Short-circuit rating
Adiabatic short-circuit rating of a conductor (IEC 60949)
- where
- adiabatic short-circuit current (kA)
- material constant (copper 226, aluminium 148) (A·s½/mm²)
- conductor cross-sectional area (mm²)
- final short-circuit temperature (°C)
- reciprocal of temperature coefficient at 0 °C (copper 234.5, aluminium 228) (K)
- initial conductor temperature (°C)
- short-circuit duration (s)
Explain this equation
Gives the short-circuit current a conductor can carry for time t without exceeding its insulation's short-circuit temperature, assuming all the heat stays in the conductor.
S is the conductor area and t the fault duration. θᵢ is the starting temperature, normally the maximum continuous temperature, and θ_f the permitted short-circuit temperature. K and β are material constants: K combines heat capacity and resistivity, and β is the temperature at which resistance would extrapolate to zero, below 0 °C.
Joule heating I²R heats the conductor while its resistance rises with temperature. Integrating the heat balance with resistance proportional to (θ + β) gives a log of the temperature ratio, so I²t is fixed for a given conductor and temperature range.
Copper XLPE from 90 °C to 250 °C works out to about 143 A·s½ per mm², matching the BS 7671 k value: 240 mm² carries about 34 kA for 1 s or 48.5 kA for 0.5 s. Aluminium gives about 94.
Being adiabatic, the result is conservative for longer faults. Check joints and terminations, which may have lower limits than the cable.
Short-circuit current a conductor can carry for time t without exceeding its insulation's short-circuit temperature, assuming no heat leaves the conductor (adiabatic).
Enter your values to see the result.
Good to know
IEC 60949: I²t = K²S² ln((θf + β)/(θi + β)). Constants: copper K = 226, β = 234.5; aluminium K = 148, β = 228; lead K = 41, β = 230; steel K = 78, β = 202. Typical temperature limits (normal max / short-circuit): XLPE 90/250 °C; EPR 90/250 °C; PVC 70/160 °C (≤ 300 mm²) or 70/140 °C (> 300 mm²); impregnated paper (solid type, belted/screened MV) normally 65–80 °C depending on voltage / 250 °C for copper, but limited lower where soldered joints or compression fittings apply (check IEC 60724 and the cable standard). With 90/250 °C copper the result reproduces k = 143 of BS 7671.
Common mistake
Starting from ambient instead of the maximum continuous operating temperature, or forgetting that joints and terminations (e.g. soldered or mechanical connectors) may have lower limits than the cable.
Limits
Adiabatic only: conservative, especially for durations above about 1–2 s and for small conductors, where IEC 60949 allows a non-adiabatic factor ε > 1 that is not calculated here. Valid in principle for t up to about 5 s.
Sources
- IEC 60949:1988+AMD1:2008 Calculation of thermally permissible short-circuit currents, taking into account non-adiabatic heating effects
- IEC 60287-1-1:2023 Electric cables – Calculation of the current rating – Part 1-1: Current rating equations (100 % load factor) and calculation of losses
- BS 7671 / IEC 60364-5-54 k values (Table 43.1): copper 90/250 °C k = 143, aluminium k = 94 (cross-check of the adiabatic constants)
- Moore, G.F. (ed.) Electric Cables Handbook, 3rd edn, Blackwell Science / Wiley
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.