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Let through Energy - Cable Sizing

Nick Parker
Why let through energy of cable is calculated and compared against protective device let through energy, when adiabatic equation and disconnection time check is used to verify the cable sizes? or this let thru energy verification is applied only for current limiting breakers / fuses?
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    Nick


    The energy let through has to be equal to or less than the thermal withstand of the cable. So Isqt <= K sq x S sq.
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    Your wording is a bit unclear to me,  but I think you are asking if the adiabatic equation for cables and the let-through energies of fuses etc are related.


    If so, yes, actually it is the same formulae with a bit of algebraic manipulation and some letter changes to confuse the unwary.



    For every conductor in the fault loop, the let through I2t represents the number of joules of heating that will occur per ohm of that part. This then relates to how hot we dare allow or want  that part to get - so for plastic coated cable that is perhaps between 100 and 150C, while  for a copper fuse wire we may want more like 1000C, so the figures for a given diameter end up rather different, but the idea is exactly the same - when things happen fast enough that there is no time for heat to escape, so we look at constant energy,and the thermal mass of the metal as if it was in isolation.

    M.


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    Like Mike, I am puzzled by the question, but t is not the maximum disconnection time, which could be 5 s for a distribution circuit. It is rather more instantaneous. How instantaneous and what current may flow depends upon the specific device, which is why manufacturers will quote I²t.


    If there is no OCPD plenty of energy will be let through before something else gives!
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    To be clear, I wanted to ask, When the cables have been already verified using adiabatic equation, Do I still need to check the cables for let through energy verification?
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    Nick Parker:

    To be clear, I wanted to ask, When the cables have been already verified using adiabatic equation, Do I still need to check the cables for let through energy verification?


    OK, if you haven't used I²t in your calculation, what values have you used for I and t? I is presumably PFC, but what value have you chosen for t?


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    To be clear, I wanted to ask, When the cables have been already verified using adiabatic equation, Do I still need to check the cables for let through energy verification?

    In principle they're both the same thing (S = √(I2t)/k is the same a S2k2 = I2t, just re-arranged (divide through by k and square both sides)) - but in practice people often refer to different conditions - e.g. the adiabatic is often only considered when sizing c.p.c.s - i.e. for Earth Faults whereas L-N, L-L and L-L-L faults are more commonly thought of when thinking of energy let-though.  Of course faults between live conductors can produce quite different levels fault currents than L-PE faults - so a calculation based on an earth fault current might not be valid for the other kinds of faults.


    As a first approximation if a conductor is "reduced" - i.e. it has a rating below that of its protective device (Iz < In) - then some check will likely be necessary.


    Also keep in mind that the worst case isn't necessarily a fault at the far end of the circuit - that gives the lowest fault current and likely the longest disconnection time - and for fuses probably the highest energy let-through but for MCBs faults with higher currents (e.g. a fault next to the MCB) often don't disconnect significantly faster than a far-off fault - so I²t can often be higher. Unfortunatley some text book examples seem to have been written with fuses in mind and miss that point.


        - Andy.
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    Nick Parker:

    Why let through energy of cable is calculated and compared against protective device let through energy, when adiabatic equation and disconnection time check is used to verify the cable sizes? or this let thru energy verification is applied only for current limiting breakers / fuses?


    The device let through time is for circuit breakers and short disconnection times.


     


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    AJJewsbury:
    To be clear, I wanted to ask, When the cables have been already verified using adiabatic equation, Do I still need to check the cables for let through energy verification?

    In principle they're both the same thing (S = √(I2t)/k is the same a S2k2 = I2t, just re-arranged (divide through by k and square both sides)) - but in practice people often refer to different conditions - e.g. the adiabatic is often only considered when sizing c.p.c.s - i.e. for Earth Faults whereas L-N, L-L and L-L-L faults are more commonly thought of when thinking of energy let-though.  Of course faults between live conductors can produce quite different levels fault currents than L-PE faults - so a calculation based on an earth fault current might not be valid for the other kinds of faults.


    As a first approximation if a conductor is "reduced" - i.e. it has a rating below that of its protective device (Iz < In) - then some check will likely be necessary.


    Also keep in mind that the worst case isn't necessarily a fault at the far end of the circuit - that gives the lowest fault current and likely the longest disconnection time - and for fuses probably the highest energy let-through but for MCBs faults with higher currents (e.g. a fault next to the MCB) often don't disconnect significantly faster than a far-off fault - so I²t can often be higher. Unfortunatley some text book examples seem to have been written with fuses in mind and miss that point.


        - Andy.


    That's not quite true, based on the question.


    For short disconnection times and circuit breakers (mcb's and RCBO's), BS 7671 refers to manufacturer's data ... so you will have to use the device data because BS 7671 doesn't have it.


    It's not possible to simply assume that if the adiabatic is met for the  highest value of current shown in BS 7671, it will be met for all higher values of current, because circuit breakers don't behave like fuses.


    Also, whilst in reality Ipsc should be measured, current guidance for small (100 A single-phase) installations, is to assume 16 kA for prospective fault current at the origin.


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    As others above have said the adiabatic can be re-arranged as I have done in my post above.


    Yes we have to verify that earth faults have to disconnect with the times set out in Chapter 41 but we also have consider the Chapter 43 requirements for over current. As Andy has pointed out above there is a requirement to protect the cable against near end and far end cable faults. Usually, but not always, the far end short circuit fault live to neutral will be a more onerous "slow blow" situation. The I squared t calculated from the neutral line short circuit current at the far end of the cable. Then the "t" time for the over current device from the time current curves in Appendix 3 and the calculated short circuit current. The "S" is the CSA of the cable and the K value comes from Table 43.1 in Chapter 43 for disconnection times up to 5s. The magjc adiabatic equation only works for calculated vales between 0.1s and 5s. For disconnection times of less than 0.1s you need to use manufacturers let through data and above 5s the heat radiation from the cable has to be considered.


    A common error is to use an RCD to provide fault protection on a very long cable without considering if the over current protection will provide  protection for short circuits. at the far end of the cable.
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    Chris Pearson:
    Nick Parker:

    To be clear, I wanted to ask, When the cables have been already verified using adiabatic equation, Do I still need to check the cables for let through energy verification?


    OK, if you haven't used I²t in your calculation, what values have you used for I and t? I is presumably PFC, but what value have you chosen for t?




    I2t is taken from the manufacturer published energy let through curves for a PFC


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