Hi, who has any idea of a long lasting and efficient refrigerator that can be used on a 1.5Kva inverter without having an adverse effect on the inverter and battery in the long run?

I have a small fridge and I recently forgot to unplug the fridge before turning off the generator, I discovered that it was able to power the fridge. I was scared to leave the fridge plugged in because of my battery. Please I need a recommendation for a good fridge or cooler that's specifically built to run on inverters and Batteries that gets freezed and cold quickly.

There's no NEPA light in my area for a long time but the Solar powered inverter gives me 24/7 supply of Electricity. But I'm forced to use Generator because of the Fridge.