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MBLES:
The measurements you made were inadequate and incomplete. I would think that electricians would have more complete training on troubleshooting voltage problems at a main panel.
I open electrical panel and took a voltage reading, on one leg i got 109-120 the voltage bounced when taking the measurement and the other phase was 134volts. I didnt know what to think of the issue. I took reading on line side of breaker so i think its coming from POCO. I also notice the home had no ground rod attached.
I assume your voltage measurements were from hots to neutral. If only one phase showed the large voltage changes, then neutral is not the primary problem. But on your apparently stable side the 134 V is abnormal.
If both hot supply lines are good including the transformer and all terminations and devices between the transformer and the main panel, then you should have a fairly steady 240 V ( or some other reasonably stable value ) reading line to line. My home voltage looks like, 1 second resolution, --- see photo P26 at
http://www.beta-a2.com/EE-photos.html .
The voltage readings you take should be from probes directly on the line side wires, not on the breaker lug, or other termination.
Is the neutral bus connected to earth by any other means than the nonexistent ground rod, such as a copper water pipe, vs only at the power company transformer? Using a high impedance DVM what is the voltage of the incoming neutral wire, again directly on the wire, relative to a screwdriver in the earth outside? I believe mine is below 1 V. There should no major fluctuation like your 10 V or 1/2 of this. If there is, then there is a neutral problem back to the transformer. My ground rod is 150 ft of 1" diameter copper water supply line.
Your 134 V reading is suspect, but if it is stable while the other phase to neutral jumps around, then your primary flicker problem is from the hot line of the flickering phase from main panel to the transformer, and could even be inside the transformer.
When you have this degree of voltage variation and suspect a neutral problem, then two 120 V low wattage ( easier to look at ) incandescent bulbs may be more useful than two meters to simultaneously monitor the two phase voltages to neutral.
If your 134 V reading was stable and read with a meter of adequate accuracy, then you need the power company to find out why.
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