Cable I²t Withstand Check Formulas

Cable short-circuit withstand formulas: the I²t limit of a conductor, the longest fault time at a current and the check against the let-through of a device.

The formulas

k is the factor of the conductor and its insulation (143 for copper with XLPE, 115 for copper with PVC up to 300 mm² and 103 above 300 mm²), S the cross-section in mm², I the fault current in amperes and t the time in seconds. The formula is for a short fault, up to about 5 s, when the heat has no time to leave the conductor. The device figure is the let-through energy of the fuse or the breaker from the maker data, and the page uses an example value. The check must hold at the lowest fault current at which the device still trips, because a lower current takes longer to clear.

Worked example: a 35 mm² XLPE copper cable

1. I²t(cable) = 143² × 35² = 25,050,000 A²s
2. At 10 kA, t = 25,050,000 / 10,000² = 0.2505 s
3. At 2 kA, t = 25,050,000 / 2,000² = 6.263 s
4. A device that lets through 800,000 A²s is below 25,050,000 A²s, so the cable is protected

Longest fault time for the 35 mm² cable by fault current

Frequently asked questions

Why is the energy I²t and not just the current?

The heat in the conductor is the square of the current times the time. For a short fault, all of that heat stays in the conductor, so the energy sets the temperature rise.

Where does the factor k come from?

From the heat capacity and resistivity of the conductor and the start and end temperatures allowed by the insulation. The standard tabulates it.

Why check the lowest fault current?

The longest clearing time comes at the lowest current that trips the device. The cable must hold for that time too.

Does this apply to long faults?

Not beyond a few seconds. Then heat leaves the conductor, and the adiabatic formula is conservative. The standard gives other methods.

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