Mine run the house all night till sunup. Some grid-tied systems can be switched for power to the house during sunshine.
My system sends excess to the grid after giving my house all it needs and after seeing the batteries fully charged.
The reason for this is two fold. First the power company doesn’t want you putting power on a line that one of their workers thinks is off, two, the power company gives the inverters the signal it needs to operate at the right frequency and phase.
Generated power in a split phase system is -120V for one half of of one cycle in a 60 cycle per second system and then +120 on the next half of the cycle. then it does the same thing on the other half of the split so that if you tie two of the splits together you have 240V.
Without a battery backup the system shuts off for safety protection on loss of grid.
Most people go with non-battery-backup systems. The inverters are less expensive and contain less logic. Adding even a modest battery will allow the inverter to keep working if you have a battery backup style inverter. Batteries however eat up a significant portion of your generated power. I’m thinking of going into grid tied mode without battery backup tied in for several days a week to see if it enhances my production If it does I will probably only hook the battery up once a week to top them off. My battery is not modest it is very large and would last me a couple weeks without sun or grid.
I always recommend battery backup and recommend modest battery if thats all you can afford. You would hate to lose all the stuff you have in your freezers and frig. It is also nice to be able to stay warm in the winter. While a big enough battery can run important loads without sun when the sun is back you would be able to run as much as your panels would make.
I have very nearly 12KW on the roof but feel lucky if I put 5 or 6 into the grid. Because of losses in wiring and battery I feel very fortunate when I’m bringing down 10KW and putting 5 or more into the grid.