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35 — Calculators

Lead length for surge protective devices

An arrester with a good protection level is worthless if it hangs on a metre of wire. Under an impulse the current rises within microseconds — and across an inductance that produces a voltage which can double the protection level. That is the reason for the rule to keep the leads short.

Input

From the data sheet of the surge protective device.

Both legs together, that is the lead to the SPD plus the connection to the earthing bar.

An empirical value for straight single conductors. Loops and wide spacing increase it.

The rise time of the impulse waveform. Shorter front times produce higher voltages across the same lead.

From the data sheet of the equipment to be protected.

Result

Effective protection level at the equipmentProtection level plus the voltage across the connecting leads.
—kV
Assessment
—
Voltage across the connecting leads
—kV
Share of the leads in the protection levelThis is where it is decided whether the installation defeats the SPD.
—%
Greatest lead length for this equipment
—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

Voltage protection level U_p of the SPD
1.5 kV
Total length of the connecting leads
1 m
Inductance per metre
1 µH/m
Impulse current through the SPD
5 kA
Front time of the impulse current
8 µs
Impulse withstand voltage U_w of the equipment
2.5 kV

Result

Effective protection level at the equipment
2.13 kV
Assessment
The effective protection level is below it, but without much margin.
Voltage across the connecting leads
0.625 kV
Share of the leads in the protection level
29.4 %
Greatest lead length for this equipment
1.6 m

Formula

  • u = L · di/dt
  • L = L′ · l
  • di/dt ≈ I / t_r
  • U_effective = U_p + u
  • l_max = (U_w − U_p) / (u per metre)

Assumptions and standards

  • The inductance per metre is an empirical value for straight single conductors and is entered here. Loops and wide conductor spacing raise it considerably.
  • The length is the sum of both legs — the lead to the arrester and the connection to the earthing bar.
  • A linear current rise is assumed. The actual impulse waveform rises more steeply at first; the calculated value is a lower estimate.
  • Contributions from coupling with neighbouring cables and from the distance between arrester and equipment are not included.

Frequently asked

Where does the half-metre rule come from?

From exactly this calculation. At usual impulse currents and rise times the voltage across the leads is of the order of a kilovolt per metre. Half a metre of total length keeps that share small enough for the arrester protection level to retain its meaning.

What if I cannot get below that length?

V-shaped wiring helps: incoming and outgoing conductors are taken directly to the arrester terminals, so the arrester lies in the current path rather than on a stub. That largely removes the additional voltage.

Why does the front time matter so much?

Because the voltage depends on the rate of rise, not on the current alone. The same peak value in half the time gives twice the voltage. That is why lightning impulses with a steep front are more critical for lead length than higher-energy but slower waveforms.

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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