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

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