Electrical Tech

Your question is not very clear to me but i will try... You are saying that when 2 gens are in parrallel... one is with leading pf and the other is with lagging pf... This situation can arise if the voltage generated by the two gens are not exact. The generator producing lower voltage will have higher power factor. Good luck

I don't understand the "island mode" except of course if you've run aground, then your problem is cooling water...

One leading, and one lagging power factor is an indication of wattless current, in other words you're using one machine as a load (the leading p.f. machine).

If the two machine sets are identical check your no-load AVR voltage with the same instrument. You want to compare excitation voltages between the two machines, and the stator output voltages, they both need to be the same (on no-load). Then check to see if you have continuity on the AVR equalising bus-bars, apart from the stators being in parallel, the AVR's should be in parallel too - for load sharing.