I have been exploring solar for myself, and have come across more of value to the OP's question about island operation. As has already been discussed, a regular line interactive inverter cannot do this, because it _must_ protect the grid from export during a power outage, in the same way that a transfer switch must separate the home from the grid in order to operate on local power.
A properly designed inverter can certainly operate in 'island mode' with proper separation from the grid. This will almost certainly require energy storage to function well.
I am pretty well biased against energy storage because I am in a location where the grid is quite reliable and where we have 'net metering', which means energy storage has a poor to negative ROI. However I have been giving it a closer look.
1) Tesla provides a very good price for their PV installation, but _requires_ that you include a powerwall in the package. To make this attractive they identify a number of energy storage incentives available in some areas. (The big one is where you join a program that allows the POCO to use your battery to support the grid; the POCO pays a pretty significant amount for such capacity _if they use it_, but I think this incentive might be oversold because if the POCO doesn't use the capacity you don't get paid. ) In any case if you have energy storage incentives than having such might be worth while, so this got me looking closer.
The incentive program has a list of inverters/batteries that are eligible, and so I started looking at a few of them. Here is the incentive info:
Home batteries can help you store your clean solar energy or simply provide backup energy in case you need it. Learn more from Eversource.
www.eversource.com
In particular I found the Sol Ark 12K inverter interesting
https://www.altestore.com/store/inv...verter-pre-wired-systems-p41381/#SOLARK12KOUT
This unit is an all in one that includes the PV connection, the utility connection, the battery interface, and a small number of backed up circuits. In the event of a grid outage the system stops feeding power to the grid (anti-islanding) but will continue to power your 'backed up' circuits from the PV array and the battery.
This inverter is more expensive than one that is only grid interactive, and you also need to pay for the batteries. IMHO it is only worth it if you have a very unreliable grid thus needing backup power frequently or if you have incentives that pay for the energy storage. But it does look interesting in that the actual batteries are separate from the unit and you can adjust to battery capacity and chemistry to suit your application.
If any of the PV professionals have comments on this system I'd appreciate hearing them, but this might get to close to a DIY discussion
-Jon