Adiabatic Temperature Rise Constant

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The adiabatic temperature rise constant k is the constant term used in the adiabatic temperature rise equation:

$A = \frac{\sqrt{i^{2}t}}{k} \,$

Where $A \,$ is the minimum cross-sectional area of the PE conductor ($mm^{2}$)

$i^{2}t \,$ is the energy of the short circuit ($A^{2}s$)
$k \,$ is the adiabatic temperature rise constant

The constant k is made up of the material properties and temperature range of the conductor material (see the derivation of the constant here).

IEC 60364-5-54 Annex A gives some guidance on the calculation of the constant k, according to the following equation:

$k = \sqrt{\frac{Q_{c} (\beta + 20 ^\circ C)}{\rho_{20}} \ln \left( 1 + \frac{\theta_{f} - \theta_{i}}{\beta + \theta_{i}} \right)}$

Where $Q_{c} \,$ is the volumetric heat capacity of the conductor material at 20oC (J/oC mm3)

$\beta \,$ is the reciprocal of the conductor temperature coefficient of resistivity at 0oC (oC)
$\rho_{20} \,$ is the electrical resistivity of the conductor material at 20oC ($\Omega$ mm)
$\theta_{i} \,$ and $\theta_{f} \,$ are the conductor initial and final temperatures respectively (oC)

Table of material values

Material $\beta \,$ $Q_{c} \,$ $\rho_{20} \,$
Copper 234.5 3.45 x 10-3 17.241 x 10-6
Aluminium 228 2.5 x 10-3 28.264 x 10-6
Lead 230 1.45 x 10-3 214 x 10-6
Steel 202 3.8 x 10-3 138 x 10-6

Table of temperature ranges for conductors not incorporated in cables and not bunched with other cables

Insulation $\theta_{i} \,$ $\theta_{f} \,$
70oC PVC 30 160 or 140(*)
90oC PVC 30 160 or 140(*)
90oC Thermosetting 30 250
60oC Rubber 30 200
85oC Rubber 30 220
Silicone rubber 30 350

(*) For PVC insulated conductors greater than 300mm2

Table of temperature ranges for bare conductors in contact with cable coverings but not bunched with other cables

Cable Covering $\theta_{i} \,$ $\theta_{f} \,$
PVC 30 200
Polyethylene 30 150
CSP 30 220

Table of temperature ranges for conductors incorporated in cables and bunched with other cables or other insulated conductors

Insulation $\theta_{i} \,$ $\theta_{f} \,$
70oC PVC 70 160 or 140(*)
90oC PVC 90 160 or 140(*)
90oC Thermosetting 90 250
60oC Rubber 60 200
85oC Rubber 85 220
Silicone rubber 180 350

(*) For PVC insulated conductors greater than 300mm2

Table of temperature ranges for protective conductors as a metallic layer of a cable, e.g. armour, metallic sheath, concentric conductor, etc

Insulation $\theta_{i} \,$ $\theta_{f} \,$
70oC PVC 60 200
90oC PVC 80 200
90oC Thermosetting 80 200
60oC Rubber 55 200
85oC Rubber 75 220
Mineral PVC covered 70 200
Mineral bare sheathed 105 250

Table of temperature ranges for bare conductors with no risk of damaging neighbouring material

Conditions $\theta_{i} \,$ Copper $\theta_{f} \,$ Aluminium $\theta_{f} \,$ Steel $\theta_{f} \,$
Visible in restricted area 30 500 300 500
Normal conditions 30 200 200 200
Fire risk 30 150 150 150