Unbalance Current Effect on LV Relay

Yes.

When the generator CB opened due to differential fault, the system (grid) voltage suffered a disturbance and became unstable.

System voltage instability is/was a result of the loss of available power on/in the grid due to sudden removal (loss) of generation which in turn required other generators either at your site or generators at other locations feeding the grid to absorb the sudden increased load.

Due to the generator protection event tripping speed, generator excitation circuits cannot possibly recover fast enough to keep the system voltage from immediately sagging and then becoming unstable.

The LV relay sensed the voltage sag and isolated your site from the grid.

You should be able to extract and view the voltage level DATA from the event recorder for a period of time beginning just before the event occurred throughout the event time period to verify the exact amount of voltage sag that occurred.

I suggest you identify the root-cause of the differential trip before putting the faulted generator back on line.

Good luck and stay safe.