Temperature rise of conductor

This is the conductor temperature rise above the ambient temperature respectively above the surface temperature in tunnel and in trough (method by Anders 2010).

For DC, the dielectric losses $W_d$ are zero and the corresponding terms disappear.

Symbol
$\Delta \theta_{c}$
Unit
K
Formulae
$W_{p} n_{cc} \left(\frac{T_{4ii}}{2} + T_{4iii}\right) + n_{c} \left(T_{d} W_{d} + T_{i} W_{c}\right) + n_{cc} \left(W_{I} + W_{d}\right) \left(T_{4i} + T_{4ii} + T_{4iii}\right)$cables in air
$W_{I} n_{cc} \left(T_{4i} + T_{4ii} + T_{4\mu} v_{4}\right) + W_{d} n_{cc} \left(T_{4i} + T_{4ii} + T_{4ss} v_{4}\right) + W_{p} n_{cc} \left(\frac{T_{4ii}}{2} + T_{4\mu} v_{4}\right) + n_{c} \left(T_{d} W_{d} + T_{i} W_{c}\right)$cables buried
$n_{c} \left(T_{d} W_{d} + T_{i} W_{c}\right) + n_{cc} \left(T_{4i} + T_{4ii}\right) \left(W_{I} + W_{d}\right)$cables in tunnel
$n_{c} \left(T_{4t} W_{I} + T_{4t} W_{d} + T_{d} W_{d} + T_{i} W_{c}\right)$cables in tunnel (IEC 60287-2-3)
$n_{c} \left(T_{d} W_{d} + T_{i} W_{c}\right) + n_{cc} \left(W_{I} + W_{d}\right) \left(T_{4i} + T_{4ii} + T_{4iii}\right)$cables in trough or channel
$\Delta \theta_{0x}$cables crossing external heat sources
$- \theta_{a} + \theta_{c}$GIL
$T_{4iii} n_{cc} \left(W_{I} + W_{d}\right) + n_{c} \left(T_{d} W_{d} + T_{i} W_{c}\right)$cables subsea
Related
$\Delta \theta_{0x}$
$\theta_{a}$
Ambient temperature [$^{\circ}$C]
$\theta_{c}$
$W_{c}$
$W_{d}$
$W_{p}$
Used in
$\Delta \theta_{s}$
$\theta_{c}$