This depends on the size and number of batteries in your system, and the items you are powering with the batteries. The larger the battery, the longer it will be able to power your appliances and lights without being re-charged by solar PV or the grid. Your contractor will help you decide on a battery size that works for the goals of your household.  For a 13.5 kWh battery, during an outage, your refrigerator could continue to run for approximately 33 hours.