9.1 Interpreting Zs Values & The 80% Rule (Rule of Thumb)

9.1 Interpreting Zs Values & The 80% Rule (Rule of Thumb)

The verification of Earth Fault Loop Impedance ($Z_s$) is one of the most critical elements of Periodic Inspection and Testing under BS 7671 and IET Guidance Note 3. Earth fault loop impedance testing determines whether the protective device (circuit breaker, RCBO, or fuse) will operate rapidly enough during an earth fault to achieve Automatic Disconnection of Supply (ADS) within the maximum disconnection times mandated by Regulation 411.3.2.

For a standard $230\text{ V}$ single-phase TN system, the maximum disconnection time is 0.4 seconds for final circuits not exceeding $32\text{ A}$ (and $63\text{ A}$ where socket-outlets are supplied), and 5 seconds for distribution circuits and final circuits exceeding $32\text{ A}$. On a TT system, the maximum disconnection time for final circuits up to $32\text{ A}$ is 0.2 seconds.

To verify compliance, the measured $Z_s$ value obtained at ambient temperature during inspection must be evaluated against the maximum permissible $Z_s$ values published in BS 7671 Tables 41.2, 41.3, and 41.4.

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BS 7671 Tabulated Maximum $Z_s$ Values

The maximum earth fault loop impedance values tabulated in Chapter 41 of BS 7671 are calculated using the fundamental Ohm's law relationship for fault protection:

$$Z_s \le \frac{U_0 \times C_{min}}{I_a}$$

Where:

• $U_0$ is the nominal line-to-earth voltage ($230\text{ V}$).
• $C_{min}$ is the minimum voltage factor introduced in Amendment 3 of BS 7671:2008 and retained in the 18th Edition, set at 0.95. This accounts for nominal voltage variations across the public distribution network, giving an effective minimum driving voltage of $230\text{ V} \times 0.95 = 218.5\text{ V}$.
• $I_a$ is the current causing automatic disconnection of the protective device within the specified time ($0.4\text{ s}$ or $5\text{ s}$).

Circuit Breakers and RCBOs (BS EN 60898 & BS EN 61009)

Table 41.2 of BS 7671 provides maximum $Z_s$ values for Type B, Type C, and Type D circuit breakers operating within $0.4\text{ s}$ and $5\text{ s}$ on a $230\text{ V}$ TN system:

• Type B MCBs: Instantaneous magnetic tripping occurs between $3 \times I_n$ and $5 \times I_n$. Therefore, $I_a = 5 \times I_n$.
• Type C MCBs: Instantaneous magnetic tripping occurs between $5 \times I_n$ and $10 \times I_n$. Therefore, $I_a = 10 \times I_n$.
• Type D MCBs: Instantaneous magnetic tripping occurs between $10 \times I_n$ and $20 \times I_n$. Therefore, $I_a = 20 \times I_n$.

Fuses to BS 88-2, BS 88-3, and BS 3036

• Table 41.3 (BS 88-2 / BS 88-3 Fuses): For industrial (BS 88-2 Bolted/Blade) and domestic (BS 88-3 Cartridge) fuses, disconnection currents are derived from time-current characteristics. For a $32\text{ A}$ BS 88-2 fuse, maximum $Z_s$ is $0.96\ \Omega$ for $0.4\text{ s}$ and $1.44\ \Omega$ for $5\text{ s}$.
• Table 41.4 (BS 3036 Semi-Enclosed Rewirable Fuses): Due to higher operating temperatures and melting characteristics, a $30\text{ A}$ BS 3036 fuse has a maximum tabulated $Z_s$ of $1.09\ \Omega$ for $0.4\text{ s}$ and $1.59\ \Omega$ for $5\text{ s}$.

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The Rationale Behind the 80% Rule of Thumb ($0.8 \times Z_s$)

A crucial concept in City & Guilds 2391-51 is understanding why a direct comparison between an ambient measured $Z_s$ and the tabulated maximum $Z_s$ in BS 7671 is technically invalid and dangerous.

Temperature Rise Under Fault Conditions

The maximum $Z_s$ values published in BS 7671 Tables 41.2 to 41.4 are derived based on conductors operating at their maximum permitted operating temperature:

• $70^\circ\text{C}$ for thermoplastic (PVC) insulated cables under normal load.
• $90^\circ\text{C}$ for thermosetting (XLPE / LSOH) insulated cables.

However, when an inspector carries out periodic testing, the installation is either dead (testing $R_1 + R_2$) or lightly loaded at ambient room temperature (typically $10^\circ\text{C}$ to $20^\circ\text{C}$).

Because electrical resistance of copper increases with temperature according to the linear relationship:

$$R_\theta = R_{20} [1 + \alpha_{20} (\theta - 20)]$$

where $\alpha_{20} \approx 0.004\text{ per }^\circ\text{C}$, a copper conductor at $70^\circ\text{C}$ has a resistance approximately 1.20 times (20% higher) than at $20^\circ\text{C}$:

$$\frac{R_{70}}{R_{20}} = 1 + 0.004 \times (70 - 20) = 1.20$$

If a circuit carries a heavy earth fault current, the conductors will rapidly heat up from ambient temperature towards their operating limit ($70^\circ\text{C}$ or fault limit $160^\circ\text{C}$). As the temperature rises, resistance increases, fault current decreases, and disconnection time may be extended beyond permitted limits.

Derivation of the 80% Factor

To ensure that an ambient measurement will not exceed BS 7671 limits when conductors heat up under fault conditions, the ambient measured value should theoretically not exceed:

$$Z_{s(\text{ambient max})} = \frac{Z_{s(\text{tabulated})}}{1.20} \approx 0.833 \times Z_{s(\text{tabulated})}$$

To provide a safe engineering margin that accommodates:

1. Instrument operational accuracy limits allowed by BS EN 61557-3 ($\pm 30\%$).
2. Minor supply voltage fluctuations.
3. Ambient temperature variations below $20^\circ\text{C}$.

IET Guidance Note 3 and the On-Site Guide establish the 80% Rule of Thumb (Rule of Thumb $0.8 \times Z_s$):

$$\text{Measured } Z_s \le 0.8 \times Z_{s(\text{tabulated max})}$$

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Step-by-Step Practical Application & Evaluation

When performing an EICR or EIC test result evaluation, the inspector must follow a systematic decision workflow:

[ Step 1: Identify Protective Device & Rating ]
                       │
                       ▼
[ Step 2: Lookup Tabulated Max Zs in BS 7671 (Tables 41.2 - 41.4) ]
                       │
                       ▼
[ Step 3: Calculate 80% Rule Limit (0.8 × Tabulated Max Zs) ]
                       │
                       ▼
[ Step 4: Compare Measured Ambient Zs against 0.8 × Max Zs ]
                       │
         ┌─────────────┴─────────────┐
         ▼                           ▼
[ Measured Zs ≤ 0.8 × Max Zs ]   [ Measured Zs > 0.8 × Max Zs ]
         │                           │
         ▼                           ▼
[ PASS: ADS Compliance Verified ] [ Perform Exact Temperature ]
                                  [ Correction (Ctu Factor) ]
                                             │
                                ┌────────────┴────────────┐
                                ▼                         ▼
                        [ Corrected Zs ≤ Max ]   [ Corrected Zs > Max ]
                                │                         │
                                ▼                         ▼
                        [ PASS: Compliant ]     [ FAIL: Code C2 / C3 ]

Worked Example:

• Circuit: $32\text{ A}$ Type B MCB protecting a ring final circuit.
• Tabulated Maximum $Z_s$ (Table 41.2): $1.37\ \Omega$.
• Calculated 80% Threshold: $1.37 \times 0.8 = 1.10\ \Omega$.
• Case A: Measured ambient $Z_s = 0.95\ \Omega$. Since $0.95\ \Omega \le 1.10\ \Omega$, the circuit passes without further calculation.
• Case B: Measured ambient $Z_s = 1.20\ \Omega$. Since $1.20\ \Omega > 1.10\ \Omega$, it fails the initial 80% rule of thumb check. However, $1.20\ \Omega < 1.37\ \Omega$. The inspector must NOT immediately record a failure; instead, exact temperature correction using factor $C_{tu}$ (Section 9.2) must be applied considering actual test ambient temperature.

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RCDs as Supplementary and Fault Protection for High $Z_s$

Where measured $Z_s$ exceeds the maximum values permitted for overcurrent protective devices (e.g. on long cable runs or TT systems), a Residual Current Device (RCD) may serve as the protective device for Automatic Disconnection of Supply in accordance with Regulation 411.4.204 (TN) or Regulation 411.5.2 (TT).

RCD Earth Fault Loop Limits

When an RCD provides fault protection, the maximum earth fault loop impedance is calculated based on the rated residual operating current ($I_{\Delta n}$):

$$Z_s \le \frac{U_0 \times C_{min}}{I_{\Delta n}}$$

For a standard $30\text{ mA}$ ($0.03\text{ A}$) RCD on a $230\text{ V}$ system:

$$Z_s \le \frac{218.5}{0.03} = 7283\ \Omega$$

However, on TT systems, Table 41.5 Note 2 recommends that $Z_s$ (or earth electrode resistance $R_A$) should not exceed $200\ \Omega$ to maintain stable operation and prevent false tripping due to environmental instability.