Three Diesel Generators Synchronizing With National Grid Problem

If it has worked for a long time and now behaves as you describe, then "something has changed".

While there are many symptoms, it is probably a single and simple item. RESIST the temptation to fiddle and adjust as this will then create additional non-standard settings that will need to be recovered.

It is either a "breakdown" or induced failure.

For induced failure, has there been ANY work done on the system that corresponds to the beginning of these observations. Somehow an adjustment/change was made that created this new situation. For instance have the engines been serviced or the control panels worked on? It may be as simple as having #3 set as master (while #1 was serviced) but #1 when returned to service was hard wired as master, so the controller is getting conflicting inputs.

If it is "breakdown", then the supplier should be able to support you with the means to diagnose this set-up by providing a sequential series of tests.

I have put the suggestions with supplier contact second only so that you can eliminate any simple local issues. The system supplier is the expert and will provide timely professional answers rather than the delays and such you will encounter with an anonymous forum.

A sticky mechanical linkage for the governor / engine output will make the engine surge. This is likely at the fuel injector linkage, where the electronic actuator actually moves a mechanical piece of equipment to adjust the fuel flow, assuming typical mechanical injectors, per this photo?

However, since the speed is stable in test mode, then perhaps the isochronous portion of the speed control is active, trying to hold speed, or the control is attempting to make the generator take on load before there is load to take on. Maybe your generator main breaker shows closed before it is, and confuses the control enough to make it speed up, then over speed takes it back down.

It is likely some moving part, some mechanical component, like a switch or similar component.

Just off the top of my head, it sounds like the generator governor is set to isochronous rather than droop mode when you are trying to parallel.

Isochronous mode will attempt to maintain an exact speed whereas droop mode will cause the generator to slow down slightly as it acquires more load. When paralleling with an existing bus, for stability, the generator governor must be in droop mode.

https://www.quora.com/What-is-droop-control-for-a-generator

Check/clean/replace your fuel filters. Dirty/clogged fuel filters can make an engine hunt.