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15 — Calculators

Greatest cable length for the disconnection condition

Voltage drop limits cable length — but often it is not the first limit. As length grows the fault current at the far end falls, and at some point it is no longer enough to operate the device. This calculation says where that limit lies.

Input

For the minimum short-circuit current. The standard you apply governs.

From the characteristic in the data sheet, matching the required disconnection time.

Result

Greatest permissible cable length
—m
Greatest permissible loop impedance
—Ω
Available for the cableWhat remains after deducting the upstream impedance.
—Ω
Length at the next size upWith the protective conductor growing along.
—m

A guide, not a design to standard. We give no warranty for the correctness of the results, the applicable standards and case-by-case verification govern.

Worked example

The default case the calculator starts with, worked through once. Change the values above and it recalculates immediately.

Inputs

System voltage (line to line)
400 V
Voltage factor c
0.95
Operating current of the protective device I_a
160 A
Upstream impedance
0.05 Ω
Line conductor cross-section
16 mm²
Protective conductor cross-section
16 mm²
Conductor material
Copper (κ = 56 m/Ω·mm²)
Conductor temperature under fault
80 °C

Result

Greatest permissible cable length
479 m
Greatest permissible loop impedance
1.37 Ω
Available for the cable
1.32 Ω
Length at the next size up
748 m

Formula

  • Z_max = c · U₀ / I_a with U₀ = U / √3
  • available for the cable: Z_max − Z_upstream
  • Loop resistance per metre: (1/(κ·A_L) + 1/(κ·A_PE)) · [1 + α · (ϑ − 20 °C)]
  • L_max = available impedance / resistance per metre

Assumptions and standards

  • The calculation uses a heated conductor, because the loop impedance is then highest.
  • The inductive component of the cable is not included. At small cross-sections that is acceptable; from about 50 mm² it shortens the permissible length further.
  • The upstream impedance is subtracted arithmetically. That is the safe side: the actual loop is geometrically somewhat smaller, so the permissible length is slightly greater than shown.
  • Voltage drop is a separate criterion and limits the length independently. The smaller of the two always governs.

Frequently asked

Which limit bites first, voltage drop or the disconnection condition?

It depends on the protective device. At small rated currents with a slow characteristic, voltage drop is usually the tighter limit. At large rated currents or a fast characteristic — that is, a high operating current — it is the disconnection condition. Calculate both and take the smaller value.

Why is the protective conductor included?

Because the fault current returns through it. A protective conductor half the size shortens the permissible length by a third. That is why it is a separate field here rather than an assumption.

What if no value is produced?

Then the upstream impedance alone already exceeds the permissible loop impedance — the device would not operate even with zero metres of cable. In that case the device is wrongly chosen, not the cable too long.

Calculating is the easy part.

A formula gives you a number. Designing a plant also demands installation method, grouping, discrimination, the standards in force and a look at the installed base. That is what we take on.

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