40,000,000
A²·s
40
kA²·s
55
mm²
9,092
A
9.092
kA
0.455
ratio
-30
mm²
2.2
ratio
40,000,000
A²·s
40
kA²·s
55
mm²
9,092
A
9.092
kA
0.455
ratio
-30
mm²
2.2
ratio
The Cable Let-Through Energy Calculator computes the I²t (current squared times time) let-through energy during a fault event and verifies whether the cable conductor size can withstand this thermal stress without damage. Cable thermal withstand is a critical safety check in protection coordination studies, ensuring that cables survive fault conditions long enough for protective devices to operate.
Let-through energy (I²t, measured in A²·s) represents the thermal energy delivered to a conductor per unit of its resistance during a fault. It is the integral of I² over the fault duration: ∫I²dt. For simplicity in design calculations, this is approximated as I²fault × tclearance for symmetrical AC faults under time-current coordination studies.
The IEC 60364-5-54 adiabatic equation for minimum conductor size under fault conditions is: S ≥ (I × √t) / k, where S is cross-sectional area in mm², I is fault current in amperes, t is fault duration in seconds, and k is a material constant. For copper conductors with PVC insulation, k = 115. For copper with XLPE insulation, k = 143. For aluminum with XLPE, k = 94.
The k factor encapsulates the conductor material's thermal capacity, resistivity, and the allowable temperature rise. PVC insulation limits conductor temperature to 160°C under short circuit (from 70°C normal operating temperature). XLPE allows up to 250°C under fault (from 90°C normal). The higher k for XLPE reflects this greater thermal headroom, meaning XLPE cables require smaller minimum sizes for the same fault withstand.
Current-limiting fuses achieve protection by limiting the I²t let-through to a very low value — much less than the cable's withstand capability. This is the 'current limiting' property that makes HRC (High Rupturing Capacity) fuses so valuable for cable protection. Circuit breakers with instantaneous trips limit t but not I (fault current flows for at least 0.5-1 cycle before opening). Fuses begin to limit current within the first half-cycle, dramatically reducing I²t.
Protection coordination requires that for every cable in the system, the let-through energy of the upstream protective device be less than the cable's thermal withstand. If the breaker or fuse lets through more energy than the cable can handle, the cable is damaged before protection operates — a fire hazard and code violation.
Let-through energy = I_fault² × t_clearance (A²·s). Minimum conductor size from IEC: S_min = I × √t / k (mm²). Thermal check ratio = actual cable (S × k) / required (I × √t). Ratio ≥ 1.0 means cable is adequate; ratio < 1.0 means cable is undersized for the fault condition and will be damaged before protection clears.
Thermal check ratio > 1.0: cable is thermally adequate for the fault condition with this clearance time. Ratio < 1.0: cable will be damaged — increase cable size or reduce clearance time (faster protection). Target ratio: 1.25-1.5 minimum for margin. Very long clearance times (>5s) for high-fault current systems often require large cables or current-limiting fuses.
Inputs
Results
FAIL: 25mm² cable cannot withstand 20 kA for 0.1s. Minimum required is 55mm² Cu. Either use 70mm² cable or reduce clearance time to <0.012s with current-limiting fuse.
Inputs
Results
PASS: 25mm² XLPE cable handles 10 kA for 50ms with 1.6x margin. Protection must clear within 50ms for this to be valid.
k is defined in IEC 60364-5-54 Table 43A and IEC 60909. Values: PVC insulated copper = 115; XLPE/EPR copper = 143; PVC aluminum = 76; XLPE aluminum = 94; bare copper busbar = 176; bare aluminum busbar = 117. Higher k allows smaller conductors for same fault withstand.
The adiabatic assumption (no heat loss during fault) is valid for faults under ~5 seconds, where heating is so rapid that negligible heat is conducted away from the conductor. For longer durations, heat dissipation reduces actual temperature rise below the adiabatic prediction. Using the adiabatic formula is conservative (safe) for most protection coordination work.
HRC fuses begin melting within the first half-cycle when fault current exceeds the fuse's current-limiting threshold. By limiting peak current to perhaps 20-40% of prospective fault current, let-through energy is reduced by a factor of 6-25× compared to a device that clears at the same time without current limiting. This is why fuse-protected cables can be significantly smaller than breaker-protected cables at the same fault level.
No. Fuse let-through energy is the I²t the fuse actually lets through (from manufacturer curves — lower than prospective I²t due to current limiting). Cable withstand I²t = (k×S)² is the maximum I²t the cable can absorb. Protection is adequate when fuse let-through I²t < cable withstand I²t. This calculator computes prospective I²t and cable withstand for initial sizing; use fuse manufacturer's let-through curves for final verification.
Standard k factors assume the conductor starts at its rated maximum normal operating temperature (70°C for PVC, 90°C for XLPE). If the cable is lightly loaded (lower temperature), more headroom exists and k is effectively higher. Conversely, if the cable is overloaded at fault inception, k is lower. Conservative design uses standard k values without temperature correction.
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