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 important for high-voltage cables because they 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 temperature range of interest.
• 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 core-screen or sheath and therefore the ratio of losses factors are equal to 2. The apportioning factor pi 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 factors are 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
$\Delta \theta_{\mathrm{d}}$
Unit
K
Formulae
 $W_{\mathrm{d}} \left(T_{\mathrm{d}} n_{\mathrm{c}} + n_{\mathrm{cc}} \left(T_{\mathrm{4i}} + T_{\mathrm{4ii}} + T_{\mathrm{4iii}}\right)\right)$ cables in air $W_{\mathrm{d}} \left(T_{\mathrm{d}} n_{\mathrm{c}} + n_{\mathrm{cc}} \left(T_{\mathrm{4i}} + T_{\mathrm{4ii}} + T_{\mathrm{4\mu}}\right)\right)$ buried cables $W_{\mathrm{d}} \left(T_{\mathrm{d}} n_{\mathrm{c}} + n_{\mathrm{cc}} \left(T_{\mathrm{4i}} + T_{\mathrm{4ii}}\right)\right)$ cables in tunnel $W_{\mathrm{d}} \left(T_{\mathrm{4t}} n_{\mathrm{cc}} + T_{\mathrm{d}} n_{\mathrm{c}}\right)$ cables in tunnel (IEC 60287-2-3)
Related
$n_{\mathrm{c}}$
$n_{\mathrm{cc}}$
$T_{\mathrm{4i}}$
$T_{\mathrm{4ii}}$
$T_{\mathrm{4iii}}$
$T_{\mathrm{4\mu}}$
$T_{\mathrm{4t}}$
$T_{\mathrm{d}}$
$W_{\mathrm{d}}$
Used in
$\Delta \theta_{\mathrm{R_{\mathrm{\infty}}}}$
$\Delta \theta_{\mathrm{s}}$
$\Delta W$
$DF_{\mathrm{X}}$
$I_{\mathrm{c}}$
$r_{\mathrm{\theta}}$