What to do on the coldest day of the year?

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:

• Coldest Day Spreadsheet

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:

• Citizen’s Advice Bureau (Gas and Electricity Meters)
• British Gas (Electricity Meters)
• British Gas (Gas Meters)

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:

•  Coldest Day Spreadsheet.

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

Temperatures 

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!

New Solar Panels

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:

• 12 Q-CELLS 340W DUO G8 panels
• A SOLIS 3.6KW 4G dual MPPT inverter

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:

• 8 JA SOLAR 390W MONO solar panels.
• A SOLIS SOL-3.6-S6-DT-DC inverter.

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.

Summary.

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.

 

 

Heating My Home

Friends, I have made a 5-minute video about heating my home with a heat pump.

It’s nonsense, but once I had thought of the idea of using coloured water to represent heat, I felt compelled to make the video: I hope you enjoy it.

Another talk about reducing CO2 emissions

Friends, this week I visited Brighton to give a talk to their Café Scientifique on reducing carbon dioxide emissions from one’s home.

I spent absolutely ages getting the Powerpoint slides ready, but tragically, on the night, the projector didn’t work and I had to ad lib and just mime the key slides!

So yesterday I sat down with my phone and recorded the presentation in two parts – links below.

Because there was no audience the presentation is a little dull – but at least I get to show people the slides!

If you would like, you can download the slides here. It’s a 40 Mb file (!) but feel free to share or steal anything you like!

Presentation#1

The first part of the presentation is 22 minutes long and considers exactly why it is that Earth’s surface temperature is so sensitive to carbon dioxide in the atmosphere.

When I went out chatting to the public recently (1, 2), this was something that people just didn’t seem to understand.

Presentation#2

The second part of the presentation is 26 minutes long and involves a consideration of how we can reduce carbon dioxide emissions both collectively and personally.

Most people don’t have the resources to do very much, but absolutely everyone can help by just talking with friends and family about the reality of what we are facing.

For those that do have the resources, the presentation outlines how installing  a heat pump, and using solar PV panels and a battery can make a big difference  to personal CO2 emissions.

Warning

These videos are unscripted! Consequently, I may inadvertently fail to speak with the level of exactitude to which I would normally aspire: please accept my apologies in advance.

Talk about Heat Pumps

Friends, this evening I will be giving a talk about Heat Pumps to the Richmond and Twickenham Branch of Friends of the Earth.

Specifically the talk is about switching from using a gas boiler to a heat pump

But I have already given the talk!

I recorded a version of the talk this morning and you can see it below!

If you want you can download the Powerpoint Slides using this link  (15 Mb)

Sadly, the talk is an hour long, but given the list of 25 things I had to talk about, I guess that was inevitable.

Viewers who liked that talk may also be interested in…

How heat pumps work

A Rule of Thumb for sizing heat pumps

Finally off gas! Well, Almost Finally.

Friends, yesterday was a happy day. Two technicians finally removed our gas hob and installed a new induction hob.

The gas oven and grill was replaced last week, and so this was the last step in a journey which has taken nearly four years.

And finally, we have no need to burn gas in this house ever again. I feel emotionally exhausted.

The Journey

The household’s smoothed daily gas consumption (kWh/day) along the journey is shown in the graph below.

Click on image for a larger version. Based on weekly readings of the gas meter, the graph shows Gas consumption in kWh per day for the last four years years, with the time-axis showing the number of days elapsed since the start of 2019. The data are averaged over 5 weeks to smooth out the noise. The pink boxes show the dates of key interventions which affected gas consumption.

Back in 2018/19 peak mid-winter gas consumption was over 110 kWh/day. This fell to first 70 kWh/day in 2019/20 and then 50 kWh/day in 2020/21.

In August 2021, the gas boiler was replaced with an Air Source Heat Pump, and since then we have just used gas for cooking – using an average of just over 1 kWh gas/day.

The graph also shows the heat output of the heat pump over the winter of 2021/2022.

The graph below shows details from the graph above.

Click on image for a larger version. Details of the graph above showing periods where gas usage was low.

Looking at summer consumption, back in summer 2019 (with my son and his girlfriend staying with us) we were using gas for hot water and cooking and our usage was around 6 kWh/day. In summer 2020 (with just my wife and I in the house) this fell to ~4 kWh/day.

Since 2021, we have used gas solely for cooking, an average of just over 1 kWh gas/day. Combined with the heat pump output of roughly 3 kWh/day for domestic hot water, this roughly matches the 4 kWh/day of gas consumption we used back in 2020.

Today’s step corresponds to Day 1360 and I have presumed to fill in ‘zeros’ ahead of time out to the end of the year.

In terms of carbon dioxide emissions the graph below shows that 3 tonnes of carbon dioxide that the house used to emit, is now finally falling to exactly zero.

Click on image for a larger version. Cumulative emissions of carbon dioxide from burning gas in the house. 

What’s wrong with ‘cooking with gas’?

Fundamentally, cooking with gas is a barely-evolved version of cooking on an open fire: it releases carbon dioxide and toxic pollutants (NOx) directly into our kitchens – a critical issue for anyone with asthma or children.

Although each installation differs, careful measurements reveal that domestic gas installations typically leak around 1% of the methane gas they consume – which practically doubles the global warming effect of using gas.

Gas cooking also wastes a large fraction of it’s embodied energy heating the room  – with typically just 40% of the gas’s energy being delivered to the food in a saucepan.

Click on image for a larger version. Left: measuring the rate of heating of 1 kg of water in a saucepan on a gas hob. Right: the equivalent measurement on an an induction hob. The lid was kept on through the experiment except for occasional stirring, and the temperature was inferred from the average temperature of two thermocouples.

The graph below shows the rate at which 1 kg of water is heated on a gas hob and on our new induction hob. The effective heating power is a factor 3.6 larger.

Click on image for a larger version. Measured rate of heating of 1 kg of water in a saucepan on a gas hob and an induction hob. The induction hob heats the water between 3 and 4 times faster than the gas hob.

What’s so good about induction hobs?

Fundamentally, the key advantage of cooking with electricity is that the electricity can come from any source, including solar PV or wind. This afternoon, as I carried out the heating experiment on the hob, the electricity was being supplied entirely by the Sun.

Installing this hob means that we have finally broken this archaic link where ‘cooking’ implies that something must be burned and carbon dioxide emitted.

Induction hobs – aside from being quick and powerful – also combine features which gas cookers never could – such as temperature-related feedback control.

And it’s not just hobs: we have also replaced our cooker, and it was such a blessed relief to get rid of that appalling gas oven. The gas oven spewed it’s exhaust gases (steam and CO2) into the oven chamber itself meaning that they had to be continually cleared out  – wasting lots of energy heating the kitchen.

Now having a high temperature in the oven no longer means that the kitchen temperature needs to rise also!

Michael: what did you mean by ‘Almost’ off gas?

Friends, nothing in life is easy.

In order to change the cooker and hob I needed to have the backing of my wife who, while not hostile to my endeavours, does not share my enthusiasm.

And as a quid pro quo for the purchase of the cooker and hob from our joint savings, my wife suggested that we retain a gas fire in the front room.

I had planned to get rid of the gas fire – which we have not used for a year or more – and have the gas supply cut off, saving the standing charge of around £98/year. But my wife suggested that we may have power cuts this winter – and she has a point –  and that having more than one kind of heating might be useful.

So for another winter season we will retain the possibility of burning gas.

In case you care, this is what we bought.

Click on image for a larger version. Features which helped us choose our particular models of cooker and hob. For the hob we liked this simple way of setting power levels rather than having to repeatedly press a button.  For the cooker, we liked the way the controls recessed into the panel for cleaning.

My wife and were both unfamiliar with cooking with electricity and so bought mainstream models from Bosch on the principle that Bosch probably know what they are doing better than we do.

For the hob, my wife was concerned that the controls might be fiddly to use if we had to repeatedly press a “+” or “-” button to set a cooking level.

To avoid that situation we picked a model (Serie 6 PXE651FC1E) in which the cooking power is set by first selecting the relevant control area, and then touching a point on a scale: based on our experiments this afternoon, this works as sweetly as we had anticipated.

For the cooker, we chose a model (Serie 4 MBS533BS0B) in which the knobs could be recessed because that seemed very pleasing.

On balance, we thought both these items were very expensive for what they were and there are probably much better bargains to had.

It’s been a sunny summer

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 2020, 2021 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

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.

Domestic Thermal Storage 2: Phase Change Material

Friends, this is the second of three articles in which I am comparing three different types of thermal storage.

In the last article I looked at the humble domestic hot water (DHW) cylinder, and in the next article I will look at large thermal stores. Here we will look at the use of a phase-change material (PCM) to store heat.

In practice a PCM thermal store looks like a regular ‘white goods’ metal box and is typically placed wherever the domestic hot water (DHW) cylinder would have been in a dwelling.

Click on the image for a larger version. Publicity images from the Sunamp web site demonstrating the small physical size of their PCM thermal stores.

But a PCM thermal store has a big advantage over a DHW cylinder: it is typically one third to one half the size for the same amount of thermal storage. Dimensions are typically 1 metre high, 60 cm deep and 40 cm wide.

Click on the image for a larger version. On the left-hand side is a commercial PCM thermal store. On the right-hand side is a schematic explanation of how it works. In this versions of the device, the PCM material is charged using an electrical immersion heater. In other versions it can be charged using a heat pump. In operation, cold water flowed into the device is rapidly heated and discharged.

Additionally a PCM store is cubical, and so makes use of the corners of spaces that DHW cylinders – being cylindrical – can’t use.

Functionally it works like a DHW cylinder. When a tap is opened, cold water flows into the device and is heated as it flows through pipes embedded in the hot PCM material – and hot water flows out.

However, the PCM thermal store has a trick up its sleeve. If the PCM stored heat in a substance at high temperature, then the temperature of the substance would have to be high initially – with high losses – and the storage medium would cool as heat was withdrawn.

PCM thermal stores get around this by using a material which melts – typically at around 55 °C to 60 °C.

• Charging the PCM involves heating it up to its melting temperature, then supplying the so-called ‘latent heat’ required to change it from one ‘phase’ (a solid) to another ‘phase’ (a liquid). It is then heated further as a liquid.
• When cold water flows through pipes embedded in the PCM, the PCM cools and freezes around the pipes. When it freezes it stays at its freezing temperature releasing its so-called ‘latent heat’ until the entire charge of of PCM has solidified.

In practice this means that one gets the benefits of a DHW cylinder in a smaller space. PCM thermal stores are particularly well-suited to smaller single-person dwellings.

PCM’s: Home experimentation

A common PCM with which you can experiment at home is candle wax.

While my wife was out at work, I put two candles into a glass container and melted them (one at a time) by putting the container in a jug of boiling water.

Click on the image for a larger version. Top-Left: Melting a candle in a jug of hot water. Right: A partially melted candle.Bottom-left: Measuring the temperature as the molten wax cooled.

When both candles were melted, I put a thermocouple into the wax, wrapped insulation around the glass vessel and then measured the temperature as the molten wax froze – i.e. changed ‘phase’ from liquid to solid (to use the technical terms). The data are shown below:

Click on the image for a larger version. The graph shows the temperature of a thermocouple embedded in 55 g of wax as it froze. Note that there is a sharp change in cooling rate when the wax starts to freeze due to the release of so-called ‘latent heat’. This allows the wax to stay above 50 °C for almost 3 hours, while if it had continued cooling at the initial rate, it would have fallen below 50 °C in under 1 hour.

What one sees is that as the molten wax cools, it looks like it will fall below 50 °C after about 50 minutes. However, once the wax starts to freeze (at about 57 °C), the cooling rate is reduced to roughly one tenth of its previous rate, and the liquid/solid mixture stays above 50 °C for around 160 minutes.

Using a very rudimentary analysis based on googled data:

• Heat Capacity of wax ~2.5 J/g/°C – assumed the same in liquid or solid state;
• Latent Heat of wax ~176 J/g;

…one can roughly estimate how much heat is released at temperatures above 50 °C.

Click on the image for a larger version. Analysis of cooling curve in the previous graph allows an estimate of the amount of heat released at temperatures above 50 °C. The latent heat of 55 g of wax amounts to just under 10,000 joules.

Although I had followed the golden rule of experimental physics, I still failed to anticipate just how long it would take the wax to solidify – the experiment took 4 hours and I was almost late preparing my wife’s dinner!

This extended experiment indicates just how much ‘latent’ heat a material can store compared with ‘sensible’ (i.e. sense-able: which can be detected with a thermometer) heat storage.

Based on the latent heat alone, 100 kg of wax – which would occupy a cube with a side of 50 cm – could store 5 kWh of thermal energy – the equivalent of a small DHW cylinder.

Commercial PCM Devices

I don’t know, but I am pretty sure that commercial PCM devices do not use wax as a storage medium.

Update: A Twitter Source tells me that the Sunamp uses “Sodium acetate tryhydrate (plus a few secret additives).”

Sunamp’s list of patents includes a variety of chemicals which can be used, but the particular chemical used and the way it is prepared is likely a trade secret. Nonetheless, I suspect their basic properties are not so different from wax.

They will have a phase change temperature ideally around 55 °C. If the phase change temperature is much higher than this, then the store will operate at too high a temperature and lose more energy. If the phase change temperature is much lower than this, then water will not be sufficiently hot when discharged.

Early models of the PCM stores were designed to be ‘charged’ electrically with a heater immersed in the PCM material. This could be powered either from the grid – ideally using off-peak electricity – or from solar PV panels. However recent versions can also be charged using a heat pump.

Summary

PCM thermal stores  represent a clever way to incorporate thermal storage in dwellings where space is at a premium. They are particularly useful in flats and households with just one or two people.

However, like all thermal storage devices, they are not perfect.

One disadvantage is that unlike a DHW cylinder, the storage medium has to ship with the device – it can’t be shipped empty. This makes the devices heavy: A PCM store equivalent to a 200 litre cylinder weighs ~ 172 kg. Of course a DHW water cylinder holding 200 litres of water would weigh more – but it can be filled and emptied in place!

Heating losses are similar to DHW cylinders – with roughly 10% of the stored energy being lost each day – and like DHW cylinders, it can be tricky to know how ‘full’ the store is because it can be difficult to work out what fraction of the PCM material is liquid or solid.

But all-in-all, the PCM thermal stores devices seem to have found a niche where they can make themselves genuinely useful.

Domestic Thermal Storage: Part 1: Hot Water

Friends, writing about the ‘Sand Battery’ fiasco the other day brought to mind smaller thermal stores that are used domestically. And so I thought it would be interesting to write about the physics of thermal storage.

But it has all got out of hand and now this this is the first of three articles over which I will compare three different types of thermal storage, one most people are familiar with, and two that are less familiar:

• A domestic hot water tank.
  • This stores thermal energy in water which is then used directly within a household.
  • A typical Domestic Hot Water (DHW) cylinder stores between 7 kWh and 10 kWh of thermal energy.
• A phase-change thermal storage device.
  • This stores thermal energy in the so-called ‘latent heat’ of a material which absorbs thermal energy when it is melted, and releases it at a constant temperature as the material freezes.
  • A typical Phase Change Thermal Store stores between 4 kWh and 8 kWh of thermal energy, comparable with a DHW cylinder, but requiring only approximately half the volume.
• A Zero Emission ‘Boiler’.
  • This stores thermal energy in the heat capacity of a ‘thermal core’ – a cylinder of concrete weighing ~300 kg – which is heated to an astonishing 800 °C.
  • This can store up to 40 kWh of thermal energy.
• A ‘big thermal store’.
  • Like a Zero Emission Boiler, but heavier – and ‘only’ heated to 500 °C.
  • This can store up to 100 kWh of thermal energy.

Click on the image for a larger version. Schematic illustration of four different types of thermal storage devices and a human being for scale.

The key role of all these devices is to separate two events:

• The time when energy is consumed from a central resource – such as the electricity grid,
• The time when energy is used domestically – such as when you take a shower.

Separating these events has two benefits:

• It allows users to store thermal energy slowly but to release large amounts of thermal energy quickly – such as when you need a flow of hot water ‘instantly’.
• It allows users to store thermal energy when it is cheap or convenient .

For each device we need to consider how it is heated (‘charged’) and how it passes on its stored heat (‘discharged’).

In this article we will look at how a domestic hot water (DHW) cylinder works and in the following articles we will look at how Phase Change Material Stores works and how Zero Emission Boilers and big thermal stores work.

Domestic Hot Water (DHW) Cylinder

When I first heard a DHW cylinder described a ‘thermal store’, I was initially confused. I had always considered them as storing water!

In the other thermal stores, heat is first stored in a material, and subsequently transferred to circulating water or DHW only when it is required. In a DHW cylinder the storage material is the water which will itself later emerge from a tap.

The amount of stored thermal energy can be estimated as the product of:

• The volume of water in the tank
• The heat capacity of water in the tank (4,200 J/°C/litre)
• The difference between the storage temperature and the charging temperature.

For a 200 litre tank storing water at 55 °C which has been heated from 20 °C this amounts to ~29 MJ or 8.2 kWh.

One can store more energy in a cylinder of a given size by storing water at a higher temperature: at 75 °C the stored energy in the cylinder above would be 12.8 kWh. To prevent discharge of scaldingly hot water, a blending valve would be used on the top of the cylinder and set to (say) 50 °C.

Click on the image for a larger version. Schematic illustration of the structure of a DHW cylinder showing the internal coil for heating the stored water. On the right is a manufacturer’s illustration of the coils within their cylinder.

A DHW cylinder can be charged in one of several ways.

• In the simplest way, an electrical heater immersed in the water heats the water directly. A 3 kW heater can charge a 200 litre cylinder to 55 °C in just under 3 hours. The heater could be powered by either grid or from excess solar PV.
• Alternatively, hot water heated by a gas boiler or a heat pump can be flowed through a coil inside the cylinder, passing on its heat to the stored water. The rate of heating in this method will generally be slower than using an immersion heater.

Discharging the cylinder is simple: one opens a tap and the mains water pressure forces water out of the top of the cylinder replacing it with cold water at the bottom.

The rate of discharge of thermal energy is given by the product of:

• The discharge flow rate (litres/second)
• The heat capacity of water in the tank (4,200 J/°C/litre)
• The difference between the storage temperature and the charging temperature.

So if 10 litres of water at 50 °C is discharged per minute, thermal energy is being released at a rate of 21 kW. This is a very high rate of energy use.

‘Combination boilers’ can provide this very high heating rate, but only at the cost of releasing (at the specified flow rate) around 0.1 kg of CO2 for each minute of operation.

Difficulties

One of the difficulties with a DHW cylinder is that natural convection within the cylinder causes the hot water to rise to the top. And the stratification within the cylinder can be very dramatic.

Since most cylinders have only a single thermometer somewhere in the middle of the cylinder, even after reading the thermometer it is difficult to know how much heat is currently stored in the cylinder.

Additionally since the heating coil or immersion heater is typically in the lower third of the cylinder, practically the whole cylinder must be re-heated before any sufficiently hot water is available at the top of the cylinder – which typically takes several hours.

Some modern cylinders made by the Mixergy company exploit the stratification by heating the water from the top and then carefully mixing it with the colder water below.

These computer-controlled cylinders can give a reasonable estimate of the state of charge of the cylinder, and also allow rapid heating of small volumes of water at the top of the cylinder. However, I don’t understand precisely how the technology works.

Update: This video gives a clear – if rather glossy – explanation of how the system works. It turns out that Robert Llewelyn was given one as part of a research study!

Click on the image for a larger version. The water in a conventional DHW cylinder is hotter at the top but the temperature gradient from top to bottom is not well-defined. More modern computer-controlled cylinders from the Mixergy company can precisely control the location of the temperature gradient.

Heat Losses 

A DHW cylinder holding 200 litres is typically 1 metre high with a diameter of 50 cm and insulated with 50 mm thick layer of polyurethane foam with a typical thermal conductivity of 0.025 W/°C/m.

Click on the image for a larger version. Heat losses from a DHW cylinder are typically 10% of the stored energy per day.

For a cylinder at 55 °C, this leads to a heat loss of roughly 35 watts, or 0.85 kWh/day. i.e. the cylinder loses about 10% of its stored energy per day.

This loss rate increases if the water is heated to a higher temperature. For a cylinder at 75 °C the loss rate is ~ 55 watts or 1.32 kWh/day – again, about 10% of its stored energy per day.

The only way to reduce the heat loss is to apply either better insulation (which is expensive) or to apply a thicker layer, which makes the cylinder larger.

Summary 

A DHW cylinder holding 200 litres is a simple way to store hot water for use around the house.

In the context of renewable energy, it allows a heat pump with a COP of 2.5 to use perhaps 1.5 kW of electricity for 2 hours (3 kWh) to fully charge a cylinder with ~8.5 kWh of thermal energy. This can then be discharged at 10 litres per minute i.e. releasing stored energy at a rate of 21 kW.

The downsides of a DHW cylinder, (large size, 10% leakage per day, unknown temperature gradient within the tank) are generally considered acceptable.

But there are alternatives and we will look at one of these in the next article.