Battery Sizing

I'm getting used to my AC3 with 8.2kwh battery and wondering how one should size a system. Clealry there must be a sweet-spot factoring in PV size, off-peak tariffs, daily consumption, capacity, seasonal variations, purchase price etc. For instance today, a decently sunny day for February, it looks like my small (2.82kwp) PV system will contribute about a 60% increase in charge. It will hopefully contribute much more in the summer but I doubt I need a bigger battery. I might conceivably have been better off on a cost-benefit basis with a smaller battery in term of payback time. I sized the system on the basis of ROI and expecting that a bigger system, even if I only use the full capacity a few days a year is still benefitting me more than the interest (0.01%) the banks are giving. Clearly adding batteries beyond a certain point becomes less and less cost effective as full capacity is used les fresquently.
For those charging from off-peak electricity the size is less dependent on seasonal fluctuations and would be more a matter of how much peak electricity do you consume each day? Buy a battery system that size with inverters that can charge it in the space of the off-peak period - if you can afford it.
So does anyone have a Drake (style) Equation that would give the optimum size for a battery system to be most cost effective?

For me I already had 2.4kw of solar and with my home being fully electric, ASHP etc the bills were higher than I would like. So I added 4.6kw more panels and a GE AC3 and 8.2kw battery. From last July until early last month I was sure I wanted/needed a second battery as my single battery was empty sometimes by midday during winter. However, looking back at my usage a second battery will only help me for 3 - 4 months of the year and only save me around £30 a month, so £150 per year. So for me it was based on my smart meter data. What I have decided to do to improve things even more is to add as much extra solar as my roof will allow, especially with an EV on the way. So I am not sure about a nice simple equation, but for me simply looking at my usage before battery then after battery was enough. 3 bed detached fully electric.

EDIT: also need to consider is 3kw usage is enough. If an AC5 was available when I ordered I would have gotten that instead to cover heavy single use items plus back ground equipment. I couldn't and can not justify 2 AC3's. 1 is doing ok.

THALL Are you, or will you be on a Time-of-use tariff too? I'm considering going that direction for winter months BUT not sure what might be available for a non-EV household. EDF seems the best so far for my purposes.

Just to add that I thought having more solar panels in kW than my inverter is rated for would be annoying, but in fact it’s not. The reason is I can produce 6kW of solar on my 5kw inverter and as long as there is battery capacity left to fill, the DC to DC transfer does not count. It’s early days for me but I think 8kw battery is enough overall, especially as after the 27th March the evening meal will be cooked in daylight. As someone rightly said more battery in the 3 months of winter would be nice, however with 6kw of planels won’t be worth the extra investment from March to October. Panels are cheap and undoubtedly batteries will get cheaper so I will hang on. Oh I think an equation would need to predict the future, so would be impossible really!

Like THALL, I too have an all electric house.
My installation is only a couple of months old, 4kw solar, 3.6 Hybrid and 2 x 8.2 batteries.
The heating is a ceiling heating system (like underfloor) that benefits from an Economy 7 system.
I therefore charge the heating overnight at the same time as the batteries. Then in the morning the batteries supply the house in the more expensive day rate.

Through January I only had 9 days that flattened the batteries, needing an additional couple of kw.
This month it has been 2 days.
I have never had a day with a requirement of more that 1.4kw daytime top up this month.

Today has been over 11kw generation, the battery was already at 58% from yesterday so is now 100% full and I am burning off kw rather than feed back into grid.

I have had an OWL meter for the last eleven years, so have minute by minute kw consumption figures/graphs for all that time. This was a big help calculating how big a battery to go for.

Last January 2021 my kw usage was 2401, this year it was 1974kw. but crucially the mix of day/night had dramatically shifted to night time. The resulting bill reducing by approx £140+.

In the end, as THALL correctly said you can specify too big on a cost efficiency basis, but I have found the additional capacity has been very flexible through the winter months.

Hopefully, in a few months, I expect the batteries to be towards empty in a morning, but full by evening with an additional reduction in nightime kw use.

It's tricky as there's so many different variables, and sometimes they aren't bought concurrently anyway (as in my case). I think a rule of thumb is to consider average house consumption per day (kWh), solar PV likely generation (array size and position/location) to cover house load and produce an excess; battery sized so that effectively the "solar" covers all house load for the day in Summer, 2/3 in early Autumn/late Spring; and a % in winter. Batteries also really help if an off-peak rate is available - that might mean a smaller array could be sized.

Buying kit to cover the peaks might not be cost effective. Similarly sizing for winter might not be effective
Personally I ruled out any consideration of EV consumption, as it's just so large - and covered that with off-peak rate.

ASHP change the calcs again.

kwmc Yes, I am on Octopus Go Faster 2130.

Just to ad to DIG's comment which is really interesting, my usage is over double his so therefore even with a 6kw system I would most often in winter not have enough surplus to fill a second battery, so cheap grid import would be practically its only use. With the longer summer days I can run manly off solar directly so once again the second battery is not worth it. Dig's setup makes sense so maybe if your solar PV output in kW is double your average usage in kWh then 2 batteries makes sense but mine is more like 1:1 so less appealing at the 2022 battery price point.

With days as we have just had in the UK, my 8.2kwh battery charges itself from my 4,5 kwh panels to 100% by mid-day. The excess is then exported to charge my car. This lasts until the sun drops and the battery then runs the house until the sun rises the next day. Cycle begins again,...... unless it's not as sunny, then an overnight cheap rate charge carries the battery through, with car been charged at that time too.
This is good when sunny, but if the car is 100% full, then excess spills to the grid.
In the winter, with very little sun generation, sometimes I wish I had another 2kwh battery, but, the killer in my house at house times is our arger cooker. So rather than spending on more battery, it's more about sizing my consumption too.

It's the initial investment of any combined battery and PV setup that will see the biggest margins of return.

The issue for me, particularly around the GE kit is the amount of peak demand purely a battery can support. With a spot of load shifting over winter (dishwasher and washing machine) the 8.2kwh battery will cover most days consumption. My grid import demand, outside of the cheap rate overnight charging, is with having sufficient battery power to run a hob and the oven at the same time as this will bust the 2.5kwp the battery and inverter can support.

Ideally I'd have another battery and hybrid inverter and split my 6kwp array into 4 strings - this would give me 6kwp using the new hybrid 5 inverter that could be via battery support alone.

Problem with that is the payback is about 35 years even at current rates.

That said I'd get as much solar as you can squeeze on your roof, the panel costs are negligible compared to scaffolding and labour for a couple more.

In hindsight I'd have got them to feed a split point into my two strings at the mid point on each on the inside of the roof so if I wanted to add another inverter later on it would be easy to wire up.

Finally you really need to understand how much electricity you use and just as importantly what your peak loads are.

Just to say that I have the 5kw hybrid inverter and I find on sunny days it’s best NOT to let my 8kw battery charge by midday. This is because my 6kw panels produce around 5.3 kw at the moment which is more than the inverter can cope with. If I restrict the battery to around 800w charging I can export / use the inverted 5kw and still dc to dc charge the battery. Effectively I’m stopping the solar output being clipped.This equates to 2 or 3 kw per day, now massive but still a gain!

I totally agree with getting as many panels as possible! So many doing internet reviews have added more to their systems, I’m sure if I had gone with the recommendation of 4.3 kw the labour charges would have been exactly the same too. Now I’m generating almost 50% more energy for several decades!