12.3 The 0.8 Temperature Correction Rule & Maximum Permitted Zs

12.3 The 0.8 Temperature Correction Rule & Maximum Permitted Zs

Core Testing Principle: The maximum permitted $Z_s$ values tabulated in BS 7671 assume that cable conductors are operating at their maximum permitted operating temperature ($70^\circ\text{C}$ for standard thermoplastic PVC). However, initial verification and periodic testing are performed on de-energised or lightly loaded cables at ambient room temperature (typically $\sim 20^\circ\text{C}$). For a quick conservative assessment, compare ambient measurements with 80% (0.8) of the applicable operating-temperature limit. A supported detailed assessment may be used where the simple screen is exceeded.

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The Physics of Conductor Temperature & Resistance

Copper is a metallic conductor possessing a positive temperature coefficient of resistance ($\alpha$). As conductor temperature increases, thermal vibrations of copper atoms within the crystal lattice impede electron flow, increasing electrical resistance:

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

Where:

• $R_{\theta}$ = Conductor resistance at operating temperature $\theta$ ($^\circ\text{C}$).
• $R_{20}$ = Conductor resistance at standard reference ambient temperature ($20^\circ\text{C}$).
• $\alpha$ = Temperature coefficient of copper at $20^\circ\text{C}$ ($0.004 / ^\circ\text{C}$ or $1 / 254.5$).

Resistance Ratio fromAmbient to Full Load

For a standard70 °C thermoplastic cable,70 °C is the usual maximum continuous conductor temperature, not the inevitable temperature at every design load. Substituting this into the formula:

$\frac{R_{70}}{R_{20}} = 1 + [0.004 \times (70 - 20)] = 1 + [0.004 \times 50] = 1 + 0.20 = 1.20$

This proves that a copper cable conductor operating at its maximum design temperature ($70^\circ\text{C}$) has $20\%$ higher resistance than when cold at $20^\circ\text{C}$.

  COPPER CONDUCTOR RESISTANCE: APPROXIMATE 20 °C TO 70 °C CHANGE
  At 20 °C: R20  ── temperature increase ──> At 70 °C: about 1.20 × R20

  This factor applies to the conductor resistance in the stated model.
  The complete fault-loop change also depends on the source and other components.

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The Voltage Factor $C_{\text{min}}$ (BS 7671 Appendix 3)

Under BS 7671, maximum earth fault loop impedance values are derived from Ohm's law:

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

Where:

• $U_0$: Nominal line-to-earth AC voltage ($230\text{ V}$).
• $C_{\text{min}}$: Minimum voltage factor;0.95 for the usual LV supply in accordance with ESQCR.
• $I_a$: The current causing automatic disconnection within the specified time (use the time required for the actual circuit and protective measure).

Why $C_{\text{min}} = 0.95$ is Mandatory

Although UK nominal voltage is declared at $230\text{ V}$, national supply regulations permit a lower tolerance of $-6\%$ ($216.2\text{ V}$). Furthermore, when a massive short-circuit or earth fault occurs, the surge of current causes a temporary voltage drop across distribution transformers and service lines. To ensure the protective device operates even during severe grid voltage depression, BS 7671 scales the effective supply voltage down by $5\%$:

$U_0 \times C_{\text{min}} = 230\text{ V} \times 0.95 = 218.5\text{ V}$

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Applying the 0.8 Screen

Appendix 3 provides the familiar measured-impedance assessment:

$Z_{s(\text{measured})}\le0.8\,Z_{s(\text{table})}$

Its algebraically equivalent form is:

$1.25\,Z_{s(\text{measured})}\le Z_{s(\text{table})}$

This conservative screen allows for conductor resistance increasing with load temperature. Use 1.25 when algebraically reversing the 0.8 screen. The approximate 20-to-70 °C copper resistance factor 1.20 applies to that conductor resistance under those assumptions; a detailed assessment separately treats the source and internal circuit components.

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Maximum Permitted $Z_s$ Reference Tables (0.4 s Disconnection, 230 V)

Inspectors reference the following core values from BS 7671 Tables 41.2, 41.3, and 41.4, compared alongside their 80% quick-screen measured limits:

Type B Circuit Breakers (BS EN 60898 / BS EN 61009)

Tripping current $I_a = 5 \times I_n$ (Instantaneous magnetic trip between $3 \times I_n$ and $5 \times I_n$)

Type C Circuit Breakers (BS EN 60898 / BS EN 61009)

Tripping current $I_a = 10 \times I_n$ (Instantaneous magnetic trip between $5 \times I_n$ and $10 \times I_n$)

Type D Circuit Breakers (BS EN 60898 / BS EN 61009)

Tripping current $I_a = 20 \times I_n$ (Instantaneous magnetic trip between $10 \times I_n$ and $20 \times I_n$)

Fuses: Use the Correct Characteristic and Time

Identify the actual fuse standard, system and rating. BS 88-2 systems E/G and BS 88-3 system C have different characteristics; BS 88-3 is not simply a generic service-fuse label. Use the applicable current edition's table or manufacturer time/current data for the required disconnection time.

Read the current $I_a$ that ensures operation within that time, then apply:

$Z_{s(\max)}=\frac{U_0C_{\min}}{I_a}$

For example, if the applicable characteristic establishes $I_a=100 A$ for the required time on a 230 V supply, the operating-temperature limit is $230\times0.95/100=2.185 Ω$. This is a calculation example, not a rating assigned to an unspecified fuse. Apply the appropriate measured-temperature assessment and record the source of the actual limit.

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Action When Measured $Z_s$ Sits in the "Grey Zone" (Between 80% and 100%)

What must an inspector do if a measured $Z_s$ value exceeds the 80% rule-of-thumb limit, but is less than the 100% BS 7671 table limit? (e.g. For a 32 A Type B MCB, table limit is $1.37\ \Omega$, 80% limit is $1.10\ \Omega$, and measured reading is $1.22\ \Omega$).

  QUICK SCREEN                         FURTHER ASSESSMENT
  Measured ≤0.8 × applicable limit      Screen exceeded
  Meets this conservative loop check   Check valid measurement, limit/source,
  Continue the remaining verification  protective measure and detailed assessment

A reading above the screen is not automatically a C2 observation. Identify whether fault protection relies on the overcurrent device or an RCD, and use the appropriate limit. Where temperature is material, apply a supported component calculation or the relevant published correction method; do not assume the external source warms to the final-circuit conductor temperature.

The Detailed Temperature Correction Formula

To establish whether the circuit complies when in the grey zone, adjust the measured internal conductor continuity $(R_1 + R_2)$ using this approximate copper-resistance model, consistent with α≈0.004/°C at 20 °C:

$(R_1 + R_2)_{\text{corrected}} = (R_1 + R_2)_{\text{measured}} \times \left[ \frac{230 + \theta_{\text{max}}}{230 + \theta_{\text{test}}} \right]$

Where:

• $\theta_{\text{max}}$ = Maximum permitted conductor temperature under normal service ($70^\circ\text{C}$ for 70°C thermoplastic PVC).
• $\theta_{\text{test}}$ = Ambient temperature at the time of testing (e.g. $15^\circ\text{C}$).

Worked Example: Grey Zone Resolution

A 32 A Type B MCB on a radial socket circuit has a measured $Z_e = 0.30\ \Omega$ and a measured $(R_1 + R_2) = 0.88\ \Omega$ taken at an ambient room temperature of $10^\circ\text{C}$:

1. Calculate Cold $Z_s$: $Z_s = 0.30 + 0.88 = 1.18\ \Omega$.
2. Compare Against Rule of Thumb: 80% limit for 32 A Type B MCB is $1.10\ \Omega$. The measured $1.18\ \Omega$ fails the 80% test ($1.18 > 1.10\ \Omega$), but is below the 100% limit ($1.37\ \Omega$).
3. Apply Detailed Calculation: $(R_1 + R_2)_{70} = 0.88 \times \left[ \frac{230 + 70}{230 + 10} \right] = 0.88 \times \left[ \frac{300}{240} \right] = 0.88 \times 1.25 = 1.10\ \Omega$
4. Calculate Final Hot $Z_s$: For this example, assume the source contribution remains 0.30 Ω and reactance is negligible; add it to the corrected internal resistance: $Z_{s(\text{corrected})} = Z_e + (R_1 + R_2)_{70} = 0.30 + 1.10 = 1.40\ \Omega$
5. Verdict: Under these stated assumptions, 1.40 Ω exceeds the 1.37 Ω limit for relying on this B32 overcurrent characteristic. Assess an appropriate design remedy or verified RCD fault-protection arrangement; an RCBO substitution alone is not a complete acceptance check. Confirm the other protective requirements and record the basis of the result.