As I've commented on other posts here we have a 15kW generator (22kW surge) and after trying many different scenarios our Model 3 won't charge from it. It will run our whole house, but since we have a 5hp well and a 5 ton HVAC system it won't run them both at the same time. Technically, it would run them both, but there isn't enough surge wattage to start one while the other is running since start up draws a lot more amperage.
The error I'm getting on the touchscreen in the car is related insufficient ground even though the generator is connected to an 8' ground rod with a 4 gauge ground cable. I've tried charging directly from the generator plugs (240v - 50amp, 240v - 30amp and 110v - 20amp) and charging from the dryer plug in the house when the generator is powering the house. I've preloaded it with another load and did finally get a few mph charge, but it was on and off. The car really didn't like it, and I got a message stating that if the condition persisted to contact Tesla Service. I don't want to damage the onboard charger.
I thought it was the age of our generator, but when testing a new, out-of-the-box Honda inverter style generator with two 110v - 20amp plugs I got the same results. And no it isn't grounded through a ground rod. There is no place to hook up an external ground provided on that particular generator. It does power other loads just fine.
My point is: Don't lull yourself into complacency, and then find out your generator won't charge your Tesla when you think/hope it will.