Is it only one appliance that causes this?
If an electrician doesn't answer on this board, you may want to call one in to look at it. Do the load analysis first, but it sounds more like something is out of phase. I'm not an electrician, but this sounds like other problems I've read about on these and other forums. The power is in two phases. Usually one side of the breaker panel is one phase, the other side is the other phase. You've got too much on one side.
Everytime the AC would kick in all the lights in the house would dim. I found out that the transformers the power company had down the street were like 40 years old and in definate need of replacing. Others on my block on a different transformer found this same issue was corrected when theirs blew up one night and the power company replaced the transformer.
As others have said it may or may not be you.
If its happening when the refrigerator comes online then you may want to look into balancing the loads.
Also you might want to check to see how many other circuits may be on the same circuit when this load comes on.
The first place to start is to call the power company and have them check if all incoming conductors are in good shape this includes their connections especially.
Also, pay attention to which appliances make it happen. Is it ALL major appliances or only certain ones? Are they on the same breaker?
If ALL lights and ALL major appliances in your house experience the problem, then it's probably the power company's area of responsiblity. Otherwise, you'll have to look further in your house.
If it's all on one circuit, then check every outlet and connector box on that circuit for tight connections, especially neutral.
A remote possibility is that the breaker for that circuit could be bad.