Source: Jianping Wang, ABB, 2013-06-14 KTH
Arc which developed at the transmission line during fault occurrence can be due to an object very near to the line or due to lightning which make the fault current to jump to the transmission tower (earth). This arc representing an equivalent value of fault resistance, Rf. This Rf value is depends on the arc length and fault current. The longer the arc length, the higher the Rf while the higher the fault current the lower the fault resistance as shown by the equation in the figure above.
The value of Rf can affects the accuracy of fault locating device and also the protection relay which uses the impedance based method (such as distance relay). For impedance based method relay, Rf can affects the accuracy of the relay in determining the tripping signal decision especially for fault near to the setting of zone reach.
