I tried to stop the battery charge and discharge for the whole day. The percentage drops from 55% to 47% within 24 hours. It lost 8% for the whole day. Is there any problem in my battery?
Battery Power leakage

I too am interested to know how much energy the inverter uses to do its thing. I cant see any figures on the GE site.
Isn't that 0.5kW for the 24hrs, Hardly worth the effort I would suggest and I'm not sure anyone's judgement would be good enough to ensure that better days weren't missed. In my case I only had 3 days in December where it would actually have been a benefit on only three days, and then only just as the lowest day was 0.3kw

NgOX10 that would be similar to what I'm seeing in my battery (same size as yours) when I fully charge it and fully discharge it there's around 0.5kWh difference. I wouldn't recommend shutting down the inverter, GE may see this as loss of internet connection for a long period which they may deem to void your warranty
NgOX10 I tried to stop the battery charge and discharge for the whole day
Why?
NgOX10 should I switch off the inverter during the cloudy date in winter?
Again, why? You'll miss any moments when there is enough sunlight to generate some power.
In the great scheme of things you are talking about pennies here. Just let the system do it's thing.
NgOX10 https://drive.google.com/file/d/1kD8qm8wPSkvPxsEJ7EcVkndGgBLC5wCr/view Page 5 > General Data > Consumption
Hi Mate,
I have any question about my battery. its percentage dropped from 24% to 2% suddenly and trigger the forced charging. May I know why does it happen? I had this situation for several times. the battery was installed less than 6 months

NgOX10
this thread will answer your question. it is massive so scroll nearer to the end.