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# Thermal Short-time Rating

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### Formulas

If a conductor which is rated to carry full load current Iload continuously is rated to carry a maximum fault current Ilimit for a time tlimit, then a lower fault current Ifault can be carried for a longer time tfault according to:

( Ilimit – Iload )2 tlimit = ( Ifault – Iload )2 tfault

Rearranging for Ifault and tfault:

Ifault = ( Ilimit – Iload ) ( tlimit / tfault )½ + Iload

tfault = tlimit ( Ilimit – Iload )2 / ( Ifault – Iload )2

If Iload is small compared with Ilimit and Ifault, then:

Ilimit2 tlimit » Ifault2 tfault

Ifault » Ilimit ( tlimit / tfault )½

tfault » tlimit ( Ilimit / Ifault )2

Note that if the current Ifault is reduced by a factor of two, then the time tfault is increased by a factor of four.

 NOTATION The symbol font is used for some notation and formulae. If the Greek symbols for alpha beta delta do not appear here [ a b d ] the symbol font needs to be installed for correct display of notation and formulae. B C E f G h I j L P Q susceptance capacitance voltage source frequency conductance h-operator current j-operator inductance active power reactive power [siemens, S] [farads, F] [volts, V] [hertz, Hz] [siemens, S] [1Ð120°] [amps, A] [1Ð90°] [henrys, H] [watts, W] [VAreactive, VArs] Q R S t V W X Y Z f w quality factor resistance apparent power time voltage drop energy reactance admittance impedance phase angle angular frequency [number] [ohms, W] [volt-amps, VA] [seconds, s] [volts, V] [joules, J] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [rad/sec]