Cable Short-Circuit Withstand Calculation: I²t and k²S² Explained
Quick answer: cable short-circuit withstand is checked by confirming that the fault energy allowed by the protective device does not exceed the conductor’s thermal capability. For an adiabatic check, I²t ≤ k²S², or equivalently S ≥ I√t/k.
Why ampacity is not enough
A cable selected for continuous load current and voltage drop can still be damaged during a short circuit. Fault current produces rapid I²R heating, and conductor temperature can rise from its normal operating value to the insulation’s short-circuit limit in a fraction of a second. The cable and protective device therefore have to be checked as a coordinated pair.
The adiabatic equations
For a specified conductor:
Maximum allowable I²t = k²S²
For a known fault current and clearing time:
Minimum S = I√t/k
S is conductor cross-section in mm². I is RMS short-circuit current in amperes. t is clearing time in seconds. k is selected from the governing standard for conductor material, insulation, initial temperature and final permitted temperature.
Worked cable check
Check a 50 mm² copper XLPE conductor for a prospective 18 kA fault cleared in 0.10 seconds. Assume k = 143 for the applicable case.
Required S = 18,000 × √0.10 / 143 = 39.8 mm²
The installed 50 mm² conductor passes this simplified thermal check. The same result can be expressed as energy:
Device energy: I²t = 18,000² × 0.10 = 32.4 × 10⁶ A²s
Cable capability: k²S² = 143² × 50² = 51.1 × 10⁶ A²s
Because 32.4 is less than 51.1, the cable passes the adiabatic comparison. For a current-limiting fuse or breaker, use the manufacturer’s published let-through I²t rather than simply multiplying prospective RMS current by total clearing time.
Which current and time belong in the calculation?
| Input | Use | Avoid |
|---|---|---|
| Fault current | Prospective current at the cable location | Using transformer-terminal current everywhere |
| Clearing time | Total relay plus breaker or fuse clearing time | Using only relay operating time |
| Let-through energy | Manufacturer I²t for current-limiting devices | Assuming constant prospective current |
| k factor | Correct material and insulation table | Copying a value from another cable type |
Complete verification workflow
- Calculate maximum short-circuit current at the start and end of the cable.
- Identify the protective device and its total clearing curve or let-through energy.
- Select k for the cable conductor and insulation system.
- Check phase, neutral and protective conductors for their relevant faults.
- Verify peak electrodynamic forces, especially for single-core cables and bus-connected runs.
- Check cable terminations, joints, screens and metallic sheaths.
- Record assumptions and coordinate them with the protection study.
Cable Short-Circuit FAQ
Does a larger breaker always require a larger cable?
Not automatically. Continuous overload protection and short-circuit energy are separate checks. The device curve, fault level, clearing time, installation method and cable properties all matter.
Why use manufacturer let-through data?
Current-limiting devices reduce both the peak and duration of the fault current. Published I²t provides a more accurate coordination check than assuming the full prospective current flows until clearing.
Does the adiabatic check cover mechanical forces?
No. It is a thermal calculation. Cable cleats, supports, spacing and terminations must also withstand peak short-circuit forces.
Continue with cable derating factors and the updated cable current-carrying capacity guide.
