Transformer hum - DC offset? Does this cause transformer breakdown?
Step One: Jamming just any sort of multimeter into a wall socket = NO! Jamming a reasonably proper one into a wall socket is slightly less no, but they still might not like high voltage AC when set on DC. The normal hobby-type multi-meters are not for high voltage or high power, way too dangerous.

To add to it, it means nothing if you do anyway, you may get a reading close to what would be a fair approximation, you may get something way off, nothing is fully guaranteed in DC mode on a normal multimeter. You'll need a true RMS meter to get some real info, or an oscilloscope for good information to act on.

"Humming" in a transformer itself can mean many things and even if you think you can "hear the difference" between all those, chances are beyond good that actually you can't. The majority of the power in your system is AC at the rated frequency, because that is what's supplied. So the transformer will always hum mostly that frequency.

But there can be mains contamination that causes it to hum more loudly, this is most likely caused by one or more devices drawing power with a non-unity power factor or by clunky old-fashioned triac dimmers (especially when dimming "affordable" LED lights). It's likely they are in your own house, but it's not guaranteed. Those contaminations can also be periodical, so they may not introduce any DC effect, but run at 2Hz, 100Hz, 500Hz, 10Hz, many kHz, or just occur balanced at the same periodicity as the mains frequency, but with sharp edges. A (much) higher than mains frequency is less likely to have enough power in a mains line to cause a laminated transformer to make any more sound, but it isn't impossible. Either way, measuring it as DC setting will still give 0V if there is any periodicity balanced around 0 that's "faster" than the meter's update rate, so DC is a very deceptive term to use here.

A power factor is a number that tells you how neatly the voltage and current signal match each other in phase. If they are exactly equal, i.e. the current is 0 when the voltage is 0 and the current is +max at a +max voltage, then the power factor is 1. When they are out of phase (i.e. the current is +max when the voltage is 0) the power factor is 0. While a power factor of -1 would just mean you are supplying energy, i.e. your solar inverter is doing its work: -max current at +max voltage. 

Capacitors and inductors in an AC system will cause the voltage and current to go out of phase, because they can store energy, but one will supply when the other takes, so they can compensate each other when you do the maths right. 

The rules for power factor are quite strict these days, but used to be slightly slack in "the early days". Power companies don't like it if you have a low power factor in your house, because it means you are using more current than is registered as power in watts, and that current determines how thick they have to make the cables, while watts determine what you pay. Their transformers will become less efficient at low power factors as well.

I would not be surprised if the autotransformer is a partial or possibly full cause of noise in your mains, they are commonly messy. Basically what you do is:







simulate this circuit &ndash; Schematic created using CircuitLab

Which means you have an inductance L1, that is over-dimensioned (to allow you to "tap" some power) to move towards transformer effect. The inductance then has an effect on the power factor, but even worse, when loaded it can have all kinds of effects, depending on what your load asks from it.



All that said; overloading also causes excessive humming...