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 34p, i.e. £460 pa. Assuming the battery costs £6,000 the payback time is about 13 years, longer than the currently expected lifetime of the battery. Taking the efficiency of the battery (about 90%) into account the saving reduces to about £420 and the payback time increases to about 14 years.