Adiabatic Temperature Rise Constant
The adiabatic temperature rise constant k is the constant term used in the adiabatic temperature rise equation:
- [math] A = \frac{\sqrt{i^{2}t}}{k} \, [/math]
Where [math]A \,[/math] is the minimum cross-sectional area of the PE conductor ([math]mm^{2}[/math])
- [math]i^{2}t \,[/math] is the energy of the short circuit ([math]A^{2}s[/math])
- [math]k \,[/math] 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:
[math]k = \sqrt{\frac{Q_{c} (\beta + 20 ^\circ C)}{\rho_{20}} \ln \left( 1 + \frac{\theta_{f} - \theta_{i}}{\beta + \theta_{i}} \right)} [/math]
Where [math]Q_{c} \,[/math] is the volumetric heat capacity of the conductor material at 20^{o}C (J/^{o}C mm^{3})
- [math]\beta \,[/math] is the reciprocal of the conductor temperature coefficient of resistivity at 0^{o}C (^{o}C)
- [math]\rho_{20} \,[/math] is the electrical resistivity of the conductor material at 20^{o}C ([math]\Omega[/math] mm)
- [math]\theta_{i} \,[/math] and [math]\theta_{f} \,[/math] are the conductor initial and final temperatures respectively (^{o}C)
Table of material values
Material | [math]\beta \,[/math] | [math]Q_{c} \,[/math] | [math]\rho_{20} \,[/math] |
---|---|---|---|
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 | [math]\theta_{i} \,[/math] | [math]\theta_{f} \,[/math] |
---|---|---|
70^{o}C PVC | 30 | 160 or 140(*) |
90^{o}C PVC | 30 | 160 or 140(*) |
90^{o}C Thermosetting | 30 | 250 |
60^{o}C Rubber | 30 | 200 |
85^{o}C Rubber | 30 | 220 |
Silicone rubber | 30 | 350 |
(*) For PVC insulated conductors greater than 300mm^{2}
Table of temperature ranges for bare conductors in contact with cable coverings but not bunched with other cables
Cable Covering | [math]\theta_{i} \,[/math] | [math]\theta_{f} \,[/math] |
---|---|---|
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 | [math]\theta_{i} \,[/math] | [math]\theta_{f} \,[/math] |
---|---|---|
70^{o}C PVC | 70 | 160 or 140(*) |
90^{o}C PVC | 90 | 160 or 140(*) |
90^{o}C Thermosetting | 90 | 250 |
60^{o}C Rubber | 60 | 200 |
85^{o}C Rubber | 85 | 220 |
Silicone rubber | 180 | 350 |
(*) For PVC insulated conductors greater than 300mm^{2}
Table of temperature ranges for protective conductors as a metallic layer of a cable, e.g. armour, metallic sheath, concentric conductor, etc
Insulation | [math]\theta_{i} \,[/math] | [math]\theta_{f} \,[/math] |
---|---|---|
70^{o}C PVC | 60 | 200 |
90^{o}C PVC | 80 | 200 |
90^{o}C Thermosetting | 80 | 200 |
60^{o}C Rubber | 55 | 200 |
85^{o}C 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 | [math]\theta_{i} \,[/math] | Copper [math]\theta_{f} \,[/math] | Aluminium [math]\theta_{f} \,[/math] | Steel [math]\theta_{f} \,[/math] |
---|---|---|---|---|
Visible in restricted area | 30 | 500 | 300 | 500 |
Normal conditions | 30 | 200 | 200 | 200 |
Fire risk | 30 | 150 | 150 | 150 |