I think it would just about break even on an economy 7 night rate saving about 17p/kWh shifting load to the overnight rate. (Might save more on a smarter tariff.)

A 12kWh system costs £5880 including VAT. Assume 95% round trip efficiency and 80% cycle each night gives savings of £565 annually.

That's about the same as the cost of a loan at 5% for the total amount paid back over an estimated useful life of 15 years.

This assumes it doesn't need servicing in that time and you can DIY install.

I don't know whether home systems like this will get much cheaper as the batteries themselves probably only make up about 20% of the system cost.

There are huge economies of scale for utility scale storage with all in project costs now down to $125/kWh meaning 12kWh would cost just $1500 rather than $6600 for this home system. So I wouldn't be confident the price differentials between day and night rates will remain as high over its expected lifetime.

My night tariff is 6.67p/kWh compared to 28.36p/kWh for daytime.

I don’t think these differentials will last either but I do like the idea of smart charging when there is too much wind. I suspect these grid storage systems currently being built won’t handle these peaks and will be designed for the average case so there will still be periods of cheap electricity.

My supplier already controls my car this way and charges it on a schedule it defines each night and also ad-hoc during low demand.

There is also some benefit to have a backup system for when the power goes out which happens a few times a year.

I pretty much agree. There seems a clear economic case to install enough grid storage to smooth out within day variations but that will fill up during multi-day windy periods so there will certainly still be periods of cheap electricity just not every day.

That likely means you'll still be able to charge your car cheaply most of the time but it probably makes home battery investments less attractive since you might only get 100-200 opportunities a year to charge it cheaply instead of 365, halving the annual savings.

But then given so much of the cost of a home system is in the inverter and control unit maybe it will become economic to buy several days consumption worth of batteries.