I just bought a 6 year old house and have noticed the lights dim momentarily when the heat pump starts up. I called the EMC power company and they sent a crew out to check everything including in the meter base as a courtesy to me. They said they checked the voltage as well. They gave it a clean bill of health. The crew chief called me and said they had been called out once before by the previous owner and had found nothing wrong with their side of the power hookup. He did offer that he has the same problem in his own home. In my last house that was serviced by an NON EMC power company I have never had this problem. The house has two panel boxes a 200 and a 100. I have not looked at the hook up to see if the 100 is a sub panel. It may be. The wiring is overhead if that matters not under ground.
This was suggested to me so I would like to ask the HVAC pros if this could be the problem. I was told it might be the start-up capacitor and/or the system may be overcharged with freon. Someone also told me to check the grounding of the house. I do not mind paying for an HVAC tech. to look at the system if you all think it is money well spent. I would like to add that the lights dimming is very momentary and has not blown any breakers nor has it caused any issues that I know of to date.