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DC Breaker for battery

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Hi all.

I need to install a DC breaker between my battery and Inverter. Its a 3kW inverter - Kodak OG3.24 running on 24v. - Giter g2500-24 (min 25,6v to be be specific).

Now the manual doesn't explicitly say what size breaker to install, only that typical amperage is 142A. Below is from the manual

image.png.9bbb947a66d2100ef863fe374e155424.png

Now here is where I get confused. If I do a simple calculation of Inverter surge/battery min power I get 6000W/25.4v = 236A

So do I install a 150A breaker due to the typical amperage or do I Install 250A to cover the surge. Or split the difference and install 200A

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