This is not straightforward and depends significantly on how much you pay to charge your battery overnight in winter: your present supplier may well not have an appropriate low night-time rate.
If you have a battery of about 10kWh and store enough electricity from your panels to keep your house running overnight (and all day during dull winter days) you may not have to buy much electricity at daytime rates. In this case the payback time could be around ten years, similar to the reasonable expectation for battery life – see below for the calculation