In case battery capacity and renewable plant capacity are properly matched, batteries can sink the energy currently not needed and source that energy in case of missing capacity from the renewable power source.
This way, yield rates regarding energy taken from the plant increase and supply stability increases as well.
The challenge is finding a sweet spot between battery capacity and system cost.
As an example from personal experience:
Combining a solar array of 10kWpeak and a battery storage of 7.5kWh can get you to 95% autonomy from April to September in Europe.
Over the whole year, still 70% can be achieved.
A larger battery won't help as the drop comes in December/January when the PV isn't sufficient to power the installation, even less so to charge the battery.
Doubling the PV-capacity would help but becomes unreasonably expensive.
Adding a small windmill would be great as typically this would generate more power in winter.
The stored energy is released during periods of low energy generation with grid integration, ensuring continuous power supply and enhancing grid stability.