Thinking about domestic batteries

My External Wall Insulation project is complete and the solar panels are installed, so I am left to simply gather data on how things are working: a retired metrologist’s work is never done!

So inevitably my mind is moving on to the ‘next thing’, which is possibly a battery, and I am left with nothing to do but write over-long articles about the possibilities.

• [Note added on 9/1/2021: If you like this article, then try also the next article on the same subject – link – I think it is a little clearer and the spreadsheet has been improved.]

The idea of using a battery is very simple: store solar electricity and use it later! But as I tried to think about it, I found myself intermittently perplexed. This could be an age thing, or just due to my lack of familiarity with solar power installations, but it was not at all obvious to me how to operate the battery in harmony with the solar panels.

This is because energy can flow in several directions.

• For example electricity from the solar panels could charge the battery, operate the domestic load, or be exported to the grid.
• Similarly, the battery could charge itself from the grid, operate the domestic load or export energy to the grid.

Understanding these things matters because domestic scale batteries are not cheap.

• A rechargeable AA battery with 5 Wh of capacity (3.3 Ah @ 1.5V) costs around £5.
• If we scale that up to 13.5 kWh (the size of Tesla battery) then 2700 rechargeable AA batteries would cost about £13,500.
• In fact there are some economies of scale, but the likely cost is still around £10,000.

After making several simulations I think I have a clearer idea how the scheme would work, so please allow me to explain.

Mode#1: Storing in the day.

At the moment the solar panels generate at the whim of the weather gods – and the iron diktats of celestial geometry.

In sunshine – even at mid-winter – the panels can generate at more than 2 kW and unless we are using that electricity in the house at the moment the Sun is shining, the power is exported to the grid.

Click for a larger version. Solar electricity (in kWh) generated daily since the solar panels were installed.

• Over the last 50 winter days the panels have generated about 136 kWh
• I have used about 60% of that, saving round 81.6 x 24.3 pence ~£19.83
• But I have given away about 40% of the electricity I have generated.
• I can arrange to sell that electricity to EDF, my electricity and gas supplier, for the grand price of 1.8 pence per unit i.e. the 54.4 units I have donated would be worth £0.98
• However, if I could have stored those units and used them later I would have saved approximately £13.22.

So using a battery to store solar energy and then use it later to displace buying full-price electricity makes some financial sense. It also makes carbon sense, displacing grid electricity with low-carbon solar energy.

In winter, a battery would make the most of the meagre solar supply and in summer it would allow us to be effectively ‘off grid’ for many days at a time.

Mode#2: Storing at night.

But batteries can also be used to store electricity generated at night time – when it is cheap. EDF charges me 24.31 pence for each unit I use between 6:30 a.m. and 11:30 p.m. (‘peak’ rate) , but only 4.75 pence for each unit I use overnight (‘off peak’ rate).

On average, we use around 11 kWh/day of electricity, around 9 kWh of which is used during ‘peak’ time. So if I could buy that electricity at the ‘off peak’ rate (costing 9 x 4.75 = 42.75 p), store it in a battery, and then use it the next day, then I would avoid spending 9 x 24.31 pence = £2.19.

This strategy would save me around £1.76 per day, or around £640 per year – a truly staggering amount of money!

It would also be slightly greener. The exact amount of carbon dioxide emitted for each unit of electricity – a quantity known as the carbon intensity – depends on how the electricity is generated,

• Electricity generated from coal has a carbon intensity of around 900 gCO2/kWh
• Electricity generated from gas has a carbon intensity of around 500 gCO2/kWh
• Electricity generated from nuclear, solar or wind has a carbon intensity of a few 10’s of gCO2/kWh

Depending on mix of generating sources, the carbon intensity of electricity varies from hour-to-hour, day-to-day and from month-to-month.

To estimate the difference in carbon intensity between ‘peak’ and ‘off peak’ electricity is quite a palava.

• I went to the site CarbonIntensity.org.uk and downloaded the data for the carbon intensity of electricity assessed every 30 minutes for the last three years.
• I then went through the data and found out the average carbon intensity for ‘Off Peak’ and ‘Peak’ electricity.
• I averaged these figures monthly.

The data are graphed below.

Click for a larger version. Carbon intensity (grams of CO2 per kWh of electricity) for UK electricity evaluated each month since the start of 2018. The red curve uses data for ‘Peak Rate’ electricity and the blue curve shows data for ‘off peak’ electricity’. The black curve shows the difference between ‘peak’ and ‘off-peak’ and the dotted red line shows the average value of the difference.

The average ‘Peak Rate’ carbon intensity over the last two years is approximately 191 g CO2 per kWh, and the ‘Off-peak’ average is approximately 25 g (or 13%) lower.

I calculated that over the last year if I used 9 peak units and 2 off-peak units per day then the carbon emissions associated with my electricity use would have been 749 kg (~three quarters of a tonne) and the cost would have been £822.

If I had instead bought all those units at night, stored them in a battery, and used them the next day the carbon emissions would have been 661 kg – a saving of 88 kg and the cost would have been just £188 – a saving of £634.

Summary so far

So these two strategies involve using the battery to:

• Store solar electricity in the day (which maximises my personal use of my personal solar electricity)
• Store grid electricity at night (which appears to be amazingly cost effective and has about 13% lower carbon emissions)

Understanding how these two strategies can be combined had been hurting my head, but I think I have got there!

I think the operating principles I need are these:

• Whenever solar electricity is available, use it.
• If the solar power exceeds immediate demand,
  • If the battery is not full, store it.
  • If the battery is full, export it for whatever marginal gain may be made.
• At night, charge the battery from the mains so that it is full before the start of the next day.

I have run a few simulations below assuming a Tesla Powerwall 2 battery with a capacity of 13.5 kWh. If you want, you can download the Excel™ spreadsheet here, or view typical outputs below.

• [Note added on 9/1/2021: Improved spreadsheet available here: Solar Battery Simuations 2.]

• Note: I hate sharing spreadsheets because as Jean Paul Satre might once have said “Hell is other people’s spreadsheets“. Please forgive me for any errors. Thanks

Battery only: No Solar

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both are zero in this graph. Both should be read against the right-hand axis.

In the first simulation the battery charges from empty using 2 kW of ‘Off Peak’ electricity and fills up just before morning. It then discharges through the day (at 0.4 kW) and is about half empty – or half full depending on your disposition – the next evening.

So the next day the battery starts charging from about 50% full and then discharges through the day and is again about 50% full at the end of the day.

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both are zero in this graph. Both should be read against the right-hand axis.

So based on this simulation, it looks like a stable daily charge and discharge rate could effectively eliminate the need to use ‘Peak-Rate’ electricity.

Each night the battery would store however much electricity had been used the day before.

Battery and solar in harmony 

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and should be read against the right-hand axis.

The simulation above, shows what would happen if there were weak solar generation typical of this wintry time of year. As the solar electricity is being generated. the rate of discharge of the battery slows – is reversed briefly – and then resumes as the solar generation fades away.

A modest generation day – typical of a bright winter day or a normal spring day – is shown below.

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both should be read against the right-hand axis.

At its peak the solar generation reaches 2 kW – and in the middle of the day re-charges the battery to capacity. When the battery reaches capacity – the solar generation covers the domestic load and the excess electricity is exported (blue curve).

On a long summer day solar generation might reach 3.6 kW but here I assume just a 2.5 kW peak. In this scenario, the battery barely discharges and solar generation covers the domestic load and exports to the grid during the day. Only in the evening does the battery discharge.

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both should be read against the right-hand axis.

Battery and heat pump and solar 

The battery and the solar panels are just a part of the wider project to reduce carbon emissions which – if you have been paying attention – involves replacing my gas boiler with an air source heat pump. This uses electricity to move heat from outside into the house.

Back in the Winter of 2018/19 the gas boiler supplied up to 100 kWh/day of heating. In the slightly milder winter of 2019/20 the boiler used on average 70 kWh/day of gas for heating. This winter the External Wall Insulation and the Triple Glazing seem to have reduced this average to about 40 kWh/day – with a peak requirement around 72 kWh on the very coldest days.

Using a heat pump with a coefficient of performance of about 3, it will require 40/3 kWh= 13.3 kWh/day of electrical energy to supply these 40 kWh of heat energy. This amounts to an additional 0.55 kW running continuously.

I have simulated this situation below by increasing the load to 1.0 kW. In this case the battery will discharge a couple of hours early and we will have to buy a couple of units of full-price electricity.

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both should be read against the right-hand axis.

And finally we come to the reasonable worst-case scenario. Here there would be effectively no solar power (dull winter days!) and the external temperature would be around 0 °C requiring around 72 kWh of heating i.e. 3 kW of heating power. This will require 1 kW of electrical power to operate the heat pump on top of the 0.4 kW of domestic load.

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both should be read against the right-hand axis.

In this scenario we would require about 8 hours of full price electricity @1.4 kW i.e. 11.2 kWh which@ 24.3 p/kWh would cost around £2.70. So if there were 10 of these days a year it would cost roughly £27/year.

I could avoid purchasing this full price electricity by buying two Tesla Powerwall batteries to give a capacity of 27 kWh. But spending an additional £8000 to avoid paying £27 year does not look like a sound investment.

Click for a larger version. The dotted (—-) red line shows the battery capacity of two Tesla Powerwall 2 batteries and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both should be read against the right-hand axis.

Summary

Overall, I think I now understand how a battery would integrate with the way we use energy in this house, and I think it makes sense.

Regarding money:

• Using a battery  I would appear to be able to save many hundreds of pounds each year by purchasing off-peak electricity instead of peak electricity.

Regarding carbon:

• Without solar panels, the switch to ‘Off Peak’ electricity should reduce annual emissions from roughly 749 kg to about 661 kg – a saving of 88 kg.
• With solar panels we should generate roughly 3700 kWh of low carbon electricity, all of which will be used either by me or by someone else, displacing carbon-producing generation. This would be true with or without a battery. But the battery allows me to personally benefit.
  • During the summer the battery should allow me to benefit from the full amount of solar energy generated, reducing grid use (and expenditure) to almost zero.
  • During the winter, where only about 2 kWh of solar generation is available each day, it should reduce carbon emissions by about 20% compared with using ‘Off Peak’ grid electricity.
  • In the worst case – when using a heat pump to heat the house on very cold days with negligible solar power – I will need to buy full price electricity for a few hours a day.

So when I replace the gas boiler with an air-source heat pump, we will inevitably rely on the grid for some full-price electricity on the few coldest days of the year. That is why I have been so keen to reduce the amount of heating required.