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

From Electrical Installation Guide

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 k² is given in Figure G52 below.

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Insulation	Conductor copper (Cu)	Conductor aluminium (Al)
PVC	13,225	5,776
XLPE	20,449	8,836

Fig. G52: Value of the constant k²

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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).

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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	29.839	13.032	46.133	19.936

Fig. G53: Maximum allowable thermal stress for cables I²t (expressed in ampere² x second x 10⁶)

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Example
Is a copper-cored XLPE cable of 4 mm² c.s.a. adequately protected by a C60N circuit-breaker?
Figure 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 connection must be strongly tightened.
For bus-trunking, rails, etc. it is also necessary to verify that the electrodynamic withstand performance is satisfactory when carrying short-circuit currents. The peak value of current, limited by the circuit-breaker or fuse, must be less than the busbar system rating. Tables of coordination ensuring adequate protection of their products are generally published by the manufacturers and provide a major advantage of such systems.