# Verification of the withstand capabilities of cables under short-circuit conditions

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In general, verification of the thermal-withstand capability of a cable is not necessary, except in cases where cables of small c.s.a. are installed close to, or feeding directly from, the main general distribution board

## Thermal constraints

When the duration of short-circuit current is brief (several tenths of a second up to five seconds maximum) all of the heat produced is assumed to remain in the conductor, causing its temperature to rise. The heating process is said to be adiabatic, an assumption that simplifies the calculation and gives a pessimistic result, i.e. a higher conductor temperature than that which would actually occur, since in practice, some heat would leave the conductor and pass into the insulation.

For a period of 5 seconds or less, the relationship I2t = k2S2 characterizes the time in seconds during which a conductor of c.s.a. S (in mm 2) can be allowed to carry a current I, before its temperature reaches a level which would damage the surrounding insulation.

The factor k is given in Figure G52 below.

Fig. G52 – Value of the constant k according to table 43A of IEC 60364-4-43
Conductor insulation
PVC
≤ 300 mm2
PVC
> 300 mm2
EPR XLPE Rubber 60 °C
Initial temperature (°C) 70 70 90 60
Final temperature (°C) 160 140 250 200
Conductor material Copper 115 103 143 141
Aluminium 76 68 94 93

The method of verification consists in checking that the thermal energy I2t per ohm of conductor material, allowed to pass by the protecting circuit-breaker (from manufacturers catalogues) is less than that permitted for the particular conductor (as given in Figure G53 below).

Fig. G53 – Maximum allowable thermal stress for cables I2t (expressed in ampere2 x second x 106)
S (mm2) PVC XLPE
Copper Aluminium Copper Aluminium
1.5 0.0297 0.0130 0.0460 0.0199
2.5 0.0826 0.0361 0.1278 0.0552
4 0.2116 0.0924 0.3272 0.1414
6 0.4761 0.2079 0.7362 0.3181
10 1.3225 0.5776 2.0450 0.8836
16 3.3856 1.4786 5.2350 2.2620
25 8.2656 3.6100 12.7806 5.5225
35 16.2006 7.0756 25.0500 10.8241
50[a] 29.839 13.032 46.133 19.936
1. ^ For 50mm2 cable, the values are calculated for the actual cross-section of 47.5mm2[1]

### Example

Is a copper-cored XLPE cable of 4 mm2 c.s.a. adequately protected by a iC60N circuit-breaker? (see Fig. G54)

Fig. G53 shows that the I2t value for the cable is 0.3272 x 106, while the maximum “let-through” value by the circuit-breaker, as given in the manufacturer’s catalogue, is considerably less ( < 0.1.106 A2s).

The cable is therefore adequately protected by the circuit-breaker up to its full rated breaking capability.

## Electrodynamic constraints

For all type of circuit (conductors or bus-trunking), it is necessary to take electrodynamic effects into account.

To withstand the electrodynamic constraints, the conductors must be solidly fixed and the connections must be strongly tightened, making traditional cable installations withstand level directly depending on the quality of the work executed by the electrical contractor.

For busways (busbar trunking systems), rails, etc. it is also necessary to verify that they will withstand the electrodynamic constraints during a short-circuit. But for busways the electrodynamic withstand performance is defined by construction, and verified by type tests according to IEC 61439-6, with a specified overcurrent protective device.

Manufacturers like Schneider Electric provide ready-to-use coordination tables between their circuit-breakers and their busways, making it quick and easy to select the optimal solution that guarantees the withstand strength of the system.

Fig. G54 – Example of coordination table between circuit-breakers and busways (Schneider Electric)
Type of Canalis busbar trunking KSA100
Isc max. in kA rms 25 kA 36 kA 50 kA
Type of circuit breaker NG125 NG125N 100 NG125H 80 NG125L 80
Compact NSXm NSXm B/F/N/H 100 NSXm F/N/H 100
Compact NSX NSX100B/F/N/H/S/L
Type of Canalis busbar trunking KSA160
Isc max. in kA rms 25 kA 36 kA 50 kA 70kA 90 kA
Type of circuit breaker Compact NSXm NSXm B/F/N/H 160 NSXm F/N/H 160 NSXm N/H 160 NSXm H 160
Compact NSX NSX100B/F/N/H/S/L NSX100F/N/H/S/L NSX100N/H/S/L NSX100H/S/L NSX100S/L
NSX160B/F/N/H/S/L NSX160F/N/H/S/L NSX160N/H/S/L NSX160H/S/L
NSX250B/F/N/H/S/L NSX250F/N/H/S/L NSX250N/H/S/L
Type of Canalis busbar trunking KSA250
Isc max. in kA rms 25 kA 36 kA 50 kA 70kA 100 kA 150 kA
Type of circuit breaker Compact NSX NSX160B/F/N/H/S/L NSX160F/N/H/S/L NSX160N/H/S/L NSX160H/S/L NSX160S/L NSX160L
NSX250B/F/N/H/S/L NSX250F/N/H/S/L NSX250N/H/S/L NSX250H/S/L NSX250S/L NSX250L
NSX400F/N/H/S/L NSX400F/N/H/S/L NSX400N/H/S/L
Type of Canalis busbar trunking KSA400
Isc max. in kA rms 25 kA 36 kA 50 kA 70kA 100 kA 150 kA
Type of circuit breaker Compact NSX NSX250B/F/N/H/S/L NSX250F/N/H/S/L NSX250N/H/S/L NSX250H/S/L NSX250S/L NSX250L
NSX400F/N/H/S/L NSX400F/N/H/S/L NSX400N/H/S/L NSX400H/S/L NSX400S/L NSX400L
NSX630F/N/H/S/L NSX630F/N/H/S/L NSX630N/H/S/L NSX630H/S/L NSX630S/L NSX630L
Compact NS NS630b N/H/L/LB NS630b L/LB NS630b L/LB NS630b LB
Type of Canalis busbar trunking KSA500
Isc max. in kA rms 25 kA 36 kA 50 kA 70kA 100 kA 150 kA
Type of circuit breaker Compact NSX NSX400F/N/H/S/L NSX400F/N/H/S/L NSX400N/H/S/L NSX400H/S/L NSX400S/L NSX400L
NSX630F/N/H/S/L NSX630F/N/H/S/L NSX630N/H/S/L NSX630H/S/L NSX630S/L NSX630L
Compact NS NS630b N/H/L/LB NS630b L/LB NS630b LB
Type of Canalis busbar trunking KSA630
Isc max. in kA rms ≤ 32 kA 36 kA 50 kA 70kA 100 kA 150 kA
Type of circuit breaker Compact NSX NSX400F/N/H/S/L NSX400N/H/S/L NSX400H/S/L NSX400S/L NSX400L
NSX630F/N/H/S/L NSX630N/H/S/L NSX630H/S/L NSX630S/L NSX630L
Compact NS NS630b N/H/L/LB NS630b L/LB NS630b LB
NS800N/H/L/LB NS800L/LB NS800LB
Masterpact MTZ1 MTZ1 06 H1/H2/H3/L1 MTZ1 06 L1
MTZ1 08 H1/H2/H3/L1 MTZ1 08 L1

## Notes

1. ^ In fact, the cable (maximum) resistance values that should be used for precise calculation are the ones given by the IEC 60228 "conductors of insulated cables" standard. Calculation of cable resistance with the formula R = ρ L / S, as used for this table, provides values that are sufficiently close to these values (in the order of 1%), except for 50 mm² cables for which a "theoretical" cross-section of 47.5 mm² should be used.