Murray loop test for open and short circuit faults

The Murray loop test is a bridge method for locating faults in underground cables. For a short-circuit or earth fault it compares the resistance of the faulty core with the resistance of a sound core (Wheatstone bridge). For an open-circuit fault it compares capacitances.

Murray loop test (short-circuit or earth fault)

This is a Wheatstone bridge method. It needs one sound core running alongside the faulty core.

   +--------------(G)--------------+
   |                               |
   B ---/\/\------+------/\/\----- A
   |     P        |        Q       |
   |           battery             |
   |              |                |
   |            earth              |
 sound core                   faulty core
   |                               x  <- fault to earth
   |                               |
   +====== loop at far end ========+

1. At the far end, connect the faulty core to the sound core with a low-resistance link, so the two cores form a loop.
2. Connect ratio arm $P$ (a variable resistor) to the test end B of the sound core and ratio arm $Q$ to the test end A of the faulty core, and connect the galvanometer across A and B. Connect the battery between the junction of $P$ and $Q$ and earth (for an earth fault). For a short circuit between two cores, connect the battery to the other shorted core instead of earth.
3. Adjust $P$ and $Q$ until the galvanometer reads zero.

Let $R_x$ be the resistance of the faulty core from the test end to the fault, and $R_L$ the resistance of the whole loop. The arm next to $P$ is the rest of the loop, $R_L - R_x$, and the arm next to $Q$ is $R_x$. At balance:

$$\frac{P}{Q} = \frac{R_L - R_x}{R_x} \;\Rightarrow\; R_x = \frac{Q}{P+Q}\,R_L$$

If both cores have the same cross-section and the cable length is $L$, resistance is proportional to length:

$$x = \frac{Q}{P+Q}\times 2L$$

Here $x$ is the distance from the test end to the fault. The fault resistance carries only battery current, so it does not affect the balance.

Murray loop test for an open-circuit (broken-conductor) fault

A broken core gives no resistance loop, so capacitance is compared instead (the Murray capacitance loop). The capacitance of a core to the sheath is proportional to its length.

1. At the far end, leave the broken core and the sound core open (insulated).
2. Connect ratio arm $P$ to the broken core and ratio arm $Q$ to the sound core. Connect an AC source (or a battery with a key and a ballistic galvanometer) between the junction of $P$ and $Q$ and the sheath, and connect a detector between the two cores at the test end.
3. Adjust $P$ and $Q$ for a null. The arm impedances are $1/\omega C_x$ (broken core up to the break, length $x$) and $1/\omega C_L$ (sound core, full length $L$). At balance:

$$\frac{P}{Q} = \frac{1/\omega C_x}{1/\omega C_L} = \frac{C_L}{C_x} \;\Rightarrow\; x = L\,\frac{C_x}{C_L} = L\,\frac{Q}{P}$$

($P$ is the arm joined to the broken core.)

Points to note

• The method needs at least one sound core of the same size.
• It is accurate when the fault resistance is low enough for a sensitive galvanometer reading.
• Fault-to-earth resistance does not affect the result, because it lies in the battery circuit.