Short Circuit Withstand: The Distribution Board Feeder — k=115 vs k=143
A 50mm² cable, 10kA fault, 0.4s clearing time. BS 7671 and IEC say FAIL with k=115 while AS/NZS says PASS with k=143. Understanding why could save your design.
The adiabatic equation is one of the most critical checks in electrical design. If a cable cannot withstand the prospective fault current for the time it takes the protective device to clear, the cable can be permanently damaged — or worse, catch fire. And here is where the standards diverge dramatically: the same cable, same fault, same clearing time can PASS under one standard and FAIL under another.
The Scenario
A sub-distribution board feeder in a commercial building:
- Cable: 50mm² copper, PVC insulated (single-core)
- Prospective fault current: 10kA at the cable origin
- Protective device clearing time: 0.4 seconds
- Initial conductor temperature: 70°C (operating temperature for PVC)
- Final conductor temperature limit: varies by standard
The Adiabatic Equation
All four standards use the same fundamental equation:
Adiabatic Equation
I²t ≤ k²S²
Where:
- I = prospective fault current (A)
- t = protective device clearing time (s)
- k = cable constant depending on insulation and conductor material
- S = cable cross-sectional area (mm²)
The energy let-through (I²t) must not exceed the cable's withstand capacity (k²S²). The critical variable is k — and this is where the standards disagree.
Side-by-Side Results
Scenario
50mm² Cu PVC cable, 10kA fault, 0.4s clearing time
| Parameter | AS/NZS | BS 7671 | IEC 60364 | NEC |
|---|---|---|---|---|
k-factor (Cu/PVC) | k = 14370°C → 160°CAS/NZS 3008.1.1, Table 52 | k = 11570°C → 160°CBS 7671, Table 43.1 | k = 11570°C → 160°CIEC 60364-4-43, Table 43A | VariesICEA P-32-382 methodNEC 110.10, 240.4 |
Cable withstand (k²S²) | 51.1 × 10⁶ A²s(143 × 50)² = 51.1M | 33.1 × 10⁶ A²s(115 × 50)² = 33.1M | 33.1 × 10⁶ A²s(115 × 50)² = 33.1M | N/ADifferent methodology |
Fault energy (I²t) | 40.0 × 10⁶ A²s10,000² × 0.4 | 40.0 × 10⁶ A²s10,000² × 0.4 | 40.0 × 10⁶ A²s10,000² × 0.4 | 40.0 × 10⁶ A²s10,000² × 0.4 |
Result: I²t ≤ k²S²? | PASS ✓40.0M < 51.1M (78%) | FAIL ✗40.0M > 33.1M (121%) | FAIL ✗40.0M > 33.1M (121%) | DependsOn protective device I²t |
Minimum cable to pass | 50mm²Current size adequate | 70mm²k²S² = 64.8M > 40M ✓ | 70mm²k²S² = 64.8M > 40M ✓ | Verify device I²tCable must exceed device let-through |
Why k = 115 vs k = 143?
This is one of the most debated differences between the Australian and international standards. The k-factor is derived from the heat capacity of the conductor-insulation system:
k-Factor Derivation
k = √(Qc × (β + 20) / ρ₂₀ × ln((β + θf) / (β + θi)))
Where Qc is the volumetric heat capacity, β is the reciprocal of the temperature coefficient of resistance, ρ₂₀ is the resistivity at 20°C, θi is the initial temperature, and θf is the final temperature.
The Temperature Assumptions
Both standards use the same temperature range (70°C to 160°C for PVC) but differ in other parameters:
| Parameter | AS/NZS 3008 | BS 7671 / IEC |
|---|---|---|
| Initial temperature | 70°C | 70°C |
| Final temperature | 160°C | 160°C |
| Resistivity model | Different coefficients | IEC coefficients |
| Heat capacity | Higher value | IEC standard value |
| Resulting k | 143 | 115 |
AS/NZS 3008 uses material property data that yields a higher k-factor. The Australian standard committee has historically argued that the IEC values are overly conservative, while the IEC committee maintains that their values include a safety margin for real-world conductor quality variations.
24% Difference in Withstand Capacity
The k-factor difference is not trivial. k=143 gives a withstand capacity of 51.1 MA²s for a 50mm² cable. k=115 gives 33.1 MA²s. That is a 54% difference in calculated thermal withstand — the AS/NZS cable can theoretically absorb 54% more fault energy before exceeding its temperature limit.
The NEC Approach
NEC doesn't prescribe a simple k-factor table. Instead:
- The cable manufacturer provides I²t withstand data per ICEA P-32-382
- The protective device manufacturer provides I²t let-through data
- The designer verifies that device I²t < cable I²t
This shifts responsibility to the device-cable combination rather than a universal equation. In practice, UL-listed combinations are pre-verified, which is why NEC engineers rarely perform manual adiabatic calculations.
The Real-World Impact
For Engineers Working Across Standards
If you design a cable installation to AS/NZS 3008 and it passes the adiabatic check at 50mm², that same design would fail under BS 7671 or IEC 60364. This has real consequences for:
- Australian firms bidding on Middle East projects (IEC 60364 applies)
- UK firms designing for Australian mining (AS/NZS 3008 applies)
- Any project with multiple jurisdictional requirements
What Happens When It Fails?
A cable that exceeds its I²t rating during a fault will:
- PVC insulation reaches above 160°C — the insulation softens and may melt
- Conductor resistance increases with temperature, generating more heat
- If the fault persists, the insulation ignites
- Adjacent cables in the same tray or conduit are also affected
Not Just the Cable at Risk
A cable that fails the adiabatic check at 50mm² won't necessarily fail catastrophically during a single fault. But it will be thermally degraded. Repeated faults (which happen in industrial installations) will progressively damage the insulation until a ground fault develops.
Solutions When BS/IEC Says FAIL
When your design passes under AS/NZS but fails under BS/IEC, you have several options:
- Increase cable size — the most straightforward solution (50mm² → 70mm²)
- Reduce clearing time — a faster protective device (0.4s → 0.2s reduces I²t by 50%)
- Current-limiting devices — MCCBs and fuses that limit the actual I²t below the prospective value
- Reduce fault level — impedance of the upstream transformer limits the prospective fault current
The most cost-effective approach is usually a current-limiting fuse or MCCB, which can reduce the actual I²t let-through to well below the cable withstand — regardless of which k-factor you use.
Key Takeaways
- k=143 (AS/NZS) vs k=115 (BS/IEC) is a 24% difference in the k-factor and 54% in withstand capacity
- Same cable, same fault, opposite results — 50mm² passes AS/NZS but fails BS/IEC at 10kA/0.4s
- BS 7671 and IEC 60364 require 70mm² where AS/NZS 3008 allows 50mm²
- NEC uses a different methodology — device-cable I²t matching instead of universal k-factors
- Always design to the applicable standard — using k=143 on a BS 7671 project is a compliance violation
Related Resources
- Fukushima: Battery System Short Circuit Calculation — DC short circuit analysis for backup battery systems
- Short Circuit: The 3 Numbers Every Engineer Must Know — Prospective fault current, breaking capacity, and let-through energy
- Arc Flash PPE: The Same MCC Panel — Where all standards converge on IEEE 1584
- The Complete Cable Sizing Comparison — k-factor summary across conductor and insulation types
- View all worked examples →
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Lead Electrical & Instrumentation Engineer
18+ years of experience in electrical engineering at large-scale mining operations. Specializing in power systems design, cable sizing, and protection coordination across BS 7671, IEC 60364, NEC, and AS/NZS standards.