Cheap 4-life
My body is 2.63 trillion volts, .07v per cell
I would want the battery/ inverter output to cover as much of the load as it can and grid takes care of the rest.Battery + utility is not a normal operation.
Except in a mobile application, where the shore power available isn't enough to power the loads.
Normally you don't want to be draining the battery when running on utility. Usually when connected to utility. You would want to be charging the battery.
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