How does the single coil buchholz relay connected to the tap changer afford transformer protection.

Here is a quote from Wikipedia:

"Buchholz relay

A Buchholz relay is a safety device sensing the accumulation of gas in large oil-filled transformers, which will alarm on slow accumulation of gas or shut down the transformer if gas is produced rapidly in the transformer oil."

Relay - Wikipedia, the free encyclopedia

It appears to be a sensor used to prevent explosions. If gas accumulates, it could mix with oxygen and explode. Oil in the transformer won't explode because it's not mixed with oxygen.

A Buchholz relay may be employed as a gas accumulation relay, that is, as gas is generated in the tap changer or transformer, it is collected in the Buchholz relay. Once the amount of gas colleected reaches the trip point the Buchholz relay may send in an alarm, trip a circuit breaker to remove the tap changer and transformer out of service, etc. A second application of a Buchholz relay is as a sudden pressure relay (although there are better relays for this purpose) and senses a rapid increase of pressure due to some failure mode of the tap cahnger or transformer.

The bottom line is that a Buchholz relay or any relay, affords protection by reacting to a set of conditions selected by the user in which the relay closes or opens a contact causing some set of protection devices (circuit breaker, etc) to operate.

Hope this helps.