Earth Loop Impedance

13.3.4 Earth Loop Impedance

A key factor in the design and choice of earth continuity conductors, e.g. cable armouring, bonding straps, and fault current protective devices is the ‘earth loop impedance’. This is especially the case for solidly earthed low voltage systems, whether they be three-phase, single-phase or even direct current systems.

The earth loop impedance is the total impedance seen by the source of voltage in a faulted circuit which involves the earthing conductors. Figure 13.10 shows the situation for a three-phase cable supplying a load such as a motor or static load.

Figure 13.10 Earth loop impedance of a three-phase circuit.

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Figure 13.11 Equivalent circuit of the earth return paths in the earth loop impedance circuit involving a cable and its armouring. This is an interpretation of BS7430 Clause 3.13.

The worst design case is shown wherein the fault occurs at the far end of the cable. The fault is assumed to be a line-to-earth fault having zero fault impedance. The equivalent circuit for this example is shown in Figure 13.11.

A pessimistic assumption can be made that the steelwork impedance Z e between the fault and the source is large compared with the parallel-connected cable armouring impedance Z a . This implies that the current will only return to the source through the cable armouring and the copper bonding connection, of impedance Z b , at the source-end of the cable. The impedance Z b includes the local steelwork at the source. The bonding is assumed to be in tact and of very low impedance compared with Z a . Hence Z b can be ignored, and so earth loop impedance Z loop simply becomes:-

Z loop =Z s +Z c +Z a ohms

The driving voltage is the phase voltage. The source impedance Z s is fixed and is usually that of the upstream supply cables and transformers, or generators (or the output impedance of supplies such as a UPS). Z s can often but not always be neglected. The cable conductor impedance Z c is easily calculated from the cable data for one phase conductor and its route length. Similarly the armouring impedance Z a can be calculated from the data, which is predominantly resistive for most types of power cables. For typical cable data see the tables in Chapter 9.

In order to safeguard against electric shock at the far end of the cable, where the AC root mean square voltage may exceed 50 V, the earth loop impedance must be limited to a particular value. This value is such that the fault current should only be passed by the protective device at the supply for a specific period of time, i.e. to satisfy the I -squared-t criterion given in sub-section 13.1.1. The correlation of loop impedance, current and time varies with the type of protective device, e.g. fuse,

EARTHING AND SCREENING

moulded case circuit breaker, miniature circuit breaker. The international standards such as IEC 60364 and Reference 10 give tables for the limiting values of the earth loop impedance for common ratings of fuses and circuit breakers. Once the limiting value for the circuit is determined from these tables it is a simple calculation procedure to find the maximum length of the cable that can be allowed, as demonstrated in 9.4.3.6.