That depends on the kind of system you have installed. The most common and prevalent system is a grid connected solar system, with no storage. In this case, your system will not work in case of a power cut or grid failure, as the solar panels are disconnected to the grid That is because your solar system generates energy and sends any excess energy to the grid. This die down in case of power cuts is critical for safety, as back feeding into the grid could potentially cause injury to someone.