The illustration below shows a typical earth fault path.
Earth Fault Loop Path
The earth fault loop impedance Zs, is given by:
Z s = Z e + Z 1 + Z 2
Zs = earth fault loop impedance, Ω
Ze = external earth fault impedance, Ω
Z1 = line conductor impednace, Ω
Z2 = Circuit Protective Conductor (CPC) impedance, Ω
The external impedance, Ze depends on the upstream network. In the illustration, the external impedance would be Z0 + ZPEN. In other arrangements, the external impedance may be derived differently.
The CPC impedance, Z2 depends on the protective conductor used (armour, separate cable, trunking, etc.).
Earth fault loop impedance is important for regulation 411 "Protective Measure: Automatic Disconnection of Supply". This regulation prescribes a minimum disconnection time for different types of circuit. The disconection time is related to the protective device and the time it takes the device to trip is dependant on the earth fault loop impedance.
Regulation 411.3.2 gives the following maximum disconnection times:
Note: in additon to minimum clearance, the regulations require an RCD for socket outlets rated 20 A or less and mobile equipment rated 32 A or less.
The characteristics of protective devices should be such that:
Z s × I a ≤ U 0 × C min
Where: Ia - current causing operation of protective device within specified time, A
U0 - nominal a.c. or d.c. line voltage to earth, V
Cmin - minimum voltage facotr (= 0.95)
Where an RCD is used for fault protection, in additon to the above the following should be satisfied (further limiting the maximum Zs ):
R A × I Δn ≤50 V
Where: RA - sum of resistances of earth electrode and protective conductor, Ω
note: where RA is not known, Zs can be used.
IΔn - rated current of the RCD, A
myCableEngineering calculates positive ( Z1 ) and zero ( Z0 ) sequence impedance in accordance with IEC 60909 "Short-circuit currents
in three-phase a.c. systems". Given the fault conditions (three phase, and single phase) at the load end of the cable, the resultant fault levels can be calculated at the remote end.
The external earth loop fault impedance Ze is calculated in complex form using earth data entered by the user:
I k2E = I E ×p f E −j I E ×sin(cos(p f E ))
U= U 0 / 3
Z e =U/ I k2E
IE - source earth fault level in A
pfE - source fault power factor
Ik2E - source earth fault current complex form, A
U - phase voltage, V
U0 - line-line voltage, V
Ze - source (external) impedance, Ω
Having obtained the source impedance, the total loop impedance ( Zt ) and load end fault level ( If ) are given by:
Z t = Z e + Z 1 + Z 0
I f =U/ Z t
The earth fault loop impedance is simply the magnitude of Zt.
The cable armour is used as the CPC in the calculation of Z0 and the earth fault loop impedance. In addition the user has the option to add an additional conductor, which will be using in parallel with any armour to form the CPC. The additional conductor can be external to the cable or internal.
Regulation 543 of BS 7671, spcifies minimum sizes for protective conductors. The user is recommended to varify that his cable design complies with this regulation.
A check on the device setting is also carried out to ensure that the relevant requirements are meet. Similar if an RCD is used.
For an example calculation, please see Example Cable Fault Calculation