Archive for the ‘Electricity Generation’ Category

Carbon Dioxide Accounting: Why I hate it.

January 7, 2023

Friends, the turn of the year is the time when Carbonistas such as myself look at their carbon dioxide accounts. Like all accounting it is tedious but sort of important.

However carbon dioxide accounting depresses me more than regular accounting because I can hardly believe any of the numbers!

Allow me to explain…

The Big Picture

Click on image for a larger version. The red line on the graph shows estimated emissions from my household if I had not undertaken any refurbishment. The data are calculated month by month out to 2040. The green line shows actual estimated emissions from my household. The black dotted-line shows the additional effect of paying Climeworks to remove CO2 from the atmosphere on my behalf.

The aim of my activities and expenditure over the last three years has been to reduce ongoing carbon dioxide emissions from all aspects of my life, but targeting especially my home.

The graph above shows how I expect household emissions to accumulate based on various assumptions. Notice the scales: the horizontal scale extends out to 2040, my targeted date of death, and the vertical scale is in tonnes of carbon dioxide. Tonnes!

  • The red line shows how I would expect emissions to accumulate if I had made no alterations to the house.
  • The green line shows how I expect emissions to accumulate based on the current plan. This is based on the amount of electricity I draw from the grid.
  • The dotted black line accounts for the activities of Climeworks who have promised to permanently remove 50 kg of CO2/month in my name. This line is dotted because I don’t personally have any evidence that Climeworks are actually removing CO2 from the atmosphere.

The net effect of my efforts will hopefully by 2040 amount to around 78 tonnes of CO2 emissions which do not take place. But in honesty, I am not very sure about these numbers.

Assumptions, Assumptions, Assumptions

Working out the data for this graph involves estimating the amount of electricity and gas that the household has consumed (not so hard) – and will consume in future (a bit harder, but still not crazily difficult).

However it also involves associating an amount of carbon dioxide with each unit of gas or electricity used – the so-called carbon intensity (CI) measured in kilograms of CO2 per kilowatt hour (kgCO2/kWh) of gas or electricity. And I genuinely do not know what numbers to use for these CI’s.

Allow me to explain my difficulty.

Assumptions for gas

For gas, a hypothetical 100% efficient boiler would produce around 0.18 kgCO2/kWh.

But it also takes energy – and thus emissions – to extract and deliver the gas to my boiler, and these emissions should also be associated with my consumption.

However, allocating these ‘up stream emissions is not straightforward. It will differ depending on the source of gas e.g. from the North Sea (~+0.013 kgCO2/kWh) or liquified natural gas shipped from (say) the US (~+0.035 kgCO2/kWh). And also it will vary with the distance gas is pumped through the gas distribution network.

And then there is the giant smelly elephant in the room: leaks.

The gas network leaks. At every point from gas platforms to our homes, leaks are very significant. Probably around 1% of the gas we consume leaks, and some of the burned gas escapes without combustion.

When methane leaks it enters the atmosphere, staying for around 10 years before reacting to form CO2 and H2O . And during that 10 years or so, it warms the atmosphere much more intensively than CO2. Averaged over 20 years – methane is around 80 times more powerful greenhouse gas than CO2.

So a leak of 1% anywhere from the gas well to our homes increase the carbon intensity associated with methane by approximately  1% x 80 x 0.18 = 0.144 gCO2/kWh. Combined with upstream emissions this practically doubles the carbon intensity of burning methane compared with the value used by most web sites.

The only way to really know the amount CO2 emitted associated with gas use, is to use no gas at all: anything multiplied by zero is zero.

Assumptions for electricity

As difficult as it is to truly know the  appropriate carbon intensity (CI) to associate with gas consumption, it is much more difficult to know the appropriate CI to associate with electricity consumption. This is because electricity is generated from several different sources, each with its own characteristic CI.

For example, as I type this, this web site tells me that the carbon intensity of the electricity I am using is 0.065 kgCO2/kWh, but this web site tells me that the carbon intensity of the electricity I am using is 0.101 kgCO2/kWh. Which should I believe? I just don’t know.

Both figures will change depending on the composition of generating technologies, but they have (I suppose) made different assumptions about how to account for some emissions. I have previously written to the web sites to ask but received no reply.

Click on image for larger version. Data from MyGridGB and National Grid on carbon intensity. the two sites give answer which differ by 0.036 kgCO2/kWh – amounting to ~30% discrepancy.

But what if I want to draw some extra electricity? If I switch on a tumble dryer, this extra demand must be met by a source which can be switched on to meet that demand, and in practice, this is always gas-fired generation, which is nominally assigned a CI of 0.45 kgCO2/kWh.

So I have to choose whether to allocate an average CI (0.101 or 0.065 kgCO2/kWh) or a marginal CI (0.45 kgCO2/kWh) to my consumption. How do I decide what is my average consumption and what is marginal? I genuinely do not know.

And additionally, the same elephant (methane leaks) that was in the room for gas consumption, is still in the room for electricity derived from gas-fired power stations. Accounting for leaks, the contribution to the average CI of gas-fired generation could practically double from 0.45 kgCO2/kWh to 0.81 kgCO2/kWh which is almost as bad as coal-fired electricity generation.

And there are similar problems accounting for electricity exported from – say – solar panels. In principle, each extra kWh exported displaces a kWh that would have been generated by gas-fired generation. And so exports of solar electricity are avoiding emissions of CO2 at the marginal rate for gas-fired emissions (0.45 kgCO2/kWh). But should this also include the effect of methane leaks avoided?

And since the CI of grid electricity is changing all the time, should I do my accounting in (say) half-hour periods? Or should I use day or night averages? Or weekly, monthly or yearly averages?

Click on image for a larger version. graph showing the variation in CI with time of day: using electricity at night is generally a bit greener because the fraction of electricity generated by wind and nuclear power is greater. Data from the Carbon Intensity web site.

And some argue that the CI of grid electricity varies from region to region! They argue that in regions where there is lots of renewable generation the ‘local’ CI is low. But this ignores the fact that it is essentially a single grid, and that if these regions were isolated, the grid would not be able to function.

Click on image for a larger version. Map showing regional sub grids together with an indication (by colour) of the ‘local’ carbon intensity. Data from the Carbon Intensity web site.

So what do I do?

Friends, this is why I hate carbon accounting: just changing the accounting basis can apparently change emissions associated with electricity or gas consumption depending on where they take place, and how many leaks are associated with the consumption. And part of this is real, and part is conventional practice, which ignores critical issues like methane leaks.

So one can find oneself making spreadsheets of enormous complexity in search of an accounting accuracy that is ultimately unattainable.

So in the face of all this complexity and ambiguity I assign the same carbon intensity to gas and electricity (imports and exports) of 0.230 kgCO2/kWh.

  • For gas this is a bit higher than higher than estimates that add upstream emissions but much lower than estimates that account for methane leaks.
  • For electricity this is roughly the average CI for the years 2019 to 2022 as specified on the MyGridGB web site. If this figure changes significantly in 2023 I will update it.

Click on image for a larger version. Map showing carbon intensity averaged over one year showing the systematic reduction in CI. Data from the MygridGB web site.

The graph at the head of the article shows progress so far and how I anticipate things unfolding over the years. In calculating that graph I disregarded…

  • Exports of solar electricity which could be considered to be avoiding emissions by displacing gas-fired generation.
  • The share of a wind farm that I bought and which should start generating from November 2023. Again, this could be considered to be avoiding emissions by displacing gas-fired generation.

If add these in to my projections, (CI = 0.23 kgCO2/kWh) then the outlook looks better. However, the uncertainties in all the numbers here are so great that I just don’t know if any of it is correct. That’s why all the lines are dotted.

Overall, I know that household gas consumption is zero and therefore so are emissions, no matter what the CI. And this year I expect that we will be more or less off-grid i.e. taking no electricity from the grid – for roughly 6 months. And so I know emissions during that period will be zero. In short, just minimising grid consumption is probably the best way to ensure that associated carbon dioxide emissions are low.

Click on image for a larger version. The red line on the graph shows estimated emissions from my household if I had not undertaken any refurbishment. The data are calculated month by month out to 2040. The green dotted line shows estimated emissions from my household accounting for electricity exported in the summer as ‘negative emissions’ i.e. I have avoided someone else emitting CO2. The black dotted-line shows the additional effect of paying Climeworks to remove CO2 from the atmosphere on my behalf. The blue dotted-line shows the ‘negative emissions’ effect of shares in a wind farm due to begin generating in November 2023.

The Great Carbon Dioxide Accountant in the Sky

Friends, on the sacred slopes of Mauna Loa in Hawaii, there is a carbon dioxide accountant far greater than I.

Click on image for larger version. Mauna Loa CO2 observatory: the  location of the great Carbon Dioxide Accountant in the sky.

Patiently this accountant has been monitoring the concentration of carbon dioxide in the atmosphere since 1959, the year of my birth.

This accountant:

  • Does not care about which value of carbon intensity I use in my calculations.
  • Does not care about whether I used the correct estimate for embodied carbon in my solar panels or triple-glazing
  • Cannot be sweet-talked with promises of future emissions reductions.

They just measure the concentration of carbon dioxide in the Earth’s atmosphere.

When the volcano is not erupting, this accountant publishes their results daily. And this global accountant shows that whatever we are doing is just not enough.

Even if this curve stabilised at its current value of around 420 ppm, the Earth would not cool. But this curve is not stabilising – it is still rising – and it is our actions that are causing this – and only our actions can stop it.

Click on image for larger version. Black Curve: Monthly average atmospheric carbon dioxide concentration versus time at Mauna Loa Observatory, Hawaii (20 °N, 156°W). Red Curve: Fossil fuel trend of a fixed fraction (57%) of the cumulative industrial emissions of CO2 from fossil fuel combustion and cement production. This fraction was calculated from a least squares fit of the fossil fuel trend to the observation record. Data from Scripps CO2 Program.

 

 

Tony Seba has got me thinking

December 4, 2022

Friends, while browsing on YouTube, The Algorithm suggested I watch videos by Tony Seba. And just as The Algorithm foresaw, I have found them fascinating.

The reason for my fascination is that he makes very specific predictions for the rate at which legacy industries (coal, oil, gas, automotive, and animal farming) will collapse.

In general he anticipates rapid changes – much more dramatic than is envisioned conventionally. He anticipates that all these industries will dramatically disrupted, and some of them eliminated, by 2030.

His reasoning is based on the idea of rational deployment of capital in a free market. His predictions do not require people to make choices on moral or environmental grounds. Rather he believes that in a free market, the collapse of these legacy industries will happen because it is economically inevitable.

I would very much like to see the collapse of the oil and automotive industries, and so some part of me would really like to believe his predictions. But while his arguments are compelling, I remain sceptical: I find it hard to believe it will all just ‘happen’: there are strong forces seeking to maintain the status quo. [Edit: The first comment on the article was also sceptical, but so well-worded that I have promoted it to the main text at the end of the article.]

So this article is about Tony Seba’s predictions, and my thoughts about whether or not they will come to pass.

Who is Tony Seba? 

Tony Seba’s web site says:

Tony Seba is a world-renowned thought leader, author, speaker, educator, angel investor and Silicon Valley entrepreneur

His work focuses on technology disruption, the convergence of technologies, business model innovation, organizational capabilities and product innovation that leads to the creation of new industries and societies and the collapse of existing ones.

Tony Seba’s basic ideas add up to Market Disruption

Tony Seba ideas focus on two types of technological change, which he calls change from above and change from below, and on developments in business models.

Change from above is when a new technology is superior to an existing technology, but initially much more expensive than a standard product. This is the case for many new products. However through the action of the learning curve (see below) the price of the superior product falls exponentially as its production volume increase. i.e. the price falls by a characteristic factor (say 20%) for each doubling of production. The compounding of these factors year-upon-year leads to dramatic and initially inconceivable falls in prices. Think Flat Screen TV’s etc.

Change from below is when a new technology is inferior to an existing technology, but much cheaper than a standard product. Through the action of the learning curve (see below) the quality of the inferior product increase exponentially as it’s production volume increase. i.e. some quality metric increases by a characteristic factor (say 20%) for each doubling of production. The compounding of these factors year-upon-year leads to the new product becoming superior to the standard product at a much lower price. Think Digital Cameras,  etc.

And aside from technological innovations, he discusses the importance of business models. For example, he discuss the demise of Kodak, a global giant in photography who made money every time anyone took a photograph or had a print made. Kodak invented digital imaging, and foresaw a world in which they would take a cut of every digital photograph taken, just like they had in the previous era. Of course, digital photography doesn’t work like that: Digital photos are essentially free and the companies that make money from digital photography are Facebook and Instagram – who use completely different business models.

Tony Seba calls the collective impact of these changes market disruption. In such processes, existing markets collapse, stable businesses operating on small margins go bankrupt even in the early stages of a transition, and new businesses emerge that work in ways that seem initially quite foreign.

In retrospect, these changes can appear to be inevitable, but that is not how they feel at the time: during a technology transition, things probably appear chaotic and confusing, with lots of hype and mis-information. Often long-standing traditions – ways of working and living that have stood for generations and seemed unalterable – disappear over short periods of time. These disruptions to the status quo are typically accompanied by the personal distress of many individuals and families, and societal upheaval. They also typically involve the creation of new industries and the destruction of old ones.

Tony Seba’s Predictions

Tony Seba has a list of technological changes (13m47s into the video below), and he looks at how convergence of these technologies, coupled with exponential changes in price or performance, will lead to disruption. [Note: exponential means changing by a constant factor per unit time, rather than changing by a constant increment per unit time]

Amongst the key technologies he looks at are:

  • Solar PV
  • Batteries
  • Computing: Artificial Intelligence

He predicts that the lowering in cost of Solar PV and Batteries, coupled with AI, will lead to disruptions of the entire energy industry, (oil and gas and coal) and transportation (automobiles, distribution). And his predictions are often quite specific and this – in general – means they are not quite right. But also not far off.

Overall, I think Tony Seba’s analysis is interesting and broadly sound, and I am grateful for even the chance to believe that Fossil Fuel industries will collapse in my lifetime. But his analysis is not beyond criticism and I have a list of comments on his work below the embedded video.

There are loads of Tony Seba videos on YouTube, and many of them are very similar. I’ve selected one long video below from April 2020 that covers most of his thoughts about this field.

Comment#1: The Learning Curve

The learning curve was something I had not fully appreciated as a general phenomena.

Tony Seba does not concern himself with the specifics of what gives rise to a particular learning curve. He takes the learning curve as an input, and then extrapolates to see what would happen if the learning trend continues.

In a way, this is a weakness, because understanding the details of how the learning curve works can really help to understand how the curve is likely to continue in the future. But in a way it is a strength, because it is very easy to get lost in details

As an example, lithium-ion batteries have fallen in price by around 19% for each doubling of cumulative production. Compounding these year-on-year change results in a factor 40 lowering price, as production increased by 50,000 times .

Click on image for a larger version. Learning Curves. The graph (with a logarithmic vertical axis) is from Our World in Data showing the decline of battery prices as cumulative production increased.

Comment#2: The S curve

A large part of Tony Seba’s analyses involve so-called S-curves that describe the way in which innovations diffuse through society. In particular, he points out that despite initial low market penetration, innovations can transform societies remarkably quickly. In almost all his talks he contrasts photographs of the New York City Easter Parade in 1900 and 1913. The parade has switched from being 99% horse-drawn carriages to 99% motor cars.

Click on image for a larger version. The S-curve describing the fractional market penetration of an innovation from 0% to 100%. In the early stages of the curve, the growth is typically exponential, but it can still be a very small fraction of the market, but full penetration of the market can happen very quickly. This graph is stolen from this excellent essay.

The importance of the S-curve is that it qualitatively describes the way technological disruptions occur: to use a literary metaphor, they happen “Slowly, then suddenly“. And when one is the lower part of the S-curve, it can be very difficult to anticipate what may be about to happen.

Comment#3: Are the Markets Free?

Perhaps my biggest concern about Tony Seba’s analysis is that there are a very large number of institutions and governments who are entangled with the oil and gas industries. These institutions value the ‘stability’ which would see oil and gas industries continuing exactly as they do now. Every extra year of extra production is a year in which existing investments in oil and gas infrastructure yield extra profit.

The switch to a renewable energy infrastructure will require colossal amounts of capital investment, but will also result in the destruction of the colossal value of existing investments which will become ‘stranded’. Consequently, existing investors, and the institutions they influence, are heavily incentivised to do everything they can to prolong the lifetime of oil and gas by slowing the development of wind, solar PV and batteries.

Tony Seba and his colleague warn about this in the video below, but don’t perhaps clearly communicate the underhand ways in which oil and gas seek to affect discussion of their industry.

Conclusion.

This article is about the future, and the future is fundamentally unknowable. But I think Tony Seba’s appreciation of some of the non-linear dynamics of markets is insightful. And it chimes with my own personal experience that the technology changes I have experienced in my lifetime have happened much faster than I personally anticipated.

But changes on the scale he foresees will bring phenomenal disruption across society and will be resisted furiously by those with vested interests in the status quo.

In the 2030’s will we look at the ruined infrastructure of coal, oil and gas as we now look at canals or closed down shipyards? Will these mighty industries be reduced to ruins, like the broken statue of Ozymandias in the desert. I do hope so.

Promoted Comment

Your skepticism is well founded because there is a fundamental error that most “free market” advocates make.

The belief is that companies will be driven to change by the pursuit of profit – that the drive to maximize shareholder value will drive them to pursue maximum profits.

However, the real motivation seems to be something adjacent but distinctly different: Companies – at least established ones – will always pursue the path of profitable least risk.

This makes sense through the “maximize shareholder value” lens: if we are making money now, why make major changes and put that at risk?

The answer of course is when the risk of getting upstaged by a competitor or upstart is sufficiently great, then _and_only_then_ will the company embrace radical change in pursuit of new profit opportunities.

The profit-maximization curve and the risk curve are related, but distinct, because the risk curve is a subject to restrictions in market access, industry inertia, and other factors that tend to retard change. Those factors are amplified significantly when there are other entities (either businesses or governments – in this case, both) that are heavily invested in the status quo.

In other words, your skepticism is warranted. The market is a useful tool, but it is far from perfect and it doesn’t work the way it’s biggest fans think it does. The economic case of non-fossil energy sources is compelling and becoming moreso every day. But we will not be able to rely on market effects alone – we’re already far behind where we need to be, and the incumbent market will do everything in its power to make sure we stay that way.

Fusion is a failure.

September 21, 2022

Friends, I listened with astonishment this morning to a Radio 4 science-tainment program called The Curious Cases of Rutherford and Fry: The Puzzle of the Plasma Doughnut.

  • I think it may have been the worst science radio program I have ever heard.

Despite fusion’s seventy years of continuous world-wide failure, the program repeatedly claimed that fusion ‘could supply limitless clean electricity‘. This was mentioned in hallowed terms as though there were no other technologies which can already do that – such as solar power or wind turbines.

The program somehow contrived to assume that ‘success’ in this noble struggle was certain – and that after success was achieved it would then ADDITIONALLY provide the power source of our next generation of interstellar rockets, and be available in miniature versions.

Anyone listening without specialist knowledge would have no idea that this entire endeavour is a colossal waste of time of money which will, in all likelihood, never result in a single electron being put onto the grid.

Astonishingly for a program nominally celebrating ‘curiosity’, the hosts Rutherford and Fry (R&F) failed to ask a single challenging question in the 30 minutes allotted to this issue. They just swallowed PR tidbits.

Here are three questions they might have asked:

Q#1: How much will fusion electricity cost?

Since they are looking to supply ‘limitless’ energy, R&F might have asked how much the electricity supplied by these fusion reactors would cost compared to the cost of renewable technologies such as solar or wind?

Of course, nobody knows the price of a product which won’t exist for decades and indeed may never exist. But it is inconceivable that it will cheaper than solar or wind.

A ball park guess would be that it might be around the same price as conventional nuclear power. Or more.

A fusion power station would use technology which was dramatically more complex and expensive than a conventional nuclear power station, and would likely to struggle in early generations to maintain 95% up-time.

And amazingly after all the hard work, since it’s fundamental output is heat – it would still throw away roughly 67% of the energy generated! Why? Because even nuclear fusion cannot beat the second law of thermodynamics that governs the extraction of electricity from hot gases.

In other words: the electricity produced will be very expensive.

Q#2: Tritium: Where will you get it from?

All fusion reactors face myriad technical challenges – I won’t go into them all here – and it would have been nice if perhaps R&F had mentioned one or two of these difficulties.

For example all fusion reactors planned aim to fuse two isotopes of hydrogen called deuterium (D) and tritium (T). Deuterium is available in vast quantities in seawater, but Tritium is amongst the rarest and most expensive radioactive substances on Earth. And fusion reactors require a lot of it. A 100 MWe fusion electricity power plant – a very small generator equivalent to say 10 modern wind turbines – would require roughly 5 kg of tritium per month. A year’s supply for a single reactor is likely more than all the tritium which currently exists on Earth.

Fusion engineers do have plans to use the fusion reactor to create tritium as part of routine reactor operation. But it is not at all obvious to me that a practical solution even exists.

Some mention of the ‘Tritium Problem’ or similar technical problems would have been nice.

Q#3: Timing: Can this help with the climate emergency?

The fusion-industry PR representative on the program said it was very important that they were ready to deploy reactors in 2050 to ‘contribute to Net Zero‘.

This is a misunderstanding. If by 2050 we have reached ‘Net Zero’, then we won’t need fusion! We will – by definition – be operating our economy without emitting CO2 and another source of expensive electricity will likely not find any market at all. Unless it’s really cheap – but electricity generated from a fusion reactor is unlikely to be ‘cheap’.

In fact, the climate emergency is right now and fusion has nothing to offer. Spending resources on fusion research now is channelling money away from things which could actually be helping humanity in the grim decades between now and 2050.

How does trash like this get on the air?

I honestly don’t know, but perhaps R&F left a clue in the additional ‘bonus’ material at the end of on-line version of the program.

After recounting an anecdote, R chuckled and said his mate Steve Cowley was someone important at a UK research lab investigating fusion and had got him a tour of the facility.

His ‘mate’ Steve would actually be Sir Steven Charles Cowley Kt FRS FREng FInstP, the CEO of the UK Atomic Energy Authority.

And it just felt like I was listening to members of a chumocracy discussing how clever they were and what whizz friends they had.

Curiously, you can actually hear R‘s mate Steve on another Radio 4 program, In our Time which discussed fusion in 2014 (link). Sadly, even this program provides only the weakest of sceptical voices.

Why am I writing this?

Normally, if I can’t find something good to write about something, I try to write nothing.

But fusion populists just take such silence as carte-blanche to propagate their delusional propaganda about ‘endless cheap renewable electricity’ and suggest that they are climate-change friendly.

In these coming decades, it is really important that we keep our eyes on ‘the prize’, and ‘the prize’ is not nuclear fusion.

In these decades we will face summers and winters of climatic extremes which will involve multiple humanitarian catastrophes.

‘The prize’ is avoiding even worse disasters in the future, and we will win ‘the prize’ by reducing carbon dioxide emissions now, as rapidly as we possibly can. By now, I mean today, and tomorrow, not next week or next year. Now.

Betting on fusion technology which has failed for decade after decade is nothing but a distraction.

So don’t be distracted: fusion is a serial failure.

Previous articles I have written about Fusion

Below is a selection of articles I written about this topic previously. Of these articles, the July 2020 article is the most-nuanced, trying to emphasise why fusion scientists are still clinging on.

Nuclear Fusion is Irrelevant (February 2022)

Are fusion scientists crazy? (July 2020)

Fusion Research is STILL a waste of money(June 2020)

Research into Nuclear Fusion is REALLY a waste of money. (December 2019)

Research into Nuclear Fusion is a waste of money (November 2019)

Controlled Nuclear Fusion: Forget about it (October 2013)

It’s been a sunny summer

September 1, 2022

Friends, it’s the 1st September: the first day of meteorological autumn. So this seems like a good time to look at solar PV generation this summer.

In case you can’t be bothered reading much further – and I would sympathise with you there – the précis is this:

  • It’s been a sunny summer.

Also comparing generation with consumption, I have devised a plan to try to increase the length of time the house is ‘off-grid’ from 4 months, to 6 months!

The Solar Installation

The 12 solar panels (340 W-peak Q-cells DUO BLK-G8) were installed in November 2020 and have been working flawlessly since.

They are installed on the sloping South and Western roofs of Podesta Towers in Teddington.

Click on image for a larger version. The arrangement of the solar cells on the roof of Podesta Towers.

2021 vs 2022

The figure below shows monthly generation for 2021 and 2022

Click on image for a larger version. Monthly generation – expressed as kWh/day – since installation in November 2020.

Looking at data above, it’s clear that (with the exception of April) generation in every month of 2022 has been larger than generation in the equivalent month in 2021

The sunny nature of 2022 also shows up in the cumulative generation data:

Click on image for a larger version. Cumulative generation in kWh throughout and 2021 and 2022. Also shown the are amounts of electricity exported.

Generation to date this year (3,140 kW) is 12% ahead of cumulative generation in 2021 (2,800 kWh). And exports to date (1,004 kWh) have already exceeded exports in the whole of 2021 (880 kWh).

For completeness, I also include the daily generation graph, but the fluctuations in this are so large that it can be difficult to interpret.

Click on image for a larger version. Daily generation in kWh/day for 2022 is shown in green. Also shown is a ±2 day running average from 20202021 and 2022. The yellow data show the expected generation based on the EU -PV sunshine database.

Analysis: Solar as a fraction of demand

The three charts below are not based upon the solar year – January to December – but the heating year July to June. Somehow this seemed more natural.

The first chart shows our typical demand for electricity through the year – an average of 9.8 kWh/day over the period July 2021 to June 2022.

Also shown (in darker green)  is the electricity used by the heat pump for space heating. This peaked in January 2022 at around 15 kWh/day making a peak demand of 25 kWh/day.

Click on image for a larger version. Average Daily electricity demand in kWh/day shown from July 2021 to June 2022. The light green section of the bars shows normally daily demand (9.8 kWh/day) and the dark green section shows electricity used by the heat pump for space heating.

The second chart shows the daily solar generation from 2021/2022. It’s clear that solar generation is irritatingly – but obviously – out-of-phase with demand.

Click on image for a larger version. Average Daily generation in kWh/day shown from July 2021 to June 2022.

The final chart shows the ratio of the two charts above showing the fraction of average demand that is met by average solar generation. This final chart is interesting.

Click on image for a larger version. The ratio of average generation to average electricity demand through the year.

First of all let’s note that this is based on just one year’s data and year-to-year variability is typically 10%. But this data shows that there are 4 months of the year (May, June, July and August) where average solar generation is able to meet average demand with more than 10% margin. And indeed with the aid of our battery, we have been off-grid for most of that time this year.

But the graph also shows that there are two more months – April and September – where average solar generation is able to meet average demand, but with a margin of less than 10%.

This means that if I could increase solar generation by even a relatively small amount, it might be possible (if the fluctuations are not too large) to take the house off-grid for a full 6 months of the year. Wow! I am getting excited at the very thought of this!

Plan

And friends that is my plan. I have asked a solar installer to add an additional 9 panels onto our array: 5 panels on the roof facing 25 °N or East and 4 on the flat roof nominal facing 25° east of south.

This addition takes the array over the 4 kW-peak installation that can be done without notifying the electricity distribution company, but the installer has told me the application is already submitted.

My hope is that over a year, the additional 9 panels will add ~1,500 kWh (167 kWh/panel) to the ~3,600 kWh (300 kWh/panel) generated by the existing 12 panels. This should be enough to raise generation in April and September above demand, and hopefully allow us to stay off grid for a whole half of a year.

Click on image for a larger version. The location of the panels in Phase#2 of the Podesta Solar Array are shown in red.

These orientations aren’t the best, but actually they are not terrible! And generating over 1 MWh per year is not negligible!

Of course, I still don’t have a date, or even an expectation of a date for doing this work.  But hopefully the panels and inverters will eventually make themselves available in the first few months of next year – hopefully before April!

Note on Embodied Carbon

I am able to afford this because although my pension lump sum is all spent, living modestly and not having to pay big bills, I have been able to save enough of my monthly pension to buy the extra panels.

And having made rough estimates of what is done with my savings, I think the best thing I can do with any resource I have available is to spend it on things that reduce carbon emissions. And there are only one or two things out there that have better ‘carbon value’ than solar panels.

Anyway: That’s the plan…

Non, Je ne regrette rien: update

August 26, 2022

Friends, last week I wrote about my embarrassingly low energy bills, and compared them with the shockingly high energy bills I would be facing if I had spent my pension lump sum on a world cruise and a car: Non, je ne regrette rien.

But after writing that article, I quickly realised that it needed updating.

  • Firstly,  although I have agreed an electricity contract for the year to September 2023, I underestimated how much I would have had to pay for gas. These new ‘energy cap’ prices were estimated early this week and confirmed today.

Energy Cap Prices (Source: Cornwall Insight)

  • Secondly, several people were puzzled about how I did the calculations for both my actual gas and electricity use, and the counterfactual estimate.

In this article I hope to clarify both of these issues.

Modelling Consumption Patterns

Since November 2018 I have read my gas and electricity meters each Saturday morning and so I know my weekly gas and electricity consumption for the last 4 years or so.

This allowed me to get a characteristic consumption pattern from June 2019 to May 2020 before the External Wall Insulation, Solar Panels, Battery and Air Source Heat Pump were installed.

To model the alternative counterfactual reality I have imagined that the 2019/20 pattern of consumption simply repeated indefinitely. I could then compare that with what has actually happened.

Modelling Costs

I have then assumed different costs for different periods as summarised in the table below.

Click for larger version. These are the prices per unit and daily charges that I have assumed. See text for details.

Working out these costs has been tricky.

Historically, I don’t recall the price of either electricity or gas changing much for the many years we have been in the house. It was not until EDF increased the price of cheap electricity by 73% that I thought to look elsewhere, and I switched to Octopus energy a year ago in August 2021.

I signed a fixed-price 1 year deal for electricity that gave me 4 hours of electricity at 5p/kWh and a peak rate of 16p/kWh.

I recently renewed that deal at increased rates of 7.5p/kWh off-peak and 46p/kWh peak.

The gas charge changes with the market and has increased from around 3p/kWh to around 7.3p/kWh but I expect that to increase

Looking ahead I have assumed that in a year’s time I will renew the electricity contract with a similar deal that will be more expensive.

Regarding future gas prices, I have assumed ‘Energy Price Cap Prices‘ for October 2022 that have recently been published. I have made conservative guesses for how these prices will vary in future – but I expect them to increase throughout the whole of 2023.

I have not included any government interventions.

Actual Costs 

The graphs below show my actual electricity and gas costs over the last three and half years, and my projected costs for the next year and a half.

Click on image for a larger version. My weekly gas and electricity costs for the last three and a half years. Also shown in red is my projection for my bills based on currently signed contracts. The figures in boxes show yearly costs. Note the vertical scale is £120/week – much larger than the scale I used in my previous article.

 

Prior to 2021 electricity usage was pretty constant at around 10 kWh/day costing around £15/week.

But after the installation of solar panels and a battery, the pattern of consumption of grid electricity changed significantly, with the house being almost off-grid for three to four months a year, and with electricity consumption usage peaking in winter.

The winter costs of this are low – peaking at £15/week – because we buy most of our electricity ‘off-peak’ and store it in the battery and then run the household from the battery for most of the next day.

Looking ahead, (red) if I assume that the coming winter is similar to last winter, then these projected costs will increase in the year ahead.

Regarding gas usage, one can see the winter consumption declining year-on-year as a result of first triple-glazing and then External Wall Insulation.

And then in 2021 gas usage flatlines after the installation of the Air Source Heat Pump. The residual gas usage is just for cooking – roughly 1 kWh/day – which I hope to stop in the next few months by switching to an induction hob – that’s why the projected gas costs for 2023 are zero.

If I had done nothing 

The graphs below show my estimates for gas and electricity costs assuming I had not installed External Wall Insulation, Solar PV, a battery and an Air Source Heat Pump.

Click on image for a larger version. Estimated weekly gas and electricity costs for the last three and a half years assuming that I had not installed External Wall Insulation, Solar PV, a battery and an Air Source Heat Pump. Also shown in red is my projection for the coming year. The figures in boxes show yearly costs. Notice that the vertical scale of this graph is £120/week – much larger than the scale I used in my previous article.

The same patterns of electricity and gas usage are repeated year after year.

The effect of forthcoming price rises for 2023 are estimates based on Octopus Energy prices.

I have assumed that the electricity price is fixed and so not affected by energy price cap rises. I have not assumed any increase in September 2023 after the fixed deal comes to an end, but there will probably be a rise of some kind.

However gas costs are extremely high and subject to whatever the market demands.

The small reduction in 2023 electricity costs (£1,447) versus 2022 (£1,475)  is because the calculation is based on weekly consumption and one year has a nominal 53 weeks versus a nominal 52 in the other year.

Comparison

Finally, the graph below compares the actual bills I have paid with my estimate for what I would have paid if I had not improved the house. The graph combines gas and electricity costs.

Click on image for a larger version. Comparison of the actual annual combined gas and electricity bills with the counterfactual scenario in which I had not installed External Wall Insulation, Solar PV, a battery and an Air Source Heat Pump. Figures for 2023 are – obviously – projections. Notice that the project costs that I would have incurred are much larger than I estimated in my previous article.

I have stared at this graph over and over and thought: Michael: you have made a mistake. And that may be true. But if I have, I can’t find it.

The models have many assumptions and some may be not quite right. But I don’t think the figures are wrong by more than about 10%.

Payback Calculation

The difference between the two realities in the graph above is – in round terms – currently around £2,000/year and will likely grow to around £4,000 year in 2023 – much larger than I calculated in my previous article.

The difference in expenditure between the two realities is External Wall Insulation (£27k), Solar PV(£4k), a battery (£10k) and an Air Source Heat Pump (£8k) which comes to around £50k.

So the return on my investment is currently 4% and might rise to 8% – which is much better (for me) than I had thought.

Something must be done

The impact of forthcoming price rises is hard to comprehend. The consequences for people with low incomes are dire – and the consequences for hospitals, schools, libraries and business are also frightening.

Clearly ‘something must be done, but I have no confidence that any measures will be well-targeted. Obviously giving people like me more money is bonkers!

But whatever financial steps are taken, I hope the that one lesson will be learned: we need a renewable energy initiative on a wartime scale to build more wind and solar farms as rapidly as possible. If done at scale this could transform our energy infrastructure within a decade.

Why I am sceptical about Geothermal Energy

June 6, 2022

Friends, some people are of the opinion that geothermal energy offers practically unlimited opportunities for the generation of electricity with low carbon dioxide emissions. For example,

  • The US Government’s GeovisionReport is an extensive and overwhelmingly positive assessment of the potential for geothermal energy generation in the US.
  • This IEA video describes new drilling technologies and possible applications in Germany.

For a more general overview, take a look at this video on the ‘Just have a think‘ channel, or read these 10 pages on How Stuff Works.

And there are indeed real possibilities. However I am sceptical that such opportunities are ‘practically unlimited’, particularly in the UK.

And since we are in an emergency situation and need to act urgently, I am doubly sceptical of novel technologies which might steal investment from known solutions.

Allow me to explain….

General Situation

Below the surface, the temperature of Earth increases at typically 25 °C to 30 °C per kilometre of depth. So a few kilometres below the surface, rocks are typically at several hundred degrees Celsius. And this thermal energy represents a potential energy resource.

The US Government’s Geovision Report outlines a number of ways in which this geothermal energy might be extracted. These are summarised in the graphic below.

Click on image for a larger version. The Geovision summary of geothermal potential.

The large-scale projects typically involve four parts.

  1. The injection of cool water down a drilled well to some hot rocks.
  2. Percolation of water through the hot rocks.
  3. Extraction of hotter water from a second well.
  4. Generation of steam and electricity.

Despite the very large volume of hot rocks available under our feet, there are two basic difficulties that all these schemes face.

  • Firstly, rocks of all kinds have a poor thermal conductivity. So if we extract heat from the surface of a rock, that surface will cool down. However heat will only flow back into the cooled rock slowly. This limits the rate at which heat can be extracted.
  • Secondly, except in a few geologically exceptional places, the upwards geothermal heat flow from the deep Earth is very low – typically less than 0.1 W/m^2.

Given these difficulties, there are a lot of technological tricks that can be exploited to optimise extraction of heat in particular circumstances.

For example in Enhanced Geothermal Systems (EGS), engineers ‘frack’ a volume of rock which increases the surface area over which water can flow. As water percolates through the rock it is then able to extract heat more efficiently.

However, no technological advance can overcome the basic fact that the heat flux from the interior of the Earth is – in most places – very low. This means that the technology is essentially ‘one-shot’ i.e. the heat extracted from the rock will be only slowly replaced by heat from the interior of the Earth.

This means that once a geothermal plant has ‘harvested’ the geothermal energy from a block of rock, it will need to move on to a new block. So the big question is: “How long will that ‘one-shot’ last?”

Simplified Model 

I have constructed a spreadsheet model to assess how much electricity could be generated from one cubic kilometre of rock, and how long that extraction could go on for. The model is illustrated in the graphic below.

Click on image for a larger version. A simple model considering how much energy could be extracted from a cubic kilometre of rock, a few cubic kilometres under the Earth. I have illustrated a cubic kilometre at a depth of 3 kilometres, but in most places the rocks would don’t reach that temperature until nearer 10 km.

The model is very crude. For example, it does not capture the dynamics of the extraction process. But it does represent a simple way to assess the resources available. I’ll discuss the shortcomings of the model below.

Details of the model are given at the end of this article, and here I just describe the results.

One cubic kilometre of rock

The model considers one cubic kilometre of ‘fracked’ rock through which water can easily percolate, and be warmed by 100 °C.

The total heat available to be extracted is ~1.6 x 10^17 joules or 45 billion kWh_th. The “_th” suffix indicates thermal energy.

If we suppose that we wish to generate 100 MW_e of electricity, then using a typical generating efficiency of 33%, we need to extract heat at a rate of 300 MW_th. The “_e” suffix indicates electrical energy. This corresponds to a very high flow rate of around 0.7 cubic metres of water per second.

Based on a uniform extraction rate, the thermal resource would be exhausted after ~17 years, a lifetime which could be extended by extracting energy at a lower rate.

But once exhausted the time to restore this thermal resource is tens of thousands of years.

Once the thermal resource has been extracted, the cubic kilometre of rock will have shrunk sufficiently that the land above it will subside by roughly 0.6 metres.

One might also usefully compare the 100 MW_e generation from 1 cubic kilometre of rock with the Solar PV generation from 1 square kilometre of the Earth’s surface.

Assuming that 1 square metre of solar panels generates 1 kWh/day in summer, then a square kilometre of solar panels will produce 1,000 MWh_e/day which can be compared with the 24 x100 = 2,400 MWh_e produced from the rock below.

If one reduced the rate of extraction by a factor 2.4 to 42 MW_e to match the solar PV generation, then the lifetime would be extended to about 40 years – similar to a normal power plant.

What might a geothermal plant look like?

The geothermal resource can be used alongside the  solar PV and wind generation to produce year-round, reliable low-carbon electricity.

If one cubic kilometre of rock could generate 42 MW_e for 40 years, then to generate say 3.5 GW_e – similar to the output of Hinkley C –  we would need roughly 3,500/42 ~ 82 square kilometres – or an area ~ 9 km x 9 km – which is a large amount of land, but small compared to our total land area of the UK.

The geothermal surface plant need not occupy much of this area, but all the area would be potentially affected by subsidence, and/or small earthquakes during the fracking process.

Additionally, the geothermal energy produces a large amount of waste heat, which might also be available for district heating or warming crops.

Discussion of the Model

I have used figures from the report  which suggest that injecting water at 200 °C and withdrawing at 300 °C represent useful operating parameters. The water would be used in a so-called ‘binary’ plant to heat a secondary fluid which would then power a generator.

The idea of warming water by 100 °C is pretty optimistic since the thermal gradient within the Earth is only 25 °C/km. And in most of the UK one would need to drill to ~10 km to reach rocks at this temperature, something which is extremely challenging. So I have just assumed that somewhere in the UK, hotter rocks are available nearer the surface.

I have also not considered any impacts on groundwater flow.

The most obvious criticism of the model is that extracting heat energy at a uniform rate is unrealistic. In practice, the heat would be extracted easily at first, and over years the rate of heat extraction would fall exponentially. This could be used to boost initial power output as the expense of a shorter lifetime. But the calculated amount of heat is the maximum energy that could be removed over the lifetime of the well.

One could of course remove heat from a greater vertical depth, but this would leader to greater subsidence, and in the UK we do not have large areas over which subsidence is acceptable. In old mining areas, subsidence is a considerable blight, and so this could only really be considered in the most isolated of places.

Conclusion

Drilling deep wells is hard work and so expensive. One figure from the ‘How stuff works‘ article suggests $20 million dollars per 10 km well.

So to extract heat from a 9 km x 9 km area would require (I guess) around 81 boreholes and so the capital cost would be in the range £1 billion to £2 billion. Even with the additional costs of generating plant, the cost would likely be less than a nuclear station (£20 billion). And the plant could be enlarged slowly with new blocks being drilled as the first blocks came on line.

So geothermal energy is a large but still finite resource from which heat is harvested and then wells are abandoned and the plant moves on to new areas., after perhaps a decade or so. And so we could imagine plants slowly ‘grazing’ across the country under areas which were insensitive to subsidence or earthquakes.

This is a rather different proposition to that which is marketed by geothermal advocates in which geothermal energy is considered as practically infinite and having negligible impact on the land. It may make sense in the western US, but I am sceptical that it makes sense at scale in the UK, especially given the potential risks.

And as I mentioned at the start we are in a Climate Emergency and need to act urgently. And this makes me doubly sceptical of novel technologies which might steal investment from known solutions.

In contrast, investments in wind and solar and batteries will definitely bring electricity costs down, reduce carbon emissions and reduce – but not yet completely eliminate – the use of gas.

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Details of the spreadsheet model

The spreadsheet model can be downloaded here and is described below. I apologise in advance for any errors I have made.

Click on image for larger version. These are the basic parameters used in the model

Click on image for larger version. This section of the spreadsheet calculates the thermal properties of one cubic kilometre of rock.

Click on image for larger version. This section of the spreadsheet calculates the operational parameters of a geothermal power plant assuming a constant rate of heat extraction.

Obviously the properties of rocks vary greatly, and the hottest rocks often occur under very hard rock – very different from the rocks through which oil and gas companies normally drill.

However, I think the spreadsheet model captures the correct order of magnitude of the geothermal resource. It’s large, but finite.

2022 to 1978: Looking Back and Looking Forwards

May 3, 2022

Friends, it’s been two years since I retired, and since leaving the chaos and bullying at NPL, retirement has felt like the gift of a new life.

I now devote myself to pastimes befitting a man of my advanced years:

  • Drinking coffee and eating Lebanese pastries for breakfast.
  • Frequenting Folk Clubs
  • Proselytising about the need for action on Climate Change
  • Properly disposing of the 99% of my possessions that will have no meaning to my children or my wife after I die.

It was while engaged in this latter activity, that I came across some old copies of Scientific American magazine.

Last year I abandoned my 40 year subscription to the magazine because it had become almost content free. But in its day, Scientific American occupied a unique niche that allowed enthusiasts in science and engineering to read detailed articles by authors at the forefront of their fields.

In the January Edition for 1978 there were a number of fascinating articles:

  • The Surgical Replacement of the Human Knee Joint
  • How Bacteria Stick
  • The Efficiency of Algorithms
  • Roman Carthage
  • The Visual Characteristics of Words

and…

  • The Carbon Dioxide Question

You can read a scanned pdf copy of the article here.

This article was written by George M Woodwell a pioneer ecologist. The particular carbon dioxide question he asked was this:

Will enough carbon be stored in forests and the ocean to avert a major change in climate?

The article did not definitively answer this question. Instead it highlighted the uncertainties in our understanding of the some of the key processes required to answer the question.

In 1978 the use of satellite analysis to assess the rate of loss of forests was in its infancy. And there were large uncertainties in estimates of the difference in storage capacity between native forests, and managed forests and croplands.

The article drew up a global ‘balance sheet’ for carbon, and concluded that there were major uncertainties in our understanding of many of the physical processes by which carbon and carbon dioxide was captured (or cycled through) Earth’s systems.

Some uncertainty still remains in these areas, but the basic picture has become clearer in the subsequent 44 years of intense study.

So what can we learn from this ‘out of date’ paper?

Three things struck me.

Thing#1

Firstly, from a 2022 perspective, I noticed that there are important things missing from the article!

In considering likely future carbon dioxide emissions, the author viewed the choices as being simply between coal and nuclear power.

Elsewhere in the magazine, the Science and the Citizen column discusses electricity generation by coal with no mention of CO2 emissions. Instead the article simply laments that coal will be in short supply and concludes that:

“There is no question… coal will supply a large part of the nation’s energy future. The required trade-offs will be costly however, particularly in terms of human life and disease.

Neither article mentions generation of electricity by gas turbines. And neither makes any mention of either wind or solar power generation – now the cheapest and fastest growing sources of electricity generation.

From this I note that in it it’s specific details, the future is very hard to see.

Thing#2

Despite the difficulties, the author did make predictions and it is fascinating from the perspective of 2022 to look back and see how those predictions from 1978 have worked out!

The article included predictions for 

  • The atmospheric concentration of CO2
  • CO2 emissions from Fossil Fuels

Click on image for a larger version. Figure from the 1978 article by George Woodwell. The curves in green (to be read against the right-hand axis) shows two predictions for atmospheric concentration of CO2. The curves in black (to be read against the left-hand axis) shows two predictions for fossil fuel emissions of CO2. In each case, the difference between the two curves represents the uncertainty caused by changes in the way CO2 would be cycled through (or captured by) the oceans and forests. See the article for a detailed rubric.

The current atmospheric concentration of carbon dioxide is roughly 420 ppm and the lowest projection from 1978 is very close.

The fossil fuel emissions estimates are given in terms of the equivalent change in atmospheric CO2, and I am not exactly sure how to interpret this correctly.

Atmospheric concentration of CO2 is currently rising at approximately 2.5 ppm per year, and roughly 56% of fossil fuel emissions end up in the atmosphere. So the annual emissions predicted for 2022 are around 2.5/0.56 ~ 4.5 ppm /year, which is rather lower than the lowest prediction of around 6 ppm/year.

The article also predicts that this will be the peak in annual emissions, but that has yet to be seen.

The predictions did not cover the warming effect of carbon dioxide emissions, the science of which was in the process of being formulated. ‘Modern’ predictions can be dated to 1981, when James Hansen and colleagues published a landmark paper in Science (Climate Impact of Increasing Atmospheric Carbon Dioxide) which predicted:

A 2 °C global warming is exceeded in the 21st century in all the CO2 scenarios we considered, except no growth and coal phaseout.

This is the path we are still on.

From this I note that the worst predictions don’t always happen, but sometimes they do.

Thing#3

The final observation concerns the prescience of the author’s conclusion in spite of his ignorance of the details.

Click on the image for a larger version. This is the author’s final conclusion in 1978

His last two sentences could not be truer:

There is almost no aspect of national or international policy that can remain unaffected by the prospect of global climatic change.

Carbon dioxide, until now an apparently innocuous trace gas in the atmosphere may be moving rapidly toward a central role as a major threat to the present world order.

 

March 2022

April 8, 2022

Friends, Spring is springing, and our first winter with a heat pump is ending.

Overall, it has been phenomenally successful. All the parts of our refurbishment have played their part.

  • The triple-glazing and external wall insulation have reduced the heating power required to heat the house.
  • The solar panels continued to deliver ~5% of our electricity requirements even in December.
  • The battery (a 13.5 kWh Tesla Powerwall) allowed us to download cheap electricity at night and use it to heat the house during the day.
  • The heat pump kept the house warm and delivered hot water, with an average Coefficient of Performance of around 3.5.

In this article I will be looking at figures for the month of March 2022.

When the heating season is a little more over than it is at present, I will write about the winter as a whole.

Solar PV and Battery

Click image for a larger version. This is on the notice board outside my house.

I have put a notice on the front of the house to advertise how little we are spending on heating and running the house. Excluding the standing charges, we spent just £14.34 heating the house and running all the electrical items in the house.

In honesty, I am embarrassed to disclose how little I am spending on fuel bills. I am embarrassed because of the suffering and anxiety that so many people will be feeling now as prices rise.

Nonetheless, when it comes to communicating the wonder of a well-insulated home powered by solar, talking about money is one way to communicate more viscerally than using kilowatt-hours and kilograms of carbon dioxide.

Energy Flows

Click image for a larger version. This graphic shows my best estimate of the energy flows around my house. There are two sources of electricity: the grid and the solar PV system. During the hours when grid electricity is cheap, the grid supplies the house directly and charges the battery. Solar PV supplies the house directly, then if household demand is met, it charges the battery, and if the battery is full, it exports electricity. My analysis suggests that the battery is only 87% efficient i.e. 13% of the energy is lost in the process of charging and discharging the battery.

The graphic above describes the energy flows in the house.

On a typical day:

  • Between 00:30 and 04:30 the house runs on cheap grid electricity, and we time the dishwasher and hot water heating to run over this period. The grid also charges the battery.
  • After 04:30 the battery runs the household and is then re-charged during daylight hours by whatever solar PV is available.
    • If the battery charge reaches 100%, then solar PV is exported.
    • If the battery discharges to 0%, then we run off full price grid electricity.

Analysing the data from the Tesla App, it looks like the battery returns 87% of the charge delivered to it. The system is specified to have a charge/discharge efficiency of 90%. I suspect that extra losses arise from the energy the battery uses to maintain its own condition.

The figure below shows the average pattern of grid use during the month. The majority of electricity is used during the cheap rate period and only a small fraction of full-price electricity is required on days when solar PV generation is insufficient to keep the battery topped up.

Click image for a larger version. This graphic shows the time of day at which the house drew electricity from the grid in March 2022. The vast majority of the electricity was consumed at night to (a) charge the battery and (b) directly operate timed loads such as the dishwasher, washing machine, and heat pump domestic hot water cycle.

Heat Pump

Click image for a larger version. Graph showing internal and external temperatures, and the temperature of water flowing in the radiators during the month of March. Data were collected every 2 minutes. The radiator flow temperature data has been smoothed. It is clear the system operates well to keep the internal temperature constant even as the external temperature varies

The average external temperature was 9.3 °C, but the month started very cold, and then later there were some exceptionally warm days (with cold nights).

The weather compensation adjusted the flow temperature in the radiators to keep the internal temperature at a comfortable average of 21.1 °C

The monthly averaged Coefficient of Performance was 3.75 which is rather more than I had hoped for.

Conclusion

When we installed the battery in March 2021, we immediately dropped of the grid for 90 days: this felt astonishing. But back then then our heating was with gas.

Now our heating and hot water systems are electrical and this adds to the daily load.

As the year progresses, Solar PV generation is growing and heating demand is falling. At some point I hope we will again be able to reduce grid use to zero for an extended period – but it will definitely not be as long as last year.

It was interesting to arrive at a figure for the battery storage efficiency. The figure of 87% was lower than I had hoped for, but since the battery is saving us so much money, it seems churlish to complain!

 

 

Analysis of 16 years of Solar PV data.

March 16, 2022

A friend from North London kindly allowed me to analyse the data they had collected on the performance of their solar PV installation over the last 16 years.

What an opportunity to discover how solar PV panels behave over the long term!

Let me tell you what I found:

The System

Installed in July 2006, the system consisted of 16 Sanyo PV panels, each 0.88 m x 1.32 m with a nominal peak output of 210 W. This implies the panels output was initially ~180 watts per square metre.

They were installed on two adjacent roofs with a tilt of about 30° and facing 25° East of South and with no nearby trees or shading structures on the horizon other than their neighbour’s house.

The data set consisted of roughly 700 readings of the solar generation meter, most of them taken weekly but with a couple of gaps for a few months, and few points that were clearly in error. Rather than try to be sophisticated, I simply omitted points that were obviously in error.

Click image for a larger version. The ‘cleaned up’ data set.

Annual Analysis

One of things I was most anxious to search for was evidence of a year-on-year decline. The annual results are shown below:

Click image for a larger version. Graph of the Annual Output (kWh) of a North London PV system from 2006 to 2021. The dotted line is a linear fit to the data showing a systematic year-on-year decline in output.

It’s clear that there is a systematic year-on-year decline. If we re-plot the data to express this as a percentage we can compare it with what we might expect.

Click image for a larger version. The same data as in the previous graph but expressed as a fraction of the average output over the years 2007 and 2008. The dotted line is a linear fit to the data showing a systematic year-on-year decline in output.

This decline is – sadly – inevitable, arising as I understand it from atomic defects created in the silicon cells by exposure to the UV radiation in sunlight. These defects trap electrons which would otherwise reach an external contact if the crystal had been undamaged.

A decline of 6.1% per decade (0.61% per year) is quite competitive. Older panels showed higher declines (link) and more modern cells claim better performance, but not much better.

For example a 2020 Q-Cells Duo panel (link) specifies 0.54%/year decline for up to 10 years,  i.e. 5.4% per decade.

Click image for a larger version. Extract from a Q-cells data sheet showing expected decline in panel output over 25 years.

Variability

In addition to a linear decline in output the data also shows significant year-to-year variability. I wondered whether this variability arose from the natural variability of available sunshine, or some other factor.

To check this I exploited the EU Photovoltaic Geographical Information System (a.k.a. a ‘Sunshine Database’) which allows the calculation of the output of PV cells at any point in Europe or Africa over the period 2005 to 2016.

I had previously used this database to model the year-to-year variability of sunshine in West London when I was planning a battery installation.

To see if this was the cause of the year-to-year variability I plotted two quantities on the same graph:

  • The so-called ‘residuals’ of the fit to the data in the second graph above.
  • The variability of EU-database data.

The results are shown below.

Click image for a larger version. The variability of the North London PV data and the natural variability of sunshine as retro-dicted by the EU sunshine database

It is clear that in the years for which the two datasets overlap they agree well, suggesting that the variability observed is not due to some other poorly understood factor.

Upgrade?

My North London friend had one final question. Would they avoid more carbon dioxide emissions if they upgraded to modern panels?

To answer this I made two models:

  • The first model assumed that they did not upgrade and the existing panels were used to out to 2050.
  • The second model assumed they were replaced in 2022 with panels which operated with an efficiency of around 200 W/m^2 at peak illumination. This is about 20% more than the panels currently generate.

I assumed that the new panels would embody around 2 tonnes of CO2 emissions because Q-cells suggest their latest panels embody 400 kgCO2 per kWp.

I then assumed that 50% of the generated electricity was exported and 50% used domestically. As the grid currently functions:

  • Exported electricity reduces gas-fired generation which emits 450 gCO2/kWhe.
  • Domestic use avoids consumption of grid electricity with a carbon intensity of around 220 gCO2/kWhe in 2022.

Based on these assumptions, there is small advantage to replacing the panels, but this would not be realised until 2035.

Click image for a larger version. Does it make carbon-sense to replace existing PV cells with new more efficient cells?

One can model variations of these parameters, but the basic result is not affected: the carbon advantage is marginal.

My friend would help the climate more effectively by allocating his capital expenditure to something which might have more impact on CO2 emissions, perhaps buying shares in a wind farm?

But the result that really struck me from this modelling was how great the solar panels were in the first place!

Installed in 2006 and given minimal maintenance, it looks like the existing cells will avoid almost 30 tonnes of CO2 emissions by 2050. Not many technologies can achieve results like that as easily as that.

Will aviation eventually become electrified?

March 2, 2022

Friends. I ‘have a feeling’ that aviation will eventually become electrified. At first sight this seems extraordinarily unlikely, but I just have this feeling…

Obviously, I could just be wrong, but let me explain my thinking.

Basics 

The current technology for aviation – jet engines on aluminium/composite frames with wings – relies on the properties of jet fuel – kerosene.

There are two basic parameters for aviation ‘fuel’.

  • Energy density – which characterises the volume required to carry fuel with a certain energy content. It can be expressed in units of megajoules per litre (MJ/l).
  • Specific energy – which characterises the mass required to carry fuel with a certain energy content. It can be expressed in units of megajoules per kilogram (MJ/kg).

Wikipedia have helpfully charted these quantities for a wide range of ‘fuels’ and this figure is shown above with five technologies highlighted:

  • Lithium batteries,
  • Liquid and Gaseous Hydrogen,
  • Kerosene and diesel.

Click on image for a larger version. Chart from Wikipedia showing the specific energy and energy density of various fuels enabled energy technologies.

A general observation is that hydrocarbon fuels  have a much higher density and specific energy than any current battery technology. Liquid Hydrogen on the other hand has an exceptionally high specific energy, but poor energy density: better than batteries but much worse than hydrocarbon fuels.

Lessons from the EVs transition:#1

I think the origin of my feeling about the aviation transition stems from the last 20 years of watching the development of battery electric vehicles (BEVs). What is notable is that the pioneers of BEVs – Tesla and Chinese companies such as Xpeng or BYD – are “all in” on BEV’s – they have no interest in Internal Combustion Engine (ICE) vehicles or hybrids. They have no legacy market in ICE vehicles to protect.

‘Legacy Auto’ (short hand for VW, GM, Ford, Toyota etc) had poked their toe in the waters of alternative drive-trains quite a few years ago. GM’s Volt and Bolt were notable and Toyota’s Mirai hydrogen fuel cell car was a wonder. But Legacy Auto were comfortable manufacturing ICE vehicles and making profits from it, and saw these alternative energy projects as ‘insurance’ in case things eventually changed.

As I write in early 2022, all the legacy auto makers are in serious trouble. They can generally manufacture BEVs, but not very well – and none of them are making money from BEVs. Aside from Tesla, they have very poor market penetration in China, the world’s largest EV car-market. In contrast Tesla are popular in China and America and Europe and make roughly 20% profit on every car they sell.

So one lesson from the BEV transition is that the legacy industry who have invested billions in an old technology, may not be the pioneers of a new way of doing things.

Lessons from the EVs transition:#2

How did BEV’s overcome the awesome advantages of hydrocarbon fuels over lithium batteries in terms of energy density and specific energy?

First of all, ICEs throw away about 75% of their advantage because of the way they operate as heat engines. This reduces their energy density advantage over batteries to just a factor 10 or so.

Secondly, there is the fact that ICE cars contain many heavy components – such as engines, gearboxes, and transmissions that aren’t needed in a BEV.

But despite this, BEV cars still generally have a weight and volume disadvantage compared to ICE cars. But this disadvantage has been overcome by careful BEV-specific design.

By placing the large, heavy, battery pack low down, designers can create pleasant vehicle interiors with good handling characteristics. And because the ability to draw power rapidly from batteries is so impressive, the extra mass doesn’t materially affect the acceleration of the vehicle.

EV range is still not as good as a diesel car with a full tank. But it is now generally ‘good enough’.

And once EVs became good enough to compete with ICE vehicles, the advantages of EVs could come to the fore – their ability to charge at home, low-running costs, quietness, potential low carbon emissions and of course, zero in situ emissions.

And significantly, BEV’s are now software platforms and full electronic control of the car allows for some capabilities that ICE vehicles will likely never have.

Lessons from the EV transition:#3

Despite Toyota’s massive and long-term investment in Hydrogen Fuel Cell (HFC) cars, it is now clear that hydrogen will be irrelevant in the transition away from ICE vehicles. Before moving on to look at aviation, it is interesting to look at why this is so.

The reason was not technological. HFC cars using compressed hydrogen fuel were excellent – I have driven one – with ranges in excess of 320 km (200 miles). And they were excellent long before BEVs were excellent. But the very concept of re-fuelling with hydrogen was the problem. Hydrogen is difficult to deal with, and fundamentally if one starts with a certain amount of electrical power – much less of it gets to the wheels with a HFC-EV than with a BEV.

The very idea of a HFC car is – I think – a product of imagining that there would be companies akin to petrochemical companies who could sell ‘a commodity’ in something like the way Oil Companies sold petrol in the 20th Century. BEV’s just don’t work that way.

Interestingly, the engineering problems of handling high-pressure hydrogen were all solved in principle. But this just became irrelevant.

Cars versus Aeroplanes

So let’s look at how energy density and specific energy affect the basic constraints on designs of cars and aeroplanes.

50 litres of diesel contains roughly 1,930 MJ of energy. The table below shows the mass and volume of other fuels or batteries which contains this same energy.

Mass (kg) Volume (l)
Kerosene 45 55
Diesel 42 50
Hydrogen HP 14 364
Hydrogen Liquid 14 193
Lithium Battery 4,825 1,930

We see that batteries look terrible – the equivalent energy storage would require 4.8 tonnes of batteries occupying almost 2 cubic metres! Surely BEVs are impossible?!

But as I mentioned earlier, internal combustion engines waste around 75% of their fuel’s embodied energy in the form of heat. So a battery with the required stored energy would only need 25% of the mass and volume in the table above.

Mass (kg) Volume (l)
Lithium Battery 1206 483

So, we see that the equivalent battery pack is about a tonne heavier than the fuel for a diesel car.

But this doesn’t include the engine required to make the diesel fuel work. So one can see how by clever design and exploiting the fact that electric motors are lighter than engines, one can create a BEV that, while heavier than an ICE car, is still competitive.

Indeed, BEVs now outperform ICE cars on almost every metric that anyone cares about, and will continue to get better for many years yet.

Let’s do the same analysis for aeroplanes. A modern jet aeroplane typically carries 100 tonnes of kerosene with an energy content of around 43 x 105 MJ. This is sufficient to fly a modern jet (200 tonnes plus 30 tonnes of passengers) around 5,000 miles or so.

The table below shows the mass and volume other fuels or batteries which contains this same energy. Notice that the units are no longer kilograms and litres but tonnes and cubic metres.

Mass (tonnes) Volume (m^3)
Kerosene 100 123
Diesel 94 111
Hydrogen HP 31 811
Hydrogen Liquid 31 430
Lithium Battery 10,750 4,300

Now things look irrecoverably impossible for batteries! The batteries would weigh 10,000 tonnes! And occupy a ridiculous volume. Also, turbines are more thermodynamically efficient than ICEs, so assuming say 50% efficiency, batteries would still weigh ~5,000 tonnes and occupy 2,000 m3.

Even with a factor 10 increase in battery energy density – which is just about conceivable but not happening any time soon – the battery would still weigh 1,000 tonnes!.

Does it get any better for shorter ranges? Not much. Consider how much energy is stored in 10 tonnes of kerosene (~43 x 104 MJ). This is sufficient to fly a modern jet – weighing around 50 tonnes unladen and carrying 20 tonnes of passengers around 500 miles or so.

Mass (tonnes) Volume (m^3)
Kerosene 10 12
Diesel 9 11
Hydrogen HP 3 81
Hydrogen Liquid 3 43
Lithium Battery 1,075 430

Even assuming 50% jet efficiency, batteries with equivalent energy would still weigh ~500 tonnes and occupy 200 m3. Even after a factor 10 increase in battery energy density, things still look pretty hopeless.

So can we conclude that battery electric aviation is impossible? Surprisingly, No.

And yet, it flies.

Jet engines burning kerosene have now reached an astonishing state of technological refinement.

But jet engines are also very expensive, which makes the economics of airlines challenging. And despite improvements, jets are also noisy. And of course, they emit CO2 and create condensation trails that affect the climate.

In contrast, electric motors are relatively cheap, which means that electric aeroplanes (if they are possible) would be much cheaper, and require dramatically less engine maintenance. These features are very attractive for airlines – the people who buy planes. And the planes would be quiet and have zero emissions – attractive for people who fly or live near airports.

And several companies are seeking to exploit these potential advantages. Obviously, given the fundamental problem of energy density I outlined above, all the projects have limitations. Mostly the aeroplanes proposed have limited numbers of passengers and limited range. But the companies all impress me as being serious about the engineering and commercial realities that they face. And I have been surprised by what appears to be possible.

Here are a few of the companies that have caught my attention.

Contenders

In the UK, Rolls Royce and partners have built an impressive single-engined aircraft which flies much faster than equivalent ICE powered aircraft.

Their Wikipedia page states the batteries have a specific energy of 0.58 MJ/kg, about 50% higher than I had assumed earlier in the article. The range of this plane is probably tiny – a few 10’s of kilometres – but this number will only increase in the coming years.

This aeroplane is really a technology demonstrator rather than a seedling commercial project. But I found it striking to see the plane actually flying.

In Sweden, Heart Aerospace have plans for a 19-seater short-hop passenger craft with 400 km of range. Funded by Bill Gates amongst others, they have a clear and realistic engineering target.

In an interview, the founder explained that he was focussing on the profitability of the plane. In this sense the enterprise differs from the Rolls Royce project. He stated that as planned, 2 minutes in the air will require 1 minute of re-charging. He had clear markets in mind in (Sweden, Norway, and New Zealand) where air travel involves many ‘short hops’ via transport hubs. And the expected first flights will be soon – 2025 if I have it correct.

In Germany, Lillium are building innovative ducted-fan planes. Whereas Heart’s planes and Rolls Royce’s demonstrator projects are conventional air-frames powered by electric motors, Lillium have settled on completely novel engineering possibilities enabled by electrical propulsion technology. Seeing their ‘Star Wars’ style aircraft take off and land is breathtaking.

Back in the UK, the Electric Aviation Group are advertising HERA as a 90-seater short route airliner with battery and hydrogen fuel-cell technology (not a turbine). This doesn’t seem to be as advanced as the other projects I have mentioned but illustrates the way that different technologies may be incorporated into electric aviation.

What about Hydrogen Turbines?

Legacy Aeromaker Airbus are advertising development of a hydrogen turbine demonstrator. It’s a gigantic A380 conventional jet airliner with a single hydrogen turbine attached. (Twitter video)

Stills from a video showing how the hydrogen turbine demonstrator will work. A single turbine will attached to kerosene driven aeroplane by 2035.

The demonstrator looks very clever, but I feel deeply suspicious of this for two sets of reasons: Technical reasons and ‘Feelings’.

Technical.

  • Fuel Volume: To have the same range and capabilities as an existing jet – the promise that seems to be being advertised – the cryogenic (roughly -250 °C) liquid hydrogen would occupy 4 times the volume of the equivalent kerosene. It likely could not be stored in the wings because of heat leakage, and so a big fraction of the useful volume within an aeroplane would be sacrificed for fuel.
  • Fuel Mass: Although the liquid hydrogen fuel itself would not weigh much, the tanks to hold it would likely be much heavier than their kerosene equivalents. My guess is that that there would not be much net benefit in terms of mass.
  • Turbine#1: Once the stored liquid hydrogen is evaporated to create gas, its energy density plummets. To operate at a similar power level to a conventional turbine, the volume of hydrogen entering the combustion chamber per second will have to be (very roughly) 40 times greater.
  • Turbine#2: Hydrogen burns in a different way from kerosene. For example embrittlement issues around the high pressure, high temperature hydrogen present at the inlets to the combustion chamber are likely to be very serious.
  • I don’t doubt that a hydrogen turbine is possible, but the 2035 target advertised seems about right given the difficulties.
  • Performance: And finally, assuming it all works as planned, the aircraft will still emit NOx, and will still be noisy.

Feelings.

  • I feel this a legacy aero-maker trying to create a future world in which they are still relevant despite the changed reality of climate crisis.
  • I suspect these engines assuming the technical problems are all solved –  will be even more expensive than current engines.
  • I feel the timeline of 2035 might as well be ‘never’. It allows Airbus to operate as normal for the next 13 years – years in which it is critical that we cut CO2 emissions.
  • I suspect that in 13 years – if electric aviation ‘gets off the ground’ (sorry!) – then it will have developed to the point where the short-haul end of the aviation business will be in their grasp. And once people have flown on smaller quieter aircraft, they will not want to go back.
  • Here is Rolls Royces short ‘Vision’ video.

And so…

I wrote this article in response to a Twitter discussion with someone who was suggesting that cryogenic liquid-hydrogen-fuelled jets would be the zero-emission future of aviation.

I feel that that the idea of a cryogenic hydrogen aircraft is the last gasp of a legacy engine industry that is trying to stay relevant in the face of a fundamentally changed reality.

In contrast, electrical aviation is on the verge of becoming a reality: planes are already flying. And motors and batteries will only get better over coming decades.

At some point, I expect that electrical aviation will reach the point where its capabilities will make conventional kerosene-fuelled aeroplanes uneconomic, first on short-haul routes, and then eventually – though I have no idea how! – on longer routes.

But…

…I could be completely wrong.


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