Oatmeal, you're sure it's the power lines?? I have a nearby noise at my QTH, and when I switch from my vertical antenna to my horizontal dipole it pretty well drops the noise completely. It also depends on the way the dipole is facing as to how much noise it will reject is what I have found also. This may not hold true for your situation, but it might not hurt to try a dipole pointed at 45 degree angle to the power lines and not parallel to them. Try to either stay below or get well above them. Like I said, my noise is from an outside source and it hits me with s3-s5 signal 24/7. Every once in a while it gets quiet.
It's weird but by just flipping to my horz dipole that is facing 45 degrees from the noise, from my vertical, the noise pretty much disappears. I can still barely and I mean just barely hear the noise. It drops all the way down to no real signal per say, or s0. Just a slight buzz. Best tuning to do might be to get a cheap one and place it up and see what happens. They can be had for less then $15 on eBay. Can't hardly build one for the price of some of the ones on eBay!! JMHO and my own experience. Like I said, it might not work at all for your particular noise issue, but it might be worth a shot as you truly never know unless you actually try it. Again, JMHO.