# Thermal resistance between one conductor and sheath

All three-core cables require fillers to fill the space between insulated cores and the belt insulation or a sheath. The fillers of extruded cables usually have higher thermal resistivities than the insulation, unlike paper-insulated cables In a paper by G. Anders from 1998, a formula was developed to take into account the different thermal resistivities. This formula has been included in the new editions of the IEC standards.

For three-core cables with a touching metallic screen made of copper tapes each core the thermal resistance of the insulation is obtained in two steps:

1. First, the cables are considered as belted cables for which $t_1/t=0.5$.
2. Second, the resulting $T_1$ is multiplied by a factor $K$, called the screening factor.
In a paper by G. Anders from 1999, a more precise formula was developed. This formula has not been included in the IEC, but is used by cableizer.

Type of screen/sheath of multi-core cables

• SS: with separate screen and separate sheaths
• SC: with separate screen and common sheath
• CC: with common screen and common sheath

Symbol
$T_{1}$
Unit
K.m/W
Formulae
 $\frac{\rho_{i} \ln{\left(1 + \frac{2 t_{1}}{d_{c}} \right)}}{2 \pi}$ single-core cables $\frac{G_{1} \rho_{i}}{2 \pi}$ multi-core cables with sector-shaped conductors / multi-core cables type SS with sheath $\frac{G_{1} K \rho_{i}}{2 \pi}$ screened three-core cables $1.13882838332462 K \left(- 0.12 d_{c} + \frac{\sqrt{3} \rho_{f}}{\rho_{i}} + 2.25\right) e^{- 7 K + \frac{t_{1}}{d_{c}}} + 0.89 T_{1}$ more accurate formula for screened cables with round conductors $\frac{G_{1} \rho_{i}}{2 \pi} + \left(0.031 \rho_{f} - 0.031 \rho_{i}\right) e^{\frac{0.67 t_{1}}{d_{c}}}$ unscreened multi-core cables with round conductors $1.07 T_{1}$ part-metallic sheathed single-core cables in trefoil formation, up to 35 kV $1.16 T_{1}$ part-metallic sheathed single-core cables in trefoil formation, from 35 to 150 kV $\frac{\theta_{c} - \theta_{encl}}{W_{conv_{ce}} + W_{rad_{ce}}}$ GIL
Related
$d_{c}$
$\rho_{f}$
$\rho_{i}$
$t_{1}$
$\theta_{c}$
$\theta_{encl}$
$W_{conv_{ce}}$
$W_{rad_{ce}}$
Used in
$d_{ct}$
$I_{c}$
$T_{B}$
$T_{d}$
$T_{eq}$
$T_{i}$
$\theta_{ar_{1}}$
$\theta_{ar_{2}}$
$\theta_{c_{z}}$
$\theta_{e}$
$\theta_{f}$
$\theta_{s}$
$\theta_{sc}$
Temperature of screen [$^{\circ}$C]
$\theta_{sh}$
Temperature of sheath [$^{\circ}$C]