What is the core system voltage and what is the continous VA rating for the inverter charger?
^^^Do this. I have a similar setup with a Victron Multiplus II 12/3000. I have 2xSOK 206Ah batteries as well and they are not enough to fully feed the 3000W Multiplus. I am going to cable it with 2 x 2/0 in anticipation of adding another battery. The reason I am using 2/0 is because I have a lot of it. In your case, I would go with the recommended 2 x 1/0 w/ 250A fuse on each. Then plan on adding another SOK 206Ah battery to fully feed the inverter.
Just in case the OP doesn't quite understand the reasoning for this statement, the inverter needs 235A (based on the calculations shown by @smoothJoey). Each SOK battery is rated to support a max continuous discharge current of 100A. With two of those in parallel you can put out 200A. Since, obviously, 200A is less than 235A your batteries can't support the full capacity of the inverter. Adding a 3rd battery would get you to 300A. Or you just need to avoid trying to pull the full 2400W out of the inverter at once. Keep it under 2000W and your batteries will be fine.
Your SOK batteries have 206Ah of capacity. That is completely separate from their 100A max continuous discharge current. A battery's capacity is independent of its charge and discharge current abilities. Those are dictated by the BMS. The capacity is a function of the size of the cells inside the battery.
For now, I am running a single 2/0 copper wire fused @ 250A. The 2/0 wire can handle that and the batteries won't put out more than 200A continuous. Just have to watch the loads when I only have the 2 batteries.
I was thinking about getting a Victron Lynx Distributor which uses mega fuses. Are you saying the Victron Distributor is no good because it uses mega fuses? That would change my mind about getting one.
