Volker Quaschning just published an excellent article (in German) about the results of a study on the optimal size of home solar systems with battery storage.
Once the feed-in tariff runs out for solar in Germany a couple of years (at the latest when the 52 GW overall cap is reached), people who want solar for economic reasons alone will want to optimize their systems so as to use the largest possible share of the generated electricity themselves, since every kWh they generate themselves cheaper than buying it from the grid helps paying back the system costs.
Quaschning found out that the highest shares of self use are achieved with the smallest systems. His graph 3 shows that systems with only 2 kW of solar panel capacity achieve 85 percent own use with 2 kWh of battery capacity, while a 5 kW solar panel system with 5 kWh of battery capacity would only achieve about 65% own use share.
This in turn means that after the phase-out of the feed-in tariff for solar it will make more sense to install a smaller system, if the short-term economics of saving costs of electricity from the grid is the only factor considered.
Quaschning also models the self reliability of these systems (that is, their ability to provide electricity without buying anything from the grid). His result is that even large systems of 10 kW solar panel and 10 kWh of battery capacity only achieve about 80 percent. The reason is that solar generation falls strongly in German winters.
On the other hand, even on a cloudy winter day, a 10 kW system is bound to produce at least something. So it would always be better than having no own production capacity in the event of a large scale grid failure. Quaschning doesn’t discuss that aspect. Maybe that’s because large grid failures don’t happen in Germany, and are even less likely to happen in the future with nuclear plants phased out.
I think this is an excellent resource. However, in his graph 1 he assumes feed-in tariffs extending to longer as 2020. I think that the 52 GW overall cap will kick in much earlier.
And these feed-in tariffs reflect only the costs of the solar panels. They don’t include the costs for batteries. Therefore, the graph 1 probably needs to be amended with values for the costs that also reflect the storage costs.