180113-1436 EST
1haz:
You have a neutral problem as you have been told.
Get a 1500 W space heater to use as a test load. Even a 250 W incandescent might be adequate. With your 15 V change from the washer I could probably find the source of the problem with a 100 W bulb and a fluke 27.
Go to the main panel. Put your meter probes directly on the incoming neutral wire and one hot wire. I really mean directly on the wires, and not on the terminations. Cycle the 1500 W heater on and off at any convenient outlet. At my main panel this approximate 10 A change produces an 0.4 V change. This was on the non-loaded phase, and on the loaded side it was 0.7 V. In your case it clearly seems to be a neutral problem, and thus the change to either phase will be nearly the same.
If you see less than 1 V change, then it is not a power company, and/or meter problem.
For tests where the change was less than 1 V or small do the following:
Keep the neutral probe were it was, and move your hot test lead to the neutral buss, and while cycling 10 A on and off, check voltage between actual incoming neutral wire and the neutral bus bar. This should be way below a 1 V change, not a lot of millivolts. If the voltage change is substantial, then you know where at least part of the problem is.
Depending upon what you see probe other places still keeping your reference point the incoming neutral wire.
For tests where the change was greater than 1 V, then you need to do others tests at various points. Provide us more data.
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