If you use #2 heating oil in your generator, you are at risk of causing serious damage. Using #2 home heating oil will void any manufactures warranty. Some of the first problems users encounter is damaged fuel pumps, fuel injectors and engine glazing.
The heating oil companies want you to buy their fuel and do not care about your engine. They will say it is the same #2 diesel fuel with red dye added to it. All they want to do is sell you fuel. If heating oil was safe for compression engines, the fuel compaies would advertise this. They do not. Many articles can be found on this topic. Not one article can be found from a fuel company telling you any differently.
Kerosene is added to diesel fuel by some suppliers, though in small quantities. Kerosene has virtually no lubrication qualities.
Kerosene is routinely added to home heating oil, in large quantities. The furnace does not know, or care. The furnace oil pump does not have the same clearances (they are more crude, greater clearances, lower pressure...) and the kerosene will not hurt them. Most will and often do run on straight kerosene. If the oil tank is outside, the mix will be either 50/50 or straight kerosene. Kerosene does not have the same heat values. You will not get the same amount of power from a gallon of kerosene, as from heating oil, or diesel fuel.
Your engine needs the fuel additives that home heating oil is missing. If you are using home heating oil, it is a sure way to cut the life of your fuel injector pump, fuel injectors and the rest of your engine.
If something fails due to fuel quality, it is not a manufacturing defect and will not be covered under any warranty.