Your concern is very genuine. In my humble opinion rather than storing in Batteries the Solar Electricity can also be used to produce Hydrogen, which can be used in suitable Gas turnine - Generator + Steam turbine - Generator (Combined Cycle Plant).
Of course overall efficiency will be relatively low but the scheme will be totally environment friendly with Zero Carbon Foot Print.
In fact Siemens has already set up such a combined cycle power plant. Please check:
https://www.siemens-energy.com/global/en/priorities/future-technologies/hydrogen/zehtc.html