Data Source and Methodology
Authoritative reference: IET Wiring Regulations — BS 7671:2018+A2:2022, including Section 41 (Protection against electric shock), Tables 41.3–41.6, and Appendix 3 (Time–current characteristics). Official publisher: The IET and BSI. See: IET BS 7671 and BSI publications.
All calculations follow standard BS 7671 design assumptions: fault current estimated from nominal voltage reduced by Cmin, loop impedance obtained from Ze and R1+R2 with temperature correction, and device instantaneous multiples for conservative checks where manufacturer curves or tabulated values are not consulted.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formulas Explained
Loop impedance from components and temperature:
$$ Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big] $$
Prospective earth fault current (conservative):
$$ I_f \;=\; \frac{C_{\min}\,U_0}{Z_s} $$
Maximum permissible Zs based on instantaneous operation:
$$ Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n $$
with typical conservative multipliers for MCBs: \(k = 5\) (Type B), \(10\) (Type C), \(20\) (Type D). For precise values use BS 7671 tables or manufacturer curves.
Glossary of Variables
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- U0: Nominal phase-to-earth voltage (V).
- Cmin: Minimum voltage factor (dimensionless, typically 0.95).
- Ze: External earth fault loop impedance (Ω).
- R1 + R2: Line plus CPC resistance at 20 °C (Ω).
- T: Estimated operating temperature of conductors (°C).
- α: Temperature coefficient of copper ≈ 0.004/°C.
- Zs: Total earth fault loop impedance (Ω).
- If: Prospective earth fault current to earth (A).
- In: Protective device rated current (A).
- Ia: Fault current ensuring automatic disconnection (A).
- Zs,max: Maximum permissible loop impedance (Ω).
How It Works: A Step-by-Step Example
Suppose U0 = 230 V, Cmin = 0.95, Ze = 0.35 Ω, R1+R2 at 20 °C = 0.40 Ω, and T = 70 °C. Device is MCB Type B with In = 32 A.
- Temperature-correct R1+R2: α = 0.004/°C, ΔT = 50 °C ⇒ factor = 1 + 0.004×50 = 1.2. Thus (R1+R2)T = 0.40 × 1.2 = 0.48 Ω.
- Total Zs: Zs = Ze + (R1+R2)T = 0.35 + 0.48 = 0.83 Ω.
- Fault current: If = (Cmin × U0) / Zs = (0.95 × 230) / 0.83 ≈ 263 A.
- Ia for Type B: k = 5 ⇒ Ia = 5 × 32 = 160 A.
- Max Zs: Zs,max = (0.95 × 230) / 160 ≈ 1.366 Ω.
- Compliance: 0.83 Ω ≤ 1.366 Ω ⇒ Pass.
Frequently Asked Questions (FAQ)
Do I need the BS 7671 tables if I use this calculator?
Yes. This tool implements the core formulas but does not replace official tables, correction notes, or manufacturer time–current data. Always verify final designs against BS 7671 and the On-Site Guide.
Why is Cmin set to 0.95?
It provides a conservative allowance for supply voltage variations under fault conditions, as commonly adopted in BS 7671 design calculations.
What if I only have a measured Zs?
Enter it directly in “Measured Zs”. The tool will prioritise it for fault current and compliance checks and ignore Ze/R1+R2 unless measured Zs is empty.
How accurate is the temperature correction?
It uses a standard linear copper coefficient (α ≈ 0.004/°C). This is appropriate for design estimates. For critical cases, consult detailed cable data and installation conditions.
Can I use this for RCBOs?
Yes, if the RCBO’s instantaneous characteristics are equivalent to the selected MCB type. For exact verification, consult the device’s time–current curves.
What if Zs is very low and If is extremely high?
That typically improves disconnection but ensure the device and conductors can withstand the thermal and mechanical stress (check PFC/PEFC and device breaking capacity).