Experience suggests that with a 10kWh battery you may be able to use about 70% of the 3,400kWh you produce even if you use only 30% directly, i.e. an extra 1,360kWh. Then, your battery will save you 1,360kWh at 30p, i.e. £408 pa. Assuming the battery costs £5,000 the payback time is a bit over 12 years, longer than the currently expected lifetime of the battery.