I have had the same problem with charge rate. I have a 3kW inverter but only got a battery charge between 2.65kW and 2.9kW. GE said it was within limit for losses but this in statement is misleading. If you look at the graphs there is an addtional inverter power tab. When the battery is charging at 2.9kW the inverter power does show 3.0kW showing a loss of 4% so within the spec. Even when charging at 2.65Kw the inveter power is 2.75kW so again show a 4% loss. This has hppened througout July-Oct so should not be a battery temerature related issue.
The trouble with my system is when I charge the battery is ALWAYS starts on the lower charge rate for a least an hour before bumping up to the max charge rate. The result means I can never pick 30 min Octopus slots to charge at the 3kWw inverter. My system is only 3 months old and I have had other issues but GE have been very poor with their support. Emails just get ignored.
EDIT - I have since looked at the data an think I know why. Looking at the forum it seems that temperature does effect charge rate. Looking back at the data it looks like the battery charges at the lower rate until it hits 20 Deg C, at which point it can be charged at the full rate. The battery and inverter is in my cellar so, even in the summer, can be a little cooler. I am now satisfied that the charge rate is now behaving normally but why GE couldn’t make this info more avaialable or replied to my emails with a satisfactory explaination then this would have avoided all this confusion!