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:

- First, the cables are considered as belted cables for which $t_1/t=0.5$.
- Second, the resulting $T_1$ is multiplied by a factor $K$, called the screening factor.

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

$T_{\mathrm{1}}$

K.m/W

$\frac{\rho_{\mathrm{i}}}{2 \pi} \ln{\left (1 + \frac{2 t_{\mathrm{1}}}{d_{\mathrm{c}}} \right )}$ | 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 |

$G_{\mathrm{1}}$

Geometric factor [-]

$K$

Screening factor [-]

$\pi$

$\rho_{\mathrm{f}}$

Thermal resistivity of filler [K.m/W]

$\rho_{\mathrm{i}}$

$t_{\mathrm{1}}$

$T_{\mathrm{conv_{\mathrm{ce}}}}$

$T_{\mathrm{rad_{\mathrm{ce}}}}$

$\Delta \theta_{\mathrm{d_{\mathrm{t}}}}$

$I_{\mathrm{c}}$

$T_{\mathrm{B}}$

$T_{\mathrm{d}}$

$T_{\mathrm{eq}}$

Equivalent thermal resistance [K.m/W]

$T_{\mathrm{i}}$

$T_{\mathrm{r}}$

Total thermal resistance [K.m/W]

$\theta_{\mathrm{ar_{\mathrm{1}}}}$

$\theta_{\mathrm{ar_{\mathrm{2}}}}$

$\theta_{\mathrm{c_{\mathrm{z}}}}$

$\theta_{\mathrm{e}}$

$\theta_{\mathrm{encl}}$

$\theta_{\mathrm{f}}$

$\theta_{\mathrm{s}}$

$\theta_{\mathrm{sc}}$

$\theta_{\mathrm{sh}}$