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More or less, I suggest of your battery bank is over roughly 800 AH in capacity, I would suggest going up to next bus voltage (800ah@12volts becomes 400ah@24volts. Same energy storage).
Mostly because in a balanced system design, this keeps battery wiring to s reasonable diameter, and meshes well with 80-90 ampere solar charge controllers (1,000 ah battery bank with 100 amps charging needs 2x solar charge controllers, vs 1x at 500ah and 50 amps).
But you also need to see which batteries are available, what weight cells you can move around and such.
Also, what a.c. inverter you want and what features. 12 volt inverters are lower wattage, few features, and good for smaller systems.
More difficult to find a low wattage 48dcv input inverter.
Your system is on the edge of 12 or 24 volts. If you want a 3.3kwh per day system and full size fridge, a 24 volt system minimum would be nice.
If you have a bunch of 12vdc native loads, perhaps 12vdv battery bus would be better.
Note that many 12 VDC loads do not like 10.5-16.0 volt range that a typical of grid battery system runs at. A major reason o suggest 120 VAC loads and inverter instead (and make the system 1.18x larger to take care of the 85% efficient inverter).
The Sunny Island has a grid/genset input and a sense input (on=genset available, off=no genset available).
I would suggest that you connect your AC input to the SunnyIsland and use the genset selector. This lets the SI change the AC input characteristics between Grid and Genset:
I have not looked in detail at the SunnyIsland--Go through the installation manual and any support documents you can find.
A question--The SunnyIsland is going to run protected loads. Is the genset only going to power the protected loads panel, or will you have other loads that may run from only the grid/genset (i.e., electric drier, large shop tools, etc.). Among your genset ATS choices--Whole house, two protected panels (genset and genset+SunnyIsland), or only one protected (SunnyIsland only).
Since you are looking at a SunnyBoy for GT solar--That should be compatible with the SunnyIsland and connected to the AC Output of the SI (protected load panel). The SI will vary line frequency a little bit to modulate the SMA GT Inverter(s) as needed (battery charging+loads). I believe the SI AC input will isolate the genset when SI is in genset mode.
Also, let us know how it all works out, with pictures.
Economics is not really science... And even economics professors do not follow their own recommendations when managing their own assets.
So much of this depends on world events, politicians, and human behaviour--That economic predictions are worse than weather forecasting.
There is too much chaos in the world to make vast/accurate long term predictions (chaos not being a bad thing... You buying peas instead of carrots because peas are cheaper or you just like peas better--I prefer that than a 5 year carrot plan implemented by a government economist).
Much better than a corrupted marketplace run by our "betters".
Are we at a low price point for solar panels in the US? Probably. Will they go up because of tariffs? Depends who can offer the biggest "bribes" to the right person/people.
500-600 watts of panel on a 240 ah @ 12 battery bank is a good match. Next time, 2x 6 volt @ ~220 ah golf cart deep cycle batteries will do you better.
Drawing more energy than the panels produce. ... That is a different issue (tilt panews if farther north/winter, conservation, and gasoline for genset).