Where can I find a luminous inverter?

When PV is charging the AC charger will be off most of the times. This inverter is sold by a number of sellers under the Luminous brand name. Google and you will find them. 3 weeks later... Thanks Scorp007, I will check out the Luminous as well.

Do I need to UG my inverter?

You could try to keep it connected in a wall socket all the time. Then you don't need to ug it in. Keep te ug socket on but you can switch the inverter off. This will ensure that you get enough time to recharge the battery. Then when power is out switch on the inverter as you have done all along.

How many modes does a hybrid inverter have?

It has two settings which can be switched On or Off, namely "Hybrid mode" and "UPS mode", so with those two settings there are essentially 4 different combinations of "modes" I guess. My setup is really simple: I would like to understand how the hybrid inverter operates with the different modes and combinations of the two settings.