A grid-connected solar power system is the most cost-effective and simple type of solar power system. The main components of a grid connect systems are solar panels and an inverter. Solar panels convert sunlight into DC electricity, and an inverter will turn DC electricity into usable AC electricity. A grid-connected solar power system will export excess solar power to the grid but maintain the use of regular power from the grid at night (when panels not producing power).
If you have a solar system with no battery storage and there is a grid power cut. Your solar system WILL NOT FUNCTION until the grid connection returns. Once it does, then your whole house will be provided power by the solar system.
If you have a solar system with battery storage and there is a grid power cut. Your solar system will engage your batteries to provide power to your essential loads until the grid power returns. Once it does, then your whole house will be provided power by the solar system.