Voltage/current stabilizing
Adding transformers will not "stabilize" anything, I have no idea where you got that idea, but it's wrong. Sometimes people step up the voltage to a higher level (like 480V) and back down again for a long distance run so that the current is less, because less current results in less voltage drop since voltage drop is a function of I (current) Squared / R (resistance, in this case of the wire itself). 

But you can ALSO just decrease the R by using larger gauge wire, which would cost you a LOT less than adding transformers. There are on-line Voltage Drop calculators that will give you the size of wire you need. According to one that I found, to have no more than a 3% VD on a full 20A load at 120V, you would use #4 Cu wire or #2 Al.