I spent ages trying to create a detailed model to work out the likely saving on electricity bills in comparison to the cost of a battery system. In the end, I realised that I could get within about 10% or so just by estimating how much battery capacity we could possibly use each day.
We have a fairly large PV system, so that reduces the daytime electricity use a lot, and even on dull days (like right now) the PV will generate enough to stop the house importing from the grid for most of the day. In our case, we have a background load at night of around 200 W (the water disinfection unit, sewage treatment plant air pump and MVHR system, mainly) and a background load in the daytime of between 250 W and 350 W. There are short duration loads that are much higher, like cooking, and appliances, but overall these aren't that significant, the dominant factor is the background load, because it's there 24/7. During winter, and assuming there's no day time charging from PV, the cost saving comes from the amount of battery energy from overnight off-peak charging that we can use during the peak period, so 17 hours at around 300 to 350 W, which is between 5 and 6 kWh, or about £0.35 - £0.42 per day. For much of the year the saving comes from being able to charge for free and then run off the battery at night, so roughly £0.45 to £0.50 per day. Over the course of a year this comes to around £150 to £160 or thereabouts.
My detailed model, which uses actual recorded energy use, in 6 minute intervals, over about 4 years, estimated a saving of about £153.50, so plenty close enough to the "quick and dirty" method. Doing these calcs has shown that we don't need a large battery pack for the house. Around 10 kWh would be plenty, as we'd rarely use more than about 6 kWh from it. The car will either be charged using excess PV generation in summer, or using off peak electricity, so has no impact on the house battery system. I also found that there was no point in sizing an inverter for a battery system to meet the peak demand from the house, especially as larger inverters have a higher phantom power level. Short duration, high power loads, like cooking, make very little difference, so having to import a bit at peak rates makes little difference to the bill. I've pretty much settled on using a 3 kW inverter if we do opt for battery storage, as that's more than enough to meet the base load plus things like boiling water for tea.
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