The df/dt protection is used to identify abnormal changes in system frequency and take remedial actions in order to prevent generator overload and the resulting blackout.  The df/dt operates faster than ordinary under frequency relays as it is able to predict the under frequency much earlier.   

df/dt relays are also known as ROCOF relays (Rate Of Change of Frequency Relays) The df/dt is usually wired to a load shedding system which trips select breakers to isolate loads. 

The df/dt functions by measuring the rate of change of frequency.  When the frequency changes too fast, it is an indicator of a forthcoming under frequency.  The setting of the df/dt relay is in Frequency/Time in seconds. e.g. 0.3Hz/second or 0.4 Hz/.5 seconds.

Some manufacturers provide a more reliable setting involves specifying two frequency set points and the time taken for the frequency to cross the two limits.  For instance, a df/dt relays can be programmed to operate if the system frequency crosses 48.5 Hz and 48 Hz in 0.4 seconds

The Factor of Earthing in a three phase system is defined as the ratio of the phase voltage (phase to earth voltage) on a healthy phase during the fault at the rated frequency to the phase voltage of the healthy phase during normal situation.  

When an earth fault occurs in one of the phases of a three phase system, the voltage vectors are distorted.  The neutral shifts in the direction of the fault phase.  This causes the voltage in the other two healthy phases to rise. 

The factor of earthing determines the rise of voltage in the healthy phases when one of the phases has a earth fault.

The factor of safety is 100% for an isolated neutral (floating neutral) system.  It is 80% for an effectively earthed system while it is 57.7% for a solidly earthed system.

The factor of safety is an important parameter while performing an insulation coordination in a system.