Below is an oscilloscope (using differential voltage probe and current probe) picture showing the voltage and the current when charging from the main supply.
Then below is how it looks like when charging at maximum power (30A at 24V) from a Stanley SG 2400 generator (non-inverter). As we can see, the voltage looks quite distorted. Also the current looks different, and does not go as high as in the case when charging from the utility supply.
The last picture shows what happens when suddenly the plug to the EPEVER inverter is pulled out of the socket.