The answer depends on whether you have energy storage on-site, and whether the storage system has been configured to work off-grid.
If you have a grid-tied system without energy storage (the majority of customers have this type of system), your inverter is required by code to shut off and stop producing power. This function is referred to as anti-islanding, and it protects utility workers when they service the lines and restore power. You will not be able to use this type of system to supply power to your house when the grid goes down. The one notable exception is the SMA Secure Power Supply (a pre-integrated function in SMA -40 and -41 inverters) which can provide up to 2kW of power without batteries, even during a grid outage.
If you have a grid-tied system with energy storage, it is important to know what type of battery you are using and how the system has been configured.
If you are using a peak-shaving or load-shifting battery without true off-grid capabilities, such as the Enphase IQ Battery, you still cannot use the power produced by the solar system or the energy stored by the batteries in the event of a grid outage. This battery is simply not designed to work in this manner.
If you have a battery system capable of going off-grid, such as an Outback or Darfon system, your system can operate for a certain period of time in the event of a grid outage. The duration would depend on the amount of sunlight received for the panels to recharge the batteries, the capacity of the battery bank, how much energy is being consumed for on-site loads, and several other factors. A properly designed system can operate indefinitely as long as these factors were taken into consideration.
Many homeowners develop an interest in energy storage systems after natural disasters and/or extended grid outages, such as Hurricane Irma (1)(2)(3) and the current PG&E power outages in California. While the cost of taking your entire home off-grid is still very expensive and out of the question for most, you can still configure a critical loads panel and design your system to support those loads.
We strongly recommend consulting with an off-grid solar design professional before attempting to assemble an off-grid system, as there are several considerations to account for. Renvu offers a handful of energy storage solutions which may be helpful to you: