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Zs, and the prospective earth fault currentWhy multiply by Cmin?
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The question at the end: Why multiply by Cmin? The answer is in the notes below.
The notes
Exactly as they are on the site.
Zs = Ze + (R1 + R2)
What it's for: the total earth fault loop impedance of the circuit, once R1 + R2 is known. That needs Ze too.
All in ohms. Simple: add the two sides of the loop together to get the whole.
We don't install Ze, the DNO does. You get Ze in three ways:
- Measurement: on site, with an earth fault loop impedance tester,
- Enquiry: phone the DNO and ask, or
- Calculation. In a question, Ze is usually just given in the scenario.
3 for a full design.
Another example: add a Ze to the radial from section 7
Ze (TN-C-S, given) = 0.35 Ω R1 + R2 (section 7) = 0.40 Ω Zs = 0.35 + 0.40 = 0.75 Ω
Prospective earth fault current and Cmin
What it's for: once you know Zs you can work out the prospective earth fault current (PEFC): how many amps would flow if there were an earth fault at that point of the circuit. It's just Ohm's law, with one extra factor.
U₀ = 230 V · Cmin = 0.95 for UK public LV supplies (Reg 411.4.4 Note 1) · Zs in ohms · PEFC in amps
Cmin is the minimum voltage factor (Reg 411.4.4, p.73). It allows for the supply voltage varying with time and place, and for low-voltage supplies it is 0.95: 230 × 0.95 = 218.5 V. Generated voltage isn't a steady, smooth 230 V. It goes up and down all the time. BS 7671 Appendix 2 (p.436) gives the UK's permitted range: 230 V +10 % / −6 %, so 216.2 V to 253.0 V. In the UK we design with 218.5 V.
Worked example: why Cmin matters
Zs = 5 Ω Without Cmin: 230 ÷ 5 = 46 A With Cmin: 218.5 ÷ 5 = 43.7 A (230 × 0.95 = 218.5 V) Difference: 2.3 A less fault current
2.3 A might not sound much, but a protective device needs enough current to operate quickly (next section). Less current means it takes longer, so things stay live longer. By designing with the worst case (the lowest voltage), you know it can't get any worse.
Another example: PEFC for Zs = 0.75 Ω
PEFC = (230 × 0.95) ÷ 0.75
= 218.5 ÷ 0.75
= 291.3 AThe maximum Zs formula uses the same U₀ × Cmin: Zs × Ia ≤ U₀ × Cmin, printed at Reg 411.4.4 (p.73).
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