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Someone tells me you need oil for the transformers because it prevents arcing. But isn't air the strongest in terms of dielectric breakdown? I remember from uni that as the dielectric constant increases, the breakdown voltage decreases. Is this correct?

Transformer oil not only prevents arcing but it also prevents the transformer from over heating at its operating temperature.

So isn’t air the best against voltage breakdown?

Well the answer to that is no. According to my experiments It shows me that yes air does have a voltage breakdown in the gap of 1 inch at a voltage of 20,000 volts. But transformer oil has a voltage breakdown of 70,000 volts per inch.

If you put it this way, as the distance from the two conductors gets larger and larger the dielectric breakdown voltage needed to arc across that distance gets larger.

Then yes you are correct.

How do you keep the wires in place? Air won't help. It's done with cardboard soaked in oil.

In addition, gases have a nasty property: they have very low pressure so randomly ionized atoms are easily moved by the electric field. If the gas pressure is low enough for the voltage, the ions and free electrons reach the counter electrode before they could recombine so you have a conducting channel, and the heat from the current flow will ionize even more atoms. Oil prevents that simply by its viscosity.

If you want to have excellent isolation with a gas, you had to use a hard to ionize gas with high viscosity, for example Sulfur hexafluoride.

Oil is predominantly used below 5MVA due to the lower cost of oil compared to dry types using epoxy and mica tape. It is necessary for cooling, thermal spreading of hotspots and for electrical insulation.

Partial Discharge (PD) is all about the flow of ions in a plasma, like aurora or corona. It needs some contaminants to collide and cause the discharge.

From my experiments on Nydas Transformer oil in a transformer factory to exceed 25kV/mm. With typical results varying 25 to 40kV.

With more expensive processing to remove ppm level contaminants, it can reach 70kV/mm. Those that can afford the $50k+ machine, use them but some skill in invisible contamination processing and process quality controls in a clean room environment is necessary.

The test is done with about 1kV/s ramp with ultraclean large (~2cm) brass flat electrodes in a clean glass beaker with tapered smooth edges.

Like Air, it is mobile contaminants and pressure changes that can lead to partial discharge that causes variability in the breakdown voltage BDV of any insulator.

For transformer oil the Partial Discharge also breaks down the large hydrocarbon chain into H2 which has a lower explosive threshold of 4% concentration.

Clean air breakdown is 3kV/mm while dirty moist air is < 500V/mm in flat to flat, while point to point is about 1/3 of these Voltage thresholds.

An ultra low vacuum gives a high BDV but a partial vacuum very low as reduction of molecules allows for less drag and higher kinetic energy when an ion in air hits the conductor. ( See Paschen law. )