Loop Tests for Locating Faults in Underground Cables

We have seen the types of faults in underground cables and how to detect them using a megger in the previous article. This article explains how to locate the exact place where the fault has occurred.
There are various methods for locating the faults in underground cables. Following are some popular methods explained.

Murray loop test for location of faults in underground cables

Murray loop test is the most common and accurate method for locating earth faults and short-circuit faults. However, to perform the Murray loop test, it is necessary that a sound (good) cable runs along the faulty cable.This test employs the principle of Wheatstone bridge for fault location.
To perform the Murray loop test, the alongside sound cable and the faulty cable are shorted with a jumper conductor at the far end. The test side end is connected through a pair of resistors to a voltage source. Also, a null detector or galvanometer is connected between the two conductors at the test end. The circuit diagram is as shown in the image below.
murray loop test for location of faults in underground cables
Once the connections are made as shown in the above circuit, adjust the values of R1 and R2 so the null detector/galvanometer shows zero reading. That is, bring the bridge to the balance. Now, in the balanced position of Wheatstone bridge, we have,
murray loop test equation 1
Now, if r is the resistance of each cable,
then, Rx + Ry + Rg = 2r
Putting this in the above equation,
murray loop test equation 2
We know, the value of resistance is proportional to the length of the cable. Therefore the value of Rx is proportional to the length Lx. Therefore,
murray loop test fault distance location formula
Where L is the total length of the cable under test. (The value of L is proportional to the value of Rg.)

Varley loop test

Varley loop test is also for locating short-circuit and earth faults in underground cables. This test also employs the principle of the wheatstone bridge. However, the difference between Murray loop test and Varley loop test is that, in Varley loop test resistances R1 and R2 are fixed, and a variable resistor is inserted in the faulted leg. If the fault resistance is high, the sensitivity of Murray loop test is reduced and Varley loop test may be more suitable.
Varley loop test for location of underground cable faults
To perform Varley loop test, connections are done as shown in the circuit diagram above. Resistors, R1 and R2 are fixed and the resistor S is variable. In this test, the switch K if first thrown to the position 1. Then the variable resistor S is varied till the galvanometer shows zero deflection (i.e. bridge is balanced). Lets say, the bridge is balanced for the value of S equal to S1 Then,
varley loop test equation 1
Now, the switch K is thrown to the position 2 and the bridge is balanced by varying the resistor S. Say, the bridge is balanced at the value of resistor S is equal to S2. Then,
varley loop test equation 2
Now, putting the result of eq.(ii) in eq.(i),
varley loop test equation 3
Since the values of R1, R2, S1 and S2 are known, Rx can be calculated. When Rx is known, the distance from the test end to the fault point Lx can be calculated as,
Lx = Rx/r
Where, r = resistance of the cable per meter.