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K8MHZ:
A suggestion.
If the transformer is in your backyard, then its ground rod is there also, and a little digging will expose the rod or the wire to it. Measure the voltage from the transformer ground rod to your main panel neutral buss. From this with high probability you can tell if there is a power company problem.
Also the two light bulb or two meter test at the main panel on the wires from the meter, not on the lugs, will tell you if the problem is before the main panel.
If the transformer is not in your backyard but some distance away and you do not want to or can not run a test wire from transformer ground to your test meter at your main panel, then drive a 12" screwdriver into the ground in a position that is in the path from the transformer to your panel. From this you can monitor the ground voltage and make an estimate of whether there is a bad neutral.
On various jobs you could run ground voltage tests to develop some experience of what to expect. I have some ground currents that run thru my yard that are not from my transformer and I can see step changes in these currents. My usual ground voltage levels are in the 100 MV range for a distance of 12 ft between two screwdrivers.
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I use a slightly different method.
I think it's much better to know how to use test equipment in order to make sure the problem isn't on the HO side before making the call to the POCO. If I see a problem at the top of the main (or bottom of the meter if for some reason it is not locked and I can get to it), I know the problem is on the POCO's side. Also, eliminating HO side issues gives you a 'standard' that you can use to base the POCO's line integrity with.
I know your experiment will produce some results, but such effort is not needed. There is no need to dig up ground rods or even go outdoors. I can check for a bad connection from inside by taking readings with different loads on different legs (NOT PHASES) and making an analysis therein.
Perhaps you misunderstood me when I said I chased the problem all over the house. I didn't mean it baffled me, I meant that I spent time in various spots checking and repairing bad connections. After I got everything on the load side of the panel up to snuff, I still had issues. It took me less than 5 minutes to know I had a POCO issue once I gained access to the top of the ancient 60 amp fuse panel.
The currents you see in your own yard are also POCO issues. How it happens has been discussed here several times under the guise of stray currents or stray voltages. To go any further down that road would certainly put the thread at risk of a hijack.
I do thank you for your time and your suggestion. It's just that over the years I have developed very quick and accurate troubleshooting methods that I can trust, and trust every time. The very basis, though, is understanding how test equipment works and what the readings you get actually mean.