I looked at the two postings above. Are you saying the charge controller for solar? or an actual inverter that takes 12V from the battery and supplies household 120V to appliances? How many watts? Which brand? Can you identify and post a google link such as an image search below?
It will be helpfull. I can't imagine anything other than green if all is normal. But there is lots to consider, Too much load? Weak battery, Faulty inverter, or miss wired and drawing current while also trying to replenish the supply through the DC whole house converter. There are so many symptoms and so little information to go on.
We can try to help with details.
https://www.google.com/search?rlz=1C...k1.cp2QpLG-ELs