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11 — Calculators

Calculate cable impedance and loop impedance

Loop impedance decides whether enough current flows under fault conditions for the protective device to disconnect. Two things are regularly overlooked: the warmer conductor under fault, and a protective conductor smaller than the line conductor.

Input

A smaller protective conductor raises the loop impedance — that decides the disconnection condition.

For the disconnection condition the heated conductor is used, because the loop impedance is then at its highest.

From the cable data sheet. For cables it is usually between 0.07 and 0.09 Ω/km and only becomes noticeable from about 50 mm² upwards.

Result

Loop impedance line–protective conductorThe governing figure for the disconnection condition.
—Ω
Resistance of one conductor (one way)
—Ω
Reactance of one conductor (one way)
—Ω
Impedance for a three-phase short circuit
—Ω
Share of reactance in the loopBelow 10 % it may be neglected, above that not.
—%

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

One-way cable length
60 m
Line conductor cross-section
16 mm²
Protective conductor cross-section
16 mm²
Conductor material
Copper (κ = 56 m/Ω·mm²)
Conductor temperature
80 °C
Inductive reactance per kilometre
0.08 Ω/km

Result

Loop impedance line–protective conductor
0.166 Ω
Resistance of one conductor (one way)
0.083 Ω
Reactance of one conductor (one way)
0.005 Ω
Impedance for a three-phase short circuit
0.083 Ω
Share of reactance in the loop
5.79 %

Formula

  • R = L / (κ · A) · [1 + α · (ϑ − 20 °C)]
  • X = X′ · L
  • Loop: Z = √[(R_L + R_PE)² + (2 · X)²]
  • Three-phase: Z = √(R_L² + X²)

Assumptions and standards

  • The disconnection condition is calculated with a heated conductor, because the loop impedance is then highest and the fault current smallest.
  • The inductive reactance per unit length comes from the cable data sheet and is entered here.
  • The upstream impedance of network and transformer is not included. It adds to this and dominates on short runs.

Frequently asked

Why does the protective conductor count?

Because the fault current returns through it. If the protective conductor is half the size of the line conductor, its resistance is twice as high — the loop becomes half as conductive again as with equal cross-sections, and the fault current falls accordingly.

When may I ignore the reactance?

As long as its share of the loop stays below roughly ten percent, which is the case at small cross-sections. From about 50 mm² it becomes noticeable; at 240 mm² it co-determines the impedance.

Why 80 °C and not 20 °C?

Because the disconnection condition has to hold in the worst case. A warm conductor has more resistance, hence less fault current. Calculating at 20 °C gives too large a fault current and therefore too optimistic an answer.

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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