LRG Vs Solid Grounded system

I assume you're talking about medium-voltage. Low resistance grounding for low voltage systems <1000 V is generally never done for safety reasons.

Low-resistance grounding at medium voltage allows for selective coordination of ground fault while still greatly limiting ground fault damage compared to solid-grounding.

High-resistance grounding further limits ground fault damage, but it is difficult to coordinate - so when a ground fault is detected the entire system is generally shut down. On HRG systems, ground faults are normally detected based on the voltage instead of current. It works well for limited systems such a generators with a unit step-up transformer. It's less common in industrial systems with extensive medium-voltage distribution. Hybrid sytsems are sometimes used whereby grounding is switched between high and low resistance grounding depending on the fault location.

Dave

High resistance grounding is not suitable for MV distribution systems where there could be extensive cabling. The cabling increases the capacitive leakage currents and thus the earth fault current cannot be limited to 10A or even 25A. IEEE Red book defines High resistance earthing to limit the earth fault current to 25A.
It is popular to limit the earth fault currents to around 300A and this is to limit the possibility of damage to the iron core laminations in motors when the fault happens to be in the stator winding slots.
It is an economical and practical possibility to rewind a motor affected by winding fault but the core damage means expensive repair or rebuilding of core.
IEEE Red book has good discussion on the earthing options for MV systems.

The following may be of interest:

Regards.


System earthings in LV



Earthing systems worldwide and evolutions