Circuit breaker rating between inverters and batteries

[Papote]

Have 2 6.5 KW inverters with the following specs:
Inverter Mode:
Rated Power: 6500VA/6500W, PF 1
DC Input: 48VDC, 153.8A
(2/0 AWG, branch protector: 200A)
AC Output: 120VAC, 50/60Hz, 54.2A, 10
(4 AWG, branch protector: 75A)
Max fault current: 125A, 100 ms

Currently have 2 wall mount 5 Kw 100 Amp 48V batteries with integrated circuit breaker. Max charge / discharge is 110 amps. I will add 2 more batteries in the future.

The cables are 3/0 AWG.

What rating circuit breaker would be needed?

 

[DIYrich]

3/0 wire is listed as 328 amps for chassis wiring. With 120% safety factor, that is 275 Amp fuse.