Domestic Batteries: Purchase decisions and realistic models

Friends, earlier this week I ordered a Tesla PowerWall 2 from the charming people at The Little Green Energy Company (TLGEC). They have given me a nominal installation date in late March 2021 and I will be sure to keep you updated.

So in my excitement I wrote another article about using batteries – and you can read it at length below. But AFTER I had spent hours calculating and graphing , I realised something very obvious but very profound.

  • The triple-glazing and external wall insulation have been ‘green’ investments. They avoid the need to burn fossil fuels.
  • The solar panels have been a ‘green’ investment. They produce low-carbon electricity.
  • The heat pump (when I install it) will be a ‘green’ investment. It will avoid the need to burn gas to heat the house.
  • But the battery is a financial investment. It will actually use extra electricity! However, it will lower the cost to me personally of making the ‘green’ investments.

My aim is to transition away from burning gas by using a heat pump. This switch requires me to use more electricity each year and without the financial savings that a battery yields this would be punitive.

More battery modelling: but using a climate re-analysis database!

I chose TLGEC over other installers because of their willingness – and ability – to answer tricky questions. And in one of their answers they gave me a jewel of link to this EU funded site with useful information about solar PV.

The site can be used like others to estimate the monthly generation from a solar PV installation. But unlike other sites the predictions are based on actual solar data over the period 2005-2016.

And uniquely – by using climate re-analysis –  it is possible to download this data for any location on Earth (!) to simulate hour-by-hour how a particular installation of panels would respond at any time during that period.

Click for a larger image. This web portal is available here.

This has enabled me to create models simulating the interaction of solar panels with a domestic battery similar to those I made previously. But instead of:

  • a minute-by minute model of a single day using simulated solar data,

I can now make…

  • an hour-by-hour model of an entire year using actual solar data.

Crucially this incorporates real-world (hour-to-hour and day-to day) variability which is one of the difficulties in trying to optimise the use of a battery.

The Model 

The Excel™ model (Solar Time Series Analysis 2005 – 2016 for Blog) is based (unsurprisingly) on a Tesla Powerwall 2 with 13.5 kWh of storage, but that can be changed in the file. Please note – this is not a simple model and is set up just for my panels in Teddington! If you want to use it for your site you will need to download data from the web portal above and place it in the spreadsheet.

The model has the following ‘features’ (default values shown in brackets)

  1. The electrical demand can have separate daily peak (1 kW) and off-peak (0.5 kW) values.
  2. The overnight charging rate can be changed (3 kW)
  3. The fractional filling of the battery in the morning can be changed seasonally between a summer value (100%) and a winter value (100%).
  4. The range of the ‘summer’ and ‘winter’ seasons can be defined (summer runs from day 60 to day 300)

The model evaluates:

  • The state of the charge of the battery hour-by-hour through the year,
  • The amount of peak and off-peak electricity which must be purchased to meet the required demand.
  • The amount of solar generation and the amount used on site, or exported.
  • The costs of different strategies.

One shortcoming of the model is that the 1-hour step is too long and so in some situations the model appears to overfill or underfill the battery. However I think the uncertainty this adds is relatively small.

The Parameters

I set the model to run with data both from individual years and from the average behaviour of all 12 years of data.

The demand I modelled was 0.5 kW overnight and 1 kW during the day. This is more than our house uses at present but is in line with the demand I expect when I install a heat pump to replace the gas boiler.

The model calculates the amount of electricity bought from the grid in both peak and off-peak periods and evaluates the fraction of demand met by solar electricity, and the cost.

I then investigated how different settings for the morning filling of the battery affected:

  • the amount of electricity bought from the grid (peak and off-peak) over the year,
  • the fraction of demand met by solar electricity,
  • the cost.

Typical Runs

The graph below shows the simulated State of Charge (SoC) of the battery during days 1 to 30 of the year 2016 i.e. January 2016.

Click for a larger view.

The graph shows daily overnight charging of the battery to 100% in the morning. The 1-hour time resolution of the simulation makes it appear the battery does not quite completely fill up, but it gets close.

The 1 kW daytime load then drains the battery completely on most days – the SoC reaches zero – and so some full price electricity must be bought.

However, there are a few days (e.g. days 7 & 8 and days 13 to 16) even in January in which strong sunlight fills the battery sufficiently that it lasts to the end of the day. These would typically be cold, crisp, clear winter days.

To indicate the variability, the equivalent graph for the year 2011 is shown below.

Click for a larger view.

But if we plot the average data from 2005 to 2016 we see it has a different character from that for individual years. Instead of the 3 or 4 bright sunny days, we have – on average – a little bit of sunshine on many more days.

Click for a larger view.

This difference between individual years and their average is important in this case, because it the intermittency of solar generation that makes a battery useful, and it is the irregularity of solar generation in any one year that makes it hard to optimise the use of a battery.

A whole year of averaged data is shown in the graph below. I have used average data to illustrate the general characteristics of the behaviour of the battery.

Click for a larger view.

In this graph the battery is charged each night to 100% SoC. In the winter it discharges through the day and the SoC reaches zero before the end of the day, requiring full price grid electricity to tide the household over to the end of the day and the start of cheap electricity.

But between days 60 and 300 there is enough solar generation – on average – such that the battery does not ever fully discharge at the end of each day. Thus in this period is not really necessary to fully charge the battery overnight.

The graph below shows the effect of only charging the battery to 70% in the mornings over this ‘summer’ period.

Click for a larger view.

The result of this is that less night-time electricity is used, and less electricity is exported. Consequently, the ‘self-use’ of solar electricity increases. However, there are now a few more occasions during the ‘summer’ when the  SoC reaches zero before the end of the day i.e. where full price electricity must be bought.

The graph below shows the same partial-charging strategy (only 70% between days 60 and 300) but using data for the year 2011: notice that the irregularity is much greater than when looking at the averaged data.

Click for a larger view.

So how does one make sense of all this? I do not want to spend my entire life optimising battery charging!

Basic Results

There are too many variables to succinctly summarise the modelling results, so here I will just summarise one investigation relevant to my own situation.

Imagining that I am running a heat pump to replace the gas boiler, I have assumed overnight use at 0.5 kW and daytime use at 1.0 kW. This amounts to 21 kWh/day or 7665 kWh/year. Due to the limited time step, the model calculates annual use as 7661 kWh – which is an error of 0.05%.

Using the solar data for each individual year – and for the average of all the years – I calculated how self-use of solar power varied as I changed the state of charge (SoC) of the battery in the morning from 0% to 100%.

By ‘self-use’ I mean that the solar electricity was either used immediately at the house or stored in the battery for later use. Nominally either of these uses is ‘free’, but in reality the storage and retrieval is only around 90% efficient.

Result#1

First of all looking at solar data from each year 2005 to 2016 I calculated that on average the panels would generate 3847 kWh/year with a standard deviation of about 5%. The average value is same as is calculated from just using the average 2006-2016 datset

Click for a larger view.

The solar generation is only around half of the anticipated demand (see below). And without a battery, most of that is exported at a relatively low price (1.8 p/kWh from EDF). This benefits the planet and EDF, but means I still have to pay EDF 23.7 p/kWh for peak time electricity to operate the heat pump.

Click for a larger view.

Next – using the solar data for each individual year – and for the average of all the years – I calculated how self-use of solar electricity varied as I changed the state of charge (SoC) of the battery in the morning from 0% to 100%.

Click for a larger view. The graph shows the number of units of solar electricity (kWh) that would have been used on site.

If we pick one year (say 2014) as an example, we that in this sunnier-than-average year, charging the battery to about 30% SoC in the morning leaves plenty of capacity to store solar electricity during the day.

In a more typical year (say 2016) the optimum morning SoC is between 40% and 50%.

  • Higher morning SoC results in solar generation being ‘lost’ to export.
  • Lower morning SoC will give rise to earlier discharge of the battery and the use of more mains electricity.

Curiously, the optimum morning SoC for any individual year (30% to 60%) is quite different from that calculated from the average of all 12 years. This is because of reduced irregularity in the averaged data.

The difference between self-use calculated from data for individual years and the self-use calculated from the average data is even more striking if we show each year’s result as a fraction of that year’s total generation.

Click for a larger view. The graph shows the fraction of total solar generation (%) that would have been used on site for each year.

We see that we might hope to get around 90% of self-use in any individual year with a morning SoC of around 40%. This is much lower than the 98% which appears possible using averaged data.

Results: Economics 101

As I whiled away happy hours with Excel I became fascinated by different possible strategies. And I filled my head with clever calculations that I might attempt.

But then I realised that none of these strategies affects the carbon reduction I achieve by installing solar panels. This happens with or without a battery and is independent of the charging strategy I adopt!

  • What these charging strategies affect is who gets the benefit!

If I export electricity at low cost (1.8 p/kWh in the case of EDF) and am then forced to buy electricity later in the day for 23.7 p/kWh (EDF) then it is EDF who gets the benefit of my investment.

Financially, the optimum strategy arises from the differences between night-time and day-time electricity, and the price paid for exports. I have illustrated this for two ‘tariffs’ below – those from EDF and those from Tesla – who have a deal with Octopus.

Click for a larger view.

If I simply bought the electricity from EDF without solar panels, then the annual cost would be just over £1600.

The solar panels should reduce this cost substantially. The investment of £4200 in the solar panels should generate a saving of around £500/year, a 12% return on investment.

The battery should lower the annual cost much further. The savings generated by this £10,000 investment should be more than £800/year.

  • Using the EDF tariff, the big difference between the price of day-time and night-time electricity makes it always preferable to have a morning SoC as high as possible, thus minimising the possibility of ever having to use full-price electricity.
  • Using the Tesla tariff – the morning SoC doesn’t matter because there is no time-of-day price difference, and no difference in price between imports and exports.

But using either tariff, I calculate the savings to be massive. So large in fact that I just can’t believe them! The battery should be installed in March and I will let you know how it goes!

Of course I could also lower the cost by switching from EDF. I checked with Octopus energy (link) and it listed 80 different tariffs. Eighty! Enough for 10 octopuses to each have a tariff for each leg.  I absolutely detest this confusopoly. In any case the cheapest night time price was around 11p. Hopefully with the battery I will be able to subsist mainly on EDF’s night-time tariff.

Summary

So after all that work, I realised something very obvious but very profound. As I said at the top the article:

  • The triple-glazing and external wall insulation have been ‘green’ investments. They avoid the need to burn fossil fuels.
  • The solar panels have been a ‘green’ investment. They produce low-carbon electricity.
  • The heat pump (when I install it) will be a ‘green’ investment. It will avoid the need to burn gas to heat the house.
  • But the battery is a financial investment. It will actually use extra electricity! However, it will lower the cost to me personally of making the ‘green’ investments.

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5 Responses to “Domestic Batteries: Purchase decisions and realistic models”

  1. rogercaiazza Says:

    Thanks for the reference to the Photovoltaic geographical information. Maybe you can answer a question about solar panels and incoming solar radiation. According to your solar installation post you have 12 panels that each generate roughly 40 V. My question is when do they generate 40 V relative to incoming solar insolation? Looking at local meteorological stations across New York https://operations.nysmesonet.org/~nbassill/ you can usually find a station that was clear all day and today the solar radiation trace peaked at 500 W/m2 and was smooth all day. Another site was more overcast and the solar radiation trace peaked at 350 W/m2 dropped down to 120 W/m2 in less than an hour with the trace squiggling all day long. How do panels respond: a constant 40V whenever the insolation is greater than X or are they proportional to the solar insolation and constantly fluctuating? Does the inverter smooth the output somehow? Have you ever found a reference that explains how this will work? Thanks

    • protonsforbreakfast Says:

      The individual wafers are (approximately) constant voltage devices. The voltage is around 0.6 V per wafer (https://en.wikipedia.org/wiki/Solar_cell). My cells are described here: https://www.q-cells.eu/fileadmin/user_upload/download_area/Solarmodule/datasheets/Q.PEAK_DUO_BLK-G8/Q_CELLS_Data_sheet_Q.PEAK_DUO_BLK-G8_335-350_2019-11_Rev01_EN.pdf

      If you look closely you will see the individual wafers are arranged in 2 groups (top and bottom) each with with 6 x 10 = 60 individual wafers. The split into 2 is a feature of this particular panel which allows is to operate as (essentially) two separate panels in parallel – this helps it operate better when a cell is partially shaded. The 60 wafers each generate about 0.6 V to give a nominal operating voltage of 36 V. AS you say this happens with minimal insolation and the voltage doesn’t vary much with the amount of sunlight: it’s fixed by the physical properties of silicon. But the more sunlight, the larger the current. And yes – typically this is current constantly fluctuating as clouds roll by.

      In my system the panels are wired in 2 banks each with a nominal voltage of 6 x 36 ~ 216 V DC. This is the input the inverter which then produces 240 V AC.

      And no: I have not found a reference: perhaps I will write one!

      Best wishes: Michael

  2. Edmond Hui Says:

    Do the batteries use extra electricity? Surely the wastage due to their inefficiency results in heat in your home that reduces the need for your heat pump?

    • protonsforbreakfast Says:

      Yes, they do. In a comment on this article (https://protonsforbreakfast.wordpress.com/2021/01/09/thinking-more-about-batteries/) a correspondent states that their 8 kWh battery uses 2.4 kWh day! I enquired about the Tesla and was told it uses about 1 kWh/day. What does it do? The Tesla has a temperature control system, but also – essentially – a computer to control its operation.

      My correspondent’s battery was placed inside the house and so would heat the house – but my battery will be outside – probably in a porch.

      Admittedly, the battery is a ‘green’ investment it enables other green investments either personally, or nationally by lowering peak grid demands. But even if the overhead were zero, I think batteries would still be a different category from the other investments.

      Best wishes: M

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