Earth fault loop impedance (Zs) is a characteristic vital to the protective measure Automatic Disconnection of Supply (ADS), which is used for fault protection in most electrical installations. The ohmic value of the earth fault loop impedance at the electrically most remote point of each circuit is required not to exceed the limiting (or maximum) value permitted by the Wiring Regulations BS 7671. The limiting value depends on the characteristics of the fuse, circuit-breaker or residual current device which affords fault protection in the circuit concerned. The intention is that, in the event of an earth fault of negligible impedance between a line conductor and an exposed-conductive-part, the fault current will be of sufficient magnitude to cause the protective device to automatically disconnect the supply to the faulty circuit within the maximum time permitted by BS 7671.

The meaning of earth fault loop impedance
Earth fault loop impedance (Zs) is the impedance of the intended path of an earth fault current (known as the earth fault loop) starting and ending at the point of the fault to earth.

Composition of the earth fault loop
The earth fault loop comprises the following, starting at the point of the fault:

• the circuit protective conductor, and

• the Main Earthing Terminal (MET) and earthing conductor of the installation

• for TN systems, the metallic return path

• for TT and IT systems, the return path through the conductive mass of Earth

• the path through the earthed neutral point of the transformer (or other source of energy, such as a diesel generator set or uninterruptible power supply)

• the transformer winding (or the equivalent in another source of energy), and

• the line conductor from the transformer (or other source of energy) to the point of fault

As indicated in items (iii) and (iv), the nature of the return path to the source of energy differs fundamentally, depending on whether the installation forms part of a TN system or part of a TT or IT system. In a TN system, the return path is metallic, and is formed by the protective conductor of the supply network - either a dedicated protective conductor (TN-S system) or a combined protective and neutral (PEN) conductor (TN-C-S or TN-C system). In a TT or IT system, the return path to the source of energy is the earth return path, comprising the installation earth electrode, the conductive (or general) mass of Earth and the source earth electrode.
Figure 1 illustrates the earth fault loop of a TN-C-S system (which is one example of a TN system).

 TN-C-S system (showing the earth fault loop)
Fig 1

The earth fault loop of a TN-C-S system, as shown in Fig 1, is typical of the earth fault loop of all types of TN system, in that it is wholly made up of metallic conductors.

The earth fault loops of the other types of TN system (TN-S and TN-C), whilst still being wholly metallic, differ from that of a TN-C-S system in the following respects:

• In a TN-S system, the return path to the source of energy is through a dedicated protective conductor of the supply, not though a combined protective and neutral (PEN) conductor

• In a TN-C system, the circuit protective conductor is combined with the neutral conductor of the installation, in a PEN conductor

Figure 2 illustrates the earth fault loop of a TT system Fig 2

The earth fault loop of a TT system, as shown in Fig 2, also typifies that of an IT system, in that with both types of system, the return path to the source of energy is through the conductive mass of Earth. However, in an IT system, the neutral point of the transformer or other source of energy is not directly connected with Earth; either there is no connection between the neutral point and Earth, or such a connection is made through a high impedance.

Impedance of the earth fault loop
The earth fault loop impedance (Zs) is the impedance of the earth fault loop starting and ending at the point of the fault to earth.
It is useful to consider the earth fault loop impedance as consisting of two major parts:

• The impedance of the part of the earth fault loop which is external to the installation (Ze), and

• The impedance of the part of the earth fault loop which is internal to the installation (Z1 + Z2).

External earth fault loop impedance (Ze)    
The impedance of the part of the earth fault loop which is external to the installation (Ze) consists of the following, starting from the source of energy:

• the line conductor from the transformer (or other source of energy) to the origin of the installation,

• for TN systems, the metallic return path,

• for TT and IT systems, the earth return path (comprising the installation earth electrode , the conductive mass of Earth and the source earth electrode),

• the path through the earthed neutral point of the transformer (or other source of energy, such as a diesel generator set or uninterruptible power supply), and

• the transformer winding (or the equivalent in another source of energy)

Internal part of the earth fault loop impedance (R1 + R2)
The impedance of the part of the earth fault loop which is internal to the installation (Z1 + Z2) consists of the following, starting from the origin of the installation:

• the line conductor from the origin to the point of earth fault,

• the circuit protective conductor from the point of earth fault to the MET of the installation, and

• the MET and earthing conductor of the installation.

It is convenient to express Zs as the sum of its external and internal parts, as shown in equation (1).

Where:

• Zs is the earth fault loop impedance

• Ze is the earth fault loop impedance of that part of the system which is external to the installation

• Z1 is the impedance of the line conductor between the origin of the installation and the point of the earth fault

• Z2 is the impedance of the earthing conductor of the installation and the circuit protective conductor between the MET of the installation and the point of the earth fault.

The expression for Zs may be simplified to that shown in equation (2) where the inductive reactance of the line and circuit protective conductors within the installation is very small compared with their resistance. This is generally the case, for example, where the conductors consist of cables, or cores of a cables, in circuits operating at a frequency§ of 50 Hz, rated at up to about 100 A, installed in accordance with the requirements of BS 7671.

Where:

• R1 is the resistance of the line conductor between the origin of the installation and the point of the earth fault

• R2 is the resistance of the earthing conductor of the installation and the circuit protective conductor between the MET of the installation and the point of the earth fault.

For a ring final circuit, the value of R1 + R2 in equation (1) includes the resistances of the two paths of both the line conductor and the circuit protective conductor to the point of the earth fault.

Requirements for earth fault loop impedance to be determined

External earth fault loop impedance (Ze)
External earth fault loop impedance (Ze) is one of the characteristics of the supply to an installation that have to be determined in order to meet the requirements of BS 7671.

Earth fault loop impedance (Zs)
It is required that, where protective measures are used which require a knowledge of the earth fault loop impedance (Zs), the relevant impedances are to be measured, or determined by an alternative method.