Sounds like you have a good solar setup, with solar powering the house during the day, and also charging batteries for use at night or blackouts. Many setups are not that sophisticated, and do not have batteries charging, and also may not work when the grid is down due to the grid restrictions somehow. I know of neighbors who have this kind of setup. Only works during the day, and when the grid is working. I don’t get it, won’t work for us, we need something like you have. Here, in N.J. with ridiculous ordinances, you have to have a seperate shed for the batteries, and it has to be some distance from the house. Initially expensive even if you have the property.
The exception to that is if your inverter(s) have the "zero report" or "zero output" feature like mine do. It's main selling point is to allow you to not automatically put power onto the grid and, therefore, have to pay high "solar fees" if your area doesn't do net metering. Those inverters also have the feature to not put power onto the grid when the grid is down. Thus, you're allowed to power your home's electrical panels without powering the grid. Thus, you're allowed to keep your home powered even when the grid is down. I had my inverters set to never put power onto the grid until I had them a while and could study a year's worth of telemetry. My power utility makes solar users pay a fee for the privilege of selling power to the grid. I made a C# program to study the telemetry and determine if the extra fees would be more than the little bit of money I'd make from selling power. Until I signed a contract half a year ago and started selling power to the grid, my utility didn't know or care if I had solar because I wasn't putting power onto the grid. As far as the utility was concerned I was a normal power consumer like everybody else only I needed a lot less power.
The more traditional solar inverters have only one cable going to your electrical panel without a separate cable going to the grid. Thus, whatever solar power you have coming in gets converted to AC and put onto your panels with the excess flowing onto the grid behind the panels, whether you want it to or not. Those are the inverters that have to automatically shut off when it detects that grid power is down. Thus a certified solar installer has to install an automatic shutoff for when the grid is down (similar to the grid down detection in a transfer switch for a backup generator). But not so with my inverters. Inverters like mine have a separate cable going to the grid, and one cable going to the electrical panels (and one cable going to the batteries, as well as the DC cables coming in from the solar panels). Thus, my inverters are more like a traffic cop able to decide which circuits get power. If the grid is down the inverters won't put power onto the cable going to the grid, but they'll keep putting power to my electrical panels. Just like if the batteries are charged the inverters won't put power onto the cable going to the batteries. (That's not exactly true. After my batteries are fully charged the inverters still put a little excess solar power to the batteries to keep them "trickle charged".) My inverter model is rated as being safe when the grid is down (just like an automated transfer switch for a generator has to be rated safe for not putting power from the generator onto a downed grid). Thus, the utility lets me keep the lights on in my house even when the grid is down.
There's a LOT of homework to do before deciding to go solar. Then lots more to do to optimize it for your specific needs based on your specific solar radiation. Especially if you care about the feasibility and things like which portions of your system do you add a lot to to take advantage of the economies of scale, but not so much that you waste money fighting the law of diminishing returns.
For me, it was worth spending extra money for an inverter that not only has the zero report feature, but also records data in 5-minute candles on how much power is coming in on each inverter string, how much power is going to or coming from the battery stack, how much power is going to each leg in the electrical panels, and how much power has to be pulled from the grid when I didn't have enough power. For the first year I had a smaller solar system so I could study the telemetry during all seasons as a kind of trying it out before getting the larger system I wanted in the end. When I did the planned upgrade, the data analysis told me which portions to upgrade the most and which to upgrade only a little to get a good ROI for most situations I face through the year.