# Temperature rise by dielectric losses

This is the conductor temperature rise above the ambient temperature caused by dielectric losses respectively above the cable oversheath temperature for cables in tunnel.

The temperature rise caused by dielectric losses is relevant for high-voltage cables because the losses are strongly voltage dependent. If the application of system voltage occurs, then an additional transient temperature rise due to the dielectric loss has to be calculated with following assumptions:

• It shall be assumed that the dielectric power factor is constant and equal to an appropriate value in the relevant temperature range.
• If the starting conductor temperature is different from the ambient temperature, then it may be assumed that the dielectric losses are included in the temperature rise obtained at the onset of the transient conditions.
• For cables at voltages up to and including 275 kV, it is sufficient to assume that half the dielectric loss is produced at the conductor and the other half at the screen or sheath (therefore the ratio of losses is equal to 2). The apportioning factor $p_i$ is the same as that used when calculating transient due to joule losses.
• For cables at voltages higher than 275 kV, the dielectric loss can be an important fraction of the total loss (i.e. paper insulated cables) and the factor used to apportion the thermal capacitance of the insulation (dielectric) to the conductor and sheath is replaced. The fraction of the dielectric loss starting from the conductor is still reckoned as 1/2 and therefore the ratio of losses is equal to 2.
• The parameter $W_d$ is the dielectric loss per unit length in a conductor at the attained voltage and assumed to be constant during the transient.

Symbol
$\Delta \theta_{d}$
Unit
K
Formulae
 $W_{d} \left(T_{d} n_{c} + n_{cc} \left(T_{4i} + T_{4ii} + T_{4iii}\right)\right)$ cables in air, trough or channel $W_{d} \left(T_{d} n_{c} + n_{cc} \left(T_{4i} + T_{4ii} + T_{4ss} v_{4}\right)\right)$ cables buried $W_{d} \left(T_{d} n_{c} + n_{cc} \left(T_{4i} + T_{4ii}\right)\right)$ cables in tunnel $W_{d} n_{c} \left(T_{4t} + T_{d}\right)$ cables in tunnel (IEC 60287-2-3) $W_{d} \left(T_{4iii} n_{cc} + T_{d} n_{c}\right)$ cables subsea
$T_{4i}$
$T_{4ii}$
$T_{4iii}$
$T_{4ss}$
$T_{4t}$
$T_{d}$
$W_{d}$
Used in
$\Delta \theta_{R_{\infty}}$
$\Delta \theta_{s}$
$\Delta W$
$I_{c}$