I use a Samlex EVO 4024 Inverter/Charger which is 24V. It is capable of 100A Charge Rate (default 40A) which is programmable.
The Generator input feed line is 120VAC., I have set it to charge @ 80A which results in 120V/27A draw from the L5:30 output of the generator.
@ 120V/27A pulls 3200W +/-200W as it floats a little. This is CONSTANT DRAW so no good for a small "3000W" Generator.
I run a 7200/9000 Watt Generator which has the L5:30 (120V/30A) which I use but also has a (NEMA L14-30R) that can output 240V/30A.
I'm using a Champion 41552 Generator (not discontinued) and have never had issues with it. In fact I built my home using this genny as a power source for the air compressor, table saw etc and it has seen a LOT of use ~ I mean LOTS ~ and with religious oil changes (synthetic only) no issues.... I've never had issues with Champion products and bang for buck, can't be beat.
IF you are looking for a new Genset then consider getting one that has the ability to be started by a GCSM Module. That will let your Inverter System auto-start & shutdown the generator IF the Inverter/Charger has AGS capability.
AGS = Auto Generator Start signal.
GCSM = Generator Control Start Module.
For one of the best GCSM's see here:
GSCM-mini-60Hz (USA & Canada) (atkinsonelectronics.com)
For the Generator Compatible Listings search this PDF:
atkinsonelectronics.com/content/product_pdfs/All Hookup Diagrams Merged.pdf
SPECIAL NOTE: If the Generator is NOT in the Atkinson list, there is likely no chance that ANY GCSM from anyone would support it.
Also a note about Generac. The Company is now owned & operated by a Capitol Investment Company. The Bean Counters had at it and quality has TANKED. Most Generator Vendors here (and there are quite a few out here in the remote regions) will NO LONGER SELL Generac ! The quality dropped & service calls are far too frequent.
BTW: Home Standby Generators which are an excellent option (so it would seem) cannot be installed on off-grid setups. Generac, Champion and others immediately VOID Warranties for such installations. I just went through looking to install one which runs on LPG and discovered "before buying" that this was indeed the case, confirmed by the Manufacturers direct support, not just what the vendors said. (two of which did not know this detail)