Cold Weather Measurements of Heat Transfer Coefficient

December 11, 2022

Friends, it’s winter and the weather is reassuringly cold: average daily temperatures in Teddington are around 0 °C. And as I wrote the other week, that offers the opportunity to make measurements of the Heat Transfer Coefficient of a dwelling.

People with Gas Boilers

This is especially valuable for people with gas boilers who are thinking about getting a heat pump.

When the outside temperature is around 0 °C, the average heating power required to heat the majority of UK homes is typically in the range 5 kW to 10 kW.

Most gas boilers have a full power of 20 kW to 30 kW and so can heat a home easily. To keep the temperature just right, the boilers cycle on and off to reduce their average output to the required level. For most houses there is no possibility that a boiler will be undersized.

Heat pumps operate differently. They are typically less powerful than boilers and the maximum heat pump output must be chosen to match the maximum heat requirement of the house.

By measuring the daily use of gas (kWh) by a boiler on a cold day one can estimate the size of heat pump required to heat the dwelling to an equivalent temperature.

I wrote about this at great length here, but at its simplest one just takes the amount of gas used on a very cold day (say 150 kilowatt hours) and divides by 24 (hours) to give the required heat pump power in kilowatts (150/24 = 6.3 kW).

People with Heat Pumps

But the cold weather is not just for people with gas boilers: Heat pump custodians and people heating their house electrically can gain insights when it’s cold.

Starting on 1st December I looked up:

  • the average daily temperature;
  • the daily heat output from the heat pump (in kWh);
  • the daily electricity consumption of the heat pump (in kWh);

The internal temperature was a pretty stable 20 °C throughout this period. So I first worked out the so-called temperature demand: that’s the difference between the desired internal temperature and the actual external temperature.

I then plotted the daily heat output from the heat pump (in kWh) versus the average daily temperature demand (°C). The data fell on a plausible straight line as one might expect. Why? Because the colder it is outside, the faster heat flows out through the fabric of the dwelling, and the greater the rate at which one must supply heat to keep the temperature constant.

In the graph below I have re-plotted this  but instead of using the average daily heat output from the heat pump (in kWh) I have divided this by 24 to give the average daily heat pump power in kilowatts.

Click on graph for a larger version. Graph of average heating power (in kW) versus temperature demand (°C) for the first 10 days of December 2022. Notice that the line of best fit does not go through the origin.

The maximum heat output from the 5 kW Vaillant Arotherm plus heat pump varies with the external temperature, but for flow temperatures of up to 45 °C, it exceeds 5.6 kW.

The maximum daily average power for the first 10 days of December is just over 3 kW, so I think the heat pump will cope well in even colder weather. Indeed I could probably have got away the next model down. But it does seem to be a general rule of heat pumps that one ends up with the model one size above the size one actually needs.

Click on image for a larger version. Specifications for the Vaillant Arotherm plus heat pump. For the 5 kW model at an external temperature of -5 °C and heating water for radiators to between 40 °C and 45 °C, the maximum output is between 5.6 kW and 6 kW.

The slope and intercept of the graph

The slope of the graph is approximately 0.166 kW/°C or 166 W/°C. This figure is known as the Heat Transfer Coefficient for a dwelling. It is the figure which characterises the so-called fabric efficiency of a dwelling.

However, as I noted many years ago when I looked at this problem using gas boiler measurements, the straight line does not go through the origin. The best-fit line suggests zero power output when the external temperature is 2.8 °C below the internal temperature.

This would imply that the heat flow through the fabric of the building was not proportional to the difference between the inside and outside temperature.

The reason for this is that there are other sources of heating in the house, and not all the heat pump output goes into the house. Specifically:

  • People: each person heats the house with around 100 W, about 2.4 kWh/day.
  • Electrical Items: All the electricity consumed by items in the house ends up as heat. For my home this amounts to around 10 kWh/day.
  • Hot Water: Heat pump output that heats domestic hot water is mostly lost when the hot water is used. My guess for this house is that this amounts to around 3

So to estimate the actual amount of heat dissipated in the house I should really take the heat pump output and:

  • Add 2.4 kWh/day for each person in the house
  • Add 10 kWh/day for all the electrical items
  • Subtract 3 kWh/day for the hot water lost.

Together this amounts to adding 9.4 kWh/day to each heating estimate. Pleasingly, plotting the same graph with these corrections, the graph now intercepts within 0.5 °C of the origin. To me this indicates that I am now accounting for all the significant sources of heat within the house reasonably well.

Click on graph for a larger version. Graph of average heating power (in kW) versus temperature demand (°C) for the first 10 days of December 2022.

I haven’t included any solar gain in these estimates because at this time of year solar gain is generally very low unless a home has large south facing windows. Previously I have noted that solar gain seemed to be much more important in spring and autumn with longer and generally sunnier days.


I also took the opportunity to evaluate how the daily averaged coefficient of performance (COP) varies with external temperature. This is based on readings from a heat meter and an electricity meter which monitors the heat pump.

The COP values below 3 are a little bit lower than I would like, but still acceptable. On subsequent cold days I will be seeing if there are adjustments I can make to the heat pump operation which can improve this.

Click on graph for a larger version. Graph of daily average COP versus daily average outside temperature (°C) for the first 10 days of December 2022. Extrapolating the trend suggests that the COP would reach unity at a temperature of – 12 °C.

Out of curiosity, I also evaluated the heat output using the Vaillant SensoApp. The figures were massively in error. For example, on 10th December the app suggested the total heat delivered to the house by the heat pump was 58 kWh. In fact the correct answer was 73.9 kWh.


Cold weather offers an opportunity to assess the so-called Fabric Efficiency of a dwelling by direct measurements of its Heat Transfer Coefficient.

The cold weather will be with us for a few more days so there’s still a chance to make measurements in your dwelling.

Annual variation in location of sunrise and sunset

December 5, 2022

Friends, we are just 16 days away from the winter solstice, and those of us who live in the UK are dismally aware that at this time of year, the Sun only rises above the horizon for about 8 hours.

And not only does the Sun rise above the horizon for a short time, it also fails to rise very high in the sky.

Together these factors make for poor yields from solar panels.

This article is about a third factor which I feel is sometimes overlooked: the location of sunrise and sunset.

The location of sunrise#1

I asked OpenAI Chatbot about this:

How does the location of sunrise vary through the year in the UK?

The location of sunrise in the UK varies significantly throughout the year. In the winter months, sunrise occurs in the southeast, while in the summer months, it appears in the northeast. The amount of daylight hours in the UK also increases as the year progresses, with the summer months having the longest days and the winter months having the shortest.

This is an excellent answer. Accurate and concise. I followed up:

How far north of east does the sun rise at the summer solstice?

At the summer solstice (the longest day of the year), the sun rises as far north as 70° north latitude in the UK, which is around halfway between East Anglia and the Shetland Islands.

In contrast, this answer is utter nonsense! So I guess I will have to write this article myself!

The location of sunrise#2

I was interested in the location of sunrise because of the new panels I am installing will face about 22° north of east – not a very favourable location.

I looked up data for each week of the year from The Time and Date website: the data below are relevant to London, but you can look up data for many other locations worldwide if you are interested.

Click on image for a larger version. This is an extract from tables at the Time and Date web site. It has both the time of sunrise and sunset and the angle of sunrise and sunset measured clockwise from due North.

I then collated the results and plotted them through the weeks of the year.

Click on image for a larger version. This graph shows how the location of sunrise and sunset vary through the year. Angles of sunrise and sunset measured clockwise from due North.

The graph above shows that the phrase: “the Sun rises in the East and sets in the West” is only approximately true. For 6 months of the year, the Sun rises north of East and sets north of West.

My New Solar Panels
This is probably not news to anyone, but I found it interesting, because I am putting solar panels on my home that face north of East.

Click on image for a larger version. Google Maps view of my house showing existing solar panels in blue and the new panels in Yellow. For 6 months of the year between spring and autumn equinoxes, the panels should produce a useful solar yield in the morning.

After plotting these lines on the map, and noting which houses the lines intercepted, I was able to translate them onto a photograph to show the expected location of sunrise through the year.

Click on image for a larger version. Photograph showing the ‘panels-eye’ view of the street-scene at the back of the house For 6 months of the year between spring and autumn equinoxes, the panels should produce a useful solar yield in the morning.

Considering all the panels on the house,- including the 12 installed in November 2020 – in summer the system should generate from early dawn – only just after 4 a.m. in mid-summer, to almost 8:00 p.m. So despite the poor orientation, the Easy-PV calculator suggests the 5 panels will generate 1,338 kWh per year (268 kWh/panel) compared with 3,860 kWh year from the original 12 panels (322 kWh/panel).

Click on image for a larger version. Charts showing the angular extent of daytime through the year. The orientation of the three sets of panels on the different roofs is shown as red arrowed lines.

Along with the 5 panels on the roof, I have installed three panels on the flat roof which are only at 12° to the horizontal. The Easy-PV calculator suggests these 3 panels will generate 919 kWh per year (306 kWh/panel), although I am not sure I properly accounted for shading.

Click on image for a larger version. The same photograph as above but now showing the panels on the flat roof.

Sadly, although the panels have been installed for more than month, no inverter has been installed and they have not been connected to the grid. Apparently, this will happen “tomorrow”.

But if the output is as I anticipate, then next year the system will generate around 6 MWh. The amount we draw from the grid should be slightly reduced as I hope we will be off-grid for 6 months rather than 4.5 months year. So considered over a year, cumulative generation should be roughly twice as much as we draw from the grid.

Consequently – considered over a year – we should export almost as much as we import, which is getting close to one definition of carbon neutrality. This is my dream!

Click on image for a larger version. Cumulative PV generation for 2022 is just under 4 MWh, in line with the MCS guidance when the system was installed. Cumulative Grid Consumption is expected to be just over 3 MWh this year. The dotted purple line shows anticipated generation next year.

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.


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.

Greta’s Climate Book: An antidote to hope

November 21, 2022

Friends, as I have written before, I love and admire Greta Thunberg.

So when I heard that Greta had edited a collection of short essays on Climate Change, I ordered a copy immediately. Quietly I thought to myself: “Well that is Christmas gifts for everyone sorted.”

And when I collected my copy from the local bookshop I was delighted to find that Greta herself had signed the book! When I got home I sat down eagerly to read.

The book is attractive, covered in Climate Stripes but at 446  pages and 1.383 ± 0.002 kg, it was larger and heavier than I had anticipated.

It is also well-written. Greta’s essays that introduce the various sections are excellent: she writes with outstanding clarity. And the general standard of the short essays is excellent. I learned a lot about many different aspects of Climate Change that I had not previously focussed on.

However, I will not be gifting this book to anyone I love. Why? Because I found it overwhelmingly depressing.

Antidote to hope

Friends, Climate Change scares me. I feel the fragility of our way of life and I feel terrified for my children. And I am acutely aware of just how profoundly bad our situation is. In many ways, I am a natural ‘Doomer‘. But I resist that temptation and prefer to focus on what I can do to try to improve things – however marginally.

My resistance is not really supported by the weight of evidence which is probably on the side of the doomers. It’s a choice I have made.

And that’s my problem with the book. It amplifies every negative aspect of our situation in a way which I found overwhelmingly depressing. I appreciate the book’s straightforward honesty, but it doesn’t help me get by from day to day.

The book implies that there is no solution to the problem of climate change without simultaneously solving multiple problems of inter-national, inter-ethnic, inter-gender and inter-generational justice – problems that seem to me to be much harder than the fundamentally technical problem of stopping emitting carbon dioxide.

There is more than one thing happening

At the moment on Earth there are two epochal changes taking place. Climate Change is one of them, and its multiple levels and scales and implications of that change are well-described by Greta’s book.

But we are also undergoing an Energy Transition which I estimate will have impacts on the same scale as the Industrial Revolution.

Solar Energy, Wind Energy and Battery storage have plummeted in price and their deployment is accelerating exponentially. I’ll be writing more about this in coming weeks, but by most measures, some combination of these technologies provides the cheapest electricity humanity has ever known.

As someone who is planning to operate their home entirely from solar power for 6 months of next year, this technological shift feels very real. And this change has taken place in my lifetime.

Cost is the key. Because these technologies are cheaper than building any other kind of power, they will – even in the face of strong opposition – inevitably win. In the end, the fossil fuel technologies will simply not be able to compete. In the end we will make the energy transition, not because it is the moral thing to do, but because it is economically essential.

And this transition seems to me to offer some hope to people living in both developed and developing countries.

The Energy Transition will not bring with it solutions to the multiple problems of inter-national, inter-ethnic, inter-gender and inter-generational justice. But it does offer at least a realistic opportunity to reduce carbon dioxide emissions relatively quickly.

And for me, that would be enough.


Is it possible to live a carbon-zero life?

November 21, 2022

Friends, on Monday 21st November 2022 – which as I write this is ‘later today’ – I will be talking to hundreds of 6th Formers in London on the topic of whether it’s possible to live a carbon-zero life.

This is part of the Physics in Action series of events. As a retired person, I had thought my days of addressing such groups were over, and I feel honoured to have been asked to speak.

In case people can’t attend, I have recorded a version of the 40 minute talk which you can see below. It’s a bit flat compared to the verve of a live event, but hopefully it’s better than nothing.

And in case people – particularly teachers – wanted them I thought I would put the Powerpoint slides here. They contain many slides which are hidden but may contain useful illustrations or animations. Somehow the file is 100 Mb in size (Link). Sorry.


The thesis of the talk is that at the moment there are two epochal changes taking place on Earth.

The first is Climate Change, and my aim in this talk is to explain exactly why our emissions of carbon dioxide matter so much.

The second change is the Energy Transition. Independent of our need to respond to Climate Change, renewable technologies (solar, wind and batteries) have become the cheapest way to make electricity in human history.

This provides an economic imperative for action where moral imperatives have failed. The switch to renewable technologies will become inevitable, not  because it’s ‘the right thing do’, but because it is the cheapest thing to do.

So the second part of the talk is about some of the technologies which will enable this transition: heat pumps, solar PV and batteries.

My aim is to provide the audience with a visceral understanding of the need to change. But I hope to also provide a clear understanding that massive reductions in carbon dioxide emissions are possible right now, without the need for any new inventions or discoveries, and without the need for degradation of our quality of life.

Energy Consciousness Raising

November 14, 2022

Friends, energy is invisible. I think this is why many people have a hard time understanding the way it ‘flows’ into and out of their homes.

But fortunately we have ‘meters’ that record the flow of energy into our homes: and all the energy which flows into our homes eventually flows out.

If you want to raise your consciousness of these energy flows, the very best way is to read your electricity and gas meters regularly. I recommend once a week.

This article is about how to read electricity and gas meters, how to record the results in a spreadsheet and how to visualise your week-by-week energy consumption.

And if you are thinking vaguely about ‘doing something’ about insulation or heat pumps, then this habit will allow you to assess the benefits of any steps you are considering.

I have made a short video which will hopefully convey the power of this simple habit.

The best time to start recording your energy usage is about one year ago. But fortunately the second best time is right now!

If you are too excited and want to get started straightaway, then feel free to ignore the one thousand helpful words I have written below, and just skip straight to the end of the article for the download links for the spreadsheets.

Reading the Meters

First of all, I am afraid I don’t have the energy to describe how to read the hundreds of different types of meter out there. But fortunately, if you have difficulty with that, there is help available:

But there is one difference between reading the meter for an energy company and reading it for yourself. When reading for the meter for the energy company they tell you to miss off the last digits. This is because they want to minimise the chance of mis-reading and transcription errors. And they know that what you don’t pay for this month you will pay for next month!

But there is information in these digits which can be useful, especially if your usage is low.


Electricity meters read in units of kilowatt hours (kWh). This is a unit of energy, and so one just writes down the number.

Gas meters record the volume of gas that flows through them, and so one needs to make a note of the units on the meter.

Click image for a larger version. Two different designs of gas meters, one reading in cubic metres and one in cubic feet.

Gas meters record your gas usage by measuring the volume of gas passing through them in cubic metres or cubic feet. To estimate the energy contained in that gas you need to multiply by a factor which tells you the energy content per unit volume (energy density) of the gas. Irritatingly, gas meters report the volume of gas that has passed through them in different units: cubic metres, cubic feet, and 100’s of cubic feet.

Click image for a larger version. Spreadsheet excerpt showing how to subtract two readings to obtain the volume of gas used in one day, and multiply them by the energy density to find the energy contained in the gas that flowed through the meter.

An example of conversion from volume units to energy units is shown in the graphic above. The spreadsheet described at the end of the article will do the conversions for you as long as you know the units.

Meter-Reading Tip

Gas and electricity meters are often placed in places that make them quite inconvenient to read. Try using a mobile phone to photograph the meter and then write down the results from the photograph rather than directly from your view of the meter.

Writing things down: A simple spreadsheet.

Having read the meters, the next thing is record the numbers in a spreadsheet. An extract from a basic spreadsheet is shown below.

Click image for a larger version. Screenshot of a simple spreadsheet recording meter readings versus date, and showing charts of gas and electricity consumption. The data is from my own home.

The graphic above shows how the meter readings in my home changed over the years since November 2018. The graphs tell an interesting story: you should be able to spot the installation of:

  • Solar PV/battery: the electricity graph flattens in the summer
  • External Wall Insulation: the gas graph shows a smaller winter ‘step’.
  • A heat pump: the gas graph goes completely flat and the the electricity graph gets steep in winter.

But the presentation is frustrating for three reasons.

  • Plotting Dates in Excel – or most other spreadsheets is horrible. We would like it to understand that we want dividing lines at yearly or monthly intervals, but Excel can’t do that!
  • The graphs are in the same units as we read the meters: we need to convert the gas volume units (cubic metres) to energy units (kilowatt hours).
  • We are actually more interested in the rate at which we use energy. This corresponds to the slope of the graphs.

Writing things down: A more complicated spreadsheet.

To overcome the problem with units, we need to convert the gas meter readings to kWh.

To overcome the problem with dates, we need to convert Excel’s date format into either a number of days, or fractions of a year.

To plot the rate at which we use energy we need to:

  • Subtract the previous meter reading from the current meter reading.
  • Divide this difference by the number of days between the readings

A spreadsheet which does all this is illustrated below and can be downloaded here.

On the graphs I have also added a smoothed line through the data that makes trends easier to see

The spreadsheet also includes additional columns for plotting the meter readings from a solar PV system.

There are two versions of the spreadsheet that you can download. The first is the spreadsheet containing my own data that you can look at to see how it works. The second is the same spreadsheet but with no data in and dates adjusted to start in 2022 instead of 2018.


Jean Paul Satre once said that “Hell is other people“. I believe if he had lived he would have changed his mind and instead said “Hell is other people’s spreadsheets“.

Personally, I love using spreadsheets to check out ideas and to record and plot data. But preparing spreadsheets for other people to use is a nightmare, so these spreadsheets come with a health warning: they may not work quite how I intended.

If you are not familiar at all with spreadsheets, then this may not be for you. But if you are looking to get on top of your energy use, this could be a great opportunity to learn about spreadsheets.

The Excel spreadsheets are downloadable at the links below:



  • Empty Spreadsheet for reading from the hand-held readout units that accompany most smart meters such those illustrated below.

Good luck!

What to do on the coldest day of the year?

November 7, 2022

Friends, the coldest day of the year affords a rare opportunity to find out the key number that describes the thermal performance of your dwelling: the Heat Transfer Coefficient (HTC).

This is particularly relevant if you heat your home with a gas boiler because, thrillingly, it also allows you to estimate the size of heat pump your dwelling will require when it’s time to switch.

The coldest day is probably still a couple of months away, and that gives you time to prepare and practice for your day of measurement.

Let me explain.

The Coldest Day?

Let me begin with the profound philosophical question: “How do we know which day is going to be the coldest?”. As the Zen master said “Even a very cold day may be followed by colder days.”

Fortunately, we don’t the need the very coldest day of the day – any reasonably cold day will do, and the weather forecast should alert you to its arrival. Ideally it would be a day with an average temperature close to 0 °C, perhaps with a nighttime minimum temperature well below 0 °C.

And seeing how the results compare on a couple of similarly cold days will help you assess the likely uncertainty in your estimates.

A Very Cold day

On this cold day you need to use your electricity and gas appliances as you would normally so that your home is as warm as you would like.

Then you need to read your electricity and gas meters before the coldest night – and then at exactly the same time the next day. Alternatively a smart meter might well give you the information more conveniently.

Finally you need to know the average temperature inside and outside your home.

I’ll explain how to do the calculation below but with these readings you can estimate the Heat Transfer Coefficient (HTC) for your dwelling and – when the time comes to change – the size of heat pump you require.

The General Idea

Let’s say you used 20 kWh of electricity and 100 kWh of gas over a period of 24 hours. Then a simple first guess would be that the total energy used for heating was 120 kWh. Over 24 hours this would correspond to an average heating power of (120 kWh)/(24 h) = 5 kW. We’ll make a more sophisticated estimate below but this would be a good first estimate of the size of heat pump you require.

If the internal temperature through the day was 20 °C and the average outside temperature was 0 °C, then you can estimate the HTC by dividing the average heating power (5 kW) by 20 °C i.e. 5 kW/20 °C = 0.25 kW/°C.

A more sophisticated estimate

Electricity. Unless you are charging large batteries or directly heating hot water with an immersion heater, all the electricity you use – for televisions, lighting etc – ends up heating your home. So the 20 kWh of electricity used would all end up as heat.

Gas. In a typical boiler, 15% of the energy in the gas that went through the meter is lost out the flue. In older boilers losses could be as much as 25%. If you don’t know better, a good first estimate would be that your boiler efficiency was 85%. So if 100 kWh of gas was metered, I would estimate that only 85 kWh  actually entered the dwelling.

Cooking with gas. The heating power of gas used for cooking is generally small (a few kWh/day) and most of the heat ends up in the home any way.

Domestic Hot water. Gas or electricity used to heat water doesn’t generally heat the home (much) and needs to be subtracted from the estimate of heat supplied to the house. The industry guideline is that each adult uses about 3 kWh/day of hot water, so if there are two adults in the house you need to subtract 2 x 3 = 6 kWh/day from the estimate of gas used for heating the house.

People. People are actually a source of heat, releasing around 2.4 kWh/day. If there were two adults in the dwelling all the time then add 2 x 2.4  = 4.8 kWh to the heating energy.

So the total heating in the dwelling would be 20 + 85 – 6 + 4.8 = 103.8 ± 5 kWh. The uncertainties are such that this can be conveniently rounded to 104 kWh rather than 120 kWh in the simple estimate.

So over 24 hours this allows you to estimate of the size of heat pump you require as being (104 kWh)/(24 h) = 4.3 kW.

If the internal temperature through the day was 20 °C and the average outside temperature was 0 °C, then the HTC is estimated as 4.3 kW/20 °C = 0.22 kW/°C.

If you wanted the heat pump to keep your home at 20 °C when it was (say) -5 °C outside, then you can use the HTC to estimate the size of heat pump required. You multiply the temperature difference (20 – (-5)) = 25 °C) by the HTC (0.22 kW/°C) to give 25 °C  x 0.22 kW/°C = 5.4 kW.

I have prepared a spreadsheet that does the calculations for you:

Why You Need a Cold Day

You can make these measurements on any day of the year, but except on the coldest days, the uncertainty in the estimate can be large.

By making the measurements on a cold day, the main heating component – the gas consumption – can be estimated modestly well, and all the corrections are relatively small. My guess is that the answers should be within about 10% of the right answer.

Reading the Meters 

If you have a smart meter with an in-home display, then one of the settings will tell you how much energy you have used in the last day. Typically, they show data for gas and electricity separately, each for a 24-hour period starting at midnight. If the weather stays cold for two days, it might be better to record energy usage over a 48 period so as to include a complete cold night.

If you don’t have a smart meter, then you will have to find out where your energy meters are in your home and read them manually. If you don’t know how to read an energy meter there is help available from:

But there is one difference between reading the meter for an energy company and reading it for yourself. When reading the meter for the energy company they tell you to miss off the last digits. This is because they want to minimise the chance of mis-reading and transcription errors. And they know that what you don’t pay for this month you will pay for next month!

But there is information in these digits which can be useful, especially if your usage is low. So record all the digits from your gas meter.

Click image for a larger version. The left-hand image shows a gas meter reading in cubic metres and the right-hand image shows a gas meter reading in cubic feet.

Gas meters record your gas usage by measuring the volume of gas passing through them in cubic metres or cubic feet. To estimate the energy contained in that gas you need to subtract the volume readings made at the start and end of your chosen 24-hour period, and then multiply by a factor which tells you the energy content per unit volume of the gas.

Click image for a larger version. Spreadsheet excerpt showing how to subtract two readings to obtain the volume of gas used in one day, and multiply them by the energy density to find the energy contained in the gas that flowed through the meter.

Older gas meters sometimes confusingly read in units of hundreds of cubic feet rather than cubic feet. An example of this is given in the illustration above. If you are unsure you can check that you have the right units because for any reasonable home heated primarily by gas, the gas used on the coldest day of the year will be somewhere between 10 kWh (a well-insulated flat) and 200 kWh (a large poorly insulated house).

Fortunately electricity meters read directly in kWh.

A spreadsheet that does the calculations for you can be downloaded here:

Click for larger version. Graphic showing the spreadsheet that will do the calculations for you.


Reading your meters can be tricky, but working the average temperature inside and outside your house can be trickier.

The best way to do this is to measure it yourself with thermometers and weather stations. For most people that’s not possible.

If you don’t have an internal thermometer, then I have been told that the average household temperature is likely to be approximately 2 °C colder than the thermostat setting. So if your thermostat is set for 20 °C, then the average temperature of the dwelling is likely to be around 18 °C.

To estimate the average external temperature you might try this web site which allows you view historical weather data in your location. This link is for London, but you can choose other locations.

Alternatively use the Weather Underground’s Wundermap to find a local weather station. You can zoom in to a local level and click on an individual weather station and then its weather station ID to get its local daily and weekly average temperatures.

Last thoughts

Friends, the essential and expensive energy which flows into and out of our homes is sadly invisible. And this makes it difficult to assess the thermal properties of your home.

But the coldest days of the year afford us an opportunity to assess the thermal properties of a home that only comes about on a few days a year.

I urge you to get ready for when the cold days arrive – perhaps by practicing on less cold days – and then you will be able to obtain valuable information about your home.

Good luck!

What I did on the hottest day of the year.

November 6, 2022

Friends, do you remember 19th July 2022: The day when temperatures in the UK reached 40 °C for the first time?

I wrote about that day on the 20th July – reflections here – but I didn’t mention that I had also had a conversation that day with Gregg from the Take it EV podcast.

It was a long conversation (80 minutes) because I tend to go on on and on and Gregg is a kind interviewer, but it is now available for your delectation either as a podcast (link) or as a YouTube video below.



New Solar Panels

October 27, 2022

Friends, back at the start of September, I noted that it had been a sunny summer and I resolved to add more solar panels to the house in order to increase the solar harvest next year.

I ordered the system just a few days after writing that article and it is now being installed.

In this article I thought I would describe the new installation and how it will (hopefully) integrate with the existing installation.

Click on image for a larger version. The arrangement of the solar cells on the roof of Podesta Towers. The grey panels have been installed for two years, and the red panels were installed this week. I had hoped to fit four panels on the flat roof, but in fact I can only fit three.

The Existing Installation

The existing system was installed back in November 2020 and consists of:

Why did I select these items? The installer recommended them and they seemed to have adequate performance. And happily, they do seem to have worked OK.

Some key features of these items are:

  • 340 watts is the nominal output of a panel illuminated perfectly by sunlight with an intensity 1000 W/m^2 – this is roughly full sunlight on a UK summer day.
  • Since the panels are 1.7 m x 1.03 m one can work out that around 20% of the solar energy is converted to electrical power.
  • The panel is constructed as two half-panels wired in parallel, each with 60 individual solar cells.
  • A silicon solar cell generates around 0.6 V so the 60 cells on a half-panel together generate around 36 V.
  • Splitting the panel like this improves the panel performance when one half of the panel is shaded.
  • The MPPT acronym stands for Maximum Power Point Transfer and is system for extracting maximum power from solar panels as the intensity of illumination changes.

The quotation suggested that I might reasonably expect 3,780 kWh of generation each year and this year we look on track to exceed that. Last year we generated only 3,517 kWh.

Click on image for a larger version. Cumulative generation from the existing solar panels in 2021 and 2022. The dotted blue lines are based on the expected output according the installer’s initial calculation.

This first installation was done quickly to take advantage of the fact we had scaffolding around the house for the external wall insulation. Because of this, we couldn’t wait six weeks for permission for a larger installation from the local Distribution Network Operator (DNO): these are the people who manage the local electricity networks.

So I opted for a standard installation (for which no permission is required) with a maximum output of 3.6 kW peak and we used the best sites available. I resolved to learn what I could about solar power, and after two years, I feel I served my apprenticeship.

The New Installation

To move beyond the standard system one needs to apply to the DNO, a process that takes about 6 weeks and which was thankfully handled on my behalf by the installer.

My aim was to get as much solar PV on the roof as I could – while not making the house look horrible! For that reason, we avoided using a patchwork of panels across the roof – sacrificing some performance for aesthetics.

Since the best sites had been taken by the first installation – I simply went with what was available.

I had noticed during the summer that in the mornings the Sun rises well north of east, and the east-facing roof of Podesta Towers was in full sun up until solar midday. Similarly, the flat roof was more or less un-shadowed over the same period.

My performance calculations using the excellent Easy PV site were very similar to the suggested performance from the installer.

  • The 5 panels on the east-facing roof will hopefully generate ~1,300 kWh/year
    • The panels are tilted at ~ 40° and face roughly ~ 20° north of east.
  • The 3 panels on the flat roof – might generate ~900 kWh/year
    • The panels are tilted at ~ 12° but face roughly 20° east of south –

This would correspond to 2,200 kWh/year, an additional 60% of generation bringing the total close to 6,000 kWh/year. If actual performance gets anywhere close to this I would be delighted.

To put these figures in perspective, we can compare them with household consumption.

  • Last year the house used ~5,400 kWh –
  • Roughly 3500 kWh of that (~65%) was for day-to-day household ‘stuff’
  • Roughly 1,900 kWh of that (~35%) was used for the heat pump.
  • The heat pump operated with an average COP of 3.6 to deliver 6,800 kWh of heat.

So the enlarged system will hopefully generate more electricity than we use in a year. Sadly the peak of generation (in May or June) is quite out of phase with the peak of demand (in January or February). But nonetheless, it’s a milestone of sorts.

The new system consists of:

Again, I just accepted the installer’s recommended suggestions.

The Panels.

The new panels are similar to the old ones: the 390 W nominal peak output of the new panels is larger than the 340 W peak of the previous panels simply because the new panels are larger. The efficiency remains around 20%.

Each panel consists of two half-panels, each with 9 rows of 6 rectangular half-cells.

Click on image for a larger version.

When illuminated, each individual cell generates a voltage between 0.5 V and 0.7 V between the top of the cell (the part you can see) and the bottom of the cell (that is at the back of the panel).

Fine aluminium wires cover the top of the cell to collect the generated electrons, and the wires then connect the top of one cell to the underside of the neighbouring cell so that their generated voltages add together. In each half-panel, 54 cells in series generate a voltage ~ 36 V at a current of roughly 5 amps.

Click on image for a larger version. Top: Illustration of the way in which sunlight generates a voltage between the bottom and the top (illuminated) surface of the cell. Right: The fine wires collect electrons generated from within the silicon. The filigree wiring pattern is optimised to collect as many photo-electrons as possible, while not blocking the sunlight. Left: Details of the wiring showing the top surface of the lower scale is connected to the underside of the neighbouring cell.

The two half panels are wired together in parallel so that the peak output of the whole panel is ~ 36 V at a current of roughly 10 amps.

Panels which are similarly illuminated are wired in series in a so-called ‘string’. In this installation, the 5 panels on the east-facing roof are wired in one string and the 3 panels on the flat roof are wired in another.

The inverter design has two independent inputs and the DC currents from the two ‘strings’ are combined to create an AC current at 220 V.

This arrangement works excellently when all cells in a panel and all panels in a string are illuminated similarly. But if one cell in a panel is shaded, then not only does that cell not generate a current, its electrical resistance increases dramatically, and this can restrict the current which is able to flow through the whole string of which it is a part. Fortunately, clever electrical tricks can minimise the shading problem as explained in this excellent video.

Peak Power.

One aspect of the installation which concerns me is whether all the electrical circuits can cope with the sheer amount of power this system might generate.

To estimate this, I downloaded generation data from 22 June this year, a day which was nearly perfect for solar generation: close to the solstice and almost completely cloudless. This data is shown in red on the graph below.

I then made guesstimates of the generation from the two new strings:

  • I guessed the 5-panels on the east-facing roof would begin generating earlier in the day and reach maximum power (5 x 390 W = 1,950 W) just before solar noon (1:00 p.m. BST). This is shown as a green dotted line.
  • I guessed the 3-panels on the flat roof would generate roughly symmetrically around solar noon (1:00 p.m. BST) with a maximum power of 3 x 390 W = 1,170 W. This is shown as a blue dotted line.

Click on image for a larger version. Graph comparing a perfect midsummer generating day with the existing system (red curve) with the likely generation from the expanded system (purple curve). See text for details.

Altogether (dotted purple line) the total power could potentially exceed 5 kW – a worryingly high power level.


Friends, as usual, I have gone on for too long. But this is a significant – and possibly final – step in the house refurbishment.

It offers the possibility of being off-grid for 6 months a year and of generating more electricity than the household consumes (averaged over a year). I think these are significant upgrades.

The cost is not completely clear yet, but looks like it will be just under £5,000. This is more than the initial system (£4,200 in November 2020) but this seems reasonable given the extra scaffolding required.

As I write, the panels are installed but the internal electrical wiring is not complete – but hopefully that will be done soon!

And if you have read this far, thank you! Please allow me to reward you with a video of the installation.



Weather Compensation: Experimental Tweaking

October 21, 2022

Friends, as I mentioned in my previous article, I have no real idea how to actually operate my 5 kW Vaillant Arotherm plus heat pump – or to check how well it is operating. That’s because there is no readable manual for the controller and the App does not do what it says it does.

But since I have an independent monitoring system, I have begun a series of experiments to tweak the heat pump weather compensation settings, and see what happens!

If ‘Reading the Manual is like taking a course in theoretical heat pumps, then this is more like a course in experimental heat pumps.

This is quite a technical article, and it is nearly 1500 words long. So if you are not really interested in heat pump arcana I would recommend giving this one a miss. On the plus side, it does have some nice graphs :-).

Weather Compensation

Weather Compensation is the idea that when the weather is mild, one can heat water in radiators or under-floor heating to a low temperature – perhaps just 25 °C. But when the weather is colder, and the heating demand is greater, one can increase the temperature of the hot water to perhaps 40 °C or 50 °C to meet the heating demand.

Using weather compensation to match the output of a heat pump to the heating demand contrasts with using a thermostat for the same purpose.

Click on image for larger version. The heating supplied to a dwelling can be changed to match demand in two ways. In a traditional thermostat-based system, the radiator flow temperature is fixed and switches on and off to maintain a constant indoor temperature. In contrast, using weather compensation the radiator flow temperature is adjusted.

In a thermostat-based heating system, the flow temperature to which water is heated is pre-set: in boilers it is often as high as 70 °C, and for heat pumps it might be 50 °C. And then to match heating to demand, the thermostat switches the heating source on and off intermittently to maintain the desired temperature.

Weather compensation is particularly valuable when using heat pumps because the coefficient of performance (COP) of the heat pump varies with both flow temperature and environmental temperature. But it can be tricky to adjust the settings for any heat pump, but especially one with no decent manual!

Weather Compensation in action

The graph below shows data taken every two minutes during the week from 00:01 on 11th October 2022.

  • The red curve shows the outside temperature
  • The grey dots show the instantaneous flow temperature.
  • The green curve shows the flow temperature averaged over 1 hour
  • The orange curve shows the internal temperature

Click on image for larger version. Weather compensation in action. When the outside temperature falls, the flow temperature in the radiators increases to maintain the internal temperature.

Notice that when the outside temperature falls, the flow temperature in the radiators increases to maintain the internal temperature.

But on day 4 of the period shown in the graph above, I changed the setting of the Weather Compensation from the curve labelled ‘0.6’ to the curve labelled ‘0.5’ in an attempt to lower internal temperature of the house. I’ll explain more about these labels below.

The graph below shows that average for the 4 days before the change was 21.0 °C and the average for the 3 days after was 20.76 °C: so it does seem to have had a small (0.24 °C) effect, but I will need to continue experiments – see the end of the article for an update.

Click on image for larger version. Graph shows the internal temperature of the house detail averaged over a period of 1 hour. The weather compensation parameter was changed on Day 4 and it does seem to have slightly lowered internal temperature.

It is striking to me how stable the internal temperature is given that – as I understand it – it is based entirely on measuring the temperature OUTSIDE the house – not INSIDE it!


To evaluate the COP, one needs to work out the ratio of the heat delivered to the electrical energy used, over some set time period.

The hourly averaged COP is shown in the graph below. The times when the COP is greater than 4 correspond to times when the difference between the flow temperature and the outside temperature is small, and so not very much heat is being delivered with these high COP values.

Click on image for larger version. Graph shows the hourly averaged COP. Considering only use for DHW the average COP was 3.1 and considering only use for space heating the average COP was 3.9. Overall, considering both DHW and space heating across  the entire period the average COP was 3.7. These averages are shown as dotted lines on the figure.

With a little spreadsheet untangling it is possible to extract the data corresponding to periods when the heat pump is heating DHW and periods when it is heating water for space heating. For DHW the average COP for heating water to 50 °C was 3.1 and for space heating the average COP was 3.9. Overall, considering both DHW and space heating across the entire period, the average COP was 3.7.

Electrical and Thermal Power

Calculation of COP requires evaluation of both electrical power consumed and thermal energy delivered. The graphs below show both these quantities measured every 2 minutes throughout the week or so under consideration.

Click on either image for larger version. Graphs show hourly averages of electrical and thermal power. The DHW cycle runs once a night using cheap rate electricity. The separation of the two uses of the heat pump is not quite perfect: sorry.


So far I have just showed a week or so of data. Now I will explain what I hope to achieve with some ‘tweaks’ First let me explain, about how Vaillant implement Weather Compensation.

Their scheme is illustrated in the figure below. The flow temperature of water in the radiators is set depending the temperature outside. The sensitivity of the weather compensation is set by picking a curve labelled by a number from 0.1 to 4. For example, when the outside temperature is 5 °C,

  • the curve labelled 0.6 would result in a flow temperature of about 34 °C but
  • the curve labelled 0.5 would result in a flow temperature of about 32 °C

Click on image for larger version. The flow temperature of water in the radiators is set depending the temperature outside. The sensitivity of the weather compensation is set by picking a curve labelled by a number from 0.1 to 4. When the outside temperature is 5 °C, the curve labelled 0.6 would result in a flow temperature of about 34 °C but using the curve labelled 0.5 would result in a flow temperature of about 32 °C.

On Day 4 I adjusted the weather compensation from 0.6 to 0.5. To see if this tweak is working we can look at the second figure in this article in this article which I have reproduced below.

Click on image for larger version. On Day 4 the weather compensation setting was changed from 0.6 to 0.5. If we look at cold spells before and after the change it does look as though as the flow temperature is perhaps a degree or two than one might otherwise have expected.

If we look at cold spells before and after the change it does look as though as the flow temperature is perhaps a degree or two cooler than one might otherwise have expected. And since this article has taken a day or two to prepare, I now have a couple more days data on the internal temperature with WC curve 0.5. It does indeed seem to have maintained an internal temperature about 0.23 °C cooler than using WC curve 0.6.

Click on image for larger version. Updated version of the second graph in this article with 3 extra days data. The graph shows the internal temperature of the house in detail averaged over a period of 1 hour. The weather compensation parameter was changed on Day 4 and it does seem to have slightly lowered internal temperature.


My main conclusion is that the weather compensation adjustment does seem to be sort-of working. I will continue experiments and let you know how they go.

My second conclusion, is that observing these effects is really hard and it takes hours of analysis to unearth this kind of insight!

My third conclusion – which you may have already spotted – is that my 5 kW heat pump is just too big. It only needs to output 1,500 W to maintain a temperature of just over 20 °C in my home when the outside temperature is 5 °C i.e. with 15 °C of demand. This seems to indicated that a 3 kW heat pump would have been adequate to heat the home down to (say) – 5°C.

This oversizing is probably responsible (at least in part) for the rapid cycling on and off of the heat pump – exactly what weather compensation was supposed to avoid!


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