To clarify, its not a constant hum, only when I change the fan speed I can hear a low frequency thump in the speaker.One of the reasons I asked for clarification of that point is that I don't think we can be totally certain that the means by which the fan or its speed controller is affecting the system is via the power wiring. I wouldn't rule out the possibility that the effect could be occurring as a result of airborne interference (RFI), in which case a dedicated line, as well as power conditioning or regeneration, would not resolve the problem. RFI would of course not be at frequencies that are low enough to be audible, but I don't think we can rule out the possibility that it might cause some circuit in the system to produce a low frequency thump.
So before going to the trouble of having a dedicated line installed, I would repeat the suggestion that was made early in the thread to try running a long extension cord to another room. If that solves the problem, then yes, a dedicated line probably would also.
Regards,
-- Al