The old meter base when they removed the old meter was burnt wondering if there was a short in the meter at some time in the past
Probably more than likely a loose and or corroded connection on one of the live phase conductors. If the connection has degraded enough the load will cause arcing in the bad connection. Arcing creates heat and burning. Enough heat can be generated to cause the insulation covering the conductor to burn at the termination. The arcing can and does cause higher than normal harmonic distortion on the Line.
Is the electrical service fed overhead?
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