Temperature rise by dielectric losses

This is the conductor temperature rise above the ambient temperature caused by dielectric losses respectively above the surface temperature of cable or duct in tunnel and above the surface temperature of the cable in riser.

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:

$\Delta \theta_d$
$W_d \left(n_c T_d+n_{cc} \left(T_{4i}+T_{4ii}+T_{4iii}\right)\right)$Cables in air, in trough
$W_d \left(n_c T_d+n_{cc} \left(T_{4i}+T_{4ii}+T_{4ss} v_4\right)\right)$Cables buried
$W_d \left(n_c T_d+n_{cc} \left(T_{4i}+T_{4ii}\right)\right)$Cables in tunnel
$W_d n_c \left(T_d+T_{4t}\right)$Cables in tunnel (IEC 60287-2-3)
$W_d \left(n_c T_d+n_{cc} T_{4iii}\right)$Cables subsea
$W_d n_c T_d$Cables in riser
$W_d \left(n_c T_d+n_{cc} T_{4ss} v_4\right)$Cables buried in ducts with bentonite filling and transient loading