First, do not assume all are caused by the same problem. Many cheaper generators have poor regulation. I have seen many that will show 120v but low hz when you raise the rpm to get 60hz the peak to peak wave form will exceed what the equipment will handle. Second issue is grounding. Newer furnaces use flame detectors (Flame Rods) that much rely on grounding. Power with a floating ground will cause the CPU to detect no flame and shut down. I have a Honda EU200 inverter generator, it will not operate my furnace unless I ground the neutral side (It has no internal ground) and make sure all including the furnace and gas line is all bonded together.
