Installation design
Loop impedance and operating current
- where
- maximum earth fault loop impedance (Ω)
- nominal voltage to earth (V)
- minimum-voltage factor
- current operating the device in the required disconnection time (A)
Explain this equation
Works out the maximum earth fault loop impedance that still lets a protective device disconnect in the required time. Use it to judge whether a circuit's Zs is acceptable.
U₀ is the nominal voltage to earth, 230 V in the UK. C_min is the minimum-voltage factor, allowing for the supply running below nominal, typically 0.95. I_a is the current that makes the device operate within the required time, read from its time-current characteristic. Z_s,max is the highest permitted loop impedance in ohms.
Fault current is voltage divided by loop impedance. For the device to operate in time, the fault current at the lowest expected voltage must reach at least I_a. Rearranging gives the largest impedance that still achieves that.
230 V × 0.95 ÷ 160 A gives about 1.37 Ω. A 32 A Type B circuit-breaker needs 5 × 32 = 160 A, so that is its limit. Double I_a and the permitted Zs halves.
Watch out: use I_a, not the device's rated current I_n. Compare the limit with Zs at operating temperature; a cold measured value needs adjusting.
Automatic disconnection depends on enough fault current flowing to operate the device within the required time. Obtain Ia from the applicable characteristic or accepted data.
Cmin allows for lower supply voltage in this calculation. It is distinct from a temperature allowance for a measured cold loop value.
Enter your values to see the result.
Common mistake
Using the device rated current In in place of Ia.
Limits
Obtain Cmin and Ia from the applicable standard and device data for the required disconnection time. A numerical limit does not demonstrate full compliance.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.