Earth Fault Loop Impedance — BS 7671 Calculation Method

Automatic disconnection of supply (ADS) is the primary protective measure against electric shock in BS 7671 installations. Regulation 411.3.2 requires that, in the event of a fault between a line conductor and an exposed-conductive-part, the protective device must disconnect the circuit within the maximum permitted time. This disconnection time depends on the nominal voltage and system type (TN or TT).

The earth fault loop impedance, Zs, is the total impedance of the fault current path — from the source, through the line conductor, through the fault, and returning via the protective conductor and earth path. If Zs is too high, the fault current will be too low to trip the protective device within the required time.

This document covers the complete Zs verification methodology as implemented in ECalPro, referencing:

• BS 7671:2018+A3, Chapter 41 — Protection against electric shock
• BS 7671:2018+A3, Appendix 3 — Tables of maximum earth fault loop impedance (Tables 41.2 through 41.6)
• IET Guidance Note 3 — Inspection and Testing (6th Edition)
• IET On-Site Guide — Tables of R1+R2 values per metre

Regulation 411.4.5 states the fundamental requirement for TN systems:

Zs x Ia ≤ Uo     — (Eq. 1)

Or equivalently:

Zs ≤ Uo / Ia     — (Eq. 2)

Where:
  Zs = earth fault loop impedance (ohms)
  Ia = current causing automatic disconnection within the required time (A)
  Uo = nominal line-to-earth voltage (V)

The value of Ia depends on the type of protective device:

For MCBs, the maximum Zs values are pre-calculated and tabulated in BS 7671 Tables 41.2 and 41.3. For fuses, the Ia values must be read from the time-current curves at the specified disconnection time.

For example, a Type B 32 A MCB at 230 V with a 0.4 s disconnection time requirement:

Ia = 5 x 32 = 160 A
Zs(max) = 230 / 160 = 1.44 ohms     — (Eq. 3)

This is the value tabulated in BS 7671 Table 41.3 for a Type B 32 A MCB: Zs = 1.44 ohms.

The earth fault loop impedance is composed of three elements in series:

Zs = Ze + (R1 + R2)     — (Eq. 4)

Where:
  Ze = external earth fault loop impedance (from the supply transformer
       to the origin of the installation)
  R1 = resistance of the line conductor from the origin to the fault point
  R2 = resistance of the protective conductor from the fault point back
       to the origin

Ze is either measured at the supply intake (typical values for UK supplies: 0.35 ohms for TN-C-S, 0.8 ohms maximum for TN-S per UKPN, up to 21 ohms for TT systems) or assumed from the DNSP's declared maximum value.

R1 + R2 is calculated from the cable parameters:

R1 + R2 = (rho_1/A_1 + rho_2/A_2) x L / 1000     — (Eq. 5)

Where:
  rho_1 = resistivity of line conductor material (ohm.mm2/m)
  rho_2 = resistivity of protective conductor material (ohm.mm2/m)
  A_1   = cross-sectional area of line conductor (mm2)
  A_2   = cross-sectional area of protective conductor (mm2)
  L     = cable length (m)

For copper conductors, the resistivity at 20 deg C is 0.0178 ohm.mm2/m. For aluminium, 0.0286 ohm.mm2/m. Per BS 7671 Appendix 3, Table 3A, the (R1+R2)/m values are pre-tabulated for common cable combinations.

Temperature correction: The tabulated Zs values in BS 7671 Tables 41.2-41.6 assume conductor resistance at the maximum operating temperature of the cable under fault conditions (typically 70 deg C for thermoplastic, 90 deg C for thermosetting insulation). The (R1+R2) values must be corrected from 20 deg C to the operating temperature:

R_t = R_20 x [1 + alpha x (t - 20)]     — (Eq. 6)

Where:
  alpha = temperature coefficient of resistance
        = 0.00393 /deg C for copper
        = 0.00403 /deg C for aluminium
  t     = conductor operating temperature (deg C)

For thermoplastic (PVC) insulation at 70 deg C:

Correction factor = 1 + 0.00393 x (70 - 20) = 1.20     — (Eq. 7)

ECalPro automatically applies this temperature correction to the calculated R1+R2 before comparing against the maximum Zs from the tables.

BS 7671 specifies different maximum disconnection times depending on the circuit type and nominal voltage:

Table 41.1 — Maximum disconnection times for TN systems (Regulation 411.3.2.2):

Table 41.2 provides maximum Zs values for fuses (BS 88-2.1 and BS 3036) at the 0.4 s and 5 s disconnection times. Table 41.3 provides maximum Zs values for MCBs (Types B, C, and D) at 0.4 s and 5 s.

Key values from Table 41.3 (MCBs, Uo = 230 V, 0.4 s disconnection time):

For distribution circuits and final circuits exceeding 32 A (5 s disconnection time), the maximum Zs values are higher because a longer trip time means a lower fault current is sufficient. However, Regulation 411.3.2.3 permits the 5 s time only if the circuit is not a final circuit supplying socket-outlets or portable equipment.

ECalPro selects the correct disconnection time based on the circuit type (final or distribution) and the nominal voltage, then looks up the appropriate Zs limit from the built-in tables.

For TT systems (where the installation earth is independent of the supply earth), Regulation 411.5.3 requires:

R_A x I_Dn ≤ 50 V     — (Eq. 8)

Where:
  R_A  = sum of the resistance of the earth electrode and the protective
         conductor connecting it to the exposed-conductive-part
  I_Dn = rated residual operating current of the RCD

In practice, TT systems almost always require RCD protection because the earth fault loop impedance through the general mass of earth is too high to guarantee adequate fault current for MCB/fuse operation within the required disconnection time.

For a 30 mA RCD:

R_A ≤ 50 / 0.030 = 1667 ohms     — (Eq. 9)

For a 100 mA RCD:

R_A ≤ 50 / 0.100 = 500 ohms     — (Eq. 10)

The maximum disconnection time for TT systems is specified in Table 41.1 as:

These are shorter than TN system times because in a TT system the touch voltage can reach the full line-to-earth voltage before the RCD operates. A 30 mA Type A or Type AC RCD with a 40 ms operating time satisfies the 0.2 s requirement at 230 V. ECalPro verifies both the R_A x I_Dn condition and the disconnection time for TT installations.

There are several situations where overcurrent protective devices alone cannot guarantee disconnection within the required time, and an RCD must be used as additional protection:

• Regulation 411.3.3: Additional protection by RCD with I_Dn ≤ 30 mA is required for socket-outlets with rated current ≤ 32 A, mobile equipment outdoors with rated current ≤ 32 A, and cables concealed in walls at a depth less than 50 mm.
• High Zs circuits: When the calculated Zs exceeds the maximum permitted value for the protective device, an RCD provides an alternative disconnection path. The RCD operates on the residual current (differential between line and neutral) rather than relying on the magnitude of the fault current.
• TT systems: As described above, RCDs are essential because the earth loop impedance through the ground electrode is inherently high and variable.
• High-impedance faults: Arcing faults and faults through resistive paths (wet masonry, contaminated surfaces) may produce fault currents well below the MCB trip threshold. An RCD with 30 mA sensitivity detects these faults effectively.

When an RCD is used for fault protection, the Zs requirement changes. Per Regulation 411.4.9, for TN systems with RCD protection, the earth fault loop impedance must still be low enough to ensure the RCD operates within the required time. However, since a 30 mA RCD typically trips at 15-25 mA within 40 ms, the Zs limit becomes:

Zs ≤ 50 / I_Dn     — (Eq. 11)

For 30 mA RCD: Zs ≤ 50 / 0.030 = 1667 ohms     — (Eq. 12)

This is far more permissive than the overcurrent device Zs limits, effectively meaning the Zs requirement is always satisfied when an RCD is present, provided the installation earthing is functional.

ECalPro checks Zs against both the overcurrent device limit and the RCD limit (if an RCD is specified in the circuit), and reports the governing constraint.

There is an important distinction between the design stage Zs calculation and the as-built Zs measurement. Per IET Guidance Note 3 and the IET On-Site Guide, the maximum tabulated Zs values in BS 7671 assume conductors at their maximum operating temperature (70 deg C for PVC, 90 deg C for XLPE).

However, when Zs is measured during initial verification or periodic inspection, the conductors are typically at ambient temperature (approximately 20 deg C). At 20 deg C, the conductor resistance is lower than at operating temperature, so the measured Zs will be lower than the value that would exist under fault conditions.

To account for this, the 0.8 multiplier rule is applied:

Zs(measured) ≤ 0.8 x Zs(max from tables)     — (Eq. 13)

Example: Type B 32 A MCB, Zs(max) = 1.44 ohms
Measured Zs must be ≤ 0.8 x 1.44 = 1.15 ohms     — (Eq. 14)

The factor of 0.8 approximates the ratio of resistance at 20 deg C to resistance at 70 deg C for copper conductors:

R_20 / R_70 = 1 / [1 + 0.00393 x (70-20)] = 1 / 1.197 = 0.836     — (Eq. 15)

The 0.8 factor is slightly conservative (actual ratio is approximately 0.84), providing a small safety margin. For thermosetting insulation (90 deg C operating temperature), the temperature correction is larger:

R_20 / R_90 = 1 / [1 + 0.00393 x (90-20)] = 1 / 1.275 = 0.784     — (Eq. 16)

ECalPro reports both the calculated Zs at operating temperature (for comparison against BS 7671 table values) and the expected Zs at ambient temperature (for comparison against the 0.8 x Zs_max limit that would be used during testing). This dual reporting helps electricians verify compliance during both the design stage and the commissioning inspection.

The ECalPro cable sizing calculator includes integrated Zs verification as part of the design output. The workflow is:

1. Input: System type (TN-S, TN-C-S, TT), Ze (measured or declared), cable type and size (for R1+R2), cable length, protective device type and rating, circuit type (final ≤ 32 A, final > 32 A, or distribution).
2. R1+R2 Calculation: From cable cross-sections, material resistivity, and length, with temperature correction per Eq. 6.
3. Zs Calculation: Ze + (R1+R2) at operating temperature per Eq. 4.
4. Zs Limit Lookup: From BS 7671 Tables 41.2-41.6, based on device type, rating, and required disconnection time.
5. Compliance Check: Zs ≤ Zs_max (design stage) and Zs_ambient ≤ 0.8 x Zs_max (testing stage).
6. RCD Check: If an RCD is specified, verifies R_A x I_Dn ≤ 50 V for TT systems.
7. Report: Traffic-light indicator (green PASS, amber WARNING, red FAIL), with all intermediate values, clause references, and the 0.8 multiplier comparison.

If the Zs check fails, ECalPro suggests remedial actions: increase cable cross-section (reduces R1+R2), reduce cable length (if possible), change protective device type (e.g., Type B to Type C has a lower Zs requirement only if the higher Ia is acceptable), or add RCD protection.