Last edit: 03/07/2025
The doubt
What’s the maximum bearable limit of a cable or of a protective device before it deteriorate, get caught on fire or even explode?
What’s the parameter to consider? The current or the energy the device is subject?
Consideration 1: The electric energy
Like we well know electrical components have a lifetime, which is calculated considering the energy that trasverse them. The electrical energy like expressed from the english physician James Prescott Joule its explained like it follows:
Q= I 2*R, from which one obtains I 2*t=Q/R, that is from the current passing through the resistance in the unit of time [A^2*s], analogue as [Joule/Ohm].
Consideration 2:The prospective short-circuit current
This value of let through energy will be correct if we won’t consider the limitation priority of the let through energy of the protective device which, precisly, limits the let through energy during the short-circuit phenomena. Important to consider for the case presented it’s the idea of the prospective short-circuit current, which is the current that would flow in a circuit if each pole of the device was replaced with a conductor with negligible impedence.
[IEC 60947-1:2008 ]: 2.5.5 prospective current (of a circuit and with respect to a switching device or a fuse)
Current that would flow in the circuit if each pole of the switching device or the fuse were replaced by a conductor of negligible impedance.
In reality, like we see in the chart, the effective short-circuit current its really smaller. The reason is correlated to the fact that the opening of the protection doesn’t determine the immediate interruption of the current. The current continue to flow undergoing the effect of the attenuation due to the current generated by the electrical-arch
The effective short-circuit current, or fault current, its the current that flows through a circuit when a short-circuit appens, or a virtually zero resistance connection between two points with different potential.
Consideration 4: The let through energy
In the case taken in exam we assume a value of net frequency of 50Hz, which implies a period in which the current is equal to 20ms
Termical and dinamic stress that verifies during the short-circuit is proportional to I^2*t, where I^2 it’s the square of the short-circuit current and t its the time used from the protection to estinguish it.
During the elimination of the given short-circuit an energy will grow, wich is let through from the protective device, that energy will be transformed in heat; it is defined as specific let through energy, or the energy dissipated during a short-circuit, which is calculated according to the intensity of the short-circuit current and for the time it persist, it can be also named as the Joule integral.
Consideration 4:The energy bearable by the cables
As regards the verification of short-circuit currents in the case of use of protective device: The let through energy trasversing the switch its minimal at the magnetical calibration (Ip). With a short-circuit current bigger than the magnetical calibration, the let through energy grows because the intervention time of the magnetical protection its costant. If the short-circuit current near the switch exceed (Iq), the cable isn’t protected by eventual overloads that could lead to an excessive increase of the temperature of the last one ,causing the explosion or the decay of it.
The energy bearable by the cables is correlated to the product of the square product of the cable section, indicated in mmq, and the square product of the value K, or a costant, which takes into account resistivity, temperature coefficient and tollerability parameters of the material, that in the case of the PVC is 115. The let through energy of the cables needs to be bigger than the one of the protection, like we can see in the picture. If we take for example a PVC cable with a section of 10mmq, its maximum let through energy will be 1 322 500 A^2*s. Refering to the chart, considering a protection of 32 A and supposing that a short-circuit of 10kA, the energy that the protection lets through is near the value of 60K A^2*s, which is smaller than the one that the cable can endure.
The formula used supposed that the cable don’t have an exchange of heat with the external environment (adiabatic phenomena).
IEC 60364-4-43] 431.5.4 Characteristics of short-circuit protective devices […]
431.5.4.2 For cables and insulated conductors, all current caused by a short-circuit occurring at any point of the circuit shall be interrupted in a time not exceeding that which brings the insulation of the conductors to the permitted limit temperature.
For operating times of protective devices < 0,1 s where asymmetry of the current is of importance and for current-limiting devices k^2*S^2 shall be greater than the value of the let-through energy I^2*t quoted by the manufacturer of the protective device.
I^2*t ≤ K^2*S^2
Conclusions
The limitation of the current of a cable isn’t only the parameter to use to protect it against fires. A protection against overload protects correctly the cable against that phenomena, but not against short-circuit. In that case the current is so high and unexpected that a protection against overload cannot provide that the cable wont decay during the short-circuit. The electrical regulation addresses this problem by thinking in terms of Passing Energy.
It’s important to notice, because it plays a role in safety, the idea of the let through energy of a protection, considering that a big part of them aren’t really an energy limitator.