You might try bringing along a battery-operated AM radio as well and wander around with it, tuning it up and down the band to see if there's a strong buzzing interference in the area. The slight leakage across insulators and through the air in high voltage AC makes a lot of pretty strong harmonics.
If it is actually due to the power fields around there, you may have to enlist the help of a Ham radio operator with some additional equipment to track down why it's affecting your battery. You may also want to check the technical service bulletins (TSBs) on your make and model to see if there's a notice on this particular problem.
Put it this way: I would not discount the idea that the power fields could be affecting something (including the on-board computer) to drain down your battery, and nowadays, if the battery voltage falls below something like 8 or 10 volts, the onboard computer goes dead and the vehicle is unresponsive. In the pre-computer age, you could still crank the engine and start the car with a much lower battery voltage than 10V.
I heard (but don't have actual knowledge) of a case where parking an older vehicle on an uphill incline made a mercury switch in the hood turn the under-the-hood engine compartment light on, which wasn't seen because the light was under the hood. This drained the battery overnight. This could also happen, I guess, with trunk lid lights, but that's not the way I heard the story. The "fix" in this case was to reset the mercury switch in its clamp, since somehow it had got bumped out of alignment slightly.
I guess they don't use mercury switches anymore, though. One broken mercury switch, and we're all gonna DIE!
Terry, 230RN