# Earth Fault Loop Impedance

## Earth Fault Loop

The illustration below shows a typical earth fault path. Earth Fault Loop Path

The earth fault loop impedance Zs, is given by:

$Z s = Z e + Z 1 + Z 2$

Where:
Zs =        earth fault loop impedance,  Ω
Ze =        external earth fault impedance, Ω
Z1  =       line conductor impedance, 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.).

## BS 7671 CPC Requirements

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 disconnection 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:

System
Maximum Disconnection Time, seconds
Socket Outlet Circuits Not Exceeding 63  A
Final Circuits Not Exceeding 32 A

Other Circuits
50Vo≤120V  120Vo≤230V  230Vo≤400  Uo>400V
a.c.  d.c.  a.c.  d.c.  a.c.  d.c.  a.c  d.c  a.c., d.c.
TN  0.8  NA  0.4  1  0.2  0.4  0.1  0.1  5.0
TT  0.3  NA  0.2  0.4  0.07  0.2  0.04  0.1  1.0
1. For  TT circuits incorporating equipotential bonding in accordance with Regulation 411.3.1.2, the maximum tripping times for a TN system may be used.
2. For TN distribution circuits and circuits not covered by the above table, a disconnection time not exceeding 5 s is allowed.
3. For TT distribution circuits and circuits not covered by the above table, a disconnection time not exceeding 1 s is allowed.

The characteristics of protective devices should be such that:

$Z s × I a ≤ U 0 × C min$        - TN, TT systems

${Z}_{s}×\left(2×{I}_{a}\right)\le {U}_{0}×{C}_{\mathrm{min}}$         - IT system (second fault, neutral/mid-point conductor not distributed)

Where:
Ia         - current causing operation of the protective device within a specified time, A
U0       - nominal a.c. or d.c. line voltage to earth, V
Cmin    - minimum voltage factor (= 0.95)

Where an RCD is used for fault protection, in addition 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
IΔn         - rated current of the RCD, A

## myCableEngineering and Earth Fault Loop

External Fault Loop Impedance

The external earth loop fault impedance Ze is calculated in the complex form using earth data entered by the user:

$I k2E = I E ×p f E −j I E ×sin(cos(p f E ))$

$U= U 0 / 3$

$Z e =U/ I k2E$

where:
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

Cable Loop Impedance

myCableEngineering calculates positive ( Z1(60909) ) and zero ( Z0(60909) ) 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.

From IEC 60909, for a line to earth short circuit (with Z2(60909) = Z1(60909)), the fault current is given by:

${I}_{k}=\frac{\sqrt{3}c{U}_{n}}{\left|2{Z}_{1\left(60909\right)}+{Z}_{2\left(60909\right)}\right|}$

giving the following conversions between IEC 60909 calculated values, and the common usage of Z1 and Z2 (or R1, R2) :

EFL Impedance IEC 60909 Equations
Ze Ze
Z1 Z1(60909)
Z2 Z1(60909)                         - single-phase system
Z1(60909) + Z0(60909)        - three-phase system

Earth Fault Loop Impedance

Having obtained the source impedance components, 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.

For common configurations, the maximum earth fault loop impedance is calculated (but can be overridden by the user).  For other configurations, the user needs to enter the required maximum earth fault loop impedance.  Circuit conditions for which the maximum earth fault loop impedance is calculated are dependant on the system type and selected protective devices.

Note: maximum earth fault loop impedance for devices listed in BS 7671 is available for 0.1, 0.2, 0.4, 1 and 5 s maximum disconnect times.  For MCCB, the impedance is available for 0.4 and 5 s disconnect times at maximum setting,

#### Circuit Protective Conductor (CPC)

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 used 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, specifies minimum sizes for protective conductors.  The user is recommended to verify that his cable design complies with this regulation.

#### Protective Device

A check on the device setting is also carried out to ensure that the relevant requirements are met.  Similar if an RCD is used.

For an example calculation, please see Cable Fault Calculation