Earth Fault-Loop Impedance Calculation

Previously, we did a simple calculation for the maximum length of the cable. We have not considered the internal impedance of the source, i.e. the transformer impedance. Likewise, we just consider the current rating of the circuit breaker without the current multiplier for instantaneous tripping. The primary reason for that is to make the calculation much simpler. If I will tell everything all at once, understanding the concept may be difficult.

Circuit breakers are classified into three (3) according to their mean tripping current. We are dealing with IEC standards here and its derivative standards, ie BS, AS, etc.and not the IEEE.

Ia (typical values) for circuit breakers are as follows:

Type B = 4 x rated current
Range : 3*I_n right 5In

Type C = 7.5 x rated current
Range : 5*I_n right 10*I_n

Type D = 12.5 x rated current
Range : 10*I_n right 20*I_n

From above formula, a Type B, 6A circuit breaker will have an instantaneous tripping current of 24A. The question may be raised, what is the circuit breaker type I need to use for my application / design. The answer is, it all depends on the application or design. for lighting and other domestic application, Type B is preferred. In normal application, Type C is normally used. For motor loads particularly where the motor starts loaded, then Type D is being used.

L_{max} = {0.8*U_O*S_{ph}*S_{pe}}/{I_a*rho*(S_{ph}+S_{pe})}

Lmax = maximum route length
U_O = nominal phase voltage (230V for a 400V system)
rho = resistivity at normal working temperature
22.5 * 10-3 ohm-mm^2 / m (Copper)
36.0 * 10-3 ohm-mm^2 / m (Aluminium)
I_a = trip-current seting for the instaneous
S_ph = active conductor size, mm^2
S_pe = protective earth conductor size, mm^2

The 0.8 factor is an assumed value if the internal impedance of the circuit is not available which means that only 80% of the phase voltage is available at the terminal of the protective device.

For cables where the active conductor and protective earth have the same size, Sph = Spe, the formula will be simplified to

L_{max} = {0.4*U_O*S_{ph}}/{I_a*rho}

If the cable impedance is known which we could find from manufacturer's datasheets, the formula will become

L_{max} = {0.8*U_O*(Z_{ph}+Z_{pe})}/{I_a*Z_{ph}*Z_{pe}}

When the size of the active conductor and protective conductor are the same

L_{max} = {0.4*U_O}/{I_a*Z_{ph}}

Zph = active conductor impedance, ohms
Zpe = protective earth conductor impedance, ohms

Please be reminded that this is the cable conductor impedance, and not the per unit (ie ohms per km) impedance of the cable.
To provide an example, we will recalculate our first example using different types of circuit breaker.

6A CB, 400V, 2.5 mm2 cable
Type B Circuit Breaker
Instantaneous trip = 4 * 6 = 24 A
Maximum Length = 406 m

Type C Circuit Breaker
Instantaneous trip = 7.5 * 6 = 45 A
Maximum Length = 216 m

Type D Circuit Breaker
Instantaneous trip = 12.5 * 6 = 75 A
Maximum Length = 129 m

The task is not finished here, we need to compare it with the allowable maximum fault loop imedance and also do not forget the ampacity of the cable.

Please note that the above is just a hypothetical example and need not be used for your design. Every manufacturer has specific values of cable impedances, always consult your vendor about it.


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