The Role of a Battery in Meeting Winter Electricity Demand

Click Image for a larger version. The 23rd November 2021 was a glorious day in West London.

Friends, these last few days of November have finally been cold enough for all the parts of my plan for a low-emissions home to come together.

• The triple glazing and external wall insulation are reducing the heating required to keep the house comfortable.
• The air source heat pump is reducing the amount of energy required to produce that heat.
• The battery is charging itself at night on cheap electricity and running the house during the day, only running out of charge in the evening.
• And on sunny days, the solar panels are topping up the battery during the day!

And so far, nothing major has gone wrong!

In this article I will outline the role of the battery in all of this by looking at how the battery operated during two recent quite chilly days, one sunny and one dull.

Battery: Capacity

The battery is a Tesla Powerwall 2, with 13.5 kWh of storage. This is large for a domestic battery but still only 25% the capacity of a typical mid-size EV battery.

We use about 10 kWh/day of electricity for day-to-day living, and in summer the battery and solar PV allow us to operate off-grid for almost 6 months.

But now we are heating our home electrically, and expect to have to provide around 50 kWh/day of heating – something achieved using around 15 kWh/day of electricity using an air source heat pump.

So winter demand is expected to be around 25 kWh/day of electricity – roughly twice as much electricity as the battery can store.

So in winter the main role of the battery is to allow us to buy cheap rate electricity, and then use it later in the day, minimising the cost of the extra electricity we are using for heating.

Battery: Losses

Intrinsically, battery cells can only store DC electricity, but the Powerwall needs to store and discharge AC electricity.

So the Powerwall, includes an AC to DC converter on its charging input and a DC to AC converter (called an inverter) on its output. Overall, it promises to deliver back 90% of the electric energy stored in it.  Tesla call this ‘90% round trip efficiency’.

Additionally the battery requires power to maintain itself: it needs to keep its internal controllers going, and to operate a heating and cooling system to maintain the battery at a suitable temperature during charging and discharging in order to ensure the longevity of the battery. Tesla guarantee that the battery will retain 80% capacity after 10 years.

These two effects – round trip efficiency and self-consumption – make it difficult to estimate the so-called ‘state of charge’ of the battery (SOC) i.e. how ‘full’ it is. This is because energy stored in the battery seems to slowly disappear and it is not clear quite how to account for that.

So I have crudely approximated both effects by a simple average power loss in the battery, typically between 100 W (2.4 kWh/day) and 150 W (3.6 kWh/day). I have then adjusted this rate to make sure the Powerwall is ’empty’ at approximately the observed time. The Powerwall also reports what ‘it’ thinks it’s internal state of charge is.

Household Demand

The graph below shows that household demand on Tuesday 23rd November 2021 and Wednesday 24th November 2021 was broadly similar.

Click Image for a larger version. Household demand on the 23rd and 24th November. Most of the roughly 1 kW of demand is from the heat pump (~0.6kW).

Normal non-heating household demand is typically ~10 kWh/day but on these days, the house used ~24 kWh of electricity with ~15 kWh being used to operate the heat pump to provide hot water and space heating:

The battery itself seemed to consume about 3 kWh with probably ~1.3 kWh of that being round-trip losses, and 1.7 kWh (~70 W) being self-consumed to maintain its temperature and operating system.

State of Charge

The graph below shows both my estimate of the state of charge of the battery (i.e. how full it is ) through each day. Also shown as red dots is the self-reported state of charge of the battery.

Click Image for a larger version. The estimated state of charge (SOC) of the battery (kWh) during the 23rd and 24th November. The green line is my estimate and the red dots show the battery’s self-reported estimate. Also shown is the solar power (kW) during the day which was substantial on the 23rd – enough to meet household demand and partially re-charge the battery – but not very substantial on the 24th. The green dotted line shows how the battery would discharge if there were no ‘solar boost’

The overall uncertainty in my estimate of the state of charge is quite large – perhaps about 0.5 kWh – as shown by the fact that on the 23rd the battery apparently ‘overfills’ and the 24th it ‘underfills’. However my estimates do coincide reasonably well with the Powerwall’s own estimates.

• On the 23rd, the battery was initially not quite empty and then charged at approximately 3.6 kW using off-peak electricity available from 0:30 to 04:30. It discharged during the day at around 1 kW, and then after being boosted by 7.4 kWh of solar PV, ran out of charge between 23:00 and 24:00. That evening I was obliged to purchase only ~ 0.5 kWh of full-price electricity.
• On the 24th, the battery was initially empty and then charged at approximately 3.6 kW using off-peak electricity available from 0:30 to 04:30. Discharging at ~1 kW as on the 23rd, but with just 0.94 kWh of ‘solar boost’, it ran out of charge between 18:00 and 19:00. That evening I was obliged to purchase ~5.4 kWh of full-price electricity!

Because the battery had been fully charged and emptied on the 24th, I could evaluate its round trip efficiency using data reported by the battery itself. It reported that it had received 13.4 kWh of charge and discharged 12.1 kWh – just over 90% of the charge, which is in line with specification. But I do not think this figure includes ‘self-consumption’ which I believe appears as a ‘phantom’ domestic load.

Click Image for a larger version. Grid use during the 23rd was almost exclusively during the cheap rate when the battery was charged while using cheap-rate electricity operate the domestic load, including a dishwasher cycle. On the 24th the battery ran out in the early evening and around 5.5 kWh of full price grid electricity was used.

This behaviour makes sense in general terms. If the battery is full (13.5 kWh) at 4:30 a.m., and demand is around 1 kW, then we would expect the battery to run out 13.5 h later i.e. around 6:00 p.m.. Each kWh of solar generation delays that time by an hour.

Costs & Carbon Emissions.

In the Table below I have summarised as best I can the costs and carbon emissions arising from the house on these two days and compared them with two alternative situations:

• The first imagines that we had the same solar PV, and heated the house with a heat pump but with no battery.
• The second imagines that we had the same solar PV, but heated the house with a gas boiler.

Click the image for a larger version of the table. Entries associated with burning gas are coloured in blue. Calaulations are bsed on Electricity prices of 5p/kWh (off-peak) and 16.3 p/kWh (peak) and gas prices of 3.83 p/kWh.

The analysis and evaluation of the alternative scenarios is tedious beyond measure, so allow me to simply summarise.

In terms of money:

• The battery saves lots of money every day, with or without the ‘solar boost’.
• It makes the use of an ASHP not only low-carbon, but also very cheap.

In terms of carbon dioxide emissions:

• The battery reduces ‘my’ carbon dioxide emissions by optimally capturing solar energy.
• On dull winter days the carbon dioxide emissions would be similar with or without a battery.
• Using an ASHP – with or without a battery – drastically reduces carbon dioxide emissions compared to using a gas boiler.

Summary.

As I have commented before, the battery is primarily a financial investment.

In summer:

• The battery it allows me to fully utilise the solar PV, taking the house essentially off-grid for around 6 months.
• This saves me hundreds of pounds a year.

In winter:

• The battery it allows me to fully utilise the small amount of solar PV available, and to time-shift the use of off-peak electricity.
• This also saves me hundreds of pounds a year.

The apparent savings in carbon dioxide emissions associated with using a battery are illusory and in fact the battery is really an additional electrical item using power and causing further emissions.

The solar PV provides low-carbon electricity, but without a battery, any mismatch between production and our domestic use of electricity is expensive.

• Overproduction of electricity is exported to the grid and I get 3p/kWh.
• Underproduction of electricity requires me to import from the grid and I must pay 16.3p/kWh.

So without a battery, the low carbon dioxide electricity is still used and still helps the planet, displacing generation from gas-fired power stations. But I don’t get much benefit for it!

Re-visiting the “washing-up dilemma”

Friends, I can remember a time when the main question about washing up was: “Who is going to do it?”

But dishwashers changed all that. At first there were questions about whether dishwashers or regular washing-up was technically superior.

However nowadays, dishwashers do a very creditable job of cleaning crockery and cutlery – and in what was a devastating blow for the British Tea Towel industry – they also do a fine job of drying.

[Aside: If you would like to see how dishwashers work – check out these Technology Connections videos:

• • Dishwashers-1
  • Dishwashers-2

But this then raised the thorny question of whether hand-washing or using a dishwasher was cheaper.

And now of course, the BIG question is which is greener i.e. has the lowest associated carbon dioxide emissions. This article is an attempt to answer this question.

Energy and Carbon Emissions

In her book “Energy and Carbon Emissions: the way we live today“, Nicola Terry does a fine job of answering such questions.

The book is a gold mine of information on all aspects of our current ‘carbon problem’.

And she looks at this problem in Chapter 7: Should I get a more efficient X?

She concludes that:

“Washing dishes by hand probably generates less carbon [dioxide] emissions if you heat water by gas – even less if you have a solar panel for hot water

And in characteristic and admirable detail, she explains the assumptions underlying her conclusion.

But as His Bobness might have commented… things have changed.

2011 versus 2021

The energy landscape has changed significantly since 2011 when Nicola Terry published her book.

• Carbon dioxide emissions from electricity are now 235 gCO2/kWh rather than 545 gCO2/kWh in 2011.
• Carbon dioxide emissions from gas are still roughly 200 gCO2/kWh assuming ~90% boiler efficiency: the same as 2011.
• In our house,
  • Hot water comes from a heat pump which produces hot water around 3 times more efficiently than a gas boiler.
  • In summer, practically all our electricity comes from solar panels with no proximate emissions: 0 gCO2/kWh
  • In winter, we set the dishwasher to run on cheap-rate electricity which typically has 10% less CO2 emissions than daytime electricity.
• In other houses,
  • Hot water might come from solar thermal panels.

So given this complexity, can we definitively compare the environmental impact of using a dishwasher and washing up by hand?

Well I have made an attempt – and below I will run through some example calculations and then I’ll collate a more extensive set of calculations at the end.

Dishwasher

Taking our recent Bosch model as typical, a dishwashing cycle seems to typically consume around 12 litres of water and around 1 kWh of electricity.

Comparing the consumption for different modes of operation, it is clear that nearly all this energy is used to heat the water. At 70 °C – way more than your hands could stand – fats within food residues soften considerably making them easier to remove in the water spray.

In the winter,

• Carbon dioxide emissions associated with running a cycle in 2021 on average would have been 235 gCO2 using electricity direct from the grid.
• At peak demand (4 pm to 7 pm), the emissions might be higher – but if run in the early hours of the morning – emissions might be ~10% lower.

In the summer,

• Carbon dioxide emissions associated with running the dishwasher are around zero because the electricity is derived from the solar panels.

So assuming a year is 50% summer and 50% winter, carbon dioxide emissions associated with running a single cycle in 2021 on average would be 0.5 x 235 = 118 gCO2 per cycle.

So running the dishwasher 3 times per week would result in emission of around 354 gCO2 per week.

Dishwashers do offer ‘eco’ modes using cooler water which could reduce this.

Washing-up by hand

In general, hand washing probably consumes a bit more water than a dishwasher, but let us assume in the first instance that the same 12 litres of water will suffice, and that the dishes are rinsed in cold water.

Heating 12 litres of water by 40 °C from (say) 10 °C to 50 °C – roughly the hottest water one might reasonably use – requires:

12 litres x 10 °C  x 4200 J/°C/litre = 2,016,000 joules

Or in more familiar units, 0.56 kWh. If this water were heated with a heat pump with a COP of 2.5, this would require 0.224 kWh of electrical energy.

In the winter,

• Carbon dioxide emissions associated with 0.224 kWh of electricity drawn from the grid would have been 0.224 x 235 gCO2/kWh ~ 53 gCO2

In the summer,

• Carbon dioxide emissions associated with 0.224 kWh of electricity from the solar PV panels would have been zero.

So assuming a year is 50% summer and 50% winter, then washing up by hand 3 times a week results in weekly emissions of 3 x 27 = 81 g CO2/week

If the water were heated by gas, the equivalent emissions would have very similar in winter, but would not be reduced in summer, resulting in emissions of about 150 gCO2/week.

And if the water were heated by direct electrical heating without a heat pump, three washes per week would result in emissions of about 158 gCO2/week.

Comparison

I have carried out these calculations for a number of situations using this spreadsheet (Dishwasher Calculations). I compared:

• Hand washing with water from a heat pump powered by solar energy and a battery for half of the year.
• Hand washing with water from a heat pump powered by grid electricity.
• Hand washing with water from a gas boiler.
• Hand washing with water heated by an immersion heater powered by solar energy and a battery for half of the year.
• Hand washing with water heated by an immersion heater using grid electricity.
• A dishwasher powered by solar energy and a battery for half of the year
• A dishwasher powered by grid electricity.

The figure below summarises my calculations assuming that a family washes up 3 times per week either by hand or with a dishwasher.

Click on the image for a larger version. Summary of calculations showing estimated annual CO2 emissions for a variety of ways to do washing up. See text for details.

It is clear that wash-for-wash, washing-up by hand results in lower CO2 emissions. This is especially striking when using a heat pump to generate the hot water.

The lower emissions arise primarily because the water used for washing-up by hand is cooler than the water used in a dishwasher.

However different households behave in different ways, and wash-for-wash comparisons may be unrealistic.

For example, in a small household, a dishwasher can store soiled dishes out of sight for a day or two, and so operating a dishwasher (say) 3 times a week is practical while not leaving out unsightly piles of unwashed dishes. However, if a similar household were relying on hand-washing, they might wash up once each day. Let’s call this Option#2.

Or for larger households, running a dishwasher once a day is more typically part of a family routine, whereas hand-washing for a larger family would be more likely – in my experience – to use rather more water – perhaps as much as twice as much. Let’s call this Option#3.

The results for Options 2 & 3 are shown below. Note that the vertical scales are different on each of the graphs shown.

Click on the image for a larger version. Summary of calculations for Option#2 showing estimated annual CO2 emissions for a variety of ways to do washing up. See text for details. Note that the vertical is different from the other figures.

Click on the image for a larger version. Summary of calculations for Option#3 showing estimated annual CO2 emissions for a variety of ways to do washing up. See text for details. Note that the vertical is different from the other figures.

The different options have a range of CO2 emissions that vary from ‘a few kilograms per year’ to ‘a few tens of kilograms per year’.

But looking across all the options, hand-washing generally results in reduced emissions, just as Nicola Terry had concluded back in 2011. But now the minimum emissions come with water heated by a heat pump.

Click on the image for a larger version. Summary of calculations for Options #1, #2, and #3 showing estimated annual CO2 emissions for a variety of ways to do washing up. See text for details.

Conclusions

My first conclusion is this: How can anyone be expected to wade through such a calculation to determine how to do the washing up!

My second conclusion is not that “Dishwashers are bad”. Indeed my wife and I own a dishwasher and use it regularly.

Personally, I am convinced of the overwhelming need for society as a whole to reduce carbon dioxide emissions, and I also feel this as an intense personal responsibility too.

Nonetheless, no decision can be entirely one-dimensional. As with many similar decisions, there are other criteria that can also be significant – criteria that have nothing to do with carbon dioxide emissions.

Off the top of my head, it could be that some people just don’t like washing up! Or it could be that some people are busy and using a dishwasher is helpful. Or perhaps that someone’s partner might just want a dishwasher for some reason, and so a dishwasher could be part of a declaration of love – an important human dimension.

But… although any decision about how to live one’s life is multi-dimensional, one of those dimensions is very likely to be the associated carbon dioxide emissions, almost no matter what the actual decision concerns.

In this case, my calculations tell me that:

• For washing up, the overwhelming contribution to the carbon emissions is caused by heating water – so using less hot water will reduce emissions no matter how the washing up is done.
• If using a dishwasher, it is a good idea to try to ensure that it is more-or-less full, and to think about using ‘eco’ modes.
• And when washing up is done by hand, it is a good idea to be mindful of the amount of hot water used – and possibly use cold water to rinse.

Finally, in future years, it is possible many of these emissions may well change again.

It is planned that the carbon intensity of UK electricity should fall to 100 gCO2/kWh by 2030 – and this will reduce the emissions of any appliances which use that electricity. Additionally, it could be that dishwashers will be built which can use hot water heated by a heat pump instead of electrically heating their own water.

Finally this calculation does not include the embodied carbon dioxide emissions from either a dishwasher, a heat pump, a battery or solar panels. My guess – for what it is worth – is that assuming reasonably long lifetimes for these items, the embodied carbon dioxide emissions will not significantly alter these conclusions.

 

Heat Pump: First Space-Heating Results

Friends, the unseasonably warm autumn has meant that I have had to wait until 23rd October for our 5 kW Vaillant Arotherm plus system to switch itself on.

I only have a couple of day’s data, but the results are interesting and promising. First I will show the data for each day and then discuss what it means at the end.

23rd October 2021

Click image for a larger version. The graph shows electrical power consumed by the heat pump and the thermal power delivered by the pump during the 24 hours of 23rd October 2021.

From midnight until 6 a.m., there is no space heating, but the heat pump operates for 1 hour to heat the domestic hot water (DHW) tank. Performance for hot water heating is described in these articles (1, 2)

From 6 a.m. until midnight the system is responding to the thermostat set at 19.5 °C and heated water is circulated around the radiators.

The heat pump operates 12 times up until 6 p.m. after which no additional heating was required.

As shown on the graph, 12.1 kWh of heat was delivered using only 2.9 kWh of electrical power. which over 12 hours amounts to an average heating power of around 1 kW using only 250 W of electrical power.

The ratio of thermal to electrical power is known as the coefficient of performance (COP) and this is summarised in the graph below

Click image for a larger version. The graph shows Coefficient of Performance (COP) of the heat pump during the 24 hours of 23rd October 2021.

The COP seems to increase slowly through the day peaking for a few minutes in each cycle at values as high as 6, but the space heating average is 4.2.

Click image for a larger version. The graph shows various temperatures relevant to heat pump operation during the 24 hours of 23rd October 2021. The external temperature; the internal temperature; the flow temperature in the radiators; the temperature of water in the DHW cylinder.

The initial flow temperature is ~34 °C which falls through the day to ~28 °C. This reduction in flow temperature is in response to the increase in external temperature from ~12 °C to ~15 °C.

This so-called ‘weather compensation’ allows the use of lower flow temperatures, which enables the system  to operate with the highest possible COP.

I was surprised that even with my unaltered radiators, flow temperatures of 35 °C were sufficient to warm the house.

24th October 2021

Here is the equivalent data to that for the 23rd – the graphs are similar and I show them only to show that the system seems to be behaving reproducibly.

Click image for a larger version. The graph shows electrical power consumed by the heat pump and the thermal power delivered by the pump during the 24 hours of 24th October 2021.

Click image for a larger version. The graph shows Coefficient of Performance (COP) of the heat pump during the 24 hours of 24th October 2021.

Click image for a larger version. The graph shows various temperatures relevant to heat pump operation during the 24 hours of 24th October 2021. The external temperature; the internal temperature; the flow temperature in the radiators; the temperature of water in the DHW cylinder.

Conclusions

My first conclusion is that the system works. This is quite a relief!

My second conclusion is that the system works slightly better than I had been hoping for.

Being able to heat the house with these low radiator temperatures means that over winter the average COP could be higher than my prior estimate of 3. This means I will use less energy, emit less CO2, and spend less than I had estimated.

My third conclusion is that average heating power was about 1 kW during both days. But the system has plenty of margin to deliver more power either by changing the duty cycle – the pump could stay on for longer – or by increasing the flow temperature.

As soon as the weather settles down to being reliably cold I will begin to carry out experiments to optimise the weather compensation.

My fourth conclusion will be the basis of another article – but I can see already that as far as heating is concerned – I am going to have a very cheap winter.

Keep warm.