When I setup my 24V 3KW Inverter/Charger, I installed a 300A T Fuse at the battery but had a 175A DC Breaker after that (I use a Midnite E-Panel)
3000W ÷ 24V = 125A leaving 50A room for surges (up to 9000w burst (375A).
When I upgraded to a 24V/4KW Inverter Charger I upgraded the main breaker to 250A
4000W ÷ 24V = 166A. But with surge capacity of 12,000W in burst (500A)
I rarely cross pushing 130A DC through the system, even when everything is on & running (like fridge & water pump, the 2 biggies here).
The Breakers will handle the momentary surge, whereas a Fuse is less tolerant so must be sized according to the biggest surge possible -10% to 15%
The Breaker Sizing was determined by Midnite Solar & Samlex recommendations who both KNOW what they are doing. Most Solar Controller & Inverter Documentation should include these requirements, heck, I've even seen cheapo Chinese "take your chances" gear have that info while other (apparently better ones) sis not....