How to select the battery (kW, kWh and charge/discharge rate)?

Question

A simplified example. The power consumption in a household during the day is 10 kWh and during the night is 4 kWh. Also, assume there are day (peak) and night (off-peak) rates. The off-peak rate is from 11 pm to 6 am (7 hours).

The idea would be to charge the battery during the night and use it during the day instead of using the peak rate electricity. How to select the battery based on the provided data, or do I need any other input? I get I need a 10 kWh battery based on the consumption during the day.

But how much kW would that be?

Does the charge/discharge rate play any role in selecting the battery? I understand the slow(er) rate would be preferable, so let's assume the battery is charged during the 6 hours. Does this affect the battery selection?

Also, if I limit the maximum and minimum state of charge to 30 % and 90 %, respectively, how would that now affect the battery selection (kW and kWh)?

Edit/Update

Are there any examples of how to design a battery system?

Assuming I have the data for the PV system and the load (both rate 1 (peak) and rate 2 (off-peak)), how to get the battery requirements? I came across peak-shaving design methods, but in my case, the idea is to charge the battery during the off-peak hours and during the peak hours supply the load from the PV and the battery.

Answer 1

You need a 10/(0.9-0.3)=16.67 kWh battery assuming no losses.

To charge it in 6 hours, you need a 2.78 kW charger, again assuming no losses.

Yes, charging slow, 6 hours or (1/6 C) puts less strain on your battery and give you more options. Above 80 %, you’re in absorption state for most chemistries so 80->90 % will take longer than 70->80 %.

You need to factor in losses in the charger, the battery itself and the inverter and scale up the battery size and charger accordingly.