Very few of my installs ever run the inverter at max and none of them would ever run at max for an hour, let alone 2 hours. In fact for smaller systems, I often have something like a 3K inverter but max load if everything is on would be more like 2KW.
However, someone
could plug in a bunch of stuff and run the inverter at 3kW for an extended time. So... does it have to be wired for > 2-hour continuous load? It would be interesting to know what an inspector would say.
The other piece of the puzzle is what type of wire is being used. I almost always use marine grade wire because of it's fleibility.
It is rated for 105C so the amp rating is a lot higher as well:
105C Marine Grade Wire Specs.
View attachment 67529
So my process is to first calculate the inverter current at low battery level. For a 3000W inverter on a 24V nominal battery
3000W/24V=125A. (This is very conservative because I try to design the system such that the battery never gets this low and I try to design the system to never run the inverter at its peak )
I then factor in the inverter efficiency. Let's assume 90%.
125A/.9=139A.
I typically use fuses so I do the 25% margin.
139A x 1.25 = 174A. I would use a 175A fuse.
I pick the Marine-grade wire that can handle 175A. In this case, it is the 2AWG.
If I were to use other types of wire typically use in buildings, it would need to be much larger wire (2/0 or 4/0)
View attachment 67530