You're going to need to be assured a power regulator or power conditioner.

Most low-cost generators, like those for construction sites, deliver "dirty power" — inconsistent voltages, surges, sags, and lots of line-level sine wave distortion. Dirty power can ruin devices like computers, televisions, etc.; with guitar amps the issue is noise. Guitar amps are primitive designs with low and weak filtering because heavy filtering makes amps too stiff and "hi-fi."