EGC sizing for server rack style batteries

[KD4UPL]

Many of the solar systems I install now are using lithium batteries with metal cases instead of the old plastic case AGM batteries. Often these metal cased batteries are installed in metal server racks; 6 to a rack. The instructions usually say something generic like "EGC must meet NEC or other local code requirements".
I'm not sure how to size the EGC since there is the potential for bi-directional power flow and many different over current devices involved.
A typical installation would have 6 batteries, each with a 100 amp breaker, installed in a metal cabinet. The output terminals of the batteries are connected to short #2 copper jumpers that connect to buss bars putting all the batteries in parallel. From these buss bars I'll run a set of 2/0 or 4/0 copper conductors for the positive and negative connection to the inverter. The positive typically connects to a 175 or maybe 250 amp breaker and then to the inverter. If the batteries are being discharged power is flowing from them to the inverter. If they are being charged it's flowing toward the batteries from the inverter.
Do I size the EGC based on the 4/0 wire, the 250 amp inverter breaker, the 100 amp battery breakers, the total of 6 100 amp battery breakers, or something else?

Thanks for your help.

 

[tortuga]

I'd go by 250.122(C) and if the max breaker is 250A a #4 CU should cover all of it.

 

[KD4UPL]

Thanks for your input. That makes sense based on maximum breaker size if it means a single breaker. I wasn't sure if you had to add breakers that are in parallel which would make the maximum "size" 600 amps.