DF/DT ROCOF

Do you have access to a relay test set? It sounds like your relay needs to be checked, 5 Hertz/sec rate of change would be indicative of an imminent system collapse. Was there any maintenance performed recently, perhaps it was set to 0.5 or 0.05 in error, that would cause tripping on almost any change in the system frequency.

It looks like that one of your dg sets is having some problem in the engine portion , better have a cylinder cut out test , which is reducing engine rpm & thus fall of frequency at full load. Also check the communication cable (load sharing) of the synchronising relay of respective dg sets.

While synchronised, the frequency varies only as the grid varies. Changes in speed setting reflect themselves as changes in loading unless generator starts to 'slip'. A df/dt relay may operate when a generator falls out of synchronisation.