The inverter can go above 8 kW without tripping, just not for sustained periods. Myself and others have had it
spike to 10-11 kW before without tripping.
Some 0.5C batteries can briefly go above 0.5C. The problem is that the discharge current is hard governed by the inverter setting. If it goes beyond that then it trips.
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For eg a 0.5C 100 Ah battery would have a discharge current of 50A, 200 Ah would be 100A etc. You can set it higher to allow for a sudden spike, but I'm hesitant to do that to protect the battery. Didn't want to risk a higher sustained discharge current then it was designed for. Would rather deal with a battery tripping than a damaged battery...