I have doubt, in one of compressor the GG speed already reached 96% while the PT speed is still 80%. When the load increased, the GG increased to 100% already while the PT is still 83%. Anyone can explain?

For me,just checked the inlet guide vent degrees for the calibration.

If GG speed has been achieved to 100 %. It means its VGV are working and enough power is available for PT however load on mechanical drive system (Pump or Compressor) has been changed due to change in suction or discharge conditions or drastic change in properties of fluid being handled by pump or compressor (whichever is being driven by Gas Turbine). Check the performance curves of driven equipment to ensure that operation at this condition is still safe or not. If suction or discharge conditions are changed enough to take operation of compressor to off optimum and inefficient zone on performance curve, then restaging is the solution (If single package is installed but in case of parallel packages in operation, one or two of the packages can be turned off to get back the operation into high efficiency zone)

The GT was running in "droop" mode for sure. Need to know if it was a generator or mechanical application. I believe it was a mechanical application.

You may need to check engine's inlet guide vanes position (IGV). Opening of IGV is a function of GG speed. If IGV failed to open at required stage you will have very high GG speed