect is the same. W&S beyond the Pollock limit yields economic destruction, It’s not complicated. It has to stop. Yes, fast neutron breeder reactors aren’t the best long term energy source, they’re the only long term economic and environmental solution IMHO.
Having done many of these calculations for different systems in different locations around the world, mainly at hourly resolution, and often covering multi year periods, I have come to the conclusion that the best renewables can manage before costs start escalating alarmingly is about 60-65% of annual demand. That’s about the point where interseasonal storage is needed to keep things balanced. Of course, by then the cost has already escalated significantly, and you still need essentially 100% of peak demand as dispatchable backup capacity.
Here’s one of the simpler analyses which us easier to follow because most of the analysis is at the monthly level.
Here are some more back-of-the-envelope calculations:https://naptownnumbers.substack.com/p/battery-grid-backup
Now do the calculation for 2023 grid scale packets installed and commissioned. $500 kW.h
That pushes the optimal overbuild much higher, and likewise the system cost.
If you add interseasonal storage the cost does explode. However, if you overbuild and allow curtailment during over-producing seasons you end up with a much more reasonable cost. However, it is grid dependent.
Nonsense. The Pollock limit means that all electricity generated during over-producing seasons by renewables exceeding the limit will be wasted. There is no, repeat no, justification for installing more wind or solar power than the relevant Pollock limits for the nation concerned. Exactly the same electricity would be generated, and at far less cost, if the wind or solar arrays exceeding the limit had not been installed at all.
Installing unreliables in excess of the Pollock limit would be justifiable only if one could store the power in static batteries or in the form of “green” hydrogen. Both of these options, however, are cripplingly costly and, therefore, make no sense at all.
Please read my write-up on Thursday Island, where I show the trade off between storage and surplus renewables generation for both wind and solar.
Very nice article. It would be nice if you had the intramonth data (or even better the hourly data) to run through. I have seen the same thing in every grid I have looked at. Somewhere between 20-80% of generation is pretty easy to fill with wind/solar depending on the grid, but then cost explodes. Florida is on the 20% side (terrible wind) while ERCOT is on the 80% side. It looks like that summer dip in wind would push Thursday Island towards ~50%. I would suspect that Thursday island would be well served with a 6 hour battery, 3MW of wind (one large modern turbine), and 5 MW of solar. However, without the hourly data (like in Joe Born’s post below) it would be difficult to put that guess to the test.
The hourly data would result in marginally worse performance than I was able to identify. The difficulty for wind is the doldrums months in mid summer – when solar is not at its peak either. That really dominates when you are looking at an all renewables solution. I think I established a fairly clear basis for the solar using the daily data from the period of Dunkelflaute , plus an assumption about need overnight and in the hours of minimal solar generation. Again, detailed data at the hourly level is only likely to make the answer marginally worse. I did try running the solar plus wind optimisation, but it came out 100% solar because of those doldrums. If you have to have the solar there is no point in adding wind to it.
I have run experiments comparing results calculated from hourly data, and then summarising the hourly input data to daily data and calculating at the lower resolution. The hourly fluctuations do produce marginally bigger extremes, but they are ripples on the surface when looking at storage issues.
You can see some of the results from my hourly calculations in charts I linked in my reply to Lord Monckton.
Nothing about unreliable redundant electricity generation is REASONABLE.
There is NO REASON to build unreliable generation since it must be backed 100% by a redundant “energy” supply and/or very expensive storage, none of which was needed BEFORE unreliables were added to the grid. AND unreliables require expansion at a high cost of the interconnecting transmission lines for NO GAIN.
Reasonable as in making your plumbing of pure gold so that it doesn’t corrode over time and have to be replaced.
The advantage of formal proof by linear algebra rather than “back-of-the-envelope calculations” is that it is definitive. In sunnier nations, the Pollock limit on the fraction of total grid generation contributable by solar power will be greater than in Scotland, which seldom sees that big yellow thing in the sky. In most Western countries, however, the Pollock limit is low enough to ensure that, regardless of how many solar panels you cover your once-productive fields with, the contribution to total grid generation will be small.
My work deals in very formal proof, by taking actual demand hour by hour, and actual wind and solar generation ditto, and then calculating what capacity can be absorbed without generating a surplus, what combination of wind and solar produces the least requirement for storage given a particular round trip efficiency, etc. using linear algebra.
Formally, let G be a matrix of hourly generation capacity factors (derived from actual hourly production by dividing by the nominal capacity) with a column for wind and a column for solar. Let D be a vector of hourly demand. Let C be a 2×1 vector of nominal capacities to be found subject to the constraints we impose on the problem.
We can write that the vector of hourly surpluses and deficits S is
S = C.G – D
If we require that S be strictly <=0 for every hour we have a locus of solutions for C giving the maximum combinations that are consistent with no surplus generation. S is then the hourly backup dispatchable generation required to meet demand. Elements that are constraining will meet the condition C.Gt=Dt where t is the time subscript. High levels of supply (high Gt capacity factors for individual hours) may or may not coincide with low levels of demand, but in the long run we can expect that will occur. So we are looking in practice at the fleet maximum generation for wind in the low demand small hours when there is no solar, which is say ~80% of nominal capacity, plus the amount of solar given that level of wind capacity which does not result in a surplus on sunny summer Sundays, at least for grids where both can contribute sensibly. The LP will find the solutions which can also be found by iterative approximation.
If we now allow for storage, we can increase the values of C to generate surpluses for some individual hours. If we partition S between hours of surplus and hours of deficit we can calculate additions and and withdrawals from storage.
Where there is a surplus we can record it as contributing St (surplus for hour t) multiplied by the efficiency of the storage process to the store – say 85% for pumped storage pumping, 60% for a PEM electrolyser or 90% for an inverter feeding a battery. These amounts may be constrained by available capacity in MW for pumping, electrolysis or inverters, resulting in wasted surplus energy. This becomes an important consideration, since the volume of surplus is highly variable, and it will never be economic to provide capacity to absorb the largest surpluses that occur only rarely when high output and low demand coincide. However, and initial calculation can be run on an unconstrained basis which permits a storage process plant duration curve to be produced to input to the economics of capacity. This chart shows some sample surplus duration curves for the UK, illustrating the difficulties of making hydrogen electrolysis an economic proposition.
Where there is a deficit we can proceed similarly: any deficit in excess of the redelivery capacity of the storage must be met by dispatchable backup. Otherwise the redelivery volume Vt reduces the store by an amount Vt divided by the efficiency of redelivery – say 95% for pumped storage hydro, 50% for a hydrogen fuelled CCGT operated intermittently, 90% for a battery inverter. Finesse the calculation by allowing for leakage from the store over time, including energy use for cooling batteries etc. ad lib. Alternatively, simplify by using the round trip efficiency on one or other leg.
By cumulating the surpluses and deficits we can derive the volume in storage. It is convenient to calculate the volume of storage required in MWh (or in reality, the significant number of TWh required) as the difference between the maximum and the minimum of the volume in storage.
As a starting point, and assuming we are dealing with data covering n years, (n integer, >=1) it makes sense to constrain the solution such that the volume in storage at the end of the period is equal to the initial volume. By optimisation we can find the combination of wind and solar that minimises the maximum storage requirement while incurring no wastage beyond round trip losses through storage. We should not be assuming that there is a stock in store for free that doesn’t need to be replenished. This chart shows the storage profile for hydrogen or a 75% round trip (pumped storage, battery) store over the course of a year for GB.
In practice, and particularly since in the real world no year is exactly like another, it makes sense to explore the sensitivities around such a solution to see how relatively robust it is, and to consider the tradeoffs between different ratios of wind to solar, and between storage and additional renewables capacity with associated wastage, and using dispatchable backup not fuelled from the storage. It is important in conducting the analysis to do so on a marginal basis to understand how the tradeoffs actually perform. We can also analyse the maximum flows required to fill storage and meet demand, and hence begin to examine the need for extra transmission capacity.
Multiyear analyses can reveal huge differences in storage and capacity requirements or potentially largely useless surpluses depending on inter year variablility of renewables performance. I have run some using over 35 year runs of refactored weather data at hourly resolution – over 300,000 rows. Covering that 1 in 35 year bad year can be tough, especially if it comes in a run of poor years. A “good” renewables year will throw up a lot of wastage if we have covered the bad year properly.
The reality is that these calculations require spreadsheets of thousands or even hundreds of thousands of rows (and good quality input data), but the actual calculations are not particularly difficult to set up, and the solutions can often be found using Goal Seek or Solver options, with iterative interpolation as a fallback because of the large number of implicit constraints. They certainly cannot be done on the back of an envelope, with the possible exception of the simplified Thursday Island example which mainly considers monthly data that makes it easy to appreciate the nature of the calculations and the importance of seasonality (even 10 degrees South of the Equator in the Torres Strait). I would encourage you to read it: I put it together having been inspired by the late Roger Andrews, who wrote a good number of articles looking at renewables intermittency and performance at Euan Mearns’ site, performing similar calculations.
“It doesnot add up” is, of course, correct that his calculations require complex spreadsheets. The advantage of Mr Pollock’s approach is that, once it is better known, people with no expertise – politicians spring to mind – can be brought to understand that there is a limit beyond which adding more unreliables is wasteful, and to understand approximately what that limit is.
It is instructive to consider some basic mathematics. Let g(x) be a capacity factor duration function, defining the proportion of capacity that is produced less than x proportion of the time. It is analytically convenient to consider functions g(x) of the form g(x)=x^n. These have the property that integral g(x) from 0 to 1 is 1/(n+1), and is the average capacity factor. Thus for n=1, g(x)=x, and average capacity factor is 1/2, or 50%; for n=2 g(x)=x^2, and average capacity factor is 1/3 or ~33%, etc. They are actually quite good approximations to real world duration curves for fleets of wind farms, although they need scaling by a fudge factor that reflects that wind is never consistent enough to achieve full capacity across a fleet of farms, but tops out at around 80% of capacity – see the recent wind record in the UK at 20.918GW plus some curtailment cf capacity of 28.5GW.
For a capacity of C, the duration curve is simply Cg(x). For demand we should also properly consider duration curves, recognising the several hours of low demand overnight, rising towards a plateau during much of the day before the early evening peak, subsiding back again to overnight levels, amplified by the weekday/weekend and seasonal factors. For simplicity I will look at convolution with baseload and peak levels of demand, respectively B and P. If the proportion of hours that are baseload is α the average demand is αB + (1-α)P. A fuller analysis looks at a full convolution integral with the different levels of demand. We shall assume that there is no correlation between wind output and time of day which is reasonable for the UK, but not true in e.g. Australia where it tends to be windier at night – or seasonally (whereas in the UK it tends to be windier on average in winter). B and P can also be thought of as low season and high season demand rather than merely diurnal fluctuations.
Following Pollock’s principles we have that all curtailment is avoided when C<=B. For C>B we expect curtailment. The expected rate of curtailment is Cg(x)-B over the interval between x:g(x)=B/C (or x=(B/C)^(1/n) ) and x=1, and the total curtailment is the integral of Cg(x)-B over that interval. Integrating the function we get (Cx^(n+1))/(n+1)-Bx which evaluates to C-B at the upper limit and C(B/C)^((n+1)/n)/(n+1)-B(B/C)^(1/n) at the lower limit, and this level of curtailment applies the proportion α of the time. While C<=P that is the source of curtailment. For C>P we have a similar analysis applying to the peak hours, applying for (1-α) as a proportion of the time. The analysis can be extended to more levels of demand in an obvious manner, and in the limit as a convolution.
For n=1: we get curtailment of
α(C-B)(1-B/C)/2 for C>B, plus a further (1-α)(C-P)(1-P/C)/2 for C>P
Marginal curtailment for an increase in capacity is found by differentiating with respect to C.
α(1-(B^2/C^2))/2, plus a further (1-α)(1-(P^2/C^2)/2 for C>P.
Marginal production is ½, and the useful production, U is ½ less marginal curtailment. The effective cost of marginal capacity is then the LCOE multiplied by 1/2U to allow for the wastage. Capacity additions are asymptotically useless as B/C and P/C tend towards 0 with increasing C. However, for values of C that are only slightly above B marginal curtailment is small, and only occur in baseload hours. If we set C equal to average demand so that total generation by wind is C/2, equal to average capacity factor multiplied by average demand – the Pollock criterion – we find that B<C<P so we are only concerned with curtailment during baseload hours, but that curtailment is positive. There are no obvious grounds for stating that it is optimal. However we have the basis for a cost curve relative to levels of grid penetration (though we should add in other costs caused elsewhere in the system to make a proper tally: already by the time there is sufficient capacity to cause curtailment there are plenty of costs for extra transmission and grid stabilisation and costs imposed on other generators as I have outlined already). An optimised grid would see marginal long run costs of different kinds of generation equal if you can define those long run costs. In practice, the optimisation would need to be risk based, reflecting probabilities for many different parameters.
We can replace B in our formulae by a demand function D(t) where 0<t<1 (year), and integrate over t to provide a convolution.
Higher values of n (including fractional values) produce more complicated expressions for curtailment, but for given C, curtailment occurs less of the time, and there is more headroom to increase capacity at little curtailment penalty. In practice, empirical capacity factor duration functions may have an interval of low to zero output and never attain a 100% capacity factor at the fleet level. Modifying the form of g(x) accordingly may provide more realistic answers, but the underlying analysis gives a feel for how the variables interact to influence the tolerable level of wind generation. Comparison with empirically determined surplus duration curves such as these
goes some way to validating the approach. In turn, they highlight the problems of trying to create an economically rational storage system as an alternative to dispatchable backup. That is perhaps the real issue here, especially when combined with the economics of storage turnover.
60-65% renewables on “Fantasy Island”, perhaps. But what about offshore NY State where Biden wants to drop quite a few $billion, real soon.
The schemes on isolated islands (add King Island, Bass Strait, El Hierro, Canaries, Graciosa, Azores) are all very costly. But none of them has attempted going beyond the 60-65% penetration level, because the costs become prohibitive. Calculations I have done on larger grids show similar patterns. The main determinants are the shape of the demand profile and the shape of the capacity factor duration functions. Because storage is so costly more or less the maximum that can be justified would allow some daily smoothing of solar output. But in practice it limits the amount of solar that can be accommodated sensibly. South Australia has about reached the limit.
Here’s Prof Michaux’ 72 page report https://tupa.gtk.fi/raportti/arkisto/16_2021.pdf . Anybody have a link for the 1,000+ page report?
OK, found it https://tupa.gtk.fi/raportti/arkisto/42_2021.pdf
“What Douglas Pollock’s brilliant and, at first blush, unexpected result means is that the miserably low capacity factor R is in fact also the fundamental limit fmax on the contribution that unreliables can make to the grid without prohibitively expensive and logistically unachievable large-scale static-battery backup.”
Which politicians and other lefties will ignore or view as a benefit.
No, the climate Communists will not be able to ignore the stupefying and entirely unaffordable cost of static backup batteries or of “green” hydrogen generation. The people are already close to mutiny on the climate issue. The establishment of the Pollock limit provides a simple but irrefutable argument against installing any unreliables in excess of that iron limit.
You have to look at the whole system costs of integrating wind. The first few turbines make little difference to overall costs, so the cost is approximated by LCOE calculations. Add more and you start to need to invest in additional grid stabilisation to cope with flicker. Add more and you start hitting the operating regimes of other plant on the grid, which gets forced to operate at reduced efficiency and with more frequent ramping that imposes wear and tear and adds to maintenance cost. Reduced running hours means that capital cost must be recovered from reduced sales volumes.
Add more and you reach the point at which wind has to be curtailed to ensure adequate inertia is available. Add more and it has to be curtailed because it exceeds demand in low demand hours and storage is unable to cope economically. Add more and the hours of curtailment increase, and the amounts of curtailment in .ow demand hours also increase. Overall curtailment increases quadratically, and wind needs to recoup its costs from uncurtailed output. Meanwhile periods of surplus imply zero or negative spot prices, requiring subsidies to keep inertia providing generation operational. Supply on windless days is barely affected by all the increased wind capacity. Storage, other than as an aid to grid stabilisation remains uneconomic.
The marginal useful output from adding more wind farms falls sharply. The result is that just the raw cost of useful power from wind (ignoring the on costs for extra transmission capacity and dented economics for other generators etc.) becomes a rapidly escalating multiple of LCOE. It can reach 10 times LCOE and still fail to replace the need for almost 100% backup generation.
Thanks, excellent summary of the argument, a physical explanation of the limits of intermittency. And yes, LCOE does indeed fail to account for curtailment – and your point, which I have not come across anyone before pointing out, is very interesting: that the consequence of increasing wind supply to increase coverage of lower wind episodes is increased curtailment.
So in effect its paradoxical. The more wind you install, the lower the usable capacity factor becomes, because you have to deduct the excess which you end up paying them not to supply. Nice point. I should like to see it worked out in quantitative terms, but its a nice argument. Good one.
Beware of unforeseen collateral consequences!
LCOE + Liars Cost of Energy
LCOE = Liars Cost of Energy
Also, yes, the important parameter is indeed the total system cost of installing the wind or solar or whatever. Count all the cash flows, first basic principal of business case production and analysis.
Yours, not Lord Monckton’s, is the actual answer.
Let’s forget your first paragraph for the moment and assume there’s no reliable generation. Even without backup, you could asymptotically approach (but not quite reach) supplying the entire load over the whole year by increasing wind and/or solar nameplate capacity. It’s just that curtailment would eat up so great a portion of the unreliables’ available output that the cost would become prohibitive.
So he’s right that the returns to adding unreliables capacity diminish precipitously. But he’s incorrect to say that:
…as shown here:
Wind + Solar contributed nearly 34% of the UK’s power output last year.
Elegant theory trumped by reality, paraphrasing Feynman.
Usually an all wind or an all solar solution are not optimal (Thursday Island proved to be an exception). Some solar compensates for sunny windless days, and allows a greater overall penetration.
I did not mean my post as an endorsement of renewables in the slightest: it was just to point out that the theory fell at the first fence.
No, the theory did not fall at the first fence: Mikehig merely failed to engage his brain. He did not understand the head posting, simple though it is.
Most UK wind generation is from offshore wind, which, as the head posting points out, has a UK Pollock limit of about 30%. One does not have to allow all that much more for solar to get up to 34%.
The central point of Mr Pollock’s argument stands: the capacity factors appropriate for the energy-generation species and territories concerned serve as the iron limit above which adding those species to the grid contributes no additional power unless that power is dumped into vastly expensive static batteries or “green”-hydrogen electrolysis.
This is a result which, when published in a learned journal, will cause shock and awe among grid operators and electricity generators.
From the post:
“For onshore wind, that capacity factor R is a depressingly low 25%. For offshore wind, one might get 30%. The reason is that a lot of the time the wind is not blowing at all, and some of the time the wind is blowing too much to allow safe rotation of the turbines.”
From the link I posted, wind alone accounted for 29.1% from a roughly 60:40 offshore:onshore mix. If onshore really is limited to 25% then offshore must have exceeded 30% by some margin to get that result….
ERCOT (Texas) is a better example. They have hit 30% (on the road to 45%) while providing electricity at a below average price and while expanding their grid.
Perhaps chadb should study an elementary textbook of meteorology. He will find that Texas is somewhat closer to the equator than the UK. Therefore, Texas gets more sunshine, more directly delivered. Thus, the capacity factor for solar generation in Texas is higher than in the UK.
While this doesn’t expressly state “no grid is capable of getting more than 25% of its power from wind and solar,” it certainly implies that. What I was doing was saying “yeah, but look over there, they did what you said couldn’t be done.” If your point is that the UK will never produce more than 25% of electricity generation by solar, then sure I’ll go with that. If your point is “there aren’t grids where wind & solar are economically viable at scale” then my response is “but ERCOT.”
Interestingly you point to solar insolation, but not wind availability. You should have pointed to that as well since average wind resource is also much better in ERCOT than in UK. Offshore is obviously better in UK, but then offshore is stupidly expensive.
However, I’d like to clarify your actual point. Is your point
a) Solar power is uneconomic in UK
b) Solar + Wind are unlikely to contribute more than ~25% of annual generation on any large grid without substantial wholesale price increases
I think the difference between those two hypotheses is pretty substantial.
Don’t quibble pettily. The head posting specifically refers to the 25% capacity factor for onshore wind and the 30% capacity factor for offshore wind as applying to Britain, and simili modo to Germany. If chadb is incapable of comprehending that, for instance, the Falkland Islands has twice as much wind as Britain and thus a wind capacity factor about double that of Britain, or that Texas has more sunshine than Britain and thus a higher capacity factor, then he should consult an elementary textbook of meteorology and do a lot less shouting and a lot more thinking.
Those averages, be they ever so high, don’t cover the times it is too cold, too hot, too still, or too cloudy.
Welcome to statistics 101. The fact that a mean is a mean does not mean that Mr Pollock’s result is unsound.
At what cost?
Since the Pollock limit for wind in the UK is of order 25%, with perhaps another 10% for solar power, perhaps Mikehig – rather than taking cheap shots – would like to look at the equations and prove Mr Pollock wrong.
Just look at the real world data for the UK, per the link I posted.
“It doesnot add up” is correct in all that he says, but so is Douglas Pollock. If Mr Born wishes to challenge Mr Pollock’s mathematics, perhaps he would be kind enough to be specific. Otherwise, Mr Pollock’s result stands.
Nothing in my experience suggests that much would be gained by my explaining the math to Lord Monckton.
But those who have the wit to profit from actual data are invited to consider Fig. 3 of my Naptown Numbers piece called “Will Batteries Make Wind and Solar Reliable?” That plot depicts so scaling ERCOT’s 2018 uncurtailed wind output as to make it average ERCOT’s average load.
In that year the wind turbines’ output averaged 37% of their nameplate capacity, implying according to Lord Monckton that wind could not on average supply more than 37% of the system load. But scaling the nameplate capacity to 2.73 times the average load results without storage in only 26% curtailment: with that much wind capacity wind would have supplied 74% of the demand.
Of course, Texas is uncommonly windy, so those results are no doubt atypical. Also, most of the best sites in that state presumably have already been taken, so I’m not suggesting that in reality adding that much capacity would produce that much useable power.
But the data still show that Lord Monckton is wrong.
Exactly the type of work I was referring to. I suspect the cutoff for wind will be closer to 10% curtailment (closer to 60% of annual generation). Once you add in solar you can push 80% generation while maintaining 10% curtailment.
Most of the best sites have indeed been taken, but there are two caveats to that:
a) they were taken early on and have smaller and less efficient turbines on them. Repowering would make a big difference
b) the less windy sites (especially along the coast) have different production profiles and so a higher penetration may be possible (generating next MW when last MW is idle aids in penetration)
Although I’m sure the data are out there somewhere, I didn’t immediately find hourly data comprehensive enough to enable me to do the calculation for a hybrid (wind + solar) system in Texas. A better researcher could no doubt do a better job than I did.
But the “Caveat” section of my Naptown Numbers post makes a hybrid-system calculation for a year in Germany, and the results suggest that a hybrid system, too, would be expensive, although less so than wind or solar individually.
Nothing I’ve seen so far has convinced me that on any very significant scale wind and/or solar would be cheaper than thermal and/or hydro. As I say, I don’t have all the data, so I’m open to being convinced otherwise. But so far solar- and wind-power proponents have not impressed me as being serious people.
I can’t pull the data right now given my vpn, but do a google search for: ercot wind solar annual generation
It will give you a page with a downloadable excel file that has all the hourly data for ERCOT going back years. I would suggest that if you touch 2021 you be very careful with February. The grid was crazy that month.
I’ve done the exact same scaling you showed above with scaling wind and solar. I have also been pretty careful in the past by scaling to a given MW rather than a pure scalar. That isn’t as big a deal for wind, but solar doubled over the past year, so you have to be careful with that one. I find that there is a pretty nice point at ~65GW of wind and ~30GW of solar that provides a lot of penetration without curtailing either renewables or nuclear significantly.
Just so you know, I’m not a solar-and-wind proponent. I honestly don’t care where the electricity comes from, mostly I want it to be cheap. If wind & solar beat the marginal cost of gas (and they did earlier this year, but don’t right now) then wind and solar will be installed until the point that they are curtailed, and that ends up being ~60% penetration for ERCOT.
Yes, 60% penetration sounds plausible as a point before which returns to additional unreliables capacity don’t drop off too precipitously. And about 2:1 wind:solar is close to what I found, too. Also, I agree that there are times when a combined thermal/solar/wind combination would temporarily be cheaper than thermal only.
But I’ve yet to see a compelling case for its being cheaper over the life of a thermal plant–although, as I say, I haven’t nailed all the data down myself.
Let’s suppose, though, that 60% is a sweet spot that would indeed be cheaper in the long run. I think ERCOT (and other organizations) have demonstrated that price-structure disparities make it fiendishly difficult to design a market that accurately reflects true cost and would therefore gravitate to that level.
I don’t profess to know the solution to the market-design problem, but as a first stab I think the bidders should all be held to the same reliability standards–which, e.g., wind-farm operators would need to meet by arranging their own battery, hydro, thermal, or other back-up rather than free-riding on competitor suppliers’ reliability as they do now.
More hand-waving from the furtively pseudonymous “chadb”. Mr Pollock’s fundamental limit, if adhered to, prevents any systemic wasting of electrical generation. In Texas, which certainly has plenty of sun and may also have plenty of wind, the combined Pollock limit will be greater than in the UK, but installing capacity beyond that limit will simply be wasteful.
Nothing in my experience suggests that much would be gained by explaining the math to Mr Born, who generously but inaccurately attributes Mr Pollock’s result to me, saying that “the data still show that Lord Monckton is wrong”.
Nice try, but no. Mr Born’s heroically half-baked and lamentably ludicrous example amply confirms that Mr Pollock’s fundamental limit on the contribution of unreliables to an electricity grid – namely, the capacity factor of the generation species in question in the relevant territory – is correctly derived.
At present, the wind capacity factor for Texas is 37% (actually, 36% averaged over the past six years, but let’s go with Mr Born’s 37%). Mr Born says, en effet, that if one were to add another 64%, so that wind power in Texas produced 101% of total annual grid output, and then threw away 26%, wind power would generate 74% of total grid output in Texas, and there was Lord Monckton saying, en effet, that wind couldn’t provide more than 37%, so Lord Monckton must be wrong, blah, blah.
Bozhe moi! It is made explicit in the head posting, which Mr Born should get his kindergarten mistress to read to him one day, that if one were to add capacity to the grid beyond the Pollock limit one would have to install prohibitively expensive and logistically unfeasible battery storage capacity [or, as some here have suggested, “green” hydrogen electrolysis] to take up the otherwise-wasted surplus generation.
Surely only Mr Born could be incompetent enough, and malevolent enough, to imagine that Mr Pollock would suggest that it was physically impossible for idiotic governments to mandate the construction of so many more unreliables that surplus electrical power would have to be thrown away.
The whole point of Mr Pollock taking the trouble to derive his eponymous limit was to discourage foolish governments from doing what the foolish Mr Born would be stupid enough to do. Who but a nitwit of the first water would suggest increasing unreliables capacity to 101% of total grid output and then throwing 41% of that surplus capacity away?
It is precisely to prevent such egregious stupidity, to say nothing of the heavy financial consequences of making the additional usable fraction of the unreliables generating capacity 41% more expensive that the existing unreliables generating capacity, to say still less of the ineluctable consequences in unaffordable and probably uncorrectable grid destabilization, that Mr Pollock did the math that has passed so completely over Mr Born’s head and revealed the existence of his limit.
If Mr Born’s latest half-witted word salad is the best the paid climate Communists on this site can do to try to impugn Mr Pollock’s result and the fatal threat it presents to their strategy of destroying the Western economies in the specious name of Saving The Planet, then Mr Pollock has nothing to fear.
Lord Monckton’s post purported to explain why the average unreliables percentage contribution to a thermally backed up system such as Germany’s hasn’t so far exceeded the capacity factor.
Here’s his explanation:
Although my post was directed to how expensive batteries are, its data show that with no batteries at all a thermally backed up system’s average unreliables percentage could still exceed the the unreliables capacity factor by a significant amount.
No amount of Monckton bluster can erase that clear fact.
Incidentally, wind’s percentage contribution would have significantly exceeded the 37% capacity factor even if we’d scaled the average uncurtailed wind output to only half the load average. In that case it would have contributed nearly 49%.
Aren’t you ignoring the time of day and time of year variability in electricity prices when you reference paying to curtail? The wind generator is paid the average annual kwh rate for curtailing midday on moderate temperature sunny and windy days. Here in California that means $0.32kwh instead of a fair market price closer to $0.03kwh. Insanity. That’s the only reason I have rooftop solar, I think it should be illegal, but I can’t pass up the money. I don’t make the rules, I just play the game.
Curtailment in the UK is paid on a cheapest to curtail bid basis. That means that wind on market prices or low subsidies can bid anything up to the market clearing subsidy level, and it is the lowest subsidies that get the curtailment payments in demerit order, leaving the most heavily subsidised onstream. When market prices are low that means generation guaranteed an expensive fixed price under a CFD stays on.
Mr Born continues, as usual, wilfully and surlily to misunderstand mathematics which, though simple, seems to be well above his pay-grade. I have already answered Mr Born’s childish point about how it is of course physically possible to install more unreliables than the Pollock limit, by explaining that waste and cost arise above that limit and increase rapidly the more the limit is exceeded. Mr Born’s original heroically stupid example is a good demonstration of that fact. Mr Born, having realized his example was stupid, now waters down the stupidity a bit by suggesting a smaller excess of unreliables installation above the Pollock limit. But there would still be wasted power, leading to very costly capacity or constraint or curtailment payments. The Pollock limit is a remarkably simple way, far simpler than Mr Born’s inspissate and characteristically obscurantist attempts at calculation, of showing where that limit is.
Any generation that exceeds demand will simply be wasted, like flaring a natural gas well.
You state: according to Lord Monckton that wind could not on average supply more than 37% of the system load. But scaling the nameplate capacity to 2.73 times the average load results without storage in only 26% curtailment: with that much wind capacity wind would have supplied 74% of the demand.
What is the economics of your system? The way I read it you’re cutting the CF dramatically and paying 26% curtailment on a much larger system plus still requiring conventional backup for 26% of the average load. Surely, the price of electricity would be less by simply completely avoiding W&S.
The whole point of my Naptown Numbers piece is that wind and solar ordinarily don’t make sense. (I say “ordinarily” because unusually high fuel prices could tilt the economics in their favor even though you’d sometimes need nearly 100% back-up capacity.)
The only point of my first comment above is that the head post’s “fundamental limit” is incorrect, not that adopting wind and/or solar on a large scale is a good idea.
I think people here are intentionally misinterpreting both you and me. Neither of us have actually argued that we should have a grid with 50% wind, merely that is is possible, contra the article’s statement that “ the maximum possible fraction of total grid generation contributable by unreliables turns out to be equal to the average fraction of the nameplate capacity of those reliables that is realistically achievable under real-world conditions.”
There isn’t any sort of hedge there, no conditional “without overbuild,” nothing like that. The statement flat says you cannot exceed capacity factor.
You generously pointed out a specific grid and showed exactly what conditions would give 74% penetration (exactly twice the capacity factor). You didn’t argue that it was a great plan, but you mathematically proved the equation wrong by providing the counterexample. What do you get for your trouble?
“Mr Born’s heroically half-baked and lamentably ludicrous example amply confirms that Mr Pollock’s fundamental limit on the contribution of unreliables to an electricity grid – namely, the capacity factor of the generation species in question in the relevant territory – is correctly derived”
The assertion: grid contributions cannot exceed the capacity factor
Your example: Here is a case where you would provide double the capacity factor
Response: See, he just showed you can’t exceed the capacity factor.
When someone cannot accept a clear and obvious proof of their mistake they are either dumb or intentionally obtuse. The author resorts to name calling in at least half his responses. I really think he should do better than that.
But he won’t.
I’ve witnessed his dishonest discourse since nearly eight years ago, when he got in over his head and I tried to throw him a line. Part of it, no doubt, is that he really is as innumerate as he seems. But he’s so consistently impervious to guidance that I suspect he lives for the approval that gushes from those NPC types his posts seem to attract, so he can’t often afford to admit that he’s wrong.
It’s a sad case, because he seems to have a flypaper mind, and the resultant ability to regurgitate facts and (gratuitous) Latin can be persuasive to a certain type of reader and would therefore help advance climate-crisis skepticism if he didn’t persist in straying into mathematics, at which he’s embarrassingly bad.
Mr Born is wrong. His own examples show that, exactly as Mr Sandberg points out, exceeding the Pollock limit is costly, wasteful and destabilizing.
Monckton of Brenchley January 12, 2023 5:46 am
Christopher, please take all of this in the spirit of friendship in which it is offered.
You’re moving the goalposts.
Your original argument was that the “Pollock limit” is “the maximum possible fraction of total grid generation contributable by unreliables”.
No hedging. No special cases. You claimed it’s “the maximum contributable”, full stop.
That’s why I went to look at the data, to see if that is true. And guess what? It’s not. I posted up several examples where that is not true.
Your argument was not that “exceeding the Pollock limit is costly, wasteful, and destabilizing”. That brand-new argument, which you are making now, is a very different and much more defensible argument … but you’ve moved the goalposts.
Finally, the antipathy and insults you’ve directed at Joe Born are not a good look on you. Insulting Joe’s excellent mathematical knowledge and ability just makes you appear weak, and it does nothing it strengthen your case.
Your friend as always,
Thanks for the kind words.
For what it’s worth, he accompanying plot implied by those ERCOT data illustrates the more-defensible argument to which Lord Monckton has now retreated. (It’s from a proposed post I sent Mr. Watts early this morning to help clarify the issue. As I expected, he won’t run it.)
Monckton has not “retreated”, as Mr Born in his characteristically malevolent fashion suggests. The head posting plainly states that “What Douglas Pollock’s brilliant and, at first blush, unexpected result means is that the miserably low capacity factor R is in fact also the fundamental limit fmax on the contribution that unreliable can make to the grid without prohibitively expensive and logistically unachievable large-scale static-battery backup.”
Without backup, the surplus generation above the Pollock limit would be substantially or wholly – and always expensively – wasted. It is a pity that Mr Born – and for that matter Mr Eschenbach – did not read the head posting with due care and attention before commenting.
The term gaslighting comes to mind.
Thank goodness for you and Willis! While I agree with most folks here that government mandated renewables are a cropper, it’s frustrating that MoB insists on defending Pollock’s ‘magic’ proof, while demeaning his critics.
For my part, I provided him with a very concise economic argument why Pollock is wrong, which you’re most welcome to read and provide feedback on here:
But my reason for commenting here, is that after being told repeatedly to ‘re-read the head piece’, I actually know where Pollock’s derivation, or MoB’s interpretation of it, runs aground.
Specifically, and avoiding most of the hocus hocus, he defines:
H [=] mean system generation,
R [=] average renewable capacity factor,
f [=] renewable generation / total generation,
N [=] min renewable nameplate capacity to meet renewable generation, and finally,
f_max [=] f given H=N, which must equal (renewable generation / total generation) given H=N, or substituting from above,
f_max = (N*R) / (N) = R
Here’s the rub – there is absolutely no support for the premise that f_max occurs when H=N, since it is quite possible for f to take on any value between 0 and 1.0!
And if my take is correct, I wouldn’t want to be the person waving Pollock’s paper around in front of a public utility commission.
Exactly. As I said above, though, “Nothing in my experience suggests that much would be gained by my explaining the math to Lord Monckton.”
The term “nitwit” comes to mind. Mr Born continues to try to maintain that I had not mentioned that if one added more unreliables to a grid one would need costly battery backup to take the surplus capacity, a point which is made explicitly, and twice, in the head posting, in a longish section devoted to the problems of battery backup.
Nearly right. In practice, curtailment (or the need for a very cheap high efficiency storage alternative) starts when maximum wind output exceeds minimum demand (perhaps adjusted down to allow adequate inertia providing generation), even absent transmission constraints. Maximum potential wind output for a fleet of wind farms will be below their nominal capacity, because the wind never blows evenly everywhere, and there are indivdual turbine outages for maintenance, etc.. Actual output will be affected also by economic or grid instructed curtailment.
In the UK and Sweden we have long seen curtailment because of insufficient transmission capacity to handle high levels of output from remote wind farms in the North. In part it is uneconomic to provide the capacity, since it is only used when output is close to maximum, which is a small percentage of the time.
A tacit assumption in my Naptown Numbers piece‘s simplified calculations was absence of any ERCOT transmission limitations. That this assumption is probably unrealistic is another reason for considering those calculations optimistic.
No., Read the head posting. It makes it quite clear that if more renewables are added to the grid than the Pollock limit the additional capacity is wasted and the costs are large.
For instance: “That means that wind and solar power cannot contribute more than about a quarter of total electricity demand on the grid, unless there is battery backup.”
The words are right there in the head posting. No ifs, no buts.
And Mr Born’s example was indeed a demonstration that the Pollock limit is correct. He had said that in Texas the capacity factor for wind is 37%, but that if one installed enough capacity to make that 101% one would be able to generate 74% of total grid output, but 26% (equivalent to 41% of the extra generation) would be wasted. The whole idea of the Pollock limit is to provide a warming of the point at which, if one goes on adding unreliables to a grid, much if not all of the additional generation will the thrown away.
I realize that this argument, however simple it seems to me, may be not so easy for others to follow. But on any view Mr Born’s proposed refutation of the Pollock limit is in reality a substantial confirmation of it.
is exactly correct
The Pollock limit is not a limit in the sense that the speed of light is a limit, a limit beyond which one may not surpass due to the immutable laws of physics.
While I am searching for a better analogy, the one that comes to mind is a speed limit. The posted speed limit doesn’t prohibit driving faster than the posted limit, it simply is a warning that there may be negative consequences if you go faster.
I prefer to think of it as an inflection point than a wall. The marginal value of renewables goes up to a point where it meets the Pollock limit, then it doesn’t drop to zero but it follows a different curve that’s likely to eventually slope downward.
Solar PV with lead-acid storage is a reliable and cost-effective solution for off-grid remote locations.
I read your “piece”. Excellent, but I need some help with this:
“We’ve also seen that even without wind turbines batteries would tend to promote base-load operation. So by combining batteries with wind and solar farms the quoted passage seems to be predicting something further, and nothing in the piece discourages the impression that wind backed up by batteries will soon be cheaper than base-load thermal plants.”
I understand that an installed and commissioned grid scale battery pack array cost is $500kW.h.and therefore forever too expensive beyond four (4) hours, much less the >100 hours required (as you know some argue for three (3) months. I can’t understand your:
“nothing in the piece discourages the impression that wind backed up by batteries will soon be cheaper than base-load thermal plants.”
Also, as believe you are saying, “batteries would tend to promote base-load operation.” You’re the only person, other than myself that has made that argument: If for some strange reason battery or molten sand would become economical it would better serve as surplus night generation at a conventional powerplant.
Thank you for the kind words.
I’m not completely sure I understand your questions, but I hope the following is somewhat responsive:
Basically, I was attempting to say that, although the Wall Street Journal article didn’t say so explicitly, it could easily have left the impression that because of battery-price reductions thermal generation could profitably be replaced completely by wind and solar backed up by batteries. One of the passages that could have encouraged that impression was the statement that “building batteries to harvest and dispatch inexpensive and clean power from wind and solar farms, and not just for a couple of hours after sunset . . . threatens not only peakers, but many traditional power plants.”
But, although I still think the article leaves that impression, the paragraph I followed that article excerpt with doesn’t seem as relevant now as I must have thought it was at the time. That paragraph merely observes that, from the point of view of operating base-load thermal units, it’s detrimental to add wind and solar but helpful to add batteries.
And in the latter connection it was obscure of me to say that “even without wind turbines batteries would tend to promote base-load operation.” The possibility that I thereby attempted but failed to state clearly was that the combination of a (“base-load”) plant that produces a more or less a steady output with one (a “peaker”) that follows load variations could profitably be replaced by the combination of batteries with the steady-output unit alone.
Sorry for the resulting confusion.
Got it. Thank you for your detailed response.
Fair enough. On the other hand renewables provide a hedge against gas prices. You effectively lock in future production at the capital cost. Anyone who did that in 2018-2021 avoided some nasty surprises in gas prices over the last year. As of now with lower gas prices and much higher interest rates I suspect the calculation goes the other way, and renewable installations will stall for the next year or so (except what has already received loans).
What “future” production? When is it produced?
It is not dispatchable so you have locked in NOTHING n a future day when the wind is not blowing.
It doesn’t matter which day. This year the cost of gas was above $8/mmBTU for extended periods of time. Every time a solar panel was operating the rate payers avoided that cost. I’m not sure if you are intentionally missing that point. I’m not arguing that solar or wind is ideal, just that the avoided fuel cost matters, especially when we have no idea what the cost of fuel will be in a year.
A better hedge would have been keeping coal open and stockpiling. In fact I recommend precisely that to UK politicians in mid 2021. Also fixing up and refuelling nuclear. Again they dithered, betting on their Saudi Arabia of wind. Better still would have been pushing for more gas production at home and abroad instead of blocking it and its financing. Again something I have been pushing ever since Carney left the BoE to become king of ESG.
You comment is one of the best in this string.
It inspired me to rewrite it, and use it in my wind/solar articles.
Here it is
You have to look at the whole electrical system costs of integrating wind.
The first few percent of annual wind contribution make little difference to overall costs, so the cost is approximated by the all-in, levelized cost of energy, All-in LCOE, calculations.
Add a few more wind percent, and you start to need to invest in additional grid stabilization to cope with flicker.
Add a few more wind percent, and you start adversely hitting the efficient operating regimes of other power plants on the grid, which are forced to operate:
1) At reduced outputs while counteracting the ups and downs of wind, which is less efficient (more Btu and CO2/kWh),
2) Imposes increased wear and tear that adds to maintenance cost, i
3) Increases the frequency of plant start/stops, which is inefficient.
4) The reduced running hours means costs, such as for capital, O&M, and all other costs must be recovered from reduced electricity sales volumes.
Add a few more wind percent, and you reach the point at which wind has to be curtailed to ensure adequate, grid-stabilizing inertia is available.
Add a few more wind percent, and wind has to be curtailed, because it exceeds demand during low-demand hours and energy storage is unable to cope economically.
Add few more wind percent, and the hours of curtailment increase, and the amounts of curtailment during low-demand hours also increase. Overall curtailment increases quadratically, and Owners need to recoup costs from un-curtailed output.
Meanwhile periods of surplus imply zero or negative spot prices, which requires extra subsidies to ensure adequate grid-stabilizing inertia remains available.
Supply on windless days is barely affected by all the increased wind capacity.
Storage, other than as an aid to grid stabilization, remains uneconomic.
Adding more and more wind percent, will more and more decrease the usefulness of its output, because more and more of it will be curtailed.
The net result of decreasing the usefulness from increased wind (ignoring the costs for increased grid expansion/augmentation, and the adverse impact on the economics of the other power plants, etc.) becomes a rapidly escalating multiple of All-in LCOE.
It can reach up to 10 times the All-in LCOE, and still fail to replace the need for almost 100% standby/backup generation.
GRID-SCALE BATTERY SYSTEMS IN NEW ENGLAND TO COUNTERACT SHORTFALL OF ONE-DAY WIND/SOLAR LULL
and the cited article goes on to say,
“The turnkey capital cost would be 259,700 MWh x $400/kWh, delivered as AC = $1.037 trillion, lasting about 15 years
A 24-h wind/solar lull, with wind/solar at 50% of the annual grid load of New England, would require a $1.0 trillion battery system, if that battery system were the only source of making up the wind/solar shortfall.
Comment: Can we now “put the final nail in the coffin”? Let’s end the pretense, grid scale wind and solar, at more than the system capacity factor, is forever too expensive.
Wind and solar is a failed 40-yearlong failed experiment and it must end now, not after Biden’s inflation inflaming Act has severely damaged our economy. Our only hope is that the Republican House can manage to withhold the funding. Don’t doubt it.
Correct. Presumably one could run many joint simulations of fuel and other variable costs, load, wind speed, cloud cover, etc. and then optimize the dispatch of conventional and renewable sources (including storage) for each simulation to obtain a joint distribution of supply cost vs. renewable percentage. One might then be able to pick an ‘optimal’ percentage of renewables on the grid. But to paraphrase the finance types, simulated performance is no guarantee of actual performance.
And in doing those optimizations, in future, grid operators will have the advantage of understanding the Pollock limit. That will make their analyses simpler and more reliable, and the resulting pattern of generation cheaper, stabler and less wasteful.
Sir, you’re treating the ‘Pollock Limit’ as if it were a physical law, e.g., the Betz Limit on wind turbines. It’s not.
I don’t care for renewables any more than you do. However, I can’t see how the Pollock Limit, as derived above, could ever succeed before a public utility commission in NY, CA or any REGGI state – the intervenors for the w+s interests would blow it out of the water.
You’re certainly right about California, but only because facts, no matter how they are presented, don’t matter. We’re woke out here.
Mr Sandberg is right and Frank from NoVA wrong. Frank is, perhaps, not familiar with elementary linear algebra. The Pollock limit is the maximum generation by unreliables on a grid that will not be egregiously wasteful by generating surplus output that must be discarded via costly constraint/capacity/curtailment payments. Whether climate-Communist administrations pay any attention to reality is quite another question.
What’s the UK wind power situation look like if the powers that be install the connection upgrade required to actually use all the wind generated electricity from the Orkney Islands? The wind blows nearly constantly there, so pretty much every good spot for a turbine has one – but they can only send a fraction of the power to the main islands due to a very undersized connection under the strait. https://www.youtube.com/watch?v=8UmsfXWzvEA
The problem is not just the capacity across the Pentland Firth, but the need to deliver power where the demand is in Southern England. All that extra transmission capacity adds enormously to cost. If you could park Orkney and its winds in the Thames Estuary you might have a winner. The London Array manages about 40% load factor.
The practically achieved load factors from Orkney actually aren’t quite as high as they are touted to be.
Tidal and wave still have a long way to go!
I can write at length on the difficulties they have encountered, and why I think they are going nowhere.
Fantastic article, thanks Christopher Monckton:
Where I live, I can see Drax, some 30 miles away, with 6 generators (2 coal 4 biofuel 🙁 ), capable of outputting c4GW.
Three miles away I can see a wind farm, 9 turbines, generating 2MW each.
Both sites occupy a similar area of land, c0.7sq miles.
For a wind farm to generate the same output as Drax, would require, c2000 turbines, and occupy c 150 sq miles.
At 25%, that increases to c 8000 turbines, and over 600 sq miles (the size of Grtr Manchester). What that doesn’t take into account, is that the topography is less than ideal, and therefore logically, more appropriate land would be required.
Apart from the obvious cost, of making the landowners even richer, there are the issues of complexity, maintenance, reliability, running costs etc.
In addition, there has been the opening of a battery farm, on the outskirts of Hull, the farm occupies the equivalent of two football pitches, and can provide just 1% of national demand for four minutes.
If wind output dropped to zero for a day, to provide the necessary demand, would require a battery farm occupying the equivalent of 72000 football pitches, nearly 200 sq miles. An area, that would include Leeds, Bradford, Otley, Dewsbury and Wakefield.
No wonder landowners love ruinables!
Those battery farms, and flywheel farms, aren’t just to take up the slack in null wind days, they also help to smooth the variability of ruinables output.
This all adds extra cost, complexity, reliability issues, and of course, they all add an extra load on the grid.
It’s absolute madness, perhaps someone should explain to the gov’t the acronym KISS.
Plus unreliable developers are now being told it can take up to 15 years for them to be connected to the UK National Grid because the Grid infrastructure has been unable to develop as fast as the unreliables are coming on stream. In its latest round of funding for the regional electricity network companies Ofgem has allocated £23 billion rather than the £25 billion they asked for.
But it hasn’t stopped Moray East from coining it in constraint payments.
“The renewables fraction f, of course, reaches its maximum fmax where hourly demand His equal to N.”
I don’t think that’s right – hourly demand H should equal N times the capacity factor R. The equations then give you fmax = 1 which is only telling you something about the assumptions made.
This doesn’t invalidate the real drawbacks with wind, such as the fact that no matter how many windmills you build, you still need backup power systems for when the wind doesn’t blow!
No. N is equal to f H / R. Therefore, H is equal to N R / f.
Yes, i set up the equation in Excel exactly as written and substituted real world values. It was going great until the last two steps. Hopefully someone has done it, got valid numbers and posts.
Well, as Sajid Javid would say, “So what?”
The significance of Mr Pollock’s result is explained in the head posting, which Ian_e may care to get someone to read to him.
The Final Nail in The Coffin Of “Renewable” Energy will have been driven when government subsidy checks fail to clear.
China and Germany are doing some “clawing back”.
Hopefully, some “net zero” sponsors will recognize natural gas as the ultimate, clean burning “renewable”, at least in a “transition phase”.
It is important to keep in mind that the term “nameplate ratings” for PV and wind turbines is at best sloppy simplistic thinking. Taking the number of modules in a PV system and multiplying by the “nameplate rating” will not tell you how much power or energy you might get out of your system, it’s not even close. They should instead be viewed as maximum ratings, numbers that are necessary for calculating safety factors in system designs.
Where do these numbers for PV come from, you might ask? Good question.
For PV, the module rating is the power (along with voltage and current) at “standard” conditions, which are:
1000 W/m2 total solar irradiance
25°C solar cell temperature (not air temperature!)
A standard solar spectral irradiance curve
What is important to take away here is that the solar conditions represent cloudless skies with low aerosol scattering—I can tell you that it is really hard to hit 1000 W/m2 in the UK. They are closer to what you might expect in the SW of America.
As for the temperature, when you put a module in sunlight, it gets hot. A module outdoors almost never operates at 25°C when the sun is out, instead it will be 20, 30, 40°C above 25°C. The efficiency is strongly temperature-dependent, so output power drops in actual use.
Current through a PV module is highly dependent on the spectral irradiance which varies Constantine throughout the day and the seasons, but the standard curve is really just a single point in time. It can’t represent wherever you have decided to put your system.
The orientation has huge effects, whenever the sun is not normal to the module surface, cosine losses reduce output. Shading is another huge problem.
Getting a capacity factor from what is on the back of a PV module is just about useless, it can’t tell you much of anything about your particular location.
Savvy PV system designers of course are aware of these things (although they don’t really talk about them)—they end up needing extra modules in the design to bring the output up to what they contract to deliver.
I’ve never a big proponent of using these so-called yield factors with PV, they are inadequate. Mr. Pollock’s calculation is a demonstration of this.
Windmill average about 14 hours a day with little or no output
No output if the blades ice up, at least not until they are defrosted with optional blade heaters (using other sources of electricity).
Solar panels at best have an annual average 6 hours of high output a day, and that’s with no clouds, usually from about 10am to 4pm, There is also an annual average about six hours a day with low output — three hours before, and three hours after, the approximate 10 am to 4pm period. Even lower in those six hours the sky is cloudy. No output if the solar panels are covered with snow
Reliability and power on demand are the key objectives of an electric grid.
Solar panels and bird and bat shredders belong in museums.
Overly broad—there are applications where PV performs very well, especially off-grid. There are communication relay stations located north of the Arctic Circle that are 100% PV-powered. The modules are oriented nearly vertical and a large lead-acid battery powers everything through the long arctic winter.
Solar in Alaska
Note the one that looks like a merry-go-round, it can collect power from any azimuth when the sun does not set. To work, the system would need multiple power conditioning units so that the modules facing away from the sun don’t cause the entire system to shut down.
It might have been simpler to have it rotate to face the sun like a radar antenna, albeit keeping the mechanism functional in Alaska might present challenges.
Fortunately, we have academics here in the UK who are perfectly able to calculate the mean UK-wide capacity factor for solar panels, and also for onshore wind power, and also for offshore wind power. Mr Pollock’s result does not in any way depend upon knowing what the capacity factor actually is. It merely demonstrates that, whatever that capacity factor is, that is the fundamental limit on the fraction of total grid generation that is, in the real world, contributable by the renewable (or for that matter thermal) source in question.
Combine the academics’ research with Mr Pollock’s result and you will be able to see the impossibility of relying significantly upon unreliables for power in the absence of static battery backup.
Whenever I see the phrase “nameplate rating”, I get triggered.
And the 2023 price for grid scale battery storage is $500 kW.h, forever too expensive beyond four (4) hours of storage.
The data are perfectly usable so long as you get actually reported generation for given nominal capacity. I think that Sheffield University does a good job with estimating solar output in the UK (and they publish their uncertainty bands too). Peak solar output is recorded as 9.89GW out of an age adjusted capacity of 13.1GW, reflecting the factors you mention plus some effects of geographical dispersion (e.g. differences in haziness on a cloudless day between coast, inland etc.)
Sunnyportal has data of varying quality across many different sites around the world. On smaller installations it is not uncommon to find gaps of months awaiting a new inverter, which is often left out of calculations.
While solar cell/arrays themselves deteriorate faster.
Module power at “standard conditions” (AKA “kWp”) is a really dumb metric, it was never intended for use in yield calculations. Instead it is for comparing efficiency of different devices from different manufacturers and fabrication techniques. Because efficiency varies with so many factors, a standard condition was necessary.
I hate to be the skunk at the picnic, but I believe the analysis, as I follow it, is incorrect. Various wind/solar proponents argue that we should overbuild wind and solar capacity, then use the “surplus” generation to produce “green” hydrogen. Ignoring the costs of doing so, if N > C, then Mr. Pollock’scalculation fails. Having said that, however, overbuilding does nothing for the periods during which there is no wind/sun. Hence, the battery capacity required to ensure reliability for such a period does not change. If I am missing something, perhaps Lord Monckton or one of the commenters can clarify.
The hydrogen still has to be transported and stored.
And not through pipelines designed for methane.
Hydrogen is a terrible solution. There are many times it flat doesn’t work, and it is explosive and corrosive. Just say no to hydrogen.
When I ran these calculations I found the lowest cost for a net-zero grid (about 30% higher than today’s cost, nowhere close to Germany’s nonsense) did the following:
Maintain all existing nuclear
Install wind & solar to 60-80% of generation (not capacity) depending on grid
Ran natural gas combined cycle for the rest
Install a very small amount of storage to manage largest summer peaks
Run direct air capture over the year to offset any CO2 released by NGCC
Alternative model (assuming next gen nuclear was low cost)
Exact same as above, but install nuclear to hit 60-80% of generation
For ERCOT you do everything except the direct air capture based on cost only. That is, at $3.50.mmBTU you install as much wind and solar as you can just to avoid fuel cost. However, you don’t waste money on direct air capture. That led to ~80% zero emissions in ERCOT driven entirely by cost considerations. Beyond that costs started rising again as you overbuild wind (much less overbuild of solar) and run direct air capture.
In no scenarios was hydrogen a cost effective option. The problem is if you want to generate hydrogen with “surplus” electricity you end up installing insanely expensive electrolysis equipment that is only used a few hundred hours a year at most. Complete waste of capital. You would be much better off spreading out direct air capture in order to run a peaker.
In response to Jonathan, the head posting (if only people would read them before rather than after commenting) makes it plain that in the absence of static-battery backup the capacity factor of an energy source is equal to the maximum fraction of total grid generation contributable by that source.
It is not difficult to work out, having read that in the head posting, that soi-disant “green” hydrogen would act in such a system in a fashion functionally similar to a static battery. The cost, like that of static battery backup, would be enormous; the risks, including risks to life, would be substantial, and, at present, the costly infrastructure that would be required does not exist.
In no way, then, does the theoretical possibility of generating “green” hydrogen from surplus unreliables generation impugn Douglas Pollock’s fascinating result.
What battery capacity? The big battery that might support the grid’s demand for 6 minutes? 6 minutes, tops.
There are rumors of large batteries that can support an office complex for a brief time, But, no glowing reviews, e.g., ‘The mystery battery kept our building lights, computers, internet, water and heating/cooling running for days perfectly.’
None of the batteries extant are capable of supplying sufficient inertia to restart or stabilize a grid.
I am in complete agreement with the thrust and general content of this article. However….the following statement appears to be incorrect. “As a direct result of this fatuity, Britain now suffers the costliest electricity prices in the world.” A few fast checks show that Germany holds this dubious distinction (in Europe at least). Attention to this kind of detail is, I think, quite important – lest the remaining content of the article then becomes subject to accusations of discredence.
Actually, the most recent cost comparison I have seen, which has also been reported in the less untrustworthy media here, is that UK electricity is now the costliest in the world. If it is not quite the costliest in the world, that is a quibble that does not in any way undermine or impugn Mr Pollock’s important result.
We spent the summer and autumn exporting electricity to France, where prices were higher on account of their capacity shortages arising from nuclear maintenance. When it turned cold in Dunkelflaute our own capacity shortage was revealed and we paid top prices for imports to keep the lights on.
Prices actually realised by wind generation are much higher than the media propaganda tell us.
The chart is based on the data for actual CFD generation by wind farm and strike price, and actual production at each band of ROCs otherwise, with ROC values as reported by OFGEM for cashout plus recycle value, and day ahead market prices as measured by the hourly Intermediate Market Reference Price used to calculate CFD payments (in practice the APX average traded price for each hour). The December 2022 data are incomplete, awaiting reconciled settlement data.