There does exist a way to design a solar PV system to be able to provide energy during a power outage. This type of system known as a solar grid-tied battery backed up system.
In this type of system, an ordinary grid-tied solar system is supplemented by a backup battery bank. This battery bank remains fully charged and under normal operating conditions is not actually utilized.
If the power from the grid goes down, the backup battery bank will kick-in to continue to power the home.
Be aware that adding a battery bank does add significant cost to the system. We recommend utilizing a backup battery bank only when it is truly warranted, for the applications such as security or life support in a commercial building or hospital respectively.