A Short Talk about my Low-Carbon Home

Friends, today I abandoned my usual Saturday morning ritual of doing a quiz and a crossword with my wife at our local café.

Instead I travelled far beyond the borders of Teddington to give a  “A Short Talk about my Low-Carbon Home” at the Kingston Efficient Homes Show. There were many celebrities there include Ed Davey, the leader of the Liberal Democrats, and the Green Man, whom Wikipedia informs me is not in fact a pagan mythological figure.

The Green Man visited the Kingston Efficient Homes Show.

I was a little discombobulated at the start of the talk because nobody turned up to introduce me, and the clock in the lecture room was slow. And so while I was just waiting to start, I should already have started. And at the end I was being told to wind up, when in fact I still had many minutes left. Hey Ho.

I promised the audience I would put the Powerpoint slides from the show here, and below is a belated re-recording of the 20 minute talk for those who missed it. Somehow, it is 30 minutes long :-(.

Reflection 

I found the event very moving: it was full of people trying to make the world a better place.

• There were slightly bewildered members of the public prepared to spend money on heat pumps and insulation and solar PV and batteries.
• There were installers – the shock troops on the front line of combating climate change.
• There were architects – including the designers of the fantastic Bale House in Hastings.
• There were members of the local Council and politicians.

But one thing annoyed me: the endless request for estimates of ‘payback time’ or ‘return on investment’.

As Bill Nye, the mild-mannered American science communicator so eloquently put it, “The planet is on fire“. And people still want to find out whether it’s worth their while to put out the fire? He was actually rather more pithy than that.

If you found that video amusing, here’s another more upbeat version.

Breville HotCup: Thermodynamic Reflections

Friends, you may recall my long-standing fascination with boiling water efficiently: see for example:

• Kettle versus Quooker (2023)
• A Watched Pan (2022)
• Gas or Electric Kettle? (2012)

So ‘boiling water’ was a topic on which I thought I had written my last word. But visiting some sophisticated neighbours, I saw that they had a Breville HotCup – a kettle that held a reservoir of water, but which then dispensed just a single cup of boiled water at the push of a button. Wow!

Remember that in a conventional kettle one almost always boils too much water, thus wasting energy. And in a Quooker one keeps several litres of water at 100 °C so it is ready when you require hot water. Could the HotCup be the clever device that boils exactly the right amount of water just when you need it, without wasting energy on ‘standby’?

Well, after reflecting on the future rubbish I was creating, I bought one and tested it. It is a perfectly pleasant item, and does indeed dispense individual cups of water quickly – and since this is how I generally consume tea – I must confess to being pleased.

But after assessing its performance from an energy efficiency standpoint, I found myself disappointed. At best, it is ~ 80% efficient, but at its worst it is only 25% efficient! It took me some time to work out how it could be so bad, but I did eventually figure it out. Allow me to explain.

What is a Breville HotCup?

There a number of HotCup models, but the key idea behind them all is that it is a kettle which holds a reservoir of water, and then boils and dispenses just a single ‘cup-full’ – variable between 150 ml and 320 ml – at a time.

The video below shows the HotCup in operation along with the equipment I used to make measurements.

Measurements

I couldn’t see immediately how the device worked, but I set out to measure its performance using the standard techniques of ‘kitchen calorimetry’.

• I weighed the HotCup when empty and then filled it with about 1.5 lites of water. I then weighed the amount of water dispensed (g).
• I measured the temperature of the water reservoir, and the maximum temperature of the dispensed water (°C).
• I recorded the electricity used on a plug-in electricity meter (in kWh).
• I timed the boiling process using the timer on my phone (s).

From the mass of water dispensed and its rise in temperature, I could work out how much heat energy had been given to the water. I could then compare this with the measured amount of electrical energy consumed. Comparing these two figures I could work out the efficiency with which the consumed energy had been converted into hot water.

Remembering the Golden Rule of Experimental Physics, I repeated the experiment multiple times to assess more or less what was going on. Then when I had practiced a couple times, I made one set of readings with the HotCup set to dispense small cups of water (~150 ml) and one with it set to dispense large cups of water (~330 ml). For each setting I repeated the measurements until the reservoir appeared to be empty. The results are shown below.

Click on image for a larger version. Results for successive SMALL cups of water dispensed. Top Left: The temperature of the reservoir was observed to rise as cups of water were dispensed reaching nearly 80 °C. Top Right: The time taken to dispense a cup of water decreased from about 50 s to about 20 s. Bottom Left: The maximum temperature recorded in the cup into which the water was dispensed. Bottom Right: The estimated efficiency of water heating. The average efficiency is only 25%.

Click on image for a larger version. Results for successive LARGE cups of water dispensed. Top Left: The temperature of the reservoir was observed to rise as cups of water were dispensed. Top Right: The time taken to dispense a cup of water was about 40 s. Bottom Left: The maximum temperature recorded in the cup into which the water was dispensed. Bottom Right: The estimated efficiency of water heating. The average efficiency is about 80%.

Conclusions

Having observed the device in operation and measured its performance, I think I can now see how it works.

I think that the HotCup always boils the same amount of water in a boiling chamber – a mini kettle-within-the-kettle. The device uses the pressure built up within the chamber to push out the boiled fluid, and then discharges the unused hot liquid back into the reservoir.

By analysing the inefficiency of the device as a function of the amount of water dispensed, I estimated the volume of the boiling chamber to be approximately 400 ml.

Click on image for a larger version. Plotting the inefficiency as a function of dispensed volume, I estimate that the ‘boiling chamber’ within the HotCup has a volume of approximately 400 ml.

The TOP LEFT graphs in the two panels above show that the reservoir temperature rises after each cupful has been dispensed. It is clear that this rise is larger for the small cup (150 ml) dispensation in which most of the hot water (400 ml – 150 ml = 250 ml) is put into the reservoir. I made a model of this – shown as a dotted red line – and this seems to roughly describe the data.

Thermodynamic Reflections

Friends, I have had this device in my house now for a couple of months, and since my wife and I generally boil the kettle for individual cups of tea, it is quite convenient.

But as a calorimetric thermodynamicist, I must confess that after making these measurements I was at first disappointed. But on reflection, the performance is actually not so bad.

The inefficiency is the exactly the same as if one used 400 ml of water in a kettle to prepare a single beverage. This volume is close to or below the minimum fill level for many kettles. And so although these results look bad, they are probably no worse than using a kettle.

However, if my wife and I both wanted to drink tea at the same time, or if I wanted to boil larger volumes of water for cooking, a conventional kettle would be more efficient.

Perfect Solar Days

Friends, March may have been depressingly dull, but the start of April has been upliftingly sunny. And Tuesday April 4th was a perfect solar day.

Perfect solar days are days in which the sun shines unremittingly from dawn until dusk, with not a cloud in the sky: such days are rare: Typically there are around 10 per year and I try record the solar PV generation from each one. I do this using data from the Tesla App which records solar generation every 5 minutes via a current transformer (CT) clamp on the cable from the inverters.

The graph below shows 12 perfect (or near perfect) solar days from 2021 and 2022. The days are not evenly spaced because I can’t control the weather!

Click on image for a larger versions. Graph showing the daily hour-by-hour generation for a series of near-perfect solar days in 2021 and 2022.

Attentive readers will recall that in November 2022 I had eight extra solar panels installed on the east-facing roofs of Podesta Towers (link). I had expected that these would contribute nothing to solar generation in winter, but that generation would be significant in spring, summer and autumn.

The graphs below show the generation profile for each day for which there is reasonably well-corresponding day from before the new panels were installed. As expected the new generation is very weak in December and January, but by April has grown significantly.

As expected the extra generation from the panels on the North and East is in the morning. Happily, the maximum power looks like it will peak in summer at less than 5 kW – the maximum rating of the cable between the inverters and the consumer unit.

Click on image for a larger versions. Graph showing the daily hour-by-hour generation for a series of near-perfect solar days in 2021 and 2022.

Overall

The aim of the installing the new panels was to create extra generation in the spring and summer which would hopefully be enough to keep the house off-grid for 6 months. This goal has been hampered by the dullness of March, but things seem to be returning to normal now. However the weather is still cold enough to require the heat pump to stay running for another month or so, increasing domestic consumption.

The graphs below all have a vertical axis of kWh/day and the data are smoothed to highlight trends: They compare:

• Domestic consumption and solar generation. One can see that solar generation is rising to be roughly equal to domestic consumption and should soon exceed it.
• Domestic consumption and Grid Consumption. In winter, the two are practically equal, but in spring, grid use is falling as we rely more on solar energy.
• Net Grid Consumption/Export and solar generation. As solar generation rises  we have become net exporters of electricity.

Click on image for a larger versions. Graphs variation of Daily Consumption, Daily Grid Consumption, Net Grid Consumption and Solar PV generation, all expressed in units of kW/day.

 

Another Heat Pump Spreadsheet: Beyond the Rule of Thumb

Friends, around a year ago I wrote an article and made a YouTube video about using a ‘Rule of Thumb’ for estimating the size of heat pump required to replace a gas boiler in a dwelling.

The ‘Rule of Thumb’ is splendidly simple: one just divides the previous year’s gas consumption by 2,900 to give the heat pump size in kilowatts. So if a dwelling used 10,000 kWh of gas the previous year, then one would estimate that it needed a 3.4 kW heat pump. The YouTube video explaining why the rule works has been watched an astonishing 37,000 times, and many people have left comments telling me they found the rule helpful and accurate.

The basic reason the rule works is because (a) most gas consumption is spent heating homes (rather than heating hot water or food) and (b) the climate of the southern half of the UK does not vary that much. The rule of thumb uses gas consumption as an indicator of the amount heat which enters a dwelling and uses climate data – in the form of heating degree days – to estimate how cold it gets in a particular locale. You can find a detailed description here, here, here and here!

But one or two people have told me that it gave them answers they thought were quite wrong. It turned out that these people often only put their gas boilers on for an hour or two per day, and so most of the time their dwellings were unheated. Alternatively, some people – particularly with families – used a lot of hot water every day – and so this formed an unusually large fraction of their gas consumption.

So I thought it would be nice to develop something just a little more sophisticated than the ‘Rule of Thumb’ that would take account of some of these factors. I did this last summer and sent it to an academic expert for feedback. The feedback was devastating: they basically told me that everything was wrong. And despite trying to modify the spreadsheet to meet their criticism, they seemed unmollified. So, shaken, I abandoned the idea for a while.

But recently I have been thinking about the idea again and decided that in fact I thought the spreadsheet was useful after all, and that it could also help with one other problem: sizing of radiators.

The reason I think this endeavour is important is that people who are thinking about installing heat pumps have faced a campaign by the fossil fuel industry and their knowing (and unknowing) shills, a campaign designed to instil fear, uncertainty and doubt (FUD). Every year of delay in installing heat pumps keeps the profits of fossil fuel companies healthy, and impoverishes the world in which our children will have to live.

This is not to say that there are not legitimate questions and uncertainties about installing a heat pump. So this spreadsheet is a transparent tool that can help people make rational choices and – I hope – help them to overcome the FUD.

• You can download the spreadsheet here:Link
• Spreadsheet updated to version 6.01 on 3/3/23

I have tried to make the spreadsheet Good For Nothing™ 🙂 . But mistakes will have slipped through: if you find one, please accept my apology in advance and let me know in the comments.

Spreadsheets Galore

The ‘spreadsheet’ is actually six spreadsheets linked together in an Excel™ Workbook. Each Spreadsheet has its own ‘tab’. Six spreadsheets may sound daunting, but really this could all be on one spreadsheet. Using several sheets actually makes things simpler.

Click on image for a larger version. The introductory ‘tab’ of the Excel™ Workbook showing the other 6 tabs. Users are recommended to save the downloaded copy and experiment with a ‘working copy’.

• The first spreadsheet helps people estimate the average temperature in their dwelling, and also the maximum temperature they like.
• The second spreadsheet helps people estimate the amount of hot water they use.
• The third spreadsheet uses the ideas behind the Rule of Thumb, but modified to take account of the estimates on the first two spreadsheets. It suggests a likely required size of heat pump and a few other building parameters that specialists might find interesting.
• The fourth spreadsheet allows people to see how the area of radiators and the type of radiators affects how hot the water flowing through the radiators needs to be in order to keep their home at the maximum temperature they desire.
• The fifth spreadsheet allows people to make more detailed calculations based on the number, size and type of radiators in their own dwelling.
• Finally, the sixth spreadsheet summarises the results from the previous spreadsheets and estimates the likely savings in cost and carbon dioxide emissions.

Let me show you each spreadsheet works in a little more detail.

Sheet 1: Household Temperature

Click on image for a larger version. Spreadsheet designed to allow a user to indicate the temperature changes in their home throughout a typical winter day.

Click on image for a larger version. As above, but showing a different temperature profile.

On this tab of the workbook, one can specify how the temperature varies inside a dwelling on a typical winter day. There are four times periods and each one can be set to one of three user-chosen temperatures.

The spreadsheet then calculates:

• The average temperature in the dwelling which is useful for calculating the average heat loss and hence energy consumption.
• The maximum temperature required which determines the required power of a heat pump able to heat the dwelling.

Sheet 2: Domestic Hot Water

Click on image for a larger version. Do you know how much hot water your dwelling uses each day.

I have been told that – in the absence of any other information – a good guess for the amount of gas used to heat hot water in a household is 3 kWh per person per day. This tab uses this figure to estimate how much of the annual gas usage is for domestic hot water.

If a user somehow has a better estimate, they can use their own estimate instead.

Sheet 3: Main Calculation

Click on image for a larger version. This ‘tab’ carries out the main heat pump size calculation.

This tab carries out the same calculation as the Rule of Thumb but now with a little more information about a particular user’s dwelling. It incorporates the data from the first two tabs on average and maximum temperatures and domestic hot water usage. It asks the user for the annual gas consumption and their approximate location (within around 100 miles). The location is used to estimate how cold the weather is likely to have been based on analysis of the heating degree-day records from 21 locations in the UK and Ireland.

Click on image for a larger version. This tab carries out the main heat pump size calculation.

The spreadsheet then estimates several parameters that characterise the level of thermal insulation of the dwelling and – most importantly from the perspective of this article – the heat pump size required for the dwelling.

Sheet 4: Radiators

Click on image for a larger version. This tab allows users to see how the area of radiators, and the type of radiators affect the performance of the heating system.

This tab allows users to see how – in general – the area of radiators, and the type of radiators affects the performance of the heating system. First one sets a maximum flow temperature for the system – this is the temperature of the hot water as it enters the radiators.

Heat pumps typically use weather compensation, which means that when the weather is cold, the heat pump increases the temperature of the water flowing in the radiators. For a heat pump the maximum flow temperature required in the coldest weather should ideally be below 50 °C.

Click on image for a larger version. This tab allows users to see how the area of radiators, and the type of radiators affect the performance of the heating system.

The table above shows – for the heat pump size calculated on the previous tab – what combinations of total radiator area and types of radiator will be able to heat the dwelling adequately.

For heat pumps to work at their very best, the temperature of the water flowing in the radiators should be as low as possible while still allowing the dwelling to be adequately heated.

In the example above the heat pump needs to transfer 5,296 watts of heating power to the dwelling.

• The table shows that this would require 9 square metres of single-panel/single-fin (Type 11) radiators, but the same heating could be done with just 5 square metres of double-panel/double-fin (Type 22) radiators.
• Alternatively one might use 9 square metres of double-panel/double-fin (Type 22) radiators because this would require a flow temperature in the radiators 39. 8°C rather than 49.2 °C – and this reduced flow temperature would result in increased heat pump efficiency, and lower running costs.

Sheet 5: More Radiators

Click on image for a larger version. This tab allows users to see how the number, size and type of radiators in their dwelling affect the performance of the heating system.

The previous tab allowed users to see in general terms how the area of radiators, and the type of radiators affect the performance of the heating system. On this tab a user can input the size (width and height) and type of their existing radiators and see whether – for the flow temperature set on the previous tab – they can release enough heat into their dwelling.

Click on image for a larger version. This TAB allows users to see how the area of radiators, and the type of radiators affect the performance of the heating system.

By putting in data on their existing radiators – the radiator type is input via a drop-down menu – the heating power of each radiator is calculated at the maximum allowed flow temperature. The heating power of each radiator is then summed up to see if the assemblage of radiators in the dwelling is capable of providing enough heating power to keep the dwelling warm on a cold day. This is shown as a percentage on a bar chart.

If a figure of 100% cannot be reached with existing radiators, then users can see whether 100% can be achieved by either adding radiators, or replacing radiators with larger ones, or radiators with more panels and fins.

Sheet 6: Summary

Click on image for a larger version. This tab summarises the results from the previous tabs and compares the cost and carbon dioxide emissions of systems using a gas boiler or alternatively, a heat pump.

Nearly finished! This summary tab collects together the conclusions from the previous spreadsheets. If a user enters the cost of their electricity and gas, the spreadsheet will then estimate the likely running costs of a gas boiler and a comparable heat pump.

The annual costs of the gas installation are estimated based on the users estimate of their own gas consumption. The running costs of the heat pump installation are based on an estimated seasonal coefficient of performance (SCOP).

The coefficient of performance (COP) of a heat pump is a measure of the efficiency of a heat pump measured over a period of typically an hour, a day or a week. In mild weather, the COP will be high (perhaps 4) and in cold weather the COP will be low (perhaps 2.5). SCOP measures the efficiency of a heat pump averaged over a whole year.

If a user experiments with different flow temperatures they will find that the lower the maximum flow temperature they plan for, the higher the achievable SCOP and the lower will be their running costs. Typically users will find that with the relative costs of electricity and gas as they are now (April 2023) at a ratio of roughly 3 to 1, a heat pump installation will commonly be a little bit cheaper to run than a gas boiler, but the difference is not very large compared with the capital cost of the installation.

Click on image for a larger version. This tab summarises the results from the previous tabs and compares the cost and carbon dioxide emissions of systems using a gas boiler or alternatively, a heat pump.

And finally – and this is the point of the entire endeavour – the spreadsheet makes a comparison of the carbon dioxide emissions from a dwelling heated either with a heat pump or a gas boiler. It is here that the entire point of running a heat pump becomes clear: carbon dioxide emissions from a heat pump installation are generally around 75% lower than an equivalent gas boiler. And that’s why this matters.

Click on image for a larger version. Graph showing the annual emissions of carbon dioxide from a gas boiler and an equivalent heat pump installations.

Solar PV Variability

Friends, March 2023 has been dull. Really. Really. Dull. I long for sunshine.

How dull has it been? The chart below shows the average daily solar PV generation (kWh/day) from our roof since November 2020. The data from 2021 and 2022 correspond to generation from 12 solar panels. But in November 2022 I installed an additional 8 panels. However, despite the 8 additional panels, generation in March 2023 has been less than in March 2022!

Click on image for a larger version. Chart showing the average daily solar PV generation (kWh/day) since November 2020. With just two generating days to go, March 2023 has produced less solar PV than March 2022, despite the installation of 8 extra panels!

Of course, I have asked myself if the new panels are working properly, and they are. On the few days when sunshine has penetrated the gloom, peak generation has exceeded 5 kW – about 2 kW more than we ever managed previously.

This persistent dullness means that our household is not yet ‘Off Grid’ for the summer. The graph below shows running averages of domestic consumption and solar generation both expressed in kWh/day. It shows that average consumption still exceeds average generation. But hopefully, April will bring better weather.

Click on image for a larger version. Graph showing daily solar generation and daily electricity consumption since March 2021, both expressed as kWh/day. The data are averaged over ±1 week, and when the average solar generation exceeds average consumption, the house can go ‘off grid’.

Is such a large variation normal?

Is such a large variation normal? To answer this, I went to the European Sunshine database (PV-GIS) which has software that can reconstruct the sunniness (technically, the solar irradiance) at any point on the Earth’s surface, hour-by-hour over the period from 2005 to 2020. Wow!

I selected my location in Teddington and downloaded monthly data for the full period (see below). The database offers irradiation data in many forms, and if one is interested in the absolute value of the irradiance, it’s important to pick the correct dataset. But I was only interested in variability. The data come in the form of kWh of irradiance per square metre.

Click on image for a larger version. The graph shows monthly averages of irradiance in Teddington expressed as (kWh/month/m^2) It is clear that not every year is the same.

First of all I evaluated the year-to-year variability, which was considerable – roughly in the range ± 6% around the average. The 6% figure is half the range seen in the data – i.e. half of [the maximum (1,158) minus the minimum (1,024)] divided by the average (1,079).

Click on image for a larger version. The graph shows annual averages of irradiance in Teddington expressed as (kWh/year/m^2). Also shown are the average value and the maximum and minimum values.

But I wanted to look at the variability of a single month – such as March – from year-to-year. This data is shown below:

Click on image for a larger version. The graph shows average irradiance in Teddington in the month of March expressed as (kWh/year/m^2) across the period 2005 to 2020. Also shown is the average value.

The fractional variability of this monthly data is much larger the fractional variability of the annual data: the March data typically fall in the range ± 25% around the average.

So if last year had been a particularly bright March – at the top end of the variability – and this year March turned out to be historically dull – as it seems to be – then there is nothing odd about generation this March being up to 40% lower than last year lower i.e. falling from 125% to 75% of the monthly average.

Variation at almost this level is expected because there are only 31 days in March and 365 days in a year. For so-called ‘normally-distributed’ data one might expect the variability of the monthly data to be larger by a factor of √(365/31) i.e. a factor 3.4 . So one might expect around 6% × 3.4 ~ ±20% monthly variation. But 25% is more than 20%. Was this significant?

To check this I examined the variability of different months. Was each month as variable as every other month? Or was March particularly susceptible to large variability?

Click on image for a larger version. The graph shows average irradiance in Teddington in each month of the year expressed as (kWh/year/m^2) across the period 2005 to 2020. Also shown are the maximum and minimum values found across the 16 year range.

I extracted the data for each month and noted that the maxima and minima were not quite symmetrically arranged around the average, with the effect being particularly clear in May (Month 5). Then from this data I calculated the fractional variability of the irradiance in each month.

Click on image for a larger version. The graph shows fractional variability of monthly averages of irradiance in Teddington in each month of the year across the period 2005 to 2020.

So over the period 2005 to 2020, it appears that February and March have historically shown the largest variability, with late summer months showing the least variability.

Reflections on the data

There are many cases when reflecting on a data set one sometimes concludes that it tells one exactly what one might reasonably have expected. This is one such occasion.

Based on ±6% annual variability, we might expect roughly ±20% monthly variability – entirely due the way random numbers work. And this is roughly what we see. But we also see a trend through the year from February to September of reducing variability.

This is really just telling us that the early or late “arrival of Spring” makes a big difference to the weather. Whereas, as the year progresses, the progression through Spring, Summer and Autumn has a certain inevitability to it.

Or alternatively, it could be that the period 2005 to 2020 is not long enough to be a historically representative period.

However, based on these 16 years of data large (roughly 40%) changes in irradiance – and hence Solar PV generation – are normal, and not uncommon in February or March.

So I will just have to wait a little while longer for the sunshine.

 

The Gas Man Cometh… for the last time

Friends, today was a special day for me. Today, the gas man came and disconnected my house from the gas grid. We haven’t used any gas for a year now – but being physically disconnected from the grid just feels sooooo good.

The gas grid

The gas grid is an international network of pumps and pipes constructed on a scale which is hard to grasp. In extent, it sprawls across Europe – take a look at this astonishing map. And locally, it extends into most individual dwellings in the UK.

When I consider the astonishing magnitude of the decades-long endeavour required to construct such a network, two thoughts occur to me: one depressing and the other uplifting.

Depressing thought

Depressingly, the people who have invested in this network will fight tooth and nail to keep extracting ‘value’ from it.  To these people – which probably includes my pension fund – the fact that the toxic gas they transport is leading to climate change is of no interest. In their perception, Climate Change is indeed an existential threat, but not because it is a threat to humanity. Instead they see Climate Change as an existential threat to their business model. They have no corporate interest in humanity.

The businesses that operate on this grid extract value from shipping stuff through it. And if governments restrict their right to sell methane – so-called ‘natural’ gas – because of its climate impacts, then they will see shipping hydrogen as an opportunity, despite its unsuitability for domestic heating.

Because they take no responsibility for the climate impacts of their business, they will use their power to lobby on behalf of using hydrogen or hydrogen-blended with methane. This is just an insidious attempt to try to continue to extract ‘value’ from their network: it is not based on rapidly reducing carbon dioxide emissions. Rather their aim is to prolong methane extraction which they will process, at a cost, to produce hydrogen.

The uplifting thought

The uplifting thought is that the colossal gas grid was constructed over decades, one project at a time. And this gives me hope. Because every new wind or solar farm, every new battery storage plant, every new electricity grid interconnection is another step in the construction of the infrastructure for renewable energy.

I believe that eventually we will look back with horror at the idea of delivering toxic, asphyxiant, explosive gas directly into people’s homes. Gas which people burned for cooking, emitting toxic irritant combustion products directly into their kitchens. And we will be appalled at the idea that we ever thought it acceptable to allow the average UK dwelling to emit more than  two tonnes of carbon dioxide every year: TWO TONNES of a gas which is changing the climate of Earth.

Friends, the future is coming, one gas-meter-removal at a time.

Assessing Powerwall battery degradation: End of Winter of 22/23

Friends, three months ago in December 2022, I wrote about my technique for estimating the degradation of the capacity of my Tesla Powerwall 2 battery (Link).

The idea was to consider data from days in which the battery is charged to 100% capacity at night, and then discharges fully to 0% during the day. This only happens in winter when household demand is high and solar PV generation is low. After correcting for any solar generation one can make a reasonable estimate for the practical working capacity of the battery.

Click on diagram for a larger version. Illustration of day in which the Powerwall fully discharged.

We have now had another 60 days during which the battery discharged fully and using the same technique I described previously, I have re-evaluated the degradation of battery capacity. The results are shown below in two graphs: it’s the same data in both graphs they are just plotted on different times scales.

Taking all the data into account, the trend line suggests that battery capacity is degrading at roughly 2.6% per year. Since the battery has a nominal capacity of 13.5 kWh, this corresponds to a loss of capacity of 0.35 kWh/year.

Click on image for a larger version. Full discharge capacity plotted versus date. The blue dots show all the data and the dots surrounded with a pink circle show data with solar contribution during the day. The trend line suggests capacity is being lost at 2.6%/year.

The Powerwall was installed in March 2021 and if the degradation were to continue at 2.6%/year in future years then the battery would lose 10% of its capacity by the winter of 2024, and 20% of its capacity by the winter of 2028.

Click on image for a larger version. Full discharge capacity plotted versus date. The blue dots show all the data and the dots surrounded with a pink circle show data with solar contribution during the day. The trend line suggests capacity is being lost at 2.6%/year.

What to do?

Nobody wants their £10,000 battery to be losing capacity. But there is very little I can do about it! It’s inherent in the nature of the batteries and of the charge/discharge cycles they experience.

One option would be to prevent the battery from fully discharging by forcing it to retain, say, 1 kWh in reserve. However, while this might reduce the rate of degradation, it would deprive me of the battery capacity that I was hoping to preserve!

So my plan is to do nothing. If the degradation continues at this rate I will still have a 10 kWh battery in 2031 – and that’s still a very useful size of battery.

If I feel the need for more storage, my thought is that it would probably eventually make sense to upgrade one of my solar PV inverters to be a hybrid inverter, and then add extra battery capacity in the loft. These batteries will have the Lithium Iron Phosphate chemistry that is supposed have very low degradation. This option would likely cost much less than buying a replacement – or additional – Powerwall.

Of course, by the time this becomes important Powerwalls may have fallen in price and be readily available (!). Or the use of batteries in vehicles for domestic storage may have become commonplace.

In short, this is tomorrow’s problem.

 

Tariff Calculation Spreadsheet

Friends, as you may or may not know, Saturday night is the night of week I like spend documenting large spreadsheets. Lucky me!

In this article I will be describing how to use the spreadsheet I have developed over the last couple of weeks and used in the last couple of articles. The spreadsheet allows one to estimate the likely costs of using particular electricity tariffs – the Octopus GO, FLUX and COSY tariffs – if your dwelling has a domestic battery and solar PV panels. My hope is that it will help people make rational choices about which option is best for them.

Download

The Excel spreadsheet can be downloaded from this link [link updated to v3.2 on 23/3/2023], If you are downloading this macro-enabled file on a Windows computer, then the macros will probably be blocked by default. To change this you may need to first close the file in Excel, then right-click on the file’s icon and select the ‘Properties’ pane. Here you should see a tick box labelled “unblock”. If you unblock the file then it should work correctly.

Please note, the spreadsheet comes with no guarantee of anything at all, and it can at times be very slow to re-calculate.

Structure

The spreadsheet consists of two parts.

• At the top are several boxes that set the parameters of the simulation, and which show the results. I think of this as a ‘dashboard’
• Below this are 8,760 rows, one for each hour of the year. The spreadsheet proceeds through the year hour-by-hour simulating the flows of electricity from solar PV panels and the grid, into and out of batteries and your dwelling.

Throughout the spreadsheet, cells which are ‘inputs’ i.e. cells that you might reasonably want to change, have a yellow background with red text. Cells which are ‘outputs’ i.e. which contain the results of calculations have a red background with white or yellow text.

Click on image for a larger version. The visual appearance of ‘inputs’ and ‘outputs’.

The Dashboard: Overview

Click on image for a larger version.

The dashboard has controls in four regions.

• Regions 1 & 2 are about the tariff being simulated and the prices of the tariffs in each of their cheap, medium and high periods.
• Region 3 sets the parameters of the battery and the charging strategy, the amount of solar PV generation, and the likely household load.
• Region 4 contains the results of the simulation.

The Dashboard: Tariff Section

Click on image for a larger version.

After selecting the tariff to be investigated in the drop down menu, the selected tariff will appear in the box on the far right.

The prices of the different tariff stages can be changed if you desire.

The timings of the tariffs cannot be changed on the spreadsheet. They are set in a Visual Basic macro with the code below. If you understand this sort of thing then you can see how you could adapt the spreadsheet to a different set of tariff timings.

Click on image for a larger version.

The Dashboard: Main Settings

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The settings for the simulation have four main parts.

The Battery Settings are as follows

• Battery capacity describes the amount of electrical energy the battery can store.
• Round trip efficiency accounts for the energy lost as electricity is stored in the battery and then later drawn from the battery.
• Charge Rate is the rate at which battery charges. This limits how much electricity can be stored in the battery over a given period.
• The initial state of charge is the assumed state of charge at midnight on the 1st January.

Click on image for a larger version.

The cells referring to summer and winter should really be in the neighbouring box about charging strategy [Edit: they have now been moved]. Why are they there? For some systems, it can be sensible to switch between different charging strategies through the year, depending on the amount of solar energy available. For my own system:

• In winter I charge the battery at night using cheap rate electricity and the battery then runs down during the day.
• In summer, there is no need to charge at night because the battery is charged for free during the day by solar PV electricity.

The two boxes allow one to choose the days of the year on which to switch strategy.

In the ‘Grid Charging Strategy‘ box one can choose between charging when electricity is cheap, and/or charging in the hour before electricity becomes expensive. Either option can be chosen to be active in summer, winter or both.

In the solar factor box, one can set the expected amount of solar generation expected. This is generated by scaling the hour-by-hour solar data by the factor shown in the box.

Note that selecting a target amount will give an accurate result if the average solar generation from 2005 to 2016 is selected in the drop down menu at the bottom of the box. If one selects solar data from a particular year then the amount of generation will vary in line with that years variable output.

Click on image for a larger version.

The final box simulates how electricity demand from the household changes through the year.

Click on Image for a larger version.

Demand consists of two components: a steady consumption every day, and a component which peaks in mid-winter simulating the use of a heat pump.

The length of winter depends on a setting from 1 to 5 as shown in the figure below.

Click on Image for a larger version.

How the simulation works.

Each row of the spreadsheet from row 48 downwards calculates the state of charge of the battery, the household demand, and the solar PV according to the settings on the dashboard.

The simulation works row-by-row proceeding hour-by-hour through the year. The columns are as follows

• A: Index
• B: The day of the year expressed as a decimal day.
• C: The hour of the day, used for calculating the appropriate tariff
• D: The season of the year WINTER or SUMMER according to dashboard settings
• E: The Tariff Rate (cheap, medium, or high) determined by the Visual Basic code described above.
• F: G: & H: The hourly background & variable consumption – and their total.
• I: The daily average of the demand
• J: The time of day expressed as a fraction of a whole day
• K: Blank
• L: The 3-day running average of solar generation (used for plotting)
• M: The hour-by-hour solar data selected in the drop down menu in the SOLAR box. This is looked up from the data table in columns AE to AQ
• N: Modified demand: this is the difference between current demand and the amount of solar PV currently being generated.
• O: The amount of energy delivered to the battery (if positive) or drawn from the battery (if negative). This is calculated according to the current state of charge of the battery.
• P: The amount of energy drawn from the grid (if positive) or sent to the grid (if negative). This is calculated according to the current state of charge of the battery.
• Q, R, S, & T : Imports: If column P indicates that electricity has been imported, columns R, S and T list the amount of it in each tariff charging rate: these columns are then totalised at the top to calculate the annual amount to be paid.
• U, V, W, & X : Exports: If column P indicates that electricity has been exported, columns U, W and X list the amount of it in each tariff charging rate: these columns are then totalised at the top to calculate the annual amount of revenue accrued.
• Y: Hourly cost of grid imports
• Z: Hourly amount due from grid exports
• AA: Depending on the charging strategy this is when the battery charges from the grid. Household consumption is also met by the grid during these periods.
• AB: The amount of electrical energy sent to the battery.
• AC: The current state of charge of the battery.
• AD: Blank
• AE to AQ. Hourly solar data for the years 2005 to 2012 downloaded for the EU Sunshine database for my 4,000 kWh/year solar system in Teddington.

Graphs

Click on Image for a larger version.

Scrolling down  the spreadsheet will show four graphs which can be helpful in understanding what is happening.

The first graph shows three quantities charted across each day of the year:

• The 3-day average of the selected solar data
• The daily household demand
• The capacity of the battery

The second graph shows the state of charge of the battery charted across each day of the year.

The third and fourth graphs show the state of charge of the battery during a typical summer and a typical winter day.

More Tariff Calculations: GO, FLUX, COSY and more

[There is a follow up article to this one with a better spreadsheet available here]

Friends, in the previous article I estimated the annual cost of running a household with various “time-of-use” (TOU) tariffs i.e. bargains with the electricity company in which the price of a unit of electricity varies through the day.

The article seemed to strike a chord with many people asking several “But what if..?” questions. This article is an attempt to answer some of those questions.

The reason that I think this is an important issue as TOU tariffs are likely to become more popular.

Why? Because getting people to avoid consuming during peak hours is cheaper and greener than building a new power station to meet that demand. It’s also cheaper and greener than using gas in an existing power station to meet that peak demand.

And as domestic batteries and solar PV installations become ever more common, avoiding consumption at peak times has become more achievable for ‘ordinary’ people.

But it has also become all but impossible to work out which TOU tariff will be cheaper (or greener). And this puts us in danger of perpetuating the confusopoly that currently exists in energy tariffs.

The only way I know to work out which tariff is cheaper is to simulate an entire year hour-by-hour with realistic consumption, solar PV and battery storage. And that is exactly what I did: please read the previous article if you want to familiarise yourself with that.

Click on image for a larger version. The concept of a Confusopoly was invented by Scott Adams.

When I began to write this article, I planned to look at

• Different Tariffs (Octopus’s GO, COSY, and FLUX tariffs – alongside the standard variable tariff)
• The effect of solar generation
• The effect of battery storage capacity
• The effect of a small (10 kWh/day) or a large (20 kWh/day) domestic consumption
• Seasonal Strategies

However as I began this program of work I realised I had bitten off more than I could chew.

So below I will look at some of these issues, but people’s requirements are so specific that I thought the best way to be helpful was to make the spreadsheet easier to use and that is what I have tried to do.

The Excel spreadsheet can be downloaded from this link. If you are downloading this macro-enabled file on a Windows computer, then the macros will probably be blocked by default. To change this you may need to right-click on the file and select the ‘Properties’ pane. Here you should see a tick box labelled “unblock”. If you unblock the file then it should work correctly. The next article will describe how the spreadsheet is structured.

One thing I won’t be looking at is the effect of charging electric vehicles. Sorry: I don’t have experience of this.

Tariffs

In this article I will investigate four tariffs: Octopus’s so-called COSY, GO, and FLUX tariffs, and a standard variable tariff (SVT) – currently (February 2023) set at 34p/kWh. The assumed costs and times of operation are shown in the figure below.

Click on Image for a larger version. Illustration of the variation in price through the day for electricity imports (left) and exports (right) on the Octopus Go FLUX and COSY tariffs. Also shown as a dotted line is current standard variable tariff (SVT).

The daily-average import prices of the FLUX and COSY tariffs are about 34p/kWh, the same as the SVT, but the average GO tariff is 37p/kWh.

The daily-average export prices of the FLUX and COSY tariffs are 22p/kWh and 15p/kWh, the same as the SVT, but the average GO export price is just 4p/kWh.

Solar PV and Demand

The standard demand that I used last time was based on my own home. It consisted of a baseload of 10 kWh/day and then a seasonally variable heating demand peaking at 15 kWh/day. The solar PV that I used previously was based on my own home generation of just under 4,000 kWh/year. But of course these are only relevant to me – and there are many combinations relevant to other people.

For example, the figure below shows four combinations of high and low demand and high and low solar generation. It’s clear that these are very different situations and that the likely cost savings will be very different in each scenario. And this does not include changing the size of the battery.

Click on Image for a larger version. Four scenarios showing the variation of daily demand and daily solar PV generation through the year. The upper graphs show high demand and the lower graphs show low demand. Solar PV generation varies from just under 2,000 kWh to just under 8,000 kWh. Also shown as a dotted line is 13.5 kWh of battery storage available in a Tesla Powerwall.

Pre-discussion

Before looking at any results it is important to understand the ways in which it is potentially possible to generate savings compared to the standard variable tariff (SVT).

• Using the battery alone it is possible to generate savings by avoiding peak tariffs.
• Using solar alone it is possible to generate savings by using solar electricity instead of drawing electricity from the grid. But solar PV doesn’t match demand minute-by-minute, sometimes oversupplying and sometimes undersupplying.
• Using battery and solar, can generate savings in several ways:
  • By avoiding peak and standard tariffs
  • By improved self-utilisation of solar electricity
  • By exporting electricity.

Bearing these factors in mind, let’s look at some results.

Charging Strategies with a 13.5 kWh Battery: No Solar PV

I compared GO, COSY and FLUX to the SVT without considering any solar PV generation, but instead I used four different charging strategies:

1. No strategy – i.e. the battery is not used at all.
2. Pre-charge the battery for an hour before the peak rate.
3. Charge the battery as much as possible in the cheap rates
4. Pre-Charge the battery before peak rate AND charge the battery during cheap rate.

The SVT for this scenario came to £1,849/year and the four strategies above differed in cost as shown below:

Click on Image for a larger version. Annual savings or extra costs compared to the £1,849 SVT when using different tariffs. This chart shows the impact of using a battery alone with no solar PV. See text for details.

• Not using the battery with COSY and GO costs several hundred more pounds per year. So don’t use one of these tariff’s if you don’t have a battery or solar!
• Pre-charging for one hour before the peak rate resulted in modest savings (~7%) compared with the SVT.
• Charging during cheap rate resulted in big savings on the GO tariff (-39%), modest savings on the FLUX tariff(-20%), but a significant increase on the COSY tariff (+17%).
• Pre-charging and Cheap Rate charging together saves a lot of money with GO, only a little (12%) with FLUX and is more expensive with COSY.

At first I thought the simulation must be in error to for COSY to cost more than SVT. But looking at the charging details I saw that in summer (when demand was lower) using the ‘charge when cheap’ rule led to overcharging on COSY because it has two cheap rates just 3 hours apart. This could be avoided with smarter programming.

My conclusion from this is that the only way to significantly save money when using a battery alone is with a tariff such as GO which offers very low prices (12p/kWh) and a large battery able to store almost a whole day’s consumption.

Charging Strategies with modest solar PV and two sizes of batteries

Next I considered a situation with a modest solar PV installation (~2000 kWh/year corresponding to ~ 6 south-facing panels) and either a small (5 kWh) or a large (13.5 kWh) battery. I then compared the different charging strategies I used in the previous section with each of the GO, COSY and FLUX tariffs to the SVT with no solar PV.

Click on Image for a larger version. Annual savings or extra costs compared to the £1,849 SVT when using different tariffs. This chart shows the impact of using a small battery (left) or large battery (right) with a small solar PV installation. See text for details.

Comparing these results with the previous ‘No Solar’ results, it is immediately obvious that – with or without a battery – even a modest solar PV installation saves a serious amount of money. The average saving from the ‘No Battery’ scenario is 33% compared to the SVT.

Pre-charging from the grid for one hour before peak rate results in extra savings on all tariffs averaging 41% independent of battery size.

Moving to a larger battery (13.5 kWh vs 5 kWh) is only really of significant benefit on the GO tariff (56% vs. 33%). For the FLUX tariff the extra battery capacity increases savings only from 33% to 42%.

Annual Variability

Next I considered the effect of annual variability. I estimated the annual cost for a scenario similar to that in my home using the GO and FLUX tariffs and solar data for each year from 2005 to 2016.

Click on Image for a larger version. Top: Annual variability in solar PV generation (kWh/year). Middle: Annual variability in estimated year cost using the GO tariff. Bottom: Annual variability in estimated year cost using the FLUX tariff. See text for details.

The year-to-year variation in solar PV yield was roughly ±10% over the years 2005 to 2016. Unsurprisingly, good solar years led to lower overall costs on both GO and FLUX and vice versa.

But there is a curious feature in the calculations. Using the FLUX tariff the average cost over the individual years 2005 to 2016 was similar to the cost calculated using the average solar data. But for the GO tariff this was not the case. Instead, the average cost over the individual years 2005 to 2016 was much higher than the cost calculated using the average solar data.

I am not sure why this is, but it may be a feature of the fact that the averaged solar data has less variability than data for any individual year.

Other scenarios 

At this point I realised that I was becoming overwhelmed. 

I realised that there was no way to systematically summarise the results of using different tariffs across all the possibilities of demand, solar PV, tariff and charging strategy. So rather than trying to calculate everything myself, I resolved to tidy up the spreadsheet and make it reasonably suitable for other people to use. The dashboard of the revised Version 3 is shown below. In the next article I will describe how to fill out the spreadsheet.

The Excel spreadsheet can be downloaded from this link. If you are downloading this macro-enabled file on a Windows computer, then the macros will probably be blocked by default. To change this you may need to right-click on the file and select the ‘Properties’ pane. Here you should see a tick box labelled “unblock”. If you unblock the file then it should work correctly.

Click on Image for a larger version. Image of the dashboard from the revised spreadsheet for evaluating the costs of different tariffs with different demand, generation, and storage scenarios.

Summary

I compared GO, COSY and FLUX tariffs to the SVT in a couple of scenarios. My conclusions are that:

• Using a battery alone is only really valuable if one uses a big battery to download very cheap electricity.
• However, even modest amounts (e.g. 2,000 kWh) of Solar PV can be very beneficial, and a battery increases the savings possible still further.
• Because the average solar data has less variability than the solar data from any individual year, some tariff’s may not generate a typical cost when using the averaged solar data.

Beyond this, I’m afraid you will need to do these calculations for yourself. More details in the next article…

 

Tariff Calculations: Octopus GO versus Octopus FLUX

[There is a follow up article to this one with a better spreadsheet available here]

Friends, I have struggled to write this article. As you may have noticed, it has taken weeks.

I started writing after I was asked on Twitter about a new electricity tariff called ‘FLUX’ offered by Octopus Energy. Would it be cheaper or more expensive than their ‘GO’ tariff?

It’s a simple question and one that is worth asking. But it is very hard to answer because it involves both hourly details, but also seasonal changes.

I could see how to get at an answer but I have struggled with my waning technical skills. Imagine if you will, an old boxer going in for one fight too many. Finding themselves on the ropes, they face the unavoidable and inevitable reality of their own decline. But bravely they struggle and finish the fight bruised and defeated, but with their dignity in tact. Similarly I have found my prowess with Excel and Visual Basic to be much diminished, but I have somehow battled through.

GO and FLUX

The Octopus GO tariff which I currently use offers 4 hours of electricity for 7.5p/kWh between 00:30 and 04:30 each day. The rest of the time the cost is 40.75p/kWh. Exports of electricity are paid for at 4.1 p/kWh.

During winter, I buy electricity cheaply at night, and then use it during the day. For most of December and January, the battery could not supply the house for the whole day and I had to purchase electricity at full price for a few hours on those days. Overall, the average price I paid was around 12p/kWh in those two months.

Click on Image for a larger version. Illustration of the variation in price through the day for electricity imports (left) and exports (right) on the Octopus Go and Octopus FLUX tariffs.

The Octopus FLUX tariff is more complicated. It has a cheap rate in the night, but only for 3 hours 02:00 to 05:00 and not so very cheap (20.4 p/kWh). But it also has a more expensive rate (47.5 p/kWh) during peak demand hours from 16:00 to 19:00 each day. The rest of the time the cost is 34 p/kWh.

Initially FLUX looks much worse than GO, but the twist is that FLUX offers much higher rates for exporting electricity: 9.4 p/kWh, 22 p/kWh, 36.5 p/kWh for the cheap medium and high rates respectively. These figures should be compared with the miserly 4.1 p/kWh on the GO tariff.

There are so many variable quantities that I really had no idea which tariff would be cheaper. The results of my calculations appear obvious in retrospect, but that didn’t make the calculations any easier! My conclusions are that:

• For small solar PV installations (<~4,000 kWh/year), the big savings from using the night time electricity on GO outweigh the gains from exporting electricity at a good price.
• For large solar PV installations (>~6,000 kWh/year), this situation is reversed: The savings from using the night time electricity on GO are outweighed by the gains from exporting electricity on the FLUX tariff.
• For medium-sized solar PV installations, the two tariffs have similar costs.

Click on Image for a larger version. Estimates of the annual cost of electricity on the Octopus Go and Octopus FLUX tariffs as a function of the amount of solar generation. This applies to my household – see text for details – and assumes a 13.5 kWh storage battery. 

It turns out that, if you have the capability to export lots of solar PV, then the FLUX tariff could result in very low – and even negative – electricity bills. In retrospect, this is sort of obvious, but it was not obvious at all to me when I began.

But the spreadsheet I developed for the calculation allowed me to do the calculations for different sizes of battery and different amounts of solar PV generation, so I’ve investigated the matter a little more deeply below.

Sadly, because the spreadsheet is Macro-enabled, for security reasons I can’t link to it from this blog and many users wouldn’t be able to download it anyway. But if you really want a copy, please ask for a copy in the comments and I will send it to you somehow. But be warned that the spreadsheet is complicated and slooooow. On my computer it takes around 1 minute to evaluate the yearly calculation.

[Update: I think you can download the spreadsheet from this Dropbox Link]

Let me explain how I made the calculation and then I’ll discuss a few more details.

How to work out which tariff is cheaper

To answer this question I wrote a spreadsheet which modelled the electricity use in a household hour-by-hour for an entire year i.e. the spreadsheet has 365 x 24 = 8,760 rows.

For each hour of the year I estimated:

• The household demand: I modelled this as being the sum of a fixed amount each day (10 kWh/day) plus an amount used for heating that peaked in winter at 25 kWh/day.
• Solar PV: Using the EU sunshine database, I downloaded hour-by-hour sunshine data for my house location from 2005 to 2016, and then averaged this to give a typical solar generation year.
• I then worked out how to supply the household demand.
  • If Solar Power exceeded demand, then the excess was used to charge the battery, and if the battery was full, the excess was exported.
  • If Solar Power was less than demand, then the solar power offset the imported electricity.
  • During winter, the battery was fully charged during the cheap hours.
  • I estimated the battery to have a round-trip storage efficiency of 90%.

The spreadsheet and associated VB Macros took days to debug, but here are the results.

Household Demand

The modelled daily demand is shown below along with the EU sunshine database estimate of PV generation amounting to ~ 4,000 kWh/year. Basic electricity demand is ~ 10 kWh/day but peaks at 25 kWh/day in mid-winter due the heat pump, and amounts to ~ 5,000 kWh/year.

Click on Image for a larger version. Graph showing the modelled daily household demand throughout the year, and the 3-day average of solar generation. The solar data is the average of the years 2005 to 2012 estimated for my location and array size in Teddington.

The relationship between Solar PV supply and household demand is such that one needs to use two different strategies depending on the time of the year.

• In the Winter: the battery is charged using cheap rate electricity and discharges during the day – sometimes running out at night.
• In the Summer: there is no night time charging and the battery charges during the day and discharges during the night.

These two modes are illustrated in the graphs below.

The first graph shows a week in winter under the two different tariffs. The four hours of cheap electricity under the GO tariff allows the battery to charge to full, but the FLUX tariff only has three hours of cheap electricity so the battery only charges to around 10 kWh. The battery then discharges to run the household, and is partially supported by the weak solar generation, but typically runs out well before the end of the day.

Click on Image for a larger version. The state of charge of the battery through 7 days in winter. The upper graph shows the Octopus GO tariff which allows the battery to be fully re-charged each night. The lower graph shows the Octopus FLUX tariff which only has enough cheap hours to enable partial filling of the battery. The solar generation is also shown in yellow.

The second graph shows a week in summer. At this time of year, solar generation is enough to run the household and charge the battery during the day, with enough left over for export.

Click on Image for a larger version. The state of charge of the battery through 7 days in summer. Also shown is the solar generation is also in yellow and electricity exports in grey.

The switch between the summer and winter strategies is made on day 90 and day 270 – an arbitrary choice but one which corresponds roughly to the point where the 3-day average of solar exceeds the average household demand. The graph below shows the state of charge of the battery throughout the entire year on both tariffs.

Click on Image for a larger version. The state of charge of the battery through the entire year. The top graph shows the estimate for the GO tariff and the lower graph shows the estimate for the FLUX tariff.

Costs

The simulation runs hour-by-hour through the entire simulated year. For each hour, I estimated how much electricity was imported and exported, and then applied the appropriate tariff rate. This allowed me to summarise the situation for my home as below.

Click on Image for a larger version. Results of calculations of cost of running my household on (top) the GO tariff and (bottom) the FLUX tariff.

Both tariffs offer the possibility of running a home very cheaply: with annualised energy bills in the range £30/month to £50/month. However the GO tariff appears to be cheaper in this simulation £34/month compared with £50/month for FLUX.

The analysis shows why: being able to fill up with electricity at 7.5 p/kWh reduces the cost the electricity dramatically – £298/year versus £648/year. The improved rates for export on the FLUX tariff (£209/year versus £38/year) aren’t enough to make up for that.

Discussion#1: The effect of extra solar generation 

My conclusion is that for me, with my existing 3,800 kWh/year PV installation, the GO tariff is more economical.

But having recently had extra panels installed, this conclusion may not hold. The difference in annual cost between the two tariffs is ~£193 and the typical difference between the FLUX and GO export tariffs is ~ £0.18. So if the new system could export ~1,000 kWh more in summer, then the balance could easily shift.

And indeed, that is what the simulations show. Notice that for 8,000 kWh of generation the annual cost of electricity would be negative i.e. the house would be a bona fide power station!

Click on Image for a larger version. Lower graph: estimates of the annual cost of electricity on the Octopus GO and Octopus FLUX tariffs as a function of the amount of solar generation. Upper graphs: Details of how the the import costs and export and rewards vary on the FLUX tariff (left) and GO tariff (right). [NOTE: The original graph had an erroneous curve plotted. This was updated at 23:27 on 23/2/2023]

If the newly installed panels generate as much as I hope, then the annual generation may approach 6,000 kWh and in this case, the FLUX tariff would be marginally cheaper.

Discussion#2: The effect of battery size 

Whilst I was making these calculations, I thought it would also be interesting to look at the effect of battery size. For my home – with solar PV generation of ~3,800 kWh/year – the simulations suggest that bigger batteries are better – no news there – but that above roughly 10 kWh the additional savings are minimal.

Click on Image for a larger version. Lower graph: estimates of the annual cost of electricity on the Octopus GO and Octopus FLUX tariffs as a function of battery size with ~ 3,800 kWh of solar generation. Upper graph: Details of how the the import costs and export and rewards vary on the FLUX tariff (left) and GO tariff (right).

This is a relief to me. It means that as the batteries degrade, the system itself is likely to continue to perform well for many years.

Discussion#3: Strategy 

Friends, life is complicated enough without having to consider battery management strategy. Nonetheless, this is where we are!

Observant readers may have noticed that I made no specific efforts to avoid consuming energy at peak hours because it doesn’t happen very often. But if it could be done, then on the FLUX tariff, there would be a reduction in both costs and carbon emissions during these dirtiest hours of the day.

The problem for me is that I am not sure whether the occult Tesla logic which controls my battery, is smart enough to avoid using electricity at peak times. If it could achieve this, then on days when the battery might be expected to run out early, the system might preemptively charge in the middle of the day (at 34p/kWh) and so avoid consuming grid electricity during the peak hours when the equivalent electricity would cost 47.5p/kWh.

For a load of around 1 kW for 3 hours the potential saving would be around 45p/day which over 60 days of winter might amount to ~£27/year.

Errors and Mistakes

Friends, writing this article has been very difficult, and I must warn you although I have carried out many checks, I might easily have made some errors. Sorry. Please feel free to point them out to me when you spot them. The results appear to be about right for my own situation and so I have modest confidence that the errors are not too major.

But overall, despite the fact there are errors and mistakes, I think this spreadsheet offers a tool for evaluating the complex interaction of solar generation, battery storage, and time-of-use tariffs. I hope it helps.