Thermal Stress of Insulated Wire
Thermal Stress of Insulated Wire
(OP)
IEEE Std 142-2007 "Grounding....Power Systems" has two equations [ 2.3a & 2.3b] that help define the thermal boundary for wire insulation protection based on I^2t, the initial wire temp, final temp, and wire xsect area. The equation 2.3a is I^2t/A = 0.0297ln[(Max Temp + 234)/(Initial Temp + 235)]. Does anyone know where this equation came from and does it match the original?
I can't get the math to correlate with the example in Part 2.7.4.4 of 142-2007.
I can't get the math to correlate with the example in Part 2.7.4.4 of 142-2007.






RE: Thermal Stress of Insulated Wire
RE: Thermal Stress of Insulated Wire
http://www.eng-tips.com/viewthread.cfm?qid=238191
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(2B)+(2B)' ?
RE: Thermal Stress of Insulated Wire
NOTE: The cable damage curve used for protective device coordination is based in this principle.
The equation presented in the IEEE standard has couple of error: a) A should A^2
b) Ln should be log10.
I^2t/A2 = 0.0297log10[(Max Temp + 234)/(Initial Temp + 234)].
After those changes, the math should correlate with the example.
RE: Thermal Stress of Insulated Wire
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(2B)+(2B)' ?
RE: Thermal Stress of Insulated Wire
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(2B)+(2B)' ?
RE: Thermal Stress of Insulated Wire
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(2B)+(2B)' ?
RE: Thermal Stress of Insulated Wire
In IEEE 142-2007, it's shown as 'in'; I slipped the 'ln' in.
IEEE does a good job on their standards don't they.
RE: Thermal Stress of Insulated Wire
I believe that the heat is generated by passing a current through the metallic conductor resistance (Q= I^2R.t). This equation assume that the heat transfer thought the insulation to the external ambient is negligible (adiabatic) since happens in a short time. This will increase the temperature of the insulation from the initial operating point to higher temperature, hopefully below the insulation limits
NOTE: This approach is conservative in the safe side in a range of 5% and 10%.
RE: Thermal Stress of Insulated Wire
In summary:
Resistive Losses From Electrical System => Stored Thermal Energy
I^2*R*t => C*deltaT
where t is time and deltaT is temperature change and
C is thermal capacity of the conductor only
If R didn't vary with temperature, we could simply solve for deltaT =I^2*R*t/C instead of needing the more complicated form of the IEEE equation.
Probably all of the above is familiar to you, but when you said: "The origin of this equation come from considering that heat generated by the conductor during short circuit is absorbed by cable insulation", it sounds like a contradiction to me, since insulation thermal capacity is neglected... the conductor is what "absorbs" the thermal energy. If the bolded portion was intended to convey that there is assumed to be no heat transfer out of the system, then I agree.
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(2B)+(2B)' ?
RE: Thermal Stress of Insulated Wire
I like your rational and detail analysis. Beside some initial semantic issues, I am glad that we are all agreeing.
As a "Grand Finale", here is a graph courtesy of Okonite to address cable allowable thermal stresses during short circuit