This doesn't sound right (correct me if wrong)... but we've ran a small one plate cooker off of a camping solar system + battery kit & off of a petrol generator

This doesn't sound right (correct me if wrong)... but we've ran a small one plate cooker off of a camping solar system + battery kit & off of a petrol generator and it all seemed fine and working as normal. Usually when putting heavy load on the generator you can hear it work harder, but with this plate it barely makes a difference. I have to note that it is rated at 2000w at max setting (6), but due to it being so potent, we've never had it set to more than 3 out of 6, anything above that is way too aggressive. So make it 1000w typical draw.