How do you do a earth loop impedance calculation?

The earth-fault loop includes the consumer's line conductor, the consumer's protective conductor, and the earth parth external to the consumer's installation (including the low-voltage winding of the transformer, the distribution line conductors to the installation, and the earth return path.

The purpose of this test is to measure the actual value of the earth-fault loop impedance and to confirm that its value complies with the tabulated maximum values listed in BS 7671:2008 Regulations for Electrical Installations, Tables 41.2 - 41.5. The value must be low enough to enable sufficient fault current to flow to cause any overcurrent protection device to operate within the periods specified -i.e. 0.4 s for circuits supplying socket outlets and fixed equipment in bathrooms, and 5.0 s for circuits supplying fixed equipment.

The theory behind the test is as follows. With no current flowing around the loop, there are no voltage drops and, so, the transformer's full open-circuit voltage (U1) will appear between the line and protective conductors at the point where the test is conducted.

A simulated earth fault is then applied, by inserting a current-limiting resistor between the line and protective conductors. The resulting fault current (IF) is then measured, together with the voltage drop (U2) across the limiting resistor. The duration of this fault should not be allowed to exceed two cycles (40 ms at 50 Hz) to avoid damaging the circuit.

The earth-fault loop impedance is then calculated by dividing the difference between the two voltages (U2 - U1) by the resulting fault current (IF), which will give the impedance of the complete loop (including the limiting resistor), from which we must then subtract the value of the limiting resistor.

As the simulated earth fault must not exceed 2 cycles, this (theoretical) test obviously cannot be conducted with a voltmeter and an ammeter, and so it is conducted with a commercial instrument, called an earth-fault loop tester, which performs all the measurements (U1, U2, IF), makes all necessary calculations, and provides an digital readout directly in ohms -while, at the same time limiting the duration of the test to less than 40 ms.

Before conducting the test, the continuity of the protective conductors must have been confirmed. If the test was to be performed with a break in the protective conductor, then the protective conductor up to the point of that break would represent a safety hazard to anyone in contact with equipment at the time.