Adiabatic Equation

I am not an electrician but have a personal technical interest in understanding the Wiring Regulations.

I have become a bit confused by some contributions on the internet which seem to suggest that the adiabatic calculation will determine the size of CPC that will "cope with" a temperature rise to the maximum temperature permitted for a given cable type.

But as I understand it, it is the insulation which has to tolerate the temperature rise. This rise is caused by the heating effect (IsquaredR) of the current flowing in the CPC (and live conductor) under a dead short earth fault condition and which flows for the time it takes for the overcurrent protective device to disconnect the supply. Exceeding the maximum permitted temperature would permanently damage the insulation which I assume would no longer insulate.

Outside the parameters of the adiabatic conditions I assume that the conductors themselves could tolerate a very much higher and longer duration current, and hence temperature rise, before they themselves would become damaged. The only damage I can think of is that an unprotected conductor would melt like a fuse.

But for the adiabatic conditions of a known maximum level of earth fault current and a known OCPD disconnection time, the equation will determine the minimum size of CPC which would generate a temperature rise in the cable to the maximum permissible temperature for the insulation. In the case of a multi core cable like twin and earth, I assume that for an earth fault the heat contribution from the live conductor is not considered because the contribution from the smaller and hence higher resistance CPC will be much greater and more significant.

I will be pleased to hear from expert readers to confirm or otherwise clarify if I have understood the theory of this correctly . Thanks

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  • The adiabatic equation assumes that the cable is heating up so fast that there's no time to dissipate any heat through the insulation.

    So it's not really considering the "contributions" of the live and CPC conductors. The two are separate.

    The CPC is thinner so it has both a higher resistance and lower thermal mass. So it will overheat faster than the live.

  • The problem is not vaporization or fusing of the copper, it is more if the cable is fit for continued service after the fuse or circuit breaker has operated after a 'worst case' fault.

    Fusing the conductors requires  many orders of magnitude more energy. Its also why current ratings for example for mineral insulated wires are noticeably  higher than PVC or polyethylene for the same copper cross-section.. 

    Considering 'not fit' for use, for example have the heated cores moved in the plastic (think hot wire cutter like) or has the insulation near the copper been converted to a conductive char, or in some other way decomposed or made brittle ? 

    The calculation is one of a maximum credible temperature rise during the time the fault current flows, and assumes the only thermal absorber is the metal itself, and that no energy is lost into the environment or into the bulk insulation,  and because some energy always is, the adiabatic approximation is always a slight over-estimate - that is to say that  a bit more current is OK.

    Mike.

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  • The problem is not vaporization or fusing of the copper, it is more if the cable is fit for continued service after the fuse or circuit breaker has operated after a 'worst case' fault.

    Fusing the conductors requires  many orders of magnitude more energy. Its also why current ratings for example for mineral insulated wires are noticeably  higher than PVC or polyethylene for the same copper cross-section.. 

    Considering 'not fit' for use, for example have the heated cores moved in the plastic (think hot wire cutter like) or has the insulation near the copper been converted to a conductive char, or in some other way decomposed or made brittle ? 

    The calculation is one of a maximum credible temperature rise during the time the fault current flows, and assumes the only thermal absorber is the metal itself, and that no energy is lost into the environment or into the bulk insulation,  and because some energy always is, the adiabatic approximation is always a slight over-estimate - that is to say that  a bit more current is OK.

    Mike.

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